LMFDB - Embedded newform 585.2.i.h.391.14

Newspace parameters

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.14
Character	$\chi$	$=$	585.391
Dual form			585.2.i.h.196.14

$q$-expansion

$f(q)$	$=$	$q+(1.26258 + 2.18685i) q^{2} +(-0.259881 - 1.71244i) q^{3} +(-2.18820 + 3.79007i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.41673 - 2.73041i) q^{6} +(0.799357 + 1.38453i) q^{7} -6.00077 q^{8} +(-2.86492 + 0.890062i) q^{9} +O(q^{10})$	\(q+(1.26258 + 2.18685i) q^{2} +(-0.259881 - 1.71244i) q^{3} +(-2.18820 + 3.79007i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.41673 - 2.73041i) q^{6} +(0.799357 + 1.38453i) q^{7} -6.00077 q^{8} +(-2.86492 + 0.890062i) q^{9} +2.52515 q^{10} +(2.68984 + 4.65893i) q^{11} +(7.05895 + 2.76220i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-2.01850 + 3.49614i) q^{14} +(-1.61296 - 0.631158i) q^{15} +(-3.20003 - 5.54262i) q^{16} +3.08624 q^{17} +(-5.56361 - 5.14138i) q^{18} +3.72202 q^{19} +(2.18820 + 3.79007i) q^{20} +(2.16319 - 1.72867i) q^{21} +(-6.79225 + 11.7645i) q^{22} +(-0.847988 + 1.46876i) q^{23} +(1.55948 + 10.2760i) q^{24} +(-0.500000 - 0.866025i) q^{25} -2.52515 q^{26} +(2.26872 + 4.67471i) q^{27} -6.99661 q^{28} +(-0.320437 - 0.555014i) q^{29} +(-0.656238 - 4.32418i) q^{30} +(-2.79393 + 4.83923i) q^{31} +(2.07980 - 3.60232i) q^{32} +(7.27912 - 5.81696i) q^{33} +(3.89662 + 6.74914i) q^{34} +1.59871 q^{35} +(2.89563 - 12.8059i) q^{36} +0.445044 q^{37} +(4.69933 + 8.13948i) q^{38} +(1.61296 + 0.631158i) q^{39} +(-3.00038 + 5.19682i) q^{40} +(3.19674 - 5.53691i) q^{41} +(6.51151 + 2.54798i) q^{42} +(-2.82920 - 4.90031i) q^{43} -23.5436 q^{44} +(-0.661646 + 2.92613i) q^{45} -4.28260 q^{46} +(-5.70445 - 9.88040i) q^{47} +(-8.65979 + 6.92029i) q^{48} +(2.22206 - 3.84872i) q^{49} +(1.26258 - 2.18685i) q^{50} +(-0.802054 - 5.28501i) q^{51} +(-2.18820 - 3.79007i) q^{52} -10.3086 q^{53} +(-7.35844 + 10.8635i) q^{54} +5.37967 q^{55} +(-4.79676 - 8.30823i) q^{56} +(-0.967280 - 6.37374i) q^{57} +(0.809153 - 1.40149i) q^{58} +(4.67420 - 8.09595i) q^{59} +(5.92161 - 4.73213i) q^{60} +(3.23867 + 5.60954i) q^{61} -14.1102 q^{62} +(-3.52241 - 3.25509i) q^{63} -2.29649 q^{64} +(0.500000 + 0.866025i) q^{65} +(21.9112 + 8.57397i) q^{66} +(7.64188 - 13.2361i) q^{67} +(-6.75331 + 11.6971i) q^{68} +(2.73554 + 1.07043i) q^{69} +(2.01850 + 3.49614i) q^{70} -5.56344 q^{71} +(17.1917 - 5.34105i) q^{72} +11.7669 q^{73} +(0.561902 + 0.973242i) q^{74} +(-1.35308 + 1.08128i) q^{75} +(-8.14451 + 14.1067i) q^{76} +(-4.30028 + 7.44830i) q^{77} +(0.656238 + 4.32418i) q^{78} +(2.66045 + 4.60803i) q^{79} -6.40006 q^{80} +(7.41558 - 5.09992i) q^{81} +16.1445 q^{82} +(4.87457 + 8.44301i) q^{83} +(1.81828 + 11.9813i) q^{84} +(1.54312 - 2.67276i) q^{85} +(7.14415 - 12.3740i) q^{86} +(-0.867154 + 0.692968i) q^{87} +(-16.1411 - 27.9572i) q^{88} -15.7300 q^{89} +(-7.23437 + 2.24754i) q^{90} -1.59871 q^{91} +(-3.71114 - 6.42787i) q^{92} +(9.01300 + 3.52683i) q^{93} +(14.4046 - 24.9495i) q^{94} +(1.86101 - 3.22336i) q^{95} +(-6.70927 - 2.62537i) q^{96} +(0.456931 + 0.791428i) q^{97} +11.2221 q^{98} +(-11.8529 - 10.9534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) $ 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.26258	+	2.18685i	0.892776	+	1.54633i	0.836533	+	0.547917i	$0.184579\pi$
$2$	1.26258	+	2.18685i	0.892776	+	1.54633i	0.0562438	+	0.998417i	$0.482088\pi$
$3$	−0.259881	−	1.71244i	−0.150042	−	0.988680i
$3$	−0.259881	−	1.71244i	−0.150042	−	0.988680i
$4$	−2.18820	+	3.79007i	−1.09410	+	1.89504i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	3.41673	−	2.73041i	1.39487	−	1.11469i
$7$	0.799357	+	1.38453i	0.302129	+	0.523302i	0.976618	−	0.214983i	$-0.0689695\pi$
$7$	0.799357	+	1.38453i	0.302129	+	0.523302i	−0.674489	+	0.738285i	$0.735636\pi$
$8$	−6.00077			−2.12159
$9$	−2.86492	+	0.890062i	−0.954975	+	0.296687i
$10$	2.52515			0.798524
$11$	2.68984	+	4.65893i	0.811016	+	1.40472i	0.912153	+	0.409849i	$0.134419\pi$
$11$	2.68984	+	4.65893i	0.811016	+	1.40472i	−0.101137	+	0.994872i	$0.532248\pi$
$12$	7.05895	+	2.76220i	2.03774	+	0.797379i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	−2.01850	+	3.49614i	−0.539466	+	0.934383i
$15$	−1.61296	−	0.631158i	−0.416464	−	0.162964i
$16$	−3.20003	−	5.54262i	−0.800008	−	1.38565i
$17$	3.08624			0.748524			0.374262	−	0.927323i	$-0.377896\pi$
$17$	3.08624			0.748524			0.374262	+	0.927323i	$0.377896\pi$
$18$	−5.56361	−	5.14138i	−1.31136	−	1.21183i
$19$	3.72202			0.853889			0.426944	−	0.904278i	$-0.359590\pi$
$19$	3.72202			0.853889			0.426944	+	0.904278i	$0.359590\pi$
$20$	2.18820	+	3.79007i	0.489296	+	0.847486i
$21$	2.16319	−	1.72867i	0.472046	−	0.377226i
$22$	−6.79225	+	11.7645i	−1.44811	+	2.50820i
$23$	−0.847988	+	1.46876i	−0.176818	+	0.306257i	−0.940789	−	0.338993i	$-0.889914\pi$
$23$	−0.847988	+	1.46876i	−0.176818	+	0.306257i	0.763971	+	0.645251i	$0.223247\pi$
$24$	1.55948	+	10.2760i	0.318328	+	2.09757i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.52515			−0.495223
$27$	2.26872	+	4.67471i	0.436615	+	0.899648i
$28$	−6.99661			−1.32223
$29$	−0.320437	−	0.555014i	−0.0595037	−	0.103063i	0.834739	−	0.550646i	$-0.185618\pi$
$29$	−0.320437	−	0.555014i	−0.0595037	−	0.103063i	−0.894243	+	0.447582i	$0.852285\pi$
$30$	−0.656238	−	4.32418i	−0.119812	−	0.789484i
$31$	−2.79393	+	4.83923i	−0.501805	+	0.869152i	0.498193	+	0.867066i	$0.333997\pi$
$31$	−2.79393	+	4.83923i	−0.501805	+	0.869152i	−0.999998	+	0.00208580i	$0.999336\pi$
$32$	2.07980	−	3.60232i	0.367660	−	0.636807i
$33$	7.27912	−	5.81696i	1.26713	−	1.01260i
$34$	3.89662	+	6.74914i	0.668264	+	1.15747i
$35$	1.59871			0.270232
$36$	2.89563	−	12.8059i	0.482604	−	2.13432i
$37$	0.445044			0.0731647			0.0365824	−	0.999331i	$-0.488353\pi$
$37$	0.445044			0.0731647			0.0365824	+	0.999331i	$0.488353\pi$
$38$	4.69933	+	8.13948i	0.762332	+	1.32040i
$39$	1.61296	+	0.631158i	0.258280	+	0.101066i
$40$	−3.00038	+	5.19682i	−0.474402	+	0.821689i
$41$	3.19674	−	5.53691i	0.499246	−	0.864720i	−0.500753	−	0.865590i	$-0.666944\pi$
$41$	3.19674	−	5.53691i	0.499246	−	0.864720i	1.00000		0.000870040i	$0.000276942\pi$
$42$	6.51151	+	2.54798i	1.00475	+	0.393163i
$43$	−2.82920	−	4.90031i	−0.431448	−	0.747290i	0.565550	−	0.824714i	$-0.308664\pi$
$43$	−2.82920	−	4.90031i	−0.431448	−	0.747290i	−0.996998	+	0.0774237i	$0.975331\pi$
$44$	−23.5436			−3.54933
$45$	−0.661646	+	2.92613i	−0.0986324	+	0.436201i
$46$	−4.28260			−0.631435
$47$	−5.70445	−	9.88040i	−0.832080	−	1.44120i	−0.896386	−	0.443274i	$-0.853817\pi$
$47$	−5.70445	−	9.88040i	−0.832080	−	1.44120i	0.0643062	−	0.997930i	$-0.479517\pi$
$48$	−8.65979	+	6.92029i	−1.24993	+	0.998858i
$49$	2.22206	−	3.84872i	0.317437	−	0.549817i
$50$	1.26258	−	2.18685i	0.178555	−	0.309267i
$51$	−0.802054	−	5.28501i	−0.112310	−	0.740050i
$52$	−2.18820	−	3.79007i	−0.303449	−	0.525588i
$53$	−10.3086			−1.41600			−0.708000	−	0.706212i	$-0.750402\pi$
$53$	−10.3086			−1.41600			−0.708000	+	0.706212i	$0.750402\pi$
$54$	−7.35844	+	10.8635i	−1.00136	+	1.47834i
$55$	5.37967			0.725395
$56$	−4.79676	−	8.30823i	−0.640993	−	1.11023i
$57$	−0.967280	−	6.37374i	−0.128119	−	0.844222i
$58$	0.809153	−	1.40149i	0.106247	−	0.184025i
$59$	4.67420	−	8.09595i	0.608529	−	1.05400i	−0.382954	−	0.923767i	$-0.625093\pi$
$59$	4.67420	−	8.09595i	0.608529	−	1.05400i	0.991483	−	0.130236i	$-0.0415734\pi$
$60$	5.92161	−	4.73213i	0.764477	−	0.610916i
$61$	3.23867	+	5.60954i	0.414669	+	0.718228i	0.995394	−	0.0958721i	$-0.0305640\pi$
$61$	3.23867	+	5.60954i	0.414669	+	0.718228i	−0.580724	+	0.814100i	$0.697231\pi$
$62$	−14.1102			−1.79200
$63$	−3.52241	−	3.25509i	−0.443782	−	0.410102i
$64$	−2.29649			−0.287062
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$	21.9112	+	8.57397i	2.69709	+	1.05538i
$67$	7.64188	−	13.2361i	0.933604	−	1.61705i	0.156498	−	0.987678i	$-0.449979\pi$
$67$	7.64188	−	13.2361i	0.933604	−	1.61705i	0.777105	−	0.629371i	$-0.216687\pi$
$68$	−6.75331	+	11.6971i	−0.818959	+	1.41848i
$69$	2.73554	+	1.07043i	0.329321	+	0.128865i
$70$	2.01850	+	3.49614i	0.241257	+	0.417869i
$71$	−5.56344			−0.660258			−0.330129	−	0.943936i	$-0.607092\pi$
$71$	−5.56344			−0.660258			−0.330129	+	0.943936i	$0.607092\pi$
$72$	17.1917	−	5.34105i	2.02607	−	0.629449i
$73$	11.7669			1.37721			0.688604	−	0.725138i	$-0.258224\pi$
$73$	11.7669			1.37721			0.688604	+	0.725138i	$0.258224\pi$
$74$	0.561902	+	0.973242i	0.0653197	+	0.113137i
$75$	−1.35308	+	1.08128i	−0.156240	+	0.124856i
$76$	−8.14451	+	14.1067i	−0.934239	+	1.61815i
$77$	−4.30028	+	7.44830i	−0.490062	+	0.848813i
$78$	0.656238	+	4.32418i	0.0743044	+	0.489617i
$79$	2.66045	+	4.60803i	0.299324	+	0.518444i	0.975981	−	0.217854i	$-0.0699056\pi$
$79$	2.66045	+	4.60803i	0.299324	+	0.518444i	−0.676658	+	0.736298i	$0.736572\pi$
$80$	−6.40006			−0.715549
$81$	7.41558	−	5.09992i	0.823953	−	0.566658i
$82$	16.1445			1.78286
$83$	4.87457	+	8.44301i	0.535054	+	0.926741i	0.999161	+	0.0409616i	$0.0130421\pi$
$83$	4.87457	+	8.44301i	0.535054	+	0.926741i	−0.464107	+	0.885779i	$0.653625\pi$
$84$	1.81828	+	11.9813i	0.198391	+	1.30727i
$85$	1.54312	−	2.67276i	0.167375	−	0.289902i
$86$	7.14415	−	12.3740i	0.770374	−	1.33433i
$87$	−0.867154	+	0.692968i	−0.0929687	+	0.0742940i
$88$	−16.1411	−	27.9572i	−1.72065	−	2.98025i
$89$	−15.7300			−1.66737			−0.833687	−	0.552237i	$-0.813774\pi$
$89$	−15.7300			−1.66737			−0.833687	+	0.552237i	$0.813774\pi$
$90$	−7.23437	+	2.24754i	−0.762570	+	0.236912i
$91$	−1.59871			−0.167591
$92$	−3.71114	−	6.42787i	−0.386913	−	0.670152i
$93$	9.01300	+	3.52683i	0.934605	+	0.365715i
$94$	14.4046	−	24.9495i	1.48572	−	2.57335i
$95$	1.86101	−	3.22336i	0.190935	−	0.330710i
$96$	−6.70927	−	2.62537i	−0.684762	−	0.267951i
$97$	0.456931	+	0.791428i	0.0463943	+	0.0803573i	0.888290	−	0.459283i	$-0.151894\pi$
$97$	0.456931	+	0.791428i	0.0463943	+	0.0803573i	−0.841896	+	0.539640i	$0.818560\pi$
$98$	11.2221			1.13360
$99$	−11.8529	−	10.9534i	−1.19126	−	1.10086i
$100$	4.37640			0.437640
$101$	−2.91268	−	5.04491i	−0.289823	−	0.501988i	0.683945	−	0.729534i	$-0.260263\pi$
$101$	−2.91268	−	5.04491i	−0.289823	−	0.501988i	−0.973767	+	0.227546i	$0.926930\pi$
$102$	10.5449	−	8.42670i	1.04410	−	0.834368i
$103$	8.54446	−	14.7994i	0.841911	−	1.45823i	−0.0463665	−	0.998924i	$-0.514764\pi$
$103$	8.54446	−	14.7994i	0.841911	−	1.45823i	0.888277	−	0.459308i	$-0.151902\pi$
$104$	3.00038	−	5.19682i	0.294212	−	0.509590i
$105$	−0.415475	−	2.73771i	−0.0405462	−	0.267173i
$106$	−13.0154	−	22.5434i	−1.26417	−	2.18961i
$107$	6.04979			0.584855			0.292428	−	0.956288i	$-0.405537\pi$
$107$	6.04979			0.584855			0.292428	+	0.956288i	$0.405537\pi$
$108$	−22.6819	−	1.63059i	−2.18257	−	0.156904i
$109$	−3.64767			−0.349383			−0.174692	−	0.984623i	$-0.555893\pi$
$109$	−3.64767			−0.349383			−0.174692	+	0.984623i	$0.555893\pi$
$110$	6.79225	+	11.7645i	0.647616	+	1.12170i
$111$	−0.115658	−	0.762112i	−0.0109778	−	0.0723365i
$112$	5.11594	−	8.86106i	0.483410	−	0.837291i
$113$	−6.16716	+	10.6818i	−0.580158	+	1.00486i	0.415302	+	0.909683i	$0.363676\pi$
$113$	−6.16716	+	10.6818i	−0.580158	+	1.00486i	−0.995460	+	0.0951792i	$0.969658\pi$
$114$	12.7171	−	10.1626i	1.19107	−	0.951817i
$115$	0.847988	+	1.46876i	0.0790753	+	0.136962i
$116$	2.80472			0.260412
$117$	0.661646	−	2.92613i	0.0611692	−	0.270521i
$118$	23.6061			2.17312
$119$	2.46701	+	4.27298i	0.226150	+	0.391704i
$120$	9.67900	+	3.78744i	0.883568	+	0.345744i
$121$	−8.97044	+	15.5373i	−0.815495	+	1.41248i
$122$	−8.17814	+	14.1649i	−0.740414	+	1.28243i
$123$	−10.3124	−	4.03529i	−0.929839	−	0.363850i
$124$	−12.2274	−	21.1784i	−1.09805	−	1.90188i
$125$	−1.00000			−0.0894427
$126$	2.67106	−	11.8128i	0.237957	−	1.05237i
$127$	14.2039			1.26039			0.630197	−	0.776435i	$-0.282974\pi$
$127$	14.2039			1.26039			0.630197	+	0.776435i	$0.282974\pi$
$128$	−7.05910	−	12.2267i	−0.623942	−	1.08070i
$129$	−7.65625	+	6.11833i	−0.674095	+	0.538689i
$130$	−1.26258	+	2.18685i	−0.110735	+	0.191799i
$131$	−9.34730	+	16.1900i	−0.816678	+	1.41453i	0.0914393	+	0.995811i	$0.470853\pi$
$131$	−9.34730	+	16.1900i	−0.816678	+	1.41453i	−0.908117	+	0.418717i	$0.862480\pi$
$132$	6.11852	+	40.3171i	0.532549	+	3.50915i
$133$	2.97522	+	5.15323i	0.257984	+	0.446842i
$134$	38.5938			3.33400
$135$	5.18278	+	0.372587i	0.446062	+	0.0320672i
$136$	−18.5198			−1.58806
$137$	−6.92932	−	12.0019i	−0.592012	−	1.02539i	−0.993961	−	0.109732i	$-0.965001\pi$
$137$	−6.92932	−	12.0019i	−0.592012	−	1.02539i	0.401950	−	0.915662i	$-0.368333\pi$
$138$	1.11297	+	7.33371i	0.0947419	+	0.624287i
$139$	−3.26336	+	5.65230i	−0.276794	+	0.479422i	−0.970586	−	0.240754i	$-0.922605\pi$
$139$	−3.26336	+	5.65230i	−0.276794	+	0.479422i	0.693792	+	0.720175i	$0.255939\pi$
$140$	−3.49830	+	6.05924i	−0.295661	+	0.512099i
$141$	−15.4371	+	12.3363i	−1.30004	+	1.03890i
$142$	−7.02426	−	12.1664i	−0.589463	−	1.02098i
$143$	−5.37967			−0.449871
$144$	14.1011	+	13.0310i	1.17509	+	1.08591i
$145$	−0.640875			−0.0532217
$146$	14.8566	+	25.7323i	1.22954	+	2.12962i
$147$	−7.16818	−	2.80494i	−0.591221	−	0.231348i
$148$	−0.973844	+	1.68675i	−0.0800495	+	0.138650i
$149$	5.88878	−	10.1997i	0.482427	−	0.835589i	−0.517369	−	0.855762i	$-0.673089\pi$
$149$	5.88878	−	10.1997i	0.482427	−	0.835589i	0.999796	+	0.0201737i	$0.00642192\pi$
$150$	−4.07297	−	1.59377i	−0.332557	−	0.130131i
$151$	4.79569	+	8.30638i	0.390268	+	0.675964i	0.992485	−	0.122369i	$-0.0390491\pi$
$151$	4.79569	+	8.30638i	0.390268	+	0.675964i	−0.602217	+	0.798332i	$0.705716\pi$
$152$	−22.3350			−1.81160
$153$	−8.84185	+	2.74695i	−0.714821	+	0.222077i
$154$	−21.7177			−1.75006
$155$	2.79393	+	4.83923i	0.224414	+	0.388697i
$156$	−5.92161	+	4.73213i	−0.474108	+	0.378874i
$157$	−3.96466	+	6.86698i	−0.316414	+	0.548045i	−0.979737	−	0.200288i	$-0.935812\pi$
$157$	−3.96466	+	6.86698i	−0.316414	+	0.548045i	0.663323	+	0.748333i	$0.269146\pi$
$158$	−6.71804	+	11.6360i	−0.534458	+	0.925709i
$159$	2.67902	+	17.6530i	0.212460	+	1.39997i
$160$	−2.07980	−	3.60232i	−0.164423	−	0.284789i
$161$	−2.71138			−0.213687
$162$	20.5155	+	9.77770i	1.61185	+	0.768209i
$163$	−2.74092			−0.214685			−0.107343	−	0.994222i	$-0.534234\pi$
$163$	−2.74092			−0.214685			−0.107343	+	0.994222i	$0.534234\pi$
$164$	13.9902	+	24.2317i	1.09245	+	1.89218i
$165$	−1.39807	−	9.21239i	−0.108840	−	0.717183i
$166$	−12.3090	+	21.3199i	−0.955367	+	1.65474i
$167$	8.88551	−	15.3902i	0.687582	−	1.19093i	−0.285036	−	0.958517i	$-0.592006\pi$
$167$	8.88551	−	15.3902i	0.687582	−	1.19093i	0.972618	−	0.232410i	$-0.0746610\pi$
$168$	−12.9808	+	10.3733i	−1.00149	+	0.800319i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	7.79323			0.597714
$171$	−10.6633	+	3.31282i	−0.815442	+	0.253338i
$172$	24.7634			1.88819
$173$	−5.28655	−	9.15657i	−0.401929	−	0.696161i	0.592030	−	0.805916i	$-0.298327\pi$
$173$	−5.28655	−	9.15657i	−0.401929	−	0.696161i	−0.993959	+	0.109755i	$0.964993\pi$
$174$	−2.61026	−	1.02141i	−0.197884	−	0.0774327i
$175$	0.799357	−	1.38453i	0.0604257	−	0.104660i
$176$	17.2151	−	29.8175i	1.29764	−	2.24758i
$177$	−15.0786	−	5.90032i	−1.13338	−	0.443495i
$178$	−19.8603	−	34.3990i	−1.48859	−	2.57832i
$179$	5.47435			0.409172			0.204586	−	0.978849i	$-0.434415\pi$
$179$	5.47435			0.409172			0.204586	+	0.978849i	$0.434415\pi$
$180$	−9.64242	−	8.91064i	−0.718704	−	0.664160i
$181$	−1.35324			−0.100585			−0.0502927	−	0.998735i	$-0.516015\pi$
$181$	−1.35324			−0.100585			−0.0502927	+	0.998735i	$0.516015\pi$
$182$	−2.01850	−	3.49614i	−0.149621	−	0.259151i
$183$	8.76435	−	7.00385i	0.647880	−	0.517739i
$184$	5.08858	−	8.81368i	0.375135	−	0.649753i
$185$	0.222522	−	0.385419i	0.0163601	−	0.0283366i
$186$	3.66697	+	24.1630i	0.268876	+	1.77171i
$187$	8.30149	+	14.3786i	0.607065	+	1.05147i
$188$	49.9299			3.64151
$189$	−4.65875	+	6.87786i	−0.338874	+	0.500291i
$190$	9.39866			0.681850
$191$	−1.83277	−	3.17445i	−0.132615	−	0.229695i	0.792069	−	0.610431i	$-0.209004\pi$
$191$	−1.83277	−	3.17445i	−0.132615	−	0.229695i	−0.924684	+	0.380736i	$0.875671\pi$
$192$	0.596814	+	3.93262i	0.0430714	+	0.283812i
$193$	4.37529	−	7.57823i	0.314940	−	0.545493i	−0.664484	−	0.747302i	$-0.731349\pi$
$193$	4.37529	−	7.57823i	0.314940	−	0.545493i	0.979425	+	0.201809i	$0.0646821\pi$
$194$	−1.15382	+	1.99848i	−0.0828395	+	0.143482i
$195$	1.35308	−	1.08128i	0.0968960	−	0.0774324i
$196$	9.72461	+	16.8435i	0.694615	+	1.20311i
$197$	−9.50585			−0.677264			−0.338632	−	0.940919i	$-0.609964\pi$
$197$	−9.50585			−0.677264			−0.338632	+	0.940919i	$0.609964\pi$
$198$	8.98813	−	39.7500i	0.638758	−	2.82491i
$199$	25.5829			1.81353			0.906763	−	0.421640i	$-0.138545\pi$
$199$	25.5829			1.81353			0.906763	+	0.421640i	$0.138545\pi$
$200$	3.00038	+	5.19682i	0.212159	+	0.367471i
$201$	−24.6521	−	9.64647i	−1.73882	−	0.680409i
$202$	7.35497	−	12.7392i	0.517494	−	0.896326i
$203$	0.512288	−	0.887308i	0.0359555	−	0.0622768i
$204$	21.7856	+	8.52482i	1.52530	+	0.596857i
$205$	−3.19674	−	5.53691i	−0.223270	−	0.386715i
$206$	43.1521			3.00655
$207$	1.12214	−	4.96265i	0.0779939	−	0.344928i
$208$	6.40006			0.443765
$209$	10.0116	+	17.3406i	0.692518	+	1.19948i
$210$	5.46238	−	4.36514i	0.376940	−	0.301224i
$211$	2.59044	−	4.48678i	0.178333	−	0.308882i	−0.762976	−	0.646426i	$-0.776263\pi$
$211$	2.59044	−	4.48678i	0.178333	−	0.308882i	0.941310	+	0.337544i	$0.109596\pi$
$212$	22.5574	−	39.0705i	1.54925	−	2.68337i
$213$	1.44583	+	9.52707i	0.0990666	+	0.652784i
$214$	7.63832	+	13.2300i	0.522145	+	0.904381i
$215$	−5.65839			−0.385899
$216$	−13.6141	−	28.0519i	−0.926319	−	1.90869i
$217$	−8.93340			−0.606439
$218$	−4.60546	−	7.97689i	−0.311921	−	0.540263i
$219$	−3.05798	−	20.1501i	−0.206639	−	1.36162i
$220$	−11.7718	+	20.3893i	−0.793654	+	1.37465i
$221$	−1.54312	+	2.67276i	−0.103802	+	0.179790i
$222$	1.52059	−	1.21515i	0.102056	−	0.0815556i
$223$	−7.52975	−	13.0419i	−0.504230	−	0.873351i	−0.999988	−	0.00489073i	$-0.998443\pi$
$223$	−7.52975	−	13.0419i	−0.504230	−	0.873351i	0.495759	−	0.868460i	$-0.334890\pi$
$224$	6.65001			0.444323
$225$	2.20328	+	2.03607i	0.146885	+	0.135738i
$226$	−31.1461			−2.07180
$227$	−10.8699	−	18.8272i	−0.721459	−	1.24960i	−0.960415	−	0.278573i	$-0.910139\pi$
$227$	−10.8699	−	18.8272i	−0.721459	−	1.24960i	0.238956	−	0.971030i	$-0.423195\pi$
$228$	26.2735	+	10.2810i	1.74001	+	0.680873i
$229$	−13.5876	+	23.5344i	−0.897892	+	1.55520i	−0.0677090	+	0.997705i	$0.521569\pi$
$229$	−13.5876	+	23.5344i	−0.897892	+	1.55520i	−0.830183	+	0.557490i	$0.811764\pi$
$230$	−2.14130	+	3.70884i	−0.141193	+	0.244554i
$231$	13.8724	+	5.42831i	0.912734	+	0.357157i
$232$	1.92287	+	3.33051i	0.126243	+	0.218659i
$233$	24.1372			1.58128			0.790641	−	0.612280i	$-0.209747\pi$
$233$	24.1372			1.58128			0.790641	+	0.612280i	$0.209747\pi$
$234$	7.23437	−	2.24754i	0.472926	−	0.146926i
$235$	−11.4089			−0.744235
$236$	20.4562	+	35.4311i	1.33158	+	2.30637i
$237$	7.19959	−	5.75340i	0.467664	−	0.373724i
$238$	−6.22957	+	10.7899i	−0.403803	+	0.699408i
$239$	−8.64007	+	14.9650i	−0.558879	+	0.968008i	0.438711	+	0.898628i	$0.355435\pi$
$239$	−8.64007	+	14.9650i	−0.558879	+	0.968008i	−0.997590	+	0.0693793i	$0.977898\pi$
$240$	1.66325	+	10.9597i	0.107363	+	0.707449i
$241$	8.28251	+	14.3457i	0.533523	+	0.924090i	0.999233	+	0.0391522i	$0.0124657\pi$
$241$	8.28251	+	14.3457i	0.533523	+	0.924090i	−0.465710	+	0.884938i	$0.654201\pi$
$242$	−45.3035			−2.91222
$243$	−10.6605	−	11.3734i	−0.683871	−	0.729603i
$244$	−28.3474			−1.81476
$245$	−2.22206	−	3.84872i	−0.141962	−	0.245885i
$246$	−4.19564	−	27.6465i	−0.267504	−	1.76268i
$247$	−1.86101	+	3.22336i	−0.118413	+	0.205097i
$248$	16.7657	−	29.0391i	1.06463	−	1.84399i
$249$	13.1914	−	10.5416i	0.835969	−	0.668047i
$250$	−1.26258	−	2.18685i	−0.0798524	−	0.138308i
$251$	10.2182			0.644965			0.322482	−	0.946575i	$-0.395483\pi$
$251$	10.2182			0.644965			0.322482	+	0.946575i	$0.395483\pi$
$252$	20.0448	−	6.22741i	1.26270	−	0.392290i
$253$	−9.12380			−0.573608
$254$	17.9335	+	31.0618i	1.12525	+	1.94899i
$255$	−4.97798	−	1.94791i	−0.311733	−	0.121983i
$256$	15.5288	−	26.8967i	0.970551	−	1.68104i
$257$	−14.2157	+	24.6224i	−0.886754	+	1.53590i	−0.0430639	+	0.999072i	$0.513712\pi$
$257$	−14.2157	+	24.6224i	−0.886754	+	1.53590i	−0.843690	+	0.536831i	$0.819621\pi$
$258$	−23.0465	−	9.01818i	−1.43481	−	0.561448i
$259$	0.355749	+	0.616175i	0.0221051	+	0.0382872i
$260$	−4.37640			−0.271413
$261$	1.41203	+	1.30486i	0.0874022	+	0.0807690i
$262$	−47.2067			−2.91644
$263$	−6.62365	−	11.4725i	−0.408432	−	0.707425i	0.586282	−	0.810107i	$-0.300591\pi$
$263$	−6.62365	−	11.4725i	−0.408432	−	0.707425i	−0.994714	+	0.102682i	$0.967258\pi$
$264$	−43.6803	+	34.9062i	−2.68834	+	2.14833i
$265$	−5.15432	+	8.92754i	−0.316627	+	0.548415i
$266$	−7.51288	+	13.0127i	−0.460644	+	0.797859i
$267$	4.08792	+	26.9367i	0.250176	+	1.64850i
$268$	33.4439	+	57.9265i	2.04291	+	3.53842i
$269$	−20.2913			−1.23718			−0.618590	−	0.785714i	$-0.712296\pi$
$269$	−20.2913			−1.23718			−0.618590	+	0.785714i	$0.712296\pi$
$270$	5.72886	+	11.8044i	0.348647	+	0.718390i
$271$	−7.28275			−0.442396			−0.221198	−	0.975229i	$-0.570997\pi$
$271$	−7.28275			−0.442396			−0.221198	+	0.975229i	$0.570997\pi$
$272$	−9.87607	−	17.1059i	−0.598825	−	1.03719i
$273$	0.415475	+	2.73771i	0.0251457	+	0.165694i
$274$	17.4976	−	30.3067i	1.05707	−	1.83090i
$275$	2.68984	−	4.65893i	0.162203	−	0.280944i
$276$	−10.0429	+	8.02559i	−0.604513	+	0.483084i
$277$	−6.87279	−	11.9040i	−0.412946	−	0.715244i	0.582264	−	0.813000i	$-0.302167\pi$
$277$	−6.87279	−	11.9040i	−0.412946	−	0.715244i	−0.995210	+	0.0977558i	$0.968834\pi$
$278$	−16.4809			−0.988461
$279$	3.69719	−	16.3508i	0.221345	−	0.978898i
$280$	−9.59351			−0.573322
$281$	0.451460	+	0.781952i	0.0269318	+	0.0466473i	0.879177	−	0.476495i	$-0.158093\pi$
$281$	0.451460	+	0.781952i	0.0269318	+	0.0466473i	−0.852245	+	0.523142i	$0.824760\pi$
$282$	−46.4681	−	18.1832i	−2.76714	−	1.08279i
$283$	13.9264	−	24.1212i	0.827836	−	1.43385i	−0.0718962	−	0.997412i	$-0.522905\pi$
$283$	13.9264	−	24.1212i	0.827836	−	1.43385i	0.899732	−	0.436442i	$-0.143762\pi$
$284$	12.1739	−	21.0858i	0.722388	−	1.25121i
$285$	−6.00346	−	2.34918i	−0.355614	−	0.139153i
$286$	−6.79225	−	11.7645i	−0.401634	−	0.695651i
$287$	10.2213			0.603346
$288$	−2.75218	+	12.1715i	−0.162174	+	0.717214i
$289$	−7.47511			−0.439713
$290$	−0.809153	−	1.40149i	−0.0475151	−	0.0822986i
$291$	1.23653	−	0.988146i	0.0724866	−	0.0579261i
$292$	−25.7482	+	44.5973i	−1.50680	+	2.60986i
$293$	1.62563	−	2.81568i	0.0949706	−	0.164494i	−0.814626	−	0.579987i	$-0.803058\pi$
$293$	1.62563	−	2.81568i	0.0949706	−	0.164494i	0.909596	+	0.415493i	$0.136391\pi$
$294$	−2.91640	−	19.2172i	−0.170088	−	1.12077i
$295$	−4.67420	−	8.09595i	−0.272142	−	0.471364i
$296$	−2.67060			−0.155226
$297$	−15.6767	+	23.1440i	−0.909653	+	1.34295i
$298$	29.7401			1.72280
$299$	−0.847988	−	1.46876i	−0.0490404	−	0.0849405i
$300$	−1.13734	−	7.49433i	−0.0656644	−	0.432686i
$301$	4.52307	−	7.83419i	0.260706	−	0.451555i
$302$	−12.1099	+	20.9749i	−0.696844	+	1.20697i
$303$	−7.88218	+	6.29888i	−0.452819	+	0.361861i
$304$	−11.9106	−	20.6297i	−0.683118	−	1.18319i
$305$	6.47734			0.370891
$306$	−17.1707	−	15.8675i	−0.981581	−	0.907087i
$307$	23.0790			1.31719			0.658593	−	0.752499i	$-0.271152\pi$
$307$	23.0790			1.31719			0.658593	+	0.752499i	$0.271152\pi$
$308$	−18.8197	−	32.5967i	−1.07235	−	1.85737i
$309$	−27.5637	−	10.7858i	−1.56805	−	0.613584i
$310$	−7.05511	+	12.2198i	−0.400703	+	0.694038i
$311$	−3.23713	+	5.60687i	−0.183561	+	0.317936i	−0.943091	−	0.332536i	$-0.892096\pi$
$311$	−3.23713	+	5.60687i	−0.183561	+	0.317936i	0.759530	+	0.650472i	$0.225429\pi$
$312$	−9.67900	−	3.78744i	−0.547965	−	0.214421i
$313$	−3.92191	−	6.79296i	−0.221680	−	0.383961i	0.733638	−	0.679540i	$-0.237821\pi$
$313$	−3.92191	−	6.79296i	−0.221680	−	0.383961i	−0.955318	+	0.295580i	$0.904487\pi$
$314$	−20.0227			−1.12995
$315$	−4.58019	+	1.42295i	−0.258065	+	0.0801744i
$316$	−23.2864			−1.30996
$317$	15.8696	+	27.4870i	0.891326	+	1.54382i	0.838287	+	0.545230i	$0.183558\pi$
$317$	15.8696	+	27.4870i	0.891326	+	1.54382i	0.0530394	+	0.998592i	$0.483109\pi$
$318$	−35.2219	+	28.1468i	−1.97514	+	1.57839i
$319$	1.72385	−	2.98579i	0.0965170	−	0.167172i
$320$	−1.14825	+	1.98882i	−0.0641889	+	0.111179i
$321$	−1.57222	−	10.3599i	−0.0877529	−	0.578234i
$322$	−3.42333	−	5.92938i	−0.190775	−	0.330431i
$323$	11.4870			0.639156
$324$	3.10229	+	39.2652i	0.172350	+	2.18140i
$325$	1.00000			0.0554700
$326$	−3.46062	−	5.99396i	−0.191666	−	0.331975i
$327$	0.947958	+	6.24642i	0.0524222	+	0.345428i
$328$	−19.1829	+	33.2257i	−1.05920	+	1.83458i
$329$	9.11979	−	15.7959i	0.502790	−	0.870858i
$330$	18.3809	−	14.6887i	1.01184	−	0.808587i
$331$	−9.05397	−	15.6819i	−0.497651	−	0.861958i	0.502345	−	0.864667i	$-0.332471\pi$
$331$	−9.05397	−	15.6819i	−0.497651	−	0.861958i	−0.999996	+	0.00270979i	$0.999137\pi$
$332$	−42.6662			−2.34161
$333$	−1.27502	+	0.396116i	−0.0698704	+	0.0217070i
$334$	44.8746			2.45543
$335$	−7.64188	−	13.2361i	−0.417520	−	0.723166i
$336$	−16.5036	−	6.45793i	−0.900345	−	0.352309i
$337$	7.48318	−	12.9613i	0.407635	−	0.706044i	−0.586989	−	0.809595i	$-0.699687\pi$
$337$	7.48318	−	12.9613i	0.407635	−	0.706044i	0.994624	+	0.103550i	$0.0330203\pi$
$338$	1.26258	−	2.18685i	0.0686751	−	0.118949i
$339$	19.8948	+	7.78491i	1.08054	+	0.422818i
$340$	6.75331	+	11.6971i	0.366250	+	0.634363i
$341$	−30.0609			−1.62789
$342$	−20.7079	−	19.1363i	−1.11975	−	1.03477i
$343$	18.2959			0.987884
$344$	16.9773	+	29.4056i	0.915357	+	1.58545i
$345$	2.29479	−	1.83383i	0.123547	−	0.0987303i
$346$	13.3493	−	23.1217i	0.717665	−	1.24303i
$347$	−5.90574	+	10.2290i	−0.317037	+	0.549124i	−0.979868	−	0.199645i	$-0.936021\pi$
$347$	−5.90574	+	10.2290i	−0.317037	+	0.549124i	0.662831	+	0.748769i	$0.269355\pi$
$348$	−0.728893	−	4.80293i	−0.0390728	−	0.257464i
$349$	11.6750	+	20.2217i	0.624949	+	1.08244i	0.988551	+	0.150889i	$0.0482137\pi$
$349$	11.6750	+	20.2217i	0.624949	+	1.08244i	−0.363602	+	0.931555i	$0.618453\pi$
$350$	4.03700			0.215787
$351$	−5.18278	−	0.372587i	−0.276636	−	0.0198872i
$352$	22.3773			1.19271
$353$	−6.78898	−	11.7589i	−0.361341	−	0.625861i	0.626841	−	0.779147i	$-0.284348\pi$
$353$	−6.78898	−	11.7589i	−0.361341	−	0.625861i	−0.988182	+	0.153286i	$0.951014\pi$
$354$	−6.13478	−	40.4242i	−0.326060	−	2.14852i
$355$	−2.78172	+	4.81808i	−0.147638	+	0.255717i
$356$	34.4203	−	59.6177i	1.82427	−	3.15973i
$357$	6.67612	−	5.33508i	0.353337	−	0.282362i
$358$	6.91178	+	11.9716i	0.365299	+	0.632716i
$359$	−5.90809			−0.311817			−0.155908	−	0.987772i	$-0.549830\pi$
$359$	−5.90809			−0.311817			−0.155908	+	0.987772i	$0.549830\pi$
$360$	3.97038	−	17.5590i	0.209258	−	0.925441i
$361$	−5.14660			−0.270874
$362$	−1.70857	−	2.95932i	−0.0898003	−	0.155539i
$363$	28.9379	+	11.3235i	1.51885	+	0.594332i
$364$	3.49830	−	6.05924i	0.183361	−	0.317590i
$365$	5.88343	−	10.1904i	0.307953	−	0.533390i
$366$	26.3820	+	10.3234i	1.37901	+	0.539613i
$367$	1.22318	+	2.11861i	0.0638494	+	0.110590i	0.896183	−	0.443685i	$-0.146329\pi$
$367$	1.22318	+	2.11861i	0.0638494	+	0.110590i	−0.832334	+	0.554275i	$0.812996\pi$
$368$	10.8544			0.565823
$369$	−4.23022	+	18.7081i	−0.220216	+	0.973906i
$370$	1.12380			0.0584237
$371$	−8.24028	−	14.2726i	−0.427814	−	0.740996i
$372$	−33.0892	+	26.4425i	−1.71559	+	1.37098i
$373$	4.09993	−	7.10128i	0.212286	−	0.367690i	−0.740143	−	0.672449i	$-0.765242\pi$
$373$	4.09993	−	7.10128i	0.212286	−	0.367690i	0.952430	+	0.304759i	$0.0985758\pi$
$374$	−20.9625	+	36.3082i	−1.08395	+	1.87745i
$375$	0.259881	+	1.71244i	0.0134202	+	0.0884302i
$376$	34.2311	+	59.2900i	1.76533	+	3.05765i
$377$	0.640875			0.0330067
$378$	−20.9229	−	1.50413i	−1.07616	−	0.0773643i
$379$	−0.155663			−0.00799586			−0.00399793	−	0.999992i	$-0.501273\pi$
$379$	−0.155663			−0.00799586			−0.00399793	+	0.999992i	$0.501273\pi$
$380$	8.14451	+	14.1067i	0.417805	+	0.723659i
$381$	−3.69133	−	24.3234i	−0.189112	−	1.24613i
$382$	4.62802	−	8.01597i	0.236790	−	0.410133i
$383$	−8.30317	+	14.3815i	−0.424272	+	0.734861i	−0.996352	−	0.0853368i	$-0.972803\pi$
$383$	−8.30317	+	14.3815i	−0.424272	+	0.734861i	0.572080	+	0.820198i	$0.306137\pi$
$384$	−19.1030	+	15.2658i	−0.974848	+	0.779030i
$385$	4.30028	+	7.44830i	0.219163	+	0.379601i
$386$	22.0966			1.12469
$387$	12.4670	+	11.5209i	0.633734	+	0.585638i
$388$	−3.99943			−0.203040
$389$	−10.4497	−	18.0994i	−0.529819	−	0.917674i	−0.999395	−	0.0347817i	$-0.988926\pi$
$389$	−10.4497	−	18.0994i	−0.529819	−	0.917674i	0.469576	−	0.882892i	$-0.344407\pi$
$390$	4.07297	+	1.59377i	0.206243	+	0.0807038i
$391$	−2.61710	+	4.53295i	−0.132352	+	0.229241i
$392$	−13.3341	+	23.0953i	−0.673471	+	1.16649i
$393$	30.1536	+	11.7993i	1.52105	+	0.595194i
$394$	−12.0019	−	20.7878i	−0.604645	−	1.04728i
$395$	5.32090			0.267723
$396$	67.4506	−	20.9553i	3.38952	−	1.05304i
$397$	−15.5139			−0.778618			−0.389309	−	0.921107i	$-0.627286\pi$
$397$	−15.5139			−0.778618			−0.389309	+	0.921107i	$0.627286\pi$
$398$	32.3004	+	55.9460i	1.61907	+	2.80432i
$399$	8.05141	−	6.43412i	0.403075	−	0.322109i
$400$	−3.20003	+	5.54262i	−0.160002	+	0.277131i
$401$	−16.8282	+	29.1473i	−0.840360	+	1.45555i	0.0492298	+	0.998787i	$0.484323\pi$
$401$	−16.8282	+	29.1473i	−0.840360	+	1.45555i	−0.889590	+	0.456759i	$0.849010\pi$
$402$	−10.0298	−	66.0897i	−0.500240	−	3.29626i
$403$	−2.79393	−	4.83923i	−0.139176	−	0.241059i
$404$	25.4941			1.26838
$405$	−0.708869	−	8.97204i	−0.0352240	−	0.445824i
$406$	2.58721			0.128401
$407$	1.19709	+	2.07343i	0.0593378	+	0.102776i
$408$	4.81294	+	31.7141i	0.238276	+	1.57008i
$409$	−10.0723	+	17.4458i	−0.498044	+	0.862638i	−0.999997	−	0.00225691i	$-0.999282\pi$
$409$	−10.0723	+	17.4458i	−0.498044	+	0.862638i	0.501953	+	0.864895i	$0.332615\pi$
$410$	8.07225	−	13.9815i	0.398660	−	0.690499i
$411$	−18.7518	+	14.9851i	−0.924960	+	0.739162i
$412$	37.3940	+	64.7682i	1.84227	+	3.19090i
$413$	14.9454			0.735416
$414$	12.2693	−	3.81178i	0.603005	−	0.187339i
$415$	9.74915			0.478567
$416$	2.07980	+	3.60232i	0.101971	+	0.176618i
$417$	10.5273	+	4.11939i	0.515525	+	0.201727i
$418$	−25.2809	+	43.7877i	−1.23653	+	2.14173i
$419$	16.7215	−	28.9625i	0.816898	−	1.41491i	−0.0910582	−	0.995846i	$-0.529025\pi$
$419$	16.7215	−	28.9625i	0.816898	−	1.41491i	0.907957	−	0.419064i	$-0.137642\pi$
$420$	11.2852	+	4.41597i	0.550664	+	0.215477i
$421$	−13.1682	−	22.8081i	−0.641781	−	1.11160i	−0.985035	−	0.172355i	$-0.944862\pi$
$421$	−13.1682	−	22.8081i	−0.641781	−	1.11160i	0.343254	−	0.939243i	$-0.388471\pi$
$422$	13.0825			0.636847
$423$	25.1370	+	23.2293i	1.22220	+	1.12945i
$424$	61.8598			3.00418
$425$	−1.54312	−	2.67276i	−0.0748524	−	0.129648i
$426$	−19.0088	+	15.1905i	−0.920978	+	0.735980i
$427$	−5.17771	+	8.96805i	−0.250567	+	0.433994i
$428$	−13.2381	+	22.9291i	−0.639890	+	1.10832i
$429$	1.39807	+	9.21239i	0.0674996	+	0.444778i
$430$	−7.14415	−	12.3740i	−0.344522	−	0.596729i
$431$	10.7108			0.515922			0.257961	−	0.966155i	$-0.416949\pi$
$431$	10.7108			0.515922			0.257961	+	0.966155i	$0.416949\pi$
$432$	18.6502	−	27.5339i	0.897306	−	1.32472i
$433$	−10.5665			−0.507795			−0.253898	−	0.967231i	$-0.581713\pi$
$433$	−10.5665			−0.507795			−0.253898	+	0.967231i	$0.581713\pi$
$434$	−11.2791	−	19.5360i	−0.541414	−	0.937757i
$435$	0.166551	+	1.09746i	0.00798551	+	0.0526193i
$436$	7.98182	−	13.8249i	0.382260	−	0.662094i
$437$	−3.15623	+	5.46674i	−0.150983	+	0.261510i
$438$	40.2042	−	32.1284i	1.92103	−	1.53515i
$439$	16.9499	+	29.3581i	0.808975	+	1.40119i	0.913574	+	0.406672i	$0.133311\pi$
$439$	16.9499	+	29.3581i	0.808975	+	1.40119i	−0.104599	+	0.994514i	$0.533356\pi$
$440$	−32.2822			−1.53899
$441$	−2.94043	+	13.0040i	−0.140020	+	0.619240i
$442$	−7.79323			−0.370686
$443$	−14.7155	−	25.4881i	−0.699157	−	1.21097i	−0.968759	−	0.248003i	$-0.920226\pi$
$443$	−14.7155	−	25.4881i	−0.699157	−	1.21097i	0.269603	−	0.962972i	$-0.413108\pi$
$444$	3.14154	+	1.22930i	0.149091	+	0.0583400i
$445$	−7.86499	+	13.6226i	−0.372836	+	0.645771i
$446$	19.0138	−	32.9328i	0.900328	−	1.55941i
$447$	−18.9967	−	7.43350i	−0.898514	−	0.351593i
$448$	−1.83572	−	3.17956i	−0.0867295	−	0.150220i
$449$	37.6658			1.77756			0.888780	−	0.458335i	$-0.151554\pi$
$449$	37.6658			1.77756			0.888780	+	0.458335i	$0.151554\pi$
$450$	−1.67076	+	7.38892i	−0.0787603	+	0.348317i
$451$	34.3948			1.61959
$452$	−26.9900	−	46.7480i	−1.26950	−	2.19884i
$453$	12.9779	−	10.3710i	0.609755	−	0.487273i
$454$	27.4481	−	47.5415i	1.28820	−	2.23123i
$455$	−0.799357	+	1.38453i	−0.0374744	+	0.0649076i
$456$	5.80442	+	38.2473i	0.271817	+	1.79110i
$457$	15.9738	+	27.6674i	0.747223	+	1.29423i	0.949149	+	0.314827i	$0.101947\pi$
$457$	15.9738	+	27.6674i	0.747223	+	1.29423i	−0.201926	+	0.979401i	$0.564720\pi$
$458$	−68.6214			−3.20647
$459$	7.00181	+	14.4273i	0.326817	+	0.673408i
$460$	−7.42227			−0.346065
$461$	7.01569	+	12.1515i	0.326753	+	0.565953i	0.981866	−	0.189578i	$-0.0607121\pi$
$461$	7.01569	+	12.1515i	0.326753	+	0.565953i	−0.655112	+	0.755531i	$0.727379\pi$
$462$	5.64402	+	37.1904i	0.262583	+	1.73025i
$463$	−20.4647	+	35.4460i	−0.951077	+	1.64731i	−0.207976	+	0.978134i	$0.566688\pi$
$463$	−20.4647	+	35.4460i	−0.951077	+	1.64731i	−0.743101	+	0.669180i	$0.766646\pi$
$464$	−2.05082	+	3.55212i	−0.0952069	+	0.164903i
$465$	7.56083	−	6.04208i	0.350625	−	0.280195i
$466$	30.4751	+	52.7844i	1.41173	+	2.44519i
$467$	−4.20484			−0.194577			−0.0972884	−	0.995256i	$-0.531017\pi$
$467$	−4.20484			−0.194577			−0.0972884	+	0.995256i	$0.531017\pi$
$468$	9.64242	+	8.91064i	0.445721	+	0.411894i
$469$	24.4343			1.12827
$470$	−14.4046	−	24.9495i	−0.664435	−	1.15084i
$471$	12.7897	+	5.00465i	0.589316	+	0.230602i
$472$	−28.0488	+	48.5819i	−1.29105	+	2.23616i
$473$	15.2201	−	26.3621i	0.699823	−	1.21213i
$474$	21.6718	+	8.48029i	0.995421	+	0.389513i
$475$	−1.86101	−	3.22336i	−0.0853889	−	0.147898i
$476$	−21.5932			−0.989724
$477$	29.5335	−	9.17533i	1.35224	−	0.420109i
$478$	−43.6350			−1.99582
$479$	−13.2705	−	22.9851i	−0.606344	−	1.05022i	−0.991838	−	0.127507i	$-0.959302\pi$
$479$	−13.2705	−	22.9851i	−0.606344	−	1.05022i	0.385494	−	0.922710i	$-0.374031\pi$
$480$	−5.62827	+	4.49772i	−0.256894	+	0.205292i
$481$	−0.222522	+	0.385419i	−0.0101461	+	0.0175736i
$482$	−20.9146	+	36.2252i	−0.952634	+	1.65001i
$483$	0.704636	+	4.64309i	0.0320620	+	0.211268i
$484$	−39.2582	−	67.9972i	−1.78446	−	3.09078i
$485$	0.913862			0.0414963
$486$	11.4122	−	37.6726i	0.517667	−	1.70887i
$487$	29.2682			1.32627			0.663135	−	0.748500i	$-0.269225\pi$
$487$	29.2682			1.32627			0.663135	+	0.748500i	$0.269225\pi$
$488$	−19.4345	−	33.6616i	−0.879759	−	1.52379i
$489$	0.712311	+	4.69366i	0.0322118	+	0.212255i
$490$	5.61103	−	9.71860i	0.253481	−	0.439041i
$491$	−11.4610	+	19.8511i	−0.517229	+	0.895867i	0.482570	+	0.875857i	$0.339703\pi$
$491$	−11.4610	+	19.8511i	−0.517229	+	0.895867i	−0.999800	+	0.0200103i	$0.993630\pi$
$492$	37.8597	−	30.2548i	1.70685	−	1.36399i
$493$	−0.988947	−	1.71291i	−0.0445399	−	0.0771454i
$494$	−9.39866			−0.422866
$495$	−15.4124	+	4.78824i	−0.692734	+	0.215215i
$496$	35.7627			1.60579
$497$	−4.44717	−	7.70273i	−0.199483	−	0.345514i
$498$	39.7080	+	15.5379i	1.77936	+	0.696271i
$499$	−2.93038	+	5.07556i	−0.131182	+	0.227213i	−0.924132	−	0.382072i	$-0.875210\pi$
$499$	−2.93038	+	5.07556i	−0.131182	+	0.227213i	0.792951	+	0.609286i	$0.208544\pi$
$500$	2.18820	−	3.79007i	0.0978592	−	0.169497i
$501$	−28.6640	−	11.2163i	−1.28061	−	0.501109i
$502$	12.9012	+	22.3456i	0.575809	+	0.997331i
$503$	0.171544			0.00764877			0.00382439	−	0.999993i	$-0.498783\pi$
$503$	0.171544			0.00764877			0.00382439	+	0.999993i	$0.498783\pi$
$504$	21.1372	+	19.5330i	0.941525	+	0.870070i
$505$	−5.82536			−0.259225
$506$	−11.5195	−	19.9524i	−0.512104	−	0.886990i
$507$	−1.35308	+	1.08128i	−0.0600924	+	0.0480215i
$508$	−31.0810	+	53.8339i	−1.37900	+	2.38849i
$509$	18.2170	−	31.5528i	0.807454	−	1.39855i	−0.107167	−	0.994241i	$-0.534178\pi$
$509$	18.2170	−	31.5528i	0.807454	−	1.39855i	0.914622	−	0.404311i	$-0.132489\pi$
$510$	−2.02531	−	13.3455i	−0.0896823	−	0.590947i
$511$	9.40593	+	16.2915i	0.416094	+	0.720696i
$512$	50.1889			2.21806
$513$	8.44421	+	17.3993i	0.372821	+	0.768200i
$514$	−71.7939			−3.16669
$515$	−8.54446	−	14.7994i	−0.376514	−	0.652141i
$516$	−6.43552	−	42.4059i	−0.283308	−	1.86681i
$517$	30.6881	−	53.1533i	1.34966	−	2.33768i
$518$	−0.898320	+	1.55594i	−0.0394699	+	0.0683639i
$519$	−14.3062	+	11.4325i	−0.627974	+	0.501832i
$520$	−3.00038	−	5.19682i	−0.131576	−	0.227896i
$521$	6.99027			0.306249			0.153125	−	0.988207i	$-0.451066\pi$
$521$	6.99027			0.306249			0.153125	+	0.988207i	$0.451066\pi$
$522$	−1.07075	+	4.73537i	−0.0468653	+	0.207262i
$523$	10.2358			0.447579			0.223790	−	0.974637i	$-0.428157\pi$
$523$	10.2358			0.447579			0.223790	+	0.974637i	$0.428157\pi$
$524$	−40.9075	−	70.8539i	−1.78705	−	3.09527i
$525$	−2.57866	−	1.00904i	−0.112542	−	0.0440382i
$526$	16.7257	−	28.9698i	0.729277	−	1.26314i
$527$	−8.62275	+	14.9350i	−0.375613	+	0.650581i
$528$	−55.5346	−	21.7309i	−2.41683	−	0.945718i
$529$	10.0618	+	17.4276i	0.437471	+	0.757722i
$530$	−26.0309			−1.13071
$531$	−6.18533	+	27.3546i	−0.268420	+	1.18709i
$532$	−26.0415			−1.12904
$533$	3.19674	+	5.53691i	0.138466	+	0.239830i
$534$	−53.7451	+	42.9493i	−2.32578	+	1.85860i
$535$	3.02489	−	5.23927i	0.130778	−	0.226513i
$536$	−45.8571	+	79.4269i	−1.98073	+	3.43072i
$537$	−1.42268	−	9.37451i	−0.0613930	−	0.404540i
$538$	−25.6193	−	44.3739i	−1.10453	−	1.91309i
$539$	23.9079			1.02979
$540$	−12.7531	+	18.8278i	−0.548805	+	0.810220i
$541$	−14.1128			−0.606755			−0.303378	−	0.952870i	$-0.598114\pi$
$541$	−14.1128			−0.606755			−0.303378	+	0.952870i	$0.598114\pi$
$542$	−9.19503	−	15.9263i	−0.394960	−	0.684092i
$543$	0.351680	+	2.31734i	0.0150920	+	0.0994467i
$544$	6.41877	−	11.1176i	0.275202	−	0.476665i
$545$	−1.82383	+	3.15897i	−0.0781244	+	0.135316i
$546$	−5.46238	+	4.36514i	−0.233768	+	0.186811i
$547$	3.24835	+	5.62631i	0.138890	+	0.240564i	0.927077	−	0.374872i	$-0.122313\pi$
$547$	3.24835	+	5.62631i	0.138890	+	0.240564i	−0.788187	+	0.615436i	$0.788980\pi$
$548$	60.6509			2.59088
$549$	−14.2714	−	13.1883i	−0.609088	−	0.562863i
$550$	13.5845			0.579245
$551$	−1.19267	−	2.06577i	−0.0508096	−	0.0880047i
$552$	−16.4154	−	6.42340i	−0.698684	−	0.273398i
$553$	−4.25329	+	7.36692i	−0.180868	+	0.313273i
$554$	17.3549	−	30.0595i	0.737337	−	1.27711i
$555$	−0.717837	−	0.280893i	−0.0304705	−	0.0119232i
$556$	−14.2817	−	24.7367i	−0.605681	−	1.04907i
$557$	13.7471			0.582483			0.291242	−	0.956650i	$-0.405932\pi$
$557$	13.7471			0.582483			0.291242	+	0.956650i	$0.405932\pi$
$558$	40.4247	−	12.5590i	1.71131	−	0.531663i
$559$	5.65839			0.239324
$560$	−5.11594	−	8.86106i	−0.216188	−	0.374448i
$561$	22.4651	−	17.9525i	0.948479	−	0.757957i
$562$	−1.14001	+	1.97455i	−0.0480882	+	0.0832913i
$563$	−0.645415	+	1.11789i	−0.0272010	+	0.0471135i	−0.879305	−	0.476258i	$-0.841993\pi$
$563$	−0.645415	+	1.11789i	−0.0272010	+	0.0471135i	0.852104	+	0.523372i	$0.175326\pi$
$564$	−12.9758	−	85.5021i	−0.546380	−	3.60029i
$565$	6.16716	+	10.6818i	0.259454	+	0.449388i
$566$	70.3324			2.95629
$567$	12.9887	+	6.19041i	0.545473	+	0.259973i
$568$	33.3849			1.40080
$569$	−5.81243	−	10.0674i	−0.243670	−	0.422048i	0.718087	−	0.695953i	$-0.245018\pi$
$569$	−5.81243	−	10.0674i	−0.243670	−	0.422048i	−0.961757	+	0.273905i	$0.911685\pi$
$570$	−2.44253	−	16.0947i	−0.102306	−	0.674132i
$571$	8.88874	−	15.3958i	0.371982	−	0.644292i	−0.617888	−	0.786266i	$-0.712012\pi$
$571$	8.88874	−	15.3958i	0.371982	−	0.644292i	0.989870	+	0.141974i	$0.0453449\pi$
$572$	11.7718	−	20.3893i	0.492203	−	0.852521i
$573$	−4.95976	+	3.96349i	−0.207197	+	0.165577i
$574$	12.9052	+	22.3525i	0.538653	+	0.932975i
$575$	1.69598			0.0707271
$576$	6.57928	−	2.04402i	0.274137	−	0.0851675i
$577$	−30.0210			−1.24979			−0.624896	−	0.780708i	$-0.714859\pi$
$577$	−30.0210			−1.24979			−0.624896	+	0.780708i	$0.714859\pi$
$578$	−9.43790	−	16.3469i	−0.392565	−	0.679942i
$579$	−14.1143	−	5.52300i	−0.586572	−	0.229528i
$580$	1.40236	−	2.42896i	0.0582299	−	0.100857i
$581$	−7.79305	+	13.4980i	−0.323310	+	0.559990i
$582$	3.72213	+	1.45649i	0.154287	+	0.0603734i
$583$	−27.7286	−	48.0273i	−1.14840	−	1.98909i
$584$	−70.6103			−2.92187
$585$	−2.20328	−	2.03607i	−0.0910943	−	0.0841810i
$586$	8.20995			0.339150
$587$	1.10857	+	1.92010i	0.0457556	+	0.0792510i	0.887996	−	0.459851i	$-0.152097\pi$
$587$	1.10857	+	1.92010i	0.0457556	+	0.0792510i	−0.842241	+	0.539102i	$0.818764\pi$
$588$	26.3163	−	21.0301i	1.08527	−	0.867268i
$589$	−10.3991	+	18.0117i	−0.428486	+	0.742159i
$590$	11.8031	−	20.4435i	0.485925	−	0.841646i
$591$	2.47039	+	16.2782i	0.101618	+	0.669597i
$592$	−1.42415	−	2.46671i	−0.0585323	−	0.101381i
$593$	15.6211			0.641483			0.320742	−	0.947167i	$-0.396068\pi$
$593$	15.6211			0.641483			0.320742	+	0.947167i	$0.396068\pi$
$594$	−70.4054	−	5.06141i	−2.88877	−	0.207672i
$595$	4.93402			0.202275
$596$	25.7716	+	44.6378i	1.05565	+	1.82843i
$597$	−6.64851	−	43.8093i	−0.272105	−	1.79300i
$598$	2.14130	−	3.70884i	0.0875643	−	0.151666i
$599$	−11.5585	+	20.0200i	−0.472269	+	0.817994i	−0.999496	−	0.0317303i	$-0.989898\pi$
$599$	−11.5585	+	20.0200i	−0.472269	+	0.817994i	0.527227	+	0.849724i	$0.323232\pi$
$600$	8.11951	−	6.48854i	0.331478	−	0.264894i
$601$	1.70480	+	2.95280i	0.0695402	+	0.120447i	0.898699	−	0.438566i	$-0.144513\pi$
$601$	1.70480	+	2.95280i	0.0695402	+	0.120447i	−0.829159	+	0.559013i	$0.811180\pi$
$602$	22.8429			0.931007
$603$	−10.1124	+	44.7222i	−0.411810	+	1.82123i
$604$	−41.9757			−1.70797
$605$	8.97044	+	15.5373i	0.364700	+	0.631679i
$606$	−23.7265	−	9.28430i	−0.963825	−	0.377149i
$607$	−10.5060	+	18.1970i	−0.426427	+	0.738593i	−0.996553	−	0.0829645i	$-0.973561\pi$
$607$	−10.5060	+	18.1970i	−0.426427	+	0.738593i	0.570126	+	0.821558i	$0.306895\pi$
$608$	7.74105	−	13.4079i	0.313941	−	0.543762i
$609$	−1.65260	−	0.646669i	−0.0669667	−	0.0262044i
$610$	8.17814	+	14.1649i	0.331123	+	0.573522i
$611$	11.4089			0.461555
$612$	8.93660	−	39.5221i	0.361241	−	1.59759i
$613$	4.34045			0.175309			0.0876546	−	0.996151i	$-0.472063\pi$
$613$	4.34045			0.175309			0.0876546	+	0.996151i	$0.472063\pi$
$614$	29.1390	+	50.4702i	1.17595	+	2.03681i
$615$	−8.65087	+	6.91317i	−0.348837	+	0.278766i
$616$	25.8050	−	44.6955i	1.03971	−	1.80083i
$617$	−12.3921	+	21.4637i	−0.498887	+	0.864098i	−0.999999	−	0.00128460i	$-0.999591\pi$
$617$	−12.3921	+	21.4637i	−0.498887	+	0.864098i	0.501112	+	0.865382i	$0.332924\pi$
$618$	−11.2144	−	73.8956i	−0.451110	−	2.97252i
$619$	−17.4471	−	30.2193i	−0.701258	−	1.21461i	−0.968025	−	0.250853i	$-0.919289\pi$
$619$	−17.4471	−	30.2193i	−0.701258	−	1.21461i	0.266767	−	0.963761i	$-0.414045\pi$
$620$	−24.4547			−0.982126
$621$	−8.78987	−	0.631899i	−0.352725	−	0.0253572i
$622$	−16.3485			−0.655514
$623$	−12.5739	−	21.7786i	−0.503761	−	0.872540i
$624$	−1.66325	−	10.9597i	−0.0665834	−	0.438741i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	9.90343	−	17.1533i	0.395821	−	0.685582i
$627$	27.0930	−	21.6508i	1.08199	−	0.864650i
$628$	−17.3509	−	30.0527i	−0.692377	−	1.19923i
$629$	1.37351			0.0547655
$630$	−8.89463	−	8.21959i	−0.354370	−	0.327476i
$631$	−27.9002			−1.11069			−0.555344	−	0.831620i	$-0.687414\pi$
$631$	−27.9002			−1.11069			−0.555344	+	0.831620i	$0.687414\pi$
$632$	−15.9647	−	27.6517i	−0.635043	−	1.09993i
$633$	−8.35656	−	3.26996i	−0.332143	−	0.129969i
$634$	−40.0732	+	69.4088i	−1.59151	+	2.75658i
$635$	7.10196	−	12.3010i	0.281833	−	0.488149i
$636$	−72.7682	−	28.4745i	−2.88545	−	1.12909i
$637$	2.22206	+	3.84872i	0.0880411	+	0.152492i
$638$	8.70596			0.344672
$639$	15.9388	−	4.95180i	0.630530	−	0.195890i
$640$	−14.1182			−0.558071
$641$	−1.63649	−	2.83448i	−0.0646374	−	0.111955i	0.831896	−	0.554932i	$-0.187256\pi$
$641$	−1.63649	−	2.83448i	−0.0646374	−	0.111955i	−0.896533	+	0.442977i	$0.853922\pi$
$642$	20.6705	−	16.5184i	0.815800	−	0.651929i
$643$	−17.2981	+	29.9612i	−0.682170	+	1.18155i	0.292148	+	0.956373i	$0.405630\pi$
$643$	−17.2981	+	29.9612i	−0.682170	+	1.18155i	−0.974317	+	0.225179i	$0.927703\pi$
$644$	5.93304	−	10.2763i	0.233795	−	0.404944i
$645$	1.47051	+	9.68967i	0.0579011	+	0.381531i
$646$	14.5033	+	25.1204i	0.570623	+	0.988349i
$647$	32.2974			1.26974			0.634871	−	0.772618i	$-0.281053\pi$
$647$	32.2974			1.26974			0.634871	+	0.772618i	$0.281053\pi$
$648$	−44.4992	+	30.6034i	−1.74809	+	1.20222i
$649$	50.2913			1.97411
$650$	1.26258	+	2.18685i	0.0495223	+	0.0857752i
$651$	2.32162	+	15.2979i	0.0909914	+	0.599574i
$652$	5.99767	−	10.3883i	0.234887	−	0.406836i
$653$	−17.7871	+	30.8081i	−0.696062	+	1.20561i	0.273760	+	0.961798i	$0.411733\pi$
$653$	−17.7871	+	30.8081i	−0.696062	+	1.20561i	−0.969821	+	0.243816i	$0.921601\pi$
$654$	−12.4631	+	9.95963i	−0.487346	+	0.389452i
$655$	9.34730	+	16.1900i	0.365229	+	0.632596i
$656$	−40.9186			−1.59760
$657$	−33.7112	+	10.4732i	−1.31520	+	0.408600i
$658$	46.0577			1.79552
$659$	15.0300	+	26.0327i	0.585484	+	1.01409i	0.994815	+	0.101703i	$0.0324290\pi$
$659$	15.0300	+	26.0327i	0.585484	+	1.01409i	−0.409330	+	0.912386i	$0.634238\pi$
$660$	37.9749	+	14.8597i	1.47817	+	0.578414i
$661$	−2.58617	+	4.47938i	−0.100590	+	0.174228i	−0.911928	−	0.410350i	$-0.865407\pi$
$661$	−2.58617	+	4.47938i	−0.100590	+	0.174228i	0.811338	+	0.584578i	$0.198740\pi$
$662$	22.8627	−	39.5993i	0.888583	−	1.53907i
$663$	4.97798	+	1.94791i	0.193329	+	0.0756505i
$664$	−29.2512	−	50.6646i	−1.13517	−	1.96617i
$665$	5.95044			0.230748
$666$	−2.47605	−	2.28814i	−0.0959450	−	0.0886635i
$667$	1.08691			0.0420853
$668$	38.8865	+	67.3535i	1.50457	+	2.60598i
$669$	−20.3767	+	16.2836i	−0.787809	+	0.629561i
$670$	19.2969	−	33.4232i	0.745504	−	1.29125i
$671$	−17.4230	+	30.1775i	−0.672607	+	1.16499i
$672$	−1.72821	−	11.3878i	−0.0666672	−	0.439293i
$673$	−5.71413	−	9.89716i	−0.220263	−	0.381507i	0.734624	−	0.678474i	$-0.237358\pi$
$673$	−5.71413	−	9.89716i	−0.220263	−	0.381507i	−0.954888	+	0.296967i	$0.904025\pi$
$674$	37.7924			1.45571
$675$	2.91406	−	4.30212i	0.112162	−	0.165589i
$676$	4.37640			0.168323
$677$	4.25402	+	7.36818i	0.163495	+	0.283182i	0.936120	−	0.351681i	$-0.114390\pi$
$677$	4.25402	+	7.36818i	0.163495	+	0.283182i	−0.772625	+	0.634863i	$0.781056\pi$
$678$	8.09426	+	53.3358i	0.310858	+	2.04835i
$679$	−0.730502	+	1.26527i	−0.0280341	+	0.0485565i
$680$	−9.25991	+	16.0386i	−0.355101	+	0.615054i
$681$	−29.4156	+	23.5069i	−1.12721	+	0.900785i
$682$	−37.9542	−	65.7386i	−1.45334	−	2.51726i
$683$	−17.6393			−0.674947			−0.337474	−	0.941335i	$-0.609572\pi$
$683$	−17.6393			−0.674947			−0.337474	+	0.941335i	$0.609572\pi$
$684$	10.7776	−	47.6638i	0.412090	−	1.82247i
$685$	−13.8586			−0.529511
$686$	23.0999	+	40.0102i	0.881959	+	1.52760i
$687$	43.8324	+	17.1518i	1.67231	+	0.654383i
$688$	−18.1070	+	31.3623i	−0.690324	+	1.19568i
$689$	5.15432	−	8.92754i	0.196364	−	0.340112i
$690$	6.90766	+	2.70300i	0.262970	+	0.102901i
$691$	−17.4651	−	30.2505i	−0.664404	−	1.15078i	−0.979447	−	0.201704i	$-0.935352\pi$
$691$	−17.4651	−	30.2505i	−0.664404	−	1.15078i	0.315042	−	0.949078i	$-0.397981\pi$
$692$	46.2721			1.75900
$693$	5.69052	−	25.1663i	0.216165	−	0.955990i
$694$	−29.8258			−1.13217
$695$	3.26336	+	5.65230i	0.123786	+	0.214404i
$696$	5.20359	−	4.15834i	0.197242	−	0.157622i
$697$	9.86590	−	17.0882i	0.373698	−	0.647263i
$698$	−29.4812	+	51.0629i	−1.11588	+	1.93276i
$699$	−6.27280	−	41.3336i	−0.237259	−	1.56338i
$700$	3.49830	+	6.05924i	0.132223	+	0.229018i
$701$	−49.5629			−1.87197			−0.935983	−	0.352045i	$-0.885486\pi$
$701$	−49.5629			−1.87197			−0.935983	+	0.352045i	$0.885486\pi$
$702$	−5.72886	−	11.8044i	−0.216222	−	0.445527i
$703$	1.65646			0.0624745
$704$	−6.17719	−	10.6992i	−0.232812	−	0.403242i
$705$	2.96495	+	19.5371i	0.111667	+	0.735810i
$706$	17.1432	−	29.6929i	0.645194	−	1.11751i
$707$	4.65655	−	8.06537i	0.175127	−	0.303330i
$708$	55.3576	−	44.2379i	2.08047	−	1.66256i
$709$	−18.0806	−	31.3165i	−0.679031	−	1.17612i	−0.975273	−	0.221003i	$-0.929067\pi$
$709$	−18.0806	−	31.3165i	−0.679031	−	1.17612i	0.296243	−	0.955113i	$-0.404266\pi$
$710$	−14.0485			−0.527232
$711$	−11.7234	−	10.8337i	−0.439662	−	0.406295i
$712$	94.3919			3.53749
$713$	−4.73845	−	8.20723i	−0.177456	−	0.307363i
$714$	20.0961	+	7.86370i	0.752078	+	0.294291i
$715$	−2.68984	+	4.65893i	−0.100594	+	0.174234i
$716$	−11.9790	+	20.7482i	−0.447675	+	0.775395i
$717$	27.8722	+	10.9065i	1.04090	+	0.407311i
$718$	−7.45941	−	12.9201i	−0.278383	−	0.482173i
$719$	21.1195			0.787624			0.393812	−	0.919191i	$-0.371156\pi$
$719$	21.1195			0.787624			0.393812	+	0.919191i	$0.371156\pi$
$720$	18.3357	−	5.69645i	0.683331	−	0.212294i
$721$	27.3203			1.01746
$722$	−6.49798	−	11.2548i	−0.241830	−	0.418861i
$723$	22.4138	−	17.9115i	0.833578	−	0.666136i
$724$	2.96115	−	5.12887i	0.110050	−	0.190613i
$725$	−0.320437	+	0.555014i	−0.0119007	+	0.0206127i
$726$	11.7735	+	77.5796i	0.436955	+	2.87925i
$727$	13.6302	+	23.6081i	0.505515	+	0.875577i	0.999980	+	0.00637961i	$0.00203071\pi$
$727$	13.6302	+	23.6081i	0.505515	+	0.875577i	−0.494465	+	0.869198i	$0.664636\pi$
$728$	9.59351			0.355559
$729$	−16.7058	+	21.2112i	−0.618734	+	0.785600i
$730$	29.7131			1.09973
$731$	−8.73158	−	15.1235i	−0.322949	−	0.559364i
$732$	7.36695	+	48.5433i	0.272290	+	1.79421i
$733$	5.80668	−	10.0575i	0.214474	−	0.371481i	−0.738635	−	0.674105i	$-0.764529\pi$
$733$	5.80668	−	10.0575i	0.214474	−	0.371481i	0.953110	+	0.302624i	$0.0978628\pi$
$734$	−3.08871	+	5.34981i	−0.114006	+	0.197465i
$735$	−6.01324	+	4.80535i	−0.221802	+	0.177248i
$736$	3.52730	+	6.10945i	0.130018	+	0.225197i
$737$	82.2216			3.02867
$738$	−46.2528	+	14.3696i	−1.70259	+	0.528952i
$739$	42.9401			1.57958			0.789788	−	0.613380i	$-0.210191\pi$
$739$	42.9401			1.57958			0.789788	+	0.613380i	$0.210191\pi$
$740$	0.973844	+	1.68675i	0.0357992	+	0.0620061i
$741$	6.00346	+	2.34918i	0.220543	+	0.0862993i
$742$	20.8080	−	36.0405i	0.763885	−	1.32309i
$743$	17.3555	−	30.0606i	0.636711	−	1.10282i	−0.349439	−	0.936959i	$-0.613628\pi$
$743$	17.3555	−	30.0606i	0.636711	−	1.10282i	0.986150	−	0.165856i	$-0.0530388\pi$
$744$	−54.0850	−	21.1637i	−1.98285	−	0.775898i
$745$	−5.88878	−	10.1997i	−0.215748	−	0.373687i
$746$	20.7059			0.758096
$747$	−21.4801	−	19.8499i	−0.785915	−	0.726270i
$748$	−72.6612			−2.65676
$749$	4.83594	+	8.37609i	0.176701	+	0.306056i
$750$	−3.41673	+	2.73041i	−0.124761	+	0.0997005i
$751$	−0.655127	+	1.13471i	−0.0239059	+	0.0414062i	−0.877731	−	0.479154i	$-0.840944\pi$
$751$	−0.655127	+	1.13471i	−0.0239059	+	0.0414062i	0.853825	+	0.520560i	$0.174277\pi$
$752$	−36.5089	+	63.2352i	−1.33134	+	2.30595i
$753$	−2.65550	−	17.4980i	−0.0967719	−	0.637663i
$754$	0.809153	+	1.40149i	0.0294676	+	0.0510394i
$755$	9.59138			0.349066
$756$	−15.8733	−	32.7071i	−0.577308	−	1.18955i
$757$	1.73705			0.0631343			0.0315671	−	0.999502i	$-0.489950\pi$
$757$	1.73705			0.0631343			0.0315671	+	0.999502i	$0.489950\pi$
$758$	−0.196536	−	0.340411i	−0.00713852	−	0.0123643i
$759$	2.37110	+	15.6240i	0.0860655	+	0.567115i
$760$	−11.1675	+	19.3426i	−0.405087	+	0.701631i
$761$	9.10484	−	15.7700i	0.330050	−	0.571663i	−0.652471	−	0.757813i	$-0.726268\pi$
$761$	9.10484	−	15.7700i	0.330050	−	0.571663i	0.982521	+	0.186150i	$0.0596010\pi$
$762$	48.5310	−	38.7825i	1.75809	−	1.40494i
$763$	−2.91579	−	5.05029i	−0.105559	−	0.182833i
$764$	16.0419			0.580374
$765$	−2.04200	+	9.03074i	−0.0738286	+	0.326507i
$766$	−41.9336			−1.51512
$767$	4.67420	+	8.09595i	0.168776	+	0.292328i
$768$	−50.0947	−	19.6023i	−1.80764	−	0.707337i
$769$	−20.5593	+	35.6098i	−0.741388	+	1.28412i	0.210475	+	0.977599i	$0.432499\pi$
$769$	−20.5593	+	35.6098i	−0.741388	+	1.28412i	−0.951863	+	0.306523i	$0.900834\pi$
$770$	−10.8589	+	18.8081i	−0.391326	+	0.677797i
$771$	45.8589	+	17.9448i	1.65157	+	0.646265i
$772$	19.1480	+	33.1653i	0.689152	+	1.19365i
$773$	21.2243			0.763384			0.381692	−	0.924290i	$-0.375342\pi$
$773$	21.2243			0.763384			0.381692	+	0.924290i	$0.375342\pi$
$774$	−9.45380	+	41.8094i	−0.339810	+	1.50281i
$775$	5.58787			0.20072

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26258 + 2.18685i) q^{2} +(-0.259881 - 1.71244i) q^{3} +(-2.18820 + 3.79007i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.41673 - 2.73041i) q^{6} +(0.799357 + 1.38453i) q^{7} -6.00077 q^{8} +(-2.86492 + 0.890062i) q^{9} +O(q^{10})\)	\(q+(1.26258 + 2.18685i) q^{2} +(-0.259881 - 1.71244i) q^{3} +(-2.18820 + 3.79007i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.41673 - 2.73041i) q^{6} +(0.799357 + 1.38453i) q^{7} -6.00077 q^{8} +(-2.86492 + 0.890062i) q^{9} +2.52515 q^{10} +(2.68984 + 4.65893i) q^{11} +(7.05895 + 2.76220i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-2.01850 + 3.49614i) q^{14} +(-1.61296 - 0.631158i) q^{15} +(-3.20003 - 5.54262i) q^{16} +3.08624 q^{17} +(-5.56361 - 5.14138i) q^{18} +3.72202 q^{19} +(2.18820 + 3.79007i) q^{20} +(2.16319 - 1.72867i) q^{21} +(-6.79225 + 11.7645i) q^{22} +(-0.847988 + 1.46876i) q^{23} +(1.55948 + 10.2760i) q^{24} +(-0.500000 - 0.866025i) q^{25} -2.52515 q^{26} +(2.26872 + 4.67471i) q^{27} -6.99661 q^{28} +(-0.320437 - 0.555014i) q^{29} +(-0.656238 - 4.32418i) q^{30} +(-2.79393 + 4.83923i) q^{31} +(2.07980 - 3.60232i) q^{32} +(7.27912 - 5.81696i) q^{33} +(3.89662 + 6.74914i) q^{34} +1.59871 q^{35} +(2.89563 - 12.8059i) q^{36} +0.445044 q^{37} +(4.69933 + 8.13948i) q^{38} +(1.61296 + 0.631158i) q^{39} +(-3.00038 + 5.19682i) q^{40} +(3.19674 - 5.53691i) q^{41} +(6.51151 + 2.54798i) q^{42} +(-2.82920 - 4.90031i) q^{43} -23.5436 q^{44} +(-0.661646 + 2.92613i) q^{45} -4.28260 q^{46} +(-5.70445 - 9.88040i) q^{47} +(-8.65979 + 6.92029i) q^{48} +(2.22206 - 3.84872i) q^{49} +(1.26258 - 2.18685i) q^{50} +(-0.802054 - 5.28501i) q^{51} +(-2.18820 - 3.79007i) q^{52} -10.3086 q^{53} +(-7.35844 + 10.8635i) q^{54} +5.37967 q^{55} +(-4.79676 - 8.30823i) q^{56} +(-0.967280 - 6.37374i) q^{57} +(0.809153 - 1.40149i) q^{58} +(4.67420 - 8.09595i) q^{59} +(5.92161 - 4.73213i) q^{60} +(3.23867 + 5.60954i) q^{61} -14.1102 q^{62} +(-3.52241 - 3.25509i) q^{63} -2.29649 q^{64} +(0.500000 + 0.866025i) q^{65} +(21.9112 + 8.57397i) q^{66} +(7.64188 - 13.2361i) q^{67} +(-6.75331 + 11.6971i) q^{68} +(2.73554 + 1.07043i) q^{69} +(2.01850 + 3.49614i) q^{70} -5.56344 q^{71} +(17.1917 - 5.34105i) q^{72} +11.7669 q^{73} +(0.561902 + 0.973242i) q^{74} +(-1.35308 + 1.08128i) q^{75} +(-8.14451 + 14.1067i) q^{76} +(-4.30028 + 7.44830i) q^{77} +(0.656238 + 4.32418i) q^{78} +(2.66045 + 4.60803i) q^{79} -6.40006 q^{80} +(7.41558 - 5.09992i) q^{81} +16.1445 q^{82} +(4.87457 + 8.44301i) q^{83} +(1.81828 + 11.9813i) q^{84} +(1.54312 - 2.67276i) q^{85} +(7.14415 - 12.3740i) q^{86} +(-0.867154 + 0.692968i) q^{87} +(-16.1411 - 27.9572i) q^{88} -15.7300 q^{89} +(-7.23437 + 2.24754i) q^{90} -1.59871 q^{91} +(-3.71114 - 6.42787i) q^{92} +(9.01300 + 3.52683i) q^{93} +(14.4046 - 24.9495i) q^{94} +(1.86101 - 3.22336i) q^{95} +(-6.70927 - 2.62537i) q^{96} +(0.456931 + 0.791428i) q^{97} +11.2221 q^{98} +(-11.8529 - 10.9534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

Introduction

L-functions

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