LMFDB - Embedded newform 819.2.fy.a.50.16

Newspace parameters

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fy (of order $12$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$84$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.16
Character	$\chi$	$=$	819.50
Dual form			819.2.fy.a.344.16

$q$-expansion

$f(q)$	$=$	$q+(-0.541434 - 2.02066i) q^{2} +(1.72494 + 0.156795i) q^{3} +(-2.05786 + 1.18811i) q^{4} +(-1.05055 - 3.92071i) q^{5} +(-0.617111 - 3.57041i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.556508 + 0.556508i) q^{8} +(2.95083 + 0.540924i) q^{9} +O(q^{10})$	\(q+(-0.541434 - 2.02066i) q^{2} +(1.72494 + 0.156795i) q^{3} +(-2.05786 + 1.18811i) q^{4} +(-1.05055 - 3.92071i) q^{5} +(-0.617111 - 3.57041i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.556508 + 0.556508i) q^{8} +(2.95083 + 0.540924i) q^{9} +(-7.35361 + 4.24561i) q^{10} +(3.17590 - 0.850980i) q^{11} +(-3.73598 + 1.72675i) q^{12} +(2.04474 - 2.96968i) q^{13} +(1.81167 + 1.04597i) q^{14} +(-1.19739 - 6.92770i) q^{15} +(-1.55302 + 2.68990i) q^{16} +(2.15361 - 3.73016i) q^{17} +(-0.504656 - 6.25550i) q^{18} +(-1.59384 + 0.427069i) q^{19} +(6.82011 + 6.82011i) q^{20} +(-1.33059 + 1.10885i) q^{21} +(-3.43908 - 5.95666i) q^{22} -7.24903 q^{23} +(0.872684 + 1.04720i) q^{24} +(-9.93815 + 5.73779i) q^{25} +(-7.10781 - 2.52384i) q^{26} +(5.00519 + 1.39574i) q^{27} +(0.615010 - 2.29525i) q^{28} +(2.76216 + 1.59473i) q^{29} +(-13.3502 + 6.17040i) q^{30} +(0.464434 - 0.124445i) q^{31} +(7.79664 + 2.08910i) q^{32} +(5.61166 - 0.969923i) q^{33} +(-8.70343 - 2.33208i) q^{34} +(3.51521 + 2.02951i) q^{35} +(-6.71508 + 2.39276i) q^{36} +(0.157111 + 0.0420979i) q^{37} +(1.72592 + 2.98939i) q^{38} +(3.99269 - 4.80192i) q^{39} +(1.59726 - 2.76654i) q^{40} +(-2.73381 + 2.73381i) q^{41} +(2.96102 + 2.08830i) q^{42} +2.53864i q^{43} +(-5.52451 + 5.52451i) q^{44} +(-0.979190 - 12.1376i) q^{45} +(3.92487 + 14.6478i) q^{46} +(-0.853614 + 3.18573i) q^{47} +(-3.10062 + 4.39641i) q^{48} -1.00000i q^{49} +(16.9750 + 16.9750i) q^{50} +(4.29972 - 6.09663i) q^{51} +(-0.679500 + 8.54058i) q^{52} +9.42441i q^{53} +(0.110330 - 10.8695i) q^{54} +(-6.67288 - 11.5578i) q^{55} -0.787021 q^{56} +(-2.81625 + 0.486761i) q^{57} +(1.72689 - 6.44483i) q^{58} +(2.75423 - 10.2789i) q^{59} +(10.6949 + 12.8336i) q^{60} -10.3465 q^{61} +(-0.502921 - 0.871085i) q^{62} +(-2.46904 + 1.70406i) q^{63} -10.6734i q^{64} +(-13.7914 - 4.89704i) q^{65} +(-4.99823 - 10.8141i) q^{66} +(8.83286 + 8.83286i) q^{67} +10.2349i q^{68} +(-12.5041 - 1.13661i) q^{69} +(2.19769 - 8.20188i) q^{70} +(-2.18019 - 8.13660i) q^{71} +(1.34113 + 1.94319i) q^{72} +(9.88411 - 9.88411i) q^{73} -0.340262i q^{74} +(-18.0424 + 8.33909i) q^{75} +(2.77251 - 2.77251i) q^{76} +(-1.64397 + 2.84743i) q^{77} +(-11.8648 - 5.46795i) q^{78} +(-2.64152 - 4.57524i) q^{79} +(12.1778 + 3.26304i) q^{80} +(8.41480 + 3.19235i) q^{81} +(7.00427 + 4.04391i) q^{82} +(2.19185 + 0.587305i) q^{83} +(1.42074 - 3.86273i) q^{84} +(-16.8874 - 4.52495i) q^{85} +(5.12973 - 1.37451i) q^{86} +(4.51451 + 3.18391i) q^{87} +(2.24099 + 1.29384i) q^{88} +(2.53372 - 9.45596i) q^{89} +(-23.9958 + 8.55032i) q^{90} +(0.654031 + 3.54574i) q^{91} +(14.9175 - 8.61263i) q^{92} +(0.820633 - 0.141839i) q^{93} +6.89945 q^{94} +(3.34883 + 5.80034i) q^{95} +(13.1212 + 4.82605i) q^{96} +(10.5814 + 10.5814i) q^{97} +(-2.02066 + 0.541434i) q^{98} +(9.83186 - 0.793176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) $ 336 * q - 12 * q^6 + 36 * q^8	$ 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) $ 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$

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 $

$2$	−0.541434	−	2.02066i	−0.382852	−	1.42882i	−0.841526	−	0.540217i	$-0.818342\pi$
$2$	−0.541434	−	2.02066i	−0.382852	−	1.42882i	0.458674	−	0.888605i	$-0.348325\pi$
$3$	1.72494	+	0.156795i	0.995894	+	0.0905257i
$3$	1.72494	+	0.156795i	0.995894	+	0.0905257i
$4$	−2.05786	+	1.18811i	−1.02893	+	0.594054i
$5$	−1.05055	−	3.92071i	−0.469820	−	1.75339i	−0.640393	−	0.768048i	$-0.721228\pi$
$5$	−1.05055	−	3.92071i	−0.469820	−	1.75339i	0.170572	−	0.985345i	$-0.445438\pi$
$6$	−0.617111	−	3.57041i	−0.251935	−	1.45761i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	0.556508	+	0.556508i	0.196755	+	0.196755i
$9$	2.95083	+	0.540924i	0.983610	+	0.180308i
$10$	−7.35361	+	4.24561i	−2.32541	+	1.34258i
$11$	3.17590	−	0.850980i	0.957570	−	0.256580i	0.253998	−	0.967205i	$-0.418254\pi$
$11$	3.17590	−	0.850980i	0.957570	−	0.256580i	0.703571	+	0.710625i	$0.251588\pi$
$12$	−3.73598	+	1.72675i	−1.07848	+	0.498470i
$13$	2.04474	−	2.96968i	0.567110	−	0.823642i
$13$	2.04474	−	2.96968i	0.567110	−	0.823642i
$14$	1.81167	+	1.04597i	0.484190	+	0.279547i
$15$	−1.19739	−	6.92770i	−0.309164	−	1.78872i
$16$	−1.55302	+	2.68990i	−0.388254	+	0.672475i
$17$	2.15361	−	3.73016i	0.522328	−	0.904698i	−0.477335	−	0.878721i	$-0.658397\pi$
$17$	2.15361	−	3.73016i	0.522328	−	0.904698i	0.999663	−	0.0259764i	$-0.00826948\pi$
$18$	−0.504656	−	6.25550i	−0.118949	−	1.47444i
$19$	−1.59384	+	0.427069i	−0.365653	+	0.0979764i	−0.436967	−	0.899478i	$-0.643947\pi$
$19$	−1.59384	+	0.427069i	−0.365653	+	0.0979764i	0.0713142	+	0.997454i	$0.477281\pi$
$20$	6.82011	+	6.82011i	1.52502	+	1.52502i
$21$	−1.33059	+	1.10885i	−0.290358	+	0.241970i
$22$	−3.43908	−	5.95666i	−0.733214	−	1.26996i
$23$	−7.24903			−1.51153			−0.755764	−	0.654845i	$-0.772734\pi$
$23$	−7.24903			−1.51153			−0.755764	+	0.654845i	$0.772734\pi$
$24$	0.872684	+	1.04720i	0.178136	+	0.213759i
$25$	−9.93815	+	5.73779i	−1.98763	+	1.14756i
$26$	−7.10781	−	2.52384i	−1.39396	−	0.494967i
$27$	5.00519	+	1.39574i	0.963249	+	0.268610i
$28$	0.615010	−	2.29525i	0.116226	−	0.433761i
$29$	2.76216	+	1.59473i	0.512920	+	0.296135i	0.734033	−	0.679114i	$-0.237636\pi$
$29$	2.76216	+	1.59473i	0.512920	+	0.296135i	−0.221113	+	0.975248i	$0.570969\pi$
$30$	−13.3502	+	6.17040i	−2.43741	+	1.12656i
$31$	0.464434	−	0.124445i	0.0834148	−	0.0223509i	−0.216870	−	0.976200i	$-0.569585\pi$
$31$	0.464434	−	0.124445i	0.0834148	−	0.0223509i	0.300285	+	0.953850i	$0.402918\pi$
$32$	7.79664	+	2.08910i	1.37826	+	0.369305i
$33$	5.61166	−	0.969923i	0.976865	−	0.168842i
$34$	−8.70343	−	2.33208i	−1.49263	−	0.399948i
$35$	3.51521	+	2.02951i	0.594179	+	0.343049i
$36$	−6.71508	+	2.39276i	−1.11918	+	0.398793i
$37$	0.157111	+	0.0420979i	0.0258290	+	0.00692085i	0.271710	−	0.962379i	$-0.412411\pi$
$37$	0.157111	+	0.0420979i	0.0258290	+	0.00692085i	−0.245881	+	0.969300i	$0.579077\pi$
$38$	1.72592	+	2.98939i	0.279982	+	0.484942i
$39$	3.99269	−	4.80192i	0.639342	−	0.768922i
$40$	1.59726	−	2.76654i	0.252550	−	0.437429i
$41$	−2.73381	+	2.73381i	−0.426949	+	0.426949i	−0.887588	−	0.460639i	$-0.847620\pi$
$41$	−2.73381	+	2.73381i	−0.426949	+	0.426949i	0.460639	+	0.887588i	$0.347620\pi$
$42$	2.96102	+	2.08830i	0.456896	+	0.322231i
$43$			2.53864i			0.387140i	0.981087	+	0.193570i	$0.0620066\pi$
$43$			2.53864i			0.387140i	−0.981087	+	0.193570i	$0.937993\pi$
$44$	−5.52451	+	5.52451i	−0.832851	+	0.832851i
$45$	−0.979190	−	12.1376i	−0.145969	−	1.80937i
$46$	3.92487	+	14.6478i	0.578691	+	2.15970i
$47$	−0.853614	+	3.18573i	−0.124512	+	0.464687i	−0.999822	−	0.0188767i	$-0.993991\pi$
$47$	−0.853614	+	3.18573i	−0.124512	+	0.464687i	0.875309	+	0.483563i	$0.160658\pi$
$48$	−3.10062	+	4.39641i	−0.447536	+	0.634567i
$49$		−	1.00000i		−	0.142857i
$50$	16.9750	+	16.9750i	2.40063	+	2.40063i
$51$	4.29972	−	6.09663i	0.602081	−	0.853699i
$52$	−0.679500	+	8.54058i	−0.0942297	+	1.18437i
$53$			9.42441i			1.29454i	0.762260	+	0.647271i	$0.224090\pi$
$53$			9.42441i			1.29454i	−0.762260	+	0.647271i	$0.775910\pi$
$54$	0.110330	−	10.8695i	0.0150141	−	1.47915i
$55$	−6.67288	−	11.5578i	−0.899771	−	1.55845i
$56$	−0.787021			−0.105170
$57$	−2.81625	+	0.486761i	−0.373021	+	0.0644731i
$58$	1.72689	−	6.44483i	0.226751	−	0.846247i
$59$	2.75423	−	10.2789i	0.358571	−	1.33820i	−0.517361	−	0.855767i	$-0.673085\pi$
$59$	2.75423	−	10.2789i	0.358571	−	1.33820i	0.875931	−	0.482436i	$-0.160248\pi$
$60$	10.6949	+	12.8336i	1.38071	+	1.65681i
$61$	−10.3465			−1.32474			−0.662369	−	0.749177i	$-0.730449\pi$
$61$	−10.3465			−1.32474			−0.662369	+	0.749177i	$0.730449\pi$
$62$	−0.502921	−	0.871085i	−0.0638710	−	0.110628i
$63$	−2.46904	+	1.70406i	−0.311070	+	0.214692i
$64$		−	10.6734i		−	1.33417i
$65$	−13.7914	−	4.89704i	−1.71061	−	0.607403i
$66$	−4.99823	−	10.8141i	−0.615239	−	1.33113i
$67$	8.83286	+	8.83286i	1.07911	+	1.07911i	0.996590	+	0.0825159i	$0.0262955\pi$
$67$	8.83286	+	8.83286i	1.07911	+	1.07911i	0.0825159	+	0.996590i	$0.473704\pi$
$68$			10.2349i			1.24116i
$69$	−12.5041	−	1.13661i	−1.50532	−	0.136832i
$70$	2.19769	−	8.20188i	0.262674	−	0.980313i
$71$	−2.18019	−	8.13660i	−0.258742	−	0.965637i	−0.965971	−	0.258652i	$-0.916722\pi$
$71$	−2.18019	−	8.13660i	−0.258742	−	0.965637i	0.707229	−	0.706984i	$-0.249945\pi$
$72$	1.34113	+	1.94319i	0.158054	+	0.229007i
$73$	9.88411	−	9.88411i	1.15685	−	1.15685i	0.171697	−	0.985150i	$-0.445075\pi$
$73$	9.88411	−	9.88411i	1.15685	−	1.15685i	0.985150	−	0.171697i	$-0.0549251\pi$
$74$		−	0.340262i		−	0.0395547i
$75$	−18.0424	+	8.33909i	−2.08335	+	0.962915i
$76$	2.77251	−	2.77251i	0.318028	−	0.318028i
$77$	−1.64397	+	2.84743i	−0.187347	+	0.324495i
$78$	−11.8648	−	5.46795i	−1.34343	−	0.619123i
$79$	−2.64152	−	4.57524i	−0.297194	−	0.514755i	0.678299	−	0.734786i	$-0.262717\pi$
$79$	−2.64152	−	4.57524i	−0.297194	−	0.514755i	−0.975493	+	0.220031i	$0.929384\pi$
$80$	12.1778	+	3.26304i	1.36152	+	0.364819i
$81$	8.41480	+	3.19235i	0.934978	+	0.354706i
$82$	7.00427	+	4.04391i	0.773492	+	0.446576i
$83$	2.19185	+	0.587305i	0.240587	+	0.0644651i	0.377098	−	0.926174i	$-0.376922\pi$
$83$	2.19185	+	0.587305i	0.240587	+	0.0644651i	−0.136511	+	0.990639i	$0.543589\pi$
$84$	1.42074	−	3.86273i	0.155015	−	0.421459i
$85$	−16.8874	−	4.52495i	−1.83169	−	0.490800i
$86$	5.12973	−	1.37451i	0.553154	−	0.148217i
$87$	4.51451	+	3.18391i	0.484006	+	0.341351i
$88$	2.24099	+	1.29384i	0.238890	+	0.137923i
$89$	2.53372	−	9.45596i	0.268573	−	1.00233i	−0.691453	−	0.722421i	$-0.743029\pi$
$89$	2.53372	−	9.45596i	0.268573	−	1.00233i	0.960027	−	0.279908i	$-0.0903041\pi$
$90$	−23.9958	+	8.55032i	−2.52938	+	0.901283i
$91$	0.654031	+	3.54574i	0.0685610	+	0.371694i
$92$	14.9175	−	8.61263i	1.55526	−	0.897929i
$93$	0.820633	−	0.141839i	0.0850957	−	0.0147080i
$94$	6.89945			0.711624
$95$	3.34883	+	5.80034i	0.343582	+	0.595102i
$96$	13.1212	+	4.82605i	1.33917	+	0.492557i
$97$	10.5814	+	10.5814i	1.07438	+	1.07438i	0.997002	+	0.0773739i	$0.0246535\pi$
$97$	10.5814	+	10.5814i	1.07438	+	1.07438i	0.0773739	+	0.997002i	$0.475346\pi$
$98$	−2.02066	+	0.541434i	−0.204117	+	0.0546931i
$99$	9.83186	−	0.793176i	0.988139	−	0.0797172i
$100$	13.6342	−	23.6152i	1.36342	−	2.36152i
$101$	−3.74115	+	6.47987i	−0.372259	+	0.644771i	−0.989913	−	0.141679i	$-0.954750\pi$
$101$	−3.74115	+	6.47987i	−0.372259	+	0.644771i	0.617654	+	0.786450i	$0.288083\pi$
$102$	−14.6472	−	5.38735i	−1.45029	−	0.533427i
$103$	1.72553	+	0.996235i	0.170022	+	0.0981620i	0.582596	−	0.812762i	$-0.302037\pi$
$103$	1.72553	+	0.996235i	0.170022	+	0.0981620i	−0.412574	+	0.910924i	$0.635370\pi$
$104$	2.79057	−	0.514735i	0.273638	−	0.0504740i
$105$	5.74530	+	4.05194i	0.560684	+	0.395429i
$106$	19.0435	−	5.10270i	1.84967	−	0.495618i
$107$	14.0693	−	8.12290i	1.36013	−	0.785270i	0.370487	−	0.928838i	$-0.379191\pi$
$107$	14.0693	−	8.12290i	1.36013	−	0.785270i	0.989641	+	0.143567i	$0.0458574\pi$
$108$	−11.9583	+	3.07447i	−1.15069	+	0.295841i
$109$	−0.990101	−	0.990101i	−0.0948345	−	0.0948345i	0.658098	−	0.752932i	$-0.271361\pi$
$109$	−0.990101	−	0.990101i	−0.0948345	−	0.0948345i	−0.752932	+	0.658098i	$0.771361\pi$
$110$	−19.7414	+	19.7414i	−1.88227	+	1.88227i
$111$	0.264407	+	0.0972506i	0.0250964	+	0.00923062i
$112$	−0.803900	−	3.00020i	−0.0759614	−	0.283492i
$113$	−1.70953	+	0.986996i	−0.160819	+	0.0928488i	−0.578250	−	0.815860i	$-0.696264\pi$
$113$	−1.70953	+	0.986996i	−0.160819	+	0.0928488i	0.417431	+	0.908709i	$0.362931\pi$
$114$	2.50839	+	5.42713i	0.234932	+	0.508297i
$115$	7.61547	+	28.4213i	0.710146	+	2.65030i
$116$	−7.57886			−0.703680
$117$	7.64007	−	7.65698i	0.706325	−	0.707888i
$118$	−22.2615			−2.04933
$119$	1.11479	+	4.16046i	0.102193	+	0.381389i
$120$	3.18896	−	4.52167i	0.291111	−	0.412770i
$121$	−0.164108	+	0.0947479i	−0.0149189	+	0.00861344i
$122$	5.60197	+	20.9068i	0.507178	+	1.89282i
$123$	−5.14430	+	4.28700i	−0.463846	+	0.386546i
$124$	−0.807888	+	0.807888i	−0.0725505	+	0.0725505i
$125$	18.5860	+	18.5860i	1.66238	+	1.66238i
$126$	4.78015	+	4.06646i	0.425850	+	0.362269i
$127$	11.3333	−	6.54328i	1.00567	−	0.580622i	0.0957471	−	0.995406i	$-0.469476\pi$
$127$	11.3333	−	6.54328i	1.00567	−	0.580622i	0.909920	+	0.414783i	$0.136143\pi$
$128$	−5.97403	+	1.60074i	−0.528035	+	0.141486i
$129$	−0.398047	+	4.37901i	−0.0350461	+	0.385550i
$130$	−2.42814	+	30.5191i	−0.212962	+	2.67670i
$131$	10.7120	+	6.18459i	0.935914	+	0.540350i	0.888677	−	0.458534i	$-0.151625\pi$
$131$	10.7120	+	6.18459i	0.935914	+	0.540350i	0.0472367	+	0.998884i	$0.484958\pi$
$132$	−10.3957	+	8.66323i	−0.904826	+	0.754037i
$133$	0.825034	−	1.42900i	0.0715395	−	0.123910i
$134$	13.0658	−	22.6306i	1.12871	−	1.95499i
$135$	0.214075	−	21.0902i	0.0184247	−	1.81515i
$136$	3.27437	−	0.877364i	0.280775	−	0.0752333i
$137$	−13.0588	−	13.0588i	−1.11569	−	1.11569i	−0.992366	−	0.123326i	$-0.960644\pi$
$137$	−13.0588	−	13.0588i	−1.11569	−	1.11569i	−0.123326	−	0.992366i	$-0.539356\pi$
$138$	4.47346	+	25.8820i	0.380806	+	2.20322i
$139$	−0.659249	−	1.14185i	−0.0559168	−	0.0968508i	0.836712	−	0.547643i	$-0.184475\pi$
$139$	−0.659249	−	1.14185i	−0.0559168	−	0.0968508i	−0.892629	+	0.450792i	$0.851141\pi$
$140$	−9.64509			−0.815159
$141$	−1.97194	+	5.36135i	−0.166067	+	0.451507i
$142$	−15.2609	+	8.81086i	−1.28066	+	0.739391i
$143$	3.96676	−	11.1715i	0.331717	−	0.934204i
$144$	−6.03772	+	7.09738i	−0.503143	+	0.591448i
$145$	3.35069	−	12.5050i	0.278260	−	1.03848i
$146$	−25.3240	−	14.6208i	−2.09583	−	1.21003i
$147$	0.156795	−	1.72494i	0.0129322	−	0.142271i
$148$	−0.373331	+	0.100034i	−0.0306876	+	0.00822272i
$149$	−8.96695	−	2.40269i	−0.734602	−	0.196836i	−0.127924	−	0.991784i	$-0.540831\pi$
$149$	−8.96695	−	2.40269i	−0.734602	−	0.196836i	−0.606677	+	0.794948i	$0.707498\pi$
$150$	26.6192	+	31.9424i	2.17345	+	2.60809i
$151$	3.74491	+	1.00345i	0.304756	+	0.0816592i	0.407956	−	0.913001i	$-0.366242\pi$
$151$	3.74491	+	1.00345i	0.304756	+	0.0816592i	−0.103200	+	0.994661i	$0.532908\pi$
$152$	−1.12465	−	0.649319i	−0.0912214	−	0.0526667i
$153$	8.37268	−	9.84214i	0.676891	−	0.795690i
$154$	6.64379	+	1.78020i	0.535372	+	0.143453i
$155$	−0.975822	−	1.69017i	−0.0783799	−	0.135758i
$156$	−2.51122	+	14.6254i	−0.201058	+	1.17097i
$157$	9.10021	−	15.7620i	0.726276	−	1.25795i	−0.232171	−	0.972675i	$-0.574583\pi$
$157$	9.10021	−	15.7620i	0.726276	−	1.25795i	0.958447	−	0.285272i	$-0.0920839\pi$
$158$	−7.81480	+	7.81480i	−0.621712	+	0.621712i
$159$	−1.47770	+	16.2565i	−0.117189	+	1.28923i
$160$		−	32.7630i		−	2.59014i
$161$	5.12584	−	5.12584i	0.403973	−	0.403973i
$162$	1.89460	−	18.7319i	0.148853	−	1.47172i
$163$	−1.40519	−	5.24424i	−0.110063	−	0.410761i	0.888807	−	0.458281i	$-0.151535\pi$
$163$	−1.40519	−	5.24424i	−0.110063	−	0.410761i	−0.998870	+	0.0475206i	$0.984868\pi$
$164$	2.37774	−	8.87385i	0.185670	−	0.692932i
$165$	−9.69811	−	20.9827i	−0.754997	−	1.63350i
$166$		−	4.74697i		−	0.368436i
$167$	11.2124	+	11.2124i	0.867641	+	0.867641i	0.992211	−	0.124570i	$-0.0397550\pi$
$167$	11.2124	+	11.2124i	0.867641	+	0.867641i	−0.124570	+	0.992211i	$0.539755\pi$
$168$	−1.35756	−	0.123401i	−0.104738	−	0.00952060i
$169$	−4.63804	−	12.1445i	−0.356772	−	0.934191i
$170$			36.5736i			2.80506i
$171$	−4.93418	+	0.398060i	−0.377326	+	0.0304404i
$172$	−3.01618	−	5.22418i	−0.229982	−	0.398340i
$173$	−6.83393			−0.519574			−0.259787	−	0.965666i	$-0.583652\pi$
$173$	−6.83393			−0.519574			−0.259787	+	0.965666i	$0.583652\pi$
$174$	3.98929	−	10.8462i	0.302427	−	0.822246i
$175$	2.97010	−	11.0846i	0.224519	−	0.837915i
$176$	−2.64317	+	9.86444i	−0.199236	+	0.743560i
$177$	6.36257	−	17.2987i	0.478240	−	1.30025i
$178$	−20.4791			−1.53497
$179$	9.09607	+	15.7549i	0.679872	+	1.17757i	0.975019	+	0.222121i	$0.0712980\pi$
$179$	9.09607	+	15.7549i	0.679872	+	1.17757i	−0.295147	+	0.955452i	$0.595369\pi$
$180$	16.4358	+	23.8141i	1.22505	+	1.77500i
$181$			24.9450i			1.85415i	0.374880	+	0.927074i	$0.377684\pi$
$181$			24.9450i			1.85415i	−0.374880	+	0.927074i	$0.622316\pi$
$182$	6.81061	−	3.24136i	0.504836	−	0.240265i
$183$	−17.8472	−	1.62229i	−1.31930	−	0.119923i
$184$	−4.03414	−	4.03414i	−0.297401	−	0.297401i
$185$		−	0.660214i		−	0.0485399i
$186$	−0.730926	−	1.58142i	−0.0535941	−	0.115956i
$187$	3.66536	−	13.6793i	0.268038	−	1.00033i
$188$	−2.02837	−	7.56998i	−0.147934	−	0.552098i
$189$	−4.52614	+	2.55227i	−0.329228	+	0.185650i
$190$	9.90733	−	9.90733i	0.718754	−	0.718754i
$191$		−	16.4181i		−	1.18797i	−0.804475	−	0.593987i	$-0.797553\pi$
$191$		−	16.4181i		−	1.18797i	0.804475	−	0.593987i	$-0.202447\pi$
$192$	1.67354	−	18.4110i	0.120777	−	1.32870i
$193$	2.73582	−	2.73582i	0.196928	−	0.196928i	−0.601754	−	0.798682i	$-0.705531\pi$
$193$	2.73582	−	2.73582i	0.196928	−	0.196928i	0.798682	+	0.601754i	$0.205531\pi$
$194$	15.6522	−	27.1105i	1.12377	−	1.94642i
$195$	−23.0214	−	10.6095i	−1.64860	−	0.759763i
$196$	1.18811	+	2.05786i	0.0848648	+	0.146990i
$197$	−10.5597	−	2.82945i	−0.752344	−	0.201590i	−0.137787	−	0.990462i	$-0.543999\pi$
$197$	−10.5597	−	2.82945i	−0.752344	−	0.201590i	−0.614558	+	0.788872i	$0.710665\pi$
$198$	−6.92604	−	19.4374i	−0.492212	−	1.38135i
$199$	4.03921	+	2.33204i	0.286332	+	0.165314i	0.636287	−	0.771453i	$-0.280470\pi$
$199$	4.03921	+	2.33204i	0.286332	+	0.165314i	−0.349954	+	0.936767i	$0.613803\pi$
$200$	−8.72378	−	2.33753i	−0.616865	−	0.165288i
$201$	13.8512	+	16.6211i	0.976988	+	1.17236i
$202$	15.1192	+	4.05118i	1.06378	+	0.285040i
$203$	−3.08079	+	0.825495i	−0.216229	+	0.0579384i
$204$	−1.60478	+	17.6546i	−0.112357	+	1.23607i
$205$	13.5904	+	7.84645i	0.949198	+	0.548020i
$206$	1.07879	−	4.02610i	0.0751630	−	0.280512i
$207$	−21.3907	−	3.92118i	−1.48675	−	0.272541i
$208$	4.81264	+	10.1121i	0.333696	+	0.701150i
$209$	−4.69846	+	2.71266i	−0.324999	+	0.187638i
$210$	5.07689	−	13.8032i	0.350339	−	0.952509i
$211$	2.64721			0.182242			0.0911208	−	0.995840i	$-0.470955\pi$
$211$	2.64721			0.182242			0.0911208	+	0.995840i	$0.470955\pi$
$212$	−11.1972	−	19.3941i	−0.769028	−	1.33200i
$213$	−2.48492	−	14.3770i	−0.170264	−	0.985094i
$214$	−24.0312	−	24.0312i	−1.64274	−	1.64274i
$215$	9.95328	−	2.66697i	0.678808	−	0.181886i
$216$	2.00869	+	3.56216i	0.136674	+	0.242375i
$217$	−0.240409	+	0.416400i	−0.0163200	+	0.0282671i
$218$	−1.46458	+	2.53673i	−0.0991940	+	0.171809i
$219$	18.5993	−	15.4997i	1.25682	−	1.04737i
$220$	27.4638	+	15.8562i	1.85161	+	1.06903i
$221$	−6.67382	−	14.0228i	−0.448930	−	0.943274i
$222$	0.0533514	−	0.586931i	0.00358071	−	0.0393922i
$223$	1.38785	−	0.371874i	0.0929374	−	0.0249025i	−0.212051	−	0.977259i	$-0.568014\pi$
$223$	1.38785	−	0.371874i	0.0929374	−	0.0249025i	0.304988	+	0.952356i	$0.401348\pi$
$224$	−6.99027	+	4.03584i	−0.467057	+	0.269656i
$225$	−32.4295	+	11.5555i	−2.16197	+	0.770365i
$226$	2.91998	+	2.91998i	0.194234	+	0.194234i
$227$	5.44603	−	5.44603i	0.361465	−	0.361465i	−0.502887	−	0.864352i	$-0.667729\pi$
$227$	5.44603	−	5.44603i	0.361465	−	0.361465i	0.864352	+	0.502887i	$0.167729\pi$
$228$	5.21712	−	4.34769i	0.345512	−	0.287933i
$229$	−6.33942	−	23.6590i	−0.418921	−	1.56343i	−0.776851	−	0.629685i	$-0.783184\pi$
$229$	−6.33942	−	23.6590i	−0.418921	−	1.56343i	0.357930	−	0.933748i	$-0.383483\pi$
$230$	53.3065	−	30.7765i	3.51493	−	2.02934i
$231$	−3.28221	+	4.65388i	−0.215953	+	0.306203i
$232$	0.649681	+	2.42464i	0.0426537	+	0.159186i
$233$	−14.8951			−0.975807			−0.487904	−	0.872897i	$-0.662238\pi$
$233$	−14.8951			−0.975807			−0.487904	+	0.872897i	$0.662238\pi$
$234$	−19.6087	−	11.2922i	−1.28186	−	0.738196i
$235$	13.3871			0.873276
$236$	6.54465	+	24.4250i	0.426020	+	1.58993i
$237$	−3.83908	−	8.30619i	−0.249375	−	0.539545i
$238$	7.80328	−	4.50523i	0.505812	−	0.292031i
$239$	5.13836	+	19.1766i	0.332373	+	1.24043i	0.906689	+	0.421799i	$0.138601\pi$
$239$	5.13836	+	19.1766i	0.332373	+	1.24043i	−0.574316	+	0.818634i	$0.694732\pi$
$240$	20.4944	+	7.53797i	1.32291	+	0.486574i
$241$	−10.0224	+	10.0224i	−0.645597	+	0.645597i	−0.951926	−	0.306329i	$-0.900899\pi$
$241$	−10.0224	+	10.0224i	−0.645597	+	0.645597i	0.306329	+	0.951926i	$0.400899\pi$
$242$	0.280307	+	0.280307i	0.0180188	+	0.0180188i
$243$	14.0145	+	6.82601i	0.899029	+	0.437889i
$244$	21.2918	−	12.2928i	1.36307	−	0.786966i
$245$	−3.92071	+	1.05055i	−0.250485	+	0.0671172i
$246$	11.4479	+	8.07374i	0.729889	+	0.514763i
$247$	−1.99074	+	5.60646i	−0.126668	+	0.356730i
$248$	0.327716	+	0.189207i	0.0208100	+	0.0120146i
$249$	3.68872	+	1.35674i	0.233763	+	0.0859797i
$250$	27.4928	−	47.6189i	1.73880	−	3.01169i
$251$	11.0554	−	19.1485i	0.697811	−	1.20864i	−0.271413	−	0.962463i	$-0.587491\pi$
$251$	11.0554	−	19.1485i	0.697811	−	1.20864i	0.969224	−	0.246181i	$-0.0791758\pi$
$252$	3.05635	−	6.44021i	0.192532	−	0.405695i
$253$	−23.0222	+	6.16878i	−1.44739	+	0.387828i
$254$	−19.3580	−	19.3580i	−1.21463	−	1.21463i
$255$	−28.4202	−	10.4531i	−1.77974	−	0.654600i
$256$	−4.20431	−	7.28208i	−0.262770	−	0.455130i
$257$	8.47200			0.528469			0.264235	−	0.964458i	$-0.414881\pi$
$257$	8.47200			0.528469			0.264235	+	0.964458i	$0.414881\pi$
$258$	9.06400	−	1.56663i	0.564300	−	0.0975338i
$259$	−0.140862	+	0.0813269i	−0.00875276	+	0.00505341i
$260$	34.1989	−	6.30818i	2.12093	−	0.391217i
$261$	7.28803	+	6.19991i	0.451118	+	0.383765i
$262$	6.69709	−	24.9939i	0.413748	−	1.54413i
$263$	25.1765	+	14.5356i	1.55245	+	0.896306i	0.997942	+	0.0641250i	$0.0204256\pi$
$263$	25.1765	+	14.5356i	1.55245	+	0.896306i	0.554505	+	0.832181i	$0.312908\pi$
$264$	3.66270	+	2.58316i	0.225424	+	0.158983i
$265$	36.9503	−	9.90081i	2.26984	−	0.608202i
$266$	−3.33423	−	0.893403i	−0.204435	−	0.0547781i
$267$	5.85316	−	15.9137i	0.358207	−	0.973901i
$268$	−28.6712	−	7.68243i	−1.75137	−	0.469279i
$269$	−7.29651	−	4.21264i	−0.444876	−	0.256849i	0.260788	−	0.965396i	$-0.416018\pi$
$269$	−7.29651	−	4.21264i	−0.444876	−	0.256849i	−0.705664	+	0.708547i	$0.749351\pi$
$270$	−42.7319	+	10.9864i	−2.60058	+	0.668609i
$271$	−5.26232	−	1.41004i	−0.319663	−	0.0856536i	0.0954195	−	0.995437i	$-0.469581\pi$
$271$	−5.26232	−	1.41004i	−0.319663	−	0.0856536i	−0.415083	+	0.909784i	$0.636247\pi$
$272$	6.68918	+	11.5860i	0.405591	+	0.702505i
$273$	0.572209	+	6.21873i	0.0346316	+	0.376375i
$274$	−19.3170	+	33.4580i	−1.16698	+	2.02127i
$275$	−26.6798	+	26.6798i	−1.60885	+	1.60885i
$276$	27.0822	−	12.5173i	1.63016	−	0.753451i
$277$		−	19.8269i		−	1.19128i	−0.803250	−	0.595641i	$-0.796898\pi$
$277$		−	19.8269i		−	1.19128i	0.803250	−	0.595641i	$-0.203102\pi$
$278$	−1.95036	+	1.95036i	−0.116975	+	0.116975i
$279$	1.43778	−	0.115992i	0.0860777	−	0.00694424i
$280$	0.826804	+	3.08568i	0.0494110	+	0.184404i
$281$	−2.01625	+	7.52476i	−0.120280	+	0.448890i	−0.999628	−	0.0272902i	$-0.991312\pi$
$281$	−2.01625	+	7.52476i	−0.120280	+	0.448890i	0.879348	+	0.476180i	$0.157979\pi$
$282$	11.9011	+	1.08180i	0.708702	+	0.0644203i
$283$			12.2082i			0.725705i	0.931847	+	0.362852i	$0.118197\pi$
$283$			12.2082i			0.725705i	−0.931847	+	0.362852i	$0.881803\pi$
$284$	14.1537	+	14.1537i	0.839867	+	0.839867i
$285$	4.86706	+	10.5303i	0.288299	+	0.623761i
$286$	−24.7214	−	1.96687i	−1.46181	−	0.116304i
$287$		−	3.86619i		−	0.228214i
$288$	21.8765	+	10.3820i	1.28909	+	0.611764i
$289$	−0.776085	−	1.34422i	−0.0456520	−	0.0790717i
$290$	−27.0824			−1.59034
$291$	16.5931	+	19.9113i	0.972706	+	1.16722i
$292$	−8.59675	+	32.0835i	−0.503087	+	1.87755i
$293$	3.73016	−	13.9212i	0.217918	−	0.813282i	−0.767200	−	0.641407i	$-0.778351\pi$
$293$	3.73016	−	13.9212i	0.217918	−	0.813282i	0.985119	−	0.171875i	$-0.0549825\pi$
$294$	−3.57041	+	0.617111i	−0.208230	+	0.0359907i
$295$	−43.1941			−2.51486
$296$	0.0640059	+	0.110861i	0.00372027	+	0.00644369i
$297$	17.0837	+	0.173408i	0.991298	+	0.0100621i
$298$			19.4201i			1.12497i
$299$	−14.8224	+	21.5273i	−0.857202	+	1.24496i
$300$	27.2210	−	38.5970i	1.57160	−	2.22840i
$301$	−1.79509	−	1.79509i	−0.103467	−	0.103467i
$302$		−	8.11049i		−	0.466706i
$303$	−7.46928	+	10.5908i	−0.429099	+	0.608425i
$304$	1.32649	−	4.95053i	0.0760794	−	0.283932i
$305$	10.8696	+	40.5657i	0.622389	+	2.32279i
$306$	−24.4209	−	11.5895i	−1.39605	−	0.662525i
$307$	−20.3301	+	20.3301i	−1.16030	+	1.16030i	−0.175888	+	0.984410i	$0.556280\pi$
$307$	−20.3301	+	20.3301i	−1.16030	+	1.16030i	−0.984410	+	0.175888i	$0.943720\pi$
$308$		−	7.81284i		−	0.445178i
$309$	2.82023	+	1.98900i	0.160437	+	0.113150i
$310$	−2.88692	+	2.88692i	−0.163966	+	0.163966i
$311$	11.5831	−	20.0625i	0.656817	−	1.13764i	−0.324618	−	0.945845i	$-0.605236\pi$
$311$	11.5831	−	20.0625i	0.656817	−	1.13764i	0.981435	−	0.191795i	$-0.0614310\pi$
$312$	4.89427	−	0.450340i	0.277083	−	0.0254955i
$313$	16.1363	+	27.9488i	0.912076	+	1.57976i	0.811127	+	0.584869i	$0.198854\pi$
$313$	16.1363	+	27.9488i	0.912076	+	1.57976i	0.100948	+	0.994892i	$0.467812\pi$
$314$	−36.7769	−	9.85433i	−2.07544	−	0.556112i
$315$	9.27498	+	7.89019i	0.522586	+	0.444562i
$316$	10.8718	+	6.27682i	0.611585	+	0.353099i
$317$	−6.07340	−	1.62736i	−0.341116	−	0.0914017i	0.0841943	−	0.996449i	$-0.473168\pi$
$317$	−6.07340	−	1.62736i	−0.341116	−	0.0914017i	−0.425310	+	0.905048i	$0.639835\pi$
$318$	33.6490	−	5.81591i	1.88694	−	0.326140i
$319$	10.1294	+	2.71417i	0.567139	+	0.151964i
$320$	−41.8473	+	11.2129i	−2.33933	+	0.626822i
$321$	25.5423	−	11.8055i	1.42563	−	0.658919i
$322$	−13.1329	−	7.58227i	−0.731867	−	0.422543i
$323$	−1.83948	+	6.86504i	−0.102352	+	0.381981i
$324$	−21.1094	+	3.42827i	−1.17274	+	0.190459i
$325$	−3.28155	+	41.2455i	−0.182028	+	2.28789i
$326$	−9.83600	+	5.67882i	−0.544766	+	0.314521i
$327$	−1.55262	−	1.86311i	−0.0858601	−	0.103030i
$328$	−3.04277			−0.168009
$329$	−1.64906	−	2.85625i	−0.0909154	−	0.157470i
$330$	−37.1481	+	30.9573i	−2.04493	+	1.70415i
$331$	1.36308	+	1.36308i	0.0749219	+	0.0749219i	0.743575	−	0.668653i	$-0.233129\pi$
$331$	1.36308	+	1.36308i	0.0749219	+	0.0749219i	−0.668653	+	0.743575i	$0.733129\pi$
$332$	−5.20831	+	1.39556i	−0.285843	+	0.0765914i
$333$	0.440837	+	0.209209i	0.0241577	+	0.0114646i
$334$	16.5857	−	28.7272i	0.907527	−	1.57188i
$335$	25.3517	−	43.9104i	1.38511	−	2.39908i
$336$	−0.916262	−	5.30120i	−0.0499862	−	0.289204i
$337$	29.8719	+	17.2465i	1.62722	+	0.939478i	0.984916	+	0.173031i	$0.0553560\pi$
$337$	29.8719	+	17.2465i	1.62722	+	0.939478i	0.642307	+	0.766447i	$0.277977\pi$
$338$	−22.0287	+	15.9473i	−1.19820	+	0.867421i
$339$	−3.10359	+	1.43446i	−0.168564	+	0.0779093i
$340$	40.1280	−	10.7523i	2.17625	−	0.583123i
$341$	1.36910	−	0.790448i	0.0741407	−	0.0428052i
$342$	3.47587	+	9.75476i	0.187954	+	0.527477i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−1.41277	+	1.41277i	−0.0761717	+	0.0761717i
$345$	8.67989	+	50.2191i	0.467310	+	2.70371i
$346$	3.70012	+	13.8090i	0.198920	+	0.742379i
$347$	11.8014	−	6.81354i	0.633532	−	0.365770i	−0.148587	−	0.988899i	$-0.547472\pi$
$347$	11.8014	−	6.81354i	0.633532	−	0.365770i	0.782119	+	0.623130i	$0.214139\pi$
$348$	−13.0731	−	1.18833i	−0.700790	−	0.0637011i
$349$	7.28102	+	27.1731i	0.389744	+	1.45454i	0.830551	+	0.556942i	$0.188026\pi$
$349$	7.28102	+	27.1731i	0.389744	+	1.45454i	−0.440807	+	0.897602i	$0.645308\pi$
$350$	−24.0063			−1.28319
$351$	14.3792	−	12.0099i	0.767507	−	0.641041i
$352$	26.5391			1.41454
$353$	−7.44675	−	27.7917i	−0.396351	−	1.47920i	−0.819468	−	0.573126i	$-0.805731\pi$
$353$	−7.44675	−	27.7917i	−0.396351	−	1.47920i	0.423117	−	0.906075i	$-0.360936\pi$
$354$	−38.3997	−	3.49049i	−2.04092	−	0.185517i
$355$	−29.6108	+	17.0958i	−1.57158	+	0.907351i
$356$	6.02066	+	22.4694i	0.319094	+	1.19088i
$357$	1.27061	+	7.35133i	0.0672477	+	0.389074i
$358$	26.9103	−	26.9103i	1.42225	−	1.42225i
$359$	−14.8917	−	14.8917i	−0.785956	−	0.785956i	0.194873	−	0.980829i	$-0.437571\pi$
$359$	−14.8917	−	14.8917i	−0.785956	−	0.785956i	−0.980829	+	0.194873i	$0.937571\pi$
$360$	6.20974	−	7.29960i	0.327282	−	0.384722i
$361$	−14.0965	+	8.13864i	−0.741923	+	0.428349i
$362$	50.4053	−	13.5061i	2.64925	−	0.709863i
$363$	−0.297933	+	0.137703i	−0.0156374	+	0.00722753i
$364$	−5.55862	−	6.51958i	−0.291351	−	0.341719i
$365$	−49.1364	−	28.3689i	−2.57192	−	1.48490i
$366$	6.38497	+	36.9414i	0.333747	+	1.93096i
$367$	−16.2224	+	28.0981i	−0.846805	+	1.46671i	0.0372402	+	0.999306i	$0.488143\pi$
$367$	−16.2224	+	28.0981i	−0.846805	+	1.46671i	−0.884045	+	0.467402i	$0.845190\pi$
$368$	11.2579	−	19.4992i	0.586856	−	1.01646i
$369$	−9.54578	+	6.58822i	−0.496933	+	0.342969i
$370$	−1.33407	+	0.357462i	−0.0693548	+	0.0185836i
$371$	−6.66407	−	6.66407i	−0.345981	−	0.345981i
$372$	−1.52023	+	1.26688i	−0.0788203	+	0.0656849i
$373$	12.9972	+	22.5118i	0.672970	+	1.16562i	0.977058	+	0.212974i	$0.0683150\pi$
$373$	12.9972	+	22.5118i	0.672970	+	1.16562i	−0.304088	+	0.952644i	$0.598352\pi$
$374$	−29.6258			−1.53191
$375$	29.1454	+	34.9738i	1.50506	+	1.80604i
$376$	−2.24793	+	1.29784i	−0.115928	+	0.0669310i
$377$	10.3838	−	4.94192i	0.534791	−	0.254522i
$378$	7.60787	+	7.76390i	0.391307	+	0.399332i
$379$	2.02535	−	7.55871i	0.104035	−	0.388265i	−0.894199	−	0.447670i	$-0.852254\pi$
$379$	2.02535	−	7.55871i	0.104035	−	0.388265i	0.998234	+	0.0594053i	$0.0189204\pi$
$380$	−13.7828	−	7.95753i	−0.707045	−	0.408213i
$381$	20.5752	−	9.50975i	1.05410	−	0.487199i
$382$	−33.1754	+	8.88933i	−1.69740	+	0.454818i
$383$	26.6648	+	7.14482i	1.36251	+	0.365083i	0.864737	−	0.502224i	$-0.167485\pi$
$383$	26.6648	+	7.14482i	1.36251	+	0.365083i	0.497772	+	0.867308i	$0.334151\pi$
$384$	−10.5558	+	1.82447i	−0.538675	+	0.0931048i
$385$	12.8910	+	3.45414i	0.656987	+	0.176039i
$386$	−7.00942	−	4.04689i	−0.356770	−	0.205981i
$387$	−1.37321	+	7.49111i	−0.0698044	+	0.380794i
$388$	−34.3468	−	9.20321i	−1.74370	−	0.467222i
$389$	−3.56435	−	6.17363i	−0.180719	−	0.313015i	0.761406	−	0.648275i	$-0.224509\pi$
$389$	−3.56435	−	6.17363i	−0.180719	−	0.313015i	−0.942126	+	0.335260i	$0.891176\pi$
$390$	−8.97364	+	52.2628i	−0.454398	+	2.64643i
$391$	−15.6116	+	27.0401i	−0.789512	+	1.36748i
$392$	0.556508	−	0.556508i	0.0281079	−	0.0281079i
$393$	17.5079	+	12.3476i	0.883155	+	0.622856i
$394$			22.8694i			1.15214i
$395$	−15.1631	+	15.1631i	−0.762940	+	0.762940i
$396$	−19.2902	+	13.3136i	−0.969371	+	0.669031i
$397$	−5.65323	−	21.0981i	−0.283727	−	1.05889i	−0.949764	−	0.312966i	$-0.898677\pi$
$397$	−5.65323	−	21.0981i	−0.283727	−	1.05889i	0.666037	−	0.745919i	$-0.267989\pi$
$398$	2.52529	−	9.42452i	0.126582	−	0.472409i
$399$	1.64719	−	2.33558i	0.0824629	−	0.116925i
$400$		−	35.6435i		−	1.78218i
$401$	−3.25011	−	3.25011i	−0.162303	−	0.162303i	0.621283	−	0.783586i	$-0.286612\pi$
$401$	−3.25011	−	3.25011i	−0.162303	−	0.162303i	−0.783586	+	0.621283i	$0.786612\pi$
$402$	26.0861	−	36.9878i	1.30105	−	1.84478i
$403$	0.580088	−	1.63368i	0.0288962	−	0.0813794i
$404$		−	17.7796i		−	0.884567i
$405$	3.67610	−	36.3457i	0.182667	−	1.80603i
$406$	3.33609	+	5.77827i	0.165567	+	0.286771i
$407$	0.534795			0.0265088
$408$	5.78565	−	0.999994i	0.286432	−	0.0495071i
$409$	−6.51727	+	24.3228i	−0.322258	+	1.20269i	0.594781	+	0.803888i	$0.297239\pi$
$409$	−6.51727	+	24.3228i	−0.322258	+	1.20269i	−0.917039	+	0.398797i	$0.869428\pi$
$410$	8.49667	−	31.7100i	0.419621	−	1.56605i
$411$	−20.4782	−	24.5733i	−1.01011	−	1.21211i
$412$	−4.73454			−0.233254
$413$	5.32077	+	9.21584i	0.261818	+	0.453482i
$414$	3.65827	+	45.3463i	0.179794	+	2.22865i
$415$		−	9.21059i		−	0.452130i
$416$	22.1461	−	18.8819i	1.08580	−	0.925760i
$417$	−0.958128	−	2.07300i	−0.0469197	−	0.101515i
$418$	8.02526	+	8.02526i	0.392528	+	0.392528i
$419$		−	5.68379i		−	0.277671i	−0.990315	−	0.138836i	$-0.955664\pi$
$419$		−	5.68379i		−	0.277671i	0.990315	−	0.138836i	$-0.0443360\pi$
$420$	−16.6372	−	1.51230i	−0.811812	−	0.0737929i
$421$	−6.34085	+	23.6644i	−0.309034	+	1.15333i	0.620383	+	0.784299i	$0.286977\pi$
$421$	−6.34085	+	23.6644i	−0.309034	+	1.15333i	−0.929417	+	0.369031i	$0.879689\pi$
$422$	−1.43329	−	5.34911i	−0.0697715	−	0.260391i
$423$	−4.24211	+	8.93881i	−0.206258	+	0.434620i
$424$	−5.24476	+	5.24476i	−0.254708	+	0.254708i
$425$			49.4279i			2.39761i
$426$	−27.7056	+	12.8054i	−1.34234	+	0.620422i
$427$	7.31611	−	7.31611i	0.354051	−	0.354051i
$428$	−19.3018	+	33.4316i	−0.932986	+	1.61598i
$429$	8.59405	−	18.6481i	0.414925	−	0.900339i
$430$	−10.7781	−	18.6682i	−0.519765	−	0.900260i
$431$	−20.4817	−	5.48806i	−0.986570	−	0.264351i	−0.270761	−	0.962647i	$-0.587275\pi$
$431$	−20.4817	−	5.48806i	−0.986570	−	0.264351i	−0.715809	+	0.698296i	$0.753942\pi$
$432$	−11.5275	+	11.2959i	−0.554619	+	0.543473i
$433$	6.26901	+	3.61941i	0.301269	+	0.173938i	0.643013	−	0.765855i	$-0.277684\pi$
$433$	6.26901	+	3.61941i	0.301269	+	0.173938i	−0.341744	+	0.939793i	$0.611017\pi$
$434$	0.971569	+	0.260331i	0.0466368	+	0.0124963i
$435$	7.74046	−	21.0449i	0.371127	−	1.00903i
$436$	3.21384	+	0.861145i	0.153915	+	0.0412414i
$437$	11.5538	−	3.09584i	0.552694	−	0.148094i
$438$	−41.3899	−	29.1907i	−1.97769	−	1.39479i
$439$	8.70168	+	5.02392i	0.415309	+	0.239779i	0.693068	−	0.720872i	$-0.256258\pi$
$439$	8.70168	+	5.02392i	0.415309	+	0.239779i	−0.277759	+	0.960651i	$0.589592\pi$
$440$	2.71848	−	10.1455i	0.129598	−	0.483668i
$441$	0.540924	−	2.95083i	0.0257583	−	0.140516i
$442$	−24.7218	+	21.0779i	−1.17590	+	1.00257i
$443$	−28.6136	+	16.5201i	−1.35947	+	0.784893i	−0.989553	−	0.144170i	$-0.953949\pi$
$443$	−28.6136	+	16.5201i	−1.35947	+	0.784893i	−0.369922	+	0.929063i	$0.620616\pi$
$444$	−0.659657	+	0.114016i	−0.0313060	+	0.00541094i
$445$	−39.7358			−1.88366
$446$	−1.50286	−	2.60303i	−0.0711625	−	0.123257i
$447$	−15.0907	−	5.55047i	−0.713767	−	0.262528i
$448$	7.54723	+	7.54723i	0.356573	+	0.356573i
$449$	−34.4406	+	9.22832i	−1.62535	+	0.435511i	−0.952567	−	0.304329i	$-0.901568\pi$
$449$	−34.4406	+	9.22832i	−1.62535	+	0.435511i	−0.672783	+	0.739840i	$0.734901\pi$
$450$	40.9081	+	59.2725i	1.92843	+	2.79413i
$451$	−6.35588	+	11.0087i	−0.299287	+	0.518380i
$452$	2.34532	−	4.06220i	0.110314	−	0.191070i
$453$	6.30241	+	2.31807i	0.296113	+	0.108912i
$454$	−13.9532	−	8.05590i	−0.654857	−	0.378082i
$455$	13.2147	−	6.28923i	0.619515	−	0.294844i
$456$	−1.83815	−	1.29638i	−0.0860792	−	0.0607084i
$457$	−12.1001	+	3.24222i	−0.566020	+	0.151665i	−0.530471	−	0.847703i	$-0.677985\pi$
$457$	−12.1001	+	3.24222i	−0.566020	+	0.151665i	−0.0355493	+	0.999368i	$0.511318\pi$
$458$	−44.3745	+	25.6196i	−2.07348	+	1.19713i
$459$	15.9856	−	15.6643i	0.746142	−	0.731147i
$460$	−49.4392	−	49.4392i	−2.30511	−	2.30511i
$461$	−25.5944	+	25.5944i	−1.19205	+	1.19205i	−0.215562	+	0.976490i	$0.569158\pi$
$461$	−25.5944	+	25.5944i	−1.19205	+	1.19205i	−0.976490	+	0.215562i	$0.930842\pi$
$462$	11.1810	+	4.11245i	0.520188	+	0.191328i
$463$	−9.04094	−	33.7412i	−0.420168	−	1.56809i	−0.774254	−	0.632875i	$-0.781874\pi$
$463$	−9.04094	−	33.7412i	−0.420168	−	1.56809i	0.354086	−	0.935213i	$-0.384792\pi$
$464$	−8.57935	+	4.95329i	−0.398286	+	0.229951i
$465$	−1.41822	−	3.06845i	−0.0657685	−	0.142296i
$466$	8.06469	+	30.0978i	0.373590	+	1.39426i
$467$	−1.65007			−0.0763563			−0.0381781	−	0.999271i	$-0.512155\pi$
$467$	−1.65007			−0.0763563			−0.0381781	+	0.999271i	$0.512155\pi$
$468$	−6.62490	+	24.8342i	−0.306236	+	1.14796i
$469$	−12.4916			−0.576806
$470$	−7.24822	−	27.0507i	−0.334335	−	1.24776i
$471$	18.1687	−	25.7617i	0.837170	−	1.18704i
$472$	7.25306	−	4.18755i	0.333849	−	0.192748i
$473$	2.16033	+	8.06248i	0.0993323	+	0.370713i
$474$	−14.7054	+	12.2547i	−0.675440	+	0.562879i
$475$	13.3894	−	13.3894i	0.614349	−	0.614349i
$476$	−7.23716	−	7.23716i	−0.331715	−	0.331715i
$477$	−5.09789	+	27.8098i	−0.233416	+	1.27333i
$478$	35.9674	−	20.7658i	1.64511	−	0.949804i
$479$	25.6057	−	6.86102i	1.16995	−	0.313488i	0.379018	−	0.925389i	$-0.376262\pi$
$479$	25.6057	−	6.86102i	1.16995	−	0.313488i	0.790934	+	0.611901i	$0.209595\pi$
$480$	5.13708	−	56.5142i	0.234475	−	2.57951i
$481$	0.446270	−	0.380492i	0.0203482	−	0.0173489i
$482$	25.6782	+	14.8253i	1.16961	+	0.675275i
$483$	9.64547	−	8.03805i	0.438884	−	0.365744i
$484$	0.225141	−	0.389956i	0.0102337	−	0.0177253i
$485$	30.3702	−	52.6027i	1.37904	−	2.38857i
$486$	6.20513	−	32.0143i	0.281471	−	1.45220i
$487$	−11.5384	+	3.09172i	−0.522857	+	0.140099i	−0.510588	−	0.859826i	$-0.670572\pi$
$487$	−11.5384	+	3.09172i	−0.522857	+	0.140099i	−0.0122691	+	0.999925i	$0.503905\pi$
$488$	−5.75793	−	5.75793i	−0.260649	−	0.260649i
$489$	−1.60160	−	9.26632i	−0.0724266	−	0.419038i
$490$	4.24561	+	7.35361i	0.191797	+	0.332202i
$491$	1.40610			0.0634562			0.0317281	−	0.999497i	$-0.489899\pi$
$491$	1.40610			0.0634562			0.0317281	+	0.999497i	$0.489899\pi$
$492$	5.49284	−	14.9340i	0.247636	−	0.673278i
$493$	11.8972	−	6.86887i	0.535825	−	0.309358i
$494$	12.4066	+	0.987086i	0.558199	+	0.0444111i
$495$	−13.4387	−	37.7145i	−0.604023	−	1.69514i
$496$	−0.386529	+	1.44255i	−0.0173557	+	0.0647723i
$497$	7.29507	+	4.21181i	0.327229	+	0.188926i
$498$	0.744302	−	8.18824i	0.0333530	−	0.366924i
$499$	14.0585	−	3.76695i	0.629343	−	0.168632i	0.0699714	−	0.997549i	$-0.477709\pi$
$499$	14.0585	−	3.76695i	0.629343	−	0.168632i	0.559371	+	0.828917i	$0.311043\pi$
$500$	−60.3295	−	16.1652i	−2.69802	−	0.722931i
$501$	17.5827	+	21.0987i	0.785535	+	0.942623i
$502$	−44.6784	−	11.9715i	−1.99410	−	0.534316i
$503$	16.8506	+	9.72872i	0.751333	+	0.433782i	0.826175	−	0.563413i	$-0.190512\pi$
$503$	16.8506	+	9.72872i	0.751333	+	0.433782i	−0.0748423	+	0.997195i	$0.523845\pi$
$504$	−2.32236	−	0.425719i	−0.103446	−	0.0189630i
$505$	29.3359	+	7.86054i	1.30543	+	0.349789i
$506$	24.9300	+	43.1800i	1.10827	+	1.91959i
$507$	−6.09614	−	21.6757i	−0.270739	−	0.962653i
$508$	−15.5482	+	26.9303i	−0.689842	+	1.19484i
$509$	4.92777	−	4.92777i	0.218419	−	0.218419i	−0.589413	−	0.807832i	$-0.700641\pi$
$509$	4.92777	−	4.92777i	0.218419	−	0.218419i	0.807832	+	0.589413i	$0.200641\pi$
$510$	−5.73456	+	63.0872i	−0.253930	+	2.79355i
$511$			13.9782i			0.618361i
$512$	−21.1848	+	21.1848i	−0.936246	+	0.936246i
$513$	−8.57357	−	0.0870257i	−0.378532	−	0.00384228i
$514$	−4.58703	−	17.1190i	−0.202325	−	0.755088i
$515$	2.09319	−	7.81189i	0.0922370	−	0.344233i
$516$	−4.38360	−	9.48432i	−0.192977	−	0.417524i
$517$			10.8440i			0.476917i
$518$	0.240602	+	0.240602i	0.0105714	+	0.0105714i
$519$	−11.7881	−	1.07153i	−0.517441	−	0.0470348i
$520$	−4.94976	−	10.4002i	−0.217061	−	0.456081i
$521$			16.0002i			0.700980i	0.936566	+	0.350490i	$0.113985\pi$
$521$			16.0002i			0.700980i	−0.936566	+	0.350490i	$0.886015\pi$
$522$	8.58191	−	18.0835i	0.375620	−	0.791492i
$523$	8.18303	+	14.1734i	0.357819	+	0.619760i	0.987596	−	0.157015i	$-0.0501872\pi$
$523$	8.18303	+	14.1734i	0.357819	+	0.619760i	−0.629777	+	0.776776i	$0.716854\pi$
$524$	−29.3918			−1.28399
$525$	6.86125	−	18.6545i	0.299450	−	0.814149i
$526$	15.7402	−	58.7431i	0.686304	−	2.56132i
$527$	0.536011	−	2.00042i	0.0233490	−	0.0871397i
$528$	−6.10600	+	16.6011i	−0.265730	+	0.722471i
$529$	29.5484			1.28471
$530$	−40.0124	−	69.3034i	−1.73803	−	3.01035i
$531$	13.6874	−	28.8416i	0.593983	−	1.25162i
$532$			3.92092i			0.169993i
$533$	2.52860	+	13.7085i	0.109526	+	0.593780i
$534$	−35.3252	−	3.21103i	−1.52867	−	0.138955i
$535$	−46.6280	−	46.6280i	−2.01590	−	2.01590i
$536$			9.83111i			0.424639i
$537$	13.2199	+	28.6024i	0.570480	+	1.23428i
$538$	−4.56174	+	17.0246i	−0.196670	+	0.733984i
$539$	−0.850980	−	3.17590i	−0.0366543	−	0.136796i
$540$	24.6169	+	43.6550i	1.05934	+	1.87861i
$541$	−1.79736	+	1.79736i	−0.0772745	+	0.0772745i	−0.744688	−	0.667413i	$-0.767402\pi$
$541$	−1.79736	+	1.79736i	−0.0772745	+	0.0772745i	0.667413	+	0.744688i	$0.267402\pi$
$542$			11.3968i			0.489535i
$543$	−3.91126	+	43.0286i	−0.167848	+	1.84653i
$544$	24.5836	−	24.5836i	1.05401	−	1.05401i
$545$	−2.84174	+	4.92204i	−0.121727	+	0.210837i
$546$	12.2561	−	4.52327i	0.524513	−	0.193578i
$547$	10.7766	+	18.6657i	0.460776	+	0.798087i	0.999000	−	0.0447147i	$-0.0142379\pi$
$547$	10.7766	+	18.6657i	0.460776	+	0.798087i	−0.538224	+	0.842802i	$0.680905\pi$
$548$	42.3886	+	11.3580i	1.81075	+	0.485190i
$549$	−30.5309	−	5.59669i	−1.30303	−	0.238861i
$550$	68.3562	+	39.4655i	2.91472	+	1.68281i
$551$	−5.08351	−	1.36212i	−0.216565	−	0.0580284i
$552$	−6.32611	−	7.59118i	−0.269257	−	0.323102i
$553$	5.10302	+	1.36735i	0.217003	+	0.0581457i
$554$	−40.0634	+	10.7350i	−1.70213	+	0.456085i
$555$	0.103518	−	1.13883i	0.00439411	−	0.0483406i
$556$	2.71329	+	1.56652i	0.115069	+	0.0664352i
$557$	−7.01507	+	26.1806i	−0.297238	+	1.10931i	0.642186	+	0.766549i	$0.278028\pi$
$557$	−7.01507	+	26.1806i	−0.297238	+	1.10931i	−0.939424	+	0.342758i	$0.888639\pi$
$558$	−1.01284	−	2.84246i	−0.0428771	−	0.120331i
$559$	7.53897	+	5.19088i	0.318864	+	0.219551i
$560$	−10.9183	+	6.30371i	−0.461384	+	0.266380i
$561$	8.46737	−	23.0213i	0.357493	−	0.971958i
$562$	16.2966			0.687433
$563$	4.31526	+	7.47425i	0.181866	+	0.315002i	0.942516	−	0.334161i	$-0.108453\pi$
$563$	4.31526	+	7.47425i	0.181866	+	0.315002i	−0.760650	+	0.649163i	$0.775119\pi$
$564$	−2.31188	−	13.3758i	−0.0973477	−	0.563223i
$565$	5.66566	+	5.66566i	0.238356	+	0.238356i
$566$	24.6687	−	6.60996i	1.03690	−	0.277837i
$567$	−8.20750	+	3.69283i	−0.344682	+	0.155084i
$568$	3.31478	−	5.74137i	0.139085	−	0.240903i
$569$	6.83812	−	11.8440i	0.286669	−	0.496525i	−0.686344	−	0.727277i	$-0.740785\pi$
$569$	6.83812	−	11.8440i	0.286669	−	0.496525i	0.973012	+	0.230752i	$0.0741188\pi$
$570$	18.6430	−	15.5361i	0.780868	−	0.650737i
$571$	−18.5955	−	10.7361i	−0.778198	−	0.449293i	0.0575930	−	0.998340i	$-0.481657\pi$
$571$	−18.5955	−	10.7361i	−0.778198	−	0.449293i	−0.835791	+	0.549047i	$0.814991\pi$
$572$	5.10983	+	27.7023i	0.213653	+	1.15829i
$573$	2.57428	−	28.3203i	0.107542	−	1.18310i
$574$	−7.81224	+	2.09328i	−0.326077	+	0.0873720i
$575$	72.0420	−	41.5934i	3.00436	−	1.73457i
$576$	5.77350	−	31.4954i	0.240563	−	1.31231i
$577$	−13.4381	−	13.4381i	−0.559436	−	0.559436i	0.369711	−	0.929147i	$-0.379457\pi$
$577$	−13.4381	−	13.4381i	−0.559436	−	0.559436i	−0.929147	+	0.369711i	$0.879457\pi$
$578$	−2.29601	+	2.29601i	−0.0955014	+	0.0955014i
$579$	5.14808	−	4.29015i	0.213947	−	0.178293i
$580$	7.96197	+	29.7145i	0.330603	+	1.23383i
$581$	−1.96516	+	1.13459i	−0.0815286	+	0.0470705i
$582$	31.2500	−	44.3097i	1.29535	−	1.83670i
$583$	8.01998	+	29.9310i	0.332154	+	1.23961i
$584$	11.0012			0.455231
$585$	−38.0470	−	21.9104i	−1.57305	−	0.905884i
$586$	−30.1495			−1.24547
$587$	−3.70014	−	13.8091i	−0.152721	−	0.569963i	−0.999290	−	0.0376836i	$-0.988002\pi$
$587$	−3.70014	−	13.8091i	−0.152721	−	0.569963i	0.846568	−	0.532280i	$-0.178665\pi$
$588$	1.72675	+	3.73598i	0.0712100	+	0.154069i
$589$	−0.687089	+	0.396691i	−0.0283110	+	0.0163454i
$590$	23.3868	+	87.2806i	0.962818	+	3.59329i
$591$	−17.7711	−	6.53633i	−0.731006	−	0.268869i
$592$	−0.357236	+	0.357236i	−0.0146823	+	0.0146823i
$593$	17.1896	+	17.1896i	0.705894	+	0.705894i	0.965669	−	0.259775i	$-0.0836485\pi$
$593$	17.1896	+	17.1896i	0.705894	+	0.705894i	−0.259775	+	0.965669i	$0.583648\pi$
$594$	−8.89931	−	34.6143i	−0.365143	−	1.42024i
$595$	15.1408	−	8.74154i	0.620712	−	0.358368i
$596$	21.3074	−	5.70931i	0.872786	−	0.233862i
$597$	6.60175	+	4.65596i	0.270191	+	0.190556i
$598$	51.5247	+	18.2954i	2.10700	+	0.748156i
$599$	−27.1610	−	15.6814i	−1.10977	−	0.640725i	−0.170999	−	0.985271i	$-0.554699\pi$
$599$	−27.1610	−	15.6814i	−1.10977	−	0.640725i	−0.938769	+	0.344546i	$0.888033\pi$
$600$	−14.6815	−	5.39994i	−0.599369	−	0.220452i
$601$	6.95720	−	12.0502i	0.283790	−	0.491539i	−0.688525	−	0.725213i	$-0.741741\pi$
$601$	6.95720	−	12.0502i	0.283790	−	0.491539i	0.972315	+	0.233674i	$0.0750748\pi$
$602$	−2.65535	+	4.59919i	−0.108224	+	0.187449i
$603$	21.2864	+	30.8422i	0.866848	+	1.25599i
$604$	−8.89871	+	2.38440i	−0.362084	+	0.0970200i
$605$	0.543882	+	0.543882i	0.0221120	+	0.0221120i
$606$	25.4445	+	9.35865i	1.03361	+	0.380169i
$607$	8.58712	+	14.8733i	0.348540	+	0.603690i	0.985990	−	0.166802i	$-0.0533441\pi$
$607$	8.58712	+	14.8733i	0.348540	+	0.603690i	−0.637450	+	0.770492i	$0.720011\pi$
$608$	−13.3188			−0.540149
$609$	−5.44361	+	0.940876i	−0.220586	+	0.0381262i
$610$	76.0844	−	43.9273i	3.08057	−	1.77857i
$611$	7.71519	+	9.04897i	0.312123	+	0.366082i
$612$	−5.53630	+	30.2014i	−0.223792	+	1.22082i
$613$	−3.35658	+	12.5269i	−0.135571	+	0.505958i	0.864424	+	0.502764i	$0.167684\pi$
$613$	−3.35658	+	12.5269i	−0.135571	+	0.505958i	−0.999995	+	0.00319450i	$0.998983\pi$
$614$	52.0875	+	30.0728i	2.10208	+	1.21364i
$615$	22.2124	+	15.6656i	0.895691	+	0.631696i
$616$	−2.49950	+	0.669738i	−0.100708	+	0.0269845i
$617$	19.2636	+	5.16166i	0.775522	+	0.207801i	0.624810	−	0.780777i	$-0.285177\pi$
$617$	19.2636	+	5.16166i	0.775522	+	0.207801i	0.150713	+	0.988578i	$0.451843\pi$
$618$	2.49212	−	6.77564i	0.100248	−	0.272556i
$619$	1.42837	+	0.382731i	0.0574111	+	0.0153833i	0.287410	−	0.957808i	$-0.407206\pi$
$619$	1.42837	+	0.382731i	0.0574111	+	0.0153833i	−0.229999	+	0.973191i	$0.573872\pi$
$620$	4.01622	+	2.31876i	0.161295	+	0.0931238i
$621$	−36.2828	−	10.1177i	−1.45598	−	0.406011i
$622$	−46.8110	−	12.5430i	−1.87695	−	0.502927i
$623$	4.89476	+	8.47798i	0.196105	+	0.339663i
$624$	6.71597	+	18.1974i	0.268854	+	0.728479i
$625$	24.6556	−	42.7048i	0.986224	−	1.70819i
$626$	47.7383	−	47.7383i	1.90801	−	1.90801i
$627$	−8.52989	+	3.94247i	−0.340651	+	0.157447i
$628$			43.2481i			1.72579i
$629$	0.495389	−	0.495389i	0.0197525	−	0.0197525i
$630$	10.9216	−	23.0136i	0.435127	−	0.916883i
$631$	2.21659	+	8.27241i	0.0882409	+	0.329319i	0.995908	−	0.0903710i	$-0.0288053\pi$
$631$	2.21659	+	8.27241i	0.0882409	+	0.329319i	−0.907667	+	0.419690i	$0.862139\pi$
$632$	1.07613	−	4.01618i	0.0428063	−	0.159755i
$633$	4.56628	+	0.415070i	0.181493	+	0.0164976i
$634$			13.1534i			0.522387i
$635$	−37.5605	−	37.5605i	−1.49054	−	1.49054i
$636$	−16.2736	−	35.2094i	−0.645291	−	1.39614i
$637$	−2.96968	−	2.04474i	−0.117663	−	0.0810157i
$638$		−	21.9377i		−	0.868520i
$639$	−2.03210	−	25.1890i	−0.0803887	−	0.996463i
$640$	12.5520	+	21.7408i	0.496163	+	0.859379i
$641$	−39.0413			−1.54204			−0.771020	−	0.636811i	$-0.780253\pi$
$641$	−39.0413			−1.54204			−0.771020	+	0.636811i	$0.780253\pi$
$642$	−37.6844	−	45.2203i	−1.48728	−	1.78470i
$643$	−5.89025	+	21.9827i	−0.232289	+	0.866913i	0.747064	+	0.664752i	$0.231463\pi$
$643$	−5.89025	+	21.9827i	−0.232289	+	0.866913i	−0.979352	+	0.202161i	$0.935204\pi$
$644$	−4.45822	+	16.6383i	−0.175679	+	0.655642i
$645$	17.5870	−	3.03974i	0.692486	−	0.119690i
$646$	14.8679			0.584968
$647$	−8.62727	−	14.9429i	−0.339173	−	0.587465i	0.645105	−	0.764094i	$-0.276814\pi$
$647$	−8.62727	−	14.9429i	−0.339173	−	0.587465i	−0.984277	+	0.176630i	$0.943480\pi$
$648$	2.90633	+	6.45947i	0.114172	+	0.253752i
$649$		−	34.9887i		−	1.37343i
$650$	85.1198	−	15.7008i	3.33867	−	0.615837i
$651$	−0.479980	+	0.680570i	−0.0188119	+	0.0266736i
$652$	9.12241	+	9.12241i	0.357261	+	0.357261i
$653$			50.2547i			1.96662i	0.181941	+	0.983309i	$0.441762\pi$
$653$			50.2547i			1.96662i	−0.181941	+	0.983309i	$0.558238\pi$
$654$	−2.92406	+	4.14607i	−0.114340	+	0.162124i
$655$	12.9944	−	48.4959i	0.507735	−	1.89489i
$656$	−3.10803	−	11.5993i	−0.121348	−	0.452877i
$657$	34.5129	−	23.8198i	1.34648	−	0.929298i
$658$	−4.87865	+	4.87865i	−0.190190	+	0.190190i
$659$			10.0825i			0.392757i	0.980528	+	0.196379i	$0.0629182\pi$
$659$			10.0825i			0.392757i	−0.980528	+	0.196379i	$0.937082\pi$
$660$	44.8871	+	31.6572i	1.74723	+	1.23225i
$661$	−2.15260	+	2.15260i	−0.0837266	+	0.0837266i	−0.747730	−	0.664003i	$-0.768856\pi$
$661$	−2.15260	+	2.15260i	−0.0837266	+	0.0837266i	0.664003	+	0.747730i	$0.268856\pi$
$662$	2.01631	−	3.49235i	0.0783661	−	0.135734i
$663$	−9.31323	−	25.2349i	−0.361696	−	0.980041i
$664$	0.892942	+	1.54662i	0.0346529	+	0.0600205i
$665$	−6.46943	−	1.73348i	−0.250874	−	0.0672214i
$666$	0.184056	−	1.00406i	0.00713202	−	0.0389064i
$667$	−20.0230	−	11.5603i	−0.775293	−	0.447615i
$668$	−36.3951	−	9.75204i	−1.40817	−	0.377318i
$669$	2.45227	−	0.423851i	0.0948101	−	0.0163870i
$670$	−102.454	−	27.4525i	−3.95815	−	1.06058i
$671$	−32.8596	+	8.80469i	−1.26853	+	0.339901i
$672$	−12.6906	+	5.86553i	−0.489550	+	0.226268i
$673$	4.15521	+	2.39901i	0.160171	+	0.0924750i	0.577943	−	0.816077i	$-0.303855\pi$
$673$	4.15521	+	2.39901i	0.160171	+	0.0924750i	−0.417772	+	0.908552i	$0.637189\pi$
$674$	18.6757	−	69.6987i	0.719361	−	2.68469i
$675$	−57.7508	+	14.8477i	−2.22283	+	0.571488i
$676$	23.9734	+	19.4812i	0.922054	+	0.749277i
$677$	17.6081	−	10.1661i	0.676736	−	0.390713i	−0.121888	−	0.992544i	$-0.538895\pi$
$677$	17.6081	−	10.1661i	0.676736	−	0.390713i	0.798624	+	0.601830i	$0.205562\pi$
$678$	4.57895	+	5.49462i	0.175853	+	0.211020i
$679$	−14.9643			−0.574278
$680$	−6.87977	−	11.9161i	−0.263827	−	0.456962i
$681$	10.2480	−	8.54015i	0.392703	−	0.327259i
$682$	−2.33850	−	2.33850i	−0.0895458	−	0.0895458i
$683$	−39.9816	+	10.7130i	−1.52985	+	0.409923i	−0.922971	−	0.384870i	$-0.874246\pi$
$683$	−39.9816	+	10.7130i	−1.52985	+	0.409923i	−0.606881	+	0.794793i	$0.707580\pi$
$684$	9.68092	−	6.68148i	0.370159	−	0.255473i
$685$	−37.4809	+	64.9189i	−1.43207	+	2.48042i
$686$	1.04597	−	1.81167i	0.0399353	−	0.0691700i
$687$	−7.22549	−	41.8044i	−0.275670	−	1.59494i
$688$	−6.82870	−	3.94255i	−0.260342	−	0.150308i
$689$	27.9875	+	19.2705i	1.06624	+	0.734148i
$690$	96.7761	−	44.7294i	3.68420	−	1.70282i
$691$	−31.5973	+	8.46646i	−1.20202	+	0.322079i	−0.803625	−	0.595136i	$-0.797098\pi$
$691$	−31.5973	+	8.46646i	−1.20202	+	0.322079i	−0.398392	+	0.917215i	$0.630432\pi$
$692$	14.0633	−	8.11944i	0.534606	−	0.308655i
$693$	−6.39131	+	7.51303i	−0.242786	+	0.285397i
$694$	−20.1575	−	20.1575i	−0.765169	−	0.765169i
$695$	−3.78430	+	3.78430i	−0.143547	+	0.143547i
$696$	0.740488	+	4.28423i	0.0280681	+	0.162393i
$697$	4.30999	+	16.0851i	0.163253	+	0.609267i
$698$	50.9654	−	29.4249i	1.92907	−	1.11375i
$699$	−25.6931	−	2.33547i	−0.971801	−	0.0883357i
$700$	7.05760	+	26.3393i	0.266752	+	0.995533i
$701$	22.9434			0.866561			0.433280	−	0.901259i	$-0.357356\pi$
$701$	22.9434			0.866561			0.433280	+	0.901259i	$0.357356\pi$
$702$	−32.0533	−	22.5530i	−1.20977	−	0.851207i
$703$	−0.268390			−0.0101225
$704$	−9.08285	−	33.8976i	−0.342323	−	1.27757i
$705$	23.0919	+	2.09903i	0.869691	+	0.0790540i
$706$	−52.1255	+	30.0947i	−1.96177	+	1.13263i
$707$	−1.93656	−	7.22736i	−0.0728320	−	0.271813i
$708$	7.45941	+	43.1578i	0.280342	+	1.62197i
$709$	9.66443	−	9.66443i	0.362955	−	0.362955i	−0.501945	−	0.864900i	$-0.667382\pi$
$709$	9.66443	−	9.66443i	0.362955	−	0.362955i	0.864900	+	0.501945i	$0.167382\pi$
$710$	50.5771	+	50.5771i	1.89812	+	1.89812i
$711$	−5.31981	−	14.9296i	−0.199509	−	0.559905i
$712$	6.67234	−	3.85228i	0.250057	−	0.144370i
$713$	−3.36670	+	0.902104i	−0.126084	+	0.0337840i
$714$	14.1666	−	6.54773i	0.530171	−	0.245042i
$715$	−47.9673	−	3.81634i	−1.79387	−	0.142723i
$716$	−37.4369	−	21.6142i	−1.39908	−	0.807761i
$717$	5.85656	+	33.8842i	0.218717	+	1.26543i
$718$	−22.0282	+	38.1540i	−0.822086	+	1.42390i
$719$	21.7543	−	37.6796i	0.811299	−	1.40521i	−0.100657	−	0.994921i	$-0.532094\pi$
$719$	21.7543	−	37.6796i	0.811299	−	1.40521i	0.911955	−	0.410289i	$-0.134572\pi$
$720$	34.1697	+	16.2160i	1.27343	+	0.604333i
$721$	−1.92458	+	0.515689i	−0.0716750	+	0.0192053i
$722$	24.0778	+	24.0778i	0.896081	+	0.896081i
$723$	−18.8594	+	15.7165i	−0.701390	+	0.584503i
$724$	−29.6373	−	51.3334i	−1.10146	−	1.90779i
$725$	−36.6010			−1.35933
$726$	0.439562	+	0.527463i	0.0163137	+	0.0195760i
$727$	18.0155	−	10.4013i	0.668160	−	0.385762i	−0.127219	−	0.991875i	$-0.540605\pi$
$727$	18.0155	−	10.4013i	0.668160	−	0.385762i	0.795379	+	0.606112i	$0.207272\pi$
$728$	−1.60926	+	2.33720i	−0.0596430	+	0.0866225i
$729$	23.1038	+	13.9719i	0.855698	+	0.517476i
$730$	−30.7198	+	114.648i	−1.13699	+	4.24331i
$731$	9.46956	+	5.46725i	0.350244	+	0.202214i
$732$	38.6544	−	17.8659i	1.42871	−	0.660342i
$733$	−18.6602	+	4.99999i	−0.689231	+	0.184679i	−0.586402	−	0.810020i	$-0.699456\pi$
$733$	−18.6602	+	4.99999i	−0.689231	+	0.184679i	−0.102829	+	0.994699i	$0.532789\pi$
$734$	65.5601	+	17.5668i	2.41987	+	0.648401i
$735$	−6.92770	+	1.19739i	−0.255532	+	0.0441663i
$736$	−56.5181	−	15.1440i	−2.08328	−	0.558214i
$737$	35.5689	+	20.5357i	1.31020	+	0.756442i
$738$	18.4810	+	15.7217i	0.680293	+	0.578723i
$739$	3.70645	+	0.993139i	0.136344	+	0.0365332i	0.326346	−	0.945251i	$-0.394183\pi$
$739$	3.70645	+	0.993139i	0.136344	+	0.0365332i	−0.190002	+	0.981784i	$0.560849\pi$
$740$	0.784405	+	1.35863i	0.0288353	+	0.0499442i
$741$	−4.31298	+	9.35866i	−0.158441	+	0.343799i
$742$	−9.85765	+	17.0740i	−0.361886	+	0.626805i
$743$	−28.8448	+	28.8448i	−1.05821	+	1.05821i	−0.0600149	+	0.998197i	$0.519115\pi$
$743$	−28.8448	+	28.8448i	−1.05821	+	1.05821i	−0.998197	+	0.0600149i	$0.980885\pi$
$744$	0.535623	+	0.377754i	0.0196369	+	0.0138491i
$745$			37.6809i			1.38052i
$746$	38.4516	−	38.4516i	1.40781	−	1.40781i
$747$	6.15009	+	2.91866i	0.225020	+	0.106788i
$748$	8.70968	+	32.5050i	0.318458	+	1.18850i
$749$	−4.20472	+	15.6922i	−0.153637	+	0.573382i
$750$	54.8898	−	77.8290i	2.00429	−	2.84191i
$751$			34.5139i			1.25943i	0.776826	+	0.629715i	$0.216828\pi$
$751$			34.5139i			1.25943i	−0.776826	+	0.629715i	$0.783172\pi$
$752$	−7.24363	−	7.24363i	−0.264148	−	0.264148i
$753$	22.0723	−	31.2966i	0.804359	−	1.14051i
$754$	−15.6081	−	18.3063i	−0.568412	−	0.666677i
$755$		−	15.7369i		−	0.572723i
$756$	6.28180	−	10.6298i	0.228467	−	0.386601i
$757$	−24.1657	−	41.8562i	−0.878318	−	1.52129i	−0.853186	−	0.521607i	$-0.825333\pi$
$757$	−24.1657	−	41.8562i	−0.878318	−	1.52129i	−0.0251319	−	0.999684i	$-0.508001\pi$
$758$	−16.3702			−0.594592
$759$	−40.6791	+	7.03100i	−1.47656	+	0.255209i
$760$	−1.36428	+	5.09158i	−0.0494878	+	0.184691i
$761$	−7.95834	+	29.7009i	−0.288489	+	1.07666i	0.657762	+	0.753226i	$0.271503\pi$
$761$	−7.95834	+	29.7009i	−0.288489	+	1.07666i	−0.946252	+	0.323432i	$0.895163\pi$
$762$	−30.3561	−	36.4266i	−1.09969	−	1.31960i
$763$	1.40021			0.0506911
$764$	19.5065	+	33.7862i	0.705720	+	1.22234i
$765$	−47.3841	−	22.4871i	−1.71317	−	0.813025i
$766$		−	57.7490i		−	2.08656i
$767$	−24.8935	−	29.1970i	−0.898852	−	1.05424i
$768$	−6.11039	−	13.2204i	−0.220490	−	0.477049i
$769$	−2.51854	−	2.51854i	−0.0908210	−	0.0908210i	0.660237	−	0.751058i	$-0.270456\pi$
$769$	−2.51854	−	2.51854i	−0.0908210	−	0.0908210i	−0.751058	+	0.660237i	$0.770456\pi$
$770$		−	27.9185i		−	1.00611i
$771$	14.6137	+	1.32837i	0.526299	+	0.0478401i
$772$	−2.37949	+	8.88038i	−0.0856397	+	0.319612i
$773$	−6.31122	−	23.5538i	−0.226999	−	0.847171i	−0.981594	−	0.190981i	$-0.938833\pi$
$773$	−6.31122	−	23.5538i	−0.226999	−	0.847171i	0.754595	−	0.656191i

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fy (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.541434 - 2.02066i) q^{2} +(1.72494 + 0.156795i) q^{3} +(-2.05786 + 1.18811i) q^{4} +(-1.05055 - 3.92071i) q^{5} +(-0.617111 - 3.57041i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.556508 + 0.556508i) q^{8} +(2.95083 + 0.540924i) q^{9} +O(q^{10})\)	\(q+(-0.541434 - 2.02066i) q^{2} +(1.72494 + 0.156795i) q^{3} +(-2.05786 + 1.18811i) q^{4} +(-1.05055 - 3.92071i) q^{5} +(-0.617111 - 3.57041i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.556508 + 0.556508i) q^{8} +(2.95083 + 0.540924i) q^{9} +(-7.35361 + 4.24561i) q^{10} +(3.17590 - 0.850980i) q^{11} +(-3.73598 + 1.72675i) q^{12} +(2.04474 - 2.96968i) q^{13} +(1.81167 + 1.04597i) q^{14} +(-1.19739 - 6.92770i) q^{15} +(-1.55302 + 2.68990i) q^{16} +(2.15361 - 3.73016i) q^{17} +(-0.504656 - 6.25550i) q^{18} +(-1.59384 + 0.427069i) q^{19} +(6.82011 + 6.82011i) q^{20} +(-1.33059 + 1.10885i) q^{21} +(-3.43908 - 5.95666i) q^{22} -7.24903 q^{23} +(0.872684 + 1.04720i) q^{24} +(-9.93815 + 5.73779i) q^{25} +(-7.10781 - 2.52384i) q^{26} +(5.00519 + 1.39574i) q^{27} +(0.615010 - 2.29525i) q^{28} +(2.76216 + 1.59473i) q^{29} +(-13.3502 + 6.17040i) q^{30} +(0.464434 - 0.124445i) q^{31} +(7.79664 + 2.08910i) q^{32} +(5.61166 - 0.969923i) q^{33} +(-8.70343 - 2.33208i) q^{34} +(3.51521 + 2.02951i) q^{35} +(-6.71508 + 2.39276i) q^{36} +(0.157111 + 0.0420979i) q^{37} +(1.72592 + 2.98939i) q^{38} +(3.99269 - 4.80192i) q^{39} +(1.59726 - 2.76654i) q^{40} +(-2.73381 + 2.73381i) q^{41} +(2.96102 + 2.08830i) q^{42} +2.53864i q^{43} +(-5.52451 + 5.52451i) q^{44} +(-0.979190 - 12.1376i) q^{45} +(3.92487 + 14.6478i) q^{46} +(-0.853614 + 3.18573i) q^{47} +(-3.10062 + 4.39641i) q^{48} -1.00000i q^{49} +(16.9750 + 16.9750i) q^{50} +(4.29972 - 6.09663i) q^{51} +(-0.679500 + 8.54058i) q^{52} +9.42441i q^{53} +(0.110330 - 10.8695i) q^{54} +(-6.67288 - 11.5578i) q^{55} -0.787021 q^{56} +(-2.81625 + 0.486761i) q^{57} +(1.72689 - 6.44483i) q^{58} +(2.75423 - 10.2789i) q^{59} +(10.6949 + 12.8336i) q^{60} -10.3465 q^{61} +(-0.502921 - 0.871085i) q^{62} +(-2.46904 + 1.70406i) q^{63} -10.6734i q^{64} +(-13.7914 - 4.89704i) q^{65} +(-4.99823 - 10.8141i) q^{66} +(8.83286 + 8.83286i) q^{67} +10.2349i q^{68} +(-12.5041 - 1.13661i) q^{69} +(2.19769 - 8.20188i) q^{70} +(-2.18019 - 8.13660i) q^{71} +(1.34113 + 1.94319i) q^{72} +(9.88411 - 9.88411i) q^{73} -0.340262i q^{74} +(-18.0424 + 8.33909i) q^{75} +(2.77251 - 2.77251i) q^{76} +(-1.64397 + 2.84743i) q^{77} +(-11.8648 - 5.46795i) q^{78} +(-2.64152 - 4.57524i) q^{79} +(12.1778 + 3.26304i) q^{80} +(8.41480 + 3.19235i) q^{81} +(7.00427 + 4.04391i) q^{82} +(2.19185 + 0.587305i) q^{83} +(1.42074 - 3.86273i) q^{84} +(-16.8874 - 4.52495i) q^{85} +(5.12973 - 1.37451i) q^{86} +(4.51451 + 3.18391i) q^{87} +(2.24099 + 1.29384i) q^{88} +(2.53372 - 9.45596i) q^{89} +(-23.9958 + 8.55032i) q^{90} +(0.654031 + 3.54574i) q^{91} +(14.9175 - 8.61263i) q^{92} +(0.820633 - 0.141839i) q^{93} +6.89945 q^{94} +(3.34883 + 5.80034i) q^{95} +(13.1212 + 4.82605i) q^{96} +(10.5814 + 10.5814i) q^{97} +(-2.02066 + 0.541434i) q^{98} +(9.83186 - 0.793176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) \) 336 * q - 12 * q^6 + 36 * q^8	\( 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) \) 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

Introduction

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