LMFDB - Embedded newform 546.2.bi.f.17.4

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			17.4
Character	$\chi$	$=$	546.17
Dual form			546.2.bi.f.257.4

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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	−0.100398	−	0.994947i	$-0.532012\pi$
$5$	1.58996	−	0.917964i	0.711052	−	0.410526i	0.811450	+	0.584421i	$0.198678\pi$
$6$	−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	−0.999912	−	0.0132573i	$-0.995780\pi$
$11$	−1.69625	−	2.93798i	−0.511437	−	0.885835i	0.488475	−	0.872578i	$-0.337553\pi$
$12$	−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	−0.958703	−	0.284410i	$-0.908202\pi$
$19$	−1.01582	+	1.75945i	−0.233045	+	0.403646i	0.725658	+	0.688056i	$0.241536\pi$
$20$	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	$-0.916904\pi$
$23$		−	2.47560i		−	0.516199i	0.966118	−	0.258099i	$-0.0830962\pi$
$24$	−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	0.659255	−	0.751920i	$-0.270872\pi$
$29$	1.81857	+	1.04995i	0.337701	+	0.194971i	−0.321554	+	0.946891i	$0.604205\pi$
$30$	−0.860135	+	3.06138i	−0.157038	+	0.558930i
$31$	−3.14345	+	5.44461i	−0.564580	+	0.977881i	0.432509	+	0.901630i	$0.357629\pi$
$31$	−3.14345	+	5.44461i	−0.564580	+	0.977881i	−0.997089	+	0.0762515i	$0.975705\pi$
$32$	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	$-0.986811\pi$
$37$		−	0.503913i		−	0.0828428i	0.999142	−	0.0414214i	$-0.0131886\pi$
$38$	−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	0.799721	−	0.600372i	$-0.204981\pi$
$41$	4.35184	+	2.51254i	0.679643	+	0.392392i	−0.120077	+	0.992765i	$0.538314\pi$
$42$	3.62196	+	2.80738i	0.558881	+	0.433189i
$43$	0.528972	+	0.916206i	0.0806674	+	0.139720i	0.903537	−	0.428511i	$-0.140962\pi$
$43$	0.528972	+	0.916206i	0.0806674	+	0.139720i	−0.822869	+	0.568231i	$0.807628\pi$
$44$	−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	0.473367	−	0.880865i	$-0.343038\pi$
$47$	10.0977	−	5.82991i	1.47290	−	0.850380i	0.999535	+	0.0304848i	$0.00970512\pi$
$48$	−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	0.0441326	−	0.999026i	$-0.485948\pi$
$53$	−5.81668	−	3.35826i	−0.798983	−	0.461293i	−0.843115	+	0.537733i	$0.819281\pi$
$54$	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	$-0.867562\pi$
$59$		−	6.20893i		−	0.808333i	0.914685	−	0.404167i	$-0.132438\pi$
$60$	−0.860135	+	3.06138i	−0.111043	+	0.395223i
$61$	10.1157	+	5.84028i	1.29518	+	0.747771i	0.979567	−	0.201118i	$-0.0644575\pi$
$61$	10.1157	+	5.84028i	1.29518	+	0.747771i	0.315610	+	0.948889i	$0.397791\pi$
$62$	−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	−0.922760	−	0.385376i	$-0.874072\pi$
$67$	−8.59785	+	4.96397i	−1.05039	+	0.606445i	−0.127634	+	0.991821i	$0.540738\pi$
$68$	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	−0.796058	−	0.605221i	$-0.793085\pi$
$71$	−7.77030	−	13.4586i	−0.922165	−	1.59724i	−0.126108	−	0.992017i	$-0.540248\pi$
$72$	0.0726040	−	2.99912i	0.00855646	−	0.353450i
$73$	−4.47574	+	7.75221i	−0.523846	+	0.907327i	0.475769	+	0.879570i	$0.342170\pi$
$73$	−4.47574	+	7.75221i	−0.523846	+	0.907327i	−0.999615	+	0.0277570i	$0.991164\pi$
$74$		−	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	0.997800	−	0.0662985i	$-0.0211189\pi$
$79$	3.92399	+	6.79656i	0.441484	+	0.764672i	−0.556316	+	0.830971i	$0.687786\pi$
$80$	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	$0.254852\pi$
$83$			13.0790i			1.43561i	−0.696246	+	0.717803i	$0.745148\pi$
$84$	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	$-0.908776\pi$
$89$		−	5.33363i		−	0.565364i	0.959214	−	0.282682i	$-0.0912240\pi$
$90$	−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	0.512621	−	0.858615i	$-0.328674\pi$
$97$	−4.79907	−	8.31223i	−0.487272	−	0.843979i	−0.999893	+	0.0146357i	$0.995341\pi$
$98$	−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	0.999298	−	0.0374637i	$-0.0119279\pi$
$101$	4.69535	+	8.13258i	0.467204	+	0.809222i	−0.532094	+	0.846686i	$0.678595\pi$
$102$	−3.94781	+	3.85339i	−0.390891	+	0.381543i
$103$	−11.5646	+	6.67680i	−1.13949	+	0.657884i	−0.946304	−	0.323278i	$-0.895215\pi$
$103$	−11.5646	+	6.67680i	−1.13949	+	0.657884i	−0.193185	+	0.981162i	$0.561882\pi$
$104$	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	$0.223688\pi$
$107$			13.3709i			1.29262i	−0.763076	+	0.646309i	$0.776312\pi$
$108$	3.53845	+	3.80518i	0.340487	+	0.366154i
$109$	3.82963	+	2.21104i	0.366812	+	0.211779i	0.672065	−	0.740492i	$-0.265408\pi$
$109$	3.82963	+	2.21104i	0.366812	+	0.211779i	−0.305253	+	0.952271i	$0.598741\pi$
$110$	−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	−0.980723	−	0.195402i	$-0.937399\pi$
$113$	−13.8390	+	7.98994i	−1.30186	+	0.751631i	−0.321139	+	0.947032i	$0.604066\pi$
$114$	−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	−0.886371	−	0.462976i	$-0.846782\pi$
$127$	−0.475986	+	0.824432i	−0.0422370	+	0.0731566i	0.844134	+	0.536132i	$0.180115\pi$
$128$	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	0.563995	−	0.825778i	$-0.309264\pi$
$131$	−4.95760	−	8.58681i	−0.433147	−	0.750233i	−0.997142	+	0.0755449i	$0.975930\pi$
$132$	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	−0.495831	−	0.868419i	$-0.665136\pi$
$139$	0.0981681	−	0.0566774i	0.00832651	−	0.00480731i	0.504157	+	0.863612i	$0.331803\pi$
$140$	−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	0.0487739	−	0.998810i	$-0.484469\pi$
$149$	10.8563	−	18.8036i	0.889382	−	1.54045i	0.840608	−	0.541644i	$-0.182198\pi$
$150$	−0.697383	−	2.73462i	−0.0569411	−	0.223281i
$151$	−4.69698	−	2.71180i	−0.382235	−	0.220684i	0.296555	−	0.955016i	$-0.404162\pi$
$151$	−4.69698	−	2.71180i	−0.382235	−	0.220684i	−0.678790	+	0.734332i	$0.737495\pi$
$152$	−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	0.999442	−	0.0333895i	$-0.0106302\pi$
$157$	18.4221	+	10.6360i	1.47025	+	0.848848i	0.470805	+	0.882237i	$0.343964\pi$
$158$	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	0.799702	−	0.600397i	$-0.204991\pi$
$163$	8.67648	+	5.00937i	0.679594	+	0.392364i	−0.120108	+	0.992761i	$0.538324\pi$
$164$	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	0.615699	−	0.787981i	$-0.288874\pi$
$167$	3.11618	+	1.79913i	0.241137	+	0.139221i	−0.374562	+	0.927202i	$0.622207\pi$
$168$	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	−0.883582	−	0.468277i	$-0.844875\pi$
$173$	−0.476807	+	0.825853i	−0.0362509	+	0.0627885i	0.847331	+	0.531066i	$0.178208\pi$
$174$	−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	0.200716	−	0.979649i	$-0.435673\pi$
$179$	15.3789	−	8.87903i	1.14948	−	0.663650i	0.948759	+	0.316000i	$0.102340\pi$
$180$	−2.63765	−	4.83513i	−0.196599	−	0.360389i
$181$			5.51564i			0.409975i	0.978765	+	0.204987i	$0.0657153\pi$
$181$			5.51564i			0.409975i	−0.978765	+	0.204987i	$0.934285\pi$
$182$	−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	0.973933	−	0.226834i	$-0.0728374\pi$
$191$	17.4751	+	10.0893i	1.26446	+	0.730034i	0.290523	+	0.956868i	$0.406171\pi$
$192$	−1.23948	+	1.20983i	−0.0894515	+	0.0873122i
$193$	3.93413	−	2.27137i	0.283185	−	0.163497i	−0.351679	−	0.936121i	$-0.614389\pi$
$193$	3.93413	−	2.27137i	0.283185	−	0.163497i	0.634864	+	0.772624i	$0.281056\pi$
$194$	−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	−0.585585	−	0.810611i	$-0.699135\pi$
$197$	5.74363	−	9.94826i	0.409217	−	0.708784i	0.994802	+	0.101826i	$0.0324687\pi$
$198$	−8.93452	+	4.87394i	−0.634949	+	0.346376i
$199$			6.86468i			0.486624i	0.969948	+	0.243312i	$0.0782339\pi$
$199$			6.86468i			0.486624i	−0.969948	+	0.243312i	$0.921766\pi$
$200$	−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	−0.942465	−	0.334305i	$-0.891498\pi$
$211$	−2.63957	+	4.57187i	−0.181715	+	0.314740i	0.760749	+	0.649046i	$0.224832\pi$
$212$	−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	−0.228896	+	0.973451i	$0.573512\pi$
$223$	−14.2982	+	24.7653i	−0.957481	+	1.65841i	−0.728585	+	0.684955i	$0.759822\pi$
$224$	−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	$0.0639133\pi$
$227$			6.00983i			0.398886i	−0.979909	+	0.199443i	$0.936087\pi$
$228$	−0.869560	−	3.40977i	−0.0575880	−	0.225818i
$229$	−7.02836	−	12.1735i	−0.464447	−	0.804446i	0.534729	−	0.845023i	$-0.320414\pi$
$229$	−7.02836	−	12.1735i	−0.464447	−	0.804446i	−0.999176	+	0.0405773i	$0.987080\pi$
$230$	−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	−0.579729	+	0.814809i	$0.696842\pi$
$233$	−24.0450	+	13.8824i	−1.57524	+	0.909465i	−0.995510	+	0.0946555i	$0.969825\pi$
$234$	−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	0.675986	−	0.736914i	$-0.263718\pi$
$251$	−4.75595	−	8.23755i	−0.300193	−	0.519950i	−0.976180	+	0.216964i	$0.930384\pi$
$252$	−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	−0.181490	−	0.983393i	$-0.558092\pi$
$263$	9.39641	−	5.42502i	0.579408	−	0.334521i	0.760898	+	0.648872i	$0.224759\pi$
$264$	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	−0.356995	−	0.934106i	$-0.616199\pi$
$283$	4.60044	−	2.65607i	0.273468	−	0.157887i	0.630463	+	0.776220i	$0.282865\pi$
$284$	−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	−0.581451	−	0.813581i	$-0.697515\pi$
$293$	−2.86877	+	1.65628i	−0.167595	+	0.0967612i	0.413856	+	0.910342i	$0.364182\pi$
$294$	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	−0.0678034	+	0.997699i	$0.521599\pi$
$311$	−15.8352	+	27.4274i	−0.897934	+	1.55527i	−0.830131	+	0.557569i	$0.811734\pi$
$312$	−1.52175	+	6.05676i	−0.0861520	+	0.342896i
$313$	12.5081	−	7.22158i	0.707002	−	0.408188i	−0.102948	−	0.994687i	$-0.532828\pi$
$313$	12.5081	−	7.22158i	0.707002	−	0.408188i	0.809950	+	0.586499i	$0.199494\pi$
$314$	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	0.961565	+	0.274577i	$0.0885379\pi$
$317$	12.7938	+	22.1596i	0.718573	+	1.24461i	−0.242992	+	0.970028i	$0.578129\pi$
$318$	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	0.685918	−	0.727679i	$-0.259401\pi$
$331$	7.25351	+	4.18782i	0.398689	+	0.230183i	−0.287229	+	0.957862i	$0.592734\pi$
$332$			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	$0.314347\pi$
$347$			31.0967i			1.66936i	−0.550736	+	0.834679i	$0.685653\pi$
$348$	−3.52435	+	0.898778i	−0.188925	+	0.0481796i
$349$	14.0331	−	24.3060i	0.751175	−	1.30107i	−0.196079	−	0.980588i	$-0.562821\pi$
$349$	14.0331	−	24.3060i	0.751175	−	1.30107i	0.947254	−	0.320485i	$-0.103846\pi$
$350$	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	0.324523	−	0.945878i	$-0.394796\pi$
$353$	24.5364	−	14.1661i	1.30594	−	0.753984i	0.981416	+	0.191894i	$0.0614629\pi$
$354$	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	−0.996193	−	0.0871698i	$-0.972218\pi$
$359$	−10.8679	−	18.8238i	−0.573588	−	0.993483i	0.422606	−	0.906314i	$-0.361116\pi$
$360$	−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	−0.0992693	−	0.995061i	$-0.531651\pi$
$367$	13.6561	−	7.88437i	0.712844	−	0.411561i	0.812113	+	0.583500i	$0.198317\pi$
$368$		−	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	−0.756871	−	0.653564i	$-0.773273\pi$
$373$	3.62253	−	6.27441i	0.187568	−	0.324877i	0.944439	+	0.328687i	$0.106606\pi$
$374$	−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	0.604979	−	0.796241i	$-0.293181\pi$
$379$	4.24213	+	2.44920i	0.217904	+	0.125807i	−0.387076	+	0.922048i	$0.626515\pi$
$380$			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	0.314543	−	0.949243i	$-0.398149\pi$
$383$	−6.85462	−	3.95752i	−0.350255	−	0.202220i	−0.664797	+	0.747024i	$0.731482\pi$
$384$	−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	0.556617	−	0.830769i	$-0.312099\pi$
$389$	2.27718	+	1.31473i	0.115458	+	0.0666595i	−0.441159	+	0.897429i	$0.645433\pi$
$390$	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	0.0666658	+	0.997775i	$0.478764\pi$
$397$	−16.5529	+	28.6705i	−0.830766	+	1.43893i	−0.897432	+	0.441153i	$0.854569\pi$
$398$			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	−0.710692	−	0.703504i	$-0.751618\pi$
$419$	5.19733	−	9.00204i	0.253906	−	0.439778i	0.964598	+	0.263725i	$0.0849512\pi$
$420$	8.33585	+	1.13880i	0.406748	+	0.0555678i
$421$		−	0.111490i		−	0.00543368i	−0.999996	−	0.00271684i	$-0.999135\pi$
$421$		−	0.111490i		−	0.00543368i	0.999996	−	0.00271684i	$-0.000864798\pi$
$422$	−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	0.782786	+	0.622291i	$0.213798\pi$
$431$	19.3138	+	33.4525i	0.930313	+	1.61135i	0.147527	+	0.989058i	$0.452869\pi$
$432$	3.53845	+	3.80518i	0.170244	+	0.183077i
$433$	−5.30602	+	3.06343i	−0.254991	+	0.147219i	−0.622047	−	0.782980i	$-0.713699\pi$
$433$	−5.30602	+	3.06343i	−0.254991	+	0.147219i	0.367056	+	0.930199i	$0.380366\pi$
$434$	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	$-0.685862\pi$
$439$		−	34.9618i		−	1.66864i	0.551284	−	0.834318i	$-0.314138\pi$
$440$	−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	−0.303996	−	0.952673i	$-0.598321\pi$
$443$	7.76750	−	4.48457i	0.369045	−	0.213068i	0.673041	+	0.739605i	$0.264988\pi$
$444$	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	0.557742	−	0.830014i	$-0.311668\pi$
$449$	−9.32220	−	16.1465i	−0.439942	−	0.762002i	−0.997684	+	0.0680121i	$0.978334\pi$
$450$	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	$-0.767815\pi$
$457$		−	28.4939i		−	1.33289i	0.745554	−	0.666445i	$-0.232185\pi$
$458$	−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	−0.242061	−	0.970261i	$-0.577823\pi$
$461$	10.2455	−	5.91523i	0.477180	−	0.275500i	0.719240	+	0.694761i	$0.244490\pi$
$462$	2.10431	−	15.4033i	0.0979016	−	0.716625i
$463$			10.9649i			0.509582i	0.966996	+	0.254791i	$0.0820067\pi$
$463$			10.9649i			0.509582i	−0.966996	+	0.254791i	$0.917993\pi$
$464$	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	0.535080	−	0.844802i	$-0.320282\pi$
$467$	−10.0288	−	17.3705i	−0.464080	−	0.803810i	−0.999159	+	0.0409918i	$0.986948\pi$
$468$	−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	−0.964395	−	0.264466i	$-0.914804\pi$
$479$	−26.6476	+	15.3850i	−1.21756	+	0.702957i	−0.253163	+	0.967424i	$0.581471\pi$
$480$	−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	$-0.697828\pi$
$487$		−	35.8831i		−	1.62602i	0.582252	−	0.813009i	$-0.302172\pi$
$488$	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	−0.460430	−	0.887696i	$-0.652305\pi$
$491$	−32.3384	−	18.6706i	−1.45941	−	0.842592i	−0.998982	+	0.0451043i	$0.985638\pi$
$492$	−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	−0.00672032	−	0.999977i	$-0.502139\pi$
$499$	19.1199	−	11.0389i	0.855925	−	0.494169i	0.862646	+	0.505809i	$0.168806\pi$
$500$			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	−0.917051	−	0.398769i	$-0.869437\pi$
$503$	−18.0289	−	31.2270i	−0.803870	−	1.39234i	0.113181	−	0.993574i	$-0.463896\pi$
$504$	−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	$0.206047\pi$
$509$			27.2107i			1.20609i	−0.797705	+	0.603047i	$0.793953\pi$
$510$	−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	−0.985569	−	0.169276i	$-0.945857\pi$
$521$	−7.90186	+	13.6864i	−0.346187	+	0.599613i	0.639382	+	0.768889i	$0.279190\pi$
$522$	3.28097	−	5.37789i	0.143604	−	0.235384i
$523$			1.76412i			0.0771397i	0.999256	+	0.0385698i	$0.0122802\pi$
$523$			1.76412i			0.0771397i	−0.999256	+	0.0385698i	$0.987720\pi$
$524$	−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	−0.0550960	−	0.998481i	$-0.517546\pi$
$541$	18.1904	−	10.5022i	0.782066	−	0.451526i	0.837162	+	0.546955i	$0.184213\pi$
$542$	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	0.657457	−	0.753492i	$-0.271632\pi$
$557$	−7.64230	−	13.2369i	−0.323815	−	0.560864i	−0.981272	+	0.192628i	$0.938299\pi$
$558$	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	$0.148990\pi$
$569$			21.5237i			0.902321i	−0.892443	+	0.451160i	$0.851010\pi$
$570$	−4.51262	−	4.62318i	−0.189013	−	0.193644i
$571$	19.8438	−	34.3705i	0.830438	−	1.43836i	−0.0672531	−	0.997736i	$-0.521424\pi$
$571$	19.8438	−	34.3705i	0.830438	−	1.43836i	0.897691	−	0.440625i	$-0.145243\pi$
$572$	−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	0.0268412	+	0.999640i	$0.491455\pi$
$577$	−20.4728	+	35.4599i	−0.852293	+	1.47621i	−0.879134	+	0.476575i	$0.841878\pi$
$578$	−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	0.989341	−	0.145616i	$-0.0465165\pi$
$587$	32.8994	+	18.9945i	1.35790	+	0.783986i	0.368563	+	0.929603i	$0.379850\pi$
$588$	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	−0.755919	−	0.654665i	$-0.772810\pi$
$593$	−13.8054	+	7.97057i	−0.566921	+	0.327312i	0.188997	+	0.981978i	$0.439476\pi$
$594$	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	0.573072	−	0.819505i	$-0.305752\pi$
$599$	3.66862	+	2.11808i	0.149896	+	0.0865423i	−0.423176	+	0.906047i	$0.639085\pi$
$600$	−0.697383	−	2.73462i	−0.0284706	−	0.111641i
$601$	−2.17316	−	1.25468i	−0.0886451	−	0.0511793i	0.455022	−	0.890480i	$-0.349631\pi$
$601$	−2.17316	−	1.25468i	−0.0886451	−	0.0511793i	−0.543667	+	0.839301i	$0.682965\pi$
$602$	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	−0.999974	−	0.00716623i	$-0.997719\pi$
$607$	−37.1080	−	21.4243i	−1.50617	−	0.869586i	−0.506193	−	0.862420i	$-0.668948\pi$
$608$	−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	−0.822003	−	0.569484i	$-0.807143\pi$
$613$	−18.3170	+	10.5753i	−0.739816	+	0.427133i	0.0821861	+	0.996617i	$0.473810\pi$
$614$	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	−0.966672	−	0.256017i	$-0.917590\pi$
$617$	−17.5132	−	30.3337i	−0.705053	−	1.22119i	0.261619	−	0.965171i	$-0.415744\pi$
$618$	6.25617	−	22.2669i	0.251660	−	0.895707i
$619$	15.4257	−	26.7180i	0.620010	−	1.07389i	−0.369473	−	0.929241i	$-0.620462\pi$
$619$	15.4257	−	26.7180i	0.620010	−	1.07389i	0.989483	−	0.144648i	$-0.0462048\pi$
$620$			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	−0.741391	−	0.671073i	$-0.765834\pi$
$631$	−13.3366	+	7.69988i	−0.530921	+	0.306527i	0.210470	+	0.977600i	$0.432500\pi$
$632$	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	$0.0588412\pi$
$641$			9.30710i			0.367608i	−0.982963	+	0.183804i	$0.941159\pi$
$642$	−16.1766	−	16.5730i	−0.638440	−	0.654083i
$643$	−3.03048	−	5.24895i	−0.119511	−	0.206998i	0.800063	−	0.599916i	$-0.204799\pi$
$643$	−3.03048	−	5.24895i	−0.119511	−	0.206998i	−0.919574	+	0.392917i	$0.871466\pi$
$644$	−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	0.955459	−	0.295124i	$-0.0953608\pi$
$647$	5.65052	+	9.78699i	0.222145	+	0.384766i	−0.733314	+	0.679890i	$0.762027\pi$
$648$	−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	$-0.751898\pi$
$653$		−	35.9225i		−	1.40576i	0.711311	−	0.702878i	$-0.248102\pi$
$654$	−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	−0.180628	−	0.983552i	$-0.557813\pi$
$659$	14.9107	−	8.60870i	0.580839	−	0.335348i	0.761467	+	0.648204i	$0.224480\pi$
$660$	10.4533	−	2.66580i	0.406894	−	0.103766i
$661$	2.99584	+	5.18895i	0.116525	+	0.201827i	0.918388	−	0.395680i	$-0.129491\pi$
$661$	2.99584	+	5.18895i	0.116525	+	0.201827i	−0.801863	+	0.597507i	$0.796158\pi$
$662$	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	0.328478	+	0.944512i	$0.393464\pi$
$673$	−16.9593	+	29.3743i	−0.653732	+	1.13230i	−0.982210	+	0.187786i	$0.939869\pi$
$674$	−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	0.701984	−	0.712193i	$-0.252298\pi$
$677$	−6.91552	−	11.9780i	−0.265785	−	0.460353i	−0.967769	+	0.251840i	$0.918964\pi$
$678$	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	$-0.767415\pi$
$701$		−	35.3397i		−	1.33476i	0.744716	−	0.667382i	$-0.232585\pi$
$702$	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	0.285613	−	0.958345i	$-0.407803\pi$
$709$	−10.6916	−	6.17279i	−0.401531	−	0.231824i	−0.687144	+	0.726521i	$0.741136\pi$
$710$	−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	−0.828840	−	0.559486i	$-0.810999\pi$
$719$	1.87992	−	3.25611i	0.0701091	−	0.121433i	0.898949	+	0.438053i	$0.144332\pi$
$720$	−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	$0.0619177\pi$
$727$			10.4236i			0.386592i	−0.981141	+	0.193296i	$0.938082\pi$
$728$	−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	0.981800	+	0.189917i	$0.0608217\pi$
$733$	17.7435	+	30.7327i	0.655373	+	1.13514i	−0.326428	+	0.945222i	$0.605845\pi$
$734$	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	−0.397309	−	0.917685i	$-0.630056\pi$
$739$	5.40360	−	3.11977i	0.198775	−	0.114763i	0.596084	+	0.802922i	$0.296723\pi$
$740$	−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	−0.135306	−	0.990804i	$-0.543202\pi$
$743$	21.5450	−	37.3170i	0.790408	−	1.36903i	0.925714	−	0.378223i	$-0.123465\pi$
$744$	−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	−0.732644	−	0.680612i	$-0.761714\pi$
$757$	6.13845	−	10.6321i	0.223106	−	0.386430i	0.955749	+	0.294182i	$0.0950472\pi$
$758$	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	0.742007	−	0.670392i	$-0.233874\pi$
$761$	14.6878	+	8.48003i	0.532434	+	0.307401i	−0.209573	+	0.977793i	$0.567207\pi$
$762$	−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	−0.322056	−	0.946720i	$-0.604374\pi$
$769$	18.2706	−	31.6457i	0.658856	−	1.14117i	0.980912	−	0.194451i	$-0.0622926\pi$
$770$	−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	$0.00555621\pi$
$773$			0.970568i			0.0349089i	−0.999848	+	0.0174545i	$0.994444\pi$
$774$	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	−0.941066	−	0.338224i	$-0.890174\pi$
$797$	−21.5529	−	37.3307i	−0.763443	−	1.32232i	0.177623	−	0.984099i	$-0.443159\pi$
$798$	−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	−0.103027	−	0.994679i	$-0.532853\pi$
$809$	20.1056	−	11.6080i	0.706876	−	0.408115i	0.809903	+	0.586563i	$0.199519\pi$
$810$	−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	−0.912803	−	0.408400i	$-0.866087\pi$
$829$	−29.2392	+	16.8813i	−1.01552	+	0.586311i	−0.102717	+	0.994711i	$0.532754\pi$
$830$	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	−0.927296	−	0.374329i	$-0.877873\pi$
$839$	−30.8994	+	17.8398i	−1.06677	+	0.615897i	−0.139469	+	0.990226i	$0.544540\pi$
$840$	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	−0.965065	−	0.262010i	$-0.915615\pi$
$857$	−7.48332	+	12.9615i	−0.255625	+	0.442756i	0.709440	+	0.704766i	$0.248948\pi$
$858$	20.3759	−	5.80288i	0.695622	−	0.198107i
$859$	42.5746	−	24.5804i	1.45263	−	0.838674i	0.453995	−	0.891004i	$-0.349998\pi$
$859$	42.5746	−	24.5804i	1.45263	−	0.838674i	0.998630	+	0.0523306i	$0.0166650\pi$
$860$	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	−0.857346	−	0.514741i	$-0.827888\pi$
$863$	−25.6886	−	44.4940i	−0.874451	−	1.51459i	−0.0171055	−	0.999854i	$-0.505445\pi$
$864$	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	−0.394113	−	0.919062i	$-0.628948\pi$
$877$	−41.0778	−	23.7163i	−1.38710	−	0.800843i	−0.992987	+	0.118219i	$0.962281\pi$
$878$		−	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	−0.938649	−	0.344873i	$-0.887922\pi$
$881$	−5.06534	+	8.77342i	−0.170656	+	0.295584i	0.767994	+	0.640457i	$0.221255\pi$
$882$	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	0.955434	−	0.295204i	$-0.0953876\pi$
$907$	6.68775	+	11.5835i	0.222063	+	0.384625i	−0.733371	+	0.679828i	$0.762054\pi$
$908$			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	$-0.882354\pi$
$911$		−	21.8063i		−	0.722475i	0.932474	−	0.361238i	$-0.117646\pi$
$912$	−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	−0.931487	−	0.363775i	$-0.881488\pi$
$919$	−4.56863	+	7.91310i	−0.150705	+	0.261029i	0.780782	+	0.624804i	$0.214821\pi$
$920$	−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	0.294614	−	0.955616i	$-0.404809\pi$
$929$	−11.7550	−	6.78673i	−0.385668	−	0.222665i	−0.680281	+	0.732951i	$0.738142\pi$
$930$	−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	$0.00336735\pi$
$937$			0.647634i			0.0211573i	−0.999944	+	0.0105786i	$0.996633\pi$
$938$	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	−0.411810	−	0.911270i	$-0.635103\pi$
$941$	−43.1576	−	24.9171i	−1.40690	−	0.812273i	−0.995088	+	0.0989966i	$0.968437\pi$
$942$	−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	−0.00260249	−	0.999997i	$-0.500828\pi$
$953$	26.6142	−	15.3657i	0.862119	−	0.497744i	0.864721	+	0.502252i	$0.167495\pi$
$954$	−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	$-0.865644\pi$
$967$		−	25.4787i		−	0.819341i	0.912234	−	0.409671i	$-0.134356\pi$
$968$	−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	−0.977758	−	0.209737i	$-0.932739\pi$
$971$	−9.57391	+	16.5825i	−0.307241	+	0.532157i	0.670517	+	0.741895i	$0.266073\pi$
$972$	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	0.888051	−	0.459746i	$-0.152060\pi$
$977$	1.43387	+	2.48354i	0.0458736	+	0.0794554i	−0.842177	+	0.539201i	$0.818726\pi$
$978$	−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	0.971667	−	0.236353i	$-0.0759521\pi$
$983$	39.2792	+	22.6779i	1.25281	+	0.723312i	0.281146	+	0.959665i	$0.409285\pi$
$984$	−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	0.578603	−	0.815609i	$-0.303598\pi$
$991$	−13.1284	−	22.7390i	−0.417037	−	0.722329i	−0.995640	+	0.0932802i	$0.970265\pi$
$992$	−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	$0.130934\pi$
$997$			25.2501i			0.799678i	−0.916585	+	0.399839i	$0.869066\pi$
$998$	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.17.4	yes	34
3.2	odd	2		546.2.bi.e.17.1	✓	34
7.5	odd	6		546.2.bn.e.173.9	yes	34
13.10	even	6		546.2.bn.f.101.9	yes	34
21.5	even	6		546.2.bn.f.173.9	yes	34
39.23	odd	6		546.2.bn.e.101.9	yes	34
91.75	odd	6		546.2.bi.e.257.1	yes	34
273.257	even	6	inner	546.2.bi.f.257.4	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.1	✓	34	3.2	odd	2
546.2.bi.e.257.1	yes	34	91.75	odd	6
546.2.bi.f.17.4	yes	34	1.1	even	1	trivial
546.2.bi.f.257.4	yes	34	273.257	even	6	inner
546.2.bn.e.101.9	yes	34	39.23	odd	6
546.2.bn.e.173.9	yes	34	7.5	odd	6
546.2.bn.f.101.9	yes	34	13.10	even	6
546.2.bn.f.173.9	yes	34	21.5	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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