LMFDB - Embedded newform 546.2.u.a.185.11

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.11
Character	$\chi$	$=$	546.185
Dual form			546.2.u.a.425.11

$q$-expansion

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.323515 + 1.70157i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.99252 + 3.45115i) q^{5} +(0.570612 - 1.63536i) q^{6} +(-2.44529 - 1.01022i) q^{7} -1.00000i q^{8} +(-2.79068 + 1.10097i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.323515 + 1.70157i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.99252 + 3.45115i) q^{5} +(0.570612 - 1.63536i) q^{6} +(-2.44529 - 1.01022i) q^{7} -1.00000i q^{8} +(-2.79068 + 1.10097i) q^{9} -3.98504i q^{10} +3.67738i q^{11} +(-1.31184 + 1.13096i) q^{12} +(3.60330 + 0.127442i) q^{13} +(1.61258 + 2.09752i) q^{14} +(-5.22776 + 4.50691i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.17224 + 2.03038i) q^{17} +(2.96728 + 0.441872i) q^{18} -4.20594i q^{19} +(-1.99252 + 3.45115i) q^{20} +(0.927864 - 4.48766i) q^{21} +(1.83869 - 3.18471i) q^{22} +(-1.85837 - 1.07293i) q^{23} +(1.70157 - 0.323515i) q^{24} +(-5.44029 + 9.42285i) q^{25} +(-3.05683 - 1.91202i) q^{26} +(-2.77620 - 4.39235i) q^{27} +(-0.347773 - 2.62280i) q^{28} +(3.39215 - 1.95846i) q^{29} +(6.78083 - 1.28922i) q^{30} +(-7.42132 - 4.28470i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-6.25732 + 1.18969i) q^{33} -2.34449i q^{34} +(-1.38589 - 10.4520i) q^{35} +(-2.34880 - 1.86631i) q^{36} +(-3.44688 + 5.97017i) q^{37} +(-2.10297 + 3.64245i) q^{38} +(0.948870 + 6.17249i) q^{39} +(3.45115 - 1.99252i) q^{40} +(-1.55096 - 2.68634i) q^{41} +(-3.04738 + 3.42249i) q^{42} +(2.70900 - 4.69212i) q^{43} +(-3.18471 + 1.83869i) q^{44} +(-9.36009 - 7.43734i) q^{45} +(1.07293 + 1.85837i) q^{46} +(5.81511 + 10.0721i) q^{47} +(-1.63536 - 0.570612i) q^{48} +(4.95892 + 4.94055i) q^{49} +(9.42285 - 5.44029i) q^{50} +(-3.07560 + 2.65151i) q^{51} +(1.69128 + 3.18427i) q^{52} +(-1.81528 - 1.04805i) q^{53} +(0.208085 + 5.19198i) q^{54} +(-12.6912 + 7.32727i) q^{55} +(-1.01022 + 2.44529i) q^{56} +(7.15670 - 1.36069i) q^{57} -3.91692 q^{58} +(4.85918 + 8.41635i) q^{59} +(-6.51698 - 2.27391i) q^{60} +0.276774i q^{61} +(4.28470 + 7.42132i) q^{62} +(7.93624 + 0.126999i) q^{63} -1.00000 q^{64} +(6.73983 + 12.6895i) q^{65} +(6.01385 + 2.09836i) q^{66} +10.7088 q^{67} +(-1.17224 + 2.03038i) q^{68} +(1.22445 - 3.50925i) q^{69} +(-4.02576 + 9.74460i) q^{70} +(-3.24128 - 1.87136i) q^{71} +(1.10097 + 2.79068i) q^{72} +(-0.474423 - 0.273908i) q^{73} +(5.97017 - 3.44688i) q^{74} +(-17.7937 - 6.20859i) q^{75} +(3.64245 - 2.10297i) q^{76} +(3.71496 - 8.99228i) q^{77} +(2.26450 - 5.81997i) q^{78} +(1.56372 + 2.70844i) q^{79} -3.98504 q^{80} +(6.57574 - 6.14489i) q^{81} +3.10192i q^{82} -13.0428 q^{83} +(4.35036 - 1.44027i) q^{84} +(-4.67144 + 8.09117i) q^{85} +(-4.69212 + 2.70900i) q^{86} +(4.42987 + 5.13839i) q^{87} +3.67738 q^{88} +(0.959464 - 1.66184i) q^{89} +(4.38740 + 11.1210i) q^{90} +(-8.68238 - 3.95175i) q^{91} -2.14586i q^{92} +(4.88980 - 14.0140i) q^{93} -11.6302i q^{94} +(14.5153 - 8.38043i) q^{95} +(1.13096 + 1.31184i) q^{96} +(-2.07811 - 1.19980i) q^{97} +(-1.82428 - 6.75811i) q^{98} +(-4.04868 - 10.2624i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.323515	+	1.70157i	0.186782	+	0.982401i
$3$	0.323515	+	1.70157i	0.186782	+	0.982401i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.99252	+	3.45115i	0.891083	+	1.54340i	0.838579	+	0.544780i	$0.183387\pi$
$5$	1.99252	+	3.45115i	0.891083	+	1.54340i	0.0525039	+	0.998621i	$0.483280\pi$
$6$	0.570612	−	1.63536i	0.232951	−	0.667633i
$7$	−2.44529	−	1.01022i	−0.924234	−	0.381826i
$7$	−2.44529	−	1.01022i	−0.924234	−	0.381826i
$8$		−	1.00000i		−	0.353553i
$9$	−2.79068	+	1.10097i	−0.930225	+	0.366989i
$10$		−	3.98504i		−	1.26018i
$11$			3.67738i			1.10877i	0.832259	+	0.554386i	$0.187047\pi$
$11$			3.67738i			1.10877i	−0.832259	+	0.554386i	$0.812953\pi$
$12$	−1.31184	+	1.13096i	−0.378697	+	0.326479i
$13$	3.60330	+	0.127442i	0.999375	+	0.0353462i
$13$	3.60330	+	0.127442i	0.999375	+	0.0353462i
$14$	1.61258	+	2.09752i	0.430980	+	0.560586i
$15$	−5.22776	+	4.50691i	−1.34980	+	1.16368i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.17224	+	2.03038i	0.284311	+	0.492441i	0.972442	−	0.233146i	$-0.0749019\pi$
$17$	1.17224	+	2.03038i	0.284311	+	0.492441i	−0.688131	+	0.725586i	$0.741569\pi$
$18$	2.96728	+	0.441872i	0.699395	+	0.104150i
$19$		−	4.20594i		−	0.964909i	−0.875921	−	0.482454i	$-0.839745\pi$
$19$		−	4.20594i		−	0.964909i	0.875921	−	0.482454i	$-0.160255\pi$
$20$	−1.99252	+	3.45115i	−0.445541	+	0.771700i
$21$	0.927864	−	4.48766i	0.202477	−	0.979287i
$22$	1.83869	−	3.18471i	0.392010	−	0.678982i
$23$	−1.85837	−	1.07293i	−0.387496	−	0.223721i	0.293578	−	0.955935i	$-0.405154\pi$
$23$	−1.85837	−	1.07293i	−0.387496	−	0.223721i	−0.681075	+	0.732214i	$0.738487\pi$
$24$	1.70157	−	0.323515i	0.347331	−	0.0660373i
$25$	−5.44029	+	9.42285i	−1.08806	+	1.88457i
$26$	−3.05683	−	1.91202i	−0.599493	−	0.374977i
$27$	−2.77620	−	4.39235i	−0.534280	−	0.845308i
$28$	−0.347773	−	2.62280i	−0.0657230	−	0.495662i
$29$	3.39215	−	1.95846i	0.629906	−	0.363677i	−0.150809	−	0.988563i	$-0.548188\pi$
$29$	3.39215	−	1.95846i	0.629906	−	0.363677i	0.780716	+	0.624886i	$0.214855\pi$
$30$	6.78083	−	1.28922i	1.23800	−	0.235379i
$31$	−7.42132	−	4.28470i	−1.33291	−	0.769555i	−0.347163	−	0.937805i	$-0.612855\pi$
$31$	−7.42132	−	4.28470i	−1.33291	−	0.769555i	−0.985744	+	0.168250i	$0.946188\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−6.25732	+	1.18969i	−1.08926	+	0.207099i
$34$		−	2.34449i		−	0.402076i
$35$	−1.38589	−	10.4520i	−0.234258	−	1.76670i
$36$	−2.34880	−	1.86631i	−0.391467	−	0.311052i
$37$	−3.44688	+	5.97017i	−0.566664	+	0.981490i	0.430229	+	0.902720i	$0.358433\pi$
$37$	−3.44688	+	5.97017i	−0.566664	+	0.981490i	−0.996893	+	0.0787705i	$0.974901\pi$
$38$	−2.10297	+	3.64245i	−0.341147	+	0.590884i
$39$	0.948870	+	6.17249i	0.151941	+	0.988390i
$40$	3.45115	−	1.99252i	0.545675	−	0.315045i
$41$	−1.55096	−	2.68634i	−0.242219	−	0.419536i	0.719127	−	0.694879i	$-0.244542\pi$
$41$	−1.55096	−	2.68634i	−0.242219	−	0.419536i	−0.961346	+	0.275343i	$0.911209\pi$
$42$	−3.04738	+	3.42249i	−0.470221	+	0.528102i
$43$	2.70900	−	4.69212i	0.413118	−	0.715541i	−0.582111	−	0.813109i	$-0.697773\pi$
$43$	2.70900	−	4.69212i	0.413118	−	0.715541i	0.995229	+	0.0975681i	$0.0311064\pi$
$44$	−3.18471	+	1.83869i	−0.480113	+	0.277193i
$45$	−9.36009	−	7.43734i	−1.39532	−	1.10869i
$46$	1.07293	+	1.85837i	0.158195	+	0.274001i
$47$	5.81511	+	10.0721i	0.848220	+	1.46916i	0.882795	+	0.469759i	$0.155659\pi$
$47$	5.81511	+	10.0721i	0.848220	+	1.46916i	−0.0345746	+	0.999402i	$0.511008\pi$
$48$	−1.63536	−	0.570612i	−0.236044	−	0.0823608i
$49$	4.95892	+	4.94055i	0.708418	+	0.705794i
$50$	9.42285	−	5.44029i	1.33259	−	0.769373i
$51$	−3.07560	+	2.65151i	−0.430670	+	0.371286i
$52$	1.69128	+	3.18427i	0.234538	+	0.441579i
$53$	−1.81528	−	1.04805i	−0.249348	−	0.143961i	0.370118	−	0.928985i	$-0.379317\pi$
$53$	−1.81528	−	1.04805i	−0.249348	−	0.143961i	−0.619466	+	0.785024i	$0.712651\pi$
$54$	0.208085	+	5.19198i	0.0283168	+	0.706540i
$55$	−12.6912	+	7.32727i	−1.71128	+	0.988009i
$56$	−1.01022	+	2.44529i	−0.134996	+	0.326766i
$57$	7.15670	−	1.36069i	0.947928	−	0.180227i
$58$	−3.91692			−0.514316
$59$	4.85918	+	8.41635i	0.632612	+	1.09572i	0.987016	+	0.160623i	$0.0513503\pi$
$59$	4.85918	+	8.41635i	0.632612	+	1.09572i	−0.354404	+	0.935092i	$0.615316\pi$
$60$	−6.51698	−	2.27391i	−0.841339	−	0.293561i
$61$			0.276774i			0.0354373i	0.999843	+	0.0177187i	$0.00564032\pi$
$61$			0.276774i			0.0354373i	−0.999843	+	0.0177187i	$0.994360\pi$
$62$	4.28470	+	7.42132i	0.544157	+	0.942508i
$63$	7.93624	+	0.126999i	0.999872	+	0.0160003i
$64$	−1.00000			−0.125000
$65$	6.73983	+	12.6895i	0.835973	+	1.57393i
$66$	6.01385	+	2.09836i	0.740253	+	0.258290i
$67$	10.7088			1.30829			0.654145	−	0.756369i	$-0.273029\pi$
$67$	10.7088			1.30829			0.654145	+	0.756369i	$0.273029\pi$
$68$	−1.17224	+	2.03038i	−0.142155	+	0.246220i
$69$	1.22445	−	3.50925i	0.147407	−	0.422464i
$70$	−4.02576	+	9.74460i	−0.481170	+	1.16470i
$71$	−3.24128	−	1.87136i	−0.384670	−	0.222089i	0.295178	−	0.955442i	$-0.404621\pi$
$71$	−3.24128	−	1.87136i	−0.384670	−	0.222089i	−0.679848	+	0.733353i	$0.737954\pi$
$72$	1.10097	+	2.79068i	0.129750	+	0.328884i
$73$	−0.474423	−	0.273908i	−0.0555270	−	0.0320586i	0.471979	−	0.881610i	$-0.343540\pi$
$73$	−0.474423	−	0.273908i	−0.0555270	−	0.0320586i	−0.527507	+	0.849551i	$0.676873\pi$
$74$	5.97017	−	3.44688i	0.694018	−	0.400692i
$75$	−17.7937	−	6.20859i	−2.05463	−	0.716906i
$76$	3.64245	−	2.10297i	0.417818	−	0.241227i
$77$	3.71496	−	8.99228i	0.423359	−	1.02477i
$78$	2.26450	−	5.81997i	0.256404	−	0.658982i
$79$	1.56372	+	2.70844i	0.175932	+	0.304723i	0.940483	−	0.339840i	$-0.110373\pi$
$79$	1.56372	+	2.70844i	0.175932	+	0.304723i	−0.764552	+	0.644563i	$0.777039\pi$
$80$	−3.98504			−0.445541
$81$	6.57574	−	6.14489i	0.730638	−	0.682765i
$82$			3.10192i			0.342550i
$83$	−13.0428			−1.43163			−0.715817	−	0.698287i	$-0.753946\pi$
$83$	−13.0428			−1.43163			−0.715817	+	0.698287i	$0.753946\pi$
$84$	4.35036	−	1.44027i	0.474663	−	0.157147i
$85$	−4.67144	+	8.09117i	−0.506689	+	0.877611i
$86$	−4.69212	+	2.70900i	−0.505964	+	0.292118i
$87$	4.42987	+	5.13839i	0.474931	+	0.550893i
$88$	3.67738			0.392010
$89$	0.959464	−	1.66184i	0.101703	−	0.176155i	−0.810683	−	0.585485i	$-0.800904\pi$
$89$	0.959464	−	1.66184i	0.101703	−	0.176155i	0.912386	+	0.409330i	$0.134238\pi$
$90$	4.38740	+	11.1210i	0.462473	+	1.17225i
$91$	−8.68238	−	3.95175i	−0.910161	−	0.414256i
$92$		−	2.14586i		−	0.223721i
$93$	4.88980	−	14.0140i	0.507049	−	1.45319i
$94$		−	11.6302i		−	1.19956i
$95$	14.5153	−	8.38043i	1.48924	−	0.859814i
$96$	1.13096	+	1.31184i	0.115428	+	0.133890i
$97$	−2.07811	−	1.19980i	−0.211000	−	0.121821i	0.390776	−	0.920486i	$-0.372207\pi$
$97$	−2.07811	−	1.19980i	−0.211000	−	0.121821i	−0.601776	+	0.798665i	$0.705540\pi$
$98$	−1.82428	−	6.75811i	−0.184280	−	0.682672i
$99$	−4.04868	−	10.2624i	−0.406908	−	1.03141i
$100$	−10.8806			−1.08806
$101$	7.53515			0.749776			0.374888	−	0.927070i	$-0.377681\pi$
$101$	7.53515			0.749776			0.374888	+	0.927070i	$0.377681\pi$
$102$	3.98931	−	0.758478i	0.395000	−	0.0751005i
$103$	7.80371	−	4.50547i	0.768922	−	0.443938i	−0.0635677	−	0.997978i	$-0.520248\pi$
$103$	7.80371	−	4.50547i	0.768922	−	0.443938i	0.832490	+	0.554040i	$0.186915\pi$
$104$	0.127442	−	3.60330i	0.0124968	−	0.353332i
$105$	17.3364	−	5.73956i	1.69186	−	0.560124i
$106$	1.04805	+	1.81528i	0.101796	+	0.176315i
$107$	11.4769	+	6.62621i	1.10952	+	0.640580i	0.938704	−	0.344724i	$-0.112027\pi$
$107$	11.4769	+	6.62621i	1.10952	+	0.640580i	0.170813	+	0.985304i	$0.445361\pi$
$108$	2.41578	−	4.60043i	0.232459	−	0.442677i
$109$	−4.23287	+	7.33155i	−0.405436	+	0.702235i	−0.994372	−	0.105944i	$-0.966213\pi$
$109$	−4.23287	+	7.33155i	−0.405436	+	0.702235i	0.588936	+	0.808179i	$0.299547\pi$
$110$	14.6545			1.39726
$111$	−11.2738	−	3.93366i	−1.07006	−	0.373367i
$112$	2.09752	−	1.61258i	0.198197	−	0.152374i
$113$	10.1766	+	5.87547i	0.957335	+	0.552717i	0.895352	−	0.445360i	$-0.146924\pi$
$113$	10.1766	+	5.87547i	0.957335	+	0.552717i	0.0619829	+	0.998077i	$0.480258\pi$
$114$	−6.87822	−	2.39996i	−0.644205	−	0.224777i
$115$		−	8.55134i		−	0.797416i
$116$	3.39215	+	1.95846i	0.314953	+	0.181838i
$117$	−10.1959	+	3.61146i	−0.942616	+	0.333880i
$118$		−	9.71836i		−	0.894648i
$119$	−0.815350	−	6.14911i	−0.0747430	−	0.563688i
$120$	4.50691	+	5.22776i	0.411423	+	0.477227i
$121$	−2.52315			−0.229377
$122$	0.138387	−	0.239694i	0.0125290	−	0.0217009i
$123$	4.06924	−	3.50814i	0.366911	−	0.316318i
$124$		−	8.56940i		−	0.769555i
$125$	−23.4343			−2.09603
$126$	−6.80948	−	4.07810i	−0.606637	−	0.363306i
$127$	0.726767	+	1.25880i	0.0644901	+	0.111700i	0.896468	−	0.443109i	$-0.146125\pi$
$127$	0.726767	+	1.25880i	0.0644901	+	0.111700i	−0.831978	+	0.554809i	$0.812791\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	8.86036	+	3.09157i	0.780112	+	0.272198i
$130$	0.507863	−	14.3593i	0.0445426	−	1.25939i
$131$	−8.82931	−	15.2928i	−0.771421	−	1.33614i	−0.936784	−	0.349907i	$-0.886213\pi$
$131$	−8.82931	−	15.2928i	−0.771421	−	1.33614i	0.165364	−	0.986233i	$-0.447120\pi$
$132$	−4.15896	−	4.82416i	−0.361991	−	0.419889i
$133$	−4.24891	+	10.2848i	−0.368427	+	0.891802i
$134$	−9.27410	−	5.35441i	−0.801161	−	0.462550i
$135$	9.62701	−	18.3329i	0.828561	−	1.57785i
$136$	2.03038	−	1.17224i	0.174104	−	0.100519i
$137$	−10.8746	+	6.27848i	−0.929084	+	0.536407i	−0.886522	−	0.462687i	$-0.846885\pi$
$137$	−10.8746	+	6.27848i	−0.929084	+	0.536407i	−0.0425621	+	0.999094i	$0.513552\pi$
$138$	−2.81503	+	2.42687i	−0.239631	+	0.206589i
$139$	13.3742	+	7.72159i	1.13438	+	0.654937i	0.945034	−	0.326973i	$-0.106029\pi$
$139$	13.3742	+	7.72159i	1.13438	+	0.654937i	0.189350	+	0.981910i	$0.439362\pi$
$140$	8.35871	−	6.42619i	0.706440	−	0.543113i
$141$	−15.2570	+	13.1533i	−1.28487	+	1.10771i
$142$	1.87136	+	3.24128i	0.157041	+	0.272002i
$143$	−0.468655	+	13.2507i	−0.0391909	+	1.10808i
$144$	0.441872	−	2.96728i	0.0368226	−	0.247273i
$145$	13.5179	+	7.80454i	1.12260	+	0.648132i
$146$	0.273908	+	0.474423i	0.0226688	+	0.0392635i
$147$	−6.80241	+	10.0363i	−0.561053	+	0.827780i
$148$	−6.89376			−0.566664
$149$		−	4.04297i		−	0.331213i	−0.986192	−	0.165607i	$-0.947042\pi$
$149$		−	4.04297i		−	0.331213i	0.986192	−	0.165607i	$-0.0529582\pi$
$150$	12.3055	+	14.2736i	1.00474	+	1.16544i
$151$	4.77604	−	8.27235i	0.388669	−	0.673194i	−0.603602	−	0.797286i	$-0.706268\pi$
$151$	4.77604	−	8.27235i	0.388669	−	0.673194i	0.992271	+	0.124092i	$0.0396017\pi$
$152$	−4.20594			−0.341147
$153$	−5.50674	−	4.37554i	−0.445193	−	0.353742i
$154$	−7.71339	+	5.93007i	−0.621563	+	0.477859i
$155$		−	34.1494i		−	2.74295i
$156$	−4.87110	+	3.90799i	−0.390000	+	0.312890i
$157$	17.0665	+	9.85334i	1.36205	+	0.786383i	0.989897	−	0.141787i	$-0.0452849\pi$
$157$	17.0665	+	9.85334i	1.36205	+	0.786383i	0.372157	+	0.928170i	$0.378618\pi$
$158$		−	3.12743i		−	0.248805i
$159$	1.19606	−	3.42788i	0.0948539	−	0.271849i
$160$	3.45115	+	1.99252i	0.272837	+	0.157523i
$161$	3.46036	+	4.50098i	0.272715	+	0.354727i
$162$	−8.76720	+	2.03376i	−0.688816	+	0.159787i
$163$	−0.359741			−0.0281771			−0.0140886	−	0.999901i	$-0.504485\pi$
$163$	−0.359741			−0.0281771			−0.0140886	+	0.999901i	$0.504485\pi$
$164$	1.55096	−	2.68634i	0.121110	−	0.209768i
$165$	−16.5737	−	19.2245i	−1.29026	−	1.49662i
$166$	11.2954	+	6.52141i	0.876694	+	0.506159i
$167$	1.89219	+	3.27738i	0.146422	+	0.253611i	0.929903	−	0.367806i	$-0.119891\pi$
$167$	1.89219	+	3.27738i	0.146422	+	0.253611i	−0.783480	+	0.621417i	$0.786557\pi$
$168$	−4.48766	−	0.927864i	−0.346230	−	0.0715863i
$169$	12.9675	+	0.918426i	0.997501	+	0.0706481i
$170$	8.09117	−	4.67144i	0.620565	−	0.358283i
$171$	4.63060	+	11.7374i	0.354111	+	0.897582i
$172$	5.41799			0.413118
$173$	21.4864			1.63358			0.816789	−	0.576937i	$-0.195752\pi$
$173$	21.4864			1.63358			0.816789	+	0.576937i	$0.195752\pi$
$174$	−1.26718	−	6.66491i	−0.0960649	−	0.505265i
$175$	22.8222	−	17.5458i	1.72520	−	1.32634i
$176$	−3.18471	−	1.83869i	−0.240056	−	0.138597i
$177$	−12.7490	+	10.9911i	−0.958272	+	0.826138i
$178$	−1.66184	+	0.959464i	−0.124560	+	0.0719149i
$179$			15.3946i			1.15065i	0.817926	+	0.575324i	$0.195124\pi$
$179$			15.3946i			1.15065i	−0.817926	+	0.575324i	$0.804876\pi$
$180$	1.76088	−	11.8247i	0.131248	−	0.881364i
$181$		−	23.9027i		−	1.77668i	−0.459189	−	0.888339i	$-0.651860\pi$
$181$		−	23.9027i		−	1.77668i	0.459189	−	0.888339i	$-0.348140\pi$
$182$	5.54329	+	7.76350i	0.410896	+	0.575469i
$183$	−0.470951	+	0.0895408i	−0.0348137	+	0.00661905i
$184$	−1.07293	+	1.85837i	−0.0790974	+	0.137001i
$185$	−27.4719			−2.01978
$186$	−11.2417	+	9.69162i	−0.824283	+	0.710624i
$187$	−7.46650	+	4.31079i	−0.546005	+	0.315236i
$188$	−5.81511	+	10.0721i	−0.424110	+	0.734580i
$189$	2.35140	+	13.5451i	0.171039	+	0.985264i
$190$	−16.7609			−1.21596
$191$		−	15.2675i		−	1.10472i	−0.833607	−	0.552359i	$-0.813728\pi$
$191$		−	15.2675i		−	1.10472i	0.833607	−	0.552359i	$-0.186272\pi$
$192$	−0.323515	−	1.70157i	−0.0233477	−	0.122800i
$193$	16.7108			1.20287			0.601436	−	0.798921i	$-0.294596\pi$
$193$	16.7108			1.20287			0.601436	+	0.798921i	$0.294596\pi$
$194$	1.19980	+	2.07811i	0.0861405	+	0.149200i
$195$	−19.4115	+	15.5735i	−1.39009	+	1.11524i
$196$	−1.79918	+	6.76483i	−0.128513	+	0.483202i
$197$	1.81961	−	1.05055i	0.129642	−	0.0748488i	−0.433776	−	0.901021i	$-0.642819\pi$
$197$	1.81961	−	1.05055i	0.129642	−	0.0748488i	0.563418	+	0.826172i	$0.309486\pi$
$198$	−1.62493	+	10.9118i	−0.115479	+	0.775470i
$199$	13.1160	−	7.57254i	0.929770	−	0.536803i	0.0430311	−	0.999074i	$-0.486299\pi$
$199$	13.1160	−	7.57254i	0.929770	−	0.536803i	0.886739	+	0.462271i	$0.152965\pi$
$200$	9.42285	+	5.44029i	0.666296	+	0.384686i
$201$	3.46447	+	18.2218i	0.244365	+	1.28527i
$202$	−6.52563	−	3.76758i	−0.459142	−	0.265086i
$203$	−10.2733	+	1.36220i	−0.721042	+	0.0956076i
$204$	−3.83408	−	1.33779i	−0.268439	−	0.0936642i
$205$	6.18065	−	10.7052i	0.431675	−	0.747683i
$206$	−9.01095			−0.627822
$207$	6.36736	+	0.948194i	0.442562	+	0.0659040i
$208$	−1.91202	+	3.05683i	−0.132575	+	0.211953i
$209$	15.4669			1.06986
$210$	−17.8835	−	3.69758i	−1.23408	−	0.255157i
$211$	−7.97522	−	13.8135i	−0.549037	−	0.950960i	−0.998341	−	0.0575808i	$-0.981661\pi$
$211$	−7.97522	−	13.8135i	−0.549037	−	0.950960i	0.449304	−	0.893379i	$-0.351672\pi$
$212$		−	2.09610i		−	0.143961i
$213$	2.13564	−	6.12068i	0.146331	−	0.419382i
$214$	−6.62621	−	11.4769i	−0.452958	−	0.784547i
$215$	21.5909			1.47249
$216$	−4.39235	+	2.77620i	−0.298861	+	0.188896i
$217$	13.8188	+	17.9745i	0.938083	+	1.22019i
$218$	7.33155	−	4.23287i	0.496555	−	0.286686i
$219$	0.312591	−	0.895878i	0.0211229	−	0.0605378i
$220$	−12.6912	−	7.32727i	−0.855641	−	0.494004i
$221$	3.96519	+	7.46548i	0.266727	+	0.502182i
$222$	7.79655	+	9.04354i	0.523270	+	0.606963i
$223$	−15.9530	+	9.21049i	−1.06829	+	0.616780i	−0.927715	−	0.373289i	$-0.878230\pi$
$223$	−15.9530	+	9.21049i	−1.06829	+	0.616780i	−0.140580	+	0.990069i	$0.544897\pi$
$224$	−2.62280	+	0.347773i	−0.175243	+	0.0232366i
$225$	4.80782	−	32.2857i	0.320521	−	2.15238i
$226$	−5.87547	−	10.1766i	−0.390830	−	0.676938i
$227$	−4.89426	−	8.47711i	−0.324843	−	0.562645i	0.656637	−	0.754207i	$-0.271978\pi$
$227$	−4.89426	−	8.47711i	−0.324843	−	0.562645i	−0.981481	+	0.191561i	$0.938645\pi$
$228$	4.75674	+	5.51754i	0.315023	+	0.365408i
$229$	−3.72044	+	2.14800i	−0.245853	+	0.141944i	−0.617864	−	0.786285i	$-0.712002\pi$
$229$	−3.72044	+	2.14800i	−0.245853	+	0.141944i	0.372011	+	0.928228i	$0.378668\pi$
$230$	−4.27567	+	7.40567i	−0.281929	+	0.488316i
$231$	16.5028	+	3.41211i	1.08581	+	0.224501i
$232$	−1.95846	−	3.39215i	−0.128579	−	0.222706i
$233$	−8.68795	+	5.01599i	−0.569167	+	0.328609i	−0.756817	−	0.653627i	$-0.773246\pi$
$233$	−8.68795	+	5.01599i	−0.569167	+	0.328609i	0.187650	+	0.982236i	$0.439913\pi$
$234$	10.6357	+	1.97035i	0.695276	+	0.128806i
$235$	−23.1735	+	40.1376i	−1.51167	+	2.61829i
$236$	−4.85918	+	8.41635i	−0.316306	+	0.547858i
$237$	−4.10271	+	3.53699i	−0.266499	+	0.229752i
$238$	−2.36844	+	5.73296i	−0.153523	+	0.371612i
$239$		−	11.8430i		−	0.766060i	−0.923736	−	0.383030i	$-0.874881\pi$
$239$		−	11.8430i		−	0.766060i	0.923736	−	0.383030i	$-0.125119\pi$
$240$	−1.28922	−	6.78083i	−0.0832190	−	0.437701i
$241$	0.818728	−	0.472693i	0.0527389	−	0.0304488i	−0.473399	−	0.880848i	$-0.656973\pi$
$241$	0.818728	−	0.472693i	0.0527389	−	0.0304488i	0.526138	+	0.850399i	$0.323640\pi$
$242$	2.18511	+	1.26158i	0.140464	+	0.0810972i
$243$	12.5833	+	9.20111i	0.807219	+	0.590252i
$244$	−0.239694	+	0.138387i	−0.0153448	+	0.00885934i
$245$	−7.16983	+	26.9581i	−0.458064	+	1.72229i
$246$	−5.27814	+	1.00352i	−0.336522	+	0.0639821i
$247$	0.536015	−	15.1553i	0.0341058	−	0.964306i
$248$	−4.28470	+	7.42132i	−0.272079	+	0.471254i
$249$	−4.21955	−	22.1933i	−0.267403	−	1.40644i
$250$	20.2947	+	11.7172i	1.28355	+	0.741059i
$251$	7.94764	−	13.7657i	0.501650	−	0.868884i	−0.498348	−	0.866977i	$-0.666060\pi$
$251$	7.94764	−	13.7657i	0.501650	−	0.868884i	0.999998	−	0.00190672i	$-0.000606929\pi$
$252$	3.85813	+	6.93648i	0.243040	+	0.436957i
$253$	3.94557	−	6.83393i	0.248056	−	0.429645i
$254$		−	1.45353i		−	0.0912028i
$255$	−15.2790	−	5.33116i	−0.956806	−	0.333850i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.0986	+	17.4913i	−0.629933	+	1.09108i	0.357632	+	0.933862i	$0.383584\pi$
$257$	−10.0986	+	17.4913i	−0.629933	+	1.09108i	−0.987565	+	0.157213i	$0.949749\pi$
$258$	−6.12752	−	7.10756i	−0.381482	−	0.442497i
$259$	14.4598	−	11.1167i	0.898489	−	0.690760i
$260$	−7.61947	+	12.1816i	−0.472540	+	0.755470i
$261$	−7.31019	+	9.20007i	−0.452489	+	0.569470i
$262$			17.6586i			1.09095i
$263$			29.8887i			1.84302i	0.388357	+	0.921509i	$0.373043\pi$
$263$			29.8887i			1.84302i	−0.388357	+	0.921509i	$0.626957\pi$
$264$	1.18969	+	6.25732i	0.0732204	+	0.385112i
$265$		−	8.35306i		−	0.513125i
$266$	8.82204	−	6.78241i	0.540914	−	0.415856i
$267$	3.13814	+	1.09496i	0.192051	+	0.0670107i
$268$	5.35441	+	9.27410i	0.327072	+	0.566506i
$269$	−6.40279	−	11.0900i	−0.390385	−	0.676166i	0.602115	−	0.798409i	$-0.294325\pi$
$269$	−6.40279	−	11.0900i	−0.390385	−	0.676166i	−0.992500	+	0.122243i	$0.960991\pi$
$270$	−17.5037	+	11.0633i	−1.06524	+	0.673290i
$271$	−27.3531	−	15.7923i	−1.66158	−	0.959313i	−0.971961	−	0.235140i	$-0.924445\pi$
$271$	−27.3531	−	15.7923i	−1.66158	−	0.959313i	−0.689618	−	0.724173i	$-0.742222\pi$
$272$	−2.34449			−0.142155
$273$	3.91529	−	16.0521i	0.236964	−	0.971518i
$274$	12.5570			0.758594
$275$	−34.6514	−	20.0060i	−2.08956	−	1.20641i
$276$	3.65133	−	0.694218i	0.219784	−	0.0417870i
$277$	−8.14386	−	14.1056i	−0.489317	−	0.847522i	0.510608	−	0.859814i	$-0.329420\pi$
$277$	−8.14386	−	14.1056i	−0.489317	−	0.847522i	−0.999924	+	0.0122922i	$0.996087\pi$
$278$	−7.72159	−	13.3742i	−0.463110	−	0.802130i
$279$	25.4278	+	3.78657i	1.52232	+	0.226696i
$280$	−10.4520	+	1.38589i	−0.624624	+	0.0828229i
$281$			13.4422i			0.801897i	0.916101	+	0.400948i	$0.131319\pi$
$281$			13.4422i			0.801897i	−0.916101	+	0.400948i	$0.868681\pi$
$282$	19.7896	−	3.76255i	1.17845	−	0.224057i
$283$			12.9575i			0.770242i	0.922866	+	0.385121i	$0.125840\pi$
$283$			12.9575i			0.770242i	−0.922866	+	0.385121i	$0.874160\pi$
$284$		−	3.74271i		−	0.222089i
$285$	18.9558	+	21.9876i	1.12285	+	1.30243i
$286$	7.03122	−	11.2411i	0.415765	−	0.664702i
$287$	1.07877	+	8.13571i	0.0636775	+	0.480236i
$288$	−1.86631	+	2.34880i	−0.109973	+	0.138405i
$289$	5.75169	−	9.96222i	0.338335	−	0.586013i
$290$	−7.80454	−	13.5179i	−0.458299	−	0.793796i
$291$	1.36924	−	3.92420i	0.0802662	−	0.230041i
$292$		−	0.547817i		−	0.0320586i
$293$	−12.9609	+	22.4489i	−0.757182	+	1.31148i	0.187101	+	0.982341i	$0.440091\pi$
$293$	−12.9609	+	22.4489i	−0.757182	+	1.31148i	−0.944282	+	0.329136i	$0.893242\pi$
$294$	10.9092	−	5.29048i	0.636238	−	0.308547i
$295$	−19.3641	+	33.5395i	−1.12742	+	1.95275i
$296$	5.97017	+	3.44688i	0.347009	+	0.200346i
$297$	16.1523	−	10.2092i	0.937254	−	0.592395i
$298$	−2.02149	+	3.50132i	−0.117102	+	0.202826i
$299$	−6.55951	−	4.10292i	−0.379347	−	0.237278i
$300$	−3.52003	−	18.5140i	−0.203229	−	1.06891i
$301$	−11.3643	+	8.73693i	−0.655030	+	0.503588i
$302$	−8.27235	+	4.77604i	−0.476020	+	0.274830i
$303$	2.43774	+	12.8216i	0.140044	+	0.736581i
$304$	3.64245	+	2.10297i	0.208909	+	0.120614i
$305$	−0.955190	+	0.551479i	−0.0546940	+	0.0315776i
$306$	2.58120	+	6.54270i	0.147558	+	0.374021i
$307$			20.1696i			1.15114i	0.817753	+	0.575569i	$0.195219\pi$
$307$			20.1696i			1.15114i	−0.817753	+	0.575569i	$0.804781\pi$
$308$	9.64502	−	1.27890i	0.549576	−	0.0728718i
$309$	10.1910	+	11.8210i	0.579746	+	0.672471i
$310$	−17.0747	+	29.5743i	−0.969778	+	1.67971i
$311$	−12.0287	+	20.8342i	−0.682082	+	1.18140i	0.292262	+	0.956338i	$0.405592\pi$
$311$	−12.0287	+	20.8342i	−0.682082	+	1.18140i	−0.974344	+	0.225063i	$0.927741\pi$
$312$	6.17249	−	0.948870i	0.349448	−	0.0537192i
$313$	−6.85676	+	3.95875i	−0.387567	+	0.223762i	−0.681105	−	0.732185i	$-0.738500\pi$
$313$	−6.85676	+	3.95875i	−0.387567	+	0.223762i	0.293539	+	0.955947i	$0.405167\pi$
$314$	−9.85334	−	17.0665i	−0.556056	−	0.963118i
$315$	15.3748	+	27.6422i	0.866274	+	1.55746i
$316$	−1.56372	+	2.70844i	−0.0879659	+	0.152361i
$317$	23.9291	−	13.8155i	1.34399	−	0.775954i	0.356601	−	0.934257i	$-0.383935\pi$
$317$	23.9291	−	13.8155i	1.34399	−	0.775954i	0.987391	+	0.158302i	$0.0506021\pi$
$318$	−2.74976	+	2.37060i	−0.154199	+	0.132937i
$319$	7.20200	+	12.4742i	0.403235	+	0.698423i
$320$	−1.99252	−	3.45115i	−0.111385	−	0.192925i
$321$	−7.56199	+	21.6725i	−0.422069	+	1.20964i
$322$	−0.746272	−	5.62814i	−0.0415881	−	0.313644i
$323$	8.53968	−	4.93038i	0.475160	−	0.274334i
$324$	8.60950	+	2.62231i	0.478305	+	0.145684i
$325$	−20.8038	+	33.2600i	−1.15399	+	1.84493i
$326$	0.311545	+	0.179871i	0.0172549	+	0.00996211i
$327$	−13.8445	−	4.83066i	−0.765605	−	0.267136i
$328$	−2.68634	+	1.55096i	−0.148329	+	0.0856375i
$329$	−4.04468	−	30.5037i	−0.222990	−	1.68172i
$330$	4.74097	+	24.9357i	0.260982	+	1.37267i
$331$	13.3256			0.732442			0.366221	−	0.930528i	$-0.380651\pi$
$331$	13.3256			0.732442			0.366221	+	0.930528i	$0.380651\pi$
$332$	−6.52141	−	11.2954i	−0.357909	−	0.619916i
$333$	3.04616	−	20.4557i	0.166928	−	1.12097i
$334$		−	3.78439i		−	0.207072i
$335$	21.3375	+	36.9577i	1.16579	+	2.01922i
$336$	3.42249	+	3.04738i	0.186712	+	0.166248i
$337$	6.30526			0.343469			0.171735	−	0.985143i	$-0.445063\pi$
$337$	6.30526			0.343469			0.171735	+	0.985143i	$0.445063\pi$
$338$	−10.7710	−	7.27914i	−0.585864	−	0.395933i
$339$	−6.70522	+	19.2170i	−0.364178	+	1.04372i
$340$	−9.34288			−0.506689
$341$	15.7565	−	27.2910i	0.853261	−	1.47789i
$342$	1.85849	−	12.4802i	0.100495	−	0.674852i
$343$	−7.13499	−	17.0907i	−0.385253	−	0.922811i
$344$	−4.69212	−	2.70900i	−0.252982	−	0.146059i
$345$	14.5507	−	2.76649i	0.783383	−	0.148943i
$346$	−18.6077	−	10.7432i	−1.00036	−	0.577557i
$347$	−12.8413	+	7.41392i	−0.689357	+	0.398000i	−0.803371	−	0.595479i	$-0.796962\pi$
$347$	−12.8413	+	7.41392i	−0.689357	+	0.398000i	0.114014	+	0.993479i	$0.463629\pi$
$348$	−2.23504	+	6.40557i	−0.119811	+	0.343375i
$349$	−2.57029	+	1.48396i	−0.137584	+	0.0794343i	−0.567212	−	0.823572i	$-0.691978\pi$
$349$	−2.57029	+	1.48396i	−0.137584	+	0.0794343i	0.429628	+	0.903006i	$0.358645\pi$
$350$	−28.5375	+	3.78397i	−1.52539	+	0.202262i
$351$	−9.44370	−	16.1807i	−0.504068	−	0.863664i
$352$	1.83869	+	3.18471i	0.0980026	+	0.169745i
$353$	−8.60692			−0.458100			−0.229050	−	0.973415i	$-0.573562\pi$
$353$	−8.60692			−0.458100			−0.229050	+	0.973415i	$0.573562\pi$
$354$	16.5365	−	3.14404i	0.878903	−	0.167104i
$355$		−	14.9149i		−	0.791599i
$356$	1.91893			0.101703
$357$	10.1994	−	3.37671i	0.539807	−	0.178714i
$358$	7.69731	−	13.3321i	0.406815	−	0.704625i
$359$	−6.89926	+	3.98329i	−0.364129	+	0.210230i	−0.670891	−	0.741556i	$-0.734088\pi$
$359$	−6.89926	+	3.98329i	−0.364129	+	0.210230i	0.306761	+	0.951786i	$0.400755\pi$
$360$	−7.43734	+	9.36009i	−0.391982	+	0.493320i
$361$	1.31007			0.0689512
$362$	−11.9514	+	20.7004i	−0.628150	+	1.08799i
$363$	−0.816278	−	4.29332i	−0.0428435	−	0.225341i
$364$	−0.918875	−	9.49503i	−0.0481622	−	0.497675i
$365$		−	2.18307i		−	0.114267i
$366$	0.452626	+	0.157931i	0.0236591	+	0.00825518i
$367$		−	22.7843i		−	1.18933i	−0.803974	−	0.594665i	$-0.797285\pi$
$367$		−	22.7843i		−	1.18933i	0.803974	−	0.594665i	$-0.202715\pi$
$368$	1.85837	−	1.07293i	0.0968741	−	0.0559303i
$369$	7.28581	+	5.78916i	0.379284	+	0.301371i
$370$	23.7914	+	13.7360i	1.23686	+	0.714099i
$371$	3.38013	+	4.39662i	0.175488	+	0.228261i
$372$	14.5814	−	2.77233i	0.756011	−	0.143739i
$373$	20.9264			1.08353			0.541765	−	0.840530i	$-0.317756\pi$
$373$	20.9264			1.08353			0.541765	+	0.840530i	$0.317756\pi$
$374$	8.62158			0.445811
$375$	−7.58137	−	39.8752i	−0.391500	−	2.05914i
$376$	10.0721	−	5.81511i	0.519427	−	0.299891i
$377$	12.4725	−	6.62461i	0.642367	−	0.341185i
$378$	4.73620	−	12.9061i	0.243604	−	0.663820i
$379$	0.0758760	+	0.131421i	0.00389749	+	0.00675064i	0.867968	−	0.496621i	$-0.165426\pi$
$379$	0.0758760	+	0.131421i	0.00389749	+	0.00675064i	−0.864070	+	0.503372i	$0.832093\pi$
$380$	14.5153	+	8.38043i	0.744620	+	0.429907i
$381$	−1.90681	+	1.64388i	−0.0976888	+	0.0842187i
$382$	−7.63375	+	13.2220i	−0.390576	+	0.676498i
$383$	−11.3500			−0.579960			−0.289980	−	0.957033i	$-0.593649\pi$
$383$	−11.3500			−0.579960			−0.289980	+	0.957033i	$0.593649\pi$
$384$	−0.570612	+	1.63536i	−0.0291189	+	0.0834541i
$385$	38.4358	−	5.09646i	1.95887	−	0.259739i
$386$	−14.4720	−	8.35541i	−0.736605	−	0.425279i
$387$	−2.39406	+	16.0767i	−0.121697	+	0.817224i
$388$		−	2.39960i		−	0.121821i
$389$	−18.4814	−	10.6702i	−0.937043	−	0.541002i	−0.0480112	−	0.998847i	$-0.515288\pi$
$389$	−18.4814	−	10.6702i	−0.937043	−	0.541002i	−0.889032	+	0.457845i	$0.848622\pi$
$390$	24.5976	−	3.78129i	1.24555	−	0.191473i
$391$		−	5.03093i		−	0.254425i
$392$	4.94055	−	4.95892i	0.249536	−	0.250463i
$393$	23.1654	−	19.9712i	1.16854	−	1.00741i
$394$	−2.10111			−0.105852
$395$	−6.23148	+	10.7932i	−0.313540	+	0.543067i
$396$	6.86315	−	8.63745i	0.344886	−	0.434048i
$397$		−	16.3409i		−	0.820125i	−0.912057	−	0.410063i	$-0.865507\pi$
$397$		−	16.3409i		−	0.820125i	0.912057	−	0.410063i	$-0.134493\pi$
$398$	−15.1451			−0.759154
$399$	−18.8748	−	3.90254i	−0.944923	−	0.195371i
$400$	−5.44029	−	9.42285i	−0.272014	−	0.471143i
$401$	24.2320	+	13.9903i	1.21009	+	0.698644i	0.962778	−	0.270293i	$-0.0871207\pi$
$401$	24.2320	+	13.9903i	1.21009	+	0.698644i	0.247308	+	0.968937i	$0.420454\pi$
$402$	6.11058	−	17.5128i	0.304768	−	0.873457i
$403$	−26.1952	−	16.3848i	−1.30487	−	0.816187i
$404$	3.76758	+	6.52563i	0.187444	+	0.324662i
$405$	34.3092	+	10.4500i	1.70484	+	0.519267i
$406$	9.57801	+	3.95694i	0.475349	+	0.196379i
$407$	−21.9546	−	12.6755i	−1.08825	−	0.628301i
$408$	2.65151	+	3.07560i	0.131269	+	0.152265i
$409$	−25.9794	+	14.9992i	−1.28460	+	0.741664i	−0.977686	−	0.210073i	$-0.932630\pi$
$409$	−25.9794	+	14.9992i	−1.28460	+	0.741664i	−0.306915	+	0.951737i	$0.599297\pi$
$410$	−10.7052	+	6.18065i	−0.528692	+	0.305240i
$411$	−14.2014	−	16.4728i	−0.700503	−	0.812542i
$412$	7.80371	+	4.50547i	0.384461	+	0.221969i
$413$	−3.37979	−	25.4893i	−0.166308	−	1.25425i
$414$	−5.04020	−	4.00484i	−0.247712	−	0.196827i
$415$	−25.9881	−	45.0127i	−1.27571	−	2.20959i
$416$	3.18427	−	1.69128i	0.156122	−	0.0829219i
$417$	−8.81206	+	25.2552i	−0.431529	+	1.23675i
$418$	−13.3947	−	7.73343i	−0.655156	−	0.378254i
$419$	−12.1211	−	20.9944i	−0.592155	−	1.02564i	−0.993942	−	0.109909i	$-0.964944\pi$
$419$	−12.1211	−	20.9944i	−0.592155	−	1.02564i	0.401787	−	0.915733i	$-0.368389\pi$
$420$	13.6388	+	12.1440i	0.665505	+	0.592564i
$421$	6.28451			0.306288			0.153144	−	0.988204i	$-0.451060\pi$
$421$	6.28451			0.306288			0.153144	+	0.988204i	$0.451060\pi$
$422$			15.9504i			0.776455i
$423$	−27.3171	−	21.7056i	−1.32820	−	1.05536i
$424$	−1.04805	+	1.81528i	−0.0508979	+	0.0881577i
$425$	−25.5094			−1.23739
$426$	−4.90986	+	4.23285i	−0.237883	+	0.205082i
$427$	0.279602	−	0.676795i	0.0135309	−	0.0327524i
$428$			13.2524i			0.640580i
$429$	−22.6986	+	3.48936i	−1.09590	+	0.168468i
$430$	−18.6983	−	10.7955i	−0.901712	−	0.520604i
$431$		−	14.5358i		−	0.700163i	−0.936719	−	0.350081i	$-0.886154\pi$
$431$		−	14.5358i		−	0.700163i	0.936719	−	0.350081i	$-0.113846\pi$
$432$	5.19198	−	0.208085i	0.249799	−	0.0100115i
$433$	−14.4330	−	8.33288i	−0.693604	−	0.400453i	0.111357	−	0.993781i	$-0.464480\pi$
$433$	−14.4330	−	8.33288i	−0.693604	−	0.400453i	−0.804961	+	0.593328i	$0.797814\pi$
$434$	−2.98021	−	22.4758i	−0.143054	−	1.07887i
$435$	−8.90673	+	25.5265i	−0.427045	+	1.22390i
$436$	−8.46574			−0.405436
$437$	−4.51267	+	7.81618i	−0.215870	+	0.373899i
$438$	−0.718650	+	0.619557i	−0.0343384	+	0.0296036i
$439$	−2.16013	−	1.24715i	−0.103098	−	0.0595234i	0.447565	−	0.894252i	$-0.352291\pi$
$439$	−2.16013	−	1.24715i	−0.103098	−	0.0595234i	−0.550662	+	0.834728i	$0.685625\pi$
$440$	7.32727	+	12.6912i	0.349314	+	0.605029i
$441$	−19.2781	−	8.32787i	−0.918007	−	0.396565i
$442$	0.298787	−	8.44788i	0.0142118	−	0.401825i
$443$	−0.249840	+	0.144245i	−0.0118703	+	0.00685329i	−0.505923	−	0.862578i	$-0.668848\pi$
$443$	−0.249840	+	0.144245i	−0.0118703	+	0.00685329i	0.494053	+	0.869432i	$0.335515\pi$
$444$	−2.23024	−	11.7302i	−0.105842	−	0.556691i
$445$	7.64701			0.362503
$446$	18.4210			0.872259
$447$	6.87940	−	1.30796i	0.325385	−	0.0618646i
$448$	2.44529	+	1.01022i	0.115529	+	0.0477283i
$449$	−3.87035	−	2.23455i	−0.182653	−	0.105455i	0.405886	−	0.913924i	$-0.366963\pi$
$449$	−3.87035	−	2.23455i	−0.182653	−	0.105455i	−0.588539	+	0.808469i	$0.700296\pi$
$450$	−20.3065	+	25.5563i	−0.957260	+	1.20474i
$451$	9.87872	−	5.70348i	0.465171	−	0.268566i
$452$			11.7509i			0.552717i
$453$	15.6211	+	5.45054i	0.733943	+	0.256089i
$454$			9.78852i			0.459398i
$455$	−3.66176	−	37.8381i	−0.171666	−	1.77388i
$456$	−1.36069	−	7.15670i	−0.0637200	−	0.335143i
$457$	16.1415	−	27.9580i	0.755069	−	1.30782i	−0.190271	−	0.981732i	$-0.560937\pi$
$457$	16.1415	−	27.9580i	0.755069	−	1.30782i	0.945340	−	0.326086i	$-0.105730\pi$
$458$	4.29599			0.200738
$459$	5.66378	−	10.7857i	0.264362	−	0.503431i
$460$	7.40567	−	4.27567i	0.345291	−	0.199354i
$461$	19.3508	−	33.5166i	0.901257	−	1.56102i	0.0753926	−	0.997154i	$-0.475979\pi$
$461$	19.3508	−	33.5166i	0.901257	−	1.56102i	0.825864	−	0.563869i	$-0.190688\pi$
$462$	−12.5858	−	11.2064i	−0.585545	−	0.521369i
$463$	3.56780			0.165810			0.0829048	−	0.996557i	$-0.473580\pi$
$463$	3.56780			0.165810			0.0829048	+	0.996557i	$0.473580\pi$
$464$			3.91692i			0.181838i
$465$	58.1076	−	11.0479i	2.69468	−	0.512332i
$466$	10.0320			0.464723
$467$	18.2961	+	31.6897i	0.846641	+	1.46643i	0.884188	+	0.467131i	$0.154712\pi$
$467$	18.2961	+	31.6897i	0.846641	+	1.46643i	−0.0375470	+	0.999295i	$0.511954\pi$
$468$	−8.22559	−	7.02422i	−0.380228	−	0.324695i
$469$	−26.1862	−	10.8182i	−1.20917	−	0.499539i
$470$	40.1376	−	23.1735i	1.85141	−	1.06891i
$471$	−11.2449	+	32.2275i	−0.518136	+	1.48497i
$472$	8.41635	−	4.85918i	0.387394	−	0.223662i
$473$	17.2547	+	9.96202i	0.793373	+	0.458054i
$474$	5.32154	−	1.01177i	0.244427	−	0.0464723i
$475$	39.6320	+	22.8815i	1.81844	+	1.04988i
$476$	4.91761	−	3.78067i	0.225398	−	0.173287i
$477$	6.21973	+	0.926209i	0.284782	+	0.0424082i
$478$	−5.92150	+	10.2563i	−0.270843	+	0.469114i
$479$	−2.07833			−0.0949612			−0.0474806	−	0.998872i	$-0.515119\pi$
$479$	−2.07833			−0.0949612			−0.0474806	+	0.998872i	$0.515119\pi$
$480$	−2.27391	+	6.51698i	−0.103789	+	0.297458i
$481$	−13.1810	+	21.0730i	−0.601001	+	0.960847i
$482$	−0.945386			−0.0430611
$483$	−6.53925	+	7.34418i	−0.297546	+	0.334172i
$484$	−1.26158	−	2.18511i	−0.0573444	−	0.0993233i
$485$		−	9.56249i		−	0.434210i
$486$	−6.29691	−	14.2600i	−0.285633	−	0.646849i
$487$	−10.8701	−	18.8275i	−0.492569	−	0.853155i	0.507394	−	0.861714i	$-0.330609\pi$
$487$	−10.8701	−	18.8275i	−0.492569	−	0.853155i	−0.999963	+	0.00855898i	$0.997276\pi$
$488$	0.276774			0.0125290
$489$	−0.116382	−	0.612125i	−0.00526297	−	0.0276812i
$490$	19.6883	−	19.7615i	0.889428	−	0.892735i
$491$	1.43244	−	0.827022i	0.0646453	−	0.0373230i	−0.467329	−	0.884083i	$-0.654784\pi$
$491$	1.43244	−	0.827022i	0.0646453	−	0.0373230i	0.531974	+	0.846761i	$0.321450\pi$
$492$	5.07276	+	1.76999i	0.228698	+	0.0797975i
$493$	7.95285	+	4.59158i	0.358178	+	0.206794i
$494$	−8.04183	+	12.8568i	−0.361819	+	0.578456i
$495$	27.3499	−	34.4206i	1.22929	−	1.54709i
$496$	7.42132	−	4.28470i	0.333227	−	0.192389i
$497$	6.03541	+	7.85042i	0.270725	+	0.352139i
$498$	−7.44239	+	21.3297i	−0.333501	+	0.955807i
$499$	20.1576	+	34.9140i	0.902378	+	1.56296i	0.824399	+	0.566009i	$0.191513\pi$
$499$	20.1576	+	34.9140i	0.902378	+	1.56296i	0.0779790	+	0.996955i	$0.475153\pi$
$500$	−11.7172	−	20.2947i	−0.524008	−	0.907608i
$501$	−4.96453	+	4.27998i	−0.221799	+	0.191215i
$502$	−13.7657	+	7.94764i	−0.614394	+	0.354720i
$503$	6.12895	−	10.6156i	0.273276	−	0.473328i	−0.696423	−	0.717632i	$-0.745226\pi$
$503$	6.12895	−	10.6156i	0.273276	−	0.473328i	0.969699	+	0.244304i	$0.0785594\pi$
$504$	0.126999	−	7.93624i	0.00565697	−	0.353508i
$505$	15.0140	+	26.0049i	0.668112	+	1.15720i
$506$	−6.83393	+	3.94557i	−0.303805	+	0.175402i
$507$	2.63243	+	22.3623i	0.116910	+	0.993142i
$508$	−0.726767	+	1.25880i	−0.0322451	+	0.0558501i
$509$	10.2279	−	17.7153i	0.453344	−	0.785216i	−0.545247	−	0.838276i	$-0.683564\pi$
$509$	10.2279	−	17.7153i	0.453344	−	0.785216i	0.998591	+	0.0530599i	$0.0168974\pi$
$510$	10.5664	+	12.2564i	0.467888	+	0.542723i
$511$	0.883397	+	1.14906i	0.0390792	+	0.0508313i
$512$			1.00000i			0.0441942i
$513$	−18.4739	+	11.6765i	−0.815645	+	0.515531i
$514$	17.4913	−	10.0986i	0.771507	−	0.445430i
$515$	31.0981	+	17.9545i	1.37035	+	0.791170i
$516$	1.75280	+	9.21909i	0.0771629	+	0.405848i
$517$	−37.0388	+	21.3844i	−1.62897	+	0.940484i
$518$	−18.0809	+	2.39747i	−0.794430	+	0.105339i
$519$	6.95117	+	36.5605i	0.305122	+	1.60483i
$520$	12.6895	−	6.73983i	0.556469	−	0.295561i
$521$	1.32358	−	2.29252i	0.0579873	−	0.100437i	−0.835575	−	0.549377i	$-0.814865\pi$
$521$	1.32358	−	2.29252i	0.0579873	−	0.100437i	0.893562	+	0.448940i	$0.148198\pi$
$522$	10.9308	−	4.31240i	0.478430	−	0.188749i
$523$	−6.15589	−	3.55411i	−0.269178	−	0.155410i	0.359336	−	0.933208i	$-0.383003\pi$
$523$	−6.15589	−	3.55411i	−0.269178	−	0.155410i	−0.628514	+	0.777798i	$0.716337\pi$
$524$	8.82931	−	15.2928i	0.385710	−	0.668070i
$525$	37.2387	+	33.1573i	1.62523	+	1.44710i
$526$	14.9444	−	25.8844i	0.651605	−	1.12861i
$527$		−	20.0908i		−	0.875171i
$528$	2.09836	−	6.01385i	0.0913194	−	0.261719i
$529$	−9.19765	−	15.9308i	−0.399898	−	0.692643i
$530$	−4.17653	+	7.23397i	−0.181417	+	0.314223i
$531$	−22.8265	−	18.1375i	−0.990587	−	0.787100i
$532$	−11.0313	+	1.46271i	−0.478268	+	0.0634167i
$533$	−5.24622	−	9.87736i	−0.227239	−	0.427836i
$534$	−2.17023	−	2.51734i	−0.0939149	−	0.108936i
$535$			52.8115i			2.28324i
$536$		−	10.7088i		−	0.462550i
$537$	−26.1950	+	4.98039i	−1.13040	+	0.214920i
$538$			12.8056i			0.552087i
$539$	−18.1683	+	18.2359i	−0.782565	+	0.785474i
$540$	20.6903	−	0.829229i	0.890368	−	0.0356844i
$541$	−11.5793	−	20.0559i	−0.497831	−	0.862269i	0.502166	−	0.864771i	$-0.332537\pi$
$541$	−11.5793	−	20.0559i	−0.497831	−	0.862269i	−0.999997	+	0.00250239i	$0.999203\pi$
$542$	15.7923	+	27.3531i	0.678337	+	1.17491i
$543$	40.6722	−	7.73291i	1.74541	−	0.331851i
$544$	2.03038	+	1.17224i	0.0870520	+	0.0502595i
$545$	−33.7364			−1.44511
$546$	−11.4168	+	11.9439i	−0.488594	+	0.511152i
$547$	22.8911			0.978751			0.489375	−	0.872073i	$-0.337225\pi$
$547$	22.8911			0.978751			0.489375	+	0.872073i	$0.337225\pi$
$548$	−10.8746	−	6.27848i	−0.464542	−	0.268203i
$549$	−0.304720	−	0.772388i	−0.0130051	−	0.0329647i
$550$	20.0060	+	34.6514i	0.853060	+	1.47754i
$551$	−8.23716	−	14.2672i	−0.350915	−	0.607802i
$552$	−3.50925	−	1.22445i	−0.149364	−	0.0521161i
$553$	−1.08764	−	8.20262i	−0.0462511	−	0.348811i
$554$			16.2877i			0.691999i
$555$	−8.88760	−	46.7454i	−0.377257	−	1.98423i
$556$			15.4432i			0.654937i
$557$			4.78799i			0.202874i	0.994842	+	0.101437i	$0.0323440\pi$
$557$			4.78799i			0.202874i	−0.994842	+	0.101437i	$0.967656\pi$
$558$	−20.1278	−	15.9932i	−0.852079	−	0.677045i
$559$	10.3593	−	16.5619i	0.438151	−	0.700492i
$560$	9.74460	+	4.02576i	0.411785	+	0.170119i
$561$	−9.75063	−	11.3102i	−0.411672	−	0.477516i
$562$	6.72112	−	11.6413i	0.283513	−	0.491060i
$563$	−2.97517	−	5.15315i	−0.125388	−	0.217179i	0.796496	−	0.604643i	$-0.206684\pi$
$563$	−2.97517	−	5.15315i	−0.125388	−	0.217179i	−0.921885	+	0.387464i	$0.873351\pi$
$564$	−19.0196	−	6.63634i	−0.800869	−	0.279440i
$565$			46.8280i			1.97007i
$566$	6.47874	−	11.2215i	0.272322	−	0.471675i
$567$	−22.2873	+	8.38313i	−0.935978	+	0.352058i
$568$	−1.87136	+	3.24128i	−0.0785204	+	0.136001i
$569$	5.25796	+	3.03569i	0.220425	+	0.127263i	0.606147	−	0.795353i	$-0.292714\pi$
$569$	5.25796	+	3.03569i	0.220425	+	0.127263i	−0.385722	+	0.922615i	$0.626048\pi$
$570$	−5.42239	−	28.5198i	−0.227119	−	1.19456i
$571$	−14.4318	+	24.9966i	−0.603951	+	1.04607i	0.388265	+	0.921548i	$0.373075\pi$
$571$	−14.4318	+	24.9966i	−0.603951	+	1.04607i	−0.992216	+	0.124527i	$0.960259\pi$
$572$	−11.7098	+	6.21949i	−0.489610	+	0.260050i
$573$	25.9787	−	4.93927i	1.08528	−	0.206341i
$574$	3.13362	−	7.58511i	0.130795	−	0.316596i
$575$	20.2201	−	11.6741i	0.843237	−	0.486843i
$576$	2.79068	−	1.10097i	0.116278	−	0.0458737i
$577$	19.0046	+	10.9723i	0.791170	+	0.456782i	0.840374	−	0.542007i	$-0.182335\pi$
$577$	19.0046	+	10.9723i	0.791170	+	0.456782i	−0.0492043	+	0.998789i	$0.515669\pi$
$578$	−9.96222	+	5.75169i	−0.414374	+	0.239239i
$579$	5.40621	+	28.4346i	0.224674	+	1.18170i
$580$			15.6091i			0.648132i
$581$	31.8935	+	13.1761i	1.32317	+	0.546636i
$582$	−3.14790	+	2.71384i	−0.130484	+	0.112492i
$583$	3.85409	−	6.67548i	0.159620	−	0.276470i
$584$	−0.273908	+	0.474423i	−0.0113344	+	0.0196318i
$585$	−32.7793	−	27.9918i	−1.35526	−	1.15732i
$586$	22.4489	−	12.9609i	0.927354	−	0.535408i
$587$	14.7245	+	25.5036i	0.607746	+	1.05265i	0.991611	+	0.129258i	$0.0412595\pi$
$587$	14.7245	+	25.5036i	0.607746	+	1.05265i	−0.383865	+	0.923389i	$0.625407\pi$
$588$	−12.0929	−	0.872910i	−0.498702	−	0.0359982i
$589$	−18.0212	+	31.2136i	−0.742550	+	1.28613i
$590$	33.5395	−	19.3641i	1.38080	−	0.797205i
$591$	2.37626	+	2.75633i	0.0977464	+	0.113380i
$592$	−3.44688	−	5.97017i	−0.141666	−	0.245373i
$593$	−14.9324	−	25.8636i	−0.613199	−	1.06209i	−0.990698	−	0.136082i	$-0.956549\pi$
$593$	−14.9324	−	25.8636i	−0.613199	−	1.06209i	0.377499	−	0.926010i	$-0.376784\pi$
$594$	−19.0929	+	0.765210i	−0.783392	+	0.0313969i
$595$	19.5969	−	15.0661i	0.803394	−	0.617651i
$596$	3.50132	−	2.02149i	0.143420	−	0.0828033i
$597$	17.1284	+	19.8680i	0.701020	+	0.813142i
$598$	3.62925	+	6.83299i	0.148411	+	0.279422i
$599$	−10.6949	−	6.17470i	−0.436981	−	0.252291i	0.265335	−	0.964156i	$-0.414517\pi$
$599$	−10.6949	−	6.17470i	−0.436981	−	0.252291i	−0.702316	+	0.711865i	$0.747851\pi$
$600$	−6.20859	+	17.7937i	−0.253464	+	0.726423i
$601$	−37.8812	+	21.8707i	−1.54521	+	0.892126i	−0.546710	+	0.837322i	$0.684120\pi$
$601$	−37.8812	+	21.8707i	−1.54521	+	0.892126i	−0.998497	+	0.0548042i	$0.982547\pi$
$602$	14.2103	−	1.88423i	0.579168	−	0.0767956i
$603$	−29.8848	+	11.7901i	−1.21700	+	0.480128i
$604$	9.55209			0.388669
$605$	−5.02744	−	8.70777i	−0.204394	−	0.354021i
$606$	4.29965	−	12.3227i	0.174661	−	0.500575i
$607$		−	31.2784i		−	1.26955i	−0.772696	−	0.634776i	$-0.781092\pi$
$607$		−	31.2784i		−	1.26955i	0.772696	−	0.634776i	$-0.218908\pi$
$608$	−2.10297	−	3.64245i	−0.0852867	−	0.147721i
$609$	−5.64144	−	17.0400i	−0.228603	−	0.690495i
$610$	1.10296			0.0446575
$611$	19.6700	+	37.0337i	0.795761	+	1.49822i
$612$	1.03596	−	6.95675i	0.0418763	−	0.281210i
$613$	1.46575			0.0592013			0.0296006	−	0.999562i	$-0.490576\pi$
$613$	1.46575			0.0592013			0.0296006	+	0.999562i	$0.490576\pi$
$614$	10.0848	−	17.4673i	0.406988	−	0.704925i
$615$	20.2152	+	7.05351i	0.815154	+	0.284425i
$616$	−8.99228	−	3.71496i	−0.362309	−	0.149680i
$617$	8.81211	+	5.08767i	0.354762	+	0.204822i	0.666781	−	0.745254i	$-0.267672\pi$
$617$	8.81211	+	5.08767i	0.354762	+	0.204822i	−0.312019	+	0.950076i	$0.601005\pi$
$618$	−2.91518	−	15.3328i	−0.117266	−	0.616774i
$619$	−21.4340	−	12.3749i	−0.861507	−	0.497391i	0.00300980	−	0.999995i	$-0.499042\pi$
$619$	−21.4340	−	12.3749i	−0.861507	−	0.497391i	−0.864517	+	0.502604i	$0.832375\pi$
$620$	29.5743	−	17.0747i	1.18773	−	0.685737i
$621$	0.446522	+	11.1413i	0.0179183	+	0.447083i
$622$	20.8342	−	12.0287i	0.835377	−	0.482305i
$623$	−4.02499	+	3.09442i	−0.161258	+	0.123975i
$624$	−5.81997	−	2.26450i	−0.232985	−	0.0906525i
$625$	−19.4920	−	33.7612i	−0.779680	−	1.35045i
$626$	7.91750			0.316447
$627$	5.00377	+	26.3179i	0.199831	+	1.05104i
$628$			19.7067i			0.786383i
$629$	−16.1623			−0.644434
$630$	0.506095	−	31.6263i	0.0201633	−	1.26002i
$631$	−1.30186	+	2.25489i	−0.0518264	+	0.0897659i	−0.890775	−	0.454445i	$-0.849838\pi$
$631$	−1.30186	+	2.25489i	−0.0518264	+	0.0897659i	0.838948	+	0.544211i	$0.183171\pi$
$632$	2.70844	−	1.56372i	0.107736	−	0.0622013i
$633$	20.9245	−	18.0393i	0.831674	−	0.716996i
$634$	−27.6309			−1.09736
$635$	−2.89620	+	5.01636i	−0.114932	+	0.199068i
$636$	3.56667	−	0.678122i	0.141427	−	0.0268893i
$637$	17.2388	+	18.4343i	0.683028	+	0.730392i
$638$		−	14.4040i		−	0.570260i
$639$	11.1057	+	1.65380i	0.439334	+	0.0654233i
$640$			3.98504i			0.157523i
$641$	6.22771	−	3.59557i	0.245980	−	0.142017i	−0.371942	−	0.928256i	$-0.621308\pi$
$641$	6.22771	−	3.59557i	0.245980	−	0.142017i	0.617922	+	0.786239i	$0.287975\pi$
$642$	17.3851	−	14.9879i	0.686136	−	0.591526i
$643$	5.48347	+	3.16588i	0.216247	+	0.124850i	0.604211	−	0.796824i	$-0.293488\pi$
$643$	5.48347	+	3.16588i	0.216247	+	0.124850i	−0.387964	+	0.921674i	$0.626822\pi$
$644$	−2.16778	+	5.24725i	−0.0854226	+	0.206771i
$645$	6.98500	+	36.7385i	0.275034	+	1.44658i
$646$	−9.86077			−0.387967
$647$	8.50212			0.334253			0.167126	−	0.985935i	$-0.446551\pi$
$647$	8.50212			0.334253			0.167126	+	0.985935i	$0.446551\pi$
$648$	−6.14489	−	6.57574i	−0.241394	−	0.258319i
$649$	−30.9501	+	17.8691i	−1.21490	+	0.701423i
$650$	34.6467	−	18.4021i	1.35895	−	0.721790i
$651$	−26.1142	+	29.3287i	−1.02350	+	1.14948i
$652$	−0.179871	−	0.311545i	−0.00704428	−	0.0122010i
$653$	−23.8853	−	13.7902i	−0.934704	−	0.539651i	−0.0464076	−	0.998923i	$-0.514777\pi$
$653$	−23.8853	−	13.7902i	−0.934704	−	0.539651i	−0.888296	+	0.459271i	$0.848111\pi$
$654$	9.57439	+	11.1057i	0.374388	+	0.434269i
$655$	35.1852	−	60.9426i	1.37480	−	2.38122i
$656$	3.10192			0.121110
$657$	1.62553	+	0.242065i	0.0634178	+	0.00944385i
$658$	−11.7490	+	28.4393i	−0.458025	+	1.10868i
$659$	21.6640	+	12.5077i	0.843908	+	0.487230i	0.858591	−	0.512662i	$-0.171341\pi$
$659$	21.6640	+	12.5077i	0.843908	+	0.487230i	−0.0146829	+	0.999892i	$0.504674\pi$
$660$	8.36205	−	23.9654i	0.325493	−	0.932853i
$661$		−	15.0253i		−	0.584418i	−0.956354	−	0.292209i	$-0.905610\pi$
$661$		−	15.0253i		−	0.584418i	0.956354	−	0.292209i	$-0.0943903\pi$
$662$	−11.5403	−	6.66281i	−0.448527	−	0.258957i
$663$	−11.4202	+	9.16223i	−0.443525	+	0.355832i
$664$			13.0428i			0.506159i
$665$	−43.9603	+	5.82898i	−1.70471	+	0.226038i
$666$	−12.8659	+	16.1921i	−0.498544	+	0.627431i
$667$	−8.40515			−0.325449
$668$	−1.89219	+	3.27738i	−0.0732112	+	0.126805i
$669$	−20.8333	−	24.1655i	−0.805464	−	0.934291i
$670$		−	42.6751i		−	1.64868i
$671$	−1.01781			−0.0392920
$672$	−1.44027	−	4.35036i	−0.0555598	−	0.167819i
$673$	−2.09904	−	3.63565i	−0.0809121	−	0.140144i	0.822730	−	0.568433i	$-0.192450\pi$
$673$	−2.09904	−	3.63565i	−0.0809121	−	0.140144i	−0.903642	+	0.428289i	$0.859117\pi$
$674$	−5.46051	−	3.15263i	−0.210331	−	0.121435i
$675$	56.4918	−	2.26409i	2.17437	−	0.0871448i
$676$	5.68838	+	11.6894i	0.218784	+	0.449593i
$677$	−18.0619	−	31.2842i	−0.694177	−	1.20235i	−0.970457	−	0.241272i	$-0.922435\pi$
$677$	−18.0619	−	31.2842i	−0.694177	−	1.20235i	0.276281	−	0.961077i	$-0.410898\pi$
$678$	15.4154	−	13.2898i	0.592025	−	0.510392i
$679$	3.86953	+	5.03320i	0.148499	+	0.193157i
$680$	8.09117	+	4.67144i	0.310282	+	0.179142i
$681$	12.8410	−	11.0704i	0.492069	−	0.424219i
$682$	−27.2910	+	15.7565i	−1.04503	+	0.603347i
$683$	8.79767	−	5.07934i	0.336634	−	0.194355i	−0.322149	−	0.946689i	$-0.604405\pi$
$683$	8.79767	−	5.07934i	0.336634	−	0.194355i	0.658782	+	0.752334i	$0.271072\pi$
$684$	−7.84960	+	9.87893i	−0.300137	+	0.377730i
$685$	−43.3359	−	25.0200i	−1.65578	−	0.955966i
$686$	−2.36627	+	18.3685i	−0.0903444	+	0.701312i
$687$	−4.85858	−	5.63567i	−0.185366	−	0.215014i
$688$	2.70900	+	4.69212i	0.103279	+	0.178885i
$689$	−6.40742	−	4.00779i	−0.244103	−	0.152684i
$690$	−13.9845	−	4.87950i	−0.532381	−	0.185759i
$691$	−6.40627	−	3.69866i	−0.243706	−	0.140704i	0.373173	−	0.927762i	$-0.378270\pi$
$691$	−6.40627	−	3.69866i	−0.243706	−	0.140704i	−0.616879	+	0.787058i	$0.711603\pi$
$692$	10.7432	+	18.6077i	0.408394	+	0.707360i
$693$	−0.467023	+	29.1846i	−0.0177407	+	1.10863i
$694$	14.8278			0.562857
$695$			61.5417i			2.33441i
$696$	5.13839	−	4.42987i	0.194770	−	0.167914i
$697$	3.63621	−	6.29810i	0.137731	−	0.238557i
$698$	2.96791			0.112337
$699$	−11.3457	−	13.1604i	−0.429136	−	0.497772i
$700$	26.6062	+	10.9917i	1.00562	+	0.415449i
$701$		−	16.0990i		−	0.608049i	−0.952664	−	0.304025i	$-0.901669\pi$
$701$		−	16.0990i		−	0.608049i	0.952664	−	0.304025i	$-0.0983306\pi$
$702$	0.0881149	+	18.7348i	0.00332568	+	0.707099i
$703$	25.1102	+	14.4974i	0.947048	+	0.546779i
$704$		−	3.67738i		−	0.138597i
$705$	−75.7939	−	26.4461i	−2.85456	−	0.996018i
$706$	7.45381	+	4.30346i	0.280528	+	0.161963i
$707$	−18.4257	−	7.61214i	−0.692968	−	0.286284i
$708$	−15.8930	−	5.54541i	−0.597296	−	0.208409i
$709$	−47.7441			−1.79307			−0.896534	−	0.442976i	$-0.853923\pi$
$709$	−47.7441			−1.79307			−0.896534	+	0.442976i	$0.853923\pi$
$710$	−7.45744	+	12.9167i	−0.279873	+	0.484753i
$711$	−7.34573	−	5.83677i	−0.275486	−	0.218896i
$712$	−1.66184	−	0.959464i	−0.0622801	−	0.0359574i
$713$	9.19435	+	15.9251i	0.344331	+	0.596399i
$714$	−10.5213	−	2.17536i	−0.393748	−	0.0814110i
$715$	−46.6640	+	24.7849i	−1.74513	+	0.926904i
$716$	−13.3321	+	7.69731i	−0.498245	+	0.287662i
$717$	20.1517	−	3.83140i	0.752579	−	0.143086i
$718$	7.96658			0.297310
$719$	−10.5889			−0.394899			−0.197449	−	0.980313i	$-0.563266\pi$
$719$	−10.5889			−0.394899			−0.197449	+	0.980313i	$0.563266\pi$
$720$	11.1210	−	4.38740i	0.414454	−	0.163509i
$721$	−23.6339	+	3.13377i	−0.880171	+	0.116708i
$722$	−1.13456	−	0.655036i	−0.0422238	−	0.0243779i
$723$	1.06919	+	1.24020i	0.0397636	+	0.0461235i
$724$	20.7004	−	11.9514i	0.769324	−	0.444169i
$725$			42.6183i			1.58280i
$726$	−1.43974	+	4.12626i	−0.0534338	+	0.153140i
$727$		−	6.29062i		−	0.233306i	−0.993173	−	0.116653i	$-0.962783\pi$
$727$		−	6.29062i		−	0.233306i	0.993173	−	0.116653i	$-0.0372166\pi$
$728$	−3.95175	+	8.68238i	−0.146462	+	0.321790i
$729$	−11.5854	+	24.3881i	−0.429090	+	0.903262i
$730$	−1.09154	+	1.89060i	−0.0403996	+	0.0699742i
$731$	12.7024			0.469815
$732$	−0.313020	−	0.363085i	−0.0115696	−	0.0134200i
$733$	−24.4353	+	14.1077i	−0.902538	+	0.521080i	−0.878023	−	0.478619i	$-0.841138\pi$
$733$	−24.4353	+	14.1077i	−0.902538	+	0.521080i	−0.0245151	+	0.999699i	$0.507804\pi$
$734$	−11.3921	+	19.7318i	−0.420492	+	0.728313i
$735$	−48.1907	−	3.47859i	−1.77754	−	0.128310i
$736$	−2.14586			−0.0790974
$737$			39.3804i			1.45060i
$738$	−3.41512	−	8.65646i	−0.125712	−	0.318649i
$739$	25.8468			0.950791			0.475396	−	0.879772i	$-0.342305\pi$
$739$	25.8468			0.950791			0.475396	+	0.879772i	$0.342305\pi$
$740$	−13.7360	−	23.7914i	−0.504944	−	0.874589i
$741$	25.9611	−	3.99089i	0.953706	−	0.146609i
$742$	−0.728969	−	5.49765i	−0.0267613	−	0.201825i
$743$	6.50706	−	3.75685i	0.238721	−	0.137826i	−0.375868	−	0.926673i	$-0.622655\pi$
$743$	6.50706	−	3.75685i	0.238721	−	0.137826i	0.614589	+	0.788848i	$0.289322\pi$
$744$	−14.0140	−	4.88980i	−0.513780	−	0.179269i
$745$	13.9529	−	8.05572i	0.511195	−	0.295139i
$746$	−18.1228	−	10.4632i	−0.663524	−	0.383086i
$747$	36.3983	−	14.3597i	1.33174	−	0.525395i
$748$	−7.46650	−	4.31079i	−0.273002	−	0.157618i
$749$	−21.3706	−	27.7972i	−0.780863	−	1.01569i
$750$	−13.3719	+	38.3236i	−0.488273	+	1.39938i
$751$	0.712950	−	1.23487i	0.0260159	−	0.0450609i	−0.852724	−	0.522361i	$-0.825051\pi$
$751$	0.712950	−	1.23487i	0.0260159	−	0.0450609i	0.878740	+	0.477300i	$0.158385\pi$
$752$	−11.6302			−0.424110
$753$	25.9945	+	9.07003i	0.947292	+	0.330530i
$754$	−14.1138	−	0.499181i	−0.513995	−	0.0181791i
$755$	38.0655			1.38534
$756$	−10.5547	+	8.80894i	−0.383872	+	0.320378i
$757$	−11.4225	−	19.7843i	−0.415157	−	0.719074i	0.580288	−	0.814412i	$-0.302940\pi$
$757$	−11.4225	−	19.7843i	−0.415157	−	0.719074i	−0.995445	+	0.0953379i	$0.969607\pi$
$758$		−	0.151752i		−	0.00551188i
$759$	12.9049	+	4.50278i	0.468417	+	0.163441i
$760$	−8.38043	−	14.5153i	−0.303990	−	0.526526i
$761$	−25.9165			−0.939474			−0.469737	−	0.882806i	$-0.655651\pi$
$761$	−25.9165			−0.939474			−0.469737	+	0.882806i	$0.655651\pi$
$762$	2.47329	−	0.470240i	0.0895977	−	0.0170350i
$763$	17.7571	−	13.6517i	0.642849	−	0.494224i
$764$	13.2220	−	7.63375i	0.478357	−	0.276179i
$765$	4.12836	−	27.7229i	0.149261	−	1.00233i
$766$	9.82943	+	5.67502i	0.355152	+	0.205047i
$767$	16.4365	+	30.9459i	0.593487	+	1.11739i
$768$	1.31184	−	1.13096i	0.0473371	−	0.0408099i
$769$	34.4344	−	19.8807i	1.24174	−	0.716918i	0.272290	−	0.962215i	$-0.412219\pi$
$769$	34.4344	−	19.8807i	1.24174	−	0.716918i	0.969448	+	0.245298i	$0.0788857\pi$
$770$	−35.8346	−	14.8043i	−1.29139	−	0.533509i
$771$	−33.0296	−	11.5247i	−1.18953	−	0.415054i
$772$	8.35541	+	14.4720i	0.300718	+	0.520859i
$773$	−16.8043	−	29.1059i	−0.604409	−	1.04687i	−0.992145	−	0.125097i	$-0.960076\pi$
$773$	−16.8043	−	29.1059i	−0.604409	−	1.04687i	0.387735	−	0.921771i	$-0.373257\pi$
$774$	10.1117	−	12.7258i	0.363456	−

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.323515 + 1.70157i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.99252 + 3.45115i) q^{5} +(0.570612 - 1.63536i) q^{6} +(-2.44529 - 1.01022i) q^{7} -1.00000i q^{8} +(-2.79068 + 1.10097i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.323515 + 1.70157i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.99252 + 3.45115i) q^{5} +(0.570612 - 1.63536i) q^{6} +(-2.44529 - 1.01022i) q^{7} -1.00000i q^{8} +(-2.79068 + 1.10097i) q^{9} -3.98504i q^{10} +3.67738i q^{11} +(-1.31184 + 1.13096i) q^{12} +(3.60330 + 0.127442i) q^{13} +(1.61258 + 2.09752i) q^{14} +(-5.22776 + 4.50691i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.17224 + 2.03038i) q^{17} +(2.96728 + 0.441872i) q^{18} -4.20594i q^{19} +(-1.99252 + 3.45115i) q^{20} +(0.927864 - 4.48766i) q^{21} +(1.83869 - 3.18471i) q^{22} +(-1.85837 - 1.07293i) q^{23} +(1.70157 - 0.323515i) q^{24} +(-5.44029 + 9.42285i) q^{25} +(-3.05683 - 1.91202i) q^{26} +(-2.77620 - 4.39235i) q^{27} +(-0.347773 - 2.62280i) q^{28} +(3.39215 - 1.95846i) q^{29} +(6.78083 - 1.28922i) q^{30} +(-7.42132 - 4.28470i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-6.25732 + 1.18969i) q^{33} -2.34449i q^{34} +(-1.38589 - 10.4520i) q^{35} +(-2.34880 - 1.86631i) q^{36} +(-3.44688 + 5.97017i) q^{37} +(-2.10297 + 3.64245i) q^{38} +(0.948870 + 6.17249i) q^{39} +(3.45115 - 1.99252i) q^{40} +(-1.55096 - 2.68634i) q^{41} +(-3.04738 + 3.42249i) q^{42} +(2.70900 - 4.69212i) q^{43} +(-3.18471 + 1.83869i) q^{44} +(-9.36009 - 7.43734i) q^{45} +(1.07293 + 1.85837i) q^{46} +(5.81511 + 10.0721i) q^{47} +(-1.63536 - 0.570612i) q^{48} +(4.95892 + 4.94055i) q^{49} +(9.42285 - 5.44029i) q^{50} +(-3.07560 + 2.65151i) q^{51} +(1.69128 + 3.18427i) q^{52} +(-1.81528 - 1.04805i) q^{53} +(0.208085 + 5.19198i) q^{54} +(-12.6912 + 7.32727i) q^{55} +(-1.01022 + 2.44529i) q^{56} +(7.15670 - 1.36069i) q^{57} -3.91692 q^{58} +(4.85918 + 8.41635i) q^{59} +(-6.51698 - 2.27391i) q^{60} +0.276774i q^{61} +(4.28470 + 7.42132i) q^{62} +(7.93624 + 0.126999i) q^{63} -1.00000 q^{64} +(6.73983 + 12.6895i) q^{65} +(6.01385 + 2.09836i) q^{66} +10.7088 q^{67} +(-1.17224 + 2.03038i) q^{68} +(1.22445 - 3.50925i) q^{69} +(-4.02576 + 9.74460i) q^{70} +(-3.24128 - 1.87136i) q^{71} +(1.10097 + 2.79068i) q^{72} +(-0.474423 - 0.273908i) q^{73} +(5.97017 - 3.44688i) q^{74} +(-17.7937 - 6.20859i) q^{75} +(3.64245 - 2.10297i) q^{76} +(3.71496 - 8.99228i) q^{77} +(2.26450 - 5.81997i) q^{78} +(1.56372 + 2.70844i) q^{79} -3.98504 q^{80} +(6.57574 - 6.14489i) q^{81} +3.10192i q^{82} -13.0428 q^{83} +(4.35036 - 1.44027i) q^{84} +(-4.67144 + 8.09117i) q^{85} +(-4.69212 + 2.70900i) q^{86} +(4.42987 + 5.13839i) q^{87} +3.67738 q^{88} +(0.959464 - 1.66184i) q^{89} +(4.38740 + 11.1210i) q^{90} +(-8.68238 - 3.95175i) q^{91} -2.14586i q^{92} +(4.88980 - 14.0140i) q^{93} -11.6302i q^{94} +(14.5153 - 8.38043i) q^{95} +(1.13096 + 1.31184i) q^{96} +(-2.07811 - 1.19980i) q^{97} +(-1.82428 - 6.75811i) q^{98} +(-4.04868 - 10.2624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

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