LMFDB - Embedded newform 546.2.q.e.335.2

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			335.2
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	546.335
Dual form			546.2.q.e.251.2

$q$-expansion

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.18614 + 1.26217i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.792287i q^{5} +(0.500000 - 1.65831i) q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.186141 + 2.99422i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.18614 + 1.26217i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.792287i q^{5} +(0.500000 - 1.65831i) q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.186141 + 2.99422i) q^{9} +(0.686141 - 0.396143i) q^{10} +(-2.18614 - 3.78651i) q^{11} +(-1.68614 + 0.396143i) q^{12} +(3.50000 + 0.866025i) q^{13} +(2.00000 - 1.73205i) q^{14} +(-1.00000 + 0.939764i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.18614 + 3.78651i) q^{17} +(2.68614 - 1.33591i) q^{18} +(-1.18614 + 2.05446i) q^{19} +(-0.686141 - 0.396143i) q^{20} +(-2.68614 + 3.71277i) q^{21} +(-2.18614 + 3.78651i) q^{22} +(-3.68614 + 2.12819i) q^{23} +(1.18614 + 1.26217i) q^{24} +4.37228 q^{25} +(-1.00000 - 3.46410i) q^{26} +(-4.00000 + 3.31662i) q^{27} +(-2.50000 - 0.866025i) q^{28} +(-2.18614 + 1.26217i) q^{29} +(1.31386 + 0.396143i) q^{30} +6.74456 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.18614 - 7.25061i) q^{33} +4.37228 q^{34} +(-2.05842 + 0.396143i) q^{35} +(-2.50000 - 1.65831i) q^{36} +(-10.1168 + 5.84096i) q^{37} +2.37228 q^{38} +(3.05842 + 5.44482i) q^{39} +0.792287i q^{40} +(8.18614 - 4.72627i) q^{41} +(4.55842 + 0.469882i) q^{42} +(2.00000 - 3.46410i) q^{43} +4.37228 q^{44} +(-2.37228 - 0.147477i) q^{45} +(3.68614 + 2.12819i) q^{46} -0.939764i q^{47} +(0.500000 - 1.65831i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(-2.18614 - 3.78651i) q^{50} +(-7.37228 + 1.73205i) q^{51} +(-2.50000 + 2.59808i) q^{52} +2.22938i q^{53} +(4.87228 + 1.80579i) q^{54} +(3.00000 - 1.73205i) q^{55} +(0.500000 + 2.59808i) q^{56} +(-4.00000 + 0.939764i) q^{57} +(2.18614 + 1.26217i) q^{58} +(5.31386 + 3.06796i) q^{59} +(-0.313859 - 1.33591i) q^{60} +(4.50000 + 2.59808i) q^{61} +(-3.37228 - 5.84096i) q^{62} +(-7.87228 + 1.01350i) q^{63} +1.00000 q^{64} +(-0.686141 + 2.77300i) q^{65} +(-7.37228 + 1.73205i) q^{66} +(10.1168 - 5.84096i) q^{67} +(-2.18614 - 3.78651i) q^{68} +(-7.05842 - 2.12819i) q^{69} +(1.37228 + 1.58457i) q^{70} +(8.05842 - 13.9576i) q^{71} +(-0.186141 + 2.99422i) q^{72} -10.7446 q^{73} +(10.1168 + 5.84096i) q^{74} +(5.18614 + 5.51856i) q^{75} +(-1.18614 - 2.05446i) q^{76} +(8.74456 - 7.57301i) q^{77} +(3.18614 - 5.37108i) q^{78} +9.62772 q^{79} +(0.686141 - 0.396143i) q^{80} +(-8.93070 - 1.11469i) q^{81} +(-8.18614 - 4.72627i) q^{82} -1.58457i q^{83} +(-1.87228 - 4.18265i) q^{84} +(-3.00000 - 1.73205i) q^{85} -4.00000 q^{86} +(-4.18614 - 1.26217i) q^{87} +(-2.18614 - 3.78651i) q^{88} +(9.30298 - 5.37108i) q^{89} +(1.05842 + 2.12819i) q^{90} +(-0.500000 + 9.52628i) q^{91} -4.25639i q^{92} +(8.00000 + 8.51278i) q^{93} +(-0.813859 + 0.469882i) q^{94} +(-1.62772 - 0.939764i) q^{95} +(-1.68614 + 0.396143i) q^{96} +(-0.372281 + 0.644810i) q^{97} +(5.50000 + 4.33013i) q^{98} +(11.7446 - 5.84096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{7} + 4 q^{8} + 5 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - q^3 - 2 * q^4 + 2 * q^6 + 2 * q^7 + 4 * q^8 + 5 * q^9	\( 4 q - 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{7} + 4 q^{8} + 5 q^{9} - 3 q^{10} - 3 q^{11} - q^{12} + 14 q^{13} + 8 q^{14} - 4 q^{15} - 2 q^{16} - 3 q^{17} + 5 q^{18} + q^{19} + 3 q^{20} - 5 q^{21} - 3 q^{22} - 9 q^{23} - q^{24} + 6 q^{25} - 4 q^{26} - 16 q^{27} - 10 q^{28} - 3 q^{29} + 11 q^{30} + 4 q^{31} - 2 q^{32} + 3 q^{33} + 6 q^{34} + 9 q^{35} - 10 q^{36} - 6 q^{37} - 2 q^{38} - 5 q^{39} + 27 q^{41} + q^{42} + 8 q^{43} + 6 q^{44} + 2 q^{45} + 9 q^{46} + 2 q^{48} - 26 q^{49} - 3 q^{50} - 18 q^{51} - 10 q^{52} + 8 q^{54} + 12 q^{55} + 2 q^{56} - 16 q^{57} + 3 q^{58} + 27 q^{59} - 7 q^{60} + 18 q^{61} - 2 q^{62} - 20 q^{63} + 4 q^{64} + 3 q^{65} - 18 q^{66} + 6 q^{67} - 3 q^{68} - 11 q^{69} - 6 q^{70} + 15 q^{71} + 5 q^{72} - 20 q^{73} + 6 q^{74} + 15 q^{75} + q^{76} + 12 q^{77} + 7 q^{78} + 50 q^{79} - 3 q^{80} - 7 q^{81} - 27 q^{82} + 4 q^{84} - 12 q^{85} - 16 q^{86} - 11 q^{87} - 3 q^{88} - 3 q^{89} - 13 q^{90} - 2 q^{91} + 32 q^{93} - 9 q^{94} - 18 q^{95} - q^{96} + 10 q^{97} + 22 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - q^3 - 2 * q^4 + 2 * q^6 + 2 * q^7 + 4 * q^8 + 5 * q^9 - 3 * q^10 - 3 * q^11 - q^12 + 14 * q^13 + 8 * q^14 - 4 * q^15 - 2 * q^16 - 3 * q^17 + 5 * q^18 + q^19 + 3 * q^20 - 5 * q^21 - 3 * q^22 - 9 * q^23 - q^24 + 6 * q^25 - 4 * q^26 - 16 * q^27 - 10 * q^28 - 3 * q^29 + 11 * q^30 + 4 * q^31 - 2 * q^32 + 3 * q^33 + 6 * q^34 + 9 * q^35 - 10 * q^36 - 6 * q^37 - 2 * q^38 - 5 * q^39 + 27 * q^41 + q^42 + 8 * q^43 + 6 * q^44 + 2 * q^45 + 9 * q^46 + 2 * q^48 - 26 * q^49 - 3 * q^50 - 18 * q^51 - 10 * q^52 + 8 * q^54 + 12 * q^55 + 2 * q^56 - 16 * q^57 + 3 * q^58 + 27 * q^59 - 7 * q^60 + 18 * q^61 - 2 * q^62 - 20 * q^63 + 4 * q^64 + 3 * q^65 - 18 * q^66 + 6 * q^67 - 3 * q^68 - 11 * q^69 - 6 * q^70 + 15 * q^71 + 5 * q^72 - 20 * q^73 + 6 * q^74 + 15 * q^75 + q^76 + 12 * q^77 + 7 * q^78 + 50 * q^79 - 3 * q^80 - 7 * q^81 - 27 * q^82 + 4 * q^84 - 12 * q^85 - 16 * q^86 - 11 * q^87 - 3 * q^88 - 3 * q^89 - 13 * q^90 - 2 * q^91 + 32 * q^93 - 9 * q^94 - 18 * q^95 - q^96 + 10 * q^97 + 22 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.18614	+	1.26217i	0.684819	+	0.728714i
$3$	1.18614	+	1.26217i	0.684819	+	0.728714i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$			0.792287i			0.354322i	0.984182	+	0.177161i	$0.0566913\pi$
$5$			0.792287i			0.354322i	−0.984182	+	0.177161i	$0.943309\pi$
$6$	0.500000	−	1.65831i	0.204124	−	0.677003i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$	1.00000			0.353553
$9$	−0.186141	+	2.99422i	−0.0620469	+	0.998073i
$10$	0.686141	−	0.396143i	0.216977	−	0.125272i
$11$	−2.18614	−	3.78651i	−0.659146	−	1.14167i	−0.980837	−	0.194830i	$-0.937584\pi$
$11$	−2.18614	−	3.78651i	−0.659146	−	1.14167i	0.321691	−	0.946845i	$-0.395749\pi$
$12$	−1.68614	+	0.396143i	−0.486747	+	0.114357i
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$14$	2.00000	−	1.73205i	0.534522	−	0.462910i
$15$	−1.00000	+	0.939764i	−0.258199	+	0.242646i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.18614	+	3.78651i	−0.530217	+	0.918363i	0.469162	+	0.883112i	$0.344556\pi$
$17$	−2.18614	+	3.78651i	−0.530217	+	0.918363i	−0.999379	+	0.0352504i	$0.988777\pi$
$18$	2.68614	−	1.33591i	0.633129	−	0.314876i
$19$	−1.18614	+	2.05446i	−0.272119	+	0.471325i	−0.969404	−	0.245470i	$-0.921058\pi$
$19$	−1.18614	+	2.05446i	−0.272119	+	0.471325i	0.697285	+	0.716794i	$0.254391\pi$
$20$	−0.686141	−	0.396143i	−0.153426	−	0.0885804i
$21$	−2.68614	+	3.71277i	−0.586164	+	0.810192i
$22$	−2.18614	+	3.78651i	−0.466087	+	0.807286i
$23$	−3.68614	+	2.12819i	−0.768613	+	0.443759i	−0.832380	−	0.554206i	$-0.813022\pi$
$23$	−3.68614	+	2.12819i	−0.768613	+	0.443759i	0.0637663	+	0.997965i	$0.479689\pi$
$24$	1.18614	+	1.26217i	0.242120	+	0.257639i
$25$	4.37228			0.874456
$26$	−1.00000	−	3.46410i	−0.196116	−	0.679366i
$27$	−4.00000	+	3.31662i	−0.769800	+	0.638285i
$28$	−2.50000	−	0.866025i	−0.472456	−	0.163663i
$29$	−2.18614	+	1.26217i	−0.405956	+	0.234379i	−0.689051	−	0.724713i	$-0.741972\pi$
$29$	−2.18614	+	1.26217i	−0.405956	+	0.234379i	0.283095	+	0.959092i	$0.408639\pi$
$30$	1.31386	+	0.396143i	0.239877	+	0.0723256i
$31$	6.74456			1.21136			0.605680	−	0.795709i	$-0.292901\pi$
$31$	6.74456			1.21136			0.605680	+	0.795709i	$0.292901\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.18614	−	7.25061i	0.380558	−	1.26217i
$34$	4.37228			0.749840
$35$	−2.05842	+	0.396143i	−0.347937	+	0.0669605i
$36$	−2.50000	−	1.65831i	−0.416667	−	0.276385i
$37$	−10.1168	+	5.84096i	−1.66320	+	0.960248i	−0.692026	+	0.721873i	$0.743282\pi$
$37$	−10.1168	+	5.84096i	−1.66320	+	0.960248i	−0.971173	+	0.238376i	$0.923385\pi$
$38$	2.37228			0.384835
$39$	3.05842	+	5.44482i	0.489739	+	0.871869i
$40$			0.792287i			0.125272i
$41$	8.18614	−	4.72627i	1.27846	−	0.738119i	0.301895	−	0.953341i	$-0.402381\pi$
$41$	8.18614	−	4.72627i	1.27846	−	0.738119i	0.976565	+	0.215222i	$0.0690474\pi$
$42$	4.55842	+	0.469882i	0.703380	+	0.0725044i
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	−0.672264	−	0.740312i	$-0.734678\pi$
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	0.977261	+	0.212041i	$0.0680112\pi$
$44$	4.37228			0.659146
$45$	−2.37228	−	0.147477i	−0.353639	−	0.0219845i
$46$	3.68614	+	2.12819i	0.543492	+	0.313785i
$47$		−	0.939764i		−	0.137079i	−0.997648	−	0.0685393i	$-0.978166\pi$
$47$		−	0.939764i		−	0.137079i	0.997648	−	0.0685393i	$-0.0218339\pi$
$48$	0.500000	−	1.65831i	0.0721688	−	0.239357i
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	−2.18614	−	3.78651i	−0.309167	−	0.535493i
$51$	−7.37228	+	1.73205i	−1.03233	+	0.242536i
$52$	−2.50000	+	2.59808i	−0.346688	+	0.360288i
$53$			2.22938i			0.306229i	0.988208	+	0.153115i	$0.0489304\pi$
$53$			2.22938i			0.306229i	−0.988208	+	0.153115i	$0.951070\pi$
$54$	4.87228	+	1.80579i	0.663034	+	0.245737i
$55$	3.00000	−	1.73205i	0.404520	−	0.233550i
$56$	0.500000	+	2.59808i	0.0668153	+	0.347183i
$57$	−4.00000	+	0.939764i	−0.529813	+	0.124475i
$58$	2.18614	+	1.26217i	0.287054	+	0.165731i
$59$	5.31386	+	3.06796i	0.691806	+	0.399414i	0.804288	−	0.594240i	$-0.202547\pi$
$59$	5.31386	+	3.06796i	0.691806	+	0.399414i	−0.112483	+	0.993654i	$0.535880\pi$
$60$	−0.313859	−	1.33591i	−0.0405191	−	0.172465i
$61$	4.50000	+	2.59808i	0.576166	+	0.332650i	0.759608	−	0.650381i	$-0.225391\pi$
$61$	4.50000	+	2.59808i	0.576166	+	0.332650i	−0.183442	+	0.983030i	$0.558724\pi$
$62$	−3.37228	−	5.84096i	−0.428280	−	0.741803i
$63$	−7.87228	+	1.01350i	−0.991814	+	0.127689i
$64$	1.00000			0.125000
$65$	−0.686141	+	2.77300i	−0.0851053	+	0.343949i
$66$	−7.37228	+	1.73205i	−0.907465	+	0.213201i
$67$	10.1168	−	5.84096i	1.23597	−	0.713587i	0.267701	−	0.963502i	$-0.413736\pi$
$67$	10.1168	−	5.84096i	1.23597	−	0.713587i	0.968268	+	0.249915i	$0.0804026\pi$
$68$	−2.18614	−	3.78651i	−0.265108	−	0.459181i
$69$	−7.05842	−	2.12819i	−0.849734	−	0.256204i
$70$	1.37228	+	1.58457i	0.164019	+	0.189393i
$71$	8.05842	−	13.9576i	0.956359	−	1.65646i	0.225131	−	0.974328i	$-0.427719\pi$
$71$	8.05842	−	13.9576i	0.956359	−	1.65646i	0.731228	−	0.682133i	$-0.238948\pi$
$72$	−0.186141	+	2.99422i	−0.0219369	+	0.352872i
$73$	−10.7446			−1.25756			−0.628778	−	0.777585i	$-0.716445\pi$
$73$	−10.7446			−1.25756			−0.628778	+	0.777585i	$0.716445\pi$
$74$	10.1168	+	5.84096i	1.17606	+	0.678998i
$75$	5.18614	+	5.51856i	0.598844	+	0.637228i
$76$	−1.18614	−	2.05446i	−0.136060	−	0.235662i
$77$	8.74456	−	7.57301i	0.996535	−	0.863025i
$78$	3.18614	−	5.37108i	0.360759	−	0.608155i
$79$	9.62772			1.08320			0.541601	−	0.840635i	$-0.317818\pi$
$79$	9.62772			1.08320			0.541601	+	0.840635i	$0.317818\pi$
$80$	0.686141	−	0.396143i	0.0767129	−	0.0442902i
$81$	−8.93070	−	1.11469i	−0.992300	−	0.123855i
$82$	−8.18614	−	4.72627i	−0.904008	−	0.521929i
$83$		−	1.58457i		−	0.173930i	−0.996211	−	0.0869648i	$-0.972283\pi$
$83$		−	1.58457i		−	0.173930i	0.996211	−	0.0869648i	$-0.0277168\pi$
$84$	−1.87228	−	4.18265i	−0.204283	−	0.456365i
$85$	−3.00000	−	1.73205i	−0.325396	−	0.187867i
$86$	−4.00000			−0.431331
$87$	−4.18614	−	1.26217i	−0.448801	−	0.135319i
$88$	−2.18614	−	3.78651i	−0.233043	−	0.403643i
$89$	9.30298	−	5.37108i	0.986114	−	0.569333i	0.0820038	−	0.996632i	$-0.473868\pi$
$89$	9.30298	−	5.37108i	0.986114	−	0.569333i	0.904111	+	0.427299i	$0.140535\pi$
$90$	1.05842	+	2.12819i	0.111567	+	0.224331i
$91$	−0.500000	+	9.52628i	−0.0524142	+	0.998625i
$92$		−	4.25639i		−	0.443759i
$93$	8.00000	+	8.51278i	0.829561	+	0.882734i
$94$	−0.813859	+	0.469882i	−0.0839432	+	0.0484646i
$95$	−1.62772	−	0.939764i	−0.167000	−	0.0964177i
$96$	−1.68614	+	0.396143i	−0.172091	+	0.0404312i
$97$	−0.372281	+	0.644810i	−0.0377994	+	0.0654706i	−0.884306	−	0.466907i	$-0.845368\pi$
$97$	−0.372281	+	0.644810i	−0.0377994	+	0.0654706i	0.846507	+	0.532378i	$0.178701\pi$
$98$	5.50000	+	4.33013i	0.555584	+	0.437409i
$99$	11.7446	−	5.84096i	1.18037	−	0.587039i
$100$	−2.18614	+	3.78651i	−0.218614	+	0.378651i
$101$	7.37228	+	12.7692i	0.733569	+	1.27058i	0.955348	+	0.295482i	$0.0954804\pi$
$101$	7.37228	+	12.7692i	0.733569	+	1.27058i	−0.221779	+	0.975097i	$0.571186\pi$
$102$	5.18614	+	5.51856i	0.513504	+	0.546419i
$103$		−	8.21782i		−	0.809726i	−0.914377	−	0.404863i	$-0.867319\pi$
$103$		−	8.21782i		−	0.809726i	0.914377	−	0.404863i	$-0.132681\pi$
$104$	3.50000	+	0.866025i	0.343203	+	0.0849208i
$105$	−2.94158	−	2.12819i	−0.287069	−	0.207690i
$106$	1.93070	−	1.11469i	0.187526	−	0.108268i
$107$	0.813859	−	0.469882i	0.0786788	−	0.0454252i	−0.460144	−	0.887844i	$-0.652202\pi$
$107$	0.813859	−	0.469882i	0.0786788	−	0.0454252i	0.538823	+	0.842419i	$0.318869\pi$
$108$	−0.872281	−	5.12241i	−0.0839353	−	0.492905i
$109$		−	19.8997i		−	1.90605i	−0.302891	−	0.953025i	$-0.597952\pi$
$109$		−	19.8997i		−	1.90605i	0.302891	−	0.953025i	$-0.402048\pi$
$110$	−3.00000	−	1.73205i	−0.286039	−	0.165145i
$111$	−19.3723	−	5.84096i	−1.83874	−	0.554400i
$112$	2.00000	−	1.73205i	0.188982	−	0.163663i
$113$	−3.25544	−	1.87953i	−0.306246	−	0.176811i	0.339000	−	0.940787i	$-0.389911\pi$
$113$	−3.25544	−	1.87953i	−0.306246	−	0.176811i	−0.645245	+	0.763975i	$0.723245\pi$
$114$	2.81386	+	2.99422i	0.263542	+	0.280434i
$115$	−1.68614	−	2.92048i	−0.157233	−	0.272336i
$116$		−	2.52434i		−	0.234379i
$117$	−3.24456	+	10.3186i	−0.299960	+	0.953952i
$118$		−	6.13592i		−	0.564857i
$119$	−10.9307	−	3.78651i	−1.00202	−	0.347108i
$120$	−1.00000	+	0.939764i	−0.0912871	+	0.0857883i
$121$	−4.05842	+	7.02939i	−0.368947	+	0.639036i
$122$		−	5.19615i		−	0.470438i
$123$	15.6753	+	4.72627i	1.41339	+	0.426153i
$124$	−3.37228	+	5.84096i	−0.302840	+	0.524534i
$125$			7.42554i			0.664160i
$126$	4.81386	+	6.31084i	0.428853	+	0.562215i
$127$	1.05842	+	1.83324i	0.0939198	+	0.162674i	0.909157	−	0.416453i	$-0.136727\pi$
$127$	1.05842	+	1.83324i	0.0939198	+	0.162674i	−0.815237	+	0.579127i	$0.803394\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	6.74456	−	1.58457i	0.593826	−	0.139514i
$130$	2.74456	−	0.792287i	0.240714	−	0.0694882i
$131$	−21.6060			−1.88772			−0.943861	−	0.330342i	$-0.892836\pi$
$131$	−21.6060			−1.88772			−0.943861	+	0.330342i	$0.892836\pi$
$132$	5.18614	+	5.51856i	0.451396	+	0.480329i
$133$	−5.93070	−	2.05446i	−0.514257	−	0.178144i
$134$	−10.1168	−	5.84096i	−0.873962	−	0.504582i
$135$	−2.62772	−	3.16915i	−0.226158	−	0.272757i
$136$	−2.18614	+	3.78651i	−0.187460	+	0.324690i
$137$	−3.68614	+	6.38458i	−0.314928	+	0.545472i	−0.979422	−	0.201822i	$-0.935314\pi$
$137$	−3.68614	+	6.38458i	−0.314928	+	0.545472i	0.664494	+	0.747294i	$0.268647\pi$
$138$	1.68614	+	7.17687i	0.143534	+	0.610936i
$139$	−7.67527	−	4.43132i	−0.651008	−	0.375859i	0.137835	−	0.990455i	$-0.455986\pi$
$139$	−7.67527	−	4.43132i	−0.651008	−	0.375859i	−0.788842	+	0.614596i	$0.789319\pi$
$140$	0.686141	−	1.98072i	0.0579895	−	0.167401i
$141$	1.18614	−	1.11469i	0.0998911	−	0.0938740i
$142$	−16.1168			−1.35250
$143$	−4.37228	−	15.1460i	−0.365629	−	1.26657i
$144$	2.68614	−	1.33591i	0.223845	−	0.111326i
$145$	−1.00000	−	1.73205i	−0.0830455	−	0.143839i
$146$	5.37228	+	9.30506i	0.444613	+	0.770093i
$147$	−10.9891	−	5.12241i	−0.906368	−	0.422490i
$148$		−	11.6819i		−	0.960248i
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	2.18614	−	7.25061i	0.178498	−	0.592010i
$151$		−	16.8781i		−	1.37352i	−0.726885	−	0.686759i	$-0.759033\pi$
$151$		−	16.8781i		−	1.37352i	0.726885	−	0.686759i	$-0.240967\pi$
$152$	−1.18614	+	2.05446i	−0.0962087	+	0.166638i
$153$	−10.9307	−	7.25061i	−0.883695	−	0.586177i
$154$	−10.9307	−	3.78651i	−0.880821	−	0.305125i
$155$			5.34363i			0.429211i
$156$	−6.24456	−	0.0737384i	−0.499965	−	0.00590380i
$157$		0			0		1.00000			$0$
$157$		0			0		−1.00000			$\pi$
$158$	−4.81386	−	8.33785i	−0.382970	−	0.663324i
$159$	−2.81386	+	2.64436i	−0.223154	+	0.209712i
$160$	−0.686141	−	0.396143i	−0.0542442	−	0.0313179i
$161$	−7.37228	−	8.51278i	−0.581017	−	0.670901i
$162$	3.50000	+	8.29156i	0.274986	+	0.651447i
$163$	−9.00000	−	5.19615i	−0.704934	−	0.406994i	0.104248	−	0.994551i	$-0.466756\pi$
$163$	−9.00000	−	5.19615i	−0.704934	−	0.406994i	−0.809183	+	0.587557i	$0.800090\pi$
$164$			9.45254i			0.738119i
$165$	5.74456	+	1.73205i	0.447214	+	0.134840i
$166$	−1.37228	+	0.792287i	−0.106510	+	0.0614934i
$167$	5.74456	−	3.31662i	0.444528	−	0.256648i	−0.260989	−	0.965342i	$-0.584049\pi$
$167$	5.74456	−	3.31662i	0.444528	−	0.256648i	0.705516	+	0.708694i	$0.250715\pi$
$168$	−2.68614	+	3.71277i	−0.207240	+	0.286446i
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$			3.46410i			0.265684i
$171$	−5.93070	−	3.93398i	−0.453532	−	0.300839i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	−0.941578	+	1.63086i	−0.0715869	+	0.123992i	−0.899597	−	0.436721i	$-0.856140\pi$
$173$	−0.941578	+	1.63086i	−0.0715869	+	0.123992i	0.828010	+	0.560713i	$0.189473\pi$
$174$	1.00000	+	4.25639i	0.0758098	+	0.322676i
$175$	2.18614	+	11.3595i	0.165257	+	0.858699i
$176$	−2.18614	+	3.78651i	−0.164787	+	0.285419i
$177$	2.43070	+	10.3460i	0.182703	+	0.777654i
$178$	−9.30298	−	5.37108i	−0.697288	−	0.402580i
$179$	4.37228	−	2.52434i	0.326800	−	0.188678i	−0.327620	−	0.944810i	$-0.606246\pi$
$179$	4.37228	−	2.52434i	0.326800	−	0.188678i	0.654419	+	0.756132i	$0.272913\pi$
$180$	1.31386	−	1.98072i	0.0979293	−	0.147634i
$181$		−	12.1244i		−	0.901196i	−0.892727	−	0.450598i	$-0.851211\pi$
$181$		−	12.1244i		−	0.901196i	0.892727	−	0.450598i	$-0.148789\pi$
$182$	8.50000	−	4.33013i	0.630062	−	0.320970i
$183$	2.05842	+	8.76144i	0.152163	+	0.647665i
$184$	−3.68614	+	2.12819i	−0.271746	+	0.156893i
$185$	−4.62772	−	8.01544i	−0.340237	−	0.589307i
$186$	3.37228	−	11.1846i	0.247268	−	0.820094i
$187$	19.1168			1.39796
$188$	0.813859	+	0.469882i	0.0593568	+	0.0342697i
$189$	−10.6168	−	8.73399i	−0.772262	−	0.635304i
$190$			1.87953i			0.136355i
$191$	10.6277	+	6.13592i	0.768995	+	0.443979i	0.832516	−	0.554001i	$-0.186900\pi$
$191$	10.6277	+	6.13592i	0.768995	+	0.443979i	−0.0635211	+	0.997980i	$0.520233\pi$
$192$	1.18614	+	1.26217i	0.0856023	+	0.0910892i
$193$	11.6168	−	6.70699i	0.836199	−	0.482780i	−0.0197716	−	0.999805i	$-0.506294\pi$
$193$	11.6168	−	6.70699i	0.836199	−	0.482780i	0.855970	+	0.517025i	$0.172961\pi$
$194$	0.744563			0.0534565
$195$	−4.31386	+	2.42315i	−0.308922	+	0.173525i
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	12.3030	+	21.3094i	0.876551	+	1.51823i	0.855101	+	0.518462i	$0.173495\pi$
$197$	12.3030	+	21.3094i	0.876551	+	1.51823i	0.0214504	+	0.999770i	$0.493172\pi$
$198$	−10.9307	−	7.25061i	−0.776811	−	0.515278i
$199$	−3.00000	−	1.73205i	−0.212664	−	0.122782i	0.389885	−	0.920864i	$-0.372515\pi$
$199$	−3.00000	−	1.73205i	−0.212664	−	0.122782i	−0.602549	+	0.798082i	$0.705848\pi$
$200$	4.37228			0.309167
$201$	19.3723	+	5.84096i	1.36642	+	0.411990i
$202$	7.37228	−	12.7692i	0.518712	−	0.898435i
$203$	−4.37228	−	5.04868i	−0.306874	−	0.354348i
$204$	2.18614	−	7.25061i	0.153060	−	0.507644i
$205$	3.74456	+	6.48577i	0.261532	+	0.452986i
$206$	−7.11684	+	4.10891i	−0.495854	+	0.286281i
$207$	−5.68614	−	11.4333i	−0.395214	−	0.794666i
$208$	−1.00000	−	3.46410i	−0.0693375	−	0.240192i
$209$	10.3723			0.717466
$210$	−0.372281	+	3.61158i	−0.0256899	+	0.249223i
$211$	−5.62772	−	9.74749i	−0.387428	−	0.671045i	0.604675	−	0.796473i	$-0.293303\pi$
$211$	−5.62772	−	9.74749i	−0.387428	−	0.671045i	−0.992103	+	0.125427i	$0.959970\pi$
$212$	−1.93070	−	1.11469i	−0.132601	−	0.0765574i
$213$	27.1753	−	6.38458i	1.86202	−	0.437464i
$214$	−0.813859	−	0.469882i	−0.0556343	−	0.0321205i
$215$	2.74456	+	1.58457i	0.187178	+	0.108067i
$216$	−4.00000	+	3.31662i	−0.272166	+	0.225668i
$217$	3.37228	+	17.5229i	0.228925	+	1.18953i
$218$	−17.2337	+	9.94987i	−1.16721	+	0.673891i
$219$	−12.7446	−	13.5615i	−0.861198	−	0.916398i
$220$			3.46410i			0.233550i
$221$	−10.9307	+	11.3595i	−0.735279	+	0.764124i
$222$	4.62772	+	19.6974i	0.310592	+	1.32200i
$223$	14.1168	+	24.4511i	0.945334	+	1.63737i	0.755082	+	0.655631i	$0.227597\pi$
$223$	14.1168	+	24.4511i	0.945334	+	1.63737i	0.190252	+	0.981735i	$0.439069\pi$
$224$	−2.50000	−	0.866025i	−0.167038	−	0.0578638i
$225$	−0.813859	+	13.0916i	−0.0542573	+	0.872771i
$226$			3.75906i			0.250049i
$227$	−16.8030	−	9.70121i	−1.11525	−	0.643892i	−0.175068	−	0.984556i	$-0.556015\pi$
$227$	−16.8030	−	9.70121i	−1.11525	−	0.643892i	−0.940185	+	0.340665i	$0.889348\pi$
$228$	1.18614	−	3.93398i	0.0785541	−	0.260534i
$229$	5.11684			0.338131			0.169065	−	0.985605i	$-0.445925\pi$
$229$	5.11684			0.338131			0.169065	+	0.985605i	$0.445925\pi$
$230$	−1.68614	+	2.92048i	−0.111181	+	0.192571i
$231$	19.9307	+	2.05446i	1.31134	+	0.135173i
$232$	−2.18614	+	1.26217i	−0.143527	+	0.0828654i
$233$			4.84630i			0.317491i	0.987320	+	0.158746i	$0.0507450\pi$
$233$			4.84630i			0.317491i	−0.987320	+	0.158746i	$0.949255\pi$
$234$	10.5584	−	2.34941i	0.690226	−	0.153586i
$235$	0.744563			0.0485699
$236$	−5.31386	+	3.06796i	−0.345903	+	0.199707i
$237$	11.4198	+	12.1518i	0.741798	+	0.789345i
$238$	2.18614	+	11.3595i	0.141706	+	0.736328i
$239$	15.6060			1.00947			0.504733	−	0.863275i	$-0.331591\pi$
$239$	15.6060			1.00947			0.504733	+	0.863275i	$0.331591\pi$
$240$	1.31386	+	0.396143i	0.0848093	+	0.0255710i
$241$	−6.37228	+	11.0371i	−0.410475	+	0.710963i	−0.994942	−	0.100454i	$-0.967970\pi$
$241$	−6.37228	+	11.0371i	−0.410475	+	0.710963i	0.584467	+	0.811418i	$0.301304\pi$
$242$	8.11684			0.521770
$243$	−9.18614	−	12.5942i	−0.589291	−	0.807921i
$244$	−4.50000	+	2.59808i	−0.288083	+	0.166325i
$245$	−2.05842	−	5.14987i	−0.131508	−	0.329013i
$246$	−3.74456	−	15.9383i	−0.238745	−	1.01619i
$247$	−5.93070	+	6.16337i	−0.377362	+	0.392166i
$248$	6.74456			0.428280
$249$	2.00000	−	1.87953i	0.126745	−	0.119110i
$250$	6.43070	−	3.71277i	0.406713	−	0.234816i
$251$	−8.05842	+	13.9576i	−0.508643	+	0.880996i	0.491307	+	0.870987i	$0.336519\pi$
$251$	−8.05842	+	13.9576i	−0.508643	+	0.880996i	−0.999950	+	0.0100091i	$0.996814\pi$
$252$	3.05842	−	7.32435i	0.192662	−	0.461390i
$253$	16.1168	+	9.30506i	1.01326	+	0.585004i
$254$	1.05842	−	1.83324i	0.0664113	−	0.115028i
$255$	−1.37228	−	5.84096i	−0.0859356	−	0.365775i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.44158	−	4.22894i	−0.152301	−	0.263794i	0.779772	−	0.626064i	$-0.215335\pi$
$257$	−2.44158	−	4.22894i	−0.152301	−	0.263794i	−0.932073	+	0.362270i	$0.882002\pi$
$258$	−4.74456	−	5.04868i	−0.295384	−	0.314317i
$259$	−20.2337	−	23.3639i	−1.25726	−	1.45176i
$260$	−2.05842	−	1.98072i	−0.127658	−	0.122839i
$261$	−3.37228	−	6.78073i	−0.208739	−	0.419716i
$262$	10.8030	+	18.7113i	0.667411	+	1.15599i
$263$	19.5475	−	11.2858i	1.20535	−	0.695911i	0.243613	−	0.969873i	$-0.421667\pi$
$263$	19.5475	−	11.2858i	1.20535	−	0.695911i	0.961741	+	0.273961i	$0.0883341\pi$
$264$	2.18614	−	7.25061i	0.134548	−	0.446244i
$265$	−1.76631			−0.108504
$266$	1.18614	+	6.16337i	0.0727270	+	0.377900i
$267$	17.8139	+	5.37108i	1.09019	+	0.328705i
$268$			11.6819i			0.713587i
$269$	0.430703	−	0.746000i	0.0262604	−	0.0454844i	−0.852597	−	0.522570i	$-0.824973\pi$
$269$	0.430703	−	0.746000i	0.0262604	−	0.0454844i	0.878857	+	0.477085i	$0.158307\pi$
$270$	−1.43070	+	3.86025i	−0.0870698	+	0.234927i
$271$	−2.00000	−	3.46410i	−0.121491	−	0.210429i	0.798865	−	0.601511i	$-0.205434\pi$
$271$	−2.00000	−	3.46410i	−0.121491	−	0.210429i	−0.920356	+	0.391082i	$0.872101\pi$
$272$	4.37228			0.265108
$273$	−12.6168	+	10.6684i	−0.763606	+	0.645682i
$274$	7.37228			0.445376
$275$	−9.55842	−	16.5557i	−0.576395	−	0.998345i
$276$	5.37228	−	5.04868i	0.323373	−	0.303895i
$277$	−6.74456	+	11.6819i	−0.405241	+	0.701899i	−0.994350	−	0.106155i	$-0.966146\pi$
$277$	−6.74456	+	11.6819i	−0.405241	+	0.701899i	0.589108	+	0.808054i	$0.299479\pi$
$278$			8.86263i			0.531545i
$279$	−1.25544	+	20.1947i	−0.0751611	+	1.20903i
$280$	−2.05842	+	0.396143i	−0.123014	+	0.0236741i
$281$	14.7446			0.879587			0.439793	−	0.898099i	$-0.355052\pi$
$281$	14.7446			0.879587			0.439793	+	0.898099i	$0.355052\pi$
$282$	−1.55842	−	0.469882i	−0.0928027	−	0.0279811i
$283$	−2.05842	+	1.18843i	−0.122360	+	0.0706449i	−0.559931	−	0.828539i	$-0.689172\pi$
$283$	−2.05842	+	1.18843i	−0.122360	+	0.0706449i	0.437571	+	0.899184i	$0.355839\pi$
$284$	8.05842	+	13.9576i	0.478179	+	0.828231i
$285$	−0.744563	−	3.16915i	−0.0441041	−	0.187724i
$286$	−10.9307	+	11.3595i	−0.646346	+	0.671703i
$287$	16.3723	+	18.9051i	0.966425	+	1.11593i
$288$	−2.50000	−	1.65831i	−0.147314	−	0.0977170i
$289$	−1.05842	−	1.83324i	−0.0622601	−	0.107838i
$290$	−1.00000	+	1.73205i	−0.0587220	+	0.101710i
$291$	−1.25544	+	0.294954i	−0.0735950	+	0.0172905i
$292$	5.37228	−	9.30506i	0.314389	−	0.544538i
$293$	3.25544	+	1.87953i	0.190185	+	0.109803i	0.592069	−	0.805887i	$-0.298311\pi$
$293$	3.25544	+	1.87953i	0.190185	+	0.109803i	−0.401884	+	0.915690i	$0.631645\pi$
$294$	1.05842	+	12.0781i	0.0617284	+	0.704407i
$295$	−2.43070	+	4.21010i	−0.141521	+	0.245122i
$296$	−10.1168	+	5.84096i	−0.588030	+	0.339499i
$297$	21.3030	+	7.89542i	1.23612	+	0.458139i
$298$	−6.00000			−0.347571
$299$	−14.7446	+	4.25639i	−0.852700	+	0.246153i
$300$	−7.37228	+	1.73205i	−0.425639	+	0.100000i
$301$	10.0000	+	3.46410i	0.576390	+	0.199667i
$302$	−14.6168	+	8.43904i	−0.841105	+	0.485612i
$303$	−7.37228	+	24.4511i	−0.423526	+	1.40468i
$304$	2.37228			0.136060
$305$	−2.05842	+	3.56529i	−0.117865	+	0.204148i
$306$	−0.813859	+	13.0916i	−0.0465252	+	0.748395i
$307$	21.2337			1.21187			0.605935	−	0.795514i	$-0.292799\pi$
$307$	21.2337			1.21187			0.605935	+	0.795514i	$0.292799\pi$
$308$	2.18614	+	11.3595i	0.124567	+	0.647269i
$309$	10.3723	−	9.74749i	0.590058	−	0.554516i
$310$	4.62772	−	2.67181i	0.262837	−	0.151749i
$311$	10.3723			0.588158			0.294079	−	0.955781i	$-0.404987\pi$
$311$	10.3723			0.588158			0.294079	+	0.955781i	$0.404987\pi$
$312$	3.05842	+	5.44482i	0.173149	+	0.308252i
$313$			13.8564i			0.783210i	0.920133	+	0.391605i	$0.128080\pi$
$313$			13.8564i			0.783210i	−0.920133	+	0.391605i	$0.871920\pi$
$314$		0			0
$315$	−0.802985	−	6.23711i	−0.0452431	−	0.351421i
$316$	−4.81386	+	8.33785i	−0.270801	+	0.469041i
$317$	15.2554			0.856831			0.428415	−	0.903582i	$-0.359072\pi$
$317$	15.2554			0.856831			0.428415	+	0.903582i	$0.359072\pi$
$318$	3.69702	+	1.11469i	0.207318	+	0.0625088i
$319$	9.55842	+	5.51856i	0.535169	+	0.308980i
$320$			0.792287i			0.0442902i
$321$	1.55842	+	0.469882i	0.0869826	+	0.0262263i
$322$	−3.68614	+	10.6410i	−0.205421	+	0.592998i
$323$	−5.18614	−	8.98266i	−0.288565	−	0.499809i
$324$	5.43070	−	7.17687i	0.301706	−	0.398715i
$325$	15.3030	+	3.78651i	0.848857	+	0.210038i
$326$			10.3923i			0.575577i
$327$	25.1168	−	23.6039i	1.38896	−	1.30530i
$328$	8.18614	−	4.72627i	0.452004	−	0.260965i
$329$	2.44158	−	0.469882i	0.134609	−	0.0259054i
$330$	−1.37228	−	5.84096i	−0.0755416	−	0.321534i
$331$	−1.88316	−	1.08724i	−0.103508	−	0.0597602i	0.447353	−	0.894358i	$-0.352367\pi$
$331$	−1.88316	−	1.08724i	−0.103508	−	0.0597602i	−0.550860	+	0.834598i	$0.685700\pi$
$332$	1.37228	+	0.792287i	0.0753137	+	0.0434824i
$333$	−15.6060	−	31.3793i	−0.855202	−	1.71957i
$334$	−5.74456	−	3.31662i	−0.314328	−	0.181478i
$335$	4.62772	+	8.01544i	0.252839	+	0.437930i
$336$	4.55842	+	0.469882i	0.248682	+	0.0256342i
$337$	−10.6060			−0.577744			−0.288872	−	0.957368i	$-0.593280\pi$
$337$	−10.6060			−0.577744			−0.288872	+	0.957368i	$0.593280\pi$
$338$	−0.500000	−	12.9904i	−0.0271964	−	0.706584i
$339$	−1.48913	−	6.33830i	−0.0808782	−	0.344249i
$340$	3.00000	−	1.73205i	0.162698	−	0.0939336i
$341$	−14.7446	−	25.5383i	−0.798463	−	1.38298i
$342$	−0.441578	+	7.10313i	−0.0238778	+	0.384093i
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	2.00000	−	3.46410i	0.107833	−	0.186772i
$345$	1.68614	−	5.59230i	0.0907788	−	0.301079i
$346$	1.88316			0.101239
$347$	−18.0475	−	10.4198i	−0.968843	−	0.559362i	−0.0699597	−	0.997550i	$-0.522287\pi$
$347$	−18.0475	−	10.4198i	−0.968843	−	0.559362i	−0.898883	+	0.438188i	$0.855620\pi$
$348$	3.18614	−	2.99422i	0.170795	−	0.160507i
$349$	−10.0584	−	17.4217i	−0.538415	−	0.932562i	−0.998990	−	0.0449411i	$-0.985690\pi$
$349$	−10.0584	−	17.4217i	−0.538415	−	0.932562i	0.460575	−	0.887621i	$-0.347643\pi$
$350$	8.74456	−	7.57301i	0.467417	−	0.404795i
$351$	−16.8723	+	8.14409i	−0.900576	+	0.434699i
$352$	4.37228			0.233043
$353$	−25.3723	+	14.6487i	−1.35043	+	0.779671i	−0.988310	−	0.152460i	$-0.951280\pi$
$353$	−25.3723	+	14.6487i	−1.35043	+	0.779671i	−0.362121	+	0.932131i	$0.617947\pi$
$354$	7.74456	−	7.27806i	0.411619	−	0.386825i
$355$	11.0584	+	6.38458i	0.586920	+	0.338858i
$356$			10.7422i			0.569333i
$357$	−8.18614	−	18.2877i	−0.433257	−	0.967889i
$358$	−4.37228	−	2.52434i	−0.231082	−	0.133415i
$359$	−16.6277			−0.877577			−0.438789	−	0.898590i	$-0.644592\pi$
$359$	−16.6277			−0.877577			−0.438789	+	0.898590i	$0.644592\pi$
$360$	−2.37228	−	0.147477i	−0.125030	−	0.00777271i
$361$	6.68614	+	11.5807i	0.351902	+	0.609512i
$362$	−10.5000	+	6.06218i	−0.551868	+	0.318621i
$363$	−13.6861	+	3.21543i	−0.718336	+	0.168767i
$364$	−8.00000	−	5.19615i	−0.419314	−	0.272352i
$365$		−	8.51278i		−	0.445579i
$366$	6.55842	−	6.16337i	0.342814	−	0.322164i
$367$	26.2337	−	15.1460i	1.36939	−	0.790616i	0.378538	−	0.925586i	$-0.376427\pi$
$367$	26.2337	−	15.1460i	1.36939	−	0.790616i	0.990850	+	0.134970i	$0.0430937\pi$
$368$	3.68614	+	2.12819i	0.192153	+	0.110940i
$369$	12.6277	+	25.3909i	0.657373	+	1.32180i
$370$	−4.62772	+	8.01544i	−0.240584	+	0.416703i
$371$	−5.79211	+	1.11469i	−0.300711	+	0.0578719i
$372$	−11.3723	+	2.67181i	−0.589625	+	0.138527i
$373$	−4.00000	+	6.92820i	−0.207112	+	0.358729i	−0.950804	−	0.309794i	$-0.899740\pi$
$373$	−4.00000	+	6.92820i	−0.207112	+	0.358729i	0.743691	+	0.668523i	$0.233073\pi$
$374$	−9.55842	−	16.5557i	−0.494254	−	0.856073i
$375$	−9.37228	+	8.80773i	−0.483983	+	0.454829i
$376$		−	0.939764i		−	0.0484646i
$377$	−8.74456	+	2.52434i	−0.450368	+	0.130010i
$378$	−2.25544	+	13.5615i	−0.116007	+	0.697526i
$379$	−4.88316	+	2.81929i	−0.250831	+	0.144817i	−0.620145	−	0.784487i	$-0.712926\pi$
$379$	−4.88316	+	2.81929i	−0.250831	+	0.144817i	0.369314	+	0.929305i	$0.379593\pi$
$380$	1.62772	−	0.939764i	0.0835002	−	0.0482089i
$381$	−1.05842	+	3.51039i	−0.0542246	+	0.179843i
$382$		−	12.2718i		−	0.627882i
$383$	−13.0693	−	7.54556i	−0.667810	−	0.385560i	0.127436	−	0.991847i	$-0.459325\pi$
$383$	−13.0693	−	7.54556i	−0.667810	−	0.385560i	−0.795246	+	0.606287i	$0.792658\pi$
$384$	0.500000	−	1.65831i	0.0255155	−	0.0846254i
$385$	6.00000	+	6.92820i	0.305788	+	0.353094i
$386$	−11.6168	−	6.70699i	−0.591282	−	0.341377i
$387$	10.0000	+	6.63325i	0.508329	+	0.337187i
$388$	−0.372281	−	0.644810i	−0.0188997	−	0.0327353i
$389$			29.2974i			1.48544i	0.669604	+	0.742718i	$0.266464\pi$
$389$			29.2974i			1.48544i	−0.669604	+	0.742718i	$0.733536\pi$
$390$	4.25544	+	2.52434i	0.215482	+	0.127825i
$391$		−	18.6101i		−	0.941155i
$392$	−6.50000	+	2.59808i	−0.328300	+	0.131223i
$393$	−25.6277	−	27.2704i	−1.29275	−	1.37561i
$394$	12.3030	−	21.3094i	0.619815	−	1.07355i
$395$			7.62792i			0.383802i
$396$	−0.813859	+	13.0916i	−0.0408980	+	0.657876i
$397$	1.12772	−	1.95327i	0.0565986	−	0.0980316i	−0.836338	−	0.548214i	$-0.815308\pi$
$397$	1.12772	−	1.95327i	0.0565986	−	0.0980316i	0.892936	+	0.450183i	$0.148641\pi$
$398$			3.46410i			0.173640i
$399$	−4.44158	−	9.92242i	−0.222357	−	0.496742i
$400$	−2.18614	−	3.78651i	−0.109307	−	0.189325i
$401$	−5.74456	−	9.94987i	−0.286870	−	0.496873i	0.686191	−	0.727421i	$-0.259281\pi$
$401$	−5.74456	−	9.94987i	−0.286870	−	0.496873i	−0.973061	+	0.230548i	$0.925948\pi$
$402$	−4.62772	−	19.6974i	−0.230810	−	0.982415i
$403$	23.6060	+	5.84096i	1.17590	+	0.290959i
$404$	−14.7446			−0.733569
$405$	0.883156	−	7.07568i	0.0438844	−	0.351593i
$406$	−2.18614	+	6.31084i	−0.108496	+	0.313202i
$407$	44.2337	+	25.5383i	2.19258	+	1.26589i
$408$	−7.37228	+	1.73205i	−0.364982	+	0.0857493i
$409$	−10.7446	+	18.6101i	−0.531284	+	0.920212i	0.468049	+	0.883703i	$0.344957\pi$
$409$	−10.7446	+	18.6101i	−0.531284	+	0.920212i	−0.999333	+	0.0365091i	$0.988376\pi$
$410$	3.74456	−	6.48577i	0.184931	−	0.320309i
$411$	−12.4307	+	2.92048i	−0.613161	+	0.144057i
$412$	7.11684	+	4.10891i	0.350622	+	0.202432i
$413$	−5.31386	+	15.3398i	−0.261478	+	0.754822i
$414$	−7.05842	+	10.6410i	−0.346903	+	0.522975i
$415$	1.25544			0.0616270
$416$	−2.50000	+	2.59808i	−0.122573	+	0.127381i
$417$	−3.51087	−	14.9436i	−0.171928	−	0.731794i
$418$	−5.18614	−	8.98266i	−0.253662	−	0.439356i
$419$	2.74456	+	4.75372i	0.134081	+	0.232235i	0.925246	−	0.379368i	$-0.123859\pi$
$419$	2.74456	+	4.75372i	0.134081	+	0.232235i	−0.791165	+	0.611602i	$0.790525\pi$
$420$	3.31386	−	1.48338i	0.161700	−	0.0723817i
$421$		−	26.8280i		−	1.30751i	−0.756704	−	0.653757i	$-0.773192\pi$
$421$		−	26.8280i		−	1.30751i	0.756704	−	0.653757i	$-0.226808\pi$
$422$	−5.62772	+	9.74749i	−0.273953	+	0.474501i
$423$	2.81386	+	0.174928i	0.136815	+	0.00850530i
$424$			2.22938i			0.108268i
$425$	−9.55842	+	16.5557i	−0.463652	+	0.803068i
$426$	−19.1168	−	20.3422i	−0.926214	−	0.985582i
$427$	−4.50000	+	12.9904i	−0.217770	+	0.628649i
$428$			0.939764i			0.0454252i
$429$	13.9307	−	23.4839i	0.672581	−	1.13381i
$430$		−	3.16915i		−	0.152830i
$431$	−12.6861	−	21.9730i	−0.611070	−	1.05840i	−0.991060	−	0.133414i	$-0.957406\pi$
$431$	−12.6861	−	21.9730i	−0.611070	−	1.05840i	0.379991	−	0.924990i	$-0.375927\pi$
$432$	4.87228	+	1.80579i	0.234418	+	0.0868811i
$433$	−21.3505	−	12.3267i	−1.02604	−	0.592385i	−0.110193	−	0.993910i	$-0.535147\pi$
$433$	−21.3505	−	12.3267i	−1.02604	−	0.592385i	−0.915848	+	0.401525i	$0.868480\pi$
$434$	13.4891	−	11.6819i	0.647499	−	0.560750i
$435$	1.00000	−	3.31662i	0.0479463	−	0.159020i
$436$	17.2337	+	9.94987i	0.825344	+	0.476513i
$437$		−	10.0974i		−	0.483022i
$438$	−5.37228	+	17.8178i	−0.256698	+	0.851369i
$439$	−21.3505	+	12.3267i	−1.01901	+	0.588323i	−0.913816	−	0.406129i	$-0.866878\pi$
$439$	−21.3505	+	12.3267i	−1.01901	+	0.588323i	−0.105190	+	0.994452i	$0.533545\pi$
$440$	3.00000	−	1.73205i	0.143019	−	0.0825723i
$441$	−6.56930	−	19.9460i	−0.312824	−	0.949811i
$442$	15.3030	+	3.78651i	0.727889	+	0.180106i
$443$			7.86797i			0.373818i	0.982377	+	0.186909i	$0.0598470\pi$
$443$			7.86797i			0.373818i	−0.982377	+	0.186909i	$0.940153\pi$
$444$	14.7446	−	13.8564i	0.699746	−	0.657596i
$445$	4.25544	+	7.37063i	0.201727	+	0.349402i
$446$	14.1168	−	24.4511i	0.668452	−	1.15779i
$447$	10.1168	−	2.37686i	0.478510	−	0.112422i
$448$	0.500000	+	2.59808i	0.0236228	+	0.122748i
$449$	−19.8030	+	34.2998i	−0.934561	+	1.61871i	−0.159145	+	0.987255i	$0.550874\pi$
$449$	−19.8030	+	34.2998i	−0.934561	+	1.61871i	−0.775416	+	0.631451i	$0.782460\pi$
$450$	11.7446	−	5.84096i	0.553644	−	0.275346i
$451$	−35.7921	−	20.6646i	−1.68538	−	0.973057i
$452$	3.25544	−	1.87953i	0.153123	−	0.0884055i
$453$	21.3030	−	20.0198i	1.00090	−	0.940611i
$454$			19.4024i			0.910600i
$455$	−7.54755	−	0.396143i	−0.353834	−	0.0185715i
$456$	−4.00000	+	0.939764i	−0.187317	+	0.0440085i
$457$	9.17527	−	5.29734i	0.429201	−	0.247799i	−0.269805	−	0.962915i	$-0.586959\pi$
$457$	9.17527	−	5.29734i	0.429201	−	0.247799i	0.699006	+	0.715116i	$0.253626\pi$
$458$	−2.55842	−	4.43132i	−0.119547	−	0.207062i
$459$	−3.81386	−	22.3966i	−0.178016	−	1.04539i
$460$	3.37228			0.157233
$461$	27.4307	+	15.8371i	1.27758	+	0.737608i	0.976402	−	0.215961i	$-0.0692884\pi$
$461$	27.4307	+	15.8371i	1.27758	+	0.737608i	0.301173	+	0.953569i	$0.402622\pi$
$462$	−8.18614	−	18.2877i	−0.380854	−	0.850822i
$463$			10.8347i			0.503533i	0.967788	+	0.251766i	$0.0810115\pi$
$463$			10.8347i			0.503533i	−0.967788	+	0.251766i	$0.918989\pi$
$464$	2.18614	+	1.26217i	0.101489	+	0.0585947i
$465$	−6.74456	+	6.33830i	−0.312772	+	0.293931i
$466$	4.19702	−	2.42315i	0.194423	−	0.112250i
$467$	−25.3723			−1.17409			−0.587045	−	0.809555i	$-0.699709\pi$
$467$	−25.3723			−1.17409			−0.587045	+	0.809555i	$0.699709\pi$
$468$	−7.31386	−	7.96916i	−0.338083	−	0.368374i
$469$	20.2337	+	23.3639i	0.934305	+	1.07884i
$470$	−0.372281	−	0.644810i	−0.0171721	−	0.0297429i
$471$		0			0
$472$	5.31386	+	3.06796i	0.244590	+	0.141214i
$473$	−17.4891			−0.804151
$474$	4.81386	−	15.9658i	0.221108	−	0.733332i
$475$	−5.18614	+	8.98266i	−0.237956	+	0.412153i
$476$	8.74456	−	7.57301i	0.400806	−	0.347108i
$477$	−6.67527	−	0.414979i	−0.305639	−	0.0190006i
$478$	−7.80298	−	13.5152i	−0.356900	−	0.618169i
$479$	−2.69702	+	1.55712i	−0.123230	+	0.0711467i	−0.560348	−	0.828257i	$-0.689333\pi$
$479$	−2.69702	+	1.55712i	−0.123230	+	0.0711467i	0.437118	+	0.899404i	$0.355999\pi$
$480$	−0.313859	−	1.33591i	−0.0143257	−	0.0609755i
$481$	−40.4674	+	11.6819i	−1.84515	+	0.532650i
$482$	12.7446			0.580499
$483$	2.00000	−	19.4024i	0.0910032	−	0.882840i
$484$	−4.05842	−	7.02939i	−0.184474	−	0.319518i
$485$	−0.510875	−	0.294954i	−0.0231976	−	0.0133932i
$486$	−6.31386	+	14.2525i	−0.286402	+	0.646509i
$487$	−26.6168	−	15.3672i	−1.20612	−	0.696356i	−0.244214	−	0.969721i	$-0.578530\pi$
$487$	−26.6168	−	15.3672i	−1.20612	−	0.696356i	−0.961910	+	0.273365i	$0.911863\pi$
$488$	4.50000	+	2.59808i	0.203705	+	0.117609i
$489$	−4.11684	−	17.5229i	−0.186170	−	0.792412i
$490$	−3.43070	+	4.35758i	−0.154983	+	0.196855i
$491$	6.60597	−	3.81396i	0.298123	−	0.172122i	−0.343476	−	0.939161i	$-0.611604\pi$
$491$	6.60597	−	3.81396i	0.298123	−	0.172122i	0.641599	+	0.767040i	$0.278271\pi$
$492$	−11.9307	+	11.2120i	−0.537878	+	0.505478i
$493$		−	11.0371i		−	0.497087i
$494$	8.30298	+	2.05446i	0.373569	+	0.0924343i
$495$	4.62772	+	9.30506i	0.208000	+	0.418232i
$496$	−3.37228	−	5.84096i	−0.151420	−	0.262267i
$497$	40.2921	+	13.9576i	1.80735	+	0.626084i
$498$	−2.62772	−	0.792287i	−0.117751	−	0.0355032i
$499$		−	16.4356i		−	0.735761i	−0.929873	−	0.367880i	$-0.880084\pi$
$499$		−	16.4356i		−	0.735761i	0.929873	−	0.367880i	$-0.119916\pi$
$500$	−6.43070	−	3.71277i	−0.287590	−	0.166040i
$501$	11.0000	+	3.31662i	0.491444	+	0.148176i
$502$	16.1168			0.719330
$503$	11.4891	−	19.8997i	0.512275	−	0.887286i	−0.487624	−	0.873054i	$-0.662136\pi$
$503$	11.4891	−	19.8997i	0.512275	−	0.887286i	0.999899	−	0.0142322i	$-0.00453039\pi$
$504$	−7.87228	+	1.01350i	−0.350659	+	0.0451450i
$505$	−10.1168	+	5.84096i	−0.450194	+	0.259919i
$506$		−	18.6101i		−	0.827321i
$507$	5.98913	+	21.7055i	0.265986	+	0.963977i
$508$	−2.11684			−0.0939198
$509$	−20.3139	+	11.7282i	−0.900396	+	0.519844i	−0.877329	−	0.479890i	$-0.840677\pi$
$509$	−20.3139	+	11.7282i	−0.900396	+	0.519844i	−0.0230673	+	0.999734i	$0.507343\pi$
$510$	−4.37228	+	4.10891i	−0.193608	+	0.181946i
$511$	−5.37228	−	27.9152i	−0.237656	−	1.23490i
$512$	1.00000			0.0441942
$513$	−2.06930	−	12.1518i	−0.0913617	−	0.536515i
$514$	−2.44158	+	4.22894i	−0.107693	+	0.186530i
$515$	6.51087			0.286903
$516$	−2.00000	+	6.63325i	−0.0880451	+	0.292013i
$517$	−3.55842	+	2.05446i	−0.156499	+	0.0903549i
$518$	−10.1168	+	29.2048i	−0.444509	+	1.28319i
$519$	−3.17527	+	0.746000i	−0.139379	+	0.0327458i
$520$	−0.686141	+	2.77300i	−0.0300893	+	0.121604i
$521$	1.11684			0.0489298			0.0244649	−	0.999701i	$-0.492212\pi$
$521$	1.11684			0.0489298			0.0244649	+	0.999701i	$0.492212\pi$
$522$	−4.18614	+	6.31084i	−0.183222	+	0.276218i
$523$	−7.50000	+	4.33013i	−0.327952	+	0.189343i	−0.654932	−	0.755688i	$-0.727303\pi$
$523$	−7.50000	+	4.33013i	−0.327952	+	0.189343i	0.326979	+	0.945031i	$0.393969\pi$
$524$	10.8030	−	18.7113i	0.471931	−	0.817408i
$525$	−11.7446	+	16.2333i	−0.512575	+	0.708478i
$526$	−19.5475	−	11.2858i	−0.852314	−	0.492083i
$527$	−14.7446	+	25.5383i	−0.642283	+	1.11247i
$528$	−7.37228	+	1.73205i	−0.320837	+	0.0753778i
$529$	−2.44158	+	4.22894i	−0.106156	+	0.183867i
$530$	0.883156	+	1.52967i	0.0383618	+	0.0664447i
$531$	−10.1753	+	15.3398i	−0.441569	+	0.665690i
$532$	4.74456	−	4.10891i	0.205703	−	0.178144i
$533$	32.7446	−	9.45254i	1.41832	−	0.409435i
$534$	−4.25544	−	18.1128i	−0.184151	−	0.783817i
$535$	0.372281	+	0.644810i	0.0160951	+	0.0278776i
$536$	10.1168	−	5.84096i	0.436981	−	0.252291i
$537$	8.37228	+	2.52434i	0.361291	+	0.108933i
$538$	−0.861407			−0.0371379
$539$	24.0475	+	18.9325i	1.03580	+	0.815482i
$540$	4.05842	−	0.691097i	0.174647	−	0.0297401i
$541$		−	1.28962i		−	0.0554451i	−0.999616	−	0.0277226i	$-0.991175\pi$
$541$		−	1.28962i		−	0.0554451i	0.999616	−	0.0277226i	$-0.00882549\pi$
$542$	−2.00000	+	3.46410i	−0.0859074	+	0.148796i
$543$	15.3030	−	14.3812i	0.656714	−	0.617156i
$544$	−2.18614	−	3.78651i	−0.0937300	−	0.162345i
$545$	15.7663			0.675355
$546$	15.5475	+	5.59230i	0.665374	+	0.239328i
$547$	8.51087			0.363899			0.181949	−	0.983308i	$-0.441759\pi$
$547$	8.51087			0.363899			0.181949	+	0.983308i	$0.441759\pi$
$548$	−3.68614	−	6.38458i	−0.157464	−	0.272736i
$549$	−8.61684	+	12.9904i	−0.367758	+	0.554416i
$550$	−9.55842	+	16.5557i	−0.407572	+	0.705936i
$551$		−	5.98844i		−	0.255116i
$552$	−7.05842	−	2.12819i	−0.300426	−	0.0905820i
$553$	4.81386	+	25.0135i	0.204706	+	1.06368i
$554$	13.4891			0.573098
$555$	4.62772	−	15.3484i	0.196436	−	0.651504i
$556$	7.67527	−	4.43132i	0.325504	−	0.187930i
$557$	−12.3030	−	21.3094i	−0.521294	−	0.902908i	−0.999693	−	0.0247655i	$-0.992116\pi$
$557$	−12.3030	−	21.3094i	−0.521294	−	0.902908i	0.478399	−	0.878143i	$-0.341217\pi$
$558$	18.1168	−	9.01011i	0.766947	−	0.381428i
$559$	10.0000	−	10.3923i	0.422955	−	0.439548i
$560$	1.37228	+	1.58457i	0.0579895	+	0.0669605i
$561$	22.6753	+	24.1287i	0.957350	+	1.01871i
$562$	−7.37228	−	12.7692i	−0.310981	−	0.538635i
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	−0.184950	−	0.982748i	$-0.559212\pi$
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	0.943560	−	0.331202i	$-0.107454\pi$
$564$	0.372281	+	1.58457i	0.0156759	+	0.0667226i
$565$	1.48913	−	2.57924i	0.0626480	−	0.108509i
$566$	2.05842	+	1.18843i	0.0865219	+	0.0499535i
$567$	−1.56930	−	23.7600i	−0.0659043	−	0.997826i
$568$	8.05842	−	13.9576i	0.338124	−	0.585648i
$569$	29.6644	−	17.1267i	1.24360	−	0.717990i	0.273772	−	0.961795i	$-0.411729\pi$
$569$	29.6644	−	17.1267i	1.24360	−	0.717990i	0.969824	+	0.243804i	$0.0783955\pi$
$570$	−2.37228	+	2.22938i	−0.0993639	+	0.0933786i
$571$	−9.48913			−0.397108			−0.198554	−	0.980090i	$-0.563624\pi$
$571$	−9.48913			−0.397108			−0.198554	+	0.980090i	$0.563624\pi$
$572$	15.3030	+	3.78651i	0.639850	+	0.158322i
$573$	4.86141	+	20.6920i	0.203088	+	0.864422i
$574$	8.18614	−	23.6314i	0.341683	−	0.986354i
$575$	−16.1168	+	9.30506i	−0.672119	+	0.388048i
$576$	−0.186141	+	2.99422i	−0.00775586	+	0.124759i
$577$	−5.76631			−0.240055			−0.120027	−	0.992771i	$-0.538298\pi$
$577$	−5.76631			−0.240055			−0.120027	+	0.992771i	$0.538298\pi$
$578$	−1.05842	+	1.83324i	−0.0440246	+	0.0762528i
$579$	22.2446	+	6.70699i	0.924452	+	0.278733i
$580$	2.00000			0.0830455
$581$	4.11684	−	0.792287i	0.170795	−	0.0328696i
$582$	0.883156	+	0.939764i	0.0366080	+	0.0389545i
$583$	8.44158	−	4.87375i	0.349614	−	0.201850i
$584$	−10.7446			−0.444613
$585$	−8.17527	−	2.57062i	−0.338006	−	0.106282i
$586$		−	3.75906i		−	0.155285i
$587$	−37.5475	+	21.6781i	−1.54975	+	0.894750i	−0.551593	+	0.834113i	$0.685980\pi$
$587$	−37.5475	+	21.6781i	−1.54975	+	0.894750i	−0.998160	+	0.0606372i	$0.980687\pi$
$588$	9.93070	−	6.95565i	0.409535	−	0.286846i
$589$	−8.00000	+	13.8564i	−0.329634	+	0.570943i
$590$	4.86141			0.200141
$591$	−12.3030	+	40.8044i	−0.506077	+	1.67847i
$592$	10.1168	+	5.84096i	0.415800	+	0.240062i
$593$		−	3.11425i		−	0.127887i	−0.997954	−	0.0639434i	$-0.979632\pi$
$593$		−	3.11425i		−	0.127887i	0.997954	−	0.0639434i	$-0.0203677\pi$
$594$	−3.81386	−	22.3966i	−0.156485	−	0.918945i
$595$	3.00000	−	8.66025i	0.122988	−	0.355036i
$596$	3.00000	+	5.19615i	0.122885	+	0.212843i
$597$	−1.37228	−	5.84096i	−0.0561637	−	0.239055i
$598$	11.0584	+	10.6410i	0.452213	+	0.435142i
$599$			22.5716i			0.922249i	0.887335	+	0.461125i	$0.152554\pi$
$599$			22.5716i			0.922249i	−0.887335	+	0.461125i	$0.847446\pi$
$600$	5.18614	+	5.51856i	0.211723	+	0.225294i
$601$	37.1168	−	21.4294i	1.51403	−	0.874124i	0.514163	−	0.857693i	$-0.328103\pi$
$601$	37.1168	−	21.4294i	1.51403	−	0.874124i	0.999865	−	0.0164316i	$-0.00523057\pi$
$602$	−2.00000	−	10.3923i	−0.0815139	−	0.423559i
$603$	15.6060	+	31.3793i	0.635524	+	1.27786i
$604$	14.6168	+	8.43904i	0.594751	+	0.343380i
$605$	−5.56930	−	3.21543i	−0.226424	−	0.130726i
$606$	24.8614	−	5.84096i	1.00993	−	0.237273i
$607$	30.3505	+	17.5229i	1.23189	+	0.711232i	0.967424	−	0.253163i	$-0.0814708\pi$
$607$	30.3505	+	17.5229i	1.23189	+	0.711232i	0.264466	+	0.964395i	$0.414804\pi$
$608$	−1.18614	−	2.05446i	−0.0481044	−	0.0833192i
$609$	1.18614	−	11.5070i	0.0480648	−	0.466287i
$610$	4.11684			0.166686
$611$	0.813859	−	3.28917i	0.0329252	−	0.133066i
$612$	11.7446	−	5.84096i	0.474746	−	0.236107i
$613$	−8.23369	+	4.75372i	−0.332556	+	0.192001i	−0.656975	−	0.753912i	$-0.728164\pi$
$613$	−8.23369	+	4.75372i	−0.332556	+	0.192001i	0.324420	+	0.945913i	$0.394831\pi$
$614$	−10.6168	−	18.3889i	−0.428461	−	0.742116i
$615$	−3.74456	+	12.4193i	−0.150995	+	0.500795i
$616$	8.74456	−	7.57301i	0.352328	−	0.305125i
$617$	−16.8030	+	29.1036i	−0.676463	+	1.17167i	0.299576	+	0.954072i	$0.403155\pi$
$617$	−16.8030	+	29.1036i	−0.676463	+	1.17167i	−0.976039	+	0.217595i	$0.930179\pi$
$618$	−13.6277	−	4.10891i	−0.548187	−	0.165285i
$619$	−33.4674			−1.34517			−0.672584	−	0.740021i	$-0.734816\pi$
$619$	−33.4674			−1.34517			−0.672584	+	0.740021i	$0.734816\pi$
$620$	−4.62772	−	2.67181i	−0.185854	−	0.107303i
$621$	7.68614	−	20.7383i	0.308434	−	0.832200i
$622$	−5.18614	−	8.98266i	−0.207945	−	0.360172i
$623$	18.6060	+	21.4843i	0.745432	+	0.860751i
$624$	3.18614	−	5.37108i	0.127548	−	0.215015i
$625$	15.9783			0.639130
$626$	12.0000	−	6.92820i	0.479616	−	0.276907i
$627$	12.3030	+	13.0916i	0.491334	+	0.522827i
$628$		0			0
$629$		−	51.0767i		−	2.03656i
$630$	−5.00000	+	3.81396i	−0.199205	+	0.151952i
$631$	−28.5000	−	16.4545i	−1.13457	−	0.655043i	−0.189488	−	0.981883i	$-0.560683\pi$
$631$	−28.5000	−	16.4545i	−1.13457	−	0.655043i	−0.945080	+	0.326841i	$0.894016\pi$
$632$	9.62772			0.382970
$633$	5.62772	−	18.6650i	0.223682	−	0.741868i
$634$	−7.62772	−	13.2116i	−0.302935	−	0.524700i
$635$	−1.45245	+	0.838574i	−0.0576388	+	0.0332778i
$636$	−0.883156	−	3.75906i	−0.0350194	−	0.149056i
$637$	−25.0000	+	3.46410i	−0.990536	+	0.137253i
$638$		−	11.0371i		−	0.436964i
$639$	40.2921	+	26.7268i	1.59393	+	1.05729i
$640$	0.686141	−	0.396143i	0.0271221	−	0.0156589i
$641$	−23.6644	−	13.6626i	−0.934687	−	0.539642i	−0.0463963	−	0.998923i	$-0.514774\pi$
$641$	−23.6644	−	13.6626i	−0.934687	−	0.539642i	−0.888291	+	0.459281i	$0.848107\pi$
$642$	−0.372281	−	1.58457i	−0.0146928	−	0.0625381i
$643$	−1.61684	+	2.80046i	−0.0637621	+	0.110439i	−0.896144	−	0.443763i	$-0.853643\pi$
$643$	−1.61684	+	2.80046i	−0.0637621	+	0.110439i	0.832382	+	0.554202i	$0.186977\pi$
$644$	11.0584	−	2.12819i	0.435763	−	0.0838626i
$645$	1.25544	+	5.34363i	0.0494328	+	0.210405i
$646$	−5.18614	+	8.98266i	−0.204046	+	0.353418i
$647$	19.9307	+	34.5210i	0.783557	+	1.35716i	0.929857	+	0.367920i	$0.119930\pi$
$647$	19.9307	+	34.5210i	0.783557	+	1.35716i	−0.146301	+	0.989240i	$0.546737\pi$
$648$	−8.93070	−	1.11469i	−0.350831	−	0.0437892i
$649$		−	26.8280i		−	1.05309i
$650$	−4.37228	−	15.1460i	−0.171495	−	0.594076i
$651$	−18.1168	+	25.0410i	−0.710055	+	0.981434i
$652$	9.00000	−	5.19615i	0.352467	−	0.203497i
$653$	9.04755	−	5.22360i	0.354058	−	0.204415i	−0.312413	−	0.949946i	$-0.601137\pi$
$653$	9.04755	−	5.22360i	0.354058	−	0.204415i	0.666471	+	0.745531i	$0.267804\pi$
$654$	−33.0000	−	9.94987i	−1.29040	−	0.389071i
$655$		−	17.1181i		−	0.668861i
$656$	−8.18614	−	4.72627i	−0.319615	−	0.184530i
$657$	2.00000	−	32.1716i	0.0780274	−	1.25513i
$658$	−1.62772	−	1.87953i	−0.0634551	−	0.0732716i
$659$	−37.1644	−	21.4569i	−1.44772	−	0.835841i	−0.449374	−	0.893344i	$-0.648353\pi$
$659$	−37.1644	−	21.4569i	−1.44772	−	0.835841i	−0.998345	+	0.0575028i	$0.981686\pi$
$660$	−4.37228	+	4.10891i	−0.170191	+	0.159939i
$661$	−10.5693	−	18.3066i	−0.411098	−	0.712043i	0.583912	−	0.811817i	$-0.301521\pi$
$661$	−10.5693	−	18.3066i	−0.411098	−	0.712043i	−0.995010	+	0.0997743i	$0.968188\pi$
$662$			2.17448i			0.0845136i
$663$	−27.3030	−	0.322405i	−1.06036	−	0.0125212i
$664$		−	1.58457i		−	0.0614934i
$665$	1.62772	−	4.69882i	0.0631202	−	0.182212i
$666$	−19.3723	+	29.2048i	−0.750661	+	1.13166i
$667$	5.37228	−	9.30506i	0.208016	−	0.360294i
$668$			6.63325i			0.256648i
$669$	−14.1168	+	46.8203i	−0.545789	+	1.81018i
$670$	4.62772	−	8.01544i	0.178784	−	0.309664i
$671$		−	22.7190i		−	0.877059i
$672$	−1.87228	−	4.18265i	−0.0722248	−	0.161349i
$673$	4.18614	+	7.25061i	0.161364	+	0.279490i	0.935358	−	0.353702i	$-0.115077\pi$
$673$	4.18614	+	7.25061i	0.161364	+	0.279490i	−0.773994	+	0.633193i	$0.781744\pi$
$674$	5.30298	+	9.18504i	0.204263	+	0.353794i
$675$	−17.4891	+	14.5012i	−0.673157	+	0.558152i
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$	1.37228			0.0527411			0.0263705	−	0.999652i	$-0.491605\pi$
$677$	1.37228			0.0527411			0.0263705	+	0.999652i	$0.491605\pi$
$678$	−4.74456	+	4.45877i	−0.182214	+	0.171238i
$679$	−1.86141	−	0.644810i	−0.0714342	−	0.0247455i
$680$	−3.00000	−	1.73205i	−0.115045	−	0.0664211i
$681$	−7.68614	−	32.7152i	−0.294534	−	1.25365i
$682$	−14.7446	+	25.5383i	−0.564598	+	0.977913i
$683$	6.86141	−	11.8843i	0.262544	−	0.454740i	−0.704373	−	0.709830i	$-0.748772\pi$
$683$	6.86141	−	11.8843i	0.262544	−	0.454740i	0.966917	+	0.255090i	$0.0821050\pi$
$684$	6.37228	−	3.16915i	0.243650	−	0.121175i
$685$	−5.05842	−	2.92048i	−0.193272	−	0.111586i
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$	6.06930	+	6.45832i	0.231558	+	0.246400i
$688$	−4.00000			−0.152499
$689$	−1.93070	+	7.80284i	−0.0735539	+	0.297265i
$690$	−5.68614	+	1.33591i	−0.216468	+	0.0508571i
$691$	10.9416	+	18.9514i	0.416237	+	0.720944i	0.995557	−	0.0941560i	$-0.0300152\pi$
$691$	10.9416	+	18.9514i	0.416237	+	0.720944i	−0.579320	+	0.815100i	$0.696682\pi$
$692$	−0.941578	−	1.63086i	−0.0357934	−	0.0619960i
$693$	21.0475	+	27.5928i	0.799530	+	1.04816i
$694$			20.8395i			0.791057i
$695$	3.51087	−	6.08101i	0.133175	−	0.230666i
$696$	−4.18614	−	1.26217i	−0.158675	−	0.0478424i
$697$			41.3292i			1.56545i
$698$	−10.0584	+	17.4217i	−0.380717	+	0.659421i
$699$	−6.11684	+	5.74839i	−0.231360	+	0.217424i
$700$	−10.9307	−	3.78651i	−0.413142	−	0.143117i
$701$		−	45.3832i		−	1.71410i	−0.515234	−	0.857049i	$-0.672295\pi$
$701$		−	45.3832i		−	1.71410i	0.515234	−	0.857049i	$-0.327705\pi$
$702$	15.4891	+	10.5398i	0.584599	+	0.397798i
$703$		−	27.7128i		−	1.04521i
$704$	−2.18614	−	3.78651i	−0.0823933	−	0.142709i
$705$	0.883156	+	0.939764i	0.0332616	+	0.0353936i
$706$	25.3723	+	14.6487i	0.954898	+	0.551311i
$707$	−29.4891	+	25.5383i	−1.10905	+	0.960468i
$708$	−10.1753	−	3.06796i	−0.382410	−	0.115301i
$709$	−22.8832	−	13.2116i	−0.859395	−	0.496172i	0.00441467	−	0.999990i	$-0.498595\pi$
$709$	−22.8832	−	13.2116i	−0.859395	−	0.496172i	−0.863810	+	0.503818i	$0.831928\pi$
$710$		−	12.7692i		−	0.479218i
$711$	−1.79211	+	28.8275i	−0.0672094	+	1.08112i
$712$	9.30298	−	5.37108i	0.348644	−	0.201290i
$713$	−24.8614	+	14.3537i	−0.931067	+	0.537552i
$714$	−11.7446	+	16.2333i	−0.439529	+	0.607515i
$715$	12.0000	−	3.46410i	0.448775	−	0.129550i
$716$			5.04868i			0.188678i
$717$	18.5109	+	19.6974i	0.691301	+	0.735612i
$718$	8.31386	+	14.4000i	0.310270	+	0.537404i
$719$	12.5584	−	21.7518i	0.468350	−	0.811206i	−0.530996	−	0.847375i	$-0.678182\pi$
$719$	12.5584	−	21.7518i	0.468350	−	0.811206i	0.999346	+	0.0361684i	$0.0115153\pi$
$720$	1.05842	+	2.12819i	0.0394451	+	0.0793131i
$721$	21.3505	−	4.10891i	0.795135	−	0.153024i
$722$	6.68614	−	11.5807i	0.248832	−	0.430990i
$723$	−21.4891	+	5.04868i	−0.799189	+	0.187762i
$724$	10.5000	+	6.06218i	0.390229	+	0.225299i
$725$	−9.55842	+	5.51856i	−0.354991	+	0.204954i
$726$	9.62772	+	10.2448i	0.357318	+	0.380221i
$727$			28.1176i			1.04282i	0.853305	+	0.521412i	$0.174594\pi$
$727$			28.1176i			1.04282i	−0.853305	+	0.521412i	$0.825406\pi$
$728$	−0.500000	+	9.52628i	−0.0185312	+	0.353067i
$729$	5.00000	−	26.5330i	0.185185	−	0.982704i
$730$	−7.37228	+	4.25639i	−0.272860	+	0.157536i
$731$	8.74456	+	15.1460i	0.323429	+	0.560196i
$732$	−8.61684	−	2.59808i	−0.318488	−	0.0960277i
$733$	−43.7446			−1.61574			−0.807871	−	0.589359i	$-0.799380\pi$
$733$	−43.7446			−1.61574			−0.807871	+	0.589359i	$0.799380\pi$
$734$	−26.2337	−	15.1460i	−0.968303	−	0.559050i
$735$	4.05842	−	8.70654i	0.149697	−	0.321146i
$736$		−	4.25639i		−	0.156893i
$737$	−44.2337	−	25.5383i	−1.62937	−	0.940717i
$738$	15.6753	−	23.6314i	0.577015	−	0.869882i
$739$	−34.1168	+	19.6974i	−1.25501	+	0.724579i	−0.972100	−	0.234567i	$-0.924633\pi$
$739$	−34.1168	+	19.6974i	−1.25501	+	0.724579i	−0.282909	+	0.959147i	$0.591299\pi$
$740$	9.25544			0.340237
$741$	−14.8139	−	0.174928i	−0.544201	−	0.00642615i
$742$	3.86141	+	4.45877i	0.141757	+	0.163687i
$743$	−1.62772	−	2.81929i	−0.0597152	−	0.103430i	0.834622	−	0.550823i	$-0.185686\pi$
$743$	−1.62772	−	2.81929i	−0.0597152	−	0.103430i	−0.894338	+	0.447393i	$0.852353\pi$
$744$	8.00000	+	8.51278i	0.293294	+	0.312094i
$745$	4.11684	+	2.37686i	0.150829	+	0.0870814i
$746$	8.00000			0.292901
$747$	4.74456	+	0.294954i	0.173594	+	0.0107918i
$748$	−9.55842	+	16.5557i	−0.349491	+	0.605335i
$749$	1.62772	+	1.87953i	0.0594755	+	0.0686764i
$750$	12.3139	+	3.71277i	0.449639	+	0.135571i
$751$	0.500000	+	0.866025i	0.0182453	+	0.0316017i	0.875004	−	0.484116i	$-0.160859\pi$
$751$	0.500000	+	0.866025i	0.0182453	+	0.0316017i	−0.856759	+	0.515718i	$0.827525\pi$
$752$	−0.813859	+	0.469882i	−0.0296784	+	0.0171348i
$753$	−27.1753	+	6.38458i	−0.990322	+	0.232667i
$754$	6.55842	+	6.31084i	0.238844	+	0.229827i
$755$	13.3723			0.486667
$756$	12.8723	−	4.82746i	0.468160	−	0.175573i
$757$	8.86141	+	15.3484i	0.322073	+	0.557847i	0.980916	−	0.194434i	$-0.0622869\pi$
$757$	8.86141	+	15.3484i	0.322073	+	0.557847i	−0.658842	+	0.752281i	$0.728954\pi$
$758$	4.88316	+	2.81929i	0.177364	+	0.102401i
$759$	7.37228	+	31.3793i	0.267597	+	1.13900i
$760$	−1.62772	−	0.939764i	−0.0590436	−	0.0340888i
$761$	3.25544	+	1.87953i	0.118010	+	0.0681328i	0.557843	−	0.829947i	$-0.311629\pi$
$761$	3.25544	+	1.87953i	0.118010	+	0.0681328i	−0.439833	+	0.898079i	$0.644963\pi$
$762$	3.56930	−	0.838574i	0.129302	−	0.0303783i
$763$	51.7011	−	9.94987i	1.87170	−	0.360210i
$764$	−10.6277	+	6.13592i	−0.384497	+	0.221990i
$765$	5.74456	−	8.66025i	0.207695	−	0.313112i
$766$			15.0911i			0.545264i
$767$	15.9416	+	15.3398i	0.575617	+	0.553888i
$768$	−1.68614	+	0.396143i	−0.0608434	+	0.0142946i
$769$	−12.1168	−	20.9870i	−0.436945	−	0.756810i	0.560508	−	0.828149i	$-0.310606\pi$
$769$	−12.1168	−	20.9870i	−0.436945	−	0.756810i	−0.997452	+	0.0713391i	$0.977273\pi$
$770$	3.00000	−	8.66025i	0.108112	−	0.312094i

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.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.18614 + 1.26217i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.792287i q^{5} +(0.500000 - 1.65831i) q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.186141 + 2.99422i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.18614 + 1.26217i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.792287i q^{5} +(0.500000 - 1.65831i) q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.186141 + 2.99422i) q^{9} +(0.686141 - 0.396143i) q^{10} +(-2.18614 - 3.78651i) q^{11} +(-1.68614 + 0.396143i) q^{12} +(3.50000 + 0.866025i) q^{13} +(2.00000 - 1.73205i) q^{14} +(-1.00000 + 0.939764i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.18614 + 3.78651i) q^{17} +(2.68614 - 1.33591i) q^{18} +(-1.18614 + 2.05446i) q^{19} +(-0.686141 - 0.396143i) q^{20} +(-2.68614 + 3.71277i) q^{21} +(-2.18614 + 3.78651i) q^{22} +(-3.68614 + 2.12819i) q^{23} +(1.18614 + 1.26217i) q^{24} +4.37228 q^{25} +(-1.00000 - 3.46410i) q^{26} +(-4.00000 + 3.31662i) q^{27} +(-2.50000 - 0.866025i) q^{28} +(-2.18614 + 1.26217i) q^{29} +(1.31386 + 0.396143i) q^{30} +6.74456 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.18614 - 7.25061i) q^{33} +4.37228 q^{34} +(-2.05842 + 0.396143i) q^{35} +(-2.50000 - 1.65831i) q^{36} +(-10.1168 + 5.84096i) q^{37} +2.37228 q^{38} +(3.05842 + 5.44482i) q^{39} +0.792287i q^{40} +(8.18614 - 4.72627i) q^{41} +(4.55842 + 0.469882i) q^{42} +(2.00000 - 3.46410i) q^{43} +4.37228 q^{44} +(-2.37228 - 0.147477i) q^{45} +(3.68614 + 2.12819i) q^{46} -0.939764i q^{47} +(0.500000 - 1.65831i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(-2.18614 - 3.78651i) q^{50} +(-7.37228 + 1.73205i) q^{51} +(-2.50000 + 2.59808i) q^{52} +2.22938i q^{53} +(4.87228 + 1.80579i) q^{54} +(3.00000 - 1.73205i) q^{55} +(0.500000 + 2.59808i) q^{56} +(-4.00000 + 0.939764i) q^{57} +(2.18614 + 1.26217i) q^{58} +(5.31386 + 3.06796i) q^{59} +(-0.313859 - 1.33591i) q^{60} +(4.50000 + 2.59808i) q^{61} +(-3.37228 - 5.84096i) q^{62} +(-7.87228 + 1.01350i) q^{63} +1.00000 q^{64} +(-0.686141 + 2.77300i) q^{65} +(-7.37228 + 1.73205i) q^{66} +(10.1168 - 5.84096i) q^{67} +(-2.18614 - 3.78651i) q^{68} +(-7.05842 - 2.12819i) q^{69} +(1.37228 + 1.58457i) q^{70} +(8.05842 - 13.9576i) q^{71} +(-0.186141 + 2.99422i) q^{72} -10.7446 q^{73} +(10.1168 + 5.84096i) q^{74} +(5.18614 + 5.51856i) q^{75} +(-1.18614 - 2.05446i) q^{76} +(8.74456 - 7.57301i) q^{77} +(3.18614 - 5.37108i) q^{78} +9.62772 q^{79} +(0.686141 - 0.396143i) q^{80} +(-8.93070 - 1.11469i) q^{81} +(-8.18614 - 4.72627i) q^{82} -1.58457i q^{83} +(-1.87228 - 4.18265i) q^{84} +(-3.00000 - 1.73205i) q^{85} -4.00000 q^{86} +(-4.18614 - 1.26217i) q^{87} +(-2.18614 - 3.78651i) q^{88} +(9.30298 - 5.37108i) q^{89} +(1.05842 + 2.12819i) q^{90} +(-0.500000 + 9.52628i) q^{91} -4.25639i q^{92} +(8.00000 + 8.51278i) q^{93} +(-0.813859 + 0.469882i) q^{94} +(-1.62772 - 0.939764i) q^{95} +(-1.68614 + 0.396143i) q^{96} +(-0.372281 + 0.644810i) q^{97} +(5.50000 + 4.33013i) q^{98} +(11.7446 - 5.84096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{7} + 4 q^{8} + 5 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - q^3 - 2 * q^4 + 2 * q^6 + 2 * q^7 + 4 * q^8 + 5 * q^9	\( 4 q - 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{7} + 4 q^{8} + 5 q^{9} - 3 q^{10} - 3 q^{11} - q^{12} + 14 q^{13} + 8 q^{14} - 4 q^{15} - 2 q^{16} - 3 q^{17} + 5 q^{18} + q^{19} + 3 q^{20} - 5 q^{21} - 3 q^{22} - 9 q^{23} - q^{24} + 6 q^{25} - 4 q^{26} - 16 q^{27} - 10 q^{28} - 3 q^{29} + 11 q^{30} + 4 q^{31} - 2 q^{32} + 3 q^{33} + 6 q^{34} + 9 q^{35} - 10 q^{36} - 6 q^{37} - 2 q^{38} - 5 q^{39} + 27 q^{41} + q^{42} + 8 q^{43} + 6 q^{44} + 2 q^{45} + 9 q^{46} + 2 q^{48} - 26 q^{49} - 3 q^{50} - 18 q^{51} - 10 q^{52} + 8 q^{54} + 12 q^{55} + 2 q^{56} - 16 q^{57} + 3 q^{58} + 27 q^{59} - 7 q^{60} + 18 q^{61} - 2 q^{62} - 20 q^{63} + 4 q^{64} + 3 q^{65} - 18 q^{66} + 6 q^{67} - 3 q^{68} - 11 q^{69} - 6 q^{70} + 15 q^{71} + 5 q^{72} - 20 q^{73} + 6 q^{74} + 15 q^{75} + q^{76} + 12 q^{77} + 7 q^{78} + 50 q^{79} - 3 q^{80} - 7 q^{81} - 27 q^{82} + 4 q^{84} - 12 q^{85} - 16 q^{86} - 11 q^{87} - 3 q^{88} - 3 q^{89} - 13 q^{90} - 2 q^{91} + 32 q^{93} - 9 q^{94} - 18 q^{95} - q^{96} + 10 q^{97} + 22 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - q^3 - 2 * q^4 + 2 * q^6 + 2 * q^7 + 4 * q^8 + 5 * q^9 - 3 * q^10 - 3 * q^11 - q^12 + 14 * q^13 + 8 * q^14 - 4 * q^15 - 2 * q^16 - 3 * q^17 + 5 * q^18 + q^19 + 3 * q^20 - 5 * q^21 - 3 * q^22 - 9 * q^23 - q^24 + 6 * q^25 - 4 * q^26 - 16 * q^27 - 10 * q^28 - 3 * q^29 + 11 * q^30 + 4 * q^31 - 2 * q^32 + 3 * q^33 + 6 * q^34 + 9 * q^35 - 10 * q^36 - 6 * q^37 - 2 * q^38 - 5 * q^39 + 27 * q^41 + q^42 + 8 * q^43 + 6 * q^44 + 2 * q^45 + 9 * q^46 + 2 * q^48 - 26 * q^49 - 3 * q^50 - 18 * q^51 - 10 * q^52 + 8 * q^54 + 12 * q^55 + 2 * q^56 - 16 * q^57 + 3 * q^58 + 27 * q^59 - 7 * q^60 + 18 * q^61 - 2 * q^62 - 20 * q^63 + 4 * q^64 + 3 * q^65 - 18 * q^66 + 6 * q^67 - 3 * q^68 - 11 * q^69 - 6 * q^70 + 15 * q^71 + 5 * q^72 - 20 * q^73 + 6 * q^74 + 15 * q^75 + q^76 + 12 * q^77 + 7 * q^78 + 50 * q^79 - 3 * q^80 - 7 * q^81 - 27 * q^82 + 4 * q^84 - 12 * q^85 - 16 * q^86 - 11 * q^87 - 3 * q^88 - 3 * q^89 - 13 * q^90 - 2 * q^91 + 32 * q^93 - 9 * q^94 - 18 * q^95 - q^96 + 10 * q^97 + 22 * q^98 + 24 * q^99

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