LMFDB - Embedded newform 507.2.e.k.484.2

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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			484.2
Root			$0.222521 + 0.385418i$ of defining polynomial
Character	$\chi$	$=$	507.484
Dual form			507.2.e.k.22.2

$q$-expansion

$f(q)$	$=$	$q+(0.222521 + 0.385418i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.900969 - 1.56052i) q^{4} +0.246980 q^{5} +(0.222521 - 0.385418i) q^{6} +(0.876510 - 1.51816i) q^{7} +1.69202 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.222521 + 0.385418i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.900969 - 1.56052i) q^{4} +0.246980 q^{5} +(0.222521 - 0.385418i) q^{6} +(0.876510 - 1.51816i) q^{7} +1.69202 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.0549581 + 0.0951903i) q^{10} +(2.82640 + 4.89546i) q^{11} -1.80194 q^{12} +0.780167 q^{14} +(-0.123490 - 0.213891i) q^{15} +(-1.42543 - 2.46891i) q^{16} +(1.90097 - 3.29257i) q^{17} -0.445042 q^{18} +(2.79105 - 4.83424i) q^{19} +(0.222521 - 0.385418i) q^{20} -1.75302 q^{21} +(-1.25786 + 2.17869i) q^{22} +(-4.17241 - 7.22682i) q^{23} +(-0.846011 - 1.46533i) q^{24} -4.93900 q^{25} +1.00000 q^{27} +(-1.57942 - 2.73563i) q^{28} +(2.96950 + 5.14333i) q^{29} +(0.0549581 - 0.0951903i) q^{30} -5.26875 q^{31} +(2.32640 - 4.02944i) q^{32} +(2.82640 - 4.89546i) q^{33} +1.69202 q^{34} +(0.216480 - 0.374955i) q^{35} +(0.900969 + 1.56052i) q^{36} +(1.59903 + 2.76960i) q^{37} +2.48427 q^{38} +0.417895 q^{40} +(0.222521 + 0.385418i) q^{41} +(-0.390084 - 0.675645i) q^{42} +(-0.856896 + 1.48419i) q^{43} +10.1860 q^{44} +(-0.123490 + 0.213891i) q^{45} +(1.85690 - 3.21624i) q^{46} +6.73556 q^{47} +(-1.42543 + 2.46891i) q^{48} +(1.96346 + 3.40081i) q^{49} +(-1.09903 - 1.90358i) q^{50} -3.80194 q^{51} -1.06100 q^{53} +(0.222521 + 0.385418i) q^{54} +(0.698062 + 1.20908i) q^{55} +(1.48307 - 2.56876i) q^{56} -5.58211 q^{57} +(-1.32155 + 2.28900i) q^{58} +(-6.85086 + 11.8660i) q^{59} -0.445042 q^{60} +(4.25786 - 7.37484i) q^{61} +(-1.17241 - 2.03067i) q^{62} +(0.876510 + 1.51816i) q^{63} -3.63102 q^{64} +2.51573 q^{66} +(2.98039 + 5.16218i) q^{67} +(-3.42543 - 5.93301i) q^{68} +(-4.17241 + 7.22682i) q^{69} +0.192685 q^{70} +(-2.85958 + 4.95295i) q^{71} +(-0.846011 + 1.46533i) q^{72} -7.35690 q^{73} +(-0.711636 + 1.23259i) q^{74} +(2.46950 + 4.27730i) q^{75} +(-5.02930 - 8.71101i) q^{76} +9.90946 q^{77} +4.45473 q^{79} +(-0.352052 - 0.609771i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.0990311 + 0.171527i) q^{82} +10.1860 q^{83} +(-1.57942 + 2.73563i) q^{84} +(0.469501 - 0.813199i) q^{85} -0.762709 q^{86} +(2.96950 - 5.14333i) q^{87} +(4.78232 + 8.28323i) q^{88} +(0.0685317 + 0.118700i) q^{89} -0.109916 q^{90} -15.0368 q^{92} +(2.63437 + 4.56287i) q^{93} +(1.49880 + 2.59600i) q^{94} +(0.689333 - 1.19396i) q^{95} -4.65279 q^{96} +(-6.84481 + 11.8556i) q^{97} +(-0.873822 + 1.51350i) q^{98} -5.65279 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 3 q^{3} + q^{4} - 8 q^{5} + q^{6} + 10 q^{7} - 3 q^{9}+O(q^{10}) $ 6 * q + q^2 - 3 * q^3 + q^4 - 8 * q^5 + q^6 + 10 * q^7 - 3 * q^9	$ 6 q + q^{2} - 3 q^{3} + q^{4} - 8 q^{5} + q^{6} + 10 q^{7} - 3 q^{9} + q^{10} - q^{11} - 2 q^{12} + 2 q^{14} + 4 q^{15} + 5 q^{16} + 7 q^{17} - 2 q^{18} + 11 q^{19} + q^{20} - 20 q^{21} + 5 q^{22} - 2 q^{23} - 10 q^{25} + 6 q^{27} - q^{28} + 8 q^{29} + q^{30} - 16 q^{31} - 4 q^{32} - q^{33} - 18 q^{35} + q^{36} + 14 q^{37} + 40 q^{38} + 14 q^{40} + q^{41} - q^{42} + 3 q^{43} + 32 q^{44} + 4 q^{45} + 3 q^{46} + 18 q^{47} + 5 q^{48} - 17 q^{49} - 11 q^{50} - 14 q^{51} - 26 q^{53} + q^{54} + 13 q^{55} - 7 q^{56} - 22 q^{57} - 12 q^{58} - 14 q^{59} - 2 q^{60} + 13 q^{61} + 16 q^{62} + 10 q^{63} + 8 q^{64} - 10 q^{66} + 5 q^{67} - 7 q^{68} - 2 q^{69} + 16 q^{70} - 6 q^{71} - 36 q^{73} - 7 q^{74} + 5 q^{75} + q^{76} - 30 q^{77} - 18 q^{79} - 16 q^{80} - 3 q^{81} - 5 q^{82} + 32 q^{83} - q^{84} - 7 q^{85} + 30 q^{86} + 8 q^{87} + 7 q^{88} - 5 q^{89} - 2 q^{90} - 34 q^{92} + 8 q^{93} - 32 q^{94} - 3 q^{95} + 8 q^{96} + 5 q^{97} - 13 q^{98} + 2 q^{99}+O(q^{100}) $ 6 * q + q^2 - 3 * q^3 + q^4 - 8 * q^5 + q^6 + 10 * q^7 - 3 * q^9 + q^10 - q^11 - 2 * q^12 + 2 * q^14 + 4 * q^15 + 5 * q^16 + 7 * q^17 - 2 * q^18 + 11 * q^19 + q^20 - 20 * q^21 + 5 * q^22 - 2 * q^23 - 10 * q^25 + 6 * q^27 - q^28 + 8 * q^29 + q^30 - 16 * q^31 - 4 * q^32 - q^33 - 18 * q^35 + q^36 + 14 * q^37 + 40 * q^38 + 14 * q^40 + q^41 - q^42 + 3 * q^43 + 32 * q^44 + 4 * q^45 + 3 * q^46 + 18 * q^47 + 5 * q^48 - 17 * q^49 - 11 * q^50 - 14 * q^51 - 26 * q^53 + q^54 + 13 * q^55 - 7 * q^56 - 22 * q^57 - 12 * q^58 - 14 * q^59 - 2 * q^60 + 13 * q^61 + 16 * q^62 + 10 * q^63 + 8 * q^64 - 10 * q^66 + 5 * q^67 - 7 * q^68 - 2 * q^69 + 16 * q^70 - 6 * q^71 - 36 * q^73 - 7 * q^74 + 5 * q^75 + q^76 - 30 * q^77 - 18 * q^79 - 16 * q^80 - 3 * q^81 - 5 * q^82 + 32 * q^83 - q^84 - 7 * q^85 + 30 * q^86 + 8 * q^87 + 7 * q^88 - 5 * q^89 - 2 * q^90 - 34 * q^92 + 8 * q^93 - 32 * q^94 - 3 * q^95 + 8 * q^96 + 5 * q^97 - 13 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.222521	+	0.385418i	0.157346	+	0.272531i	0.933911	−	0.357506i	$-0.116373\pi$
$2$	0.222521	+	0.385418i	0.157346	+	0.272531i	−0.776565	+	0.630037i	$0.783040\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.900969	−	1.56052i	0.450484	−	0.780262i
$5$	0.246980			0.110453			0.0552263	−	0.998474i	$-0.482412\pi$
$5$	0.246980			0.110453			0.0552263	+	0.998474i	$0.482412\pi$
$6$	0.222521	−	0.385418i	0.0908438	−	0.157346i
$7$	0.876510	−	1.51816i	0.331290	−	0.573811i	−0.651475	−	0.758670i	$-0.725850\pi$
$7$	0.876510	−	1.51816i	0.331290	−	0.573811i	0.982765	+	0.184859i	$0.0591829\pi$
$8$	1.69202			0.598220
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.0549581	+	0.0951903i	0.0173793	+	0.0301018i
$11$	2.82640	+	4.89546i	0.852191	+	1.47604i	0.879227	+	0.476403i	$0.158060\pi$
$11$	2.82640	+	4.89546i	0.852191	+	1.47604i	−0.0270365	+	0.999634i	$0.508607\pi$
$12$	−1.80194			−0.520175
$13$		0			0
$13$		0			0
$14$	0.780167			0.208509
$15$	−0.123490	−	0.213891i	−0.0318849	−	0.0552263i
$16$	−1.42543	−	2.46891i	−0.356357	−	0.617228i
$17$	1.90097	−	3.29257i	0.461053	−	0.798567i	−0.537961	−	0.842970i	$-0.680805\pi$
$17$	1.90097	−	3.29257i	0.461053	−	0.798567i	0.999014	+	0.0444031i	$0.0141386\pi$
$18$	−0.445042			−0.104897
$19$	2.79105	−	4.83424i	0.640311	−	1.10905i	−0.345052	−	0.938584i	$-0.612139\pi$
$19$	2.79105	−	4.83424i	0.640311	−	1.10905i	0.985363	−	0.170468i	$-0.0545280\pi$
$20$	0.222521	−	0.385418i	0.0497572	−	0.0861820i
$21$	−1.75302			−0.382540
$22$	−1.25786	+	2.17869i	−0.268178	+	0.464497i
$23$	−4.17241	−	7.22682i	−0.870007	−	1.50690i	−0.861988	−	0.506929i	$-0.830781\pi$
$23$	−4.17241	−	7.22682i	−0.870007	−	1.50690i	−0.00801894	−	0.999968i	$-0.502553\pi$
$24$	−0.846011	−	1.46533i	−0.172691	−	0.299110i
$25$	−4.93900			−0.987800
$26$		0			0
$27$	1.00000			0.192450
$28$	−1.57942	−	2.73563i	−0.298482	−	0.516986i
$29$	2.96950	+	5.14333i	0.551422	+	0.955092i	0.998172	+	0.0604327i	$0.0192481\pi$
$29$	2.96950	+	5.14333i	0.551422	+	0.955092i	−0.446750	+	0.894659i	$0.647419\pi$
$30$	0.0549581	−	0.0951903i	0.0100339	−	0.0173793i
$31$	−5.26875			−0.946295			−0.473148	−	0.880983i	$-0.656882\pi$
$31$	−5.26875			−0.946295			−0.473148	+	0.880983i	$0.656882\pi$
$32$	2.32640	−	4.02944i	0.411253	−	0.712311i
$33$	2.82640	−	4.89546i	0.492012	−	0.852191i
$34$	1.69202			0.290179
$35$	0.216480	−	0.374955i	0.0365918	−	0.0633789i
$36$	0.900969	+	1.56052i	0.150161	+	0.260087i
$37$	1.59903	+	2.76960i	0.262879	+	0.455320i	0.967006	−	0.254754i	$-0.0819946\pi$
$37$	1.59903	+	2.76960i	0.262879	+	0.455320i	−0.704127	+	0.710074i	$0.748661\pi$
$38$	2.48427			0.403002
$39$		0			0
$40$	0.417895			0.0660750
$41$	0.222521	+	0.385418i	0.0347519	+	0.0601921i	0.882878	−	0.469602i	$-0.155603\pi$
$41$	0.222521	+	0.385418i	0.0347519	+	0.0601921i	−0.848126	+	0.529794i	$0.822269\pi$
$42$	−0.390084	−	0.675645i	−0.0601912	−	0.104254i
$43$	−0.856896	+	1.48419i	−0.130675	+	0.226336i	−0.923937	−	0.382544i	$-0.875048\pi$
$43$	−0.856896	+	1.48419i	−0.130675	+	0.226336i	0.793262	+	0.608881i	$0.208381\pi$
$44$	10.1860			1.53559
$45$	−0.123490	+	0.213891i	−0.0184088	+	0.0318849i
$46$	1.85690	−	3.21624i	0.273784	−	0.474208i
$47$	6.73556			0.982483			0.491241	−	0.871024i	$-0.336543\pi$
$47$	6.73556			0.982483			0.491241	+	0.871024i	$0.336543\pi$
$48$	−1.42543	+	2.46891i	−0.205743	+	0.356357i
$49$	1.96346	+	3.40081i	0.280494	+	0.485830i
$50$	−1.09903	−	1.90358i	−0.155426	−	0.269207i
$51$	−3.80194			−0.532378
$52$		0			0
$53$	−1.06100			−0.145739			−0.0728697	−	0.997341i	$-0.523216\pi$
$53$	−1.06100			−0.145739			−0.0728697	+	0.997341i	$0.523216\pi$
$54$	0.222521	+	0.385418i	0.0302813	+	0.0524487i
$55$	0.698062	+	1.20908i	0.0941267	+	0.163032i
$56$	1.48307	−	2.56876i	0.198184	−	0.343265i
$57$	−5.58211			−0.739368
$58$	−1.32155	+	2.28900i	−0.173528	+	0.300560i
$59$	−6.85086	+	11.8660i	−0.891905	+	1.54483i	−0.0543169	+	0.998524i	$0.517298\pi$
$59$	−6.85086	+	11.8660i	−0.891905	+	1.54483i	−0.837589	+	0.546302i	$0.816035\pi$
$60$	−0.445042			−0.0574547
$61$	4.25786	−	7.37484i	0.545164	−	0.944251i	−0.453433	−	0.891290i	$-0.649801\pi$
$61$	4.25786	−	7.37484i	0.545164	−	0.944251i	0.998597	−	0.0529608i	$-0.0168658\pi$
$62$	−1.17241	−	2.03067i	−0.148896	−	0.257895i
$63$	0.876510	+	1.51816i	0.110430	+	0.191270i
$64$	−3.63102			−0.453878
$65$		0			0
$66$	2.51573			0.309665
$67$	2.98039	+	5.16218i	0.364112	+	0.630661i	0.988633	−	0.150347i	$-0.0480392\pi$
$67$	2.98039	+	5.16218i	0.364112	+	0.630661i	−0.624521	+	0.781008i	$0.714706\pi$
$68$	−3.42543	−	5.93301i	−0.415394	−	0.719484i
$69$	−4.17241	+	7.22682i	−0.502299	+	0.870007i
$70$	0.192685			0.0230303
$71$	−2.85958	+	4.95295i	−0.339370	+	0.587806i	−0.984314	−	0.176423i	$-0.943547\pi$
$71$	−2.85958	+	4.95295i	−0.339370	+	0.587806i	0.644944	+	0.764230i	$0.276881\pi$
$72$	−0.846011	+	1.46533i	−0.0997033	+	0.172691i
$73$	−7.35690			−0.861060			−0.430530	−	0.902576i	$-0.641673\pi$
$73$	−7.35690			−0.861060			−0.430530	+	0.902576i	$0.641673\pi$
$74$	−0.711636	+	1.23259i	−0.0827260	+	0.143286i
$75$	2.46950	+	4.27730i	0.285153	+	0.493900i
$76$	−5.02930	−	8.71101i	−0.576901	−	0.999221i
$77$	9.90946			1.12929
$78$		0			0
$79$	4.45473			0.501196			0.250598	−	0.968091i	$-0.419373\pi$
$79$	4.45473			0.501196			0.250598	+	0.968091i	$0.419373\pi$
$80$	−0.352052	−	0.609771i	−0.0393606	−	0.0681745i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.0990311	+	0.171527i	−0.0109362	+	0.0189420i
$83$	10.1860			1.11806			0.559028	−	0.829149i	$-0.311174\pi$
$83$	10.1860			1.11806			0.559028	+	0.829149i	$0.311174\pi$
$84$	−1.57942	+	2.73563i	−0.172329	+	0.298482i
$85$	0.469501	−	0.813199i	0.0509245	−	0.0882038i
$86$	−0.762709			−0.0822450
$87$	2.96950	−	5.14333i	0.318364	−	0.551422i
$88$	4.78232	+	8.28323i	0.509797	+	0.882995i
$89$	0.0685317	+	0.118700i	0.00726434	+	0.0125822i	0.869635	−	0.493696i	$-0.164354\pi$
$89$	0.0685317	+	0.118700i	0.00726434	+	0.0125822i	−0.862370	+	0.506278i	$0.831021\pi$
$90$	−0.109916			−0.0115862
$91$		0			0
$92$	−15.0368			−1.56770
$93$	2.63437	+	4.56287i	0.273172	+	0.473148i
$94$	1.49880	+	2.59600i	0.154590	+	0.267757i
$95$	0.689333	−	1.19396i	0.0707241	−	0.122498i
$96$	−4.65279			−0.474874
$97$	−6.84481	+	11.8556i	−0.694986	+	1.20375i	0.275200	+	0.961387i	$0.411256\pi$
$97$	−6.84481	+	11.8556i	−0.694986	+	1.20375i	−0.970186	+	0.242363i	$0.922077\pi$
$98$	−0.873822	+	1.51350i	−0.0882693	+	0.152887i
$99$	−5.65279			−0.568127
$100$	−4.44989	+	7.70743i	−0.444989	+	0.770743i
$101$	2.70560	+	4.68623i	0.269217	+	0.466297i	0.968660	−	0.248391i	$-0.0799019\pi$
$101$	2.70560	+	4.68623i	0.269217	+	0.466297i	−0.699443	+	0.714688i	$0.746569\pi$
$102$	−0.846011	−	1.46533i	−0.0837675	−	0.145090i
$103$	13.7560			1.35542			0.677710	−	0.735330i	$-0.262973\pi$
$103$	13.7560			1.35542			0.677710	+	0.735330i	$0.262973\pi$
$104$		0			0
$105$	−0.432960			−0.0422526
$106$	−0.236094	−	0.408928i	−0.0229315	−	0.0397186i
$107$	6.40850	+	11.0999i	0.619533	+	1.07306i	0.989571	+	0.144046i	$0.0460114\pi$
$107$	6.40850	+	11.0999i	0.619533	+	1.07306i	−0.370038	+	0.929017i	$0.620655\pi$
$108$	0.900969	−	1.56052i	0.0866958	−	0.150161i
$109$	−12.1468			−1.16345			−0.581724	−	0.813386i	$-0.697622\pi$
$109$	−12.1468			−1.16345			−0.581724	+	0.813386i	$0.697622\pi$
$110$	−0.310667	+	0.538091i	−0.0296209	+	0.0513050i
$111$	1.59903	−	2.76960i	0.151773	−	0.262879i
$112$	−4.99761			−0.472229
$113$	0.818864	−	1.41831i	0.0770322	−	0.133424i	−0.824936	−	0.565226i	$-0.808789\pi$
$113$	0.818864	−	1.41831i	0.0770322	−	0.133424i	0.901968	+	0.431802i	$0.142122\pi$
$114$	−1.24214	−	2.15144i	−0.116337	−	0.201501i
$115$	−1.03050	−	1.78488i	−0.0960946	−	0.166441i
$116$	10.7017			0.993629
$117$		0			0
$118$	−6.09783			−0.561351
$119$	−3.33244	−	5.77195i	−0.305484	−	0.529114i
$120$	−0.208947	−	0.361908i	−0.0190742	−	0.0330375i
$121$	−10.4770	+	18.1468i	−0.952458	+	1.64970i
$122$	3.78986			0.343117
$123$	0.222521	−	0.385418i	0.0200640	−	0.0347519i
$124$	−4.74698	+	8.22201i	−0.426291	+	0.738358i
$125$	−2.45473			−0.219558
$126$	−0.390084	+	0.675645i	−0.0347514	+	0.0601912i
$127$	−5.39977	−	9.35268i	−0.479152	−	0.829916i	0.520562	−	0.853824i	$-0.325723\pi$
$127$	−5.39977	−	9.35268i	−0.479152	−	0.829916i	−0.999714	+	0.0239078i	$0.992389\pi$
$128$	−5.46077	−	9.45833i	−0.482669	−	0.836006i
$129$	1.71379			0.150891
$130$		0			0
$131$	0.907542			0.0792923			0.0396462	−	0.999214i	$-0.487377\pi$
$131$	0.907542			0.0792923			0.0396462	+	0.999214i	$0.487377\pi$
$132$	−5.09299	−	8.82132i	−0.443288	−	0.767797i
$133$	−4.89277	−	8.47453i	−0.424257	−	0.734835i
$134$	−1.32640	+	2.29739i	−0.114583	+	0.198464i
$135$	0.246980			0.0212566
$136$	3.21648	−	5.57111i	0.275811	−	0.477718i
$137$	−4.77413	+	8.26903i	−0.407881	+	0.706471i	−0.994652	−	0.103282i	$-0.967066\pi$
$137$	−4.77413	+	8.26903i	−0.407881	+	0.706471i	0.586771	+	0.809753i	$0.300399\pi$
$138$	−3.71379			−0.316139
$139$	2.04623	−	3.54417i	0.173559	−	0.300613i	−0.766103	−	0.642718i	$-0.777807\pi$
$139$	2.04623	−	3.54417i	0.173559	−	0.300613i	0.939662	+	0.342105i	$0.111140\pi$
$140$	−0.390084	−	0.675645i	−0.0329681	−	0.0571024i
$141$	−3.36778	−	5.83317i	−0.283618	−	0.491241i
$142$	−2.54527			−0.213594
$143$		0			0
$144$	2.85086			0.237571
$145$	0.733406	+	1.27030i	0.0609061	+	0.105492i
$146$	−1.63706	−	2.83548i	−0.135484	−	0.234666i
$147$	1.96346	−	3.40081i	0.161943	−	0.280494i
$148$	5.76271			0.473692
$149$	−7.69418	+	13.3267i	−0.630332	+	1.09177i	0.357152	+	0.934046i	$0.383748\pi$
$149$	−7.69418	+	13.3267i	−0.630332	+	1.09177i	−0.987484	+	0.157720i	$0.949586\pi$
$150$	−1.09903	+	1.90358i	−0.0897355	+	0.155426i
$151$	3.67456			0.299032			0.149516	−	0.988759i	$-0.452228\pi$
$151$	3.67456			0.299032			0.149516	+	0.988759i	$0.452228\pi$
$152$	4.72252	−	8.17965i	0.383047	−	0.663457i
$153$	1.90097	+	3.29257i	0.153684	+	0.266189i
$154$	2.20506	+	3.81928i	0.177689	+	0.307766i
$155$	−1.30127			−0.104521
$156$		0			0
$157$	−4.87800			−0.389307			−0.194653	−	0.980872i	$-0.562358\pi$
$157$	−4.87800			−0.389307			−0.194653	+	0.980872i	$0.562358\pi$
$158$	0.991271	+	1.71693i	0.0788613	+	0.136592i
$159$	0.530499	+	0.918852i	0.0420713	+	0.0728697i
$160$	0.574572	−	0.995189i	0.0454239	−	0.0786766i
$161$	−14.6286			−1.15290
$162$	0.222521	−	0.385418i	0.0174829	−	0.0302813i
$163$	4.31551	−	7.47468i	0.338017	−	0.585462i	−0.646043	−	0.763301i	$-0.723577\pi$
$163$	4.31551	−	7.47468i	0.338017	−	0.585462i	0.984060	+	0.177839i	$0.0569106\pi$
$164$	0.801938			0.0626208
$165$	0.698062	−	1.20908i	0.0543441	−	0.0941267i
$166$	2.26659	+	3.92586i	0.175922	+	0.304706i
$167$	4.73490	+	8.20108i	0.366397	+	0.634619i	0.988999	−	0.147920i	$-0.0472577\pi$
$167$	4.73490	+	8.20108i	0.366397	+	0.634619i	−0.622602	+	0.782539i	$0.713924\pi$
$168$	−2.96615			−0.228843
$169$		0			0
$170$	0.417895			0.0320511
$171$	2.79105	+	4.83424i	0.213437	+	0.369684i
$172$	1.54407	+	2.67441i	0.117734	+	0.203922i
$173$	−2.38740	+	4.13509i	−0.181510	+	0.314385i	−0.942395	−	0.334502i	$-0.891432\pi$
$173$	−2.38740	+	4.13509i	−0.181510	+	0.314385i	0.760885	+	0.648887i	$0.224765\pi$
$174$	2.64310			0.200373
$175$	−4.32908	+	7.49819i	−0.327248	+	0.566810i
$176$	8.05765	−	13.9563i	0.607368	−	1.05199i
$177$	13.7017			1.02988
$178$	−0.0304995	+	0.0528266i	−0.00228603	+	0.00395952i
$179$	−1.71768	−	2.97510i	−0.128385	−	0.222370i	0.794666	−	0.607047i	$-0.207646\pi$
$179$	−1.71768	−	2.97510i	−0.128385	−	0.222370i	−0.923051	+	0.384677i	$0.874313\pi$
$180$	0.222521	+	0.385418i	0.0165857	+	0.0287273i
$181$	−13.4862			−1.00242			−0.501210	−	0.865326i	$-0.667112\pi$
$181$	−13.4862			−1.00242			−0.501210	+	0.865326i	$0.667112\pi$
$182$		0			0
$183$	−8.51573			−0.629501
$184$	−7.05980	−	12.2279i	−0.520456	−	0.901455i
$185$	0.394928	+	0.684035i	0.0290357	+	0.0502913i
$186$	−1.17241	+	2.03067i	−0.0859651	+	0.148896i
$187$	21.4916			1.57162
$188$	6.06853	−	10.5110i	0.442593	−	0.766594i
$189$	0.876510	−	1.51816i	0.0637567	−	0.110430i
$190$	0.613564			0.0445126
$191$	0.650637	−	1.12694i	0.0470784	−	0.0815422i	−0.841526	−	0.540217i	$-0.818342\pi$
$191$	0.650637	−	1.12694i	0.0470784	−	0.0815422i	0.888604	+	0.458674i	$0.151676\pi$
$192$	1.81551	+	3.14456i	0.131023	+	0.226939i
$193$	−4.59783	−	7.96368i	−0.330959	−	0.573238i	0.651741	−	0.758442i	$-0.274039\pi$
$193$	−4.59783	−	7.96368i	−0.330959	−	0.573238i	−0.982700	+	0.185203i	$0.940706\pi$
$194$	−6.09246			−0.437413
$195$		0			0
$196$	7.07606			0.505433
$197$	2.05615	+	3.56136i	0.146495	+	0.253737i	0.929930	−	0.367737i	$-0.119867\pi$
$197$	2.05615	+	3.56136i	0.146495	+	0.253737i	−0.783435	+	0.621474i	$0.786534\pi$
$198$	−1.25786	−	2.17869i	−0.0893926	−	0.154832i
$199$	12.3862	−	21.4535i	0.878034	−	1.52080i	0.0245395	−	0.999699i	$-0.492188\pi$
$199$	12.3862	−	21.4535i	0.878034	−	1.52080i	0.853495	−	0.521101i	$-0.174479\pi$
$200$	−8.35690			−0.590922
$201$	2.98039	−	5.16218i	0.210220	−	0.364112i
$202$	−1.20410	+	2.08557i	−0.0847204	+	0.146740i
$203$	10.4112			0.730722
$204$	−3.42543	+	5.93301i	−0.239828	+	0.415394i
$205$	0.0549581	+	0.0951903i	0.00383844	+	0.00664838i
$206$	3.06100	+	5.30181i	0.213270	+	0.369394i
$207$	8.34481			0.580005
$208$		0			0
$209$	31.5545			2.18267
$210$	−0.0963427	−	0.166870i	−0.00664828	−	0.0115152i
$211$	2.96950	+	5.14333i	0.204429	+	0.354081i	0.949951	−	0.312400i	$-0.101133\pi$
$211$	2.96950	+	5.14333i	0.204429	+	0.354081i	−0.745522	+	0.666481i	$0.767800\pi$
$212$	−0.955927	+	1.65571i	−0.0656533	+	0.113715i
$213$	5.71917			0.391871
$214$	−2.85205	+	4.93990i	−0.194962	+	0.337684i
$215$	−0.211636	+	0.366564i	−0.0144334	+	0.0249995i
$216$	1.69202			0.115127
$217$	−4.61811	+	7.99881i	−0.313498	+	0.542994i
$218$	−2.70291	−	4.68157i	−0.183064	−	0.317076i
$219$	3.67845	+	6.37126i	0.248566	+	0.430530i
$220$	2.51573			0.169610
$221$		0			0
$222$	1.42327			0.0955237
$223$	7.10052	+	12.2985i	0.475486	+	0.823566i	0.999606	−	0.0280785i	$-0.00893883\pi$
$223$	7.10052	+	12.2985i	0.475486	+	0.823566i	−0.524120	+	0.851645i	$0.675605\pi$
$224$	−4.07822	−	7.06368i	−0.272488	−	0.471962i
$225$	2.46950	−	4.27730i	0.164633	−	0.285153i
$226$	0.728857			0.0484829
$227$	8.00365	−	13.8627i	0.531221	−	0.920101i	−0.468115	−	0.883667i	$-0.655067\pi$
$227$	8.00365	−	13.8627i	0.531221	−	0.920101i	0.999336	−	0.0364340i	$-0.0115999\pi$
$228$	−5.02930	+	8.71101i	−0.333074	+	0.576901i
$229$	−1.84117			−0.121668			−0.0608339	−	0.998148i	$-0.519376\pi$
$229$	−1.84117			−0.121668			−0.0608339	+	0.998148i	$0.519376\pi$
$230$	0.458615	−	0.794345i	0.0302402	−	0.0523776i
$231$	−4.95473	−	8.58185i	−0.325997	−	0.564644i
$232$	5.02446	+	8.70262i	0.329872	+	0.571355i
$233$	−23.4252			−1.53464			−0.767318	−	0.641267i	$-0.778409\pi$
$233$	−23.4252			−1.53464			−0.767318	+	0.641267i	$0.778409\pi$
$234$		0			0
$235$	1.66355			0.108518
$236$	12.3448	+	21.3818i	0.803579	+	1.39184i
$237$	−2.22737	−	3.85791i	−0.144683	−	0.250598i
$238$	1.48307	−	2.56876i	0.0961334	−	0.166508i
$239$	−14.6015			−0.944491			−0.472246	−	0.881467i	$-0.656556\pi$
$239$	−14.6015			−0.944491			−0.472246	+	0.881467i	$0.656556\pi$
$240$	−0.352052	+	0.609771i	−0.0227248	+	0.0393606i
$241$	4.31551	−	7.47468i	0.277987	−	0.481487i	−0.692898	−	0.721036i	$-0.743666\pi$
$241$	4.31551	−	7.47468i	0.277987	−	0.481487i	0.970884	+	0.239549i	$0.0769996\pi$
$242$	−9.32544			−0.599462
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−7.67241	−	13.2890i	−0.491176	−	0.850741i
$245$	0.484935	+	0.839931i	0.0309813	+	0.0536612i
$246$	0.198062			0.0126280
$247$		0			0
$248$	−8.91484			−0.566093
$249$	−5.09299	−	8.82132i	−0.322755	−	0.559028i
$250$	−0.546229	−	0.946096i	−0.0345466	−	0.0598364i
$251$	1.90097	−	3.29257i	0.119988	−	0.207825i	−0.799775	−	0.600300i	$-0.795048\pi$
$251$	1.90097	−	3.29257i	0.119988	−	0.207825i	0.919763	+	0.392475i	$0.128381\pi$
$252$	3.15883			0.198988
$253$	23.5858	−	40.8517i	1.48282	−	2.56833i
$254$	2.40312	−	4.16233i	0.150785	−	0.261168i
$255$	−0.939001			−0.0588025
$256$	−1.20075	+	2.07976i	−0.0750469	+	0.129985i
$257$	10.2981	+	17.8368i	0.642375	+	1.11263i	0.984901	+	0.173118i	$0.0553841\pi$
$257$	10.2981	+	17.8368i	0.642375	+	1.11263i	−0.342526	+	0.939508i	$0.611283\pi$
$258$	0.381355	+	0.660525i	0.0237421	+	0.0411225i
$259$	5.60627			0.348357
$260$		0			0
$261$	−5.93900			−0.367615
$262$	0.201947	+	0.349783i	0.0124763	+	0.0216096i
$263$	−0.166366	−	0.288155i	−0.0102586	−	0.0177684i	0.860851	−	0.508858i	$-0.169932\pi$
$263$	−0.166366	−	0.288155i	−0.0102586	−	0.0177684i	−0.871109	+	0.491089i	$0.836599\pi$
$264$	4.78232	−	8.28323i	0.294332	−	0.509797i
$265$	−0.262045			−0.0160973
$266$	2.17749	−	3.77152i	0.133510	−	0.231247i
$267$	0.0685317	−	0.118700i	0.00419407	−	0.00726434i
$268$	10.7409			0.656107
$269$	−13.6516	+	23.6453i	−0.832353	+	1.44168i	0.0638154	+	0.997962i	$0.479673\pi$
$269$	−13.6516	+	23.6453i	−0.832353	+	1.44168i	−0.896168	+	0.443715i	$0.853660\pi$
$270$	0.0549581	+	0.0951903i	0.00334465	+	0.00579310i
$271$	13.9928	+	24.2362i	0.850000	+	1.47224i	0.881207	+	0.472730i	$0.156731\pi$
$271$	13.9928	+	24.2362i	0.850000	+	1.47224i	−0.0312076	+	0.999513i	$0.509935\pi$
$272$	−10.8388			−0.657197
$273$		0			0
$274$	−4.24937			−0.256714
$275$	−13.9596	−	24.1787i	−0.841794	−	1.45803i
$276$	7.51842	+	13.0223i	0.452556	+	0.783849i
$277$	1.05161	−	1.82143i	0.0631849	−	0.109439i	−0.832703	−	0.553721i	$-0.813208\pi$
$277$	1.05161	−	1.82143i	0.0631849	−	0.109439i	0.895887	+	0.444281i	$0.146541\pi$
$278$	1.82132			0.109235
$279$	2.63437	−	4.56287i	0.157716	−	0.273172i
$280$	0.366289	−	0.634431i	0.0218900	−	0.0379145i
$281$	−27.2349			−1.62470			−0.812349	−	0.583172i	$-0.801811\pi$
$281$	−27.2349			−1.62470			−0.812349	+	0.583172i	$0.801811\pi$
$282$	1.49880	−	2.59600i	0.0892525	−	0.154590i
$283$	−2.64191	−	4.57592i	−0.157045	−	0.272010i	0.776757	−	0.629801i	$-0.216863\pi$
$283$	−2.64191	−	4.57592i	−0.157045	−	0.272010i	−0.933802	+	0.357791i	$0.883530\pi$
$284$	5.15279	+	8.92490i	0.305762	+	0.529595i
$285$	−1.37867			−0.0816651
$286$		0			0
$287$	0.780167			0.0460518
$288$	2.32640	+	4.02944i	0.137084	+	0.237437i
$289$	1.27263	+	2.20427i	0.0748609	+	0.129663i
$290$	−0.326396	+	0.565335i	−0.0191667	+	0.0331976i
$291$	13.6896			0.802500
$292$	−6.62833	+	11.4806i	−0.387894	+	0.671852i
$293$	16.3312	−	28.2865i	0.954081	−	1.65252i	0.217625	−	0.976033i	$-0.430169\pi$
$293$	16.3312	−	28.2865i	0.954081	−	1.65252i	0.736457	−	0.676485i	$-0.236498\pi$
$294$	1.74764			0.101925
$295$	−1.69202	+	2.93067i	−0.0985133	+	0.170630i
$296$	2.70560	+	4.68623i	0.157260	+	0.272381i
$297$	2.82640	+	4.89546i	0.164004	+	0.284064i
$298$	−6.84846			−0.396721
$299$		0			0
$300$	8.89977			0.513829
$301$	1.50216	+	2.60181i	0.0865828	+	0.149966i
$302$	0.817667	+	1.41624i	0.0470515	+	0.0814955i
$303$	2.70560	−	4.68623i	0.155432	−	0.269217i
$304$	−15.9138			−0.912717
$305$	1.05161	−	1.82143i	0.0602148	−	0.104295i
$306$	−0.846011	+	1.46533i	−0.0483632	+	0.0837675i
$307$	20.7614			1.18491			0.592457	−	0.805602i	$-0.298158\pi$
$307$	20.7614			1.18491			0.592457	+	0.805602i	$0.298158\pi$
$308$	8.92812	−	15.4640i	0.508727	−	0.881140i
$309$	−6.87800	−	11.9130i	−0.391276	−	0.677710i
$310$	−0.289561	−	0.501534i	−0.0164459	−	0.0284852i
$311$	−11.3013			−0.640836			−0.320418	−	0.947276i	$-0.603823\pi$
$311$	−11.3013			−0.640836			−0.320418	+	0.947276i	$0.603823\pi$
$312$		0			0
$313$	−4.27173			−0.241453			−0.120726	−	0.992686i	$-0.538522\pi$
$313$	−4.27173			−0.241453			−0.120726	+	0.992686i	$0.538522\pi$
$314$	−1.08546	−	1.88007i	−0.0612559	−	0.106098i
$315$	0.216480	+	0.374955i	0.0121973	+	0.0211263i
$316$	4.01357	−	6.95171i	0.225781	−	0.391064i
$317$	−15.4776			−0.869307			−0.434653	−	0.900598i	$-0.643129\pi$
$317$	−15.4776			−0.869307			−0.434653	+	0.900598i	$0.643129\pi$
$318$	−0.236094	+	0.408928i	−0.0132395	+	0.0229315i
$319$	−16.7860	+	29.0742i	−0.939834	+	1.62784i
$320$	−0.896789			−0.0501320
$321$	6.40850	−	11.0999i	0.357688	−	0.619533i
$322$	−3.25518	−	5.63813i	−0.181404	−	0.314201i
$323$	−10.6114	−	18.3795i	−0.590435	−	1.02266i
$324$	−1.80194			−0.100108
$325$		0			0
$326$	3.84117			0.212743
$327$	6.07338	+	10.5194i	0.335858	+	0.581724i
$328$	0.376510	+	0.652135i	0.0207893	+	0.0360081i
$329$	5.90379	−	10.2257i	0.325486	−	0.563759i
$330$	0.621334			0.0342033
$331$	3.03415	−	5.25530i	0.166772	−	0.288857i	−0.770511	−	0.637426i	$-0.779999\pi$
$331$	3.03415	−	5.25530i	0.166772	−	0.288857i	0.937283	+	0.348569i	$0.113332\pi$
$332$	9.17725	−	15.8955i	0.503667	−	0.872377i
$333$	−3.19806			−0.175253
$334$	−2.10723	+	3.64983i	−0.115302	+	0.199710i
$335$	0.736094	+	1.27495i	0.0402171	+	0.0696581i
$336$	2.49880	+	4.32805i	0.136321	+	0.236115i
$337$	12.1239			0.660432			0.330216	−	0.943905i	$-0.392878\pi$
$337$	12.1239			0.660432			0.330216	+	0.943905i	$0.392878\pi$
$338$		0			0
$339$	−1.63773			−0.0889491
$340$	−0.846011	−	1.46533i	−0.0458814	−	0.0794689i
$341$	−14.8916	−	25.7930i	−0.806424	−	1.39677i
$342$	−1.24214	+	2.15144i	−0.0671670	+	0.116337i
$343$	19.1551			1.03428
$344$	−1.44989	+	2.51128i	−0.0781726	+	0.135399i
$345$	−1.03050	+	1.78488i	−0.0554802	+	0.0960946i
$346$	−2.12498			−0.114240
$347$	−11.5749	+	20.0483i	−0.621371	+	1.07625i	0.367859	+	0.929882i	$0.380091\pi$
$347$	−11.5749	+	20.0483i	−0.621371	+	1.07625i	−0.989231	+	0.146365i	$0.953242\pi$
$348$	−5.35086	−	9.26795i	−0.286836	−	0.496814i
$349$	−11.0978	−	19.2220i	−0.594053	−	1.02893i	−0.993680	−	0.112253i	$-0.964193\pi$
$349$	−11.0978	−	19.2220i	−0.594053	−	1.02893i	0.399626	−	0.916678i	$-0.369140\pi$
$350$	−3.85325			−0.205965
$351$		0			0
$352$	26.3013			1.40186
$353$	−2.53534	−	4.39134i	−0.134943	−	0.233728i	0.790633	−	0.612291i	$-0.209752\pi$
$353$	−2.53534	−	4.39134i	−0.134943	−	0.233728i	−0.925576	+	0.378563i	$0.876418\pi$
$354$	3.04892	+	5.28088i	0.162048	+	0.280676i
$355$	−0.706259	+	1.22328i	−0.0374843	+	0.0649248i
$356$	0.246980			0.0130899
$357$	−3.33244	+	5.77195i	−0.176371	+	0.305484i
$358$	0.764438	−	1.32405i	0.0404018	−	0.0699780i
$359$	16.6746			0.880050			0.440025	−	0.897986i	$-0.354970\pi$
$359$	16.6746			0.880050			0.440025	+	0.897986i	$0.354970\pi$
$360$	−0.208947	+	0.361908i	−0.0110125	+	0.0190742i
$361$	−6.07995	−	10.5308i	−0.319997	−	0.554252i
$362$	−3.00096	−	5.19781i	−0.157727	−	0.273191i
$363$	20.9541			1.09980
$364$		0			0
$365$	−1.81700			−0.0951063
$366$	−1.89493	−	3.28211i	−0.0990495	−	0.171559i
$367$	0.589638	+	1.02128i	0.0307789	+	0.0533105i	0.881005	−	0.473108i	$-0.156868\pi$
$367$	0.589638	+	1.02128i	0.0307789	+	0.0533105i	−0.850226	+	0.526418i	$0.823535\pi$
$368$	−11.8949	+	20.6026i	−0.620066	+	1.07399i
$369$	−0.445042			−0.0231680
$370$	−0.175760	+	0.304424i	−0.00913730	+	0.0158263i
$371$	−0.929976	+	1.61077i	−0.0482820	+	0.0836268i
$372$	9.49396			0.492239
$373$	15.0462	−	26.0608i	0.779064	−	1.34938i	−0.153417	−	0.988161i	$-0.549028\pi$
$373$	15.0462	−	26.0608i	0.779064	−	1.34938i	0.932482	−	0.361217i	$-0.117639\pi$
$374$	4.78232	+	8.28323i	0.247288	+	0.428315i
$375$	1.22737	+	2.12586i	0.0633809	+	0.109779i
$376$	11.3967			0.587741
$377$		0			0
$378$	0.780167			0.0401275
$379$	−9.58157	−	16.5958i	−0.492172	−	0.852467i	0.507787	−	0.861483i	$-0.330464\pi$
$379$	−9.58157	−	16.5958i	−0.492172	−	0.852467i	−0.999959	+	0.00901515i	$0.997130\pi$
$380$	−1.24214	−	2.15144i	−0.0637202	−	0.110367i
$381$	−5.39977	+	9.35268i	−0.276639	+	0.479152i
$382$	0.579121			0.0296304
$383$	−7.69418	+	13.3267i	−0.393154	+	0.680963i	−0.992864	−	0.119255i	$-0.961949\pi$
$383$	−7.69418	+	13.3267i	−0.393154	+	0.680963i	0.599710	+	0.800218i	$0.295283\pi$
$384$	−5.46077	+	9.45833i	−0.278669	+	0.482669i
$385$	2.44743			0.124733
$386$	2.04623	−	3.54417i	0.104150	−	0.180394i
$387$	−0.856896	−	1.48419i	−0.0435585	−	0.0754455i
$388$	12.3339	+	21.3630i	0.626160	+	1.08454i
$389$	−24.0315			−1.21844			−0.609222	−	0.793000i	$-0.708518\pi$
$389$	−24.0315			−1.21844			−0.609222	+	0.793000i	$0.708518\pi$
$390$		0			0
$391$	−31.7265			−1.60448
$392$	3.32222	+	5.75425i	0.167797	+	0.290633i
$393$	−0.453771	−	0.785955i	−0.0228897	−	0.0396462i
$394$	−0.915075	+	1.58496i	−0.0461008	+	0.0798489i
$395$	1.10023			0.0553585
$396$	−5.09299	+	8.82132i	−0.255932	+	0.443288i
$397$	14.8007	−	25.6356i	0.742828	−	1.28662i	−0.208375	−	0.978049i	$-0.566817\pi$
$397$	14.8007	−	25.6356i	0.742828	−	1.28662i	0.951203	−	0.308567i	$-0.0998493\pi$
$398$	11.0248			0.552621
$399$	−4.89277	+	8.47453i	−0.244945	+	0.424257i
$400$	7.04019	+	12.1940i	0.352009	+	0.609698i
$401$	−10.5516	−	18.2759i	−0.526922	−	0.912656i	−0.999508	−	0.0313711i	$-0.990013\pi$
$401$	−10.5516	−	18.2759i	−0.526922	−	0.912656i	0.472586	−	0.881285i	$-0.343321\pi$
$402$	2.65279			0.132309
$403$		0			0
$404$	9.75063			0.485112
$405$	−0.123490	−	0.213891i	−0.00613626	−	0.0106283i
$406$	2.31671	+	4.01266i	0.114976	+	0.199145i
$407$	−9.03899	+	15.6560i	−0.448046	+	0.776039i
$408$	−6.43296			−0.318479
$409$	−18.0112	+	31.1963i	−0.890596	+	1.54256i	−0.0514328	+	0.998676i	$0.516379\pi$
$409$	−18.0112	+	31.1963i	−0.890596	+	1.54256i	−0.839163	+	0.543880i	$0.816955\pi$
$410$	−0.0244587	+	0.0423637i	−0.00120793	+	0.00209219i
$411$	9.54825			0.470981
$412$	12.3937	−	21.4666i	0.610595	−	1.05758i
$413$	12.0097	+	20.8014i	0.590958	+	1.02357i
$414$	1.85690	+	3.21624i	0.0912615	+	0.158069i
$415$	2.51573			0.123492
$416$		0			0
$417$	−4.09246			−0.200409
$418$	7.02153	+	12.1617i	0.343434	+	0.594846i
$419$	−2.98427	−	5.16891i	−0.145791	−	0.252518i	0.783877	−	0.620917i	$-0.213239\pi$
$419$	−2.98427	−	5.16891i	−0.145791	−	0.252518i	−0.929668	+	0.368399i	$0.879906\pi$
$420$	−0.390084	+	0.675645i	−0.0190341	+	0.0329681i
$421$	2.09544			0.102126			0.0510628	−	0.998695i	$-0.483739\pi$
$421$	2.09544			0.102126			0.0510628	+	0.998695i	$0.483739\pi$
$422$	−1.32155	+	2.28900i	−0.0643321	+	0.111427i
$423$	−3.36778	+	5.83317i	−0.163747	+	0.283618i
$424$	−1.79523			−0.0871842
$425$	−9.38889	+	16.2620i	−0.455428	+	0.788824i
$426$	1.27263	+	2.20427i	0.0616594	+	0.106797i
$427$	−7.46412	−	12.9282i	−0.361214	−	0.625641i
$428$	23.0954			1.11636
$429$		0			0
$430$	−0.188374			−0.00908418
$431$	−1.44289	−	2.49915i	−0.0695014	−	0.120380i	0.829181	−	0.558981i	$-0.188807\pi$
$431$	−1.44289	−	2.49915i	−0.0695014	−	0.120380i	−0.898682	+	0.438601i	$0.855474\pi$
$432$	−1.42543	−	2.46891i	−0.0685809	−	0.118786i
$433$	6.32424	−	10.9539i	0.303924	−	0.526411i	−0.673097	−	0.739554i	$-0.735037\pi$
$433$	6.32424	−	10.9539i	0.303924	−	0.526411i	0.977021	+	0.213143i	$0.0683699\pi$
$434$	−4.11051			−0.197311
$435$	0.733406	−	1.27030i	0.0351641	−	0.0609061i
$436$	−10.9438	+	18.9553i	−0.524115	+	0.907794i
$437$	−46.5816			−2.22830
$438$	−1.63706	+	2.83548i	−0.0782219	+	0.135484i
$439$	5.46346	+	9.46299i	0.260757	+	0.451644i	0.966443	−	0.256880i	$-0.0826946\pi$
$439$	5.46346	+	9.46299i	0.260757	+	0.451644i	−0.705687	+	0.708524i	$0.749361\pi$
$440$	1.18114	+	2.04579i	0.0563085	+	0.0975291i
$441$	−3.92692			−0.186996
$442$		0			0
$443$	−19.2403			−0.914133			−0.457067	−	0.889433i	$-0.651100\pi$
$443$	−19.2403			−0.914133			−0.457067	+	0.889433i	$0.651100\pi$
$444$	−2.88135	−	4.99065i	−0.136743	−	0.236846i
$445$	0.0169259	+	0.0293166i	0.000802366	+	0.00138974i
$446$	−3.16003	+	5.47333i	−0.149632	+	0.259170i
$447$	15.3884			0.727844
$448$	−3.18263	+	5.51247i	−0.150365	+	0.260440i
$449$	−14.4100	+	24.9588i	−0.680050	+	1.17788i	0.294916	+	0.955523i	$0.404708\pi$
$449$	−14.4100	+	24.9588i	−0.680050	+	1.17788i	−0.974965	+	0.222357i	$0.928625\pi$
$450$	2.19806			0.103618
$451$	−1.25786	+	2.17869i	−0.0592305	+	0.102590i
$452$	−1.47554	−	2.55571i	−0.0694036	−	0.120211i
$453$	−1.83728	−	3.18226i	−0.0863230	−	0.149516i
$454$	7.12392			0.334342
$455$		0			0
$456$	−9.44504			−0.442305
$457$	−9.03534	−	15.6497i	−0.422656	−	0.732061i	0.573543	−	0.819176i	$-0.305569\pi$
$457$	−9.03534	−	15.6497i	−0.422656	−	0.732061i	−0.996198	+	0.0871147i	$0.972235\pi$
$458$	−0.409698	−	0.709618i	−0.0191439	−	0.0331583i
$459$	1.90097	−	3.29257i	0.0887296	−	0.153684i
$460$	−3.71379			−0.173156
$461$	−3.78382	+	6.55376i	−0.176230	+	0.305239i	−0.940586	−	0.339555i	$-0.889724\pi$
$461$	−3.78382	+	6.55376i	−0.176230	+	0.305239i	0.764356	+	0.644794i	$0.223057\pi$
$462$	2.20506	−	3.81928i	0.102589	−	0.177689i
$463$	−35.3551			−1.64309			−0.821545	−	0.570143i	$-0.806888\pi$
$463$	−35.3551			−1.64309			−0.821545	+	0.570143i	$0.806888\pi$
$464$	8.46562	−	14.6629i	0.393006	−	0.680707i
$465$	0.650637	+	1.12694i	0.0301726	+	0.0522604i
$466$	−5.21260	−	9.02848i	−0.241469	−	0.418236i
$467$	13.0000			0.601568			0.300784	−	0.953692i	$-0.402752\pi$
$467$	13.0000			0.601568			0.300784	+	0.953692i	$0.402752\pi$
$468$		0			0
$469$	10.4494			0.482506
$470$	0.370174	+	0.641160i	0.0170748	+	0.0295745i
$471$	2.43900	+	4.22447i	0.112383	+	0.194653i
$472$	−11.5918	+	20.0776i	−0.533556	+	0.924145i
$473$	−9.68771			−0.445441
$474$	0.991271	−	1.71693i	0.0455306	−	0.0788613i
$475$	−13.7850	+	23.8763i	−0.632500	+	1.09552i
$476$	−12.0097			−0.550463
$477$	0.530499	−	0.918852i	0.0242899	−	0.0420713i
$478$	−3.24914	−	5.62767i	−0.148612	−	0.257404i
$479$	−12.7632	−	22.1066i	−0.583167	−	1.01008i	−0.995101	−	0.0988618i	$-0.968480\pi$
$479$	−12.7632	−	22.1066i	−0.583167	−	1.01008i	0.411934	−	0.911214i	$-0.364853\pi$
$480$	−1.14914			−0.0524510
$481$		0			0
$482$	3.84117			0.174960
$483$	7.31431	+	12.6688i	0.332813	+	0.576449i
$484$	18.8790	+	32.6993i	0.858135	+	1.48633i
$485$	−1.69053	+	2.92808i	−0.0767630	+	0.132957i
$486$	−0.445042			−0.0201875
$487$	8.00365	−	13.8627i	0.362680	−	0.628180i	−0.625721	−	0.780047i	$-0.715195\pi$
$487$	8.00365	−	13.8627i	0.362680	−	0.628180i	0.988401	+	0.151867i	$0.0485285\pi$
$488$	7.20440	−	12.4784i	0.326128	−	0.564870i
$489$	−8.63102			−0.390308
$490$	−0.215816	+	0.373805i	−0.00974958	+	0.0168868i
$491$	−10.3693	−	17.9601i	−0.467959	−	0.810528i	0.531371	−	0.847139i	$-0.321677\pi$
$491$	−10.3693	−	17.9601i	−0.467959	−	0.810528i	−0.999330	+	0.0366110i	$0.988344\pi$
$492$	−0.400969	−	0.694498i	−0.0180771	−	0.0313104i
$493$	22.5797			1.01694
$494$		0			0
$495$	−1.39612			−0.0627511
$496$	7.51022	+	13.0081i	0.337219	+	0.584080i
$497$	5.01291	+	8.68261i	0.224860	+	0.389468i
$498$	2.26659	−	3.92586i	0.101569	−	0.175922i
$499$	8.06770			0.361160			0.180580	−	0.983560i	$-0.442203\pi$
$499$	8.06770			0.361160			0.180580	+	0.983560i	$0.442203\pi$
$500$	−2.21164	+	3.83067i	−0.0989074	+	0.171313i
$501$	4.73490	−	8.20108i	0.211540	−	0.366397i
$502$	1.69202			0.0755186
$503$	15.1211	−	26.1905i	0.674216	−	1.16778i	−0.302481	−	0.953155i	$-0.597815\pi$
$503$	15.1211	−	26.1905i	0.674216	−	1.16778i	0.976697	−	0.214622i	$-0.0688518\pi$
$504$	1.48307	+	2.56876i	0.0660614	+	0.114422i
$505$	0.668227	+	1.15740i	0.0297357	+	0.0515037i
$506$	20.9933			0.933266
$507$		0			0
$508$	−19.4601			−0.863403
$509$	8.02475	+	13.8993i	0.355691	+	0.616075i	0.987236	−	0.159264i	$-0.0509122\pi$
$509$	8.02475	+	13.8993i	0.355691	+	0.616075i	−0.631545	+	0.775339i	$0.717579\pi$
$510$	−0.208947	−	0.361908i	−0.00925235	−	0.0160255i
$511$	−6.44839	+	11.1689i	−0.285260	+	0.494085i
$512$	−22.9119			−1.01257
$513$	2.79105	−	4.83424i	0.123228	−	0.213437i
$514$	−4.58306	+	7.93810i	−0.202150	+	0.350135i
$515$	3.39745			0.149710
$516$	1.54407	−	2.67441i	0.0679740	−	0.117734i
$517$	19.0374	+	32.9737i	0.837262	+	1.45018i
$518$	1.24751	+	2.16075i	0.0548125	+	0.0949381i
$519$	4.77479			0.209590
$520$		0			0
$521$	−2.69309			−0.117986			−0.0589931	−	0.998258i	$-0.518789\pi$
$521$	−2.69309			−0.117986			−0.0589931	+	0.998258i	$0.518789\pi$
$522$	−1.32155	−	2.28900i	−0.0578428	−	0.100187i
$523$	−17.6978	−	30.6535i	−0.773872	−	1.34039i	−0.935426	−	0.353522i	$-0.884984\pi$
$523$	−17.6978	−	30.6535i	−0.773872	−	1.34039i	0.161554	−	0.986864i	$-0.448349\pi$
$524$	0.817667	−	1.41624i	0.0357200	−	0.0618688i
$525$	8.65817			0.377874
$526$	0.0740400	−	0.128241i	0.00322830	−	0.00559157i
$527$	−10.0157	+	17.3478i	−0.436292	+	0.755680i
$528$	−16.1153			−0.701328
$529$	−23.3180	+	40.3879i	−1.01382	+	1.75600i
$530$	−0.0583105	−	0.100997i	−0.00253285	−	0.00438702i
$531$	−6.85086	−	11.8660i	−0.297302	−	0.514942i
$532$	−17.6329			−0.764485
$533$		0			0
$534$	0.0609989			0.00263968
$535$	1.58277	+	2.74144i	0.0684291	+	0.118523i
$536$	5.04288	+	8.73452i	0.217819	+	0.377274i
$537$	−1.71768	+	2.97510i	−0.0741232	+	0.128385i
$538$	−12.1511			−0.523870
$539$	−11.0990	+	19.2241i	−0.478069	+	0.828040i
$540$	0.222521	−	0.385418i	0.00957578	−	0.0165857i
$541$	34.7338			1.49332			0.746660	−	0.665205i	$-0.231656\pi$
$541$	34.7338			1.49332			0.746660	+	0.665205i	$0.231656\pi$
$542$	−6.22737	+	10.7861i	−0.267488	+	0.463303i
$543$	6.74309	+	11.6794i	0.289374	+	0.501210i
$544$	−8.84481	−	15.3197i	−0.379218	−	0.656825i
$545$	−3.00000			−0.128506
$546$		0			0
$547$	−26.1183			−1.11674			−0.558368	−	0.829593i	$-0.688572\pi$
$547$	−26.1183			−1.11674			−0.558368	+	0.829593i	$0.688572\pi$
$548$	8.60268	+	14.9003i	0.367488	+	0.636508i
$549$	4.25786	+	7.37484i	0.181721	+	0.314750i
$550$	6.21260	−	10.7605i	0.264906	−	0.458831i
$551$	33.1521			1.41233
$552$	−7.05980	+	12.2279i	−0.300485	+	0.520456i
$553$	3.90462	−	6.76299i	0.166041	−	0.287592i
$554$	0.936017			0.0397676
$555$	0.394928	−	0.684035i	0.0167638	−	0.0290357i
$556$	−3.68718	−	6.38638i	−0.156371	−	0.270843i
$557$	12.3874	+	21.4556i	0.524871	+	0.909103i	0.999581	+	0.0289605i	$0.00921969\pi$
$557$	12.3874	+	21.4556i	0.524871	+	0.909103i	−0.474710	+	0.880142i	$0.657447\pi$
$558$	2.34481			0.0992639
$559$		0			0
$560$	−1.23431			−0.0521590
$561$	−10.7458	−	18.6122i	−0.453687	−	0.785809i
$562$	−6.06033	−	10.4968i	−0.255640	−	0.442781i
$563$	−2.63049	+	4.55614i	−0.110862	+	0.192019i	−0.916118	−	0.400909i	$-0.868694\pi$
$563$	−2.63049	+	4.55614i	−0.110862	+	0.192019i	0.805256	+	0.592927i	$0.202028\pi$
$564$	−12.1371			−0.511063
$565$	0.202243	−	0.350294i	0.00850841	−	0.0147370i
$566$	1.17576	−	2.03648i	0.0494209	−	0.0855994i
$567$	−1.75302			−0.0736199
$568$	−4.83848	+	8.38049i	−0.203018	+	0.351638i
$569$	16.8729	+	29.2248i	0.707350	+	1.22517i	0.965837	+	0.259151i	$0.0834427\pi$
$569$	16.8729	+	29.2248i	0.707350	+	1.22517i	−0.258487	+	0.966015i	$0.583224\pi$
$570$	−0.306782	−	0.531362i	−0.0128497	−	0.0222563i
$571$	23.0887			0.966234			0.483117	−	0.875556i	$-0.339505\pi$
$571$	23.0887			0.966234			0.483117	+	0.875556i	$0.339505\pi$
$572$		0			0
$573$	−1.30127			−0.0543615
$574$	0.173604	+	0.300690i	0.00724607	+	0.0125506i
$575$	20.6075	+	35.6933i	0.859393	+	1.48851i
$576$	1.81551	−	3.14456i	0.0756463	−	0.131023i
$577$	−3.57002			−0.148622			−0.0743110	−	0.997235i	$-0.523676\pi$
$577$	−3.57002			−0.148622			−0.0743110	+	0.997235i	$0.523676\pi$
$578$	−0.566376	+	0.980992i	−0.0235581	+	0.0408039i
$579$	−4.59783	+	7.96368i	−0.191079	+	0.330959i
$580$	2.64310			0.109749
$581$	8.92812	−	15.4640i	0.370401	−	0.641553i
$582$	3.04623	+	5.27622i	0.126270	+	0.218706i
$583$	−2.99880	−	5.19408i	−0.124198	−	0.215117i
$584$	−12.4480			−0.515103
$585$		0			0
$586$	14.5362			0.600484
$587$	−5.73125	−	9.92682i	−0.236554	−	0.409724i	0.723169	−	0.690671i	$-0.242685\pi$
$587$	−5.73125	−	9.92682i	−0.236554	−	0.409724i	−0.959723	+	0.280947i	$0.909351\pi$
$588$	−3.53803	−	6.12805i	−0.145906	−	0.252717i
$589$	−14.7054	+	25.4704i	−0.605924	+	1.04949i
$590$	−1.50604			−0.0620027
$591$	2.05615	−	3.56136i	0.0845789	−	0.146495i
$592$	4.55861	−	7.89574i	0.187358	−	0.324513i
$593$	21.8538			0.897430			0.448715	−	0.893675i	$-0.351882\pi$
$593$	21.8538			0.897430			0.448715	+	0.893675i	$0.351882\pi$
$594$	−1.25786	+	2.17869i	−0.0516108	+	0.0893926i
$595$	−0.823044	−	1.42555i	−0.0337415	−	0.0584420i
$596$	13.8644	+	24.0139i	0.567909	+	0.983647i
$597$	−24.7724			−1.01387
$598$		0			0
$599$	27.0573			1.10553			0.552765	−	0.833337i	$-0.313573\pi$
$599$	27.0573			1.10553			0.552765	+	0.833337i	$0.313573\pi$
$600$	4.17845	+	7.23728i	0.170584	+	0.295461i
$601$	−5.43900	−	9.42063i	−0.221861	−	0.384275i	0.733512	−	0.679677i	$-0.237880\pi$
$601$	−5.43900	−	9.42063i	−0.221861	−	0.384275i	−0.955373	+	0.295401i	$0.904547\pi$
$602$	−0.668522	+	1.15791i	−0.0272469	+	0.0471931i
$603$	−5.96077			−0.242741
$604$	3.31067	−	5.73424i	0.134709	−	0.233323i
$605$	−2.58761	+	4.48188i	−0.105201	+	0.182214i
$606$	2.40821			0.0978267
$607$	14.8180	−	25.6655i	0.601443	−	1.04173i	−0.391160	−	0.920323i	$-0.627926\pi$
$607$	14.8180	−	25.6655i	0.601443	−	1.04173i	0.992603	−	0.121407i	$-0.0387405\pi$
$608$	−12.9862	−	22.4927i	−0.526660	−	0.912201i
$609$	−5.20560	−	9.01636i	−0.210941	−	0.365361i
$610$	0.936017			0.0378982
$611$		0			0
$612$	6.85086			0.276929
$613$	5.11715	+	8.86317i	0.206680	+	0.357980i	0.950667	−	0.310214i	$-0.100401\pi$
$613$	5.11715	+	8.86317i	0.206680	+	0.357980i	−0.743987	+	0.668194i	$0.767067\pi$
$614$	4.61984	+	8.00180i	0.186442	+	0.322926i
$615$	0.0549581	−	0.0951903i	0.00221613	−	0.00383844i
$616$	16.7670			0.675563
$617$	13.1414	−	22.7615i	0.529052	−	0.916345i	−0.470374	−	0.882467i	$-0.655881\pi$
$617$	13.1414	−	22.7615i	0.529052	−	0.916345i	0.999426	−	0.0338776i	$-0.0107856\pi$
$618$	3.06100	−	5.30181i	0.123131	−	0.213270i
$619$	−29.0834			−1.16896			−0.584479	−	0.811408i	$-0.698701\pi$
$619$	−29.0834			−1.16896			−0.584479	+	0.811408i	$0.698701\pi$
$620$	−1.17241	+	2.03067i	−0.0470850	+	0.0815536i
$621$	−4.17241	−	7.22682i	−0.167433	−	0.290002i
$622$	−2.51477	−	4.35571i	−0.100833	−	0.174648i
$623$	0.240275			0.00962641
$624$		0			0
$625$	24.0887			0.963549
$626$	−0.950550	−	1.64640i	−0.0379916	−	0.0658034i
$627$	−15.7772	−	27.3270i	−0.630082	−	1.09133i
$628$	−4.39493	+	7.61224i	−0.175377	+	0.303761i
$629$	12.1588			0.484804
$630$	−0.0963427	+	0.166870i	−0.00383839	+	0.00664828i
$631$	12.7240	−	22.0386i	0.506535	−	0.877344i	−0.493436	−	0.869782i	$-0.664259\pi$
$631$	12.7240	−	22.0386i	0.506535	−	0.877344i	0.999971	−	0.00756243i	$-0.00240722\pi$
$632$	7.53750			0.299826
$633$	2.96950	−	5.14333i	0.118027	−	0.204429i
$634$	−3.44408	−	5.96533i	−0.136782	−	0.236913i
$635$	−1.33363	−	2.30992i	−0.0529236	−	0.0916664i
$636$	1.91185			0.0758099
$637$		0			0
$638$	−14.9409			−0.591517
$639$	−2.85958	−	4.95295i	−0.113123	−	0.195935i
$640$	−1.34870	−	2.33602i	−0.0533120	−	0.0923391i
$641$	13.3705	−	23.1583i	0.528102	−	0.914699i	−0.471361	−	0.881940i	$-0.656237\pi$
$641$	13.3705	−	23.1583i	0.528102	−	0.914699i	0.999463	−	0.0327590i	$-0.0104294\pi$
$642$	5.70410			0.225123
$643$	−16.4807	+	28.5454i	−0.649935	+	1.12572i	0.333203	+	0.942855i	$0.391870\pi$
$643$	−16.4807	+	28.5454i	−0.649935	+	1.12572i	−0.983138	+	0.182865i	$0.941463\pi$
$644$	−13.1799	+	22.8283i	−0.519362	+	0.899562i
$645$	0.423272			0.0166663
$646$	4.72252	−	8.17965i	0.185805	−	0.321824i
$647$	−17.2473	−	29.8732i	−0.678060	−	1.17443i	−0.975564	−	0.219714i	$-0.929487\pi$
$647$	−17.2473	−	29.8732i	−0.678060	−	1.17443i	0.297504	−	0.954721i	$-0.403846\pi$
$648$	−0.846011	−	1.46533i	−0.0332344	−	0.0575637i
$649$	−77.4529			−3.04029
$650$		0			0
$651$	9.23623			0.361996
$652$	−7.77628	−	13.4689i	−0.304543	−	0.527483i
$653$	−18.0758	−	31.3083i	−0.707362	−	1.22519i	−0.965832	−	0.259167i	$-0.916552\pi$
$653$	−18.0758	−	31.3083i	−0.707362	−	1.22519i	0.258471	−	0.966019i	$-0.416781\pi$
$654$	−2.70291	+	4.68157i	−0.105692	+	0.183064i
$655$	0.224144			0.00875805
$656$	0.634375	−	1.09877i	0.0247682	−	0.0428997i
$657$	3.67845	−	6.37126i	0.143510	−	0.248566i
$658$	5.25487			0.204856
$659$	3.40850	−	5.90370i	0.132776	−	0.229975i	−0.791969	−	0.610561i	$-0.790944\pi$
$659$	3.40850	−	5.90370i	0.132776	−	0.229975i	0.924746	+	0.380585i	$0.124277\pi$
$660$	−1.25786	−	2.17869i	−0.0489623	−	0.0848052i
$661$	−5.44720	−	9.43482i	−0.211871	−	0.366972i	0.740429	−	0.672135i	$-0.234622\pi$
$661$	−5.44720	−	9.43482i	−0.211871	−	0.366972i	−0.952300	+	0.305163i	$0.901289\pi$
$662$	2.70065			0.104964
$663$		0			0
$664$	17.2349			0.668844
$665$	−1.20841	−	2.09304i	−0.0468603	−	0.0811645i
$666$	−0.711636	−	1.23259i	−0.0275753	−	0.0477619i
$667$	24.7799	−	42.9201i	0.959483	−	1.66187i
$668$	17.0640			0.660225
$669$	7.10052	−	12.2985i	0.274522	−	0.475486i
$670$	−0.327593	+	0.567407i	−0.0126560	+	0.0219209i
$671$	48.1377			1.85833
$672$	−4.07822	+	7.06368i	−0.157321	+	0.272488i
$673$	−10.3693	−	17.9601i	−0.399706	−	0.692311i	0.593983	−	0.804477i	$-0.297554\pi$
$673$	−10.3693	−	17.9601i	−0.399706	−	0.692311i	−0.993689	+	0.112166i	$0.964221\pi$
$674$	2.69783	+	4.67277i	0.103916	+	0.179988i
$675$	−4.93900			−0.190102
$676$		0			0
$677$	−25.5786			−0.983067			−0.491534	−	0.870859i	$-0.663564\pi$
$677$	−25.5786			−0.983067			−0.491534	+	0.870859i	$0.663564\pi$
$678$	−0.364429	−	0.631209i	−0.0139958	−	0.0242414i
$679$	11.9991	+	20.7830i	0.460483	+	0.797580i
$680$	0.794405	−	1.37595i	0.0304640	−	0.0527653i
$681$	−16.0073			−0.613401
$682$	6.62737	−	11.4789i	0.253775	−	0.439552i
$683$	10.8155	−	18.7330i	0.413844	−	0.716799i	−0.581462	−	0.813573i	$-0.697519\pi$
$683$	10.8155	−	18.7330i	0.413844	−	0.716799i	0.995306	+	0.0967744i	$0.0308525\pi$
$684$	10.0586			0.384600
$685$	−1.17911	+	2.04228i	−0.0450516	+	0.0780316i
$686$	4.26241	+	7.38272i	0.162740	+	0.281873i
$687$	0.920583	+	1.59450i	0.0351224	+	0.0608339i
$688$	4.88577			0.186268
$689$		0			0
$690$	−0.917231			−0.0349184
$691$	1.31498	+	2.27761i	0.0500242	+	0.0866444i	0.889953	−	0.456052i	$-0.150737\pi$
$691$	1.31498	+	2.27761i	0.0500242	+	0.0866444i	−0.839929	+	0.542696i	$0.817404\pi$
$692$	4.30194	+	7.45117i	0.163535	+	0.283251i
$693$	−4.95473	+	8.58185i	−0.188215	+	0.325997i
$694$	−10.3026			−0.391081
$695$	0.505377	−	0.875338i	0.0191700	−	0.0332035i
$696$	5.02446	−	8.70262i	0.190452	−	0.329872i
$697$	1.69202			0.0640899
$698$	4.93900	−	8.55460i	0.186944	−	0.323796i
$699$	11.7126	+	20.2868i	0.443011	+	0.767318i
$700$	7.80074	+	13.5113i	0.294840	+	0.510678i
$701$	40.0925			1.51427			0.757136	−	0.653258i	$-0.226598\pi$
$701$	40.0925			1.51427			0.757136	+	0.653258i	$0.226598\pi$
$702$		0			0
$703$	17.8519			0.673298
$704$	−10.2627	−	17.7755i	−0.386790	−	0.669941i
$705$	−0.831773	−	1.44067i	−0.0313264	−	0.0542589i
$706$	1.12833	−	1.95433i	0.0424654	−	0.0735523i
$707$	9.48593			0.356755
$708$	12.3448	−	21.3818i	0.463947	−	0.803579i
$709$	11.6048	−	20.1002i	0.435829	−	0.754877i	−0.561534	−	0.827454i	$-0.689789\pi$
$709$	11.6048	−	20.1002i	0.435829	−	0.754877i	0.997363	+	0.0725761i	$0.0231220\pi$
$710$	−0.628630			−0.0235921
$711$	−2.22737	+	3.85791i	−0.0835327	+	0.144683i
$712$	0.115957	+	0.200844i	0.00434567	+	0.00752693i
$713$	21.9834	+	38.0763i	0.823284	+	1.42597i
$714$	−2.96615			−0.111005
$715$		0			0
$716$	−6.19029			−0.231342
$717$	7.30074	+	12.6453i	0.272651	+	0.472246i
$718$	3.71044	+	6.42667i	0.138472	+	0.239841i
$719$	13.0073	−	22.5293i	0.485090	−	0.840201i	−0.514763	−	0.857333i	$-0.672120\pi$
$719$	13.0073	−	22.5293i	0.485090	−	0.840201i	0.999853	+	0.0171315i	$0.00545340\pi$
$720$	0.704103			0.0262404
$721$	12.0573	−	20.8838i	0.449036	−	0.777754i
$722$	2.70583	−	4.68664i	0.100701	−	0.174419i
$723$	−8.63102			−0.320991
$724$	−12.1506	+	21.0455i	−0.451575	+	0.782151i
$725$	−14.6664	−	25.4029i	−0.544695	−	0.943440i
$726$	4.66272	+	8.07607i	0.173050	+	0.299731i
$727$	−16.5472			−0.613701			−0.306851	−	0.951758i	$-0.599275\pi$
$727$	−16.5472			−0.613701			−0.306851	+	0.951758i	$0.599275\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−0.404321	−	0.700305i	−0.0149646	−	0.0259194i
$731$	3.25786	+	5.64279i	0.120496	+	0.208706i
$732$	−7.67241	+	13.2890i	−0.283580	+	0.491176i
$733$	−18.8750			−0.697165			−0.348582	−	0.937278i	$-0.613337\pi$
$733$	−18.8750			−0.697165			−0.348582	+	0.937278i	$0.613337\pi$
$734$	−0.262414	+	0.454514i	−0.00968586	+	0.0167764i
$735$	0.484935	−	0.839931i	0.0178871	−	0.0309813i
$736$	−38.8267			−1.43117
$737$	−16.8475	+	29.1807i	−0.620586	+	1.07489i
$738$	−0.0990311	−	0.171527i	−0.00364539	−	0.00631399i
$739$	23.6619	+	40.9837i	0.870419	+	1.50761i	0.861564	+	0.507649i	$0.169485\pi$
$739$	23.6619	+	40.9837i	0.870419	+	1.50761i	0.00885483	+	0.999961i	$0.497181\pi$
$740$	1.42327			0.0523205
$741$		0			0
$742$	−0.827757			−0.0303879
$743$	−4.44385	−	7.69697i	−0.163029	−	0.282374i	0.772925	−	0.634498i	$-0.218793\pi$
$743$	−4.44385	−	7.69697i	−0.163029	−	0.282374i	−0.935954	+	0.352124i	$0.885460\pi$
$744$	4.45742	+	7.72048i	0.163417	+	0.283046i
$745$	−1.90030	+	3.29142i	−0.0696218	+	0.120588i
$746$	13.3924			0.490331
$747$	−5.09299	+	8.82132i	−0.186343	+	0.322755i
$748$	19.3632	−	33.5381i	0.707990	−	1.22627i
$749$	22.4685			0.820980
$750$	−0.546229	+	0.946096i	−0.0199455	+	0.0345466i
$751$	−0.355404	−	0.615578i	−0.0129689	−	0.0224627i	0.859468	−	0.511189i	$-0.170795\pi$
$751$	−0.355404	−	0.615578i	−0.0129689	−	0.0224627i	−0.872437	+	0.488727i	$0.837462\pi$
$752$	−9.60106	−	16.6295i	−0.350114	−	0.606416i
$753$	−3.80194			−0.138550
$754$		0			0
$755$	0.907542			0.0330288
$756$	−1.57942	−	2.73563i	−0.0574428	−	0.0994939i
$757$	−4.89277	−	8.47453i	−0.177831	−	0.308012i	0.763306	−	0.646037i	$-0.223575\pi$
$757$	−4.89277	−	8.47453i	−0.177831	−	0.308012i	−0.941137	+	0.338025i	$0.890241\pi$
$758$	4.26420	−	7.38581i	0.154883	−	0.268265i
$759$	−47.1715			−1.71222
$760$	1.16637	−	2.02021i	0.0423086	−	0.0732806i
$761$	−9.44049	+	16.3514i	−0.342218	+	0.592738i	−0.984844	−	0.173441i	$-0.944511\pi$
$761$	−9.44049	+	16.3514i	−0.342218	+	0.592738i	0.642627	+	0.766180i	$0.277845\pi$
$762$	−4.80625			−0.174112
$763$	−10.6468	+	18.4407i	−0.385438	+	0.667599i
$764$	−1.17241	−	2.03067i	−0.0424162	−	0.0734670i
$765$	0.469501	+	0.813199i	0.0169748	+	0.0294013i
$766$	−6.84846			−0.247445
$767$		0			0
$768$	2.40150			0.0866567
$769$	−6.21744	−	10.7689i	−0.224207	−	0.388337i	0.731875	−	0.681439i	$-0.238646\pi$
$769$	−6.21744	−	10.7689i	−0.224207	−	0.388337i	−0.956081	+	0.293102i	$0.905312\pi$
$770$	0.544605	+	0.943284i	0.0196262	+	0.0339936i
$771$	10.2981	−	17.8368i	0.370875	−	0.642375i
$772$	−16.5700			−0.596368
$773$	22.8373	−	39.5553i	0.821400	−	1.42271i	−0.0832399	−	0.996530i	$-0.526527\pi$
$773$	22.8373	−	39.5553i	0.821400	−	1.42271i	0.904640	−	0.426177i	$-0.140140\pi$
$774$	0.381355	−	0.660525i	0.0137075	−	0.0237421i
$775$	26.0224			0.934751
$776$	−11.5816	+	20.0599i	−0.415754	+	0.720107i
$777$	−2.80313	−	4.85517i	−0.100562	−	0.174178i

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)

\(f(q)\)	\(=\)	\(q+(0.222521 + 0.385418i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.900969 - 1.56052i) q^{4} +0.246980 q^{5} +(0.222521 - 0.385418i) q^{6} +(0.876510 - 1.51816i) q^{7} +1.69202 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.222521 + 0.385418i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.900969 - 1.56052i) q^{4} +0.246980 q^{5} +(0.222521 - 0.385418i) q^{6} +(0.876510 - 1.51816i) q^{7} +1.69202 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.0549581 + 0.0951903i) q^{10} +(2.82640 + 4.89546i) q^{11} -1.80194 q^{12} +0.780167 q^{14} +(-0.123490 - 0.213891i) q^{15} +(-1.42543 - 2.46891i) q^{16} +(1.90097 - 3.29257i) q^{17} -0.445042 q^{18} +(2.79105 - 4.83424i) q^{19} +(0.222521 - 0.385418i) q^{20} -1.75302 q^{21} +(-1.25786 + 2.17869i) q^{22} +(-4.17241 - 7.22682i) q^{23} +(-0.846011 - 1.46533i) q^{24} -4.93900 q^{25} +1.00000 q^{27} +(-1.57942 - 2.73563i) q^{28} +(2.96950 + 5.14333i) q^{29} +(0.0549581 - 0.0951903i) q^{30} -5.26875 q^{31} +(2.32640 - 4.02944i) q^{32} +(2.82640 - 4.89546i) q^{33} +1.69202 q^{34} +(0.216480 - 0.374955i) q^{35} +(0.900969 + 1.56052i) q^{36} +(1.59903 + 2.76960i) q^{37} +2.48427 q^{38} +0.417895 q^{40} +(0.222521 + 0.385418i) q^{41} +(-0.390084 - 0.675645i) q^{42} +(-0.856896 + 1.48419i) q^{43} +10.1860 q^{44} +(-0.123490 + 0.213891i) q^{45} +(1.85690 - 3.21624i) q^{46} +6.73556 q^{47} +(-1.42543 + 2.46891i) q^{48} +(1.96346 + 3.40081i) q^{49} +(-1.09903 - 1.90358i) q^{50} -3.80194 q^{51} -1.06100 q^{53} +(0.222521 + 0.385418i) q^{54} +(0.698062 + 1.20908i) q^{55} +(1.48307 - 2.56876i) q^{56} -5.58211 q^{57} +(-1.32155 + 2.28900i) q^{58} +(-6.85086 + 11.8660i) q^{59} -0.445042 q^{60} +(4.25786 - 7.37484i) q^{61} +(-1.17241 - 2.03067i) q^{62} +(0.876510 + 1.51816i) q^{63} -3.63102 q^{64} +2.51573 q^{66} +(2.98039 + 5.16218i) q^{67} +(-3.42543 - 5.93301i) q^{68} +(-4.17241 + 7.22682i) q^{69} +0.192685 q^{70} +(-2.85958 + 4.95295i) q^{71} +(-0.846011 + 1.46533i) q^{72} -7.35690 q^{73} +(-0.711636 + 1.23259i) q^{74} +(2.46950 + 4.27730i) q^{75} +(-5.02930 - 8.71101i) q^{76} +9.90946 q^{77} +4.45473 q^{79} +(-0.352052 - 0.609771i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.0990311 + 0.171527i) q^{82} +10.1860 q^{83} +(-1.57942 + 2.73563i) q^{84} +(0.469501 - 0.813199i) q^{85} -0.762709 q^{86} +(2.96950 - 5.14333i) q^{87} +(4.78232 + 8.28323i) q^{88} +(0.0685317 + 0.118700i) q^{89} -0.109916 q^{90} -15.0368 q^{92} +(2.63437 + 4.56287i) q^{93} +(1.49880 + 2.59600i) q^{94} +(0.689333 - 1.19396i) q^{95} -4.65279 q^{96} +(-6.84481 + 11.8556i) q^{97} +(-0.873822 + 1.51350i) q^{98} -5.65279 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 3 q^{3} + q^{4} - 8 q^{5} + q^{6} + 10 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q + q^2 - 3 * q^3 + q^4 - 8 * q^5 + q^6 + 10 * q^7 - 3 * q^9	\( 6 q + q^{2} - 3 q^{3} + q^{4} - 8 q^{5} + q^{6} + 10 q^{7} - 3 q^{9} + q^{10} - q^{11} - 2 q^{12} + 2 q^{14} + 4 q^{15} + 5 q^{16} + 7 q^{17} - 2 q^{18} + 11 q^{19} + q^{20} - 20 q^{21} + 5 q^{22} - 2 q^{23} - 10 q^{25} + 6 q^{27} - q^{28} + 8 q^{29} + q^{30} - 16 q^{31} - 4 q^{32} - q^{33} - 18 q^{35} + q^{36} + 14 q^{37} + 40 q^{38} + 14 q^{40} + q^{41} - q^{42} + 3 q^{43} + 32 q^{44} + 4 q^{45} + 3 q^{46} + 18 q^{47} + 5 q^{48} - 17 q^{49} - 11 q^{50} - 14 q^{51} - 26 q^{53} + q^{54} + 13 q^{55} - 7 q^{56} - 22 q^{57} - 12 q^{58} - 14 q^{59} - 2 q^{60} + 13 q^{61} + 16 q^{62} + 10 q^{63} + 8 q^{64} - 10 q^{66} + 5 q^{67} - 7 q^{68} - 2 q^{69} + 16 q^{70} - 6 q^{71} - 36 q^{73} - 7 q^{74} + 5 q^{75} + q^{76} - 30 q^{77} - 18 q^{79} - 16 q^{80} - 3 q^{81} - 5 q^{82} + 32 q^{83} - q^{84} - 7 q^{85} + 30 q^{86} + 8 q^{87} + 7 q^{88} - 5 q^{89} - 2 q^{90} - 34 q^{92} + 8 q^{93} - 32 q^{94} - 3 q^{95} + 8 q^{96} + 5 q^{97} - 13 q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q + q^2 - 3 * q^3 + q^4 - 8 * q^5 + q^6 + 10 * q^7 - 3 * q^9 + q^10 - q^11 - 2 * q^12 + 2 * q^14 + 4 * q^15 + 5 * q^16 + 7 * q^17 - 2 * q^18 + 11 * q^19 + q^20 - 20 * q^21 + 5 * q^22 - 2 * q^23 - 10 * q^25 + 6 * q^27 - q^28 + 8 * q^29 + q^30 - 16 * q^31 - 4 * q^32 - q^33 - 18 * q^35 + q^36 + 14 * q^37 + 40 * q^38 + 14 * q^40 + q^41 - q^42 + 3 * q^43 + 32 * q^44 + 4 * q^45 + 3 * q^46 + 18 * q^47 + 5 * q^48 - 17 * q^49 - 11 * q^50 - 14 * q^51 - 26 * q^53 + q^54 + 13 * q^55 - 7 * q^56 - 22 * q^57 - 12 * q^58 - 14 * q^59 - 2 * q^60 + 13 * q^61 + 16 * q^62 + 10 * q^63 + 8 * q^64 - 10 * q^66 + 5 * q^67 - 7 * q^68 - 2 * q^69 + 16 * q^70 - 6 * q^71 - 36 * q^73 - 7 * q^74 + 5 * q^75 + q^76 - 30 * q^77 - 18 * q^79 - 16 * q^80 - 3 * q^81 - 5 * q^82 + 32 * q^83 - q^84 - 7 * q^85 + 30 * q^86 + 8 * q^87 + 7 * q^88 - 5 * q^89 - 2 * q^90 - 34 * q^92 + 8 * q^93 - 32 * q^94 - 3 * q^95 + 8 * q^96 + 5 * q^97 - 13 * q^98 + 2 * q^99

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