LMFDB - Embedded newform 507.2.e.c.22.1

Newspace parameters

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.e (of order $3$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	507.22
Dual form			507.2.e.c.484.1

$q$-expansion

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} +3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} +3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-1.00000 + 1.73205i) q^{11} +1.00000 q^{12} +2.00000 q^{14} +(0.500000 - 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.50000 + 6.06218i) q^{17} -1.00000 q^{18} +(-3.00000 - 5.19615i) q^{19} +(0.500000 + 0.866025i) q^{20} +2.00000 q^{21} +(1.00000 + 1.73205i) q^{22} +(3.00000 - 5.19615i) q^{23} +(1.50000 - 2.59808i) q^{24} -4.00000 q^{25} -1.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} +(0.500000 - 0.866025i) q^{29} +(-0.500000 - 0.866025i) q^{30} -4.00000 q^{31} +(2.50000 + 4.33013i) q^{32} +(1.00000 + 1.73205i) q^{33} +7.00000 q^{34} +(1.00000 + 1.73205i) q^{35} +(0.500000 - 0.866025i) q^{36} +(0.500000 - 0.866025i) q^{37} -6.00000 q^{38} +3.00000 q^{40} +(4.50000 - 7.79423i) q^{41} +(1.00000 - 1.73205i) q^{42} +(-3.00000 - 5.19615i) q^{43} -2.00000 q^{44} +(-0.500000 - 0.866025i) q^{45} +(-3.00000 - 5.19615i) q^{46} -6.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +(-2.00000 + 3.46410i) q^{50} +7.00000 q^{51} -9.00000 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.00000 + 1.73205i) q^{55} +(3.00000 + 5.19615i) q^{56} -6.00000 q^{57} +(-0.500000 - 0.866025i) q^{58} +1.00000 q^{60} +(-0.500000 - 0.866025i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(1.00000 - 1.73205i) q^{63} +7.00000 q^{64} +2.00000 q^{66} +(-1.00000 + 1.73205i) q^{67} +(-3.50000 + 6.06218i) q^{68} +(-3.00000 - 5.19615i) q^{69} +2.00000 q^{70} +(3.00000 + 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} -11.0000 q^{73} +(-0.500000 - 0.866025i) q^{74} +(-2.00000 + 3.46410i) q^{75} +(3.00000 - 5.19615i) q^{76} -4.00000 q^{77} -4.00000 q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.50000 - 7.79423i) q^{82} +14.0000 q^{83} +(1.00000 + 1.73205i) q^{84} +(3.50000 + 6.06218i) q^{85} -6.00000 q^{86} +(-0.500000 - 0.866025i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(-7.00000 + 12.1244i) q^{89} -1.00000 q^{90} +6.00000 q^{92} +(-2.00000 + 3.46410i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(-3.00000 - 5.19615i) q^{95} +5.00000 q^{96} +(-1.00000 - 1.73205i) q^{97} +(-1.50000 - 2.59808i) q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 + q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 - q^9	$ 2 q + q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} - q^{9} + q^{10} - 2 q^{11} + 2 q^{12} + 4 q^{14} + q^{15} + q^{16} + 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21} + 2 q^{22} + 6 q^{23} + 3 q^{24} - 8 q^{25} - 2 q^{27} - 2 q^{28} + q^{29} - q^{30} - 8 q^{31} + 5 q^{32} + 2 q^{33} + 14 q^{34} + 2 q^{35} + q^{36} + q^{37} - 12 q^{38} + 6 q^{40} + 9 q^{41} + 2 q^{42} - 6 q^{43} - 4 q^{44} - q^{45} - 6 q^{46} - 12 q^{47} - q^{48} + 3 q^{49} - 4 q^{50} + 14 q^{51} - 18 q^{53} - q^{54} - 2 q^{55} + 6 q^{56} - 12 q^{57} - q^{58} + 2 q^{60} - q^{61} - 4 q^{62} + 2 q^{63} + 14 q^{64} + 4 q^{66} - 2 q^{67} - 7 q^{68} - 6 q^{69} + 4 q^{70} + 6 q^{71} - 3 q^{72} - 22 q^{73} - q^{74} - 4 q^{75} + 6 q^{76} - 8 q^{77} - 8 q^{79} + q^{80} - q^{81} - 9 q^{82} + 28 q^{83} + 2 q^{84} + 7 q^{85} - 12 q^{86} - q^{87} - 6 q^{88} - 14 q^{89} - 2 q^{90} + 12 q^{92} - 4 q^{93} - 6 q^{94} - 6 q^{95} + 10 q^{96} - 2 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 + q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 - q^9 + q^10 - 2 * q^11 + 2 * q^12 + 4 * q^14 + q^15 + q^16 + 7 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + 4 * q^21 + 2 * q^22 + 6 * q^23 + 3 * q^24 - 8 * q^25 - 2 * q^27 - 2 * q^28 + q^29 - q^30 - 8 * q^31 + 5 * q^32 + 2 * q^33 + 14 * q^34 + 2 * q^35 + q^36 + q^37 - 12 * q^38 + 6 * q^40 + 9 * q^41 + 2 * q^42 - 6 * q^43 - 4 * q^44 - q^45 - 6 * q^46 - 12 * q^47 - q^48 + 3 * q^49 - 4 * q^50 + 14 * q^51 - 18 * q^53 - q^54 - 2 * q^55 + 6 * q^56 - 12 * q^57 - q^58 + 2 * q^60 - q^61 - 4 * q^62 + 2 * q^63 + 14 * q^64 + 4 * q^66 - 2 * q^67 - 7 * q^68 - 6 * q^69 + 4 * q^70 + 6 * q^71 - 3 * q^72 - 22 * q^73 - q^74 - 4 * q^75 + 6 * q^76 - 8 * q^77 - 8 * q^79 + q^80 - q^81 - 9 * q^82 + 28 * q^83 + 2 * q^84 + 7 * q^85 - 12 * q^86 - q^87 - 6 * q^88 - 14 * q^89 - 2 * q^90 + 12 * q^92 - 4 * q^93 - 6 * q^94 - 6 * q^95 + 10 * q^96 - 2 * q^97 - 3 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	−0.633316	−	0.773893i	$-0.718307\pi$
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	0.986869	+	0.161521i	$0.0516399\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	0.990766	−	0.135583i	$-0.0432908\pi$
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	−0.612801	+	0.790237i	$0.709957\pi$
$8$	3.00000			1.06066
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	1.00000			0.288675
$13$		0			0
$13$		0			0
$14$	2.00000			0.534522
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	3.50000	+	6.06218i	0.848875	+	1.47029i	0.882213	+	0.470850i	$0.156053\pi$
$17$	3.50000	+	6.06218i	0.848875	+	1.47029i	−0.0333386	+	0.999444i	$0.510614\pi$
$18$	−1.00000			−0.235702
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	2.00000			0.436436
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	1.50000	−	2.59808i	0.306186	−	0.530330i
$25$	−4.00000			−0.800000
$26$		0			0
$27$	−1.00000			−0.192450
$28$	−1.00000	+	1.73205i	−0.188982	+	0.327327i
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	−0.815861	−	0.578249i	$-0.803736\pi$
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	0.908708	+	0.417432i	$0.137070\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	2.50000	+	4.33013i	0.441942	+	0.765466i
$33$	1.00000	+	1.73205i	0.174078	+	0.301511i
$34$	7.00000			1.20049
$35$	1.00000	+	1.73205i	0.169031	+	0.292770i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−6.00000			−0.973329
$39$		0			0
$40$	3.00000			0.474342
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	−0.264704	−	0.964330i	$-0.585274\pi$
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	0.967486	−	0.252924i	$-0.0813924\pi$
$42$	1.00000	−	1.73205i	0.154303	−	0.267261i
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	0.541332	−	0.840809i	$-0.317920\pi$
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	−0.998828	+	0.0484030i	$0.984587\pi$
$44$	−2.00000			−0.301511
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$	7.00000			0.980196
$52$		0			0
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−1.00000	+	1.73205i	−0.134840	+	0.233550i
$56$	3.00000	+	5.19615i	0.400892	+	0.694365i
$57$	−6.00000			−0.794719
$58$	−0.500000	−	0.866025i	−0.0656532	−	0.113715i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	1.00000			0.129099
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	−2.00000	+	3.46410i	−0.254000	+	0.439941i
$63$	1.00000	−	1.73205i	0.125988	−	0.218218i
$64$	7.00000			0.875000
$65$		0			0
$66$	2.00000			0.246183
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$	−3.50000	+	6.06218i	−0.424437	+	0.735147i
$69$	−3.00000	−	5.19615i	−0.361158	−	0.625543i
$70$	2.00000			0.239046
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	−11.0000			−1.28745			−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000			−1.28745			−0.643726	+	0.765256i	$0.722612\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$	−2.00000	+	3.46410i	−0.230940	+	0.400000i
$76$	3.00000	−	5.19615i	0.344124	−	0.596040i
$77$	−4.00000			−0.455842
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.50000	−	7.79423i	−0.496942	−	0.860729i
$83$	14.0000			1.53670			0.768350	−	0.640030i	$-0.221078\pi$
$83$	14.0000			1.53670			0.768350	+	0.640030i	$0.221078\pi$
$84$	1.00000	+	1.73205i	0.109109	+	0.188982i
$85$	3.50000	+	6.06218i	0.379628	+	0.657536i
$86$	−6.00000			−0.646997
$87$	−0.500000	−	0.866025i	−0.0536056	−	0.0928477i
$88$	−3.00000	+	5.19615i	−0.319801	+	0.553912i
$89$	−7.00000	+	12.1244i	−0.741999	+	1.28518i	0.209585	+	0.977790i	$0.432789\pi$
$89$	−7.00000	+	12.1244i	−0.741999	+	1.28518i	−0.951584	+	0.307389i	$0.900545\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	6.00000			0.625543
$93$	−2.00000	+	3.46410i	−0.207390	+	0.359211i
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$	−3.00000	−	5.19615i	−0.307794	−	0.533114i
$96$	5.00000			0.510310
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	−1.50000	−	2.59808i	−0.151523	−	0.262445i
$99$	2.00000			0.201008
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	−0.930953	−	0.365140i	$-0.881021\pi$
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	0.781697	+	0.623658i	$0.214354\pi$
$102$	3.50000	−	6.06218i	0.346552	−	0.600245i
$103$	6.00000			0.591198			0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000			0.591198			0.295599	+	0.955312i	$0.404481\pi$
$104$		0			0
$105$	2.00000			0.195180
$106$	−4.50000	+	7.79423i	−0.437079	+	0.757042i
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	−0.683793	−	0.729676i	$-0.739671\pi$
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	0.973814	+	0.227345i	$0.0730044\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$	1.00000	+	1.73205i	0.0953463	+	0.165145i
$111$	−0.500000	−	0.866025i	−0.0474579	−	0.0821995i
$112$	2.00000			0.188982
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	0.966496	+	0.256681i	$0.0826291\pi$
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	−0.260955	+	0.965351i	$0.584038\pi$
$114$	−3.00000	+	5.19615i	−0.280976	+	0.486664i
$115$	3.00000	−	5.19615i	0.279751	−	0.484544i
$116$	1.00000			0.0928477
$117$		0			0
$118$		0			0
$119$	−7.00000	+	12.1244i	−0.641689	+	1.11144i
$120$	1.50000	−	2.59808i	0.136931	−	0.237171i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−1.00000			−0.0905357
$123$	−4.50000	−	7.79423i	−0.405751	−	0.702782i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	−9.00000			−0.804984
$126$	−1.00000	−	1.73205i	−0.0890871	−	0.154303i
$127$	−10.0000	+	17.3205i	−0.887357	+	1.53695i	−0.0443678	+	0.999015i	$0.514127\pi$
$127$	−10.0000	+	17.3205i	−0.887357	+	1.53695i	−0.842989	+	0.537931i	$0.819206\pi$
$128$	−1.50000	+	2.59808i	−0.132583	+	0.229640i
$129$	−6.00000			−0.528271
$130$		0			0
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$	−1.00000	+	1.73205i	−0.0870388	+	0.150756i
$133$	6.00000	−	10.3923i	0.520266	−	0.901127i
$134$	1.00000	+	1.73205i	0.0863868	+	0.149626i
$135$	−1.00000			−0.0860663
$136$	10.5000	+	18.1865i	0.900368	+	1.55948i
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$	−6.00000			−0.510754
$139$	−6.00000	−	10.3923i	−0.508913	−	0.881464i	−0.999947	−	0.0103230i	$-0.996714\pi$
$139$	−6.00000	−	10.3923i	−0.508913	−	0.881464i	0.491033	−	0.871141i	$-0.336619\pi$
$140$	−1.00000	+	1.73205i	−0.0845154	+	0.146385i
$141$	−3.00000	+	5.19615i	−0.252646	+	0.437595i
$142$	6.00000			0.503509
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	0.500000	−	0.866025i	0.0415227	−	0.0719195i
$146$	−5.50000	+	9.52628i	−0.455183	+	0.788400i
$147$	−1.50000	−	2.59808i	−0.123718	−	0.214286i
$148$	1.00000			0.0821995
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	0.920904	−	0.389789i	$-0.127452\pi$
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	−0.798019	+	0.602632i	$0.794119\pi$
$150$	2.00000	+	3.46410i	0.163299	+	0.282843i
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$	−9.00000	−	15.5885i	−0.729996	−	1.26439i
$153$	3.50000	−	6.06218i	0.282958	−	0.490098i
$154$	−2.00000	+	3.46410i	−0.161165	+	0.279145i
$155$	−4.00000			−0.321288
$156$		0			0
$157$	−3.00000			−0.239426			−0.119713	−	0.992809i	$-0.538197\pi$
$157$	−3.00000			−0.239426			−0.119713	+	0.992809i	$0.538197\pi$
$158$	−2.00000	+	3.46410i	−0.159111	+	0.275589i
$159$	−4.50000	+	7.79423i	−0.356873	+	0.618123i
$160$	2.50000	+	4.33013i	0.197642	+	0.342327i
$161$	12.0000			0.945732
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$	9.00000			0.702782
$165$	1.00000	+	1.73205i	0.0778499	+	0.134840i
$166$	7.00000	−	12.1244i	0.543305	−	0.941033i
$167$	8.00000	−	13.8564i	0.619059	−	1.07224i	−0.370599	−	0.928793i	$-0.620848\pi$
$167$	8.00000	−	13.8564i	0.619059	−	1.07224i	0.989658	−	0.143448i	$-0.0458190\pi$
$168$	6.00000			0.462910
$169$		0			0
$170$	7.00000			0.536875
$171$	−3.00000	+	5.19615i	−0.229416	+	0.397360i
$172$	3.00000	−	5.19615i	0.228748	−	0.396203i
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$	−1.00000			−0.0758098
$175$	−4.00000	−	6.92820i	−0.302372	−	0.523723i
$176$	1.00000	+	1.73205i	0.0753778	+	0.130558i
$177$		0			0
$178$	7.00000	+	12.1244i	0.524672	+	0.908759i
$179$	1.00000	−	1.73205i	0.0747435	−	0.129460i	−0.826231	−	0.563331i	$-0.809520\pi$
$179$	1.00000	−	1.73205i	0.0747435	−	0.129460i	0.900975	+	0.433872i	$0.142853\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$	−1.00000			−0.0739221
$184$	9.00000	−	15.5885i	0.663489	−	1.14920i
$185$	0.500000	−	0.866025i	0.0367607	−	0.0636715i
$186$	2.00000	+	3.46410i	0.146647	+	0.254000i
$187$	−14.0000			−1.02378
$188$	−3.00000	−	5.19615i	−0.218797	−	0.378968i
$189$	−1.00000	−	1.73205i	−0.0727393	−	0.125988i
$190$	−6.00000			−0.435286
$191$	2.00000	+	3.46410i	0.144715	+	0.250654i	0.929267	−	0.369410i	$-0.120440\pi$
$191$	2.00000	+	3.46410i	0.144715	+	0.250654i	−0.784552	+	0.620063i	$0.787107\pi$
$192$	3.50000	−	6.06218i	0.252591	−	0.437500i
$193$	−4.50000	+	7.79423i	−0.323917	+	0.561041i	−0.981293	−	0.192522i	$-0.938333\pi$
$193$	−4.50000	+	7.79423i	−0.323917	+	0.561041i	0.657376	+	0.753563i	$0.271667\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	3.00000			0.214286
$197$	3.00000	−	5.19615i	0.213741	−	0.370211i	−0.739141	−	0.673550i	$-0.764768\pi$
$197$	3.00000	−	5.19615i	0.213741	−	0.370211i	0.952882	+	0.303340i	$0.0981018\pi$
$198$	1.00000	−	1.73205i	0.0710669	−	0.123091i
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	0.503774	−	0.863836i	$-0.331945\pi$
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	−0.999990	+	0.00436292i	$0.998611\pi$
$200$	−12.0000			−0.848528
$201$	1.00000	+	1.73205i	0.0705346	+	0.122169i
$202$	1.50000	+	2.59808i	0.105540	+	0.182800i
$203$	2.00000			0.140372
$204$	3.50000	+	6.06218i	0.245049	+	0.424437i
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$	3.00000	−	5.19615i	0.209020	−	0.362033i
$207$	−6.00000			−0.417029
$208$		0			0
$209$	12.0000			0.830057
$210$	1.00000	−	1.73205i	0.0690066	−	0.119523i
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	−0.694857	−	0.719148i	$-0.744533\pi$
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	0.970229	+	0.242190i	$0.0778659\pi$
$212$	−4.50000	−	7.79423i	−0.309061	−	0.535310i
$213$	6.00000			0.411113
$214$	−3.00000	−	5.19615i	−0.205076	−	0.355202i
$215$	−3.00000	−	5.19615i	−0.204598	−	0.354375i
$216$	−3.00000			−0.204124
$217$	−4.00000	−	6.92820i	−0.271538	−	0.470317i
$218$	1.00000	−	1.73205i	0.0677285	−	0.117309i
$219$	−5.50000	+	9.52628i	−0.371656	+	0.643726i
$220$	−2.00000			−0.134840
$221$		0			0
$222$	−1.00000			−0.0671156
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	−0.463409	−	0.886145i	$-0.653374\pi$
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	0.999128	−	0.0417488i	$-0.0132929\pi$
$224$	−5.00000	+	8.66025i	−0.334077	+	0.578638i
$225$	2.00000	+	3.46410i	0.133333	+	0.230940i
$226$	15.0000			0.997785
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	0.534577	−	0.845120i	$-0.320471\pi$
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	−0.999184	+	0.0403978i	$0.987137\pi$
$228$	−3.00000	−	5.19615i	−0.198680	−	0.344124i
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$	−3.00000	−	5.19615i	−0.197814	−	0.342624i
$231$	−2.00000	+	3.46410i	−0.131590	+	0.227921i
$232$	1.50000	−	2.59808i	0.0984798	−	0.170572i
$233$	10.0000			0.655122			0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000			0.655122			0.327561	+	0.944830i	$0.393773\pi$
$234$		0			0
$235$	−6.00000			−0.391397
$236$		0			0
$237$	−2.00000	+	3.46410i	−0.129914	+	0.225018i
$238$	7.00000	+	12.1244i	0.453743	+	0.785905i
$239$	−30.0000			−1.94054			−0.970269	−	0.242028i	$-0.922188\pi$
$239$	−30.0000			−1.94054			−0.970269	+	0.242028i	$0.922188\pi$
$240$	−0.500000	−	0.866025i	−0.0322749	−	0.0559017i
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	0.956456	−	0.291877i	$-0.0942799\pi$
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	−0.731001	+	0.682376i	$0.760947\pi$
$242$	7.00000			0.449977
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	0.500000	−	0.866025i	0.0320092	−	0.0554416i
$245$	1.50000	−	2.59808i	0.0958315	−	0.165985i
$246$	−9.00000			−0.573819
$247$		0			0
$248$	−12.0000			−0.762001
$249$	7.00000	−	12.1244i	0.443607	−	0.768350i
$250$	−4.50000	+	7.79423i	−0.284605	+	0.492950i
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	0.612159	−	0.790735i	$-0.290301\pi$
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	−0.990876	+	0.134778i	$0.956968\pi$
$252$	2.00000			0.125988
$253$	6.00000	+	10.3923i	0.377217	+	0.653359i
$254$	10.0000	+	17.3205i	0.627456	+	1.08679i
$255$	7.00000			0.438357
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	3.50000	−	6.06218i	0.218324	−	0.378148i	−0.735972	−	0.677012i	$-0.763274\pi$
$257$	3.50000	−	6.06218i	0.218324	−	0.378148i	0.954296	+	0.298864i	$0.0966077\pi$
$258$	−3.00000	+	5.19615i	−0.186772	+	0.323498i
$259$	2.00000			0.124274
$260$		0			0
$261$	−1.00000			−0.0618984
$262$	−4.00000	+	6.92820i	−0.247121	+	0.428026i
$263$	15.0000	−	25.9808i	0.924940	−	1.60204i	0.133281	−	0.991078i	$-0.457449\pi$
$263$	15.0000	−	25.9808i	0.924940	−	1.60204i	0.791658	−	0.610964i	$-0.209218\pi$
$264$	3.00000	+	5.19615i	0.184637	+	0.319801i
$265$	−9.00000			−0.552866
$266$	−6.00000	−	10.3923i	−0.367884	−	0.637193i
$267$	7.00000	+	12.1244i	0.428393	+	0.741999i
$268$	−2.00000			−0.122169
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	0.996586	−	0.0825561i	$-0.0263084\pi$
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	−0.569789	+	0.821791i	$0.692975\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$271$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$272$	7.00000			0.424437
$273$		0			0
$274$	−3.00000			−0.181237
$275$	4.00000	−	6.92820i	0.241209	−	0.417786i
$276$	3.00000	−	5.19615i	0.180579	−	0.312772i
$277$	15.5000	+	26.8468i	0.931305	+	1.61307i	0.781094	+	0.624413i	$0.214662\pi$
$277$	15.5000	+	26.8468i	0.931305	+	1.61307i	0.150210	+	0.988654i	$0.452005\pi$
$278$	−12.0000			−0.719712
$279$	2.00000	+	3.46410i	0.119737	+	0.207390i
$280$	3.00000	+	5.19615i	0.179284	+	0.310530i
$281$	19.0000			1.13344			0.566722	−	0.823909i	$-0.308211\pi$
$281$	19.0000			1.13344			0.566722	+	0.823909i	$0.308211\pi$
$282$	3.00000	+	5.19615i	0.178647	+	0.309426i
$283$	9.00000	−	15.5885i	0.534994	−	0.926638i	−0.464169	−	0.885747i	$-0.653647\pi$
$283$	9.00000	−	15.5885i	0.534994	−	0.926638i	0.999164	−	0.0408910i	$-0.0130196\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$	−6.00000			−0.355409
$286$		0			0
$287$	18.0000			1.06251
$288$	2.50000	−	4.33013i	0.147314	−	0.255155i
$289$	−16.0000	+	27.7128i	−0.941176	+	1.63017i
$290$	−0.500000	−	0.866025i	−0.0293610	−	0.0508548i
$291$	−2.00000			−0.117242
$292$	−5.50000	−	9.52628i	−0.321863	−	0.557483i
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$	−3.00000			−0.174964
$295$		0			0
$296$	1.50000	−	2.59808i	0.0871857	−	0.151010i
$297$	1.00000	−	1.73205i	0.0580259	−	0.100504i
$298$	3.00000			0.173785
$299$		0			0
$300$	−4.00000			−0.230940
$301$	6.00000	−	10.3923i	0.345834	−	0.599002i
$302$	1.00000	−	1.73205i	0.0575435	−	0.0996683i
$303$	1.50000	+	2.59808i	0.0861727	+	0.149256i
$304$	−6.00000			−0.344124
$305$	−0.500000	−	0.866025i	−0.0286299	−	0.0495885i
$306$	−3.50000	−	6.06218i	−0.200082	−	0.346552i
$307$	−14.0000			−0.799022			−0.399511	−	0.916728i	$-0.630820\pi$
$307$	−14.0000			−0.799022			−0.399511	+	0.916728i	$0.630820\pi$
$308$	−2.00000	−	3.46410i	−0.113961	−	0.197386i
$309$	3.00000	−	5.19615i	0.170664	−	0.295599i
$310$	−2.00000	+	3.46410i	−0.113592	+	0.196748i
$311$	18.0000			1.02069			0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000			1.02069			0.510343	+	0.859971i	$0.329518\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$	−1.50000	+	2.59808i	−0.0846499	+	0.146618i
$315$	1.00000	−	1.73205i	0.0563436	−	0.0975900i
$316$	−2.00000	−	3.46410i	−0.112509	−	0.194871i
$317$	25.0000			1.40414			0.702070	−	0.712108i	$-0.252259\pi$
$317$	25.0000			1.40414			0.702070	+	0.712108i	$0.252259\pi$
$318$	4.50000	+	7.79423i	0.252347	+	0.437079i
$319$	1.00000	+	1.73205i	0.0559893	+	0.0969762i
$320$	7.00000			0.391312
$321$	−3.00000	−	5.19615i	−0.167444	−	0.290021i
$322$	6.00000	−	10.3923i	0.334367	−	0.579141i
$323$	21.0000	−	36.3731i	1.16847	−	2.02385i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−4.00000			−0.221540
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$	13.5000	−	23.3827i	0.745413	−	1.29109i
$329$	−6.00000	−	10.3923i	−0.330791	−	0.572946i
$330$	2.00000			0.110096
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	0.805812	−	0.592172i	$-0.201729\pi$
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	−0.915742	+	0.401768i	$0.868396\pi$
$332$	7.00000	+	12.1244i	0.384175	+	0.665410i
$333$	−1.00000			−0.0547997
$334$	−8.00000	−	13.8564i	−0.437741	−	0.758189i
$335$	−1.00000	+	1.73205i	−0.0546358	+	0.0946320i
$336$	1.00000	−	1.73205i	0.0545545	−	0.0944911i
$337$	−33.0000			−1.79762			−0.898812	−	0.438334i	$-0.855569\pi$
$337$	−33.0000			−1.79762			−0.898812	+	0.438334i	$0.855569\pi$
$338$		0			0
$339$	15.0000			0.814688
$340$	−3.50000	+	6.06218i	−0.189814	+	0.328768i
$341$	4.00000	−	6.92820i	0.216612	−	0.375183i
$342$	3.00000	+	5.19615i	0.162221	+	0.280976i
$343$	20.0000			1.07990
$344$	−9.00000	−	15.5885i	−0.485247	−	0.840473i
$345$	−3.00000	−	5.19615i	−0.161515	−	0.279751i
$346$	6.00000			0.322562
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	0.516667	−	0.856186i	$-0.327172\pi$
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	−0.999813	+	0.0193540i	$0.993839\pi$
$348$	0.500000	−	0.866025i	0.0268028	−	0.0464238i
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	0.274011	+	0.961727i	$0.411649\pi$
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	−0.969885	+	0.243563i	$0.921684\pi$
$350$	−8.00000			−0.427618
$351$		0			0
$352$	−10.0000			−0.533002
$353$	−5.50000	+	9.52628i	−0.292735	+	0.507033i	−0.974456	−	0.224580i	$-0.927899\pi$
$353$	−5.50000	+	9.52628i	−0.292735	+	0.507033i	0.681720	+	0.731613i	$0.261232\pi$
$354$		0			0
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$	−14.0000			−0.741999
$357$	7.00000	+	12.1244i	0.370479	+	0.641689i
$358$	−1.00000	−	1.73205i	−0.0528516	−	0.0915417i
$359$	18.0000			0.950004			0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000			0.950004			0.475002	+	0.879985i	$0.342447\pi$
$360$	−1.50000	−	2.59808i	−0.0790569	−	0.136931i
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	−3.50000	+	6.06218i	−0.183956	+	0.318621i
$363$	7.00000			0.367405
$364$		0			0
$365$	−11.0000			−0.575766
$366$	−0.500000	+	0.866025i	−0.0261354	+	0.0452679i
$367$	−5.00000	+	8.66025i	−0.260998	+	0.452062i	−0.966507	−	0.256639i	$-0.917385\pi$
$367$	−5.00000	+	8.66025i	−0.260998	+	0.452062i	0.705509	+	0.708700i	$0.250718\pi$
$368$	−3.00000	−	5.19615i	−0.156386	−	0.270868i
$369$	−9.00000			−0.468521
$370$	−0.500000	−	0.866025i	−0.0259938	−	0.0450225i
$371$	−9.00000	−	15.5885i	−0.467257	−	0.809312i
$372$	−4.00000			−0.207390
$373$	5.50000	+	9.52628i	0.284779	+	0.493252i	0.972556	−	0.232671i	$-0.0747464\pi$
$373$	5.50000	+	9.52628i	0.284779	+	0.493252i	−0.687776	+	0.725923i	$0.741413\pi$
$374$	−7.00000	+	12.1244i	−0.361961	+	0.626936i
$375$	−4.50000	+	7.79423i	−0.232379	+	0.402492i
$376$	−18.0000			−0.928279
$377$		0			0
$378$	−2.00000			−0.102869
$379$	−18.0000	+	31.1769i	−0.924598	+	1.60145i	−0.132391	+	0.991198i	$0.542266\pi$
$379$	−18.0000	+	31.1769i	−0.924598	+	1.60145i	−0.792207	+	0.610253i	$0.791068\pi$
$380$	3.00000	−	5.19615i	0.153897	−	0.266557i
$381$	10.0000	+	17.3205i	0.512316	+	0.887357i
$382$	4.00000			0.204658
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	0.949938	−	0.312437i	$-0.101145\pi$
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	−0.745548	+	0.666452i	$0.767812\pi$
$384$	1.50000	+	2.59808i	0.0765466	+	0.132583i
$385$	−4.00000			−0.203859
$386$	4.50000	+	7.79423i	0.229044	+	0.396716i
$387$	−3.00000	+	5.19615i	−0.152499	+	0.264135i
$388$	1.00000	−	1.73205i	0.0507673	−	0.0879316i
$389$	19.0000			0.963338			0.481669	−	0.876353i	$-0.340031\pi$
$389$	19.0000			0.963338			0.481669	+	0.876353i	$0.340031\pi$
$390$		0			0
$391$	42.0000			2.12403
$392$	4.50000	−	7.79423i	0.227284	−	0.393668i
$393$	−4.00000	+	6.92820i	−0.201773	+	0.349482i
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$	−4.00000			−0.201262
$396$	1.00000	+	1.73205i	0.0502519	+	0.0870388i
$397$	−17.0000	−	29.4449i	−0.853206	−	1.47780i	−0.878300	−	0.478110i	$-0.841322\pi$
$397$	−17.0000	−	29.4449i	−0.853206	−	1.47780i	0.0250943	−	0.999685i	$-0.492011\pi$
$398$	−14.0000			−0.701757
$399$	−6.00000	−	10.3923i	−0.300376	−	0.520266i
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	0.500000	−	0.866025i	0.0249688	−	0.0432472i	−0.853271	−	0.521468i	$-0.825385\pi$
$401$	0.500000	−	0.866025i	0.0249688	−	0.0432472i	0.878240	+	0.478220i	$0.158718\pi$
$402$	2.00000			0.0997509
$403$		0			0
$404$	−3.00000			−0.149256
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	1.00000	−	1.73205i	0.0496292	−	0.0859602i
$407$	1.00000	+	1.73205i	0.0495682	+	0.0858546i
$408$	21.0000			1.03965
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	0.939490	−	0.342578i	$-0.111300\pi$
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	−0.766426	+	0.642333i	$0.777967\pi$
$410$	−4.50000	−	7.79423i	−0.222239	−	0.384930i
$411$	−3.00000			−0.147979
$412$	3.00000	+	5.19615i	0.147799	+	0.255996i
$413$		0			0
$414$	−3.00000	+	5.19615i	−0.147442	+	0.255377i
$415$	14.0000			0.687233
$416$		0			0
$417$	−12.0000			−0.587643
$418$	6.00000	−	10.3923i	0.293470	−	0.508304i
$419$	−8.00000	+	13.8564i	−0.390826	+	0.676930i	−0.992559	−	0.121768i	$-0.961144\pi$
$419$	−8.00000	+	13.8564i	−0.390826	+	0.676930i	0.601733	+	0.798697i	$0.294477\pi$
$420$	1.00000	+	1.73205i	0.0487950	+	0.0845154i
$421$	19.0000			0.926003			0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000			0.926003			0.463002	+	0.886357i	$0.346772\pi$
$422$	−4.00000	−	6.92820i	−0.194717	−	0.337260i
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$	−27.0000			−1.31124
$425$	−14.0000	−	24.2487i	−0.679100	−	1.17624i
$426$	3.00000	−	5.19615i	0.145350	−	0.251754i
$427$	1.00000	−	1.73205i	0.0483934	−	0.0838198i
$428$	6.00000			0.290021
$429$		0			0
$430$	−6.00000			−0.289346
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	0.237460	+	0.971397i	$0.423685\pi$
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	−0.959985	+	0.280052i	$0.909648\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−9.50000	−	16.4545i	−0.456541	−	0.790752i	0.542234	−	0.840227i	$-0.317578\pi$
$433$	−9.50000	−	16.4545i	−0.456541	−	0.790752i	−0.998775	+	0.0494752i	$0.984245\pi$
$434$	−8.00000			−0.384012
$435$	−0.500000	−	0.866025i	−0.0239732	−	0.0415227i
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	−36.0000			−1.72211
$438$	5.50000	+	9.52628i	0.262800	+	0.455183i
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	−0.983310	−	0.181938i	$-0.941763\pi$
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	0.649218	+	0.760602i	$0.275096\pi$
$440$	−3.00000	+	5.19615i	−0.143019	+	0.247717i
$441$	−3.00000			−0.142857
$442$		0			0
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$	0.500000	−	0.866025i	0.0237289	−	0.0410997i
$445$	−7.00000	+	12.1244i	−0.331832	+	0.574750i
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$	3.00000			0.141895
$448$	7.00000	+	12.1244i	0.330719	+	0.572822i
$449$	17.0000	+	29.4449i	0.802280	+	1.38959i	0.918112	+	0.396320i	$0.129713\pi$
$449$	17.0000	+	29.4449i	0.802280	+	1.38959i	−0.115833	+	0.993269i	$0.536954\pi$
$450$	4.00000			0.188562
$451$	9.00000	+	15.5885i	0.423793	+	0.734032i
$452$	−7.50000	+	12.9904i	−0.352770	+	0.611016i
$453$	1.00000	−	1.73205i	0.0469841	−	0.0813788i
$454$	−14.0000			−0.657053
$455$		0			0
$456$	−18.0000			−0.842927
$457$	−6.50000	+	11.2583i	−0.304057	+	0.526642i	−0.977051	−	0.213006i	$-0.931675\pi$
$457$	−6.50000	+	11.2583i	−0.304057	+	0.526642i	0.672994	+	0.739648i	$0.265008\pi$
$458$	11.0000	−	19.0526i	0.513996	−	0.890268i
$459$	−3.50000	−	6.06218i	−0.163366	−	0.282958i
$460$	6.00000			0.279751
$461$	9.50000	+	16.4545i	0.442459	+	0.766362i	0.997871	−	0.0652135i	$-0.0207728\pi$
$461$	9.50000	+	16.4545i	0.442459	+	0.766362i	−0.555412	+	0.831575i	$0.687440\pi$
$462$	2.00000	+	3.46410i	0.0930484	+	0.161165i
$463$	26.0000			1.20832			0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000			1.20832			0.604161	+	0.796862i	$0.293508\pi$
$464$	−0.500000	−	0.866025i	−0.0232119	−	0.0402042i
$465$	−2.00000	+	3.46410i	−0.0927478	+	0.160644i
$466$	5.00000	−	8.66025i	0.231621	−	0.401179i
$467$	6.00000			0.277647			0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000			0.277647			0.138823	+	0.990317i	$0.455668\pi$
$468$		0			0
$469$	−4.00000			−0.184703
$470$	−3.00000	+	5.19615i	−0.138380	+	0.239681i
$471$	−1.50000	+	2.59808i	−0.0691164	+	0.119713i
$472$		0			0
$473$	12.0000			0.551761
$474$	2.00000	+	3.46410i	0.0918630	+	0.159111i
$475$	12.0000	+	20.7846i	0.550598	+	0.953663i
$476$	−14.0000			−0.641689
$477$	4.50000	+	7.79423i	0.206041	+	0.356873i
$478$	−15.0000	+	25.9808i	−0.686084	+	1.18833i
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$	5.00000			0.228218
$481$		0			0
$482$	7.00000			0.318841
$483$	6.00000	−	10.3923i	0.273009	−	0.472866i
$484$	−3.50000	+	6.06218i	−0.159091	+	0.275554i
$485$	−1.00000	−	1.73205i	−0.0454077	−	0.0786484i
$486$	1.00000			0.0453609
$487$	9.00000	+	15.5885i	0.407829	+	0.706380i	0.994646	−	0.103339i	$-0.0329526\pi$
$487$	9.00000	+	15.5885i	0.407829	+	0.706380i	−0.586817	+	0.809719i	$0.699619\pi$
$488$	−1.50000	−	2.59808i	−0.0679018	−	0.117609i
$489$	−4.00000			−0.180886
$490$	−1.50000	−	2.59808i	−0.0677631	−	0.117369i
$491$	−3.00000	+	5.19615i	−0.135388	+	0.234499i	−0.925746	−	0.378147i	$-0.876561\pi$
$491$	−3.00000	+	5.19615i	−0.135388	+	0.234499i	0.790358	+	0.612646i	$0.209895\pi$
$492$	4.50000	−	7.79423i	0.202876	−	0.351391i
$493$	7.00000			0.315264
$494$		0			0
$495$	2.00000			0.0898933
$496$	−2.00000	+	3.46410i	−0.0898027	+	0.155543i
$497$	−6.00000	+	10.3923i	−0.269137	+	0.466159i
$498$	−7.00000	−	12.1244i	−0.313678	−	0.543305i
$499$	−24.0000			−1.07439			−0.537194	−	0.843459i	$-0.680516\pi$
$499$	−24.0000			−1.07439			−0.537194	+	0.843459i	$0.680516\pi$
$500$	−4.50000	−	7.79423i	−0.201246	−	0.348569i
$501$	−8.00000	−	13.8564i	−0.357414	−	0.619059i
$502$	−12.0000			−0.535586
$503$	1.00000	+	1.73205i	0.0445878	+	0.0772283i	0.887458	−	0.460889i	$-0.152469\pi$
$503$	1.00000	+	1.73205i	0.0445878	+	0.0772283i	−0.842870	+	0.538117i	$0.819136\pi$
$504$	3.00000	−	5.19615i	0.133631	−	0.231455i
$505$	−1.50000	+	2.59808i	−0.0667491	+	0.115613i
$506$	12.0000			0.533465
$507$		0			0
$508$	−20.0000			−0.887357
$509$	3.50000	−	6.06218i	0.155135	−	0.268701i	−0.777973	−	0.628297i	$-0.783752\pi$
$509$	3.50000	−	6.06218i	0.155135	−	0.268701i	0.933108	+	0.359596i	$0.117085\pi$
$510$	3.50000	−	6.06218i	0.154983	−	0.268438i
$511$	−11.0000	−	19.0526i	−0.486611	−	0.842836i
$512$	11.0000			0.486136
$513$	3.00000	+	5.19615i	0.132453	+	0.229416i
$514$	−3.50000	−	6.06218i	−0.154378	−	0.267391i
$515$	6.00000			0.264392
$516$	−3.00000	−	5.19615i	−0.132068	−	0.228748i
$517$	6.00000	−	10.3923i	0.263880	−	0.457053i
$518$	1.00000	−	1.73205i	0.0439375	−	0.0761019i
$519$	6.00000			0.263371
$520$		0			0
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$	−0.500000	+	0.866025i	−0.0218844	+	0.0379049i
$523$	−7.00000	+	12.1244i	−0.306089	+	0.530161i	−0.977503	−	0.210921i	$-0.932354\pi$
$523$	−7.00000	+	12.1244i	−0.306089	+	0.530161i	0.671414	+	0.741082i	$0.265687\pi$
$524$	−4.00000	−	6.92820i	−0.174741	−	0.302660i
$525$	−8.00000			−0.349149
$526$	−15.0000	−	25.9808i	−0.654031	−	1.13282i
$527$	−14.0000	−	24.2487i	−0.609850	−	1.05629i
$528$	2.00000			0.0870388
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	−4.50000	+	7.79423i	−0.195468	+	0.338560i
$531$		0			0
$532$	12.0000			0.520266
$533$		0			0
$534$	14.0000			0.605839
$535$	3.00000	−	5.19615i	0.129701	−	0.224649i
$536$	−3.00000	+	5.19615i	−0.129580	+	0.224440i
$537$	−1.00000	−	1.73205i	−0.0431532	−	0.0747435i
$538$	14.0000			0.603583
$539$	3.00000	+	5.19615i	0.129219	+	0.223814i
$540$	−0.500000	−	0.866025i	−0.0215166	−	0.0372678i
$541$	−45.0000			−1.93470			−0.967351	−	0.253442i	$-0.918437\pi$
$541$	−45.0000			−1.93470			−0.967351	+	0.253442i	$0.918437\pi$
$542$		0			0
$543$	−3.50000	+	6.06218i	−0.150199	+	0.260153i
$544$	−17.5000	+	30.3109i	−0.750306	+	1.29957i
$545$	2.00000			0.0856706
$546$		0			0
$547$	−26.0000			−1.11168			−0.555840	−	0.831289i	$-0.687603\pi$
$547$	−26.0000			−1.11168			−0.555840	+	0.831289i	$0.687603\pi$
$548$	1.50000	−	2.59808i	0.0640768	−	0.110984i
$549$	−0.500000	+	0.866025i	−0.0213395	+	0.0369611i
$550$	−4.00000	−	6.92820i	−0.170561	−	0.295420i
$551$	−6.00000			−0.255609
$552$	−9.00000	−	15.5885i	−0.383065	−	0.663489i
$553$	−4.00000	−	6.92820i	−0.170097	−	0.294617i
$554$	31.0000			1.31706
$555$	−0.500000	−	0.866025i	−0.0212238	−	0.0367607i
$556$	6.00000	−	10.3923i	0.254457	−	0.440732i
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	−0.945473	−	0.325701i	$-0.894400\pi$
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	0.754802	+	0.655953i	$0.227733\pi$
$558$	4.00000			0.169334
$559$		0			0
$560$	2.00000			0.0845154
$561$	−7.00000	+	12.1244i	−0.295540	+	0.511891i
$562$	9.50000	−	16.4545i	0.400733	−	0.694090i
$563$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$563$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$564$	−6.00000			−0.252646
$565$	7.50000	+	12.9904i	0.315527	+	0.546509i
$566$	−9.00000	−	15.5885i	−0.378298	−	0.655232i
$567$	−2.00000			−0.0839921
$568$	9.00000	+	15.5885i	0.377632	+	0.654077i
$569$	−11.0000	+	19.0526i	−0.461144	+	0.798725i	−0.999018	−	0.0443003i	$-0.985894\pi$
$569$	−11.0000	+	19.0526i	−0.461144	+	0.798725i	0.537874	+	0.843025i	$0.319228\pi$
$570$	−3.00000	+	5.19615i	−0.125656	+	0.217643i
$571$	26.0000			1.08807			0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000			1.08807			0.544033	+	0.839064i	$0.316897\pi$
$572$		0			0
$573$	4.00000			0.167102
$574$	9.00000	−	15.5885i	0.375653	−	0.650650i
$575$	−12.0000	+	20.7846i	−0.500435	+	0.866778i
$576$	−3.50000	−	6.06218i	−0.145833	−	0.252591i
$577$	−11.0000			−0.457936			−0.228968	−	0.973434i	$-0.573535\pi$
$577$	−11.0000			−0.457936			−0.228968	+	0.973434i	$0.573535\pi$
$578$	16.0000	+	27.7128i	0.665512	+	1.15270i
$579$	4.50000	+	7.79423i	0.187014	+	0.323917i
$580$	1.00000			0.0415227
$581$	14.0000	+	24.2487i	0.580818	+	1.00601i
$582$	−1.00000	+	1.73205i	−0.0414513	+	0.0717958i
$583$	9.00000	−	15.5885i	0.372742	−	0.645608i
$584$	−33.0000			−1.36555
$585$		0			0
$586$	−9.00000			−0.371787
$587$	8.00000	−	13.8564i	0.330195	−	0.571915i	−0.652355	−	0.757914i	$-0.726219\pi$
$587$	8.00000	−	13.8564i	0.330195	−	0.571915i	0.982550	+	0.185999i	$0.0595520\pi$
$588$	1.50000	−	2.59808i	0.0618590	−	0.107143i
$589$	12.0000	+	20.7846i	0.494451	+	0.856415i
$590$		0			0
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$	−0.500000	−	0.866025i	−0.0205499	−	0.0355934i
$593$	−13.0000			−0.533846			−0.266923	−	0.963718i	$-0.586007\pi$
$593$	−13.0000			−0.533846			−0.266923	+	0.963718i	$0.586007\pi$
$594$	−1.00000	−	1.73205i	−0.0410305	−	0.0710669i
$595$	−7.00000	+	12.1244i	−0.286972	+	0.497050i
$596$	−1.50000	+	2.59808i	−0.0614424	+	0.106421i
$597$	−14.0000			−0.572982
$598$		0			0
$599$	−16.0000			−0.653742			−0.326871	−	0.945069i	$-0.605994\pi$
$599$	−16.0000			−0.653742			−0.326871	+	0.945069i	$0.605994\pi$
$600$	−6.00000	+	10.3923i	−0.244949	+	0.424264i
$601$	2.50000	−	4.33013i	0.101977	−	0.176630i	−0.810522	−	0.585708i	$-0.800816\pi$
$601$	2.50000	−	4.33013i	0.101977	−	0.176630i	0.912499	+	0.409079i	$0.134150\pi$
$602$	−6.00000	−	10.3923i	−0.244542	−	0.423559i
$603$	2.00000			0.0814463
$604$	1.00000	+	1.73205i	0.0406894	+	0.0704761i
$605$	3.50000	+	6.06218i	0.142295	+	0.246463i
$606$	3.00000			0.121867
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	0.773358	−	0.633970i	$-0.218576\pi$
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	−0.935713	+	0.352763i	$0.885242\pi$
$608$	15.0000	−	25.9808i	0.608330	−	1.05366i
$609$	1.00000	−	1.73205i	0.0405220	−	0.0701862i
$610$	−1.00000			−0.0404888
$611$		0			0
$612$	7.00000			0.282958
$613$	−11.5000	+	19.9186i	−0.464481	+	0.804504i	−0.999178	−	0.0405396i	$-0.987092\pi$
$613$	−11.5000	+	19.9186i	−0.464481	+	0.804504i	0.534697	+	0.845044i	$0.320426\pi$
$614$	−7.00000	+	12.1244i	−0.282497	+	0.489299i
$615$	−4.50000	−	7.79423i	−0.181458	−	0.314294i
$616$	−12.0000			−0.483494
$617$	6.50000	+	11.2583i	0.261680	+	0.453243i	0.966689	−	0.255956i	$-0.0823901\pi$
$617$	6.50000	+	11.2583i	0.261680	+	0.453243i	−0.705008	+	0.709199i	$0.749057\pi$
$618$	−3.00000	−	5.19615i	−0.120678	−	0.209020i
$619$	24.0000			0.964641			0.482321	−	0.875995i	$-0.339794\pi$
$619$	24.0000			0.964641			0.482321	+	0.875995i	$0.339794\pi$
$620$	−2.00000	−	3.46410i	−0.0803219	−	0.139122i
$621$	−3.00000	+	5.19615i	−0.120386	+	0.208514i
$622$	9.00000	−	15.5885i	0.360867	−	0.625040i
$623$	−28.0000			−1.12180
$624$		0			0
$625$	11.0000			0.440000
$626$	3.00000	−	5.19615i	0.119904	−	0.207680i
$627$	6.00000	−	10.3923i	0.239617	−	0.415029i
$628$	−1.50000	−	2.59808i	−0.0598565	−	0.103675i
$629$	7.00000			0.279108
$630$	−1.00000	−	1.73205i	−0.0398410	−	0.0690066i
$631$	10.0000	+	17.3205i	0.398094	+	0.689519i	0.993491	−	0.113913i	$-0.0363385\pi$
$631$	10.0000	+	17.3205i	0.398094	+	0.689519i	−0.595397	+	0.803432i	$0.703005\pi$
$632$	−12.0000			−0.477334
$633$	−4.00000	−	6.92820i	−0.158986	−	0.275371i
$634$	12.5000	−	21.6506i	0.496438	−	0.859857i
$635$	−10.0000	+	17.3205i	−0.396838	+	0.687343i
$636$	−9.00000			−0.356873
$637$		0			0
$638$	2.00000			0.0791808
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	15.5000	+	26.8468i	0.612213	+	1.06038i	0.990867	+	0.134846i	$0.0430539\pi$
$641$	15.5000	+	26.8468i	0.612213	+	1.06038i	−0.378653	+	0.925539i	$0.623613\pi$
$642$	−6.00000			−0.236801
$643$	−8.00000	−	13.8564i	−0.315489	−	0.546443i	0.664052	−	0.747686i	$-0.268835\pi$
$643$	−8.00000	−	13.8564i	−0.315489	−	0.546443i	−0.979541	+	0.201243i	$0.935502\pi$
$644$	6.00000	+	10.3923i	0.236433	+	0.409514i
$645$	−6.00000			−0.236250
$646$	−21.0000	−	36.3731i	−0.826234	−	1.43108i
$647$	16.0000	−	27.7128i	0.629025	−	1.08950i	−0.358723	−	0.933444i	$-0.616788\pi$
$647$	16.0000	−	27.7128i	0.629025	−	1.08950i	0.987748	−	0.156059i	$-0.0498790\pi$
$648$	−1.50000	+	2.59808i	−0.0589256	+	0.102062i
$649$		0			0
$650$		0			0
$651$	−8.00000			−0.313545
$652$	2.00000	−	3.46410i	0.0783260	−	0.135665i
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	−0.801337	−	0.598213i	$-0.795878\pi$
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	0.918736	+	0.394872i	$0.129211\pi$
$654$	−1.00000	−	1.73205i	−0.0391031	−	0.0677285i
$655$	−8.00000			−0.312586
$656$	−4.50000	−	7.79423i	−0.175695	−	0.304314i
$657$	5.50000	+	9.52628i	0.214575	+	0.371656i
$658$	−12.0000			−0.467809
$659$	4.00000	+	6.92820i	0.155818	+	0.269884i	0.933357	−	0.358951i	$-0.116865\pi$
$659$	4.00000	+	6.92820i	0.155818	+	0.269884i	−0.777539	+	0.628835i	$0.783532\pi$
$660$	−1.00000	+	1.73205i	−0.0389249	+	0.0674200i
$661$	22.5000	−	38.9711i	0.875149	−	1.51580i	0.0185442	−	0.999828i	$-0.494097\pi$
$661$	22.5000	−	38.9711i	0.875149	−	1.51580i	0.856604	−	0.515974i	$-0.172570\pi$
$662$	−4.00000			−0.155464
$663$		0			0
$664$	42.0000			1.62992
$665$	6.00000	−	10.3923i	0.232670	−	0.402996i
$666$	−0.500000	+	0.866025i	−0.0193746	+	0.0335578i
$667$	−3.00000	−	5.19615i	−0.116160	−	0.201196i
$668$	16.0000			0.619059
$669$	−8.00000	−	13.8564i	−0.309298	−	0.535720i
$670$	1.00000	+	1.73205i	0.0386334	+	0.0669150i
$671$	2.00000			0.0772091
$672$	5.00000	+	8.66025i	0.192879	+	0.334077i
$673$	14.5000	−	25.1147i	0.558934	−	0.968102i	−0.438652	−	0.898657i	$-0.644544\pi$
$673$	14.5000	−	25.1147i	0.558934	−	0.968102i	0.997586	−	0.0694449i	$-0.0221228\pi$
$674$	−16.5000	+	28.5788i	−0.635556	+	1.10082i
$675$	4.00000			0.153960
$676$		0			0
$677$	34.0000			1.30673			0.653363	−	0.757045i	$-0.273358\pi$
$677$	34.0000			1.30673			0.653363	+	0.757045i	$0.273358\pi$
$678$	7.50000	−	12.9904i	0.288036	−	0.498893i
$679$	2.00000	−	3.46410i	0.0767530	−	0.132940i
$680$	10.5000	+	18.1865i	0.402657	+	0.697422i
$681$	−14.0000			−0.536481
$682$	−4.00000	−	6.92820i	−0.153168	−	0.265295i
$683$	−12.0000	−	20.7846i	−0.459167	−	0.795301i	0.539750	−	0.841825i	$-0.318519\pi$
$683$	−12.0000	−	20.7846i	−0.459167	−	0.795301i	−0.998917	+	0.0465244i	$0.985185\pi$
$684$	−6.00000			−0.229416
$685$	−1.50000	−	2.59808i	−0.0573121	−	0.0992674i
$686$	10.0000	−	17.3205i	0.381802	−	0.661300i
$687$	11.0000	−	19.0526i	0.419676	−	0.726900i
$688$	−6.00000			−0.228748
$689$		0			0
$690$	−6.00000			−0.228416
$691$	21.0000	−	36.3731i	0.798878	−	1.38370i	−0.121470	−	0.992595i	$-0.538761\pi$
$691$	21.0000	−	36.3731i	0.798878	−	1.38370i	0.920348	−	0.391102i	$-0.127906\pi$
$692$	−3.00000	+	5.19615i	−0.114043	+	0.197528i
$693$	2.00000	+	3.46410i	0.0759737	+	0.131590i
$694$	−18.0000			−0.683271
$695$	−6.00000	−	10.3923i	−0.227593	−	0.394203i
$696$	−1.50000	−	2.59808i	−0.0568574	−	0.0984798i
$697$	63.0000			2.38630
$698$	13.0000	+	22.5167i	0.492057	+	0.852268i
$699$	5.00000	−	8.66025i	0.189117	−	0.327561i
$700$	4.00000	−	6.92820i	0.151186	−	0.261861i
$701$	2.00000			0.0755390			0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000			0.0755390			0.0377695	+	0.999286i	$0.487975\pi$
$702$		0			0
$703$	−6.00000			−0.226294
$704$	−7.00000	+	12.1244i	−0.263822	+	0.456954i
$705$	−3.00000	+	5.19615i	−0.112987	+	0.195698i
$706$	5.50000	+	9.52628i	0.206995	+	0.358526i
$707$	−6.00000			−0.225653
$708$		0			0
$709$	−5.50000	−	9.52628i	−0.206557	−	0.357767i	0.744071	−	0.668101i	$-0.232892\pi$
$709$	−5.50000	−	9.52628i	−0.206557	−	0.357767i	−0.950628	+	0.310334i	$0.899559\pi$
$710$	6.00000			0.225176
$711$	2.00000	+	3.46410i	0.0750059	+	0.129914i
$712$	−21.0000	+	36.3731i	−0.787008	+	1.36314i
$713$	−12.0000	+	20.7846i	−0.449404	+	0.778390i
$714$	14.0000			0.523937
$715$		0			0
$716$	2.00000			0.0747435
$717$	−15.0000	+	25.9808i	−0.560185	+	0.970269i
$718$	9.00000	−	15.5885i	0.335877	−	0.581756i
$719$	24.0000	+	41.5692i	0.895049	+	1.55027i	0.833744	+	0.552151i	$0.186193\pi$
$719$	24.0000	+	41.5692i	0.895049	+	1.55027i	0.0613050	+	0.998119i	$0.480474\pi$
$720$	−1.00000			−0.0372678
$721$	6.00000	+	10.3923i	0.223452	+	0.387030i
$722$	8.50000	+	14.7224i	0.316337	+	0.547912i
$723$	7.00000			0.260333
$724$	−3.50000	−	6.06218i	−0.130076	−	0.225299i
$725$	−2.00000	+	3.46410i	−0.0742781	+	0.128654i
$726$	3.50000	−	6.06218i	0.129897	−	0.224989i
$727$	14.0000			0.519231			0.259616	−	0.965712i	$-0.416404\pi$
$727$	14.0000			0.519231			0.259616	+	0.965712i	$0.416404\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−5.50000	+	9.52628i	−0.203564	+	0.352583i
$731$	21.0000	−	36.3731i	0.776713	−	1.34531i
$732$	−0.500000	−	0.866025i	−0.0184805	−	0.0320092i
$733$	15.0000			0.554038			0.277019	−	0.960864i	$-0.410654\pi$
$733$	15.0000			0.554038			0.277019	+	0.960864i	$0.410654\pi$
$734$	5.00000	+	8.66025i	0.184553	+	0.319656i
$735$	−1.50000	−	2.59808i	−0.0553283	−	0.0958315i
$736$	30.0000			1.10581
$737$	−2.00000	−	3.46410i	−0.0736709	−	0.127602i
$738$	−4.50000	+	7.79423i	−0.165647	+	0.286910i
$739$	−8.00000	+	13.8564i	−0.294285	+	0.509716i	−0.974818	−	0.223001i	$-0.928415\pi$
$739$	−8.00000	+	13.8564i	−0.294285	+	0.509716i	0.680534	+	0.732717i	$0.261748\pi$
$740$	1.00000			0.0367607
$741$		0			0
$742$	−18.0000			−0.660801
$743$	−18.0000	+	31.1769i	−0.660356	+	1.14377i	0.320166	+	0.947361i	$0.396261\pi$
$743$	−18.0000	+	31.1769i	−0.660356	+	1.14377i	−0.980522	+	0.196409i	$0.937072\pi$
$744$	−6.00000	+	10.3923i	−0.219971	+	0.381000i
$745$	1.50000	+	2.59808i	0.0549557	+	0.0951861i
$746$	11.0000			0.402739
$747$	−7.00000	−	12.1244i	−0.256117	−	0.443607i
$748$	−7.00000	−	12.1244i	−0.255945	−	0.443310i
$749$	12.0000			0.438470
$750$	4.50000	+	7.79423i	0.164317	+	0.284605i
$751$	17.0000	−	29.4449i	0.620339	−	1.07446i	−0.369084	−	0.929396i	$-0.620328\pi$
$751$	17.0000	−	29.4449i	0.620339	−	1.07446i	0.989423	−	0.145062i	$-0.0463382\pi$
$752$	−3.00000	+	5.19615i	−0.109399	+	0.189484i
$753$	−12.0000			−0.437304
$754$		0			0
$755$	2.00000			0.0727875
$756$	1.00000	−	1.73205i	0.0363696	−	0.0629941i
$757$	25.0000	−	43.3013i	0.908640	−	1.57381i	0.0926859	−	0.995695i	$-0.470455\pi$
$757$	25.0000	−	43.3013i	0.908640	−	1.57381i	0.815955	−	0.578116i	$-0.196212\pi$
$758$	18.0000	+	31.1769i	0.653789	+	1.13240i
$759$	12.0000			0.435572
$760$	−9.00000	−	15.5885i	−0.326464	−	0.565453i
$761$	25.0000	+	43.3013i	0.906249	+	1.56967i	0.819231	+	0.573463i	$0.194400\pi$
$761$	25.0000	+	43.3013i	0.906249	+	1.56967i	0.0870179	+	0.996207i	$0.472266\pi$
$762$	20.0000			0.724524
$763$	2.00000	+	3.46410i	0.0724049	+	0.125409i
$764$	−2.00000	+	3.46410i	−0.0723575	+	0.125327i
$765$	3.50000	−	6.06218i	0.126543	−	0.219179i
$766$	8.00000			0.289052
$767$		0			0
$768$	17.0000			0.613435
$769$	15.0000	−	25.9808i	0.540914	−	0.936890i	−0.457938	−	0.888984i	$-0.651412\pi$
$769$	15.0000	−	25.9808i	0.540914	−	0.936890i	0.998852	−	0.0479061i	$-0.0152548\pi$
$770$	−2.00000	+	3.46410i	−0.0720750	+	0.124838i
$771$	−3.50000	−	6.06218i	−0.126049	−	0.218324i
$772$	−9.00000			−0.323917
$773$	−7.00000	−	12.1244i	−0.251773	−	0.436083i	0.712241	−	0.701935i	$-0.247680\pi$
$773$	−7.00000	−	12.1244i	−0.251773	−	0.436083i	−0.964014	+	0.265852i	$0.914347\pi$
$774$	3.00000	+	5.19615i	0.107833	+	0.186772i
$775$	16.0000			0.574737
$776$	−3.00000	−	5.19615i	−0.107694	−	0.186531i
$777$	1.00000	−	1.73205i	0.0358748	−	0.0621370i
$778$	9.50000	−	16.4545i	0.340592	−	0.589922i

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} +3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} +3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-1.00000 + 1.73205i) q^{11} +1.00000 q^{12} +2.00000 q^{14} +(0.500000 - 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.50000 + 6.06218i) q^{17} -1.00000 q^{18} +(-3.00000 - 5.19615i) q^{19} +(0.500000 + 0.866025i) q^{20} +2.00000 q^{21} +(1.00000 + 1.73205i) q^{22} +(3.00000 - 5.19615i) q^{23} +(1.50000 - 2.59808i) q^{24} -4.00000 q^{25} -1.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} +(0.500000 - 0.866025i) q^{29} +(-0.500000 - 0.866025i) q^{30} -4.00000 q^{31} +(2.50000 + 4.33013i) q^{32} +(1.00000 + 1.73205i) q^{33} +7.00000 q^{34} +(1.00000 + 1.73205i) q^{35} +(0.500000 - 0.866025i) q^{36} +(0.500000 - 0.866025i) q^{37} -6.00000 q^{38} +3.00000 q^{40} +(4.50000 - 7.79423i) q^{41} +(1.00000 - 1.73205i) q^{42} +(-3.00000 - 5.19615i) q^{43} -2.00000 q^{44} +(-0.500000 - 0.866025i) q^{45} +(-3.00000 - 5.19615i) q^{46} -6.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +(-2.00000 + 3.46410i) q^{50} +7.00000 q^{51} -9.00000 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.00000 + 1.73205i) q^{55} +(3.00000 + 5.19615i) q^{56} -6.00000 q^{57} +(-0.500000 - 0.866025i) q^{58} +1.00000 q^{60} +(-0.500000 - 0.866025i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(1.00000 - 1.73205i) q^{63} +7.00000 q^{64} +2.00000 q^{66} +(-1.00000 + 1.73205i) q^{67} +(-3.50000 + 6.06218i) q^{68} +(-3.00000 - 5.19615i) q^{69} +2.00000 q^{70} +(3.00000 + 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} -11.0000 q^{73} +(-0.500000 - 0.866025i) q^{74} +(-2.00000 + 3.46410i) q^{75} +(3.00000 - 5.19615i) q^{76} -4.00000 q^{77} -4.00000 q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.50000 - 7.79423i) q^{82} +14.0000 q^{83} +(1.00000 + 1.73205i) q^{84} +(3.50000 + 6.06218i) q^{85} -6.00000 q^{86} +(-0.500000 - 0.866025i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(-7.00000 + 12.1244i) q^{89} -1.00000 q^{90} +6.00000 q^{92} +(-2.00000 + 3.46410i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(-3.00000 - 5.19615i) q^{95} +5.00000 q^{96} +(-1.00000 - 1.73205i) q^{97} +(-1.50000 - 2.59808i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 + q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 - q^9	\( 2 q + q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} - q^{9} + q^{10} - 2 q^{11} + 2 q^{12} + 4 q^{14} + q^{15} + q^{16} + 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21} + 2 q^{22} + 6 q^{23} + 3 q^{24} - 8 q^{25} - 2 q^{27} - 2 q^{28} + q^{29} - q^{30} - 8 q^{31} + 5 q^{32} + 2 q^{33} + 14 q^{34} + 2 q^{35} + q^{36} + q^{37} - 12 q^{38} + 6 q^{40} + 9 q^{41} + 2 q^{42} - 6 q^{43} - 4 q^{44} - q^{45} - 6 q^{46} - 12 q^{47} - q^{48} + 3 q^{49} - 4 q^{50} + 14 q^{51} - 18 q^{53} - q^{54} - 2 q^{55} + 6 q^{56} - 12 q^{57} - q^{58} + 2 q^{60} - q^{61} - 4 q^{62} + 2 q^{63} + 14 q^{64} + 4 q^{66} - 2 q^{67} - 7 q^{68} - 6 q^{69} + 4 q^{70} + 6 q^{71} - 3 q^{72} - 22 q^{73} - q^{74} - 4 q^{75} + 6 q^{76} - 8 q^{77} - 8 q^{79} + q^{80} - q^{81} - 9 q^{82} + 28 q^{83} + 2 q^{84} + 7 q^{85} - 12 q^{86} - q^{87} - 6 q^{88} - 14 q^{89} - 2 q^{90} + 12 q^{92} - 4 q^{93} - 6 q^{94} - 6 q^{95} + 10 q^{96} - 2 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 + q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 - q^9 + q^10 - 2 * q^11 + 2 * q^12 + 4 * q^14 + q^15 + q^16 + 7 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + 4 * q^21 + 2 * q^22 + 6 * q^23 + 3 * q^24 - 8 * q^25 - 2 * q^27 - 2 * q^28 + q^29 - q^30 - 8 * q^31 + 5 * q^32 + 2 * q^33 + 14 * q^34 + 2 * q^35 + q^36 + q^37 - 12 * q^38 + 6 * q^40 + 9 * q^41 + 2 * q^42 - 6 * q^43 - 4 * q^44 - q^45 - 6 * q^46 - 12 * q^47 - q^48 + 3 * q^49 - 4 * q^50 + 14 * q^51 - 18 * q^53 - q^54 - 2 * q^55 + 6 * q^56 - 12 * q^57 - q^58 + 2 * q^60 - q^61 - 4 * q^62 + 2 * q^63 + 14 * q^64 + 4 * q^66 - 2 * q^67 - 7 * q^68 - 6 * q^69 + 4 * q^70 + 6 * q^71 - 3 * q^72 - 22 * q^73 - q^74 - 4 * q^75 + 6 * q^76 - 8 * q^77 - 8 * q^79 + q^80 - q^81 - 9 * q^82 + 28 * q^83 + 2 * q^84 + 7 * q^85 - 12 * q^86 - q^87 - 6 * q^88 - 14 * q^89 - 2 * q^90 + 12 * q^92 - 4 * q^93 - 6 * q^94 - 6 * q^95 + 10 * q^96 - 2 * q^97 - 3 * q^98 + 4 * q^99

Introduction

L-functions

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