LMFDB - Embedded newform 570.2.i.h.391.1

Newspace parameters

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.i (of order $3$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{19})$
Defining polynomial:	$x^{4} + 19 x^{2} + 361$
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.1
Root			$2.17945 - 3.77492i$ of defining polynomial
Character	$\chi$	$=$	570.391
Dual form			570.2.i.h.121.1

$q$-expansion

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} -4.35890 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} -4.35890 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} -3.00000 q^{11} +1.00000 q^{12} +(2.00000 + 3.46410i) q^{13} +(-2.17945 + 3.77492i) q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.67945 + 2.90889i) q^{17} -1.00000 q^{18} +(-2.17945 + 3.77492i) q^{19} -1.00000 q^{20} +(2.17945 - 3.77492i) q^{21} +(-1.50000 + 2.59808i) q^{22} +(1.50000 + 2.59808i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +4.00000 q^{26} +1.00000 q^{27} +(2.17945 + 3.77492i) q^{28} +(-4.67945 - 8.10504i) q^{29} +1.00000 q^{30} -10.7178 q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +(1.67945 + 2.90889i) q^{34} +(-2.17945 + 3.77492i) q^{35} +(-0.500000 + 0.866025i) q^{36} -7.00000 q^{37} +(2.17945 + 3.77492i) q^{38} -4.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(3.17945 - 5.50697i) q^{41} +(-2.17945 - 3.77492i) q^{42} +(5.00000 - 8.66025i) q^{43} +(1.50000 + 2.59808i) q^{44} -1.00000 q^{45} +3.00000 q^{46} +(3.00000 + 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{48} +12.0000 q^{49} -1.00000 q^{50} +(-1.67945 - 2.90889i) q^{51} +(2.00000 - 3.46410i) q^{52} +(6.53835 + 11.3248i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-1.50000 + 2.59808i) q^{55} +4.35890 q^{56} +(-2.17945 - 3.77492i) q^{57} -9.35890 q^{58} +(-6.35890 + 11.0139i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-2.67945 - 4.64094i) q^{61} +(-5.35890 + 9.28189i) q^{62} +(2.17945 + 3.77492i) q^{63} +1.00000 q^{64} +4.00000 q^{65} +(-1.50000 - 2.59808i) q^{66} +(-5.67945 - 9.83710i) q^{67} +3.35890 q^{68} -3.00000 q^{69} +(2.17945 + 3.77492i) q^{70} +(5.03835 - 8.72668i) q^{71} +(0.500000 + 0.866025i) q^{72} +(-2.32055 + 4.01931i) q^{73} +(-3.50000 + 6.06218i) q^{74} +1.00000 q^{75} +4.35890 q^{76} +13.0767 q^{77} +(-2.00000 + 3.46410i) q^{78} +(2.35890 - 4.08573i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.17945 - 5.50697i) q^{82} -6.00000 q^{83} -4.35890 q^{84} +(1.67945 + 2.90889i) q^{85} +(-5.00000 - 8.66025i) q^{86} +9.35890 q^{87} +3.00000 q^{88} +(-0.179449 - 0.310816i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-8.71780 - 15.0997i) q^{91} +(1.50000 - 2.59808i) q^{92} +(5.35890 - 9.28189i) q^{93} +6.00000 q^{94} +(2.17945 + 3.77492i) q^{95} -1.00000 q^{96} +(7.03835 - 12.1908i) q^{97} +(6.00000 - 10.3923i) q^{98} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{5} + 2q^{6} - 4q^{8} - 2q^{9} + O(q^{10}) $	$ 4q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{5} + 2q^{6} - 4q^{8} - 2q^{9} - 2q^{10} - 12q^{11} + 4q^{12} + 8q^{13} + 2q^{15} - 2q^{16} + 2q^{17} - 4q^{18} - 4q^{20} - 6q^{22} + 6q^{23} + 2q^{24} - 2q^{25} + 16q^{26} + 4q^{27} - 10q^{29} + 4q^{30} - 8q^{31} + 2q^{32} + 6q^{33} - 2q^{34} - 2q^{36} - 28q^{37} - 16q^{39} - 2q^{40} + 4q^{41} + 20q^{43} + 6q^{44} - 4q^{45} + 12q^{46} + 12q^{47} - 2q^{48} + 48q^{49} - 4q^{50} + 2q^{51} + 8q^{52} + 2q^{54} - 6q^{55} - 20q^{58} - 8q^{59} + 2q^{60} - 2q^{61} - 4q^{62} + 4q^{64} + 16q^{65} - 6q^{66} - 14q^{67} - 4q^{68} - 12q^{69} - 6q^{71} + 2q^{72} - 18q^{73} - 14q^{74} + 4q^{75} - 8q^{78} - 8q^{79} + 2q^{80} - 2q^{81} - 4q^{82} - 24q^{83} - 2q^{85} - 20q^{86} + 20q^{87} + 12q^{88} + 8q^{89} - 2q^{90} + 6q^{92} + 4q^{93} + 24q^{94} - 4q^{96} + 2q^{97} + 24q^{98} + 6q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−4.35890			−1.64751			−0.823754	−	0.566947i	$-0.808125\pi$
$7$	−4.35890			−1.64751			−0.823754	+	0.566947i	$0.808125\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$	1.00000			0.288675
$13$	2.00000	+	3.46410i	0.554700	+	0.960769i	0.997927	+	0.0643593i	$0.0205004\pi$
$13$	2.00000	+	3.46410i	0.554700	+	0.960769i	−0.443227	+	0.896410i	$0.646166\pi$
$14$	−2.17945	+	3.77492i	−0.582482	+	1.00889i
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.67945	+	2.90889i	−0.407326	+	0.705510i	−0.994589	−	0.103886i	$-0.966872\pi$
$17$	−1.67945	+	2.90889i	−0.407326	+	0.705510i	0.587263	+	0.809396i	$0.300205\pi$
$18$	−1.00000			−0.235702
$19$	−2.17945	+	3.77492i	−0.500000	+	0.866025i
$19$	−2.17945	+	3.77492i	−0.500000	+	0.866025i
$20$	−1.00000			−0.223607
$21$	2.17945	−	3.77492i	0.475595	−	0.823754i
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	4.00000			0.784465
$27$	1.00000			0.192450
$28$	2.17945	+	3.77492i	0.411877	+	0.713392i
$29$	−4.67945	−	8.10504i	−0.868952	−	1.50507i	−0.863069	−	0.505086i	$-0.831461\pi$
$29$	−4.67945	−	8.10504i	−0.868952	−	1.50507i	−0.00588307	−	0.999983i	$-0.501873\pi$
$30$	1.00000			0.182574
$31$	−10.7178			−1.92497			−0.962487	−	0.271329i	$-0.912537\pi$
$31$	−10.7178			−1.92497			−0.962487	+	0.271329i	$0.912537\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$	1.67945	+	2.90889i	0.288023	+	0.498871i
$35$	−2.17945	+	3.77492i	−0.368394	+	0.638077i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−7.00000			−1.15079			−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000			−1.15079			−0.575396	+	0.817875i	$0.695152\pi$
$38$	2.17945	+	3.77492i	0.353553	+	0.612372i
$39$	−4.00000			−0.640513
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	3.17945	−	5.50697i	0.496547	−	0.860044i	−0.503445	−	0.864027i	$-0.667935\pi$
$41$	3.17945	−	5.50697i	0.496547	−	0.860044i	0.999992	+	0.00398308i	$0.00126786\pi$
$42$	−2.17945	−	3.77492i	−0.336296	−	0.582482i
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	−0.179069	−	0.983836i	$-0.557309\pi$
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	0.941562	−	0.336840i	$-0.109358\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$	−1.00000			−0.149071
$46$	3.00000			0.442326
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	12.0000			1.71429
$50$	−1.00000			−0.141421
$51$	−1.67945	−	2.90889i	−0.235170	−	0.407326i
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$	6.53835	+	11.3248i	0.898111	+	1.55557i	0.829906	+	0.557903i	$0.188394\pi$
$53$	6.53835	+	11.3248i	0.898111	+	1.55557i	0.0682050	+	0.997671i	$0.478273\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−1.50000	+	2.59808i	−0.202260	+	0.350325i
$56$	4.35890			0.582482
$57$	−2.17945	−	3.77492i	−0.288675	−	0.500000i
$58$	−9.35890			−1.22888
$59$	−6.35890	+	11.0139i	−0.827858	+	1.43389i	0.0718571	+	0.997415i	$0.477107\pi$
$59$	−6.35890	+	11.0139i	−0.827858	+	1.43389i	−0.899715	+	0.436477i	$0.856226\pi$
$60$	0.500000	−	0.866025i	0.0645497	−	0.111803i
$61$	−2.67945	−	4.64094i	−0.343068	−	0.594212i	0.641933	−	0.766761i	$-0.278133\pi$
$61$	−2.67945	−	4.64094i	−0.343068	−	0.594212i	−0.985001	+	0.172549i	$0.944800\pi$
$62$	−5.35890	+	9.28189i	−0.680581	+	1.17880i
$63$	2.17945	+	3.77492i	0.274585	+	0.475595i
$64$	1.00000			0.125000
$65$	4.00000			0.496139
$66$	−1.50000	−	2.59808i	−0.184637	−	0.319801i
$67$	−5.67945	−	9.83710i	−0.693855	−	1.20179i	−0.970565	−	0.240839i	$-0.922577\pi$
$67$	−5.67945	−	9.83710i	−0.693855	−	1.20179i	0.276710	−	0.960953i	$-0.410756\pi$
$68$	3.35890			0.407326
$69$	−3.00000			−0.361158
$70$	2.17945	+	3.77492i	0.260494	+	0.451189i
$71$	5.03835	−	8.72668i	0.597942	−	1.03567i	−0.395183	−	0.918603i	$-0.629319\pi$
$71$	5.03835	−	8.72668i	0.597942	−	1.03567i	0.993124	−	0.117063i	$-0.0373480\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−2.32055	+	4.01931i	−0.271600	+	0.470425i	−0.969272	−	0.245993i	$-0.920886\pi$
$73$	−2.32055	+	4.01931i	−0.271600	+	0.470425i	0.697672	+	0.716418i	$0.254219\pi$
$74$	−3.50000	+	6.06218i	−0.406867	+	0.704714i
$75$	1.00000			0.115470
$76$	4.35890			0.500000
$77$	13.0767			1.49023
$78$	−2.00000	+	3.46410i	−0.226455	+	0.392232i
$79$	2.35890	−	4.08573i	0.265397	−	0.459681i	−0.702271	−	0.711910i	$-0.747830\pi$
$79$	2.35890	−	4.08573i	0.265397	−	0.459681i	0.967668	+	0.252229i	$0.0811637\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.17945	−	5.50697i	−0.351111	−	0.608143i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	−4.35890			−0.475595
$85$	1.67945	+	2.90889i	0.182162	+	0.315514i
$86$	−5.00000	−	8.66025i	−0.539164	−	0.933859i
$87$	9.35890			1.00338
$88$	3.00000			0.319801
$89$	−0.179449	−	0.310816i	−0.0190216	−	0.0329464i	0.856358	−	0.516383i	$-0.172722\pi$
$89$	−0.179449	−	0.310816i	−0.0190216	−	0.0329464i	−0.875380	+	0.483436i	$0.839388\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	−8.71780	−	15.0997i	−0.913874	−	1.58288i
$92$	1.50000	−	2.59808i	0.156386	−	0.270868i
$93$	5.35890	−	9.28189i	0.555692	−	0.962487i
$94$	6.00000			0.618853
$95$	2.17945	+	3.77492i	0.223607	+	0.387298i
$96$	−1.00000			−0.102062
$97$	7.03835	−	12.1908i	0.714636	−	1.23779i	−0.248464	−	0.968641i	$-0.579926\pi$
$97$	7.03835	−	12.1908i	0.714636	−	1.23779i	0.963100	−	0.269145i	$-0.0867410\pi$
$98$	6.00000	−	10.3923i	0.606092	−	1.04978i
$99$	1.50000	+	2.59808i	0.150756	+	0.261116i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	6.35890	+	11.0139i	0.632734	+	1.09593i	0.986990	+	0.160779i	$0.0514007\pi$
$101$	6.35890	+	11.0139i	0.632734	+	1.09593i	−0.354256	+	0.935148i	$0.615266\pi$
$102$	−3.35890			−0.332581
$103$	−10.3589			−1.02069			−0.510346	−	0.859969i	$-0.670483\pi$
$103$	−10.3589			−1.02069			−0.510346	+	0.859969i	$0.670483\pi$
$104$	−2.00000	−	3.46410i	−0.196116	−	0.339683i
$105$	−2.17945	−	3.77492i	−0.212692	−	0.368394i
$106$	13.0767			1.27012
$107$	9.35890			0.904759			0.452379	−	0.891826i	$-0.350575\pi$
$107$	9.35890			0.904759			0.452379	+	0.891826i	$0.350575\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−5.32055	+	9.21546i	−0.509616	+	0.882681i	0.490322	+	0.871542i	$0.336879\pi$
$109$	−5.32055	+	9.21546i	−0.509616	+	0.882681i	−0.999938	+	0.0111398i	$0.996454\pi$
$110$	1.50000	+	2.59808i	0.143019	+	0.247717i
$111$	3.50000	−	6.06218i	0.332205	−	0.575396i
$112$	2.17945	−	3.77492i	0.205939	−	0.356696i
$113$	3.35890			0.315979			0.157989	−	0.987441i	$-0.449499\pi$
$113$	3.35890			0.315979			0.157989	+	0.987441i	$0.449499\pi$
$114$	−4.35890			−0.408248
$115$	3.00000			0.279751
$116$	−4.67945	+	8.10504i	−0.434476	+	0.752534i
$117$	2.00000	−	3.46410i	0.184900	−	0.320256i
$118$	6.35890	+	11.0139i	0.585384	+	1.01391i
$119$	7.32055	−	12.6796i	0.671074	−	1.16233i
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	−2.00000			−0.181818
$122$	−5.35890			−0.485172
$123$	3.17945	+	5.50697i	0.286681	+	0.496547i
$124$	5.35890	+	9.28189i	0.481243	+	0.833538i
$125$	−1.00000			−0.0894427
$126$	4.35890			0.388322
$127$	5.17945	+	8.97107i	0.459602	+	0.796054i	0.998940	−	0.0460357i	$-0.0146588\pi$
$127$	5.17945	+	8.97107i	0.459602	+	0.796054i	−0.539338	+	0.842089i	$0.681325\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	5.00000	+	8.66025i	0.440225	+	0.762493i
$130$	2.00000	−	3.46410i	0.175412	−	0.303822i
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	−0.793028	−	0.609185i	$-0.791497\pi$
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	0.924084	+	0.382190i	$0.124830\pi$
$132$	−3.00000			−0.261116
$133$	9.50000	−	16.4545i	0.823754	−	1.42678i
$134$	−11.3589			−0.981259
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	1.67945	−	2.90889i	0.144012	−	0.249435i
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$	−1.50000	+	2.59808i	−0.127688	+	0.221163i
$139$	−0.641101	−	1.11042i	−0.0543775	−	0.0941846i	0.837555	−	0.546353i	$-0.183984\pi$
$139$	−0.641101	−	1.11042i	−0.0543775	−	0.0941846i	−0.891933	+	0.452168i	$0.850651\pi$
$140$	4.35890			0.368394
$141$	−6.00000			−0.505291
$142$	−5.03835	−	8.72668i	−0.422809	−	0.732326i
$143$	−6.00000	−	10.3923i	−0.501745	−	0.869048i
$144$	1.00000			0.0833333
$145$	−9.35890			−0.777214
$146$	2.32055	+	4.01931i	0.192050	+	0.332641i
$147$	−6.00000	+	10.3923i	−0.494872	+	0.857143i
$148$	3.50000	+	6.06218i	0.287698	+	0.498308i
$149$	5.03835	−	8.72668i	0.412758	−	0.714917i	−0.582433	−	0.812879i	$-0.697899\pi$
$149$	5.03835	−	8.72668i	0.412758	−	0.714917i	0.995190	+	0.0979619i	$0.0312323\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−2.07670			−0.168999			−0.0844996	−	0.996424i	$-0.526929\pi$
$151$	−2.07670			−0.168999			−0.0844996	+	0.996424i	$0.526929\pi$
$152$	2.17945	−	3.77492i	0.176777	−	0.306186i
$153$	3.35890			0.271551
$154$	6.53835	−	11.3248i	0.526875	−	0.912574i
$155$	−5.35890	+	9.28189i	−0.430437	+	0.745539i
$156$	2.00000	+	3.46410i	0.160128	+	0.277350i
$157$	−2.50000	+	4.33013i	−0.199522	+	0.345582i	−0.948373	−	0.317156i	$-0.897272\pi$
$157$	−2.50000	+	4.33013i	−0.199522	+	0.345582i	0.748852	+	0.662738i	$0.230606\pi$
$158$	−2.35890	−	4.08573i	−0.187664	−	0.325043i
$159$	−13.0767			−1.03705
$160$	1.00000			0.0790569
$161$	−6.53835	−	11.3248i	−0.515294	−	0.892515i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−4.71780			−0.369526			−0.184763	−	0.982783i	$-0.559152\pi$
$163$	−4.71780			−0.369526			−0.184763	+	0.982783i	$0.559152\pi$
$164$	−6.35890			−0.496547
$165$	−1.50000	−	2.59808i	−0.116775	−	0.202260i
$166$	−3.00000	+	5.19615i	−0.232845	+	0.403300i
$167$	11.2178	+	19.4298i	0.868059	+	1.50352i	0.863977	+	0.503531i	$0.167966\pi$
$167$	11.2178	+	19.4298i	0.868059	+	1.50352i	0.00408215	+	0.999992i	$0.498701\pi$
$168$	−2.17945	+	3.77492i	−0.168148	+	0.291241i
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$	3.35890			0.257616
$171$	4.35890			0.333333
$172$	−10.0000			−0.762493
$173$	−9.17945	+	15.8993i	−0.697901	+	1.20880i	0.271292	+	0.962497i	$0.412549\pi$
$173$	−9.17945	+	15.8993i	−0.697901	+	1.20880i	−0.969193	+	0.246302i	$0.920784\pi$
$174$	4.67945	−	8.10504i	0.354748	−	0.614442i
$175$	2.17945	+	3.77492i	0.164751	+	0.285357i
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$	−6.35890	−	11.0139i	−0.477964	−	0.827858i
$178$	−0.358899			−0.0269006
$179$	15.7178			1.17480			0.587402	−	0.809296i	$-0.300151\pi$
$179$	15.7178			1.17480			0.587402	+	0.809296i	$0.300151\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	−9.03835	−	15.6549i	−0.671815	−	1.16362i	−0.977389	−	0.211450i	$-0.932182\pi$
$181$	−9.03835	−	15.6549i	−0.671815	−	1.16362i	0.305574	−	0.952168i	$-0.401152\pi$
$182$	−17.4356			−1.29241
$183$	5.35890			0.396141
$184$	−1.50000	−	2.59808i	−0.110581	−	0.191533i
$185$	−3.50000	+	6.06218i	−0.257325	+	0.445700i
$186$	−5.35890	−	9.28189i	−0.392934	−	0.680581i
$187$	5.03835	−	8.72668i	0.368441	−	0.638158i
$188$	3.00000	−	5.19615i	0.218797	−	0.378968i
$189$	−4.35890			−0.317063
$190$	4.35890			0.316228
$191$	−19.4356			−1.40631			−0.703155	−	0.711036i	$-0.748226\pi$
$191$	−19.4356			−1.40631			−0.703155	+	0.711036i	$0.748226\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−12.0383	+	20.8510i	−0.866539	+	1.50089i	−0.00102867	+	0.999999i	$0.500327\pi$
$193$	−12.0383	+	20.8510i	−0.866539	+	1.50089i	−0.865511	+	0.500891i	$0.833006\pi$
$194$	−7.03835	−	12.1908i	−0.505324	−	0.875247i
$195$	−2.00000	+	3.46410i	−0.143223	+	0.248069i
$196$	−6.00000	−	10.3923i	−0.428571	−	0.742307i
$197$	−5.64110			−0.401912			−0.200956	−	0.979600i	$-0.564405\pi$
$197$	−5.64110			−0.401912			−0.200956	+	0.979600i	$0.564405\pi$
$198$	3.00000			0.213201
$199$	−8.32055	−	14.4116i	−0.589828	−	1.02161i	−0.994255	−	0.107042i	$-0.965862\pi$
$199$	−8.32055	−	14.4116i	−0.589828	−	1.02161i	0.404426	−	0.914571i	$-0.367471\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	11.3589			0.801195
$202$	12.7178			0.894821
$203$	20.3972	+	35.3291i	1.43161	+	2.47961i
$204$	−1.67945	+	2.90889i	−0.117585	+	0.203663i
$205$	−3.17945	−	5.50697i	−0.222062	−	0.384623i
$206$	−5.17945	+	8.97107i	−0.360869	+	0.625044i
$207$	1.50000	−	2.59808i	0.104257	−	0.180579i
$208$	−4.00000			−0.277350
$209$	6.53835	−	11.3248i	0.452267	−	0.783349i
$210$	−4.35890			−0.300793
$211$	−7.53835	+	13.0568i	−0.518961	+	0.898867i	0.480796	+	0.876833i	$0.340348\pi$
$211$	−7.53835	+	13.0568i	−0.518961	+	0.898867i	−0.999757	+	0.0220348i	$0.992986\pi$
$212$	6.53835	−	11.3248i	0.449056	−	0.777787i
$213$	5.03835	+	8.72668i	0.345222	+	0.597942i
$214$	4.67945	−	8.10504i	0.319881	−	0.554049i
$215$	−5.00000	−	8.66025i	−0.340997	−	0.590624i
$216$	−1.00000			−0.0680414
$217$	46.7178			3.17141
$218$	5.32055	+	9.21546i	0.360353	+	0.624150i
$219$	−2.32055	−	4.01931i	−0.156808	−	0.271600i
$220$	3.00000			0.202260
$221$	−13.4356			−0.903776
$222$	−3.50000	−	6.06218i	−0.234905	−	0.406867i
$223$	−10.1794	+	17.6313i	−0.681666	+	1.18068i	0.292806	+	0.956172i	$0.405411\pi$
$223$	−10.1794	+	17.6313i	−0.681666	+	1.18068i	−0.974472	+	0.224509i	$0.927922\pi$
$224$	−2.17945	−	3.77492i	−0.145621	−	0.252222i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	1.67945	−	2.90889i	0.111715	−	0.193497i
$227$	−3.35890			−0.222938			−0.111469	−	0.993768i	$-0.535556\pi$
$227$	−3.35890			−0.222938			−0.111469	+	0.993768i	$0.535556\pi$
$228$	−2.17945	+	3.77492i	−0.144338	+	0.250000i
$229$	8.71780			0.576088			0.288044	−	0.957617i	$-0.406995\pi$
$229$	8.71780			0.576088			0.288044	+	0.957617i	$0.406995\pi$
$230$	1.50000	−	2.59808i	0.0989071	−	0.171312i
$231$	−6.53835	+	11.3248i	−0.430192	+	0.745114i
$232$	4.67945	+	8.10504i	0.307221	+	0.532122i
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$	−2.00000	−	3.46410i	−0.130744	−	0.226455i
$235$	6.00000			0.391397
$236$	12.7178			0.827858
$237$	2.35890	+	4.08573i	0.153227	+	0.265397i
$238$	−7.32055	−	12.6796i	−0.474521	−	0.821894i
$239$	−13.4356			−0.869076			−0.434538	−	0.900653i	$-0.643088\pi$
$239$	−13.4356			−0.869076			−0.434538	+	0.900653i	$0.643088\pi$
$240$	−1.00000			−0.0645497
$241$	2.00000	+	3.46410i	0.128831	+	0.223142i	0.923224	−	0.384262i	$-0.125544\pi$
$241$	2.00000	+	3.46410i	0.128831	+	0.223142i	−0.794393	+	0.607404i	$0.792211\pi$
$242$	−1.00000	+	1.73205i	−0.0642824	+	0.111340i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−2.67945	+	4.64094i	−0.171534	+	0.297106i
$245$	6.00000	−	10.3923i	0.383326	−	0.663940i
$246$	6.35890			0.405429
$247$	−17.4356			−1.10940
$248$	10.7178			0.680581
$249$	3.00000	−	5.19615i	0.190117	−	0.329293i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	0.990876	−	0.134778i	$-0.0430322\pi$
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	−0.612159	+	0.790735i	$0.709699\pi$
$252$	2.17945	−	3.77492i	0.137292	−	0.237797i
$253$	−4.50000	−	7.79423i	−0.282913	−	0.490019i
$254$	10.3589			0.649975
$255$	−3.35890			−0.210342
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.71780	+	6.43941i	0.231910	+	0.401680i	0.958370	−	0.285529i	$-0.0921692\pi$
$257$	3.71780	+	6.43941i	0.231910	+	0.401680i	−0.726460	+	0.687208i	$0.758836\pi$
$258$	10.0000			0.622573
$259$	30.5123			1.89594
$260$	−2.00000	−	3.46410i	−0.124035	−	0.214834i
$261$	−4.67945	+	8.10504i	−0.289651	+	0.501690i
$262$	−1.50000	−	2.59808i	−0.0926703	−	0.160510i
$263$	4.14110	−	7.17260i	0.255351	−	0.442281i	−0.709640	−	0.704565i	$-0.751142\pi$
$263$	4.14110	−	7.17260i	0.255351	−	0.442281i	0.964991	+	0.262284i	$0.0844756\pi$
$264$	−1.50000	+	2.59808i	−0.0923186	+	0.159901i
$265$	13.0767			0.803295
$266$	−9.50000	−	16.4545i	−0.582482	−	1.00889i
$267$	0.358899			0.0219643
$268$	−5.67945	+	9.83710i	−0.346928	+	0.600896i
$269$	−1.67945	+	2.90889i	−0.102398	+	0.177358i	−0.912672	−	0.408693i	$-0.865985\pi$
$269$	−1.67945	+	2.90889i	−0.102398	+	0.177358i	0.810274	+	0.586051i	$0.199318\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	2.35890	−	4.08573i	0.143293	−	0.248191i	−0.785442	−	0.618935i	$-0.787564\pi$
$271$	2.35890	−	4.08573i	0.143293	−	0.248191i	0.928735	+	0.370745i	$0.120898\pi$
$272$	−1.67945	−	2.90889i	−0.101832	−	0.176377i
$273$	17.4356			1.05525
$274$	−12.0000			−0.724947
$275$	1.50000	+	2.59808i	0.0904534	+	0.156670i
$276$	1.50000	+	2.59808i	0.0902894	+	0.156386i
$277$	−4.00000			−0.240337			−0.120168	−	0.992754i	$-0.538343\pi$
$277$	−4.00000			−0.240337			−0.120168	+	0.992754i	$0.538343\pi$
$278$	−1.28220			−0.0769014
$279$	5.35890	+	9.28189i	0.320829	+	0.555692i
$280$	2.17945	−	3.77492i	0.130247	−	0.225594i
$281$	−0.538348	−	0.932447i	−0.0321152	−	0.0556251i	0.849521	−	0.527555i	$-0.176891\pi$
$281$	−0.538348	−	0.932447i	−0.0321152	−	0.0556251i	−0.881636	+	0.471930i	$0.843558\pi$
$282$	−3.00000	+	5.19615i	−0.178647	+	0.309426i
$283$	−4.35890	+	7.54983i	−0.259110	+	0.448791i	−0.966004	−	0.258528i	$-0.916762\pi$
$283$	−4.35890	+	7.54983i	−0.259110	+	0.448791i	0.706894	+	0.707319i	$0.250096\pi$
$284$	−10.0767			−0.597942
$285$	−4.35890			−0.258199
$286$	−12.0000			−0.709575
$287$	−13.8589	+	24.0043i	−0.818065	+	1.41693i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	2.85890	+	4.95176i	0.168171	+	0.291280i
$290$	−4.67945	+	8.10504i	−0.274787	+	0.475945i
$291$	7.03835	+	12.1908i	0.412595	+	0.714636i
$292$	4.64110			0.271600
$293$	5.64110			0.329557			0.164778	−	0.986331i	$-0.447309\pi$
$293$	5.64110			0.329557			0.164778	+	0.986331i	$0.447309\pi$
$294$	6.00000	+	10.3923i	0.349927	+	0.606092i
$295$	6.35890	+	11.0139i	0.370229	+	0.641256i
$296$	7.00000			0.406867
$297$	−3.00000			−0.174078
$298$	−5.03835	−	8.72668i	−0.291864	−	0.505523i
$299$	−6.00000	+	10.3923i	−0.346989	+	0.601003i
$300$	−0.500000	−	0.866025i	−0.0288675	−	0.0500000i
$301$	−21.7945	+	37.7492i	−1.25621	+	2.17583i
$302$	−1.03835	+	1.79847i	−0.0597502	+	0.103490i
$303$	−12.7178			−0.730618
$304$	−2.17945	−	3.77492i	−0.125000	−	0.216506i
$305$	−5.35890			−0.306850
$306$	1.67945	−	2.90889i	0.0960077	−	0.166290i
$307$	0.679449	−	1.17684i	0.0387782	−	0.0671659i	−0.845985	−	0.533207i	$-0.820987\pi$
$307$	0.679449	−	1.17684i	0.0387782	−	0.0671659i	0.884763	+	0.466041i	$0.154320\pi$
$308$	−6.53835	−	11.3248i	−0.372557	−	0.645288i
$309$	5.17945	−	8.97107i	0.294649	−	0.510346i
$310$	5.35890	+	9.28189i	0.304365	+	0.527176i
$311$	1.43560			0.0814052			0.0407026	−	0.999171i	$-0.487040\pi$
$311$	1.43560			0.0814052			0.0407026	+	0.999171i	$0.487040\pi$
$312$	4.00000			0.226455
$313$	8.71780	+	15.0997i	0.492759	+	0.853484i	0.999965	−	0.00834102i	$-0.00265506\pi$
$313$	8.71780	+	15.0997i	0.492759	+	0.853484i	−0.507206	+	0.861825i	$0.669322\pi$
$314$	2.50000	+	4.33013i	0.141083	+	0.244363i
$315$	4.35890			0.245596
$316$	−4.71780			−0.265397
$317$	−9.53835	−	16.5209i	−0.535727	−	0.927906i	−0.999128	−	0.0417576i	$-0.986704\pi$
$317$	−9.53835	−	16.5209i	−0.535727	−	0.927906i	0.463401	−	0.886149i	$-0.346629\pi$
$318$	−6.53835	+	11.3248i	−0.366652	+	0.635061i
$319$	14.0383	+	24.3151i	0.785997	+	1.36139i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−4.67945	+	8.10504i	−0.261181	+	0.452379i
$322$	−13.0767			−0.728736
$323$	−7.32055	−	12.6796i	−0.407326	−	0.705510i
$324$	1.00000			0.0555556
$325$	2.00000	−	3.46410i	0.110940	−	0.192154i
$326$	−2.35890	+	4.08573i	−0.130647	+	0.226288i
$327$	−5.32055	−	9.21546i	−0.294227	−	0.509616i
$328$	−3.17945	+	5.50697i	−0.175556	+	0.304071i
$329$	−13.0767	−	22.6495i	−0.720942	−	1.24871i
$330$	−3.00000			−0.165145
$331$	14.3589			0.789236			0.394618	−	0.918845i	$-0.370877\pi$
$331$	14.3589			0.789236			0.394618	+	0.918845i	$0.370877\pi$
$332$	3.00000	+	5.19615i	0.164646	+	0.285176i
$333$	3.50000	+	6.06218i	0.191799	+	0.332205i
$334$	22.4356			1.22762
$335$	−11.3589			−0.620603
$336$	2.17945	+	3.77492i	0.118899	+	0.205939i
$337$	−11.0767	+	19.1854i	−0.603386	+	1.04510i	0.388918	+	0.921272i	$0.372849\pi$
$337$	−11.0767	+	19.1854i	−0.603386	+	1.04510i	−0.992304	+	0.123823i	$0.960484\pi$
$338$	1.50000	+	2.59808i	0.0815892	+	0.141317i
$339$	−1.67945	+	2.90889i	−0.0912152	+	0.157989i
$340$	1.67945	−	2.90889i	0.0910809	−	0.157757i
$341$	32.1534			1.74120
$342$	2.17945	−	3.77492i	0.117851	−	0.204124i
$343$	−21.7945			−1.17679
$344$	−5.00000	+	8.66025i	−0.269582	+	0.466930i
$345$	−1.50000	+	2.59808i	−0.0807573	+	0.139876i
$346$	9.17945	+	15.8993i	0.493490	+	0.854750i
$347$	3.71780	−	6.43941i	0.199582	−	0.345686i	−0.748811	−	0.662784i	$-0.769375\pi$
$347$	3.71780	−	6.43941i	0.199582	−	0.345686i	0.948393	+	0.317098i	$0.102708\pi$
$348$	−4.67945	−	8.10504i	−0.250845	−	0.434476i
$349$	0.0766968			0.00410549			0.00205274	−	0.999998i	$-0.499347\pi$
$349$	0.0766968			0.00410549			0.00205274	+	0.999998i	$0.499347\pi$
$350$	4.35890			0.232993
$351$	2.00000	+	3.46410i	0.106752	+	0.184900i
$352$	−1.50000	−	2.59808i	−0.0799503	−	0.138478i
$353$	−10.0767			−0.536328			−0.268164	−	0.963373i	$-0.586417\pi$
$353$	−10.0767			−0.536328			−0.268164	+	0.963373i	$0.586417\pi$
$354$	−12.7178			−0.675943
$355$	−5.03835	−	8.72668i	−0.267408	−	0.463164i
$356$	−0.179449	+	0.310816i	−0.00951080	+	0.0164732i
$357$	7.32055	+	12.6796i	0.387445	+	0.671074i
$358$	7.85890	−	13.6120i	0.415356	−	0.719417i
$359$	−7.67945	+	13.3012i	−0.405306	+	0.702010i	−0.994357	−	0.106085i	$-0.966168\pi$
$359$	−7.67945	+	13.3012i	−0.405306	+	0.702010i	0.589051	+	0.808096i	$0.299502\pi$
$360$	1.00000			0.0527046
$361$	−9.50000	−	16.4545i	−0.500000	−	0.866025i
$362$	−18.0767			−0.950090
$363$	1.00000	−	1.73205i	0.0524864	−	0.0909091i
$364$	−8.71780	+	15.0997i	−0.456937	+	0.791438i
$365$	2.32055	+	4.01931i	0.121463	+	0.210380i
$366$	2.67945	−	4.64094i	0.140057	−	0.242586i
$367$	−7.35890	−	12.7460i	−0.384131	−	0.665335i	0.607517	−	0.794307i	$-0.292166\pi$
$367$	−7.35890	−	12.7460i	−0.384131	−	0.665335i	−0.991648	+	0.128972i	$0.958832\pi$
$368$	−3.00000			−0.156386
$369$	−6.35890			−0.331031
$370$	3.50000	+	6.06218i	0.181956	+	0.315158i
$371$	−28.5000	−	49.3634i	−1.47965	−	2.56282i
$372$	−10.7178			−0.555692
$373$	11.0000			0.569558			0.284779	−	0.958593i	$-0.408080\pi$
$373$	11.0000			0.569558			0.284779	+	0.958593i	$0.408080\pi$
$374$	−5.03835	−	8.72668i	−0.260527	−	0.451246i
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	18.7178	−	32.4202i	0.964016	−	1.66972i
$378$	−2.17945	+	3.77492i	−0.112099	+	0.194161i
$379$	14.7178			0.756002			0.378001	−	0.925805i	$-0.376611\pi$
$379$	14.7178			0.756002			0.378001	+	0.925805i	$0.376611\pi$
$380$	2.17945	−	3.77492i	0.111803	−	0.193649i
$381$	−10.3589			−0.530702
$382$	−9.71780	+	16.8317i	−0.497206	+	0.861186i
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	−0.932436	−	0.361335i	$-0.882321\pi$
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	0.779143	+	0.626846i	$0.215654\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	6.53835	−	11.3248i	0.333225	−	0.577163i
$386$	12.0383	+	20.8510i	0.612736	+	1.06129i
$387$	−10.0000			−0.508329
$388$	−14.0767			−0.714636
$389$	−2.03835	−	3.53052i	−0.103348	−	0.179005i	0.809714	−	0.586825i	$-0.199622\pi$
$389$	−2.03835	−	3.53052i	−0.103348	−	0.179005i	−0.913062	+	0.407820i	$0.866289\pi$
$390$	2.00000	+	3.46410i	0.101274	+	0.175412i
$391$	−10.0767			−0.509600
$392$	−12.0000			−0.606092
$393$	1.50000	+	2.59808i	0.0756650	+	0.131056i
$394$	−2.82055	+	4.88534i	−0.142097	+	0.246120i
$395$	−2.35890	−	4.08573i	−0.118689	−	0.205576i
$396$	1.50000	−	2.59808i	0.0753778	−	0.130558i
$397$	−3.21780	+	5.57339i	−0.161497	+	0.279720i	−0.935406	−	0.353576i	$-0.884965\pi$
$397$	−3.21780	+	5.57339i	−0.161497	+	0.279720i	0.773909	+	0.633297i	$0.218299\pi$
$398$	−16.6411			−0.834143
$399$	9.50000	+	16.4545i	0.475595	+	0.823754i
$400$	1.00000			0.0500000
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	−0.548911	−	0.835881i	$-0.684957\pi$
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	0.998350	+	0.0574304i	$0.0182907\pi$
$402$	5.67945	−	9.83710i	0.283265	−	0.490630i
$403$	−21.4356	−	37.1275i	−1.06778	−	1.84945i
$404$	6.35890	−	11.0139i	0.316367	−	0.547964i
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$	40.7945			2.02460
$407$	21.0000			1.04093
$408$	1.67945	+	2.90889i	0.0831451	+	0.144012i
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	0.697406	−	0.716677i	$-0.254338\pi$
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	−0.969363	+	0.245633i	$0.921004\pi$
$410$	−6.35890			−0.314044
$411$	12.0000			0.591916
$412$	5.17945	+	8.97107i	0.255173	+	0.441973i
$413$	27.7178	−	48.0086i	1.36390	−	2.36235i
$414$	−1.50000	−	2.59808i	−0.0737210	−	0.127688i
$415$	−3.00000	+	5.19615i	−0.147264	+	0.255069i
$416$	−2.00000	+	3.46410i	−0.0980581	+	0.169842i
$417$	1.28220			0.0627897
$418$	−6.53835	−	11.3248i	−0.319801	−	0.553912i
$419$	15.7178			0.767865			0.383932	−	0.923361i	$-0.374570\pi$
$419$	15.7178			0.767865			0.383932	+	0.923361i	$0.374570\pi$
$420$	−2.17945	+	3.77492i	−0.106346	+	0.184197i
$421$	−18.0383	+	31.2433i	−0.879135	+	1.52271i	−0.0268440	+	0.999640i	$0.508546\pi$
$421$	−18.0383	+	31.2433i	−0.879135	+	1.52271i	−0.852291	+	0.523067i	$0.824788\pi$
$422$	7.53835	+	13.0568i	0.366961	+	0.635595i
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$	−6.53835	−	11.3248i	−0.317530	−	0.549979i
$425$	3.35890			0.162931
$426$	10.0767			0.488218
$427$	11.6794	+	20.2294i	0.565208	+	0.978969i
$428$	−4.67945	−	8.10504i	−0.226190	−	0.391772i
$429$	12.0000			0.579365
$430$	−10.0000			−0.482243
$431$	−5.39725	−	9.34831i	−0.259976	−	0.450292i	0.706259	−	0.707954i	$-0.250381\pi$
$431$	−5.39725	−	9.34831i	−0.259976	−	0.450292i	−0.966235	+	0.257661i	$0.917048\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−18.3972	−	31.8650i	−0.884115	−	1.53133i	−0.846724	−	0.532032i	$-0.821429\pi$
$433$	−18.3972	−	31.8650i	−0.884115	−	1.53133i	−0.0373910	−	0.999301i	$-0.511905\pi$
$434$	23.3589	−	40.4588i	1.12126	−	1.94208i
$435$	4.67945	−	8.10504i	0.224362	−	0.388607i
$436$	10.6411			0.509616
$437$	−13.0767			−0.625543
$438$	−4.64110			−0.221760
$439$	−11.6794	+	20.2294i	−0.557430	+	0.965497i	0.440280	+	0.897860i	$0.354879\pi$
$439$	−11.6794	+	20.2294i	−0.557430	+	0.965497i	−0.997710	+	0.0676362i	$0.978454\pi$
$440$	1.50000	−	2.59808i	0.0715097	−	0.123858i
$441$	−6.00000	−	10.3923i	−0.285714	−	0.494872i
$442$	−6.71780	+	11.6356i	−0.319533	+	0.553447i
$443$	1.32055	+	2.28726i	0.0627412	+	0.108671i	0.895690	−	0.444679i	$-0.146682\pi$
$443$	1.32055	+	2.28726i	0.0627412	+	0.108671i	−0.832949	+	0.553350i	$0.813349\pi$
$444$	−7.00000			−0.332205
$445$	−0.358899			−0.0170134
$446$	10.1794	+	17.6313i	0.482011	+	0.834867i
$447$	5.03835	+	8.72668i	0.238306	+	0.412758i
$448$	−4.35890			−0.205939
$449$	0.358899			0.0169375			0.00846874	−	0.999964i	$-0.497304\pi$
$449$	0.358899			0.0169375			0.00846874	+	0.999964i	$0.497304\pi$
$450$	0.500000	+	0.866025i	0.0235702	+	0.0408248i
$451$	−9.53835	+	16.5209i	−0.449143	+	0.777939i
$452$	−1.67945	−	2.90889i	−0.0789947	−	0.136823i
$453$	1.03835	−	1.79847i	0.0487859	−	0.0844996i
$454$	−1.67945	+	2.90889i	−0.0788205	+	0.136521i
$455$	−17.4356			−0.817393
$456$	2.17945	+	3.77492i	0.102062	+	0.176777i
$457$	−30.6411			−1.43333			−0.716665	−	0.697417i	$-0.754332\pi$
$457$	−30.6411			−1.43333			−0.716665	+	0.697417i	$0.754332\pi$
$458$	4.35890	−	7.54983i	0.203678	−	0.352781i
$459$	−1.67945	+	2.90889i	−0.0783900	+	0.135775i
$460$	−1.50000	−	2.59808i	−0.0699379	−	0.121136i
$461$	−9.00000	+	15.5885i	−0.419172	+	0.726027i	−0.995856	−	0.0909401i	$-0.971013\pi$
$461$	−9.00000	+	15.5885i	−0.419172	+	0.726027i	0.576685	+	0.816967i	$0.304346\pi$
$462$	6.53835	+	11.3248i	0.304191	+	0.526875i
$463$	−17.7945			−0.826980			−0.413490	−	0.910509i	$-0.635690\pi$
$463$	−17.7945			−0.826980			−0.413490	+	0.910509i	$0.635690\pi$
$464$	9.35890			0.434476
$465$	−5.35890	−	9.28189i	−0.248513	−	0.430437i
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	28.7945			1.33245			0.666225	−	0.745751i	$-0.267909\pi$
$467$	28.7945			1.33245			0.666225	+	0.745751i	$0.267909\pi$
$468$	−4.00000			−0.184900
$469$	24.7561	+	42.8789i	1.14313	+	1.97996i
$470$	3.00000	−	5.19615i	0.138380	−	0.239681i
$471$	−2.50000	−	4.33013i	−0.115194	−	0.199522i
$472$	6.35890	−	11.0139i	0.292692	−	0.506957i
$473$	−15.0000	+	25.9808i	−0.689701	+	1.19460i
$474$	4.71780			0.216696
$475$	4.35890			0.200000
$476$	−14.6411			−0.671074
$477$	6.53835	−	11.3248i	0.299370	−	0.518525i
$478$	−6.71780	+	11.6356i	−0.307265	+	0.532198i
$479$	11.0383	+	19.1190i	0.504355	+	0.873569i	0.999987	+	0.00503606i	$0.00160303\pi$
$479$	11.0383	+	19.1190i	0.504355	+	0.873569i	−0.495632	+	0.868532i	$0.665064\pi$
$480$	−0.500000	+	0.866025i	−0.0228218	+	0.0395285i
$481$	−14.0000	−	24.2487i	−0.638345	−	1.10565i
$482$	4.00000			0.182195
$483$	13.0767			0.595010
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	−7.03835	−	12.1908i	−0.319595	−	0.553555i
$486$	−1.00000			−0.0453609
$487$	−9.64110			−0.436880			−0.218440	−	0.975850i	$-0.570097\pi$
$487$	−9.64110			−0.436880			−0.218440	+	0.975850i	$0.570097\pi$
$488$	2.67945	+	4.64094i	0.121293	+	0.210086i
$489$	2.35890	−	4.08573i	0.106673	−	0.184763i
$490$	−6.00000	−	10.3923i	−0.271052	−	0.469476i
$491$	−7.50000	+	12.9904i	−0.338470	+	0.586248i	−0.984145	−	0.177365i	$-0.943243\pi$
$491$	−7.50000	+	12.9904i	−0.338470	+	0.586248i	0.645675	+	0.763612i	$0.276576\pi$
$492$	3.17945	−	5.50697i	0.143341	−	0.248273i
$493$	31.4356			1.41579
$494$	−8.71780	+	15.0997i	−0.392232	+	0.679366i
$495$	3.00000			0.134840
$496$	5.35890	−	9.28189i	0.240622	−	0.416769i
$497$	−21.9617	+	38.0387i	−0.985115	+	1.70627i
$498$	−3.00000	−	5.19615i	−0.134433	−	0.232845i
$499$	7.82055	−	13.5456i	0.350096	−	0.606384i	−0.636170	−	0.771549i	$-0.719482\pi$
$499$	7.82055	−	13.5456i	0.350096	−	0.606384i	0.986266	+	0.165165i	$0.0528157\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−22.4356			−1.00235
$502$	12.0000			0.535586
$503$	−14.9356	−	25.8692i	−0.665945	−	1.15345i	−0.979028	−	0.203725i	$-0.934695\pi$
$503$	−14.9356	−	25.8692i	−0.665945	−	1.15345i	0.313083	−	0.949726i	$-0.398638\pi$
$504$	−2.17945	−	3.77492i	−0.0970804	−	0.168148i
$505$	12.7178			0.565935
$506$	−9.00000			−0.400099
$507$	−1.50000	−	2.59808i	−0.0666173	−	0.115385i
$508$	5.17945	−	8.97107i	0.229801	−	0.398027i
$509$	−12.3589	−	21.4062i	−0.547799	−	0.948815i	−0.998425	−	0.0561023i	$-0.982133\pi$
$509$	−12.3589	−	21.4062i	−0.547799	−	0.948815i	0.450626	−	0.892713i	$-0.351201\pi$
$510$	−1.67945	+	2.90889i	−0.0743673	+	0.128808i
$511$	10.1150	−	17.5198i	0.447463	−	0.775029i
$512$	−1.00000			−0.0441942
$513$	−2.17945	+	3.77492i	−0.0962250	+	0.166667i
$514$	7.43560			0.327970
$515$	−5.17945	+	8.97107i	−0.228234	+	0.395313i
$516$	5.00000	−	8.66025i	0.220113	−	0.381246i
$517$	−9.00000	−	15.5885i	−0.395820	−	0.685580i
$518$	15.2561	−	26.4244i	0.670317	−	1.16102i
$519$	−9.17945	−	15.8993i	−0.402933	−	0.697901i
$520$	−4.00000			−0.175412
$521$	23.2822			1.02001			0.510006	−	0.860171i	$-0.329643\pi$
$521$	23.2822			1.02001			0.510006	+	0.860171i	$0.329643\pi$
$522$	4.67945	+	8.10504i	0.204814	+	0.354748i
$523$	19.3972	+	33.5970i	0.848182	+	1.46910i	0.882829	+	0.469695i	$0.155636\pi$
$523$	19.3972	+	33.5970i	0.848182	+	1.46910i	−0.0346461	+	0.999400i	$0.511030\pi$
$524$	−3.00000			−0.131056
$525$	−4.35890			−0.190238
$526$	−4.14110	−	7.17260i	−0.180561	−	0.312740i
$527$	18.0000	−	31.1769i	0.784092	−	1.35809i
$528$	1.50000	+	2.59808i	0.0652791	+	0.113067i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	6.53835	−	11.3248i	0.284008	−	0.491916i
$531$	12.7178			0.551905
$532$	−19.0000			−0.823754
$533$	25.4356			1.10174
$534$	0.179449	−	0.310816i	0.00776554	−	0.0134503i
$535$	4.67945	−	8.10504i	0.202310	−	0.350412i
$536$	5.67945	+	9.83710i	0.245315	+	0.424898i
$537$	−7.85890	+	13.6120i	−0.339137	+	0.587402i
$538$	1.67945	+	2.90889i	0.0724062	+	0.125411i
$539$	−36.0000			−1.55063
$540$	−1.00000			−0.0430331
$541$	4.64110	+	8.03862i	0.199537	+	0.345607i	0.948378	−	0.317142i	$-0.102723\pi$
$541$	4.64110	+	8.03862i	0.199537	+	0.345607i	−0.748842	+	0.662749i	$0.769390\pi$
$542$	−2.35890	−	4.08573i	−0.101323	−	0.175497i
$543$	18.0767			0.775745
$544$	−3.35890			−0.144012
$545$	5.32055	+	9.21546i	0.227907	+	0.394747i
$546$	8.71780	−	15.0997i	0.373087	−	0.646206i
$547$	3.07670	+	5.32900i	0.131550	+	0.227851i	0.924274	−	0.381729i	$-0.124671\pi$
$547$	3.07670	+	5.32900i	0.131550	+	0.227851i	−0.792724	+	0.609580i	$0.791338\pi$
$548$	−6.00000	+	10.3923i	−0.256307	+	0.443937i
$549$	−2.67945	+	4.64094i	−0.114356	+	0.198071i
$550$	3.00000			0.127920
$551$	40.7945			1.73790
$552$	3.00000			0.127688
$553$	−10.2822	+	17.8093i	−0.437244	+	0.757328i
$554$	−2.00000	+	3.46410i	−0.0849719	+	0.147176i
$555$	−3.50000	−	6.06218i	−0.148567	−	0.257325i
$556$	−0.641101	+	1.11042i	−0.0271887	+	0.0470923i
$557$	5.46165	+	9.45986i	0.231418	+	0.400827i	0.958226	−	0.286014i	$-0.0923303\pi$
$557$	5.46165	+	9.45986i	0.231418	+	0.400827i	−0.726808	+	0.686841i	$0.758997\pi$
$558$	10.7178			0.453721
$559$	40.0000			1.69182
$560$	−2.17945	−	3.77492i	−0.0920985	−	0.159519i
$561$	5.03835	+	8.72668i	0.212719	+	0.368441i
$562$	−1.07670			−0.0454177
$563$	12.0000			0.505740			0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000			0.505740			0.252870	+	0.967500i	$0.418626\pi$
$564$	3.00000	+	5.19615i	0.126323	+	0.218797i
$565$	1.67945	−	2.90889i	0.0706550	−	0.122378i
$566$	4.35890	+	7.54983i	0.183218	+	0.317343i
$567$	2.17945	−	3.77492i	0.0915283	−	0.158532i
$568$	−5.03835	+	8.72668i	−0.211404	+	0.366163i
$569$	−37.7945			−1.58443			−0.792214	−	0.610244i	$-0.791072\pi$
$569$	−37.7945			−1.58443			−0.792214	+	0.610244i	$0.791072\pi$
$570$	−2.17945	+	3.77492i	−0.0912871	+	0.158114i
$571$	34.1534			1.42928			0.714638	−	0.699495i	$-0.246592\pi$
$571$	34.1534			1.42928			0.714638	+	0.699495i	$0.246592\pi$
$572$	−6.00000	+	10.3923i	−0.250873	+	0.434524i
$573$	9.71780	−	16.8317i	0.405967	−	0.703155i
$574$	13.8589	+	24.0043i	0.578459	+	1.00192i
$575$	1.50000	−	2.59808i	0.0625543	−	0.108347i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	18.7945			0.782425			0.391213	−	0.920300i	$-0.372056\pi$
$577$	18.7945			0.782425			0.391213	+	0.920300i	$0.372056\pi$
$578$	5.71780			0.237829
$579$	−12.0383	−	20.8510i	−0.500297	−	0.866539i
$580$	4.67945	+	8.10504i	0.194304	+	0.336544i
$581$	26.1534			1.08503
$582$	14.0767			0.583498
$583$	−19.6150	−	33.9743i	−0.812372	−	1.40707i
$584$	2.32055	−	4.01931i	0.0960251	−	0.166320i
$585$	−2.00000	−	3.46410i	−0.0826898	−	0.143223i
$586$	2.82055	−	4.88534i	0.116516	−	0.201811i
$587$	21.3589	−	36.9947i	0.881576	−	1.52693i	0.0319878	−	0.999488i	$-0.489816\pi$
$587$	21.3589	−	36.9947i	0.881576	−	1.52693i	0.849588	−	0.527446i	$-0.176850\pi$
$588$	12.0000			0.494872
$589$	23.3589	−	40.4588i	0.962487	−	1.66708i
$590$	12.7178			0.523583
$591$	2.82055	−	4.88534i	0.116022	−	0.200956i
$592$	3.50000	−	6.06218i	0.143849	−	0.249154i
$593$	−3.96165	−	6.86178i	−0.162686	−	0.281780i	0.773145	−	0.634229i	$-0.218682\pi$
$593$	−3.96165	−	6.86178i	−0.162686	−	0.281780i	−0.935831	+	0.352449i	$0.885349\pi$
$594$	−1.50000	+	2.59808i	−0.0615457	+	0.106600i
$595$	−7.32055	−	12.6796i	−0.300113	−	0.519812i
$596$	−10.0767			−0.412758
$597$	16.6411			0.681075
$598$	6.00000	+	10.3923i	0.245358	+	0.424973i
$599$	−13.3206	−	23.0719i	−0.544263	−	0.942691i	−0.998653	−	0.0518882i	$-0.983476\pi$
$599$	−13.3206	−	23.0719i	−0.544263	−	0.942691i	0.454390	−	0.890803i	$-0.349857\pi$
$600$	−1.00000			−0.0408248
$601$	5.71780			0.233234			0.116617	−	0.993177i	$-0.462795\pi$
$601$	5.71780			0.233234			0.116617	+	0.993177i	$0.462795\pi$
$602$	21.7945	+	37.7492i	0.888277	+	1.53854i
$603$	−5.67945	+	9.83710i	−0.231285	+	0.400597i
$604$	1.03835	+	1.79847i	0.0422498	+	0.0731788i
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$	−6.35890	+	11.0139i	−0.258313	+	0.447411i
$607$	−35.7945			−1.45285			−0.726427	−	0.687244i	$-0.758820\pi$
$607$	−35.7945			−1.45285			−0.726427	+	0.687244i	$0.758820\pi$
$608$	−4.35890			−0.176777
$609$	−40.7945			−1.65308
$610$	−2.67945	+	4.64094i	−0.108488	+	0.187906i
$611$	−12.0000	+	20.7846i	−0.485468	+	0.840855i
$612$	−1.67945	−	2.90889i	−0.0678877	−	0.117585i
$613$	−3.21780	+	5.57339i	−0.129966	+	0.225107i	−0.923663	−	0.383206i	$-0.874820\pi$
$613$	−3.21780	+	5.57339i	−0.129966	+	0.225107i	0.793697	+	0.608313i	$0.208153\pi$
$614$	−0.679449	−	1.17684i	−0.0274203	−	0.0474934i
$615$	6.35890			0.256416
$616$	−13.0767			−0.526875
$617$	0.717798	+	1.24326i	0.0288975	+	0.0500519i	0.880112	−	0.474765i	$-0.157467\pi$
$617$	0.717798	+	1.24326i	0.0288975	+	0.0500519i	−0.851215	+	0.524817i	$0.824134\pi$
$618$	−5.17945	−	8.97107i	−0.208348	−	0.360869i
$619$	−3.64110			−0.146348			−0.0731741	−	0.997319i	$-0.523313\pi$
$619$	−3.64110			−0.146348			−0.0731741	+	0.997319i	$0.523313\pi$
$620$	10.7178			0.430437
$621$	1.50000	+	2.59808i	0.0601929	+	0.104257i
$622$	0.717798	−	1.24326i	0.0287811	−	0.0498503i
$623$	0.782202	+	1.35481i	0.0313383	+	0.0542795i
$624$	2.00000	−	3.46410i	0.0800641	−	0.138675i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	17.4356			0.696867
$627$	6.53835	+	11.3248i	0.261116	+	0.452267i
$628$	5.00000			0.199522
$629$	11.7561	−	20.3622i	0.468748	−	0.811896i
$630$	2.17945	−	3.77492i	0.0868313	−	0.150396i
$631$	−20.6794	−	35.8179i	−0.823236	−	1.42589i	−0.903260	−	0.429093i	$-0.858833\pi$
$631$	−20.6794	−	35.8179i	−0.823236	−	1.42589i	0.0800242	−	0.996793i	$-0.474500\pi$
$632$	−2.35890	+	4.08573i	−0.0938320	+	0.162522i
$633$	−7.53835	−	13.0568i	−0.299622	−	0.518961i
$634$	−19.0767			−0.757632
$635$	10.3589			0.411080
$636$	6.53835	+	11.3248i	0.259262	+	0.449056i
$637$	24.0000	+	41.5692i	0.950915	+	1.64703i
$638$	28.0767			1.11157
$639$	−10.0767			−0.398628
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	5.64110	−	9.77067i	0.222810	−	0.385918i	−0.732850	−	0.680390i	$-0.761810\pi$
$641$	5.64110	−	9.77067i	0.222810	−	0.385918i	0.955660	+	0.294472i	$0.0951437\pi$
$642$	4.67945	+	8.10504i	0.184683	+	0.319881i
$643$	19.7561	−	34.2186i	0.779106	−	1.34945i	−0.153351	−	0.988172i	$-0.549007\pi$
$643$	19.7561	−	34.2186i	0.779106	−	1.34945i	0.932457	−	0.361280i	$-0.117660\pi$
$644$	−6.53835	+	11.3248i	−0.257647	+	0.446258i
$645$	10.0000			0.393750
$646$	−14.6411			−0.576046
$647$	−17.1534			−0.674369			−0.337185	−	0.941438i	$-0.609475\pi$
$647$	−17.1534			−0.674369			−0.337185	+	0.941438i	$0.609475\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	19.0767	−	33.0418i	0.748826	−	1.29700i
$650$	−2.00000	−	3.46410i	−0.0784465	−	0.135873i
$651$	−23.3589	+	40.4588i	−0.915507	+	1.58571i
$652$	2.35890	+	4.08573i	0.0923816	+	0.160010i
$653$	−25.0767			−0.981327			−0.490663	−	0.871349i	$-0.663246\pi$
$653$	−25.0767			−0.981327			−0.490663	+	0.871349i	$0.663246\pi$
$654$	−10.6411			−0.416100
$655$	−1.50000	−	2.59808i	−0.0586098	−	0.101515i
$656$	3.17945	+	5.50697i	0.124137	+	0.215011i
$657$	4.64110			0.181067
$658$	−26.1534			−1.01957
$659$	19.8589	+	34.3966i	0.773593	+	1.33990i	0.935582	+	0.353110i	$0.114876\pi$
$659$	19.8589	+	34.3966i	0.773593	+	1.33990i	−0.161989	+	0.986793i	$0.551791\pi$
$660$	−1.50000	+	2.59808i	−0.0583874	+	0.101130i
$661$	8.71780	+	15.0997i	0.339083	+	0.587309i	0.984261	−	0.176724i	$-0.0565499\pi$
$661$	8.71780	+	15.0997i	0.339083	+	0.587309i	−0.645177	+	0.764033i	$0.723217\pi$
$662$	7.17945	−	12.4352i	0.279037	−	0.483307i
$663$	6.71780	−	11.6356i	0.260898	−	0.451888i
$664$	6.00000			0.232845
$665$	−9.50000	−	16.4545i	−0.368394	−	0.638077i
$666$	7.00000			0.271244
$667$	14.0383	−	24.3151i	0.543567	−	0.941486i
$668$	11.2178	−	19.4298i	0.434030	−	0.751761i
$669$	−10.1794	−	17.6313i	−0.393560	−	0.681666i
$670$	−5.67945	+	9.83710i	−0.219416	+	0.380040i
$671$	8.03835	+	13.9228i	0.310317	+	0.537485i
$672$	4.35890			0.168148
$673$	−21.2822			−0.820369			−0.410184	−	0.912003i	$-0.634536\pi$
$673$	−21.2822			−0.820369			−0.410184	+	0.912003i	$0.634536\pi$
$674$	11.0767	+	19.1854i	0.426658	+	0.738994i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	3.00000			0.115385
$677$	7.07670			0.271980			0.135990	−	0.990710i	$-0.456579\pi$
$677$	7.07670			0.271980			0.135990	+	0.990710i	$0.456579\pi$
$678$	1.67945	+	2.90889i	0.0644989	+	0.111715i
$679$	−30.6794	+	53.1384i	−1.17737	+	2.03926i
$680$	−1.67945	−	2.90889i	−0.0644039	−	0.111551i
$681$	1.67945	−	2.90889i	0.0643566	−	0.111469i
$682$	16.0767	−	27.8457i	0.615609	−	1.06627i
$683$	−22.7945			−0.872207			−0.436104	−	0.899896i	$-0.643642\pi$
$683$	−22.7945			−0.872207			−0.436104	+	0.899896i	$0.643642\pi$
$684$	−2.17945	−	3.77492i	−0.0833333	−	0.144338i
$685$	−12.0000			−0.458496
$686$	−10.8972	+	18.8746i	−0.416059	+	0.720635i
$687$	−4.35890	+	7.54983i	−0.166302	+	0.288044i
$688$	5.00000	+	8.66025i	0.190623	+	0.330169i
$689$	−26.1534	+	45.2990i	−0.996365	+	1.72575i
$690$	1.50000	+	2.59808i	0.0571040	+	0.0989071i
$691$	31.6411			1.20368			0.601842	−	0.798615i	$-0.294434\pi$
$691$	31.6411			1.20368			0.601842	+	0.798615i	$0.294434\pi$
$692$	18.3589			0.697901
$693$	−6.53835	−	11.3248i	−0.248371	−	0.430192i
$694$	−3.71780	−	6.43941i	−0.141126	−	0.244437i
$695$	−1.28220			−0.0486367
$696$	−9.35890			−0.354748
$697$	10.6794	+	18.4973i	0.404513	+	0.700637i
$698$	0.0383484	−	0.0664214i	0.00145151	−	0.00251409i
$699$	−3.00000	−	5.19615i	−0.113470	−	0.196537i
$700$	2.17945	−	3.77492i	0.0823754	−	0.142678i
$701$	−9.00000	+	15.5885i	−0.339925	+	0.588768i	−0.984418	−	0.175842i	$-0.943735\pi$
$701$	−9.00000	+	15.5885i	−0.339925	+	0.588768i	0.644493	+	0.764610i	$0.277068\pi$
$702$	4.00000			0.150970
$703$	15.2561	−	26.4244i	0.575396	−	0.996616i
$704$	−3.00000			−0.113067
$705$	−3.00000	+	5.19615i	−0.112987	+	0.195698i
$706$	−5.03835	+	8.72668i	−0.189621	+	0.328433i
$707$	−27.7178	−	48.0086i	−1.04244	−	1.80555i
$708$	−6.35890	+	11.0139i	−0.238982	+	0.413929i
$709$	13.3972	+	23.2047i	0.503144	+	0.871471i	0.999993	+	0.00363441i	$0.00115687\pi$
$709$	13.3972	+	23.2047i	0.503144	+	0.871471i	−0.496849	+	0.867837i	$0.665510\pi$
$710$	−10.0767			−0.378172
$711$	−4.71780			−0.176931
$712$	0.179449	+	0.310816i	0.00672515	+	0.0116483i
$713$	−16.0767	−	27.8457i	−0.602077	−	1.04283i
$714$	14.6411			0.547929
$715$	−12.0000			−0.448775
$716$	−7.85890	−	13.6120i	−0.293701	−	0.508705i
$717$	6.71780	−	11.6356i	0.250881	−	0.434538i
$718$	7.67945	+	13.3012i	0.286595	+	0.496396i
$719$	8.64110	−	14.9668i	0.322259	−	0.558168i	−0.658695	−	0.752410i	$-0.728891\pi$
$719$	8.64110	−	14.9668i	0.322259	−	0.558168i	0.980954	+	0.194242i	$0.0622246\pi$
$720$	0.500000	−	0.866025i	0.0186339	−	0.0322749i
$721$	45.1534			1.68160
$722$	−19.0000			−0.707107
$723$	−4.00000			−0.148762
$724$	−9.03835	+	15.6549i	−0.335908	+	0.581809i
$725$	−4.67945	+	8.10504i	−0.173790	+	0.301014i
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$	15.0767	−	26.1136i	0.559164	−	0.968500i	−0.438403	−	0.898779i	$-0.644456\pi$
$727$	15.0767	−	26.1136i	0.559164	−	0.968500i	0.997567	−	0.0697214i	$-0.0222110\pi$
$728$	8.71780	+	15.0997i	0.323103	+	0.559631i
$729$	1.00000			0.0370370
$730$	4.64110			0.171775
$731$	16.7945	+	29.0889i	0.621167	+	1.07589i
$732$	−2.67945	−	4.64094i	−0.0990353	−	0.171534i
$733$	9.56440			0.353269			0.176635	−	0.984276i	$-0.443479\pi$
$733$	9.56440			0.353269			0.176635	+	0.984276i	$0.443479\pi$
$734$	−14.7178			−0.543244
$735$	6.00000	+	10.3923i	0.221313	+	0.383326i
$736$	−1.50000	+	2.59808i	−0.0552907	+	0.0957664i
$737$	17.0383	+	29.5113i	0.627616	+	1.08706i
$738$	−3.17945	+	5.50697i	−0.117037	+	0.202714i
$739$	8.17945	−	14.1672i	0.300886	−	0.521150i	−0.675451	−	0.737405i	$-0.736051\pi$
$739$	8.17945	−	14.1672i	0.300886	−	0.521150i	0.976337	+	0.216255i	$0.0693843\pi$
$740$	7.00000			0.257325
$741$	8.71780	−	15.0997i	0.320256	−	0.554700i
$742$	−57.0000			−2.09254
$743$	−4.50000	+	7.79423i	−0.165089	+	0.285943i	−0.936687	−	0.350168i	$-0.886124\pi$
$743$	−4.50000	+	7.79423i	−0.165089	+	0.285943i	0.771598	+	0.636111i	$0.219458\pi$
$744$	−5.35890	+	9.28189i	−0.196467	+	0.340290i
$745$	−5.03835	−	8.72668i	−0.184591	−	0.319721i
$746$	5.50000	−	9.52628i	0.201369	−	0.348782i
$747$	3.00000	+	5.19615i	0.109764	+	0.190117i
$748$	−10.0767			−0.368441
$749$	−40.7945			−1.49060
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	−11.4356	−	19.8070i	−0.417291	−	0.722769i	0.578375	−	0.815771i	$-0.303687\pi$
$751$	−11.4356	−	19.8070i	−0.417291	−	0.722769i	−0.995666	+	0.0930021i	$0.970354\pi$
$752$	−6.00000			−0.218797
$753$	−12.0000			−0.437304
$754$	−18.7178	−	32.4202i	−0.681662	−	1.18067i
$755$	−1.03835	+	1.79847i	−0.0377894	+	0.0654531i
$756$	2.17945	+	3.77492i	0.0792658	+	0.137292i
$757$	−24.9356	+	43.1897i	−0.906300	+	1.56976i	−0.0871365	+	0.996196i	$0.527772\pi$
$757$	−24.9356	+	43.1897i	−0.906300	+	1.56976i	−0.819163	+	0.573561i	$0.805562\pi$
$758$	7.35890	−	12.7460i	0.267287	−	0.462955i
$759$	9.00000			0.326679
$760$	−2.17945	−	3.77492i	−0.0790569	−	0.136931i
$761$	−7.07670			−0.256530			−0.128265	−	0.991740i	$-0.540941\pi$
$761$	−7.07670			−0.256530			−0.128265	+	0.991740i	$0.540941\pi$
$762$	−5.17945	+	8.97107i	−0.187632	+	0.324988i
$763$	23.1917	−	40.1693i	0.839597	−	1.45423i
$764$	9.71780	+	16.8317i	0.351578	+	0.608950i
$765$	1.67945	−	2.90889i	0.0607206	−	0.105171i
$766$	3.00000	+	5.19615i	0.108394	+	0.187745i
$767$	−50.8712			−1.83685
$768$	1.00000			0.0360844
$769$	−1.35890	−	2.35368i	−0.0490031	−	0.0848759i	0.840483	−	0.541837i	$-0.182271\pi$
$769$	−1.35890	−	2.35368i	−0.0490031	−	0.0848759i	−0.889487	+	0.456961i	$0.848938\pi$
$770$	−6.53835	−	11.3248i	−0.235626	−	0.408116i
$771$	−7.43560			−0.267786
$772$	24.0767			0.866539
$773$	0.897247	+	1.55408i	0.0322717	+	0.0558963i	0.881710	−	0.471791i	$-0.156392\pi$
$773$	0.897247	+	1.55408i	0.0322717	+	0.0558963i	−0.849438	+	0.527688i	$0.823059\pi$
$774$	−5.00000	+	8.66025i	−0.179721	+	0.311286i
$775$	5.35890	+	9.28189i	0.192497	+	0.333415i
$776$	−7.03835	+	12.1908i	−0.252662	+	0.437623i
$777$	−15.2561	+	26.4244i	−0.547311	+	0.947971i
$778$	−4.07670

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} -4.35890 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} -4.35890 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} -3.00000 q^{11} +1.00000 q^{12} +(2.00000 + 3.46410i) q^{13} +(-2.17945 + 3.77492i) q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.67945 + 2.90889i) q^{17} -1.00000 q^{18} +(-2.17945 + 3.77492i) q^{19} -1.00000 q^{20} +(2.17945 - 3.77492i) q^{21} +(-1.50000 + 2.59808i) q^{22} +(1.50000 + 2.59808i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +4.00000 q^{26} +1.00000 q^{27} +(2.17945 + 3.77492i) q^{28} +(-4.67945 - 8.10504i) q^{29} +1.00000 q^{30} -10.7178 q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +(1.67945 + 2.90889i) q^{34} +(-2.17945 + 3.77492i) q^{35} +(-0.500000 + 0.866025i) q^{36} -7.00000 q^{37} +(2.17945 + 3.77492i) q^{38} -4.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(3.17945 - 5.50697i) q^{41} +(-2.17945 - 3.77492i) q^{42} +(5.00000 - 8.66025i) q^{43} +(1.50000 + 2.59808i) q^{44} -1.00000 q^{45} +3.00000 q^{46} +(3.00000 + 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{48} +12.0000 q^{49} -1.00000 q^{50} +(-1.67945 - 2.90889i) q^{51} +(2.00000 - 3.46410i) q^{52} +(6.53835 + 11.3248i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-1.50000 + 2.59808i) q^{55} +4.35890 q^{56} +(-2.17945 - 3.77492i) q^{57} -9.35890 q^{58} +(-6.35890 + 11.0139i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-2.67945 - 4.64094i) q^{61} +(-5.35890 + 9.28189i) q^{62} +(2.17945 + 3.77492i) q^{63} +1.00000 q^{64} +4.00000 q^{65} +(-1.50000 - 2.59808i) q^{66} +(-5.67945 - 9.83710i) q^{67} +3.35890 q^{68} -3.00000 q^{69} +(2.17945 + 3.77492i) q^{70} +(5.03835 - 8.72668i) q^{71} +(0.500000 + 0.866025i) q^{72} +(-2.32055 + 4.01931i) q^{73} +(-3.50000 + 6.06218i) q^{74} +1.00000 q^{75} +4.35890 q^{76} +13.0767 q^{77} +(-2.00000 + 3.46410i) q^{78} +(2.35890 - 4.08573i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.17945 - 5.50697i) q^{82} -6.00000 q^{83} -4.35890 q^{84} +(1.67945 + 2.90889i) q^{85} +(-5.00000 - 8.66025i) q^{86} +9.35890 q^{87} +3.00000 q^{88} +(-0.179449 - 0.310816i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-8.71780 - 15.0997i) q^{91} +(1.50000 - 2.59808i) q^{92} +(5.35890 - 9.28189i) q^{93} +6.00000 q^{94} +(2.17945 + 3.77492i) q^{95} -1.00000 q^{96} +(7.03835 - 12.1908i) q^{97} +(6.00000 - 10.3923i) q^{98} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{5} + 2q^{6} - 4q^{8} - 2q^{9} + O(q^{10}) \)	\( 4q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{5} + 2q^{6} - 4q^{8} - 2q^{9} - 2q^{10} - 12q^{11} + 4q^{12} + 8q^{13} + 2q^{15} - 2q^{16} + 2q^{17} - 4q^{18} - 4q^{20} - 6q^{22} + 6q^{23} + 2q^{24} - 2q^{25} + 16q^{26} + 4q^{27} - 10q^{29} + 4q^{30} - 8q^{31} + 2q^{32} + 6q^{33} - 2q^{34} - 2q^{36} - 28q^{37} - 16q^{39} - 2q^{40} + 4q^{41} + 20q^{43} + 6q^{44} - 4q^{45} + 12q^{46} + 12q^{47} - 2q^{48} + 48q^{49} - 4q^{50} + 2q^{51} + 8q^{52} + 2q^{54} - 6q^{55} - 20q^{58} - 8q^{59} + 2q^{60} - 2q^{61} - 4q^{62} + 4q^{64} + 16q^{65} - 6q^{66} - 14q^{67} - 4q^{68} - 12q^{69} - 6q^{71} + 2q^{72} - 18q^{73} - 14q^{74} + 4q^{75} - 8q^{78} - 8q^{79} + 2q^{80} - 2q^{81} - 4q^{82} - 24q^{83} - 2q^{85} - 20q^{86} + 20q^{87} + 12q^{88} + 8q^{89} - 2q^{90} + 6q^{92} + 4q^{93} + 24q^{94} - 4q^{96} + 2q^{97} + 24q^{98} + 6q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more about