LMFDB - Embedded newform 570.2.s.a.221.6

Newspace parameters

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.s (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			221.6
Character	$\chi$	$=$	570.221
Dual form			570.2.s.a.521.6

$q$-expansion

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.0903420 - 1.72969i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.54313 + 0.786608i) q^{6} +2.34168 q^{7} +1.00000 q^{8} +(-2.98368 - 0.312528i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.0903420 - 1.72969i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.54313 + 0.786608i) q^{6} +2.34168 q^{7} +1.00000 q^{8} +(-2.98368 - 0.312528i) q^{9} +(-0.866025 - 0.500000i) q^{10} -2.39841i q^{11} +(1.45279 + 0.943085i) q^{12} +(-0.414577 - 0.239356i) q^{13} +(-1.17084 - 2.02795i) q^{14} +(-0.786608 - 1.54313i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.40013 - 1.38572i) q^{17} +(1.22118 + 2.74020i) q^{18} +(0.994947 - 4.24383i) q^{19} +1.00000i q^{20} +(0.211552 - 4.05038i) q^{21} +(-2.07709 + 1.19921i) q^{22} +(-1.80040 - 1.03946i) q^{23} +(0.0903420 - 1.72969i) q^{24} +(0.500000 - 0.866025i) q^{25} +0.478712i q^{26} +(-0.810128 + 5.13261i) q^{27} +(-1.17084 + 2.02795i) q^{28} +(0.313727 - 0.543392i) q^{29} +(-0.943085 + 1.45279i) q^{30} -2.05113i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-4.14852 - 0.216677i) q^{33} +(-2.40013 - 1.38572i) q^{34} +(2.02795 - 1.17084i) q^{35} +(1.76250 - 2.42768i) q^{36} +5.67577i q^{37} +(-4.17274 + 1.26026i) q^{38} +(-0.451467 + 0.695467i) q^{39} +(0.866025 - 0.500000i) q^{40} +(-1.04624 - 1.81214i) q^{41} +(-3.61351 + 1.84198i) q^{42} +(-3.77271 - 6.53452i) q^{43} +(2.07709 + 1.19921i) q^{44} +(-2.74020 + 1.22118i) q^{45} +2.07892i q^{46} +(-1.94389 - 1.12231i) q^{47} +(-1.54313 + 0.786608i) q^{48} -1.51654 q^{49} -1.00000 q^{50} +(-2.18003 - 4.27668i) q^{51} +(0.414577 - 0.239356i) q^{52} +(-6.64114 + 11.5028i) q^{53} +(4.85004 - 1.86471i) q^{54} +(-1.19921 - 2.07709i) q^{55} +2.34168 q^{56} +(-7.25064 - 2.10435i) q^{57} -0.627455 q^{58} +(3.13769 + 5.43465i) q^{59} +(1.72969 + 0.0903420i) q^{60} +(1.25195 - 2.16845i) q^{61} +(-1.77633 + 1.02556i) q^{62} +(-6.98681 - 0.731839i) q^{63} +1.00000 q^{64} -0.478712 q^{65} +(1.88661 + 3.70106i) q^{66} +(11.3258 + 6.53894i) q^{67} +2.77143i q^{68} +(-1.96060 + 3.02023i) q^{69} +(-2.02795 - 1.17084i) q^{70} +(2.68385 + 4.64856i) q^{71} +(-2.98368 - 0.312528i) q^{72} +(-5.81045 - 10.0640i) q^{73} +(4.91536 - 2.83789i) q^{74} +(-1.45279 - 0.943085i) q^{75} +(3.17779 + 2.98356i) q^{76} -5.61632i q^{77} +(0.828026 + 0.0432478i) q^{78} +(10.1589 - 5.86527i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(8.80465 + 1.86496i) q^{81} +(-1.04624 + 1.81214i) q^{82} +11.3081i q^{83} +(3.40196 + 2.20840i) q^{84} +(1.38572 - 2.40013i) q^{85} +(-3.77271 + 6.53452i) q^{86} +(-0.911558 - 0.591743i) q^{87} -2.39841i q^{88} +(4.97362 - 8.61457i) q^{89} +(2.42768 + 1.76250i) q^{90} +(-0.970806 - 0.560495i) q^{91} +(1.80040 - 1.03946i) q^{92} +(-3.54782 - 0.185303i) q^{93} +2.24461i q^{94} +(-1.26026 - 4.17274i) q^{95} +(1.45279 + 0.943085i) q^{96} +(7.49209 - 4.32556i) q^{97} +(0.758271 + 1.31336i) q^{98} +(-0.749571 + 7.15609i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24q - 12q^{2} + 4q^{3} - 12q^{4} - 2q^{6} - 12q^{7} + 24q^{8} - 4q^{9} + O(q^{10}) $	$ 24q - 12q^{2} + 4q^{3} - 12q^{4} - 2q^{6} - 12q^{7} + 24q^{8} - 4q^{9} - 2q^{12} + 18q^{13} + 6q^{14} - 12q^{16} + 12q^{17} + 2q^{18} + 6q^{19} - 6q^{21} + 18q^{22} + 4q^{24} + 12q^{25} + 28q^{27} + 6q^{28} - 12q^{32} - 22q^{33} - 12q^{34} + 2q^{36} + 6q^{38} + 40q^{39} + 6q^{41} - 6q^{42} - 22q^{43} - 18q^{44} + 8q^{45} + 12q^{47} - 2q^{48} + 12q^{49} - 24q^{50} - 20q^{51} - 18q^{52} + 8q^{53} + 4q^{54} - 12q^{56} + 26q^{59} + 22q^{61} - 18q^{62} + 6q^{63} + 24q^{64} + 8q^{65} + 8q^{66} - 48q^{67} - 64q^{69} + 24q^{71} - 4q^{72} - 8q^{73} + 30q^{74} + 2q^{75} - 12q^{76} - 38q^{78} + 18q^{79} - 12q^{81} + 6q^{82} + 12q^{84} - 22q^{86} - 24q^{87} + 28q^{89} + 8q^{90} + 18q^{91} + 2q^{93} - 2q^{96} + 6q^{97} - 6q^{98} + 2q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	0.0903420	−	1.72969i	0.0521590	−	0.998639i
$3$	0.0903420	−	1.72969i	0.0521590	−	0.998639i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	−1.54313	+	0.786608i	−0.629980	+	0.321131i
$7$	2.34168			0.885071			0.442536	−	0.896751i	$-0.354079\pi$
$7$	2.34168			0.885071			0.442536	+	0.896751i	$0.354079\pi$
$8$	1.00000			0.353553
$9$	−2.98368	−	0.312528i	−0.994559	−	0.104176i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$		−	2.39841i		−	0.723149i	−0.932343	−	0.361575i	$-0.882239\pi$
$11$		−	2.39841i		−	0.723149i	0.932343	−	0.361575i	$-0.117761\pi$
$12$	1.45279	+	0.943085i	0.419384	+	0.272245i
$13$	−0.414577	−	0.239356i	−0.114983	−	0.0663855i	0.441406	−	0.897308i	$-0.354480\pi$
$13$	−0.414577	−	0.239356i	−0.114983	−	0.0663855i	−0.556389	+	0.830922i	$0.687813\pi$
$14$	−1.17084	−	2.02795i	−0.312920	−	0.541993i
$15$	−0.786608	−	1.54313i	−0.203101	−	0.398434i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.40013	−	1.38572i	0.582117	−	0.336086i	−0.179857	−	0.983693i	$-0.557564\pi$
$17$	2.40013	−	1.38572i	0.582117	−	0.336086i	0.761974	+	0.647607i	$0.224230\pi$
$18$	1.22118	+	2.74020i	0.287835	+	0.645872i
$19$	0.994947	−	4.24383i	0.228256	−	0.973601i
$19$	0.994947	−	4.24383i	0.228256	−	0.973601i
$20$			1.00000i			0.223607i
$21$	0.211552	−	4.05038i	0.0461644	−	0.883866i
$22$	−2.07709	+	1.19921i	−0.442837	+	0.255672i
$23$	−1.80040	−	1.03946i	−0.375409	−	0.216743i	0.300410	−	0.953810i	$-0.402877\pi$
$23$	−1.80040	−	1.03946i	−0.375409	−	0.216743i	−0.675819	+	0.737068i	$0.736210\pi$
$24$	0.0903420	−	1.72969i	0.0184410	−	0.353072i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$			0.478712i			0.0938832i
$27$	−0.810128	+	5.13261i	−0.155909	+	0.987771i
$28$	−1.17084	+	2.02795i	−0.221268	+	0.383247i
$29$	0.313727	−	0.543392i	0.0582577	−	0.100905i	−0.835426	−	0.549603i	$-0.814779\pi$
$29$	0.313727	−	0.543392i	0.0582577	−	0.100905i	0.893683	+	0.448698i	$0.148112\pi$
$30$	−0.943085	+	1.45279i	−0.172183	+	0.265241i
$31$		−	2.05113i		−	0.368394i	−0.982889	−	0.184197i	$-0.941032\pi$
$31$		−	2.05113i		−	0.368394i	0.982889	−	0.184197i	$-0.0589684\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−4.14852	−	0.216677i	−0.722165	−	0.0377187i
$34$	−2.40013	−	1.38572i	−0.411619	−	0.237648i
$35$	2.02795	−	1.17084i	0.342787	−	0.197908i
$36$	1.76250	−	2.42768i	0.293749	−	0.404613i
$37$			5.67577i			0.933091i	0.884497	+	0.466546i	$0.154502\pi$
$37$			5.67577i			0.933091i	−0.884497	+	0.466546i	$0.845498\pi$
$38$	−4.17274	+	1.26026i	−0.676907	+	0.204442i
$39$	−0.451467	+	0.695467i	−0.0722925	+	0.111364i
$40$	0.866025	−	0.500000i	0.136931	−	0.0790569i
$41$	−1.04624	−	1.81214i	−0.163395	−	0.283008i	0.772689	−	0.634785i	$-0.218911\pi$
$41$	−1.04624	−	1.81214i	−0.163395	−	0.283008i	−0.936084	+	0.351776i	$0.885578\pi$
$42$	−3.61351	+	1.84198i	−0.557577	+	0.284224i
$43$	−3.77271	−	6.53452i	−0.575333	−	0.996506i	−0.996005	−	0.0892931i	$-0.971539\pi$
$43$	−3.77271	−	6.53452i	−0.575333	−	0.996506i	0.420673	−	0.907213i	$-0.361794\pi$
$44$	2.07709	+	1.19921i	0.313133	+	0.180787i
$45$	−2.74020	+	1.22118i	−0.408485	+	0.182043i
$46$			2.07892i			0.306520i
$47$	−1.94389	−	1.12231i	−0.283546	−	0.163705i	0.351482	−	0.936195i	$-0.385678\pi$
$47$	−1.94389	−	1.12231i	−0.283546	−	0.163705i	−0.635028	+	0.772490i	$0.719011\pi$
$48$	−1.54313	+	0.786608i	−0.222732	+	0.113537i
$49$	−1.51654			−0.216649
$50$	−1.00000			−0.141421
$51$	−2.18003	−	4.27668i	−0.305265	−	0.598855i
$52$	0.414577	−	0.239356i	0.0574915	−	0.0331927i
$53$	−6.64114	+	11.5028i	−0.912231	+	1.58003i	−0.101325	+	0.994853i	$0.532308\pi$
$53$	−6.64114	+	11.5028i	−0.912231	+	1.58003i	−0.810906	+	0.585176i	$0.801025\pi$
$54$	4.85004	−	1.86471i	0.660006	−	0.253755i
$55$	−1.19921	−	2.07709i	−0.161701	−	0.280074i
$56$	2.34168			0.312920
$57$	−7.25064	−	2.10435i	−0.960370	−	0.278728i
$58$	−0.627455			−0.0823889
$59$	3.13769	+	5.43465i	0.408493	+	0.707531i	0.994721	−	0.102615i	$-0.0327211\pi$
$59$	3.13769	+	5.43465i	0.408493	+	0.707531i	−0.586228	+	0.810146i	$0.699388\pi$
$60$	1.72969	+	0.0903420i	0.223302	+	0.0116631i
$61$	1.25195	−	2.16845i	0.160296	−	0.277641i	−0.774679	−	0.632355i	$-0.782088\pi$
$61$	1.25195	−	2.16845i	0.160296	−	0.277641i	0.934975	+	0.354714i	$0.115422\pi$
$62$	−1.77633	+	1.02556i	−0.225594	+	0.130247i
$63$	−6.98681	−	0.731839i	−0.880255	−	0.0922031i
$64$	1.00000			0.125000
$65$	−0.478712			−0.0593770
$66$	1.88661	+	3.70106i	0.232226	+	0.455569i
$67$	11.3258	+	6.53894i	1.38366	+	0.798859i	0.992591	−	0.121501i	$-0.0387707\pi$
$67$	11.3258	+	6.53894i	1.38366	+	0.798859i	0.391073	+	0.920360i	$0.372104\pi$
$68$			2.77143i			0.336086i
$69$	−1.96060	+	3.02023i	−0.236028	+	0.363593i
$70$	−2.02795	−	1.17084i	−0.242387	−	0.139942i
$71$	2.68385	+	4.64856i	0.318514	+	0.551682i	0.980178	−	0.198118i	$-0.0634829\pi$
$71$	2.68385	+	4.64856i	0.318514	+	0.551682i	−0.661664	+	0.749800i	$0.730150\pi$
$72$	−2.98368	−	0.312528i	−0.351630	−	0.0368317i
$73$	−5.81045	−	10.0640i	−0.680062	−	1.17790i	−0.974962	−	0.222373i	$-0.928620\pi$
$73$	−5.81045	−	10.0640i	−0.680062	−	1.17790i	0.294900	−	0.955528i	$-0.404714\pi$
$74$	4.91536	−	2.83789i	0.571399	−	0.329898i
$75$	−1.45279	−	0.943085i	−0.167753	−	0.108898i
$76$	3.17779	+	2.98356i	0.364517	+	0.342238i
$77$		−	5.61632i		−	0.640038i
$78$	0.828026	+	0.0432478i	0.0937554	+	0.00489685i
$79$	10.1589	−	5.86527i	1.14297	−	0.659894i	0.195806	−	0.980643i	$-0.437268\pi$
$79$	10.1589	−	5.86527i	1.14297	−	0.659894i	0.947164	+	0.320749i	$0.103934\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	8.80465	+	1.86496i	0.978295	+	0.207218i
$82$	−1.04624	+	1.81214i	−0.115538	+	0.200117i
$83$			11.3081i			1.24123i	0.784115	+	0.620615i	$0.213117\pi$
$83$			11.3081i			1.24123i	−0.784115	+	0.620615i	$0.786883\pi$
$84$	3.40196	+	2.20840i	0.371184	+	0.240956i
$85$	1.38572	−	2.40013i	0.150302	−	0.260331i
$86$	−3.77271	+	6.53452i	−0.406822	+	0.704636i
$87$	−0.911558	−	0.591743i	−0.0977293	−	0.0634415i
$88$		−	2.39841i		−	0.255672i
$89$	4.97362	−	8.61457i	0.527203	−	0.913142i	−0.472294	−	0.881441i	$-0.656574\pi$
$89$	4.97362	−	8.61457i	0.527203	−	0.913142i	0.999497	−	0.0317016i	$-0.0100926\pi$
$90$	2.42768	+	1.76250i	0.255900	+	0.185783i
$91$	−0.970806	−	0.560495i	−0.101768	−	0.0587559i
$92$	1.80040	−	1.03946i	0.187705	−	0.108371i
$93$	−3.54782	−	0.185303i	−0.367892	−	0.0192150i
$94$			2.24461i			0.231514i
$95$	−1.26026	−	4.17274i	−0.129300	−	0.428114i
$96$	1.45279	+	0.943085i	0.148274	+	0.0962532i
$97$	7.49209	−	4.32556i	0.760706	−	0.439194i	−0.0688431	−	0.997627i	$-0.521931\pi$
$97$	7.49209	−	4.32556i	0.760706	−	0.439194i	0.829549	+	0.558434i	$0.188597\pi$
$98$	0.758271	+	1.31336i	0.0765970	+	0.132670i
$99$	−0.749571	+	7.15609i	−0.0753347	+	0.719214i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−3.96069	−	2.28671i	−0.394103	−	0.227536i	0.289833	−	0.957077i	$-0.406400\pi$
$101$	−3.96069	−	2.28671i	−0.394103	−	0.227536i	−0.683937	+	0.729542i	$0.739733\pi$
$102$	−2.61370	+	4.02630i	−0.258794	+	0.398663i
$103$			2.29913i			0.226540i	0.993564	+	0.113270i	$0.0361325\pi$
$103$			2.29913i			0.226540i	−0.993564	+	0.113270i	$0.963867\pi$
$104$	−0.414577	−	0.239356i	−0.0406526	−	0.0234708i
$105$	−1.84198	−	3.61351i	−0.179759	−	0.352643i
$106$	13.2823			1.29009
$107$	12.1841			1.17788			0.588939	−	0.808177i	$-0.299546\pi$
$107$	12.1841			1.17788			0.588939	+	0.808177i	$0.299546\pi$
$108$	−4.03991	−	3.26790i	−0.388740	−	0.314454i
$109$	−0.624429	+	0.360514i	−0.0598095	+	0.0345310i	−0.529607	−	0.848243i	$-0.677660\pi$
$109$	−0.624429	+	0.360514i	−0.0598095	+	0.0345310i	0.469797	+	0.882774i	$0.344327\pi$
$110$	−1.19921	+	2.07709i	−0.114340	+	0.198043i
$111$	9.81735	+	0.512760i	0.931821	+	0.0486691i
$112$	−1.17084	−	2.02795i	−0.110634	−	0.191624i
$113$	−9.99505			−0.940255			−0.470128	−	0.882598i	$-0.655792\pi$
$113$	−9.99505			−0.940255			−0.470128	+	0.882598i	$0.655792\pi$
$114$	1.80290	+	7.33141i	0.168857	+	0.686649i
$115$	−2.07892			−0.193860
$116$	0.313727	+	0.543392i	0.0291289	+	0.0504527i
$117$	1.16216	+	0.843728i	0.107442	+	0.0780027i
$118$	3.13769	−	5.43465i	0.288848	−	0.500300i
$119$	5.62033	−	3.24490i	0.515215	−	0.297460i
$120$	−0.786608	−	1.54313i	−0.0718072	−	0.140868i
$121$	5.24761			0.477055
$122$	−2.50391			−0.226693
$123$	−3.22896	+	1.64596i	−0.291146	+	0.148411i
$124$	1.77633	+	1.02556i	0.159519	+	0.0920984i
$125$		−	1.00000i		−	0.0894427i
$126$	2.85961	+	6.41668i	0.254755	+	0.571643i
$127$	9.58763	+	5.53542i	0.850764	+	0.491189i	0.860909	−	0.508760i	$-0.169896\pi$
$127$	9.58763	+	5.53542i	0.850764	+	0.491189i	−0.0101444	+	0.999949i	$0.503229\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−11.6436	+	5.93529i	−1.02516	+	0.522573i
$130$	0.239356	+	0.414577i	0.0209929	+	0.0363608i
$131$	13.3817	−	7.72594i	1.16917	−	0.675018i	0.215683	−	0.976464i	$-0.430802\pi$
$131$	13.3817	−	7.72594i	1.16917	−	0.675018i	0.953484	+	0.301445i	$0.0974690\pi$
$132$	2.26191	−	3.48439i	0.196874	−	0.303277i
$133$	2.32985	−	9.93768i	0.202023	−	0.861706i
$134$		−	13.0779i		−	1.12976i
$135$	1.86471	+	4.85004i	0.160489	+	0.417425i
$136$	2.40013	−	1.38572i	0.205810	−	0.118824i
$137$	7.57874	+	4.37559i	0.647496	+	0.373832i	0.787496	−	0.616320i	$-0.211377\pi$
$137$	7.57874	+	4.37559i	0.647496	+	0.373832i	−0.140000	+	0.990151i	$0.544710\pi$
$138$	3.59590	+	0.187814i	0.306103	+	0.0159878i
$139$	3.74921	−	6.49383i	0.318004	−	0.550799i	−0.662067	−	0.749444i	$-0.730321\pi$
$139$	3.74921	−	6.49383i	0.318004	−	0.550799i	0.980071	+	0.198645i	$0.0636541\pi$
$140$			2.34168i			0.197908i
$141$	−2.11686	+	3.26094i	−0.178272	+	0.274621i
$142$	2.68385	−	4.64856i	0.225223	−	0.390098i
$143$	−0.574075	+	0.994328i	−0.0480066	+	0.0831499i
$144$	1.22118	+	2.74020i	0.101765	+	0.228350i
$145$		−	0.627455i		−	0.0521073i
$146$	−5.81045	+	10.0640i	−0.480876	+	0.832902i
$147$	−0.137007	+	2.62315i	−0.0113002	+	0.216354i
$148$	−4.91536	−	2.83789i	−0.404040	−	0.233273i
$149$	−10.5955	+	6.11734i	−0.868020	+	0.501152i	−0.866690	−	0.498847i	$-0.833757\pi$
$149$	−10.5955	+	6.11734i	−0.868020	+	0.501152i	−0.00133030	+	0.999999i	$0.500423\pi$
$150$	−0.0903420	+	1.72969i	−0.00737639	+	0.141229i
$151$			16.0545i			1.30650i	0.757143	+	0.653250i	$0.226595\pi$
$151$			16.0545i			1.30650i	−0.757143	+	0.653250i	$0.773405\pi$
$152$	0.994947	−	4.24383i	0.0807009	−	0.344220i
$153$	−7.59429	+	3.38442i	−0.613962	+	0.273614i
$154$	−4.86387	+	2.80816i	−0.391942	+	0.226288i
$155$	−1.02556	−	1.77633i	−0.0823753	−	0.142678i
$156$	−0.376559	−	0.738715i	−0.0301489	−	0.0591445i
$157$	−0.836254	−	1.44843i	−0.0667404	−	0.115598i	0.830724	−	0.556684i	$-0.187927\pi$
$157$	−0.836254	−	1.44843i	−0.0667404	−	0.115598i	−0.897465	+	0.441086i	$0.854593\pi$
$158$	−10.1589	−	5.86527i	−0.808202	−	0.466616i
$159$	19.2963	+	12.5263i	1.53030	+	0.993402i
$160$			1.00000i			0.0790569i
$161$	−4.21595	−	2.43408i	−0.332264	−	0.191833i
$162$	−2.78722	−	8.55753i	−0.218985	−	0.672343i
$163$	12.4272			0.973371			0.486686	−	0.873577i	$-0.338206\pi$
$163$	12.4272			0.973371			0.486686	+	0.873577i	$0.338206\pi$
$164$	2.09248			0.163395
$165$	−3.70106	+	1.88661i	−0.288127	+	0.146873i
$166$	9.79314	−	5.65407i	0.760095	−	0.438841i
$167$	−0.136815	+	0.236971i	−0.0105871	+	0.0183374i	−0.871270	−	0.490803i	$-0.836703\pi$
$167$	−0.136815	+	0.236971i	−0.0105871	+	0.0183374i	0.860683	+	0.509141i	$0.170037\pi$
$168$	0.211552	−	4.05038i	0.0163216	−	0.312494i
$169$	−6.38542	−	11.0599i	−0.491186	−	0.850759i
$170$	−2.77143			−0.212559
$171$	−4.29491	+	12.3513i	−0.328440	+	0.944525i
$172$	7.54542			0.575333
$173$	12.1946	+	21.1216i	0.927137	+	1.60585i	0.788088	+	0.615563i	$0.211071\pi$
$173$	12.1946	+	21.1216i	0.927137	+	1.60585i	0.139049	+	0.990286i	$0.455596\pi$
$174$	−0.0566855	+	1.08530i	−0.00429732	+	0.0822767i
$175$	1.17084	−	2.02795i	0.0885071	−	0.153299i
$176$	−2.07709	+	1.19921i	−0.156566	+	0.0903936i
$177$	9.68374	−	4.93627i	0.727874	−	0.371033i
$178$	−9.94725			−0.745578
$179$	20.0769			1.50062			0.750309	−	0.661087i	$-0.229905\pi$
$179$	20.0769			1.50062			0.750309	+	0.661087i	$0.229905\pi$
$180$	0.312528	−	2.98368i	0.0232944	−	0.222390i
$181$	10.2054	+	5.89207i	0.758559	+	0.437954i	0.828778	−	0.559578i	$-0.189037\pi$
$181$	10.2054	+	5.89207i	0.758559	+	0.437954i	−0.0702194	+	0.997532i	$0.522370\pi$
$182$			1.12099i			0.0830933i
$183$	−3.63765	−	2.36140i	−0.268902	−	0.174560i
$184$	−1.80040	−	1.03946i	−0.132727	−	0.0766301i
$185$	2.83789	+	4.91536i	0.208646	+	0.361385i
$186$	1.61344	+	3.16516i	0.118303	+	0.232081i
$187$	−3.32352	−	5.75651i	−0.243040	−	0.420958i
$188$	1.94389	−	1.12231i	0.141773	−	0.0818526i
$189$	−1.89706	+	12.0189i	−0.137991	+	0.874248i
$190$	−2.98356	+	3.17779i	−0.216450	+	0.230541i
$191$		−	7.36887i		−	0.533193i	−0.963808	−	0.266596i	$-0.914101\pi$
$191$		−	7.36887i		−	0.533193i	0.963808	−	0.266596i	$-0.0858991\pi$
$192$	0.0903420	−	1.72969i	0.00651987	−	0.124830i
$193$	−6.47095	+	3.73601i	−0.465789	+	0.268924i	−0.714475	−	0.699661i	$-0.753335\pi$
$193$	−6.47095	+	3.73601i	−0.465789	+	0.268924i	0.248686	+	0.968584i	$0.420001\pi$
$194$	−7.49209	−	4.32556i	−0.537900	−	0.310557i
$195$	−0.0432478	+	0.828026i	−0.00309704	+	0.0592961i
$196$	0.758271	−	1.31336i	0.0541622	−	0.0938118i
$197$			20.2370i			1.44183i	0.693025	+	0.720913i	$0.256277\pi$
$197$			20.2370i			1.44183i	−0.693025	+	0.720913i	$0.743723\pi$
$198$	6.57214	−	2.92890i	0.467062	−	0.208148i
$199$	−5.62306	+	9.73942i	−0.398608	+	0.690409i	−0.993554	−	0.113356i	$-0.963840\pi$
$199$	−5.62306	+	9.73942i	−0.398608	+	0.690409i	0.594946	+	0.803765i	$0.297173\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	12.3336	−	18.9994i	0.869942	−	1.34011i
$202$			4.57341i			0.321784i
$203$	0.734649	−	1.27245i	0.0515622	−	0.0893084i
$204$	4.79373	+	0.250377i	0.335628	+	0.0175299i
$205$	−1.81214	−	1.04624i	−0.126565	−	0.0730725i
$206$	1.99110	−	1.14956i	0.138727	−	0.0800940i
$207$	5.04695	+	3.66409i	0.350787	+	0.254672i
$208$			0.478712i			0.0331927i
$209$	−10.1785	−	2.38630i	−0.704059	−	0.165063i
$210$	−2.20840	+	3.40196i	−0.152394	+	0.234758i
$211$	−22.9716	+	13.2627i	−1.58143	+	0.913040i	−0.586781	+	0.809745i	$0.699605\pi$
$211$	−22.9716	+	13.2627i	−1.58143	+	0.913040i	−0.994651	+	0.103295i	$0.967061\pi$
$212$	−6.64114	−	11.5028i	−0.456115	−	0.790015i
$213$	8.28304	−	4.22227i	0.567545	−	0.289305i
$214$	−6.09204	−	10.5517i	−0.416443	−	0.721301i
$215$	−6.53452	−	3.77271i	−0.445651	−	0.257297i
$216$	−0.810128	+	5.13261i	−0.0551222	+	0.349230i
$217$		−	4.80309i		−	0.326055i
$218$	0.624429	+	0.360514i	0.0422917	+	0.0244171i
$219$	−17.9325	+	9.14109i	−1.21177	+	0.617698i
$220$	2.39841			0.161701
$221$	−1.32672			−0.0892448
$222$	−4.46461	−	8.75845i	−0.299645	−	0.587829i
$223$	−13.2112	+	7.62747i	−0.884685	+	0.510773i	−0.872200	−	0.489149i	$-0.837307\pi$
$223$	−13.2112	+	7.62747i	−0.884685	+	0.510773i	−0.0124845	+	0.999922i	$0.503974\pi$
$224$	−1.17084	+	2.02795i	−0.0782300	+	0.135498i
$225$	−1.76250	+	2.42768i	−0.117500	+	0.161845i
$226$	4.99753	+	8.65597i	0.332430	+	0.575786i
$227$	−1.74109			−0.115560			−0.0577800	−	0.998329i	$-0.518402\pi$
$227$	−1.74109			−0.115560			−0.0577800	+	0.998329i	$0.518402\pi$
$228$	5.44774	−	5.22706i	0.360785	−	0.346171i
$229$	−16.6454			−1.09996			−0.549979	−	0.835179i	$-0.685364\pi$
$229$	−16.6454			−1.09996			−0.549979	+	0.835179i	$0.685364\pi$
$230$	1.03946	+	1.80040i	0.0685400	+	0.118715i
$231$	−9.71450	−	0.507389i	−0.639167	−	0.0333837i
$232$	0.313727	−	0.543392i	0.0205972	−	0.0356754i
$233$	−7.51278	+	4.33751i	−0.492179	+	0.284160i	−0.725478	−	0.688245i	$-0.758381\pi$
$233$	−7.51278	+	4.33751i	−0.492179	+	0.284160i	0.233299	+	0.972405i	$0.425048\pi$
$234$	0.149611	−	1.42832i	0.00978037	−	0.0933724i
$235$	−2.24461			−0.146422
$236$	−6.27539			−0.408493
$237$	−9.22733	−	18.1017i	−0.599380	−	1.17583i
$238$	−5.62033	−	3.24490i	−0.364312	−	0.210336i
$239$		−	19.1483i		−	1.23860i	−0.785153	−	0.619302i	$-0.787416\pi$
$239$		−	19.1483i		−	1.23860i	0.785153	−	0.619302i	$-0.212584\pi$
$240$	−0.943085	+	1.45279i	−0.0608759	+	0.0937770i
$241$	−16.6382	−	9.60606i	−1.07176	−	0.618781i	−0.143098	−	0.989709i	$-0.545706\pi$
$241$	−16.6382	−	9.60606i	−1.07176	−	0.618781i	−0.928662	+	0.370928i	$0.879040\pi$
$242$	−2.62380	−	4.54456i	−0.168665	−	0.292135i
$243$	4.02124	−	15.0609i	0.257963	−	0.966155i
$244$	1.25195	+	2.16845i	0.0801481	+	0.138821i
$245$	−1.31336	+	0.758271i	−0.0839078	+	0.0484442i
$246$	3.03992	+	1.97338i	0.193818	+	0.125818i
$247$	−1.42827	+	1.52125i	−0.0908786	+	0.0967947i
$248$		−	2.05113i		−	0.130247i
$249$	19.5596	+	1.02160i	1.23954	+	0.0647413i
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$	10.8299	+	6.25262i	0.683574	+	0.394662i	0.801200	−	0.598396i	$-0.204195\pi$
$251$	10.8299	+	6.25262i	0.683574	+	0.394662i	−0.117626	+	0.993058i	$0.537528\pi$
$252$	4.12720	−	5.68484i	0.259989	−	0.358111i
$253$	−2.49306	+	4.31810i	−0.156737	+	0.271477i
$254$		−	11.0708i		−	0.694646i
$255$	−4.02630	−	2.61370i	−0.252137	−	0.163676i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.733753	−	1.27090i	0.0457702	−	0.0792764i	−0.842233	−	0.539114i	$-0.818759\pi$
$257$	0.733753	−	1.27090i	0.0457702	−	0.0792764i	0.888003	+	0.459838i	$0.152092\pi$
$258$	10.9619	+	7.11597i	0.682457	+	0.443021i
$259$			13.2908i			0.825852i
$260$	0.239356	−	0.414577i	0.0148442	−	0.0257110i
$261$	−1.10589	+	1.52326i	−0.0684526	+	0.0942873i
$262$	−13.3817	−	7.72594i	−0.826725	−	0.477310i
$263$	12.2015	−	7.04453i	0.752376	−	0.434384i	−0.0741759	−	0.997245i	$-0.523633\pi$
$263$	12.2015	−	7.04453i	0.752376	−	0.434384i	0.826552	+	0.562861i	$0.190299\pi$
$264$	−4.14852	−	0.216677i	−0.255324	−	0.0133356i
$265$			13.2823i			0.815924i
$266$	−9.77121	+	2.95113i	−0.599111	+	0.180946i
$267$	−14.4512	−	9.38110i	−0.884401	−	0.574114i
$268$	−11.3258	+	6.53894i	−0.691832	+	0.399429i
$269$	−9.48574	−	16.4298i	−0.578356	−	1.00174i	−0.995668	−	0.0929788i	$-0.970361\pi$
$269$	−9.48574	−	16.4298i	−0.578356	−	1.00174i	0.417312	−	0.908763i	$-0.362972\pi$
$270$	3.26790	−	4.03991i	0.198878	−	0.245861i
$271$	12.6913	+	21.9819i	0.770940	+	1.33531i	0.937048	+	0.349200i	$0.113547\pi$
$271$	12.6913	+	21.9819i	0.770940	+	1.33531i	−0.166108	+	0.986108i	$0.553120\pi$
$272$	−2.40013	−	1.38572i	−0.145529	−	0.0840214i
$273$	−1.05719	+	1.62856i	−0.0639840	+	0.0985650i
$274$		−	8.75118i		−	0.528678i
$275$	−2.07709	−	1.19921i	−0.125253	−	0.0723149i
$276$	−1.63530	−	3.20804i	−0.0984333	−	0.193102i
$277$	8.10858			0.487198			0.243599	−	0.969876i	$-0.421672\pi$
$277$	8.10858			0.487198			0.243599	+	0.969876i	$0.421672\pi$
$278$	−7.49842			−0.449726
$279$	−0.641035	+	6.11991i	−0.0383778	+	0.366389i
$280$	2.02795	−	1.17084i	0.121193	−	0.0699710i
$281$	12.6467	−	21.9047i	0.754438	−	1.30672i	−0.191216	−	0.981548i	$-0.561243\pi$
$281$	12.6467	−	21.9047i	0.754438	−	1.30672i	0.945653	−	0.325176i	$-0.105424\pi$
$282$	3.88249	+	0.202783i	0.231199	+	0.0120755i
$283$	0.496185	+	0.859418i	0.0294952	+	0.0510871i	0.880396	−	0.474239i	$-0.157277\pi$
$283$	0.496185	+	0.859418i	0.0294952	+	0.0510871i	−0.850901	+	0.525326i	$0.823943\pi$
$284$	−5.36769			−0.318514
$285$	−7.33141	+	1.80290i	−0.434275	+	0.106794i
$286$	1.14815			0.0678916
$287$	−2.44995	−	4.24344i	−0.144616	−	0.250483i
$288$	1.76250	−	2.42768i	0.103856	−	0.143052i
$289$	−4.65958	+	8.07063i	−0.274093	+	0.474743i
$290$	−0.543392	+	0.313727i	−0.0319091	+	0.0184227i
$291$	−6.80504	−	13.3498i	−0.398918	−	0.782578i
$292$	11.6209			0.680062
$293$	23.3348			1.36323			0.681617	−	0.731709i	$-0.261277\pi$
$293$	23.3348			1.36323			0.681617	+	0.731709i	$0.261277\pi$
$294$	2.34022	−	1.19293i	0.136485	−	0.0695728i
$295$	5.43465	+	3.13769i	0.316417	+	0.182684i
$296$			5.67577i			0.329898i
$297$	12.3101	+	1.94302i	0.714306	+	0.112746i
$298$	10.5955	+	6.11734i	0.613783	+	0.354368i
$299$	0.497603	+	0.861873i	0.0287771	+	0.0498434i
$300$	1.54313	−	0.786608i	0.0890926	−	0.0454148i
$301$	−8.83447	−	15.3018i	−0.509210	−	0.881978i
$302$	13.9036	−	8.02727i	0.800064	−	0.461917i
$303$	−4.31311	+	6.64419i	−0.247782	+	0.381699i
$304$	−4.17274	+	1.26026i	−0.239323	+	0.0722811i
$305$		−	2.50391i		−	0.143373i
$306$	6.72814	+	4.88464i	0.384622	+	0.279236i
$307$	−21.4512	+	12.3849i	−1.22429	+	0.706842i	−0.965829	−	0.259180i	$-0.916548\pi$
$307$	−21.4512	+	12.3849i	−1.22429	+	0.706842i	−0.258458	+	0.966023i	$0.583214\pi$
$308$	4.86387	+	2.80816i	0.277145	+	0.160010i
$309$	3.97679	+	0.207708i	0.226232	+	0.0118161i
$310$	−1.02556	+	1.77633i	−0.0582482	+	0.100889i
$311$		−	11.2512i		−	0.637999i	−0.947755	−	0.318999i	$-0.896653\pi$
$311$		−	11.2512i		−	0.637999i	0.947755	−	0.318999i	$-0.103347\pi$
$312$	−0.451467	+	0.695467i	−0.0255593	+	0.0393731i
$313$	5.46644	−	9.46816i	0.308982	−	0.535172i	−0.669158	−	0.743120i	$-0.733345\pi$
$313$	5.46644	−	9.46816i	0.308982	−	0.535172i	0.978140	+	0.207948i	$0.0666785\pi$
$314$	−0.836254	+	1.44843i	−0.0471926	+	0.0817399i
$315$	−6.41668	+	2.85961i	−0.361539	+	0.161121i
$316$			11.7305i			0.659894i
$317$	−8.95027	+	15.5023i	−0.502697	+	0.870697i	0.497298	+	0.867580i	$0.334326\pi$
$317$	−8.95027	+	15.5023i	−0.502697	+	0.870697i	−0.999995	+	0.00311703i	$0.999008\pi$
$318$	1.19995	−	22.9743i	0.0672897	−	1.28833i
$319$	−1.30328	−	0.752448i	−0.0729696	−	0.0421290i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	1.10073	−	21.0747i	0.0614369	−	1.17628i
$322$			4.86817i			0.271292i
$323$	−3.49274	−	11.5645i	−0.194341	−	0.643464i
$324$	−6.01743	+	6.69257i	−0.334302	+	0.371810i
$325$	−0.414577	+	0.239356i	−0.0229966	+	0.0132771i
$326$	−6.21359	−	10.7622i	−0.344139	−	0.596066i
$327$	0.567167	+	1.11264i	0.0313644	+	0.0615291i
$328$	−1.04624	−	1.81214i	−0.0577688	−	0.100059i
$329$	−4.55197	−	2.62808i	−0.250958	−	0.144891i
$330$	3.48439	+	2.26191i	0.191809	+	0.124514i
$331$		−	10.3625i		−	0.569572i	−0.958591	−	0.284786i	$-0.908077\pi$
$331$		−	10.3625i		−	0.569572i	0.958591	−	0.284786i	$-0.0919226\pi$
$332$	−9.79314	−	5.65407i	−0.537468	−	0.310308i
$333$	1.77384	−	16.9347i	0.0972056	−	0.928014i
$334$	0.273631			0.0149724
$335$	13.0779			0.714521
$336$	−3.61351	+	1.84198i	−0.197133	+	0.100488i
$337$	−23.7499	+	13.7120i	−1.29374	+	0.746939i	−0.979315	−	0.202344i	$-0.935144\pi$
$337$	−23.7499	+	13.7120i	−1.29374	+	0.746939i	−0.314422	+	0.949283i	$0.601811\pi$
$338$	−6.38542	+	11.0599i	−0.347321	+	0.601577i
$339$	−0.902972	+	17.2884i	−0.0490427	+	0.938975i
$340$	1.38572	+	2.40013i	0.0751510	+	0.130165i
$341$	−4.91946			−0.266404
$342$	12.8440	−	2.45613i	0.694522	−	0.132812i
$343$	−19.9430			−1.07682
$344$	−3.77271	−	6.53452i	−0.203411	−	0.352318i
$345$	−0.187814	+	3.59590i	−0.0101116	+	0.193597i
$346$	12.1946	−	21.1216i	0.655585	−	1.13551i
$347$	−22.5112	+	12.9969i	−1.20847	+	0.697709i	−0.962424	−	0.271551i	$-0.912464\pi$
$347$	−22.5112	+	12.9969i	−1.20847	+	0.697709i	−0.246042	+	0.969259i	$0.579130\pi$
$348$	0.968244	−	0.493561i	0.0519033	−	0.0264577i
$349$	8.16697			0.437168			0.218584	−	0.975818i	$-0.429856\pi$
$349$	8.16697			0.437168			0.218584	+	0.975818i	$0.429856\pi$
$350$	−2.34168			−0.125168
$351$	1.56438	−	1.93395i	0.0835006	−	0.103227i
$352$	2.07709	+	1.19921i	0.110709	+	0.0639180i
$353$			23.1015i			1.22957i	0.788696	+	0.614783i	$0.210757\pi$
$353$			23.1015i			1.22957i	−0.788696	+	0.614783i	$0.789243\pi$
$354$	−9.11681	−	5.91823i	−0.484553	−	0.314550i
$355$	4.64856	+	2.68385i	0.246720	+	0.142444i
$356$	4.97362	+	8.61457i	0.263602	+	0.456571i
$357$	−5.10493	−	10.0146i	−0.270182	−	0.530029i
$358$	−10.0385	−	17.3871i	−0.530549	−	0.918937i
$359$	17.3948	−	10.0429i	0.918063	−	0.530044i	0.0350462	−	0.999386i	$-0.488842\pi$
$359$	17.3948	−	10.0429i	0.918063	−	0.530044i	0.883017	+	0.469342i	$0.155509\pi$
$360$	−2.74020	+	1.22118i	−0.144421	+	0.0643619i
$361$	−17.0202	−	8.44477i	−0.895798	−	0.444462i
$362$		−	11.7841i		−	0.619361i
$363$	0.474079	−	9.07675i	0.0248827	−	0.476406i
$364$	0.970806	−	0.560495i	0.0508841	−	0.0293779i
$365$	−10.0640	−	5.81045i	−0.526773	−	0.304133i
$366$	−0.226208	+	4.33099i	−0.0118241	+	0.226385i
$367$	4.83084	−	8.36726i	0.252168	−	0.436768i	−0.711955	−	0.702226i	$-0.752190\pi$
$367$	4.83084	−	8.36726i	0.252168	−	0.436768i	0.964122	+	0.265458i	$0.0855231\pi$
$368$			2.07892i			0.108371i
$369$	2.55529	+	5.73381i	0.133023	+	0.298490i
$370$	2.83789	−	4.91536i	0.147535	−	0.255538i
$371$	−15.5514	+	26.9358i	−0.807389	+	1.39844i
$372$	1.93439	−	2.97985i	0.100293	−	0.154498i
$373$		−	16.8317i		−	0.871515i	−0.900064	−	0.435757i	$-0.856481\pi$
$373$		−	16.8317i		−	0.871515i	0.900064	−	0.435757i	$-0.143519\pi$
$374$	−3.32352	+	5.75651i	−0.171855	+	0.297662i
$375$	−1.72969	−	0.0903420i	−0.0893210	−	0.00466524i
$376$	−1.94389	−	1.12231i	−0.100249	−	0.0578785i
$377$	−0.260128	+	0.150185i	−0.0133973	+	0.00773493i
$378$	11.3572	−	4.36656i	0.584152	−	0.224592i
$379$			31.6110i			1.62375i	0.583834	+	0.811873i	$0.301552\pi$
$379$			31.6110i			1.62375i	−0.583834	+	0.811873i	$0.698448\pi$
$380$	4.24383	+	0.994947i	0.217704	+	0.0510397i
$381$	10.4407	−	16.0836i	0.534895	−	0.823986i
$382$	−6.38163	+	3.68444i	−0.326513	+	0.188512i
$383$	−14.8637	−	25.7447i	−0.759500	−	1.31549i	−0.943106	−	0.332493i	$-0.892110\pi$
$383$	−14.8637	−	25.7447i	−0.759500	−	1.31549i	0.183605	−	0.983000i	$-0.441223\pi$
$384$	−1.54313	+	0.786608i	−0.0787475	+	0.0401414i
$385$	−2.80816	−	4.86387i	−0.143117	−	0.247886i
$386$	6.47095	+	3.73601i	0.329363	+	0.190158i
$387$	9.21432	+	20.6760i	0.468390	+	1.05102i
$388$			8.65112i			0.439194i
$389$	−6.06103	−	3.49934i	−0.307307	−	0.177424i	0.338414	−	0.940997i	$-0.390110\pi$
$389$	−6.06103	−	3.49934i	−0.307307	−	0.177424i	−0.645721	+	0.763574i	$0.723443\pi$
$390$	0.738715	−	0.376559i	0.0374063	−	0.0190678i
$391$	−5.76159			−0.291376
$392$	−1.51654			−0.0765970
$393$	−12.1546	−	23.8442i	−0.613117	−	1.20278i
$394$	17.5258	−	10.1185i	0.882935	−	0.509763i
$395$	5.86527	−	10.1589i	0.295114	−	0.511152i
$396$	−5.82257	−	4.22719i	−0.292595	−	0.212425i
$397$	14.8564	+	25.7320i	0.745621	+	1.29145i	0.949904	+	0.312542i	$0.101180\pi$
$397$	14.8564	+	25.7320i	0.745621	+	1.29145i	−0.204283	+	0.978912i	$0.565486\pi$
$398$	11.2461			0.563717
$399$	−16.9787	−	4.92771i	−0.849996	−	0.246694i
$400$	−1.00000			−0.0500000
$401$	14.8000	+	25.6344i	0.739079	+	1.28012i	0.952910	+	0.303252i	$0.0980724\pi$
$401$	14.8000	+	25.6344i	0.739079	+	1.28012i	−0.213831	+	0.976871i	$0.568594\pi$
$402$	−22.6207	−	1.18148i	−1.12822	−	0.0589270i
$403$	−0.490951	+	0.850351i	−0.0244560	+	0.0423590i
$404$	3.96069	−	2.28671i	0.197052	−	0.113768i
$405$	8.55753	−	2.78722i	0.425227	−	0.138498i
$406$	−1.46930			−0.0729200
$407$	13.6129			0.674764
$408$	−2.18003	−	4.27668i	−0.107928	−	0.211727i
$409$	−1.05270	−	0.607777i	−0.0520527	−	0.0300526i	0.473748	−	0.880661i	$-0.342901\pi$
$409$	−1.05270	−	0.607777i	−0.0520527	−	0.0300526i	−0.525800	+	0.850608i	$0.676234\pi$
$410$			2.09248i			0.103340i
$411$	8.25310	−	12.7136i	0.407096	−	0.627116i
$412$	−1.99110	−	1.14956i	−0.0980947	−	0.0566350i
$413$	7.34747	+	12.7262i	0.361545	+	0.626215i
$414$	0.649721	−	6.20283i	0.0319320	−	0.304852i
$415$	5.65407	+	9.79314i	0.277547	+	0.480726i
$416$	0.414577	−	0.239356i	0.0203263	−	0.0117354i
$417$	−10.8936	−	7.07165i	−0.533463	−	0.346300i
$418$	3.02264	+	10.0080i	0.147842	+	0.489505i
$419$			3.26405i			0.159459i	0.996817	+	0.0797297i	$0.0254057\pi$
$419$			3.26405i			0.159459i	−0.996817	+	0.0797297i	$0.974594\pi$
$420$	4.05038	+	0.211552i	0.197639	+	0.0103227i
$421$	−18.4508	+	10.6526i	−0.899236	+	0.519174i	−0.876952	−	0.480578i	$-0.840427\pi$
$421$	−18.4508	+	10.6526i	−0.899236	+	0.519174i	−0.0222837	+	0.999752i	$0.507094\pi$
$422$	22.9716	+	13.2627i	1.11824	+	0.645617i
$423$	5.44919	+	3.95612i	0.264949	+	0.192353i
$424$	−6.64114	+	11.5028i	−0.322522	+	0.558625i
$425$		−	2.77143i		−	0.134434i
$426$	−7.79812	−	5.06219i	−0.377820	−	0.245264i
$427$	2.93167	−	5.07781i	0.141874	−	0.245732i
$428$	−6.09204	+	10.5517i	−0.294470	+	0.510037i
$429$	1.66802	+	1.08280i	0.0805327	+	0.0522783i
$430$			7.54542i			0.363872i
$431$	2.14280	−	3.71143i	0.103215	−	0.178774i	−0.809793	−	0.586716i	$-0.800420\pi$
$431$	2.14280	−	3.71143i	0.103215	−	0.178774i	0.913007	+	0.407943i	$0.133754\pi$
$432$	4.85004	−	1.86471i	0.233347	−	0.0897161i
$433$	18.0367	+	10.4135i	0.866789	+	0.500441i	0.866280	−	0.499559i	$-0.166505\pi$
$433$	18.0367	+	10.4135i	0.866789	+	0.500441i	0.000509428		1.00000i	$0.499838\pi$
$434$	−4.15959	+	2.40154i	−0.199667	+	0.115278i
$435$	−1.08530	−	0.0566855i	−0.0520364	−	0.00271786i
$436$		−	0.721029i		−	0.0345310i
$437$	−6.20259	+	6.60638i	−0.296710	+	0.316026i
$438$	16.8827	+	10.9595i	0.806686	+	0.523665i
$439$	14.9323	−	8.62117i	0.712680	−	0.411466i	−0.0993728	−	0.995050i	$-0.531684\pi$
$439$	14.9323	−	8.62117i	0.712680	−	0.411466i	0.812052	+	0.583584i	$0.198350\pi$
$440$	−1.19921	−	2.07709i	−0.0571700	−	0.0990213i
$441$	4.52487	+	0.473962i	0.215470	+	0.0225696i
$442$	0.663360	+	1.14897i	0.0315528	+	0.0546510i
$443$	−19.6711	−	11.3571i	−0.934602	−	0.539592i	−0.0463376	−	0.998926i	$-0.514755\pi$
$443$	−19.6711	−	11.3571i	−0.934602	−	0.539592i	−0.888264	+	0.459333i	$0.848088\pi$
$444$	−5.35274	+	8.24569i	−0.254030	+	0.391323i
$445$		−	9.94725i		−	0.471545i
$446$	13.2112	+	7.62747i	0.625566	+	0.361171i
$447$	9.62389	+	18.8797i	0.455194	+	0.892978i
$448$	2.34168			0.110634
$449$	−24.4007			−1.15154			−0.575770	−	0.817612i	$-0.695298\pi$
$449$	−24.4007			−1.15154			−0.575770	+	0.817612i	$0.695298\pi$
$450$	2.98368	+	0.312528i	0.140652	+	0.0147327i
$451$	−4.34626	+	2.50931i	−0.204657	+	0.118159i
$452$	4.99753	−	8.65597i	0.235064	−	0.407142i
$453$	27.7694	+	1.45040i	1.30472	+	0.0681456i
$454$	0.870543	+	1.50782i	0.0408566	+	0.0707657i
$455$	−1.12099			−0.0525528
$456$	−7.25064	−	2.10435i	−0.339542	−	0.0985452i
$457$	5.57921			0.260984			0.130492	−	0.991449i	$-0.458344\pi$
$457$	5.57921			0.260984			0.130492	+	0.991449i	$0.458344\pi$
$458$	8.32269	+	14.4153i	0.388894	+	0.673584i
$459$	5.16793	+	13.4415i	0.241218	+	0.627398i
$460$	1.03946	−	1.80040i	0.0484651	−	0.0839440i
$461$	−13.2971	+	7.67711i	−0.619310	+	0.357559i	−0.776600	−	0.629994i	$-0.783057\pi$
$461$	−13.2971	+	7.67711i	−0.619310	+	0.357559i	0.157291	+	0.987552i	$0.449724\pi$
$462$	4.41784	+	8.66670i	0.205536	+	0.403211i
$463$	29.0927			1.35205			0.676027	−	0.736877i	$-0.263700\pi$
$463$	29.0927			1.35205			0.676027	+	0.736877i	$0.263700\pi$
$464$	−0.627455			−0.0291289
$465$	−3.16516	+	1.61344i	−0.146781	+	0.0748213i
$466$	7.51278	+	4.33751i	0.348023	+	0.200931i
$467$			30.7109i			1.42113i	0.703630	+	0.710567i	$0.251561\pi$
$467$			30.7109i			1.42113i	−0.703630	+	0.710567i	$0.748439\pi$
$468$	−1.31177	+	0.584595i	−0.0606366	+	0.0270229i
$469$	26.5213	+	15.3121i	1.22464	+	0.707047i
$470$	1.12231	+	1.94389i	0.0517681	+	0.0896650i
$471$	−2.58090	+	1.31561i	−0.118921	+	0.0606201i
$472$	3.13769	+	5.43465i	0.144424	+	0.250150i
$473$	−15.6725	+	9.04852i	−0.720622	+	0.416051i
$474$	−11.0629	+	17.0420i	−0.508135	+	0.782764i
$475$	−3.17779	−	2.98356i	−0.145807	−	0.136895i
$476$			6.48980i			0.297460i
$477$	23.4100	−	32.2451i	1.07187	−	1.47640i
$478$	−16.5830	+	9.57417i	−0.758487	+	0.437912i
$479$	22.3097	+	12.8805i	1.01935	+	0.588525i	0.913917	−	0.405901i	$-0.133042\pi$
$479$	22.3097	+	12.8805i	1.01935	+	0.588525i	0.105438	+	0.994426i	$0.466376\pi$
$480$	1.72969	+	0.0903420i	0.0789493	+	0.00412353i
$481$	1.35853	−	2.35305i	0.0619437	−	0.107290i
$482$			19.2121i			0.875088i
$483$	−4.59109	+	7.07241i	−0.208902	+	0.321806i
$484$	−2.62380	+	4.54456i	−0.119264	+	0.206571i
$485$	4.32556	−	7.49209i	0.196413	−	0.340198i
$486$	−15.0537	+	4.04793i	−0.682850	+	0.183618i
$487$			19.2342i			0.871583i	0.900048	+	0.435791i	$0.143531\pi$
$487$			19.2342i			0.871583i	−0.900048	+	0.435791i	$0.856469\pi$
$488$	1.25195	−	2.16845i	0.0566733	−	0.0981610i
$489$	1.12270	−	21.4952i	0.0507700	−	0.972046i
$490$	1.31336	+	0.758271i	0.0593318	+	0.0342552i
$491$	18.7155	−	10.8054i	0.844619	−	0.487641i	−0.0142124	−	0.999899i	$-0.504524\pi$
$491$	18.7155	−	10.8054i	0.844619	−	0.487641i	0.858832	+	0.512258i	$0.171191\pi$
$492$	0.189038	−	3.61934i	0.00852251	−	0.163173i
$493$		−	1.73895i		−	0.0783183i
$494$	2.03157	+	0.476294i	0.0914048	+	0.0214295i
$495$	2.92890	+	6.57214i	0.131644	+	0.295396i
$496$	−1.77633	+	1.02556i	−0.0797596	+	0.0460492i
$497$	6.28470	+	10.8854i	0.281908	+	0.488278i
$498$	−8.89508	−	17.4499i	−0.398598	−	0.781950i
$499$	−9.49912	−	16.4530i	−0.425239	−	0.736535i	0.571204	−	0.820808i	$-0.306477\pi$
$499$	−9.49912	−	16.4530i	−0.425239	−	0.736535i	−0.996443	+	0.0842728i	$0.973143\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	0.397527	+	0.258057i	0.0177602	+	0.0115291i
$502$		−	12.5052i		−	0.558136i
$503$	17.2526	+	9.96081i	0.769256	+	0.444130i	0.832609	−	0.553861i	$-0.186846\pi$
$503$	17.2526	+	9.96081i	0.769256	+	0.444130i	−0.0633529	+	0.997991i	$0.520179\pi$
$504$	−6.98681	−	0.731839i	−0.311217	−	0.0325987i
$505$	−4.57341			−0.203514
$506$	4.98612			0.221660
$507$	−19.7070	+	10.0456i	−0.875221	+	0.446143i
$508$	−9.58763	+	5.53542i	−0.425382	+	0.245594i
$509$	15.7560	−	27.2902i	0.698372	−	1.20962i	−0.270658	−	0.962675i	$-0.587241\pi$
$509$	15.7560	−	27.2902i	0.698372	−	1.20962i	0.969031	−	0.246941i	$-0.0794253\pi$
$510$	−0.250377	+	4.79373i	−0.0110869	+	0.212270i
$511$	−13.6062	−	23.5666i	−0.601903	−	1.04253i
$512$	1.00000			0.0441942
$513$	20.9759	+	8.54472i	0.926108	+	0.377259i
$514$	−1.46751			−0.0647289
$515$	1.14956	+	1.99110i	0.0506559	+	0.0877385i
$516$	0.681668	−	13.0513i	0.0300088	−	0.574550i
$517$	−2.69176	+	4.66226i	−0.118383	+	0.205046i
$518$	11.5102	−	6.64542i	0.505729	−	0.291983i
$519$	37.6356	−	19.1847i	1.65202	−	0.842115i
$520$	−0.478712			−0.0209929
$521$	−11.3505			−0.497273			−0.248637	−	0.968597i	$-0.579982\pi$
$521$	−11.3505			−0.497273			−0.248637	+	0.968597i	$0.579982\pi$
$522$	1.87212	+	0.196097i	0.0819406	+	0.00858294i
$523$	31.9970	+	18.4735i	1.39913	+	0.807788i	0.994301	−	0.106605i	$-0.0339980\pi$
$523$	31.9970	+	18.4735i	1.39913	+	0.807788i	0.404828	+	0.914393i	$0.367331\pi$
$524$			15.4519i			0.675018i
$525$	−3.40196	−	2.20840i	−0.148474	−	0.0963825i
$526$	−12.2015	−	7.04453i	−0.532010	−	0.307156i
$527$	−2.84228	−	4.92298i	−0.123812	−	0.214448i
$528$	1.88661	+	3.70106i	0.0821043	+	0.161068i
$529$	−9.33904	−	16.1757i	−0.406045	−	0.703291i
$530$	11.5028	−	6.64114i	0.499649	−	0.288473i
$531$	−7.66339	−	17.1958i	−0.332563	−	0.746236i
$532$	7.44136	+	6.98655i	0.322624	+	0.302905i
$533$			1.00169i			0.0433882i
$534$	−0.898654	+	17.2057i	−0.0388886	+	0.744563i
$535$	10.5517	−	6.09204i	0.456191	−	0.263382i
$536$	11.3258	+	6.53894i	0.489199	+	0.282439i
$537$	1.81379	−	34.7269i	0.0782707	−	1.49858i
$538$	−9.48574	+	16.4298i	−0.408959	+	0.708339i
$539$			3.63730i			0.156670i
$540$	−5.13261	−	0.810128i	−0.220872	−	0.0348624i
$541$	15.2223	−	26.3657i	0.654456	−	1.13355i	−0.327574	−	0.944826i	$-0.606231\pi$
$541$	15.2223	−	26.3657i	0.654456	−	1.13355i	0.982030	−	0.188725i	$-0.0604356\pi$
$542$	12.6913	−	21.9819i	0.545137	−	0.944205i
$543$	11.1134	−	17.1198i	0.476924	−	0.734683i
$544$			2.77143i			0.118824i
$545$	−0.360514	+	0.624429i	−0.0154427	+	0.0267476i
$546$	1.93897	+	0.101272i	0.0829802	+	0.00433406i
$547$	−7.08775	−	4.09212i	−0.303050	−	0.174966i	0.340762	−	0.940150i	$-0.389315\pi$
$547$	−7.08775	−	4.09212i	−0.303050	−	0.174966i	−0.643812	+	0.765183i	$0.722648\pi$
$548$	−7.57874	+	4.37559i	−0.323748	+	0.186916i
$549$	−4.41313	+	6.07868i	−0.188348	+	0.259432i
$550$			2.39841i			0.102269i
$551$	−1.99392	−	1.87205i	−0.0849438	−	0.0797521i
$552$	−1.96060	+	3.02023i	−0.0834487	+	0.128550i
$553$	23.7890	−	13.7346i	1.01161	−	0.584053i
$554$	−4.05429	−	7.02224i	−0.172250	−	0.298346i
$555$	8.75845	−	4.46461i	0.371776	−	0.189512i
$556$	3.74921	+	6.49383i	0.159002	+	0.275400i
$557$	−1.37346	−	0.792970i	−0.0581956	−	0.0335992i	0.470620	−	0.882336i	$-0.344030\pi$
$557$	−1.37346	−	0.792970i	−0.0581956	−	0.0335992i	−0.528815	+	0.848737i	$0.677364\pi$
$558$	5.62051	−	2.50480i	0.237935	−	0.106037i
$559$			3.61209i			0.152775i
$560$	−2.02795	−	1.17084i	−0.0856966	−	0.0494770i
$561$	−10.2572	+	5.22862i	−0.433061	+	0.220752i
$562$	−25.2934			−1.06694
$563$	−12.2083			−0.514519			−0.257260	−	0.966342i	$-0.582820\pi$
$563$	−12.2083			−0.514519			−0.257260	+	0.966342i	$0.582820\pi$
$564$	−1.76563	−	3.46373i	−0.0743465	−	0.145849i
$565$	−8.65597	+	4.99753i	−0.364159	+	0.210247i
$566$	0.496185	−	0.859418i	0.0208562	−	0.0361240i
$567$	20.6177	+	4.36714i	0.865861	+	0.183403i
$568$	2.68385	+	4.64856i	0.112612	+	0.195049i
$569$	−30.1807			−1.26524			−0.632620	−	0.774462i	$-0.718021\pi$
$569$	−30.1807			−1.26524			−0.632620	+	0.774462i	$0.718021\pi$
$570$	5.22706	+	5.44774i	0.218937	+	0.228181i
$571$	−35.1445			−1.47075			−0.735375	−	0.677660i	$-0.762994\pi$
$571$	−35.1445			−1.47075			−0.735375	+	0.677660i	$0.762994\pi$
$572$	−0.574075	−	0.994328i	−0.0240033	−	0.0415749i
$573$	−12.7459	−	0.665718i	−0.532467	−	0.0278108i
$574$	−2.44995	+	4.24344i	−0.102259	+	0.177118i
$575$	−1.80040	+	1.03946i	−0.0750818	+	0.0433485i
$576$	−2.98368	−	0.312528i	−0.124320	−	0.0130220i
$577$	3.33452			0.138818			0.0694088	−	0.997588i	$-0.477889\pi$
$577$	3.33452			0.138818			0.0694088	+	0.997588i	$0.477889\pi$
$578$	9.31916			0.387626
$579$	5.87755	+	11.5303i	0.244262	+	0.479182i
$580$	0.543392	+	0.313727i	0.0225631	+	0.0130268i
$581$			26.4800i			1.09858i
$582$	−8.15874	+	12.5682i	−0.338191	+	0.520970i
$583$	27.5885	+	15.9282i	1.14260	+	0.659679i
$584$	−5.81045	−	10.0640i	−0.240438	−	0.416451i
$585$	1.42832	+	0.149611i	0.0590539	+	0.00618565i
$586$	−11.6674	−	20.2085i	−0.481976	−	0.834807i
$587$	−6.62612	+	3.82559i	−0.273489	+	0.157899i	−0.630472	−	0.776212i	$-0.717139\pi$
$587$	−6.62612	+	3.82559i	−0.273489	+	0.157899i	0.356983	+	0.934111i	$0.383805\pi$
$588$	−2.20321	−	1.43023i	−0.0908590	−	0.0589816i
$589$	−8.70464	−	2.04077i	−0.358668	−	0.0840883i
$590$		−	6.27539i		−	0.258354i
$591$	35.0038	+	1.82825i	1.43986	+	0.0752042i
$592$	4.91536	−	2.83789i	0.202020	−	0.116636i
$593$	16.7538	+	9.67281i	0.687996	+	0.397215i	0.802861	−	0.596166i	$-0.203310\pi$
$593$	16.7538	+	9.67281i	0.687996	+	0.397215i	−0.114865	+	0.993381i	$0.536643\pi$
$594$	−4.47236	−	11.6324i	−0.183503	−	0.477283i
$595$	3.24490	−	5.62033i	0.133028	−	0.230411i
$596$		−	12.2347i		−	0.501152i
$597$	16.3382	+	10.6060i	0.668678	+	0.434076i
$598$	0.497603	−	0.861873i	0.0203485	−	0.0352446i
$599$	0.00576144	−	0.00997910i	0.000235406	−	0.000407735i	−0.865908	−	0.500204i	$-0.833258\pi$
$599$	0.00576144	−	0.00997910i	0.000235406	−	0.000407735i	0.866143	+	0.499796i	$0.166592\pi$
$600$	−1.45279	−	0.943085i	−0.0593098	−	0.0385013i
$601$		−	19.6294i		−	0.800698i	−0.916363	−	0.400349i	$-0.868889\pi$
$601$		−	19.6294i		−	0.800698i	0.916363	−	0.400349i	$-0.131111\pi$
$602$	−8.83447	+	15.3018i	−0.360066	+	0.623653i
$603$	−31.7489	−	23.0497i	−1.29291	−	0.938657i
$604$	−13.9036	−	8.02727i	−0.565731	−	0.326625i
$605$	4.54456	−	2.62380i	0.184763	−	0.106673i
$606$	7.91060	+	0.413171i	0.321346	+	0.0167839i
$607$		−	48.4715i		−	1.96740i	−0.179821	−	0.983699i	$-0.557552\pi$
$607$		−	48.4715i		−	1.96740i	0.179821	−	0.983699i	$-0.442448\pi$
$608$	3.17779	+	2.98356i	0.128876	+	0.120999i
$609$	−2.13458	−	1.38567i	−0.0864974	−	0.0561503i
$610$	−2.16845	+	1.25195i	−0.0877979	+	0.0506901i
$611$	0.537262	+	0.930565i	0.0217353	+	0.0376466i
$612$	0.866149	−	8.26906i	0.0350120	−	0.334257i
$613$	17.8645	+	30.9422i	0.721539	+	1.24974i	0.960383	+	0.278685i	$0.0898985\pi$
$613$	17.8645	+	30.9422i	0.721539	+	1.24974i	−0.238843	+	0.971058i	$0.576768\pi$
$614$	21.4512	+	12.3849i	0.865702	+	0.499813i
$615$	−1.97338	+	3.03992i	−0.0795745	+	0.122582i
$616$		−	5.61632i		−	0.226288i
$617$	−28.5725	−	16.4963i	−1.15028	−	0.664117i	−0.201328	−	0.979524i	$-0.564526\pi$
$617$	−28.5725	−	16.4963i	−1.15028	−	0.664117i	−0.948957	+	0.315407i	$0.897859\pi$
$618$	−1.80851	−	3.54785i	−0.0727491	−	0.142716i
$619$	−33.4945			−1.34626			−0.673129	−	0.739525i	$-0.735050\pi$
$619$	−33.4945			−1.34626			−0.673129	+	0.739525i	$0.735050\pi$
$620$	2.05113			0.0823753
$621$	6.79370	−	8.39865i	0.272622	−	0.337026i
$622$	−9.74385	+	5.62562i	−0.390693	+	0.225567i
$623$	11.6466	−	20.1725i	0.466612	−	0.808196i
$624$	0.828026	+	0.0432478i	0.0331476	+	0.00173130i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−10.9329			−0.436966
$627$	−5.04710	+	17.3900i	−0.201562	+	0.694491i
$628$	1.67251			0.0667404
$629$	7.86501	+	13.6226i	0.313598	+	0.543169i
$630$	5.68484	+	4.12720i	0.226489	+	0.164431i
$631$	−11.0092	+	19.0686i	−0.438271	+	0.759108i	−0.997556	−	0.0698675i	$-0.977742\pi$
$631$	−11.0092	+	19.0686i	−0.438271	+	0.759108i	0.559285	+	0.828975i	$0.311076\pi$
$632$	10.1589	−	5.86527i	0.404101	−	0.233308i
$633$	20.8651	+	40.9320i	0.829312	+	1.62690i
$634$	17.9005			0.710921
$635$	11.0708			0.439333
$636$	−20.4963	+	10.4479i	−0.812730	+	0.414288i
$637$	0.628724	+	0.362994i	0.0249110	+	0.0143823i
$638$			1.50490i			0.0595794i
$639$	−6.55493	−	14.7086i	−0.259309	−	0.581862i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$	−7.33431	−	12.7034i	−0.289688	−	0.501754i	0.684047	−	0.729438i	$-0.260218\pi$
$641$	−7.33431	−	12.7034i	−0.289688	−	0.501754i	−0.973735	+	0.227684i	$0.926885\pi$
$642$	−18.8016	+	9.58409i	−0.742040	+	0.378254i
$643$	−15.3180	−	26.5315i	−0.604082	−	1.04630i	−0.992196	−	0.124690i	$-0.960207\pi$
$643$	−15.3180	−	26.5315i	−0.604082	−	1.04630i	0.388114	−	0.921612i	$-0.373127\pi$
$644$	4.21595	−	2.43408i	0.166132	−	0.0959163i
$645$	−7.11597	+	10.9619i	−0.280191	+	0.431624i
$646$	−8.26874	+	8.80703i	−0.325329	+	0.346508i
$647$		−	9.82606i		−	0.386302i	−0.981169	−	0.193151i	$-0.938129\pi$
$647$		−	9.82606i		−	0.386302i	0.981169	−	0.193151i	$-0.0618707\pi$
$648$	8.80465	+	1.86496i	0.345879	+	0.0732627i
$649$	13.0345	−	7.52549i	0.511650	−	0.295401i
$650$	0.414577	+	0.239356i	0.0162611	+	0.00938832i
$651$	−8.30786	−	0.433920i	−0.325611	−	0.0170067i
$652$	−6.21359	+	10.7622i	−0.243343	+	0.421482i
$653$			31.4026i			1.22888i	0.788964	+	0.614440i	$0.210618\pi$
$653$			31.4026i			1.22888i	−0.788964	+	0.614440i	$0.789382\pi$
$654$	0.679991	−	1.04750i	0.0265898	−	0.0409605i
$655$	7.72594	−	13.3817i	0.301877	−	0.522867i
$656$	−1.04624	+	1.81214i	−0.0408487	+	0.0707521i
$657$	14.1912	+	31.8436i	0.553652	+	1.24234i
$658$			5.25616i			0.204906i
$659$	−1.68244	+	2.91407i	−0.0655385	+	0.113516i	−0.896933	−	0.442167i	$-0.854210\pi$
$659$	−1.68244	+	2.91407i	−0.0655385	+	0.113516i	0.831394	+	0.555683i	$0.187543\pi$
$660$	0.216677	−	4.14852i	0.00843416	−	0.161481i
$661$	−6.16334	−	3.55840i	−0.239726	−	0.138406i	0.375325	−	0.926893i	$-0.377531\pi$
$661$	−6.16334	−	3.55840i	−0.239726	−	0.138406i	−0.615051	+	0.788487i	$0.710865\pi$
$662$	−8.97416	+	5.18123i	−0.348790	+	0.201374i
$663$	−0.119858	+	2.29482i	−0.00465491	+	0.0891233i
$664$			11.3081i			0.438841i
$665$	−2.95113	−	9.77121i	−0.114440	−	0.378911i
$666$	−15.5528	+	6.93115i	−0.602658	+	0.268577i
$667$	−1.12967	+	0.652215i	−0.0437410	+	0.0252539i
$668$	−0.136815	−	0.236971i	−0.00529355	−	0.00916869i
$669$	11.9997	+	23.5403i	0.463933	+	0.910122i
$670$	−6.53894	−	11.3258i	−0.252621	−	0.437553i
$671$	−5.20084	−	3.00270i	−0.200776	−	0.115918i
$672$	3.40196	+	2.20840i	0.131233	+	0.0851909i
$673$			26.5117i			1.02195i	0.859596	+	0.510975i	$0.170716\pi$
$673$			26.5117i			1.02195i	−0.859596	+	0.510975i	$0.829284\pi$
$674$	23.7499	+	13.7120i	0.914810	+	0.528166i
$675$	4.03991	+	3.26790i	0.155496	+	0.125781i
$676$	12.7708			0.491186
$677$	−42.3166			−1.62636			−0.813179	−	0.582013i	$-0.802265\pi$
$677$	−42.3166			−1.62636			−0.813179	+	0.582013i	$0.802265\pi$
$678$	15.4237	−	7.86219i	0.592342	−	0.301946i
$679$	17.5441	−	10.1291i	0.673279	−	0.388718i
$680$	1.38572	−	2.40013i	0.0531398	−	0.0920408i
$681$	−0.157293	+	3.01154i	−0.00602748	+	0.115403i
$682$	2.45973	+	4.26038i	0.0941879	+	0.163138i
$683$	11.0677			0.423493			0.211746	−	0.977325i	$-0.432085\pi$
$683$	11.0677			0.423493			0.211746	+	0.977325i	$0.432085\pi$
$684$	−8.54905	−	9.89514i	−0.326881	−	0.378350i
$685$	8.75118			0.334365
$686$	9.97150	+	17.2711i	0.380714	+	0.659415i
$687$	−1.50378	+	28.7914i	−0.0573726	+	1.09846i
$688$	−3.77271	+	6.53452i	−0.143833	+	0.249126i
$689$	5.50653	−	3.17920i	0.209782	−	0.121118i
$690$	3.20804	−	1.63530i	0.122128	−	0.0622547i
$691$	20.2406			0.769990			0.384995	−	0.922919i	$-0.374203\pi$
$691$	20.2406			0.769990			0.384995	+	0.922919i	$0.374203\pi$
$692$	−24.3892			−0.927137
$693$	−1.75525	+	16.7573i	−0.0666766	+	0.636556i
$694$	22.5112	+	12.9969i	0.854515	+	0.493354i
$695$		−	7.49842i		−	0.284431i
$696$	−0.911558	−	0.591743i	−0.0345525	−	0.0224300i
$697$	−5.02222	−	2.89958i	−0.190230	−	0.109829i
$698$	−4.08348	−	7.07280i	−0.154562	−	0.267710i
$699$	6.82384	+	13.3867i	0.258101	+	0.506330i
$700$	1.17084	+	2.02795i	0.0442536	+	0.0766494i
$701$	−12.8127	+	7.39742i	−0.483929	+	0.279397i	−0.722053	−	0.691838i	$-0.756801\pi$
$701$	−12.8127	+	7.39742i	−0.483929	+	0.279397i	0.238123	+	0.971235i	$0.423468\pi$
$702$	−2.45704	−	0.387819i	−0.0927352	−	0.0146373i
$703$	24.0870	+	5.64709i	0.908459	+	0.212984i
$704$		−	2.39841i		−	0.0903936i
$705$	−0.202783	+	3.88249i	−0.00763724	+	0.146223i
$706$	20.0065	−	11.5507i	0.752953	−	0.434718i
$707$	−9.27466	−	5.35473i	−0.348810	−	0.201385i
$708$	−0.566931	+	10.8545i	−0.0213066	+	0.407937i
$709$	−0.506440	+	0.877179i	−0.0190197	+	0.0329432i	−0.875379	−	0.483438i	$-0.839388\pi$
$709$	−0.506440	+	0.877179i	−0.0190197	+	0.0329432i	0.856359	+	0.516381i	$0.172721\pi$
$710$		−	5.36769i		−	0.201446i
$711$	−32.1440	+	14.3251i	−1.20550	+	0.537234i
$712$	4.97362	−	8.61457i	0.186394	−	0.322845i
$713$	−2.13207	+	3.69285i	−0.0798466	+	0.138298i
$714$	−6.12044	+	9.42830i	−0.229052	+	0.352845i
$715$			1.14815i			0.0429384i
$716$	−10.0385	+	17.3871i	−0.375155	+	0.649787i
$717$	−33.1208	−	1.72990i	−1.23692	−	0.0646043i
$718$	−17.3948	−	10.0429i	−0.649168	−	0.374798i
$719$	2.95761	−	1.70758i	0.110300	−	0.0636819i	−0.443835	−	0.896109i	$-0.646382\pi$
$719$	2.95761	−	1.70758i	0.110300	−	0.0636819i	0.554135	+	0.832427i	$0.313049\pi$
$720$	2.42768	+	1.76250i	0.0904741	+	0.0656843i
$721$			5.38382i			0.200504i
$722$	1.19670	+	18.9623i	0.0445364	+	0.705703i
$723$	−18.1187	+	27.9111i	−0.673840	+	1.03803i
$724$	−10.2054	+	5.89207i	−0.379279	+	0.218977i
$725$	−0.313727	−	0.543392i	−0.0116515	−	0.0201811i
$726$	−8.09774	+	4.12781i	−0.300535	+	0.153197i
$727$	−20.0624	−	34.7491i	−0.744074	−	1.28877i	−0.950626	−	0.310338i	$-0.899558\pi$
$727$	−20.0624	−	34.7491i	−0.744074	−	1.28877i	0.206552	−	0.978436i	$-0.433776\pi$
$728$	−0.970806	−	0.560495i	−0.0359805	−	0.0207733i
$729$	−25.6874	−	8.31615i	−0.951385	−	0.308005i
$730$			11.6209i			0.430109i
$731$	−18.1100	−	10.4558i	−0.669822	−	0.386722i
$732$	3.86385	−	1.96959i	0.142812	−	0.0727983i
$733$	42.4761			1.56889			0.784446	−	0.620197i	$-0.212947\pi$
$733$	42.4761			1.56889			0.784446	+	0.620197i	$0.212947\pi$
$734$	−9.66168			−0.356619
$735$	1.19293	+	2.34022i	0.0440017	+	0.0863204i
$736$	1.80040	−	1.03946i	0.0663636	−	0.0383150i
$737$	15.6831	−	27.1639i	0.577694	−	1.00060i
$738$	3.68798	−	5.07985i	0.135756	−	0.186992i
$739$	−25.6660	−	44.4548i	−0.944139	−	1.63530i	−0.757466	−	0.652874i	$-0.773563\pi$
$739$	−25.6660	−	44.4548i	−0.944139	−	1.63530i	−0.186673	−	0.982422i	$-0.559770\pi$
$740$	−5.67577			−0.208646
$741$	2.50226	+	2.60790i	0.0919228	+	0.0958036i
$742$	31.1028			1.14182
$743$	−14.7044	−	25.4688i	−0.539454	−	0.934361i	−0.998933	−	0.0461730i	$-0.985297\pi$
$743$	−14.7044	−	25.4688i	−0.539454	−	0.934361i	0.459480	−	0.888188i	$-0.348036\pi$
$744$	−3.54782	−	0.185303i	−0.130070	−	0.00679354i
$745$	−6.11734	+	10.5955i	−0.224122	+	0.388190i
$746$	−14.5767	+	8.41587i	−0.533692	+	0.308127i
$747$	3.53411	−	33.7398i	0.129306	−	1.23448i
$748$	6.64704			0.243040
$749$	28.5312			1.04251
$750$	0.786608	+	1.54313i	0.0287229	+	0.0563471i
$751$	9.26493	+	5.34911i	0.338082	+	0.195192i	0.659424	−	0.751772i	$-0.270800\pi$
$751$	9.26493	+	5.34911i	0.338082	+	0.195192i	−0.321342	+	0.946963i	$0.604134\pi$
$752$			2.24461i			0.0818526i
$753$	11.7935	−	18.1675i	0.429779	−	0.662059i
$754$	0.260128	+	0.150185i	0.00947332	+	0.00546942i
$755$	8.02727	+	13.9036i	0.292142	+	0.506005i
$756$	−9.46016	−	7.65236i	−0.344063	−	0.278314i
$757$	−8.59944	−	14.8947i	−0.312552	−	0.541356i	0.666362	−	0.745628i	$-0.267851\pi$
$757$	−8.59944	−	14.8947i	−0.312552	−	0.541356i	−0.978914	+	0.204272i	$0.934517\pi$
$758$	27.3759	−	15.8055i	0.994337	−	0.574081i
$759$	7.24376	+	4.70233i	0.262932	+	0.170684i
$760$	−1.26026	−	4.17274i	−0.0457146	−	0.151361i
$761$			35.2476i			1.27772i	0.769321	+	0.638862i	$0.220595\pi$
$761$			35.2476i			1.27772i	−0.769321	+	0.638862i	$0.779405\pi$
$762$	−19.1492	−	1.00016i	−0.693701	−	0.0362320i
$763$	−1.46221	+	0.844208i	−0.0529356	+	0.0305624i
$764$	6.38163	+	3.68444i	0.230879	+	0.133298i
$765$	−4.88464	+	6.72814i	−0.176604	+	0.243256i
$766$	−14.8637	+	25.7447i	−0.537048	+	0.930194i
$767$		−	3.00411i		−	0.108472i
$768$	1.45279	+	0.943085i	0.0524229	+	0.0340306i
$769$	−16.3809	+	28.3725i	−0.590710	+	1.02314i	0.403427	+	0.915012i	$0.367819\pi$
$769$	−16.3809	+	28.3725i	−0.590710	+	1.02314i	−0.994137	+	0.108128i	$0.965514\pi$
$770$	−2.80816	+	4.86387i	−0.101199	+	0.175282i
$771$	−2.13197	−	1.38398i	−0.0767811	−	0.0498429i
$772$		−	7.47201i		−	0.268924i
$773$	9.83728	−	17.0387i	0.353822	−	0.612838i	−0.633093	−	0.774075i	$-0.718215\pi$
$773$	9.83728	−	17.0387i	0.353822	−	0.612838i	0.986916	+	0.161237i	$0.0515484\pi$
$774$	13.2988	−	18.3178i	0.478014	−	0.658421i
$775$	−1.77633	−	1.02556i	−0.0638077	−

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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.0903420 - 1.72969i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.54313 + 0.786608i) q^{6} +2.34168 q^{7} +1.00000 q^{8} +(-2.98368 - 0.312528i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.0903420 - 1.72969i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.54313 + 0.786608i) q^{6} +2.34168 q^{7} +1.00000 q^{8} +(-2.98368 - 0.312528i) q^{9} +(-0.866025 - 0.500000i) q^{10} -2.39841i q^{11} +(1.45279 + 0.943085i) q^{12} +(-0.414577 - 0.239356i) q^{13} +(-1.17084 - 2.02795i) q^{14} +(-0.786608 - 1.54313i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.40013 - 1.38572i) q^{17} +(1.22118 + 2.74020i) q^{18} +(0.994947 - 4.24383i) q^{19} +1.00000i q^{20} +(0.211552 - 4.05038i) q^{21} +(-2.07709 + 1.19921i) q^{22} +(-1.80040 - 1.03946i) q^{23} +(0.0903420 - 1.72969i) q^{24} +(0.500000 - 0.866025i) q^{25} +0.478712i q^{26} +(-0.810128 + 5.13261i) q^{27} +(-1.17084 + 2.02795i) q^{28} +(0.313727 - 0.543392i) q^{29} +(-0.943085 + 1.45279i) q^{30} -2.05113i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-4.14852 - 0.216677i) q^{33} +(-2.40013 - 1.38572i) q^{34} +(2.02795 - 1.17084i) q^{35} +(1.76250 - 2.42768i) q^{36} +5.67577i q^{37} +(-4.17274 + 1.26026i) q^{38} +(-0.451467 + 0.695467i) q^{39} +(0.866025 - 0.500000i) q^{40} +(-1.04624 - 1.81214i) q^{41} +(-3.61351 + 1.84198i) q^{42} +(-3.77271 - 6.53452i) q^{43} +(2.07709 + 1.19921i) q^{44} +(-2.74020 + 1.22118i) q^{45} +2.07892i q^{46} +(-1.94389 - 1.12231i) q^{47} +(-1.54313 + 0.786608i) q^{48} -1.51654 q^{49} -1.00000 q^{50} +(-2.18003 - 4.27668i) q^{51} +(0.414577 - 0.239356i) q^{52} +(-6.64114 + 11.5028i) q^{53} +(4.85004 - 1.86471i) q^{54} +(-1.19921 - 2.07709i) q^{55} +2.34168 q^{56} +(-7.25064 - 2.10435i) q^{57} -0.627455 q^{58} +(3.13769 + 5.43465i) q^{59} +(1.72969 + 0.0903420i) q^{60} +(1.25195 - 2.16845i) q^{61} +(-1.77633 + 1.02556i) q^{62} +(-6.98681 - 0.731839i) q^{63} +1.00000 q^{64} -0.478712 q^{65} +(1.88661 + 3.70106i) q^{66} +(11.3258 + 6.53894i) q^{67} +2.77143i q^{68} +(-1.96060 + 3.02023i) q^{69} +(-2.02795 - 1.17084i) q^{70} +(2.68385 + 4.64856i) q^{71} +(-2.98368 - 0.312528i) q^{72} +(-5.81045 - 10.0640i) q^{73} +(4.91536 - 2.83789i) q^{74} +(-1.45279 - 0.943085i) q^{75} +(3.17779 + 2.98356i) q^{76} -5.61632i q^{77} +(0.828026 + 0.0432478i) q^{78} +(10.1589 - 5.86527i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(8.80465 + 1.86496i) q^{81} +(-1.04624 + 1.81214i) q^{82} +11.3081i q^{83} +(3.40196 + 2.20840i) q^{84} +(1.38572 - 2.40013i) q^{85} +(-3.77271 + 6.53452i) q^{86} +(-0.911558 - 0.591743i) q^{87} -2.39841i q^{88} +(4.97362 - 8.61457i) q^{89} +(2.42768 + 1.76250i) q^{90} +(-0.970806 - 0.560495i) q^{91} +(1.80040 - 1.03946i) q^{92} +(-3.54782 - 0.185303i) q^{93} +2.24461i q^{94} +(-1.26026 - 4.17274i) q^{95} +(1.45279 + 0.943085i) q^{96} +(7.49209 - 4.32556i) q^{97} +(0.758271 + 1.31336i) q^{98} +(-0.749571 + 7.15609i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24q - 12q^{2} + 4q^{3} - 12q^{4} - 2q^{6} - 12q^{7} + 24q^{8} - 4q^{9} + O(q^{10}) \)	\( 24q - 12q^{2} + 4q^{3} - 12q^{4} - 2q^{6} - 12q^{7} + 24q^{8} - 4q^{9} - 2q^{12} + 18q^{13} + 6q^{14} - 12q^{16} + 12q^{17} + 2q^{18} + 6q^{19} - 6q^{21} + 18q^{22} + 4q^{24} + 12q^{25} + 28q^{27} + 6q^{28} - 12q^{32} - 22q^{33} - 12q^{34} + 2q^{36} + 6q^{38} + 40q^{39} + 6q^{41} - 6q^{42} - 22q^{43} - 18q^{44} + 8q^{45} + 12q^{47} - 2q^{48} + 12q^{49} - 24q^{50} - 20q^{51} - 18q^{52} + 8q^{53} + 4q^{54} - 12q^{56} + 26q^{59} + 22q^{61} - 18q^{62} + 6q^{63} + 24q^{64} + 8q^{65} + 8q^{66} - 48q^{67} - 64q^{69} + 24q^{71} - 4q^{72} - 8q^{73} + 30q^{74} + 2q^{75} - 12q^{76} - 38q^{78} + 18q^{79} - 12q^{81} + 6q^{82} + 12q^{84} - 22q^{86} - 24q^{87} + 28q^{89} + 8q^{90} + 18q^{91} + 2q^{93} - 2q^{96} + 6q^{97} - 6q^{98} + 2q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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