LMFDB - Embedded newform 546.2.bi.e.17.1

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			17.1
Character	$\chi$	$=$	546.17
Dual form			546.2.bi.e.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.66749 + 0.468501i) q^{3} +1.00000 q^{4} +(-1.58996 + 0.917964i) q^{5} +(1.66749 - 0.468501i) q^{6} +(-0.364289 - 2.62055i) q^{7} -1.00000 q^{8} +(2.56101 - 1.56244i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.66749 + 0.468501i) q^{3} +1.00000 q^{4} +(-1.58996 + 0.917964i) q^{5} +(1.66749 - 0.468501i) q^{6} +(-0.364289 - 2.62055i) q^{7} -1.00000 q^{8} +(2.56101 - 1.56244i) q^{9} +(1.58996 - 0.917964i) q^{10} +(1.69625 + 2.93798i) q^{11} +(-1.66749 + 0.468501i) q^{12} +(3.07128 - 1.88872i) q^{13} +(0.364289 + 2.62055i) q^{14} +(2.22117 - 2.27559i) q^{15} +1.00000 q^{16} -3.18506 q^{17} +(-2.56101 + 1.56244i) q^{18} +(-1.01582 + 1.75945i) q^{19} +(-1.58996 + 0.917964i) q^{20} +(1.83518 + 4.19906i) q^{21} +(-1.69625 - 2.93798i) q^{22} +2.47560i q^{23} +(1.66749 - 0.468501i) 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} +(-2.22117 + 2.27559i) q^{30} +(-3.14345 + 5.44461i) q^{31} -1.00000 q^{32} +(-4.20491 - 4.10435i) q^{33} +3.18506 q^{34} +(2.98478 + 3.83217i) q^{35} +(2.56101 - 1.56244i) q^{36} -0.503913i q^{37} +(1.01582 - 1.75945i) q^{38} +(-4.23645 + 4.58830i) q^{39} +(1.58996 - 0.917964i) q^{40} +(-4.35184 - 2.51254i) q^{41} +(-1.83518 - 4.19906i) 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} +(-1.66749 + 0.468501i) q^{48} +(-6.73459 + 1.90927i) q^{49} +(0.814684 - 1.41107i) q^{50} +(5.31104 - 1.49220i) 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} +(2.22117 - 2.27559i) q^{60} +(10.1157 + 5.84028i) q^{61} +(3.14345 - 5.44461i) q^{62} +(-5.02740 - 6.14209i) q^{63} +1.00000 q^{64} +(-3.14944 + 5.82231i) q^{65} +(4.20491 + 4.10435i) q^{66} +(-8.59785 + 4.96397i) q^{67} -3.18506 q^{68} +(-1.15982 - 4.12803i) q^{69} +(-2.98478 - 3.83217i) q^{70} +(7.77030 + 13.4586i) q^{71} +(-2.56101 + 1.56244i) 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} +(4.23645 - 4.58830i) q^{78} +(3.92399 + 6.79656i) q^{79} +(-1.58996 + 0.917964i) q^{80} +(4.11758 - 8.00285i) q^{81} +(4.35184 + 2.51254i) q^{82} -13.0790i q^{83} +(1.83518 + 4.19906i) 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} +(1.66749 - 0.468501i) 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} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * 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 - 3 * 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
$3$	−1.66749	+	0.468501i	−0.962723	+	0.270489i
$3$	−1.66749	+	0.468501i	−0.962723	+	0.270489i
$4$	1.00000			0.500000
$5$	−1.58996	+	0.917964i	−0.711052	+	0.410526i	−0.811450	−	0.584421i	$-0.801322\pi$
$5$	−1.58996	+	0.917964i	−0.711052	+	0.410526i	0.100398	+	0.994947i	$0.467988\pi$
$6$	1.66749	−	0.468501i	0.680748	−	0.191265i
$7$	−0.364289	−	2.62055i	−0.137688	−	0.990476i
$7$	−0.364289	−	2.62055i	−0.137688	−	0.990476i
$8$	−1.00000			−0.353553
$9$	2.56101	−	1.56244i	0.853671	−	0.520813i
$10$	1.58996	−	0.917964i	0.502790	−	0.290286i
$11$	1.69625	+	2.93798i	0.511437	+	0.885835i	0.999912	+	0.0132573i	$0.00422005\pi$
$11$	1.69625	+	2.93798i	0.511437	+	0.885835i	−0.488475	+	0.872578i	$0.662447\pi$
$12$	−1.66749	+	0.468501i	−0.481361	+	0.135245i
$13$	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
$15$	2.22117	−	2.27559i	0.573503	−	0.587555i
$16$	1.00000			0.250000
$17$	−3.18506			−0.772490			−0.386245	−	0.922396i	$-0.626228\pi$
$17$	−3.18506			−0.772490			−0.386245	+	0.922396i	$0.626228\pi$
$18$	−2.56101	+	1.56244i	−0.603637	+	0.368270i
$19$	−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
$21$	1.83518	+	4.19906i	0.400469	+	0.916310i
$22$	−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	$0.916904\pi$
$24$	1.66749	−	0.468501i	0.340374	−	0.0956324i
$25$	−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	$-0.395795\pi$
$29$	−1.81857	−	1.04995i	−0.337701	−	0.194971i	−0.659255	+	0.751920i	$0.729128\pi$
$30$	−2.22117	+	2.27559i	−0.405528	+	0.415464i
$31$	−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
$33$	−4.20491	−	4.10435i	−0.731981	−	0.714476i
$34$	3.18506			0.546233
$35$	2.98478	+	3.83217i	0.504519	+	0.647755i
$36$	2.56101	−	1.56244i	0.426836	−	0.260406i
$37$		−	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
$39$	−4.23645	+	4.58830i	−0.678374	+	0.734716i
$40$	1.58996	−	0.917964i	0.251395	−	0.145143i
$41$	−4.35184	−	2.51254i	−0.679643	−	0.392392i	0.120077	−	0.992765i	$-0.461686\pi$
$41$	−4.35184	−	2.51254i	−0.679643	−	0.392392i	−0.799721	+	0.600372i	$0.795019\pi$
$42$	−1.83518	−	4.19906i	−0.283174	−	0.647929i
$43$	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	−0.999535	−	0.0304848i	$-0.990295\pi$
$47$	−10.0977	+	5.82991i	−1.47290	+	0.850380i	−0.473367	+	0.880865i	$0.656962\pi$
$48$	−1.66749	+	0.468501i	−0.240681	+	0.0676223i
$49$	−6.73459	+	1.90927i	−0.962084	+	0.272754i
$50$	0.814684	−	1.41107i	0.115214	−	0.199556i
$51$	5.31104	−	1.49220i	0.743694	−	0.208950i
$52$	3.07128	−	1.88872i	0.425910	−	0.261918i
$53$	5.81668	+	3.35826i	0.798983	+	0.461293i	0.843115	−	0.537733i	$-0.180719\pi$
$53$	5.81668	+	3.35826i	0.798983	+	0.461293i	−0.0441326	+	0.999026i	$0.514052\pi$
$54$	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	$0.867562\pi$
$60$	2.22117	−	2.27559i	0.286752	−	0.293777i
$61$	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
$63$	−5.02740	−	6.14209i	−0.633393	−	0.773831i
$64$	1.00000			0.125000
$65$	−3.14944	+	5.82231i	−0.390640	+	0.722168i
$66$	4.20491	+	4.10435i	0.517589	+	0.505211i
$67$	−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
$69$	−1.15982	−	4.12803i	−0.139626	−	0.496956i
$70$	−2.98478	−	3.83217i	−0.356749	−	0.458032i
$71$	7.77030	+	13.4586i	0.922165	+	1.59724i	0.796058	+	0.605221i	$0.206915\pi$
$71$	7.77030	+	13.4586i	0.922165	+	1.59724i	0.126108	+	0.992017i	$0.459752\pi$
$72$	−2.56101	+	1.56244i	−0.301818	+	0.184135i
$73$	−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
$78$	4.23645	−	4.58830i	0.479683	−	0.519523i
$79$	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
$81$	4.11758	−	8.00285i	0.457509	−	0.889205i
$82$	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	$-0.254852\pi$
$84$	1.83518	+	4.19906i	0.200234	+	0.458155i
$85$	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
$96$	1.66749	−	0.468501i	0.170187	−	0.0478162i
$97$	−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	0.532094	−	0.846686i	$-0.321405\pi$
$101$	−4.69535	−	8.13258i	−0.467204	−	0.809222i	−0.999298	+	0.0374637i	$0.988072\pi$
$102$	−5.31104	+	1.49220i	−0.525871	+	0.147750i
$103$	−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
$105$	−6.77245	−	4.99172i	−0.660923	−	0.487142i
$106$	−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	0.672065	−	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
$111$	0.236084	+	0.840268i	0.0224081	+	0.0797547i
$112$	−0.364289	−	2.62055i	−0.0344220	−	0.247619i
$113$	13.8390	−	7.98994i	1.30186	−	0.751631i	0.321139	−	0.947032i	$-0.395934\pi$
$113$	13.8390	−	7.98994i	1.30186	−	0.751631i	0.980723	+	0.195402i	$0.0626010\pi$
$114$	−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
$117$	4.91459	−	9.63571i	0.454354	−	0.890821i
$118$		−	6.20893i		−	0.571578i
$119$	1.16028	+	8.34661i	0.106363	+	0.765133i
$120$	−2.22117	+	2.27559i	−0.202764	+	0.207732i
$121$	−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
$126$	5.02740	+	6.14209i	0.447876	+	0.547181i
$127$	−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
$129$	−1.31130	−	1.27994i	−0.115453	−	0.112692i
$130$	3.14944	−	5.82231i	0.276224	−	0.510650i
$131$	4.95760	+	8.58681i	0.433147	+	0.750233i	0.997142	−	0.0755449i	$-0.0240696\pi$
$131$	4.95760	+	8.58681i	0.433147	+	0.750233i	−0.563995	+	0.825778i	$0.690736\pi$
$132$	−4.20491	−	4.10435i	−0.365991	−	0.357238i
$133$	4.98079	+	2.02106i	0.431889	+	0.175248i
$134$	8.59785	−	4.96397i	0.742741	−	0.428822i
$135$	2.13297	−	9.29825i	0.183577	−	0.800266i
$136$	3.18506			0.273117
$137$	−3.18307			−0.271948			−0.135974	−	0.990712i	$-0.543416\pi$
$137$	−3.18307			−0.271948			−0.135974	+	0.990712i	$0.543416\pi$
$138$	1.15982	+	4.12803i	0.0987306	+	0.351401i
$139$	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
$141$	14.1065	−	14.4521i	1.18798	−	1.21709i
$142$	−7.77030	−	13.4586i	−0.652069	−	1.12942i
$143$	10.7587	+	5.81964i	0.899684	+	0.486663i
$144$	2.56101	−	1.56244i	0.213418	−	0.130203i
$145$	3.85528			0.320164
$146$	4.47574	−	7.75221i	0.370415	−	0.641577i
$147$	10.3353	−	6.33885i	0.852443	−	0.522820i
$148$		−	0.503913i		−	0.0414214i
$149$	−10.8563	+	18.8036i	−0.889382	+	1.54045i	−0.0487739	+	0.998810i	$0.515531\pi$
$149$	−10.8563	+	18.8036i	−0.889382	+	1.54045i	−0.840608	+	0.541644i	$0.817802\pi$
$150$	−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
$153$	−8.15698	+	4.97646i	−0.659453	+	0.402323i
$154$	−7.08122	+	5.51537i	−0.570621	+	0.444441i
$155$		−	11.5423i		−	0.927099i
$156$	−4.23645	+	4.58830i	−0.339187	+	0.367358i
$157$	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
$162$	−4.11758	+	8.00285i	−0.323507	+	0.628763i
$163$	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	0.374562	−	0.927202i	$-0.377793\pi$
$167$	−3.11618	−	1.79913i	−0.241137	−	0.139221i	−0.615699	+	0.787981i	$0.711126\pi$
$168$	−1.83518	−	4.19906i	−0.141587	−	0.323965i
$169$	5.86551	−	11.6015i	0.451193	−	0.892426i
$170$	−5.06412	+	2.92377i	−0.388400	+	0.224243i
$171$	0.147505	+	6.09314i	0.0112800	+	0.465954i
$172$	0.528972	+	0.916206i	0.0403337	+	0.0698600i
$173$	0.476807	−	0.825853i	0.0362509	−	0.0627885i	−0.847331	−	0.531066i	$-0.821792\pi$
$173$	0.476807	−	0.825853i	0.0362509	−	0.0627885i	0.883582	+	0.468277i	$0.155125\pi$
$174$	−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
$177$	−2.90889	−	10.3533i	−0.218645	−	0.778201i
$178$		−	5.33363i		−	0.399772i
$179$	−15.3789	+	8.87903i	−1.14948	+	0.663650i	−0.948759	−	0.316000i	$-0.897660\pi$
$179$	−15.3789	+	8.87903i	−1.14948	+	0.663650i	−0.200716	+	0.979649i	$0.564327\pi$
$180$	−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
$189$	11.2607	+	7.88650i	0.819094	+	0.573659i
$190$			3.72995i			0.270599i
$191$	−17.4751	−	10.0893i	−1.26446	−	0.730034i	−0.290523	−	0.956868i	$-0.593829\pi$
$191$	−17.4751	−	10.0893i	−1.26446	−	0.730034i	−0.973933	+	0.226834i	$0.927163\pi$
$192$	−1.66749	+	0.468501i	−0.120340	+	0.0338112i
$193$	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
$195$	2.52389	−	11.1841i	0.180739	−	0.800912i
$196$	−6.73459	+	1.90927i	−0.481042	+	0.136377i
$197$	−5.74363	+	9.94826i	−0.409217	+	0.708784i	−0.994802	−	0.101826i	$-0.967531\pi$
$197$	−5.74363	+	9.94826i	−0.409217	+	0.708784i	0.585585	+	0.810611i	$0.300865\pi$
$198$	−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
$201$	12.0112	−	12.3054i	0.847202	−	0.867959i
$202$	4.69535	+	8.13258i	0.330363	+	0.572206i
$203$	−2.08897	+	5.14815i	−0.146617	+	0.361329i
$204$	5.31104	−	1.49220i	0.371847	−	0.104475i
$205$	9.22567			0.644349
$206$	11.5646	−	6.67680i	0.805741	−	0.465195i
$207$	3.86797	+	6.34005i	0.268843	+	0.440664i
$208$	3.07128	−	1.88872i	0.212955	−	0.130959i
$209$	−6.89232			−0.476752
$210$	6.77245	+	4.99172i	0.467343	+	0.344461i
$211$	−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
$213$	−19.2622	−	18.8016i	−1.31983	−	1.28826i
$214$			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
$222$	−0.236084	−	0.840268i	−0.0158449	−	0.0563951i
$223$	−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
$225$	0.118299	+	4.88667i	0.00788657	+	0.325778i
$226$	−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	0.534729	−	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
$231$	−9.22386	+	12.5144i	−0.606886	+	0.823384i
$232$	1.81857	+	1.04995i	0.119395	+	0.0689328i
$233$	24.0450	−	13.8824i	1.57524	−	0.909465i	0.579729	−	0.814809i	$-0.303158\pi$
$233$	24.0450	−	13.8824i	1.57524	−	0.909465i	0.995510	−	0.0946555i	$-0.0301750\pi$
$234$	−4.91459	+	9.63571i	−0.321277	+	0.629906i
$235$	10.7033	−	18.5387i	0.698207	−	1.20933i
$236$			6.20893i			0.404167i
$237$	−9.72740	−	9.49476i	−0.631862	−	0.616751i
$238$	−1.16028	−	8.34661i	−0.0752098	−	0.541031i
$239$	−5.31347			−0.343700			−0.171850	−	0.985123i	$-0.554974\pi$
$239$	−5.31347			−0.343700			−0.171850	+	0.985123i	$0.554974\pi$
$240$	2.22117	−	2.27559i	0.143376	−	0.146889i
$241$	−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
$243$	−3.11666	+	15.2737i	−0.199934	+	0.979809i
$244$	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
$249$	6.12753	+	21.8090i	0.388316	+	1.38209i
$250$			12.1710i			0.769764i
$251$	4.75595	+	8.23755i	0.300193	+	0.519950i	0.976180	−	0.216964i	$-0.0696156\pi$
$251$	4.75595	+	8.23755i	0.300193	+	0.519950i	−0.675986	+	0.736914i	$0.736282\pi$
$252$	−5.02740	−	6.14209i	−0.316696	−	0.386915i
$253$	−7.27328	+	4.19923i	−0.457267	+	0.264003i
$254$	0.475986	−	0.824432i	0.0298660	−	0.0517295i
$255$	−7.07455	+	7.24789i	−0.443026	+	0.453880i
$256$	1.00000			0.0625000
$257$	5.26373			0.328343			0.164171	−	0.986432i	$-0.447505\pi$
$257$	5.26373			0.328343			0.164171	+	0.986432i	$0.447505\pi$
$258$	1.31130	+	1.27994i	0.0816377	+	0.0796853i
$259$	−1.32053	+	0.183570i	−0.0820538	+	0.0114065i
$260$	−3.14944	+	5.82231i	−0.195320	+	0.361084i
$261$	−6.29788	+	0.152462i	−0.389829	+	0.00943714i
$262$	−4.95760	−	8.58681i	−0.306281	−	0.530495i
$263$	−9.39641	+	5.42502i	−0.579408	+	0.334521i	−0.760898	−	0.648872i	$-0.775241\pi$
$263$	−9.39641	+	5.42502i	−0.579408	+	0.334521i	0.181490	+	0.983393i	$0.441908\pi$
$264$	4.20491	+	4.10435i	0.258794	+	0.252605i
$265$	−12.3311			−0.757491
$266$	−4.98079	−	2.02106i	−0.305392	−	0.123919i
$267$	−2.49881	−	8.89375i	−0.152925	−	0.544288i
$268$	−8.59785	+	4.96397i	−0.525197	+	0.303223i
$269$	18.1117			1.10429			0.552146	−	0.833747i	$-0.313809\pi$
$269$	18.1117			1.10429			0.552146	+	0.833747i	$0.313809\pi$
$270$	−2.13297	+	9.29825i	−0.129809	+	0.565874i
$271$	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
$273$	13.5672	+	9.43036i	0.821123	+	0.570752i
$274$	3.18307			0.192296
$275$	−5.52761			−0.333328
$276$	−1.15982	−	4.12803i	−0.0698131	−	0.248478i
$277$	−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
$279$	0.456454	+	18.8552i	0.0273272	+	1.12883i
$280$	−2.98478	−	3.83217i	−0.178375	−	0.229016i
$281$	2.73779			0.163323			0.0816614	−	0.996660i	$-0.473977\pi$
$281$	2.73779			0.163323			0.0816614	+	0.996660i	$0.473977\pi$
$282$	−14.1065	+	14.4521i	−0.840027	+	0.860609i
$283$	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
$285$	1.74748	+	6.21963i	0.103512	+	0.368419i
$286$	−10.7587	−	5.81964i	−0.636173	−	0.344123i
$287$	−4.99890	+	12.3195i	−0.295076	+	0.727198i
$288$	−2.56101	+	1.56244i	−0.150909	+	0.0920675i
$289$	−6.85540			−0.403259
$290$	−3.85528			−0.226390
$291$	11.8967	+	11.6122i	0.697395	+	0.680716i
$292$	−4.47574	+	7.75221i	−0.261923	+	0.453664i
$293$	2.86877	−	1.65628i	0.167595	−	0.0967612i	−0.413856	−	0.910342i	$-0.635818\pi$
$293$	2.86877	−	1.65628i	0.167595	−	0.0967612i	0.581451	+	0.813581i	$0.302485\pi$
$294$	−10.3353	+	6.33885i	−0.602769	+	0.369689i
$295$	−5.69957	−	9.87195i	−0.331842	−	0.574767i
$296$			0.503913i			0.0292894i
$297$	−17.1816	−	3.94138i	−0.996979	−	0.228702i
$298$	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
$303$	11.6395	+	11.3612i	0.668674	+	0.652683i
$304$	−1.01582	+	1.75945i	−0.0582613	+	0.100912i
$305$	−21.4447			−1.22792
$306$	8.15698	−	4.97646i	0.466303	−	0.284485i
$307$	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
$309$	16.1556	−	16.5515i	0.919062	−	0.941580i
$310$			11.5423i			0.655558i
$311$	15.8352	−	27.4274i	0.897934	−	1.55527i	0.0678034	−	0.997699i	$-0.478401\pi$
$311$	15.8352	−	27.4274i	0.897934	−	1.55527i	0.830131	−	0.557569i	$-0.188266\pi$
$312$	4.23645	−	4.58830i	0.239842	−	0.259761i
$313$	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
$315$	13.6316	+	5.15071i	0.768053	+	0.290210i
$316$	3.92399	+	6.79656i	0.220742	+	0.382336i
$317$	−12.7938	−	22.1596i	−0.718573	−	1.24461i	−0.961565	−	0.274577i	$-0.911462\pi$
$317$	−12.7938	−	22.1596i	−0.718573	−	1.24461i	0.242992	−	0.970028i	$-0.421871\pi$
$318$	11.2726	+	2.87473i	0.632135	+	0.161207i
$319$		−	7.12392i		−	0.398863i
$320$	−1.58996	+	0.917964i	−0.0888815	+	0.0513158i
$321$	6.26430	+	22.2958i	0.349639	+	1.24443i
$322$	−6.48744	+	0.901834i	−0.361531	+	0.0502572i
$323$	3.23545	−	5.60396i	0.180025	−	0.311813i
$324$	4.11758	−	8.00285i	0.228754	−	0.444603i
$325$	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
$333$	−0.787333	−	1.29053i	−0.0431456	−	0.0707205i
$334$	3.11618	+	1.79913i	0.170510	+	0.0984438i
$335$	9.11349	−	15.7850i	0.497923	−	0.862428i
$336$	1.83518	+	4.19906i	0.100117	+	0.229078i
$337$	−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
$339$	−19.3330	+	19.8067i	−1.05002	+	1.07575i
$340$	5.06412	−	2.92377i	0.274640	−	0.158564i
$341$	−21.3282			−1.15499
$342$	−0.147505	−	6.09314i	−0.00797617	−	0.329479i
$343$	7.45669	+	16.9528i	0.402623	+	0.915366i
$344$	−0.528972	−	0.916206i	−0.0285202	−	0.0493985i
$345$	5.63345	+	5.49873i	0.303295	+	0.296042i
$346$	−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	−0.196079	−	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
$351$	−3.68066	+	18.3699i	−0.196459	+	0.980512i
$352$	−1.69625	−	2.93798i	−0.0904102	−	0.156595i
$353$	−24.5364	+	14.1661i	−1.30594	+	0.753984i	−0.981416	−	0.191894i	$-0.938537\pi$
$353$	−24.5364	+	14.1661i	−1.30594	+	0.753984i	−0.324523	+	0.945878i	$0.605204\pi$
$354$	2.90889	+	10.3533i	0.154606	+	0.550271i
$355$	−24.7090	−	14.2657i	−1.31142	−	0.757146i
$356$			5.33363i			0.282682i
$357$	−5.84515	−	13.3743i	−0.309358	−	0.707841i
$358$	15.3789	−	8.87903i	0.812802	−	0.469271i
$359$	10.8679	+	18.8238i	0.573588	+	0.993483i	0.996193	+	0.0871698i	$0.0277823\pi$
$359$	10.8679	+	18.8238i	0.573588	+	0.993483i	−0.422606	+	0.906314i	$0.638884\pi$
$360$	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
$369$	−15.0708	+	0.364840i	−0.784554	+	0.0189928i
$370$	−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
$375$	5.70215	+	20.2950i	0.294458	+	1.04803i
$376$	10.0977	−	5.82991i	0.520750	−	0.300655i
$377$	−7.56841	+	0.210065i	−0.389793	+	0.0108189i
$378$	−11.2607	−	7.88650i	−0.579187	−	0.405638i
$379$	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	0.664797	−	0.747024i	$-0.268518\pi$
$383$	6.85462	+	3.95752i	0.350255	+	0.202220i	−0.314543	+	0.949243i	$0.601851\pi$
$384$	1.66749	−	0.468501i	0.0850935	−	0.0239081i
$385$	−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	$-0.354567\pi$
$389$	−2.27718	−	1.31473i	−0.115458	−	0.0666595i	−0.556617	+	0.830769i	$0.687901\pi$
$390$	−2.52389	+	11.1841i	−0.127802	+	0.566330i
$391$		−	7.88494i		−	0.398758i
$392$	6.73459	−	1.90927i	0.340148	−	0.0964329i
$393$	−12.2897	−	11.9957i	−0.619931	−	0.605105i
$394$	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
$399$	−9.25226	−	1.03658i	−0.463192	−	0.0518941i
$400$	−0.814684	+	1.41107i	−0.0407342	+	0.0705537i
$401$	−6.99738			−0.349433			−0.174716	−	0.984619i	$-0.555901\pi$
$401$	−6.99738			−0.349433			−0.174716	+	0.984619i	$0.555901\pi$
$402$	−12.0112	+	12.3054i	−0.599062	+	0.613740i
$403$	0.628914	+	22.6590i	0.0313284	+	1.12873i
$404$	−4.69535	−	8.13258i	−0.233602	−	0.404611i
$405$	0.799540	+	16.5040i	0.0397294	+	0.820090i
$406$	2.08897	−	5.14815i	0.103674	−	0.255498i
$407$	1.48049	−	0.854760i	0.0733851	−	0.0423689i
$408$	−5.31104	+	1.49220i	−0.262936	+	0.0738751i
$409$	−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
$411$	5.30772	−	1.49127i	0.261811	−	0.0735590i
$412$	−11.5646	+	6.67680i	−0.569745	+	0.328942i
$413$	16.2708	−	2.26184i	0.800634	−	0.111298i
$414$	−3.86797	−	6.34005i	−0.190100	−	0.311596i
$415$	12.0061	+	20.7951i	0.589354	+	1.02079i
$416$	−3.07128	+	1.88872i	−0.150582	+	0.0926019i
$417$	−0.137140	+	0.140501i	−0.00671580	+	0.00688034i
$418$	6.89232			0.337114
$419$	−5.19733	+	9.00204i	−0.253906	+	0.439778i	−0.964598	−	0.263725i	$-0.915049\pi$
$419$	−5.19733	+	9.00204i	−0.253906	+	0.439778i	0.710692	+	0.703504i	$0.248382\pi$
$420$	−6.77245	−	4.99172i	−0.330462	−	0.243571i
$421$		−	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
$426$	19.2622	+	18.8016i	0.933257	+	0.910938i
$427$	11.6197	−	28.6362i	0.562318	−	1.38580i
$428$		−	13.3709i		−	0.646309i
$429$	−20.6664	−	4.66372i	−0.997784	−	0.225167i
$430$	1.68209	+	0.971154i	0.0811175	+	0.0468332i
$431$	−19.3138	−	33.4525i	−0.930313	−	1.61135i	−0.782786	−	0.622291i	$-0.786202\pi$
$431$	−19.3138	−	33.4525i	−0.930313	−	1.61135i	−0.147527	−	0.989058i	$-0.547131\pi$
$432$	−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
$435$	−6.42862	+	1.80620i	−0.308229	+	0.0866008i
$436$	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
$441$	−14.2642	+	15.4121i	−0.679250	+	0.733907i
$442$	9.78221	−	6.01567i	0.465292	−	0.286136i
$443$	−7.76750	+	4.48457i	−0.369045	+	0.213068i	−0.673041	−	0.739605i	$-0.735012\pi$
$443$	−7.76750	+	4.48457i	−0.369045	+	0.213068i	0.303996	+	0.952673i	$0.401679\pi$
$444$	0.236084	+	0.840268i	0.0112040	+	0.0398773i
$445$	−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	$-0.0216657\pi$
$449$	9.32220	+	16.1465i	0.439942	+	0.762002i	−0.557742	+	0.830014i	$0.688332\pi$
$450$	−0.118299	−	4.88667i	−0.00557665	−	0.230360i
$451$		−	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	−0.719240	−	0.694761i	$-0.755510\pi$
$461$	−10.2455	+	5.91523i	−0.477180	+	0.275500i	0.242061	+	0.970261i	$0.422177\pi$
$462$	9.22386	−	12.5144i	0.429133	−	0.582221i
$463$			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
$465$	5.40758	+	19.2466i	0.250770	+	0.892540i
$466$	−24.0450	+	13.8824i	−1.11386	+	0.643089i
$467$	10.0288	+	17.3705i	0.464080	+	0.803810i	0.999159	−	0.0409918i	$-0.0130517\pi$
$467$	10.0288	+	17.3705i	0.464080	+	0.803810i	−0.535080	+	0.844802i	$0.679718\pi$
$468$	4.91459	−	9.63571i	0.227177	−	0.445411i
$469$	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
$474$	9.72740	+	9.49476i	0.446794	+	0.436109i
$475$	−1.65514	−	2.86679i	−0.0759432	−	0.131538i
$476$	1.16028	+	8.34661i	0.0531814	+	0.382566i
$477$	20.1437	−	0.487646i	0.922316	−	0.0223278i
$478$	5.31347			0.243033
$479$	26.6476	−	15.3850i	1.21756	−	0.702957i	0.253163	−	0.967424i	$-0.418529\pi$
$479$	26.6476	−	15.3850i	1.21756	−	0.702957i	0.964395	+	0.264466i	$0.0851958\pi$
$480$	−2.22117	+	2.27559i	−0.101382	+	0.103866i
$481$	−0.951748	−	1.54766i	−0.0433960	−	0.0705671i
$482$	19.2577			0.877164
$483$	−10.3952	+	4.54317i	−0.472998	+	0.206721i
$484$	−0.254496	+	0.440801i	−0.0115680	+	0.0200364i
$485$	15.2607	+	8.81074i	0.692951	+	0.400075i
$486$	3.11666	−	15.2737i	0.141374	−	0.692830i
$487$		−	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	0.998982	−	0.0451043i	$-0.0143620\pi$
$491$	32.3384	+	18.6706i	1.45941	+	0.842592i	0.460430	+	0.887696i	$0.347695\pi$
$492$	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
$495$	−18.6796	+	0.452204i	−0.839587	+	0.0203251i
$496$	−3.14345	+	5.44461i	−0.141145	+	0.244470i
$497$	32.4382	−	25.2653i	1.45505	−	1.13330i
$498$	−6.12753	−	21.8090i	−0.274581	−	0.977286i
$499$	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	$0.130563\pi$
$503$	18.0289	+	31.2270i	0.803870	+	1.39234i	−0.113181	+	0.993574i	$0.536104\pi$
$504$	5.02740	+	6.14209i	0.223938	+	0.273590i
$505$	14.9308	+	8.62032i	0.664413	+	0.383599i
$506$	7.27328	−	4.19923i	0.323337	−	0.186678i
$507$	−4.34532	+	22.0934i	−0.192982	+	0.981202i
$508$	−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	$-0.206047\pi$
$510$	7.07455	−	7.24789i	0.313266	−	0.320942i
$511$	21.9455	+	8.90487i	0.970813	+	0.393928i
$512$	−1.00000			−0.0441942
$513$	−3.10060	−	10.0911i	−0.136895	−	0.445533i
$514$	−5.26373			−0.232173
$515$	12.2581	−	21.2317i	0.540157	−	0.935580i
$516$	−1.31130	−	1.27994i	−0.0577266	−	0.0563460i
$517$	−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	$-0.720810\pi$
$521$	7.90186	−	13.6864i	0.346187	−	0.599613i	0.985569	+	0.169276i	$0.0541430\pi$
$522$	6.29788	−	0.152462i	0.275651	−	0.00667306i
$523$			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
$525$	−7.42027	−	0.831337i	−0.323847	−	0.0362825i
$526$	9.39641	−	5.42502i	0.409703	−	0.236542i
$527$	10.0121	−	17.3414i	0.436133	−	0.755404i
$528$	−4.20491	−	4.10435i	−0.182995	−	0.178619i
$529$	16.8714			0.733539
$530$	12.3311			0.535627
$531$	9.70106	+	15.9011i	0.420990	+	0.690051i
$532$	4.98079	+	2.02106i	0.215945	+	0.0876241i
$533$	−18.1112	+	0.502686i	−0.784482	+	0.0217737i
$534$	2.49881	+	8.89375i	0.108134	+	0.384870i
$535$	12.2740	+	21.2593i	0.530653	+	0.919118i
$536$	8.59785	−	4.96397i	0.371370	−	0.214411i
$537$	21.4843	−	22.0107i	0.927116	−	0.949832i
$538$	−18.1117			−0.780853
$539$	−17.0329	−	16.5475i	−0.733660	−	0.712752i
$540$	2.13297	−	9.29825i	0.0917886	−	0.400133i
$541$	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
$543$	−2.58409	−	9.19726i	−0.110894	−	0.394692i
$544$	3.18506			0.136558
$545$	−8.11861			−0.347763
$546$	−13.5672	−	9.43036i	−0.580621	−	0.403582i
$547$	−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
$549$	35.0314	−	0.848054i	1.49510	−	0.0361941i
$550$	5.52761			0.235698
$551$	3.69469	−	2.13313i	0.157399	−	0.0908743i
$552$	1.15982	+	4.12803i	0.0493653	+	0.175701i
$553$	16.3813	−	12.7589i	0.696602	−	0.542565i
$554$	18.2835			0.776792
$555$	−1.14670	−	1.11928i	−0.0486747	−	0.0475106i
$556$	0.0981681	−	0.0566774i	0.00416326	−	0.00240366i
$557$	7.64230	+	13.2369i	0.323815	+	0.560864i	0.981272	−	0.192628i	$-0.0617012\pi$
$557$	7.64230	+	13.2369i	0.323815	+	0.560864i	−0.657457	+	0.753492i	$0.728368\pi$
$558$	−0.456454	−	18.8552i	−0.0193232	−	0.798203i
$559$	3.35507	+	1.81485i	0.141904	+	0.0767598i
$560$	2.98478	+	3.83217i	0.126130	+	0.161939i
$561$	13.3929	+	13.0726i	0.565448	+	0.551926i
$562$	−2.73779			−0.115487
$563$	18.7941			0.792079			0.396039	−	0.918234i	$-0.370384\pi$
$563$	18.7941			0.792079			0.396039	+	0.918234i	$0.370384\pi$
$564$	14.1065	−	14.4521i	0.593989	−	0.608543i
$565$	−14.6690	+	25.4074i	−0.617128	+	1.06890i
$566$	−4.60044	+	2.65607i	−0.193371	+	0.111643i
$567$	−22.4719	−	7.87498i	−0.943730	−	0.330718i
$568$	−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	$-0.148990\pi$
$570$	−1.74748	−	6.21963i	−0.0731941	−	0.260512i
$571$	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
$576$	2.56101	−	1.56244i	0.106709	−	0.0651016i
$577$	−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
$579$	−5.49597	+	5.63063i	−0.228405	+	0.234001i
$580$	3.85528			0.160082
$581$	−34.2742	+	4.76453i	−1.42193	+	0.197666i
$582$	−11.8967	−	11.6122i	−0.493133	−	0.481339i
$583$			22.7857i			0.943689i
$584$	4.47574	−	7.75221i	0.185207	−	0.320789i
$585$	1.03123	+	19.8318i	0.0426362	+	0.819944i
$586$	−2.86877	+	1.65628i	−0.118508	+	0.0684205i
$587$	−32.8994	−	18.9945i	−1.35790	−	0.783986i	−0.368563	−	0.929603i	$-0.620150\pi$
$587$	−32.8994	−	18.9945i	−1.35790	−	0.783986i	−0.989341	+	0.145616i	$0.953483\pi$
$588$	10.3353	−	6.33885i	0.426222	−	0.261410i
$589$	−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	$-0.560524\pi$
$593$	13.8054	−	7.97057i	0.566921	−	0.327312i	0.755919	+	0.654665i	$0.227190\pi$
$594$	17.1816	+	3.94138i	0.704971	+	0.161717i
$595$	−9.50669	−	12.2057i	−0.389736	−	0.500385i
$596$	−10.8563	+	18.8036i	−0.444691	+	0.770227i
$597$	−3.21611	−	11.4467i	−0.131627	−	0.468484i
$598$	−4.67571	−	7.60326i	−0.191204	−	0.310921i
$599$	−3.66862	−	2.11808i	−0.149896	−	0.0865423i	0.423176	−	0.906047i	$-0.360915\pi$
$599$	−3.66862	−	2.11808i	−0.149896	−	0.0865423i	−0.573072	+	0.819505i	$0.694248\pi$
$600$	−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
$606$	−11.6395	−	11.3612i	−0.472824	−	0.461516i
$607$	−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
$609$	1.07142	−	9.56315i	0.0434160	−	0.387519i
$610$	21.4447			0.868269
$611$	−20.0018	+	36.9770i	−0.809188	+	1.49593i
$612$	−8.15698	+	4.97646i	−0.329726	+	0.201161i
$613$	−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
$615$	−15.3837	+	4.32224i	−0.620329	+	0.174289i
$616$	−7.08122	+	5.51537i	−0.285310	+	0.222221i
$617$	17.5132	+	30.3337i	0.705053	+	1.22119i	0.966672	+	0.256017i	$0.0824102\pi$
$617$	17.5132	+	30.3337i	0.705053	+	1.22119i	−0.261619	+	0.965171i	$0.584256\pi$
$618$	−16.1556	+	16.5515i	−0.649875	+	0.665798i
$619$	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
$624$	−4.23645	+	4.58830i	−0.169594	+	0.183679i
$625$	7.09916	+	12.2961i	0.283967	+	0.491844i
$626$	−12.5081	+	7.22158i	−0.499926	+	0.288632i
$627$	11.4928	−	3.22906i	0.458980	−	0.128956i
$628$	18.4221	+	10.6360i	0.735124	+	0.424424i
$629$			1.60499i			0.0639953i
$630$	−13.6316	−	5.15071i	−0.543095	−	0.205209i
$631$	−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	$-0.941159\pi$
$641$		−	9.30710i		−	0.367608i	0.982963	−	0.183804i	$-0.0588412\pi$
$642$	−6.26430	−	22.2958i	−0.247232	−	0.879947i
$643$	−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	0.733314	−	0.679890i	$-0.237973\pi$
$647$	−5.65052	−	9.78699i	−0.222145	−	0.384766i	−0.955459	+	0.295124i	$0.904639\pi$
$648$	−4.11758	+	8.00285i	−0.161754	+	0.314382i
$649$	−18.2417	+	10.5319i	−0.716050	+	0.413412i
$650$	−0.162995	−	5.87251i	−0.00639318	−	0.230339i
$651$	−28.6311	−	3.20770i	−1.12214	−	0.125720i
$652$	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
$657$	0.649913	+	26.8466i	0.0253555	+	1.04738i
$658$	−18.9561	−	24.3378i	−0.738985	−	0.948786i
$659$	−14.9107	+	8.60870i	−0.580839	+	0.335348i	−0.761467	−	0.648204i	$-0.775520\pi$
$659$	−14.9107	+	8.60870i	−0.580839	+	0.335348i	0.180628	+	0.983552i	$0.442187\pi$
$660$	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
$663$	13.4933	−	14.6140i	0.524038	−	0.567561i
$664$			13.0790i			0.507564i
$665$	−9.77452	+	1.35878i	−0.379040	+	0.0526911i
$666$	0.787333	+	1.29053i	0.0305085	+	0.0500070i
$667$	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
$672$	−1.83518	−	4.19906i	−0.0707935	−	0.161982i
$673$	−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
$675$	−2.48667	−	8.09303i	−0.0957120	−	0.311501i
$676$	5.86551	−	11.6015i	0.225597	−	0.446213i
$677$	6.91552	+	11.9780i	0.265785	+	0.460353i	0.967769	−	0.251840i	$-0.0810356\pi$
$677$	6.91552	+	11.9780i	0.265785	+	0.460353i	−0.701984	+	0.712193i	$0.747702\pi$
$678$	19.3330	−	19.8067i	0.742480	−	0.760671i
$679$	−20.0344	+	15.6043i	−0.768849	+	0.598836i
$680$	−5.06412	+	2.92377i	−0.194200	+	0.112121i
$681$	2.81561	+	10.0213i	0.107894	+	0.384017i
$682$	21.3282			0.816701
$683$	−4.69607			−0.179690			−0.0898451	−	0.995956i	$-0.528637\pi$
$683$	−4.69607			−0.179690			−0.0898451	+	0.995956i	$0.528637\pi$
$684$	0.147505	+	6.09314i	0.00564000	+	0.232977i
$685$	5.06095	−	2.92194i	0.193369	−	0.111642i
$686$	−7.45669	−	16.9528i	−0.284698	−	0.647261i
$687$	17.4230	+	17.0063i	0.664728	+	0.648831i
$688$	0.528972	+	0.916206i	0.0201669	+	0.0349300i
$689$	24.2075	−	0.671892i	0.922231	−	0.0255970i
$690$	−5.63345	−	5.49873i	−0.214462	−	0.209333i
$691$	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
$693$	9.51766	−	25.1889i	0.361546	−	0.956847i
$694$			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
$699$	−33.5907	+	34.4138i	−1.27052	+	1.30165i
$700$	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	$0.767415\pi$
$702$	3.68066	−	18.3699i	0.138918	−	0.693327i
$703$	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
$708$	−2.90889	−	10.3533i	−0.109323	−	0.389101i
$709$	−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
$714$	5.84515	+	13.3743i	0.218749	+	0.500519i
$715$	−22.4481	+	0.623059i	−0.839510	+	0.0233011i
$716$	−15.3789	+	8.87903i	−0.574738	+	0.331825i
$717$	8.86014	−	2.48937i	0.330888	−	0.0929672i
$718$	−10.8679	−	18.8238i	−0.405588	−	0.702499i
$719$	−1.87992	+	3.25611i	−0.0701091	+	0.121433i	−0.898949	−	0.438053i	$-0.855668\pi$
$719$	−1.87992	+	3.25611i	−0.0701091	+	0.121433i	0.828840	+	0.559486i	$0.189001\pi$
$720$	−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
$723$	32.1119	−	9.02225i	1.19426	−	0.335541i
$724$			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
$735$	−10.6139	+	19.5660i	−0.391501	+	0.721702i
$736$		−	2.47560i		−	0.0912519i
$737$	−29.1681	−	16.8402i	−1.07442	−	0.620317i
$738$	15.0708	−	0.364840i	0.554764	−	0.0134299i
$739$	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
$741$	−3.76943	−	12.1147i	−0.138473	−	0.445045i
$742$	−6.68155	+	16.4663i	−0.245287	+	0.604497i
$743$	−21.5450	+	37.3170i	−0.790408	+	1.36903i	0.135306	+	0.990804i	$0.456798\pi$
$743$	−21.5450	+	37.3170i	−0.790408	+	1.36903i	−0.925714	+	0.378223i	$0.876535\pi$
$744$	−2.69085	+	10.5515i	−0.0986512	+	0.386838i
$745$		−	39.8627i		−	1.46046i
$746$	−3.62253	+	6.27441i	−0.132630	+	0.229723i
$747$	−20.4351	−	33.4955i	−0.747682	−	1.22554i
$748$	−5.40264	−	9.35765i	−0.197540	−	0.342150i
$749$	−35.0393	+	4.87088i	−1.28031	+	0.177978i
$750$	−5.70215	−	20.2950i	−0.208213	−	0.741070i
$751$	−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
$753$	−11.7898	−	11.5078i	−0.429644	−	0.419368i
$754$	7.56841	−	0.210065i	0.275625	−	0.00765013i
$755$	9.95736			0.362385
$756$	11.2607	+	7.88650i	0.409547	+	0.286829i
$757$	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
$759$	10.1607	−	10.4097i	0.368811	−	0.377848i
$760$			3.72995i			0.135299i
$761$	−14.6878	−	8.48003i	−0.532434	−	0.307401i	0.209573	−	0.977793i	$-0.432793\pi$
$761$	−14.6878	−	8.48003i	−0.532434	−	0.307401i	−0.742007	+	0.670392i	$0.766126\pi$
$762$	−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
$768$	−1.66749	+	0.468501i	−0.0601702	+	0.0169056i
$769$	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
$771$	−8.77720	+	2.46606i	−0.316103	+	0.0888132i
$772$	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
$777$	2.11596	−	0.924770i	0.0759097	−	0.0331759i
$778$	2.27718	+	1.31473i	0.0816408	+	0.0471354i
$779$	8.84137	−	5.10457i	0.316775	−	0.182890i
$780$	2.52389	−	11.1841i	0.0903696	−	0.400456i
$781$	−26.3607	+	45.6580i	−0.943259	+	1.63377i
$782$			7.88494i			0.281965i
$783$	10.4302	−	3.20479i	0.372744	−	0.114530i
$784$	−6.73459	+	1.90927i	−0.240521	+	0.0681884i
$785$	−39.0540			−1.39390
$786$	12.2897	+	11.9957i	0.438357	+	0.427874i
$787$	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
$789$	13.1267	−	13.4484i	0.467325	−	0.478775i
$790$	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
$795$	20.5619	−	5.77712i	0.729254	−	0.204893i
$796$			6.86468i			0.243312i
$797$	21.5529	+	37.3307i	0.763443	+	1.32232i	0.941066	+	0.338224i	$0.109826\pi$
$797$	21.5529	+	37.3307i	0.763443	+	1.32232i	−0.177623	+	0.984099i	$0.556841\pi$
$798$	9.25226	+	1.03658i	0.327526	+	0.0366947i
$799$	32.1618	−	18.5686i	1.13780	−	0.656911i
$800$	0.814684	−	1.41107i	0.0288034	−	0.0498890i
$801$	8.33346	+	13.6595i	0.294448	+	0.482634i
$802$	6.99738			0.247086
$803$	−30.3678			−1.07166
$804$	12.0112	−	12.3054i	0.423601	−	0.433980i
$805$	−9.48693	+	7.38912i	−0.334370	+	0.260432i
$806$	−0.628914	−	22.6590i	−0.0221525	−	0.798129i
$807$	−30.2011	+	8.48538i	−1.06313	+	0.298699i
$808$	4.69535	+	8.13258i	0.165182	+	0.286103i
$809$	−20.1056	+	11.6080i	−0.706876	+	0.408115i	−0.809903	−	0.586563i	$-0.800481\pi$
$809$	−20.1056	+	11.6080i	−0.706876	+	0.408115i	0.103027	+	0.994679i	$0.467147\pi$
$810$	−0.799540	−	16.5040i	−0.0280930	−	0.579891i
$811$	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
$813$	−14.4626	+	4.06345i	−0.507225	+	0.142511i
$814$	−1.48049	+	0.854760i	−0.0518911	+	0.0299593i
$815$	−18.3937			−0.644303
$816$	5.31104	−	1.49220i	0.185924	−	0.0522376i
$817$	−2.14936			−0.0751966
$818$	31.8405			1.11328
$819$	−27.0412	−	9.36875i	−0.944896	−	0.327371i
$820$	9.22567			0.322174
$821$	12.0434			0.420317			0.210158	−	0.977667i	$-0.432602\pi$
$821$	12.0434			0.420317			0.210158	+	0.977667i	$0.432602\pi$
$822$	−5.30772	+	1.49127i	−0.185128	+	0.0520141i
$823$	−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
$825$	9.21721	−	2.58969i	0.320902	−	0.0901616i
$826$	−16.2708	+	2.26184i	−0.566134	+	0.0786995i
$827$	−12.7766			−0.444287			−0.222144	−	0.975014i	$-0.571305\pi$
$827$	−12.7766			−0.444287			−0.222144	+	0.975014i	$0.571305\pi$
$828$	3.86797	+	6.34005i	0.134421	+	0.220332i
$829$	−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
$831$	30.4875	−	8.56585i	1.05760	−	0.297146i
$832$	3.07128	−	1.88872i	0.106477	−	0.0654794i
$833$	21.4501	−	6.08115i	0.743201	−	0.210699i
$834$	0.137140	−	0.140501i	0.00474879	−	0.00486514i
$835$	6.60613			0.228615
$836$	−6.89232			−0.238376
$837$	−9.59480	−	31.2269i	−0.331645	−	1.07936i
$838$	5.19733	−	9.00204i	0.179539	−	0.310970i
$839$	30.8994	−	17.8398i	1.06677	−	0.615897i	0.139469	−	0.990226i	$-0.455460\pi$
$839$	30.8994	−	17.8398i	1.06677	−	0.615897i	0.927296	+	0.374329i	$0.122127\pi$
$840$	6.77245	+	4.99172i	0.233672	+	0.172231i
$841$	−12.2952	−	21.2959i	−0.423972	−	0.734341i
$842$			0.111490i			0.00384219i
$843$	−4.56522	+	1.28266i	−0.157235	+	0.0441771i
$844$	−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
$849$	−6.42680	+	6.58426i	−0.220567	+	0.225971i
$850$	−2.59482	+	4.49435i	−0.0890014	+	0.154155i
$851$	1.24749			0.0427634
$852$	−19.2622	−	18.8016i	−0.659913	−	0.644131i
$853$	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
$855$	−5.82781	−	9.55244i	−0.199307	−	0.326687i
$856$			13.3709i			0.457009i
$857$	7.48332	−	12.9615i	0.255625	−	0.442756i	−0.709440	−	0.704766i	$-0.751052\pi$
$857$	7.48332	−	12.9615i	0.255625	−	0.442756i	0.965065	+	0.262010i	$0.0843854\pi$
$858$	20.6664	+	4.66372i	0.705540	+	0.159217i
$859$	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
$861$	2.56389	−	22.8846i	0.0873773	−	0.779905i
$862$	19.3138	+	33.4525i	0.657830	+	1.13940i
$863$	25.6886	+	44.4940i	0.874451	+	1.51459i	0.857346	+	0.514741i	$0.172112\pi$
$863$	25.6886	+	44.4940i	0.874451	+	1.51459i	0.0171055	+	0.999854i	$0.494555\pi$
$864$	3.53845	−	3.80518i	0.120380	−	0.129455i
$865$			1.75077i			0.0595278i
$866$	5.30602	−	3.06343i	0.180306	−	0.104100i
$867$	11.4313	−	3.21176i	0.388226	−	0.109077i
$868$	15.4130	+	6.25416i	0.523152	+	0.212280i
$869$	−13.3121	+	23.0573i	−0.451582	+	0.782164i
$870$	6.42862	−	1.80620i	0.217951	−	0.0612360i
$871$	−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
$879$	−4.00766	+	4.10585i	−0.135175	+	0.138487i
$880$	−5.39393	−	3.11418i	−0.181829	−	0.104979i
$881$	5.06534	−	8.77342i	0.170656	−	0.295584i	−0.767994	−	0.640457i	$-0.778745\pi$
$881$	5.06534	−	8.77342i	0.170656	−	0.295584i	0.938649	+	0.344873i	$0.112078\pi$
$882$	14.2642	−	15.4121i	0.480302	−	0.518951i
$883$	−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
$885$	14.1290	+	13.7911i	0.474940	+	0.463582i
$886$	7.76750	−	4.48457i	0.260954	−	0.150662i
$887$	4.05982			0.136315			0.0681576	−	0.997675i	$-0.478288\pi$
$887$	4.05982			0.136315			0.0681576	+	0.997675i	$0.478288\pi$
$888$	−0.236084	−	0.840268i	−0.00792246	−	0.0281975i
$889$	2.33386	+	0.947016i	0.0782753	+	0.0317619i
$890$	4.89608	+	8.48026i	0.164117	+	0.284259i
$891$	30.4966	−	1.47742i	1.02168	−	0.0494953i
$892$	−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
$897$	−11.3588	−	10.4878i	−0.379260	−	0.350176i
$898$	−9.32220	−	16.1465i	−0.311086	−	0.538817i
$899$	11.4332	−	6.60095i	0.381318	−	0.220154i
$900$	0.118299	+	4.88667i	0.00394328	+	0.162889i
$901$	−18.5265	−	10.6963i	−0.617206	−	0.356344i
$902$			17.0475i			0.567620i
$903$	−2.87645	+	3.90258i	−0.0957222	+	0.129870i
$904$	−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	$0.117646\pi$
$911$			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
$915$	35.7587	−	10.0468i	1.18214	−	0.332139i
$916$	−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
$921$	−39.8218	+	11.1884i	−1.31217	+	0.368672i
$922$	10.2455	−	5.91523i	0.337417	−	0.194808i
$923$	49.2842	+	26.6591i	1.62221	+	0.877495i
$924$	−9.22386	+	12.5144i	−0.303443	+	0.411692i
$925$	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	$-0.261858\pi$
$929$	11.7550	+	6.78673i	0.385668	+	0.222665i	−0.294614	+	0.955616i	$0.595191\pi$
$930$	−5.40758	−	19.2466i	−0.177321	−	0.631121i
$931$	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
$936$	−4.91459	+	9.63571i	−0.160638	+	0.314953i
$937$			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
$939$	−17.4738	+	17.9019i	−0.570236	+	0.584208i
$940$	10.7033	−	18.5387i	0.349103	−	0.604665i
$941$	43.1576	+	24.9171i	1.40690	+	0.812273i	0.995088	−	0.0989966i	$-0.0315633\pi$
$941$	43.1576	+	24.9171i	1.40690	+	0.812273i	0.411810	+	0.911270i	$0.364897\pi$
$942$	35.7017	+	9.10463i	1.16322	+	0.296645i
$943$	6.22004	−	10.7734i	0.202552	−	0.350831i
$944$			6.20893i			0.202083i
$945$	−25.1436	−	2.20232i	−0.817921	−	0.0716415i
$946$	1.79453	−	3.10822i	0.0583452	−	0.101057i
$947$	−10.8705			−0.353243			−0.176621	−	0.984279i	$-0.556517\pi$
$947$	−10.8705			−0.353243			−0.176621	+	0.984279i	$0.556517\pi$
$948$	−9.72740	−	9.49476i	−0.315931	−	0.308375i
$949$	0.895466	+	32.2626i	0.0290681	+	1.04729i
$950$	1.65514	+	2.86679i	0.0537000	+	0.0930111i
$951$	31.7153	+	30.9568i	1.02844	+	1.00384i
$952$	−1.16028	−	8.34661i	−0.0376049	−	0.270515i
$953$	−26.6142	+	15.3657i	−0.862119	+	0.497744i	−0.864721	−	0.502252i	$-0.832505\pi$
$953$	−26.6142	+	15.3657i	−0.862119	+	0.497744i	0.00260249	+	0.999997i	$0.499172\pi$
$954$	−20.1437	+	0.487646i	−0.652176	+	0.0157881i
$955$	37.0464			1.19879
$956$	−5.31347			−0.171850
$957$	3.33756	+	11.8790i	0.107888	+	0.383994i
$958$	−26.6476	+	15.3850i	−0.860943	+	0.497066i
$959$	1.15956	+	8.34140i	0.0374440	+	0.269358i
$960$	2.22117	−	2.27559i	0.0716879	−	0.0734444i
$961$	−4.26254	−	7.38293i	−0.137501	−	0.238159i
$962$	0.951748	+	1.54766i	0.0306856	+	0.0498985i
$963$	−20.8913	−	34.2432i	−0.673212	−	1.10347i
$964$	−19.2577			−0.620249
$965$	−4.17008	+	7.22278i	−0.134240	+	0.232510i
$966$	10.3952	−	4.54317i	0.334460	−	0.146174i
$967$		−	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	−0.670517	−	0.741895i	$-0.733927\pi$
$971$	9.57391	−	16.5825i	0.307241	−	0.532157i	0.977758	+	0.209737i	$0.0672608\pi$
$972$	−3.11666	+	15.2737i	−0.0999668	+	0.489905i
$973$	−0.184288	−	0.236608i	−0.00590799	−	0.00758530i
$974$			35.8831i			1.14977i
$975$	−3.02307	−	9.71595i	−0.0968156	−	0.311160i
$976$	10.1157	+	5.84028i	0.323794	+	0.186943i
$977$	−1.43387	−	2.48354i	−0.0458736	−	0.0794554i	0.842177	−	0.539201i	$-0.181274\pi$
$977$	−1.43387	−	2.48354i	−0.0458736	−	0.0794554i	−0.888051	+	0.459746i	$0.847940\pi$
$978$	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
$981$	13.2623	−	0.321060i	0.423434	−	0.0102507i
$982$	−32.3384	−	18.6706i	−1.03196	−	0.595802i
$983$	−39.2792	−	22.6779i	−1.25281	−	0.723312i	−0.281146	−	0.959665i	$-0.590715\pi$
$983$	−39.2792	−	22.6779i	−1.25281	−	0.723312i	−0.971667	+	0.236353i	$0.924048\pi$
$984$	−8.43375	−	2.15077i	−0.268858	−	0.0685642i
$985$		−	21.0898i		−	0.671977i
$986$	−5.79226	−	3.34416i	−0.184463	−	0.106500i
$987$	−43.0113	−	31.7020i	−1.36906	−	1.00909i
$988$	0.203236	+	7.32236i	0.00646581	+	0.232955i
$989$	−2.26816	+	1.30952i	−0.0721233	+	0.0416404i
$990$	18.6796	−	0.452204i	0.593678	−	0.0143720i
$991$	−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
$996$	6.12753	+	21.8090i	0.194158	+	0.691046i
$997$			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.e.17.1	✓	34
3.2	odd	2		546.2.bi.f.17.4	yes	34
7.5	odd	6		546.2.bn.f.173.9	yes	34
13.10	even	6		546.2.bn.e.101.9	yes	34
21.5	even	6		546.2.bn.e.173.9	yes	34
39.23	odd	6		546.2.bn.f.101.9	yes	34
91.75	odd	6		546.2.bi.f.257.4	yes	34
273.257	even	6	inner	546.2.bi.e.257.1	yes	34

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.66749 + 0.468501i) q^{3} +1.00000 q^{4} +(-1.58996 + 0.917964i) q^{5} +(1.66749 - 0.468501i) q^{6} +(-0.364289 - 2.62055i) q^{7} -1.00000 q^{8} +(2.56101 - 1.56244i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.66749 + 0.468501i) q^{3} +1.00000 q^{4} +(-1.58996 + 0.917964i) q^{5} +(1.66749 - 0.468501i) q^{6} +(-0.364289 - 2.62055i) q^{7} -1.00000 q^{8} +(2.56101 - 1.56244i) q^{9} +(1.58996 - 0.917964i) q^{10} +(1.69625 + 2.93798i) q^{11} +(-1.66749 + 0.468501i) q^{12} +(3.07128 - 1.88872i) q^{13} +(0.364289 + 2.62055i) q^{14} +(2.22117 - 2.27559i) q^{15} +1.00000 q^{16} -3.18506 q^{17} +(-2.56101 + 1.56244i) q^{18} +(-1.01582 + 1.75945i) q^{19} +(-1.58996 + 0.917964i) q^{20} +(1.83518 + 4.19906i) q^{21} +(-1.69625 - 2.93798i) q^{22} +2.47560i q^{23} +(1.66749 - 0.468501i) 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} +(-2.22117 + 2.27559i) q^{30} +(-3.14345 + 5.44461i) q^{31} -1.00000 q^{32} +(-4.20491 - 4.10435i) q^{33} +3.18506 q^{34} +(2.98478 + 3.83217i) q^{35} +(2.56101 - 1.56244i) q^{36} -0.503913i q^{37} +(1.01582 - 1.75945i) q^{38} +(-4.23645 + 4.58830i) q^{39} +(1.58996 - 0.917964i) q^{40} +(-4.35184 - 2.51254i) q^{41} +(-1.83518 - 4.19906i) 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} +(-1.66749 + 0.468501i) q^{48} +(-6.73459 + 1.90927i) q^{49} +(0.814684 - 1.41107i) q^{50} +(5.31104 - 1.49220i) 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} +(2.22117 - 2.27559i) q^{60} +(10.1157 + 5.84028i) q^{61} +(3.14345 - 5.44461i) q^{62} +(-5.02740 - 6.14209i) q^{63} +1.00000 q^{64} +(-3.14944 + 5.82231i) q^{65} +(4.20491 + 4.10435i) q^{66} +(-8.59785 + 4.96397i) q^{67} -3.18506 q^{68} +(-1.15982 - 4.12803i) q^{69} +(-2.98478 - 3.83217i) q^{70} +(7.77030 + 13.4586i) q^{71} +(-2.56101 + 1.56244i) 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} +(4.23645 - 4.58830i) q^{78} +(3.92399 + 6.79656i) q^{79} +(-1.58996 + 0.917964i) q^{80} +(4.11758 - 8.00285i) q^{81} +(4.35184 + 2.51254i) q^{82} -13.0790i q^{83} +(1.83518 + 4.19906i) 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} +(1.66749 - 0.468501i) q^{96} +(-4.79907 - 8.31223i) q^{97} +(6.73459 - 1.90927i) q^{98} +(8.93452 + 4.87394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * 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 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more