LMFDB - Embedded newform 510.2.l.g.443.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(137,510)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(510, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("510.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			443.2
Character	$\chi$	$=$	510.443
Dual form			510.2.l.g.137.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.58179 - 0.705653i) q^{3} +1.00000i q^{4} +(-2.23394 - 0.0974809i) q^{5} +(0.619522 + 1.61746i) q^{6} +(-3.25954 + 3.25954i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.00411 + 2.23239i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.58179 - 0.705653i) q^{3} +1.00000i q^{4} +(-2.23394 - 0.0974809i) q^{5} +(0.619522 + 1.61746i) q^{6} +(-3.25954 + 3.25954i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.00411 + 2.23239i) q^{9} +(1.51071 + 1.64857i) q^{10} -3.90269i q^{11} +(0.705653 - 1.58179i) q^{12} +(2.89233 + 2.89233i) q^{13} +4.60968 q^{14} +(3.46484 + 1.73058i) q^{15} -1.00000 q^{16} +(-0.707107 - 0.707107i) q^{17} +(0.161416 - 2.99565i) q^{18} -5.28003i q^{19} +(0.0974809 - 2.23394i) q^{20} +(7.45600 - 2.85580i) q^{21} +(-2.75962 + 2.75962i) q^{22} +(1.08718 - 1.08718i) q^{23} +(-1.61746 + 0.619522i) q^{24} +(4.98099 + 0.435533i) q^{25} -4.09037i q^{26} +(-1.59479 - 4.94537i) q^{27} +(-3.25954 - 3.25954i) q^{28} -1.81942 q^{29} +(-1.22630 - 3.67371i) q^{30} +7.47022 q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.75395 + 6.17324i) q^{33} +1.00000i q^{34} +(7.59936 - 6.96388i) q^{35} +(-2.23239 + 2.00411i) q^{36} +(-3.81301 + 3.81301i) q^{37} +(-3.73355 + 3.73355i) q^{38} +(-2.53407 - 6.61602i) q^{39} +(-1.64857 + 1.51071i) q^{40} +3.03782i q^{41} +(-7.29154 - 3.25283i) q^{42} +(-3.66501 - 3.66501i) q^{43} +3.90269 q^{44} +(-4.25945 - 5.18238i) q^{45} -1.53751 q^{46} +(3.79800 + 3.79800i) q^{47} +(1.58179 + 0.705653i) q^{48} -14.2492i q^{49} +(-3.21413 - 3.83006i) q^{50} +(0.619522 + 1.61746i) q^{51} +(-2.89233 + 2.89233i) q^{52} +(8.80475 - 8.80475i) q^{53} +(-2.36922 + 4.62459i) q^{54} +(-0.380438 + 8.71839i) q^{55} +4.60968i q^{56} +(-3.72587 + 8.35189i) q^{57} +(1.28652 + 1.28652i) q^{58} +8.47740 q^{59} +(-1.73058 + 3.46484i) q^{60} +10.1169 q^{61} +(-5.28225 - 5.28225i) q^{62} +(-13.8090 - 0.744077i) q^{63} -1.00000i q^{64} +(-6.17934 - 6.74323i) q^{65} +(6.31247 - 2.41780i) q^{66} +(4.29168 - 4.29168i) q^{67} +(0.707107 - 0.707107i) q^{68} +(-2.48687 + 0.952520i) q^{69} +(-10.2978 - 0.449356i) q^{70} -3.19160i q^{71} +(2.99565 + 0.161416i) q^{72} +(7.14647 + 7.14647i) q^{73} +5.39241 q^{74} +(-7.57154 - 4.20377i) q^{75} +5.28003 q^{76} +(12.7210 + 12.7210i) q^{77} +(-2.88638 + 6.47009i) q^{78} +3.97142i q^{79} +(2.23394 + 0.0974809i) q^{80} +(-0.967094 + 8.94789i) q^{81} +(2.14806 - 2.14806i) q^{82} +(3.62800 - 3.62800i) q^{83} +(2.85580 + 7.45600i) q^{84} +(1.51071 + 1.64857i) q^{85} +5.18310i q^{86} +(2.87794 + 1.28388i) q^{87} +(-2.75962 - 2.75962i) q^{88} -7.98362 q^{89} +(-0.652613 + 6.67638i) q^{90} -18.8553 q^{91} +(1.08718 + 1.08718i) q^{92} +(-11.8163 - 5.27138i) q^{93} -5.37118i q^{94} +(-0.514702 + 11.7953i) q^{95} +(-0.619522 - 1.61746i) q^{96} +(9.40927 - 9.40927i) q^{97} +(-10.0757 + 10.0757i) q^{98} +(8.71232 - 7.82142i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{7}+O(q^{10}) $ 28 * q + 4 * q^7	$ 28 q + 4 q^{7} - 12 q^{10} - 8 q^{13} + 8 q^{15} - 28 q^{16} - 16 q^{18} + 48 q^{21} + 20 q^{22} + 40 q^{25} - 36 q^{27} + 4 q^{28} - 12 q^{30} + 16 q^{31} + 8 q^{33} + 8 q^{37} - 8 q^{40} - 48 q^{42} + 48 q^{43} + 36 q^{45} - 64 q^{46} + 8 q^{52} - 36 q^{55} - 32 q^{57} + 20 q^{58} + 12 q^{60} - 16 q^{61} - 56 q^{63} + 32 q^{66} + 112 q^{67} - 28 q^{70} + 16 q^{72} + 12 q^{73} + 16 q^{75} - 8 q^{76} - 32 q^{78} - 48 q^{81} + 24 q^{82} - 12 q^{85} - 44 q^{87} + 20 q^{88} - 20 q^{90} - 80 q^{91} + 28 q^{93} + 60 q^{97}+O(q^{100}) $ 28 * q + 4 * q^7 - 12 * q^10 - 8 * q^13 + 8 * q^15 - 28 * q^16 - 16 * q^18 + 48 * q^21 + 20 * q^22 + 40 * q^25 - 36 * q^27 + 4 * q^28 - 12 * q^30 + 16 * q^31 + 8 * q^33 + 8 * q^37 - 8 * q^40 - 48 * q^42 + 48 * q^43 + 36 * q^45 - 64 * q^46 + 8 * q^52 - 36 * q^55 - 32 * q^57 + 20 * q^58 + 12 * q^60 - 16 * q^61 - 56 * q^63 + 32 * q^66 + 112 * q^67 - 28 * q^70 + 16 * q^72 + 12 * q^73 + 16 * q^75 - 8 * q^76 - 32 * q^78 - 48 * q^81 + 24 * q^82 - 12 * q^85 - 44 * q^87 + 20 * q^88 - 20 * q^90 - 80 * q^91 + 28 * q^93 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−1.58179	−	0.705653i	−0.913246	−	0.407409i
$3$	−1.58179	−	0.705653i	−0.913246	−	0.407409i
$4$			1.00000i			0.500000i
$5$	−2.23394	−	0.0974809i	−0.999049	−	0.0435948i
$5$	−2.23394	−	0.0974809i	−0.999049	−	0.0435948i
$6$	0.619522	+	1.61746i	0.252919	+	0.660327i
$7$	−3.25954	+	3.25954i	−1.23199	+	1.23199i	−0.268791	+	0.963199i	$0.586624\pi$
$7$	−3.25954	+	3.25954i	−1.23199	+	1.23199i	−0.963199	+	0.268791i	$0.913376\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.00411	+	2.23239i	0.668036	+	0.744129i
$10$	1.51071	+	1.64857i	0.477727	+	0.521322i
$11$		−	3.90269i		−	1.17671i	−0.808604	−	0.588353i	$-0.799776\pi$
$11$		−	3.90269i		−	1.17671i	0.808604	−	0.588353i	$-0.200224\pi$
$12$	0.705653	−	1.58179i	0.203704	−	0.456623i
$13$	2.89233	+	2.89233i	0.802187	+	0.802187i	0.983437	−	0.181250i	$-0.0580144\pi$
$13$	2.89233	+	2.89233i	0.802187	+	0.802187i	−0.181250	+	0.983437i	$0.558014\pi$
$14$	4.60968			1.23199
$15$	3.46484	+	1.73058i	0.894617	+	0.446834i
$16$	−1.00000			−0.250000
$17$	−0.707107	−	0.707107i	−0.171499	−	0.171499i
$17$	−0.707107	−	0.707107i	−0.171499	−	0.171499i
$18$	0.161416	−	2.99565i	0.0380461	−	0.706082i
$19$		−	5.28003i		−	1.21132i	−0.795723	−	0.605661i	$-0.792909\pi$
$19$		−	5.28003i		−	1.21132i	0.795723	−	0.605661i	$-0.207091\pi$
$20$	0.0974809	−	2.23394i	0.0217974	−	0.499525i
$21$	7.45600	−	2.85580i	1.62703	−	0.623186i
$22$	−2.75962	+	2.75962i	−0.588353	+	0.588353i
$23$	1.08718	−	1.08718i	0.226693	−	0.226693i	−0.584616	−	0.811310i	$-0.698755\pi$
$23$	1.08718	−	1.08718i	0.226693	−	0.226693i	0.811310	+	0.584616i	$0.198755\pi$
$24$	−1.61746	+	0.619522i	−0.330164	+	0.126459i
$25$	4.98099	+	0.435533i	0.996199	+	0.0871067i
$26$		−	4.09037i		−	0.802187i
$27$	−1.59479	−	4.94537i	−0.306917	−	0.951736i
$28$	−3.25954	−	3.25954i	−0.615995	−	0.615995i
$29$	−1.81942			−0.337858			−0.168929	−	0.985628i	$-0.554031\pi$
$29$	−1.81942			−0.337858			−0.168929	+	0.985628i	$0.554031\pi$
$30$	−1.22630	−	3.67371i	−0.223891	−	0.670725i
$31$	7.47022			1.34169			0.670846	−	0.741597i	$-0.265931\pi$
$31$	7.47022			1.34169			0.670846	+	0.741597i	$0.265931\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−2.75395	+	6.17324i	−0.479400	+	1.07462i
$34$			1.00000i			0.171499i
$35$	7.59936	−	6.96388i	1.28453	−	1.17711i
$36$	−2.23239	+	2.00411i	−0.372064	+	0.334018i
$37$	−3.81301	+	3.81301i	−0.626855	+	0.626855i	−0.947275	−	0.320421i	$-0.896176\pi$
$37$	−3.81301	+	3.81301i	−0.626855	+	0.626855i	0.320421	+	0.947275i	$0.396176\pi$
$38$	−3.73355	+	3.73355i	−0.605661	+	0.605661i
$39$	−2.53407	−	6.61602i	−0.405776	−	1.05941i
$40$	−1.64857	+	1.51071i	−0.260661	+	0.238864i
$41$			3.03782i			0.474428i	0.971457	+	0.237214i	$0.0762343\pi$
$41$			3.03782i			0.474428i	−0.971457	+	0.237214i	$0.923766\pi$
$42$	−7.29154	−	3.25283i	−1.12511	−	0.501923i
$43$	−3.66501	−	3.66501i	−0.558908	−	0.558908i	0.370088	−	0.928997i	$-0.379327\pi$
$43$	−3.66501	−	3.66501i	−0.558908	−	0.558908i	−0.928997	+	0.370088i	$0.879327\pi$
$44$	3.90269			0.588353
$45$	−4.25945	−	5.18238i	−0.634961	−	0.772544i
$46$	−1.53751			−0.226693
$47$	3.79800	+	3.79800i	0.553995	+	0.553995i	0.927591	−	0.373597i	$-0.121876\pi$
$47$	3.79800	+	3.79800i	0.553995	+	0.553995i	−0.373597	+	0.927591i	$0.621876\pi$
$48$	1.58179	+	0.705653i	0.228311	+	0.101852i
$49$		−	14.2492i		−	2.03560i
$50$	−3.21413	−	3.83006i	−0.454546	−	0.541653i
$51$	0.619522	+	1.61746i	0.0867504	+	0.226490i
$52$	−2.89233	+	2.89233i	−0.401093	+	0.401093i
$53$	8.80475	−	8.80475i	1.20942	−	1.20942i	0.238212	−	0.971213i	$-0.423439\pi$
$53$	8.80475	−	8.80475i	1.20942	−	1.20942i	0.971213	−	0.238212i	$-0.0765612\pi$
$54$	−2.36922	+	4.62459i	−0.322410	+	0.629327i
$55$	−0.380438	+	8.71839i	−0.0512983	+	1.17559i
$56$			4.60968i			0.615995i
$57$	−3.72587	+	8.35189i	−0.493503	+	1.10624i
$58$	1.28652	+	1.28652i	0.168929	+	0.168929i
$59$	8.47740			1.10366			0.551832	−	0.833955i	$-0.313929\pi$
$59$	8.47740			1.10366			0.551832	+	0.833955i	$0.313929\pi$
$60$	−1.73058	+	3.46484i	−0.223417	+	0.447308i
$61$	10.1169			1.29533			0.647666	−	0.761924i	$-0.275745\pi$
$61$	10.1169			1.29533			0.647666	+	0.761924i	$0.275745\pi$
$62$	−5.28225	−	5.28225i	−0.670846	−	0.670846i
$63$	−13.8090	−	0.744077i	−1.73977	−	0.0937449i
$64$		−	1.00000i		−	0.125000i
$65$	−6.17934	−	6.74323i	−0.766453	−	0.836395i
$66$	6.31247	−	2.41780i	0.777011	−	0.297611i
$67$	4.29168	−	4.29168i	0.524312	−	0.524312i	−0.394559	−	0.918871i	$-0.629103\pi$
$67$	4.29168	−	4.29168i	0.524312	−	0.524312i	0.918871	+	0.394559i	$0.129103\pi$
$68$	0.707107	−	0.707107i	0.0857493	−	0.0857493i
$69$	−2.48687	+	0.952520i	−0.299384	+	0.114670i
$70$	−10.2978	−	0.449356i	−1.23082	−	0.0537083i
$71$		−	3.19160i		−	0.378773i	−0.981903	−	0.189387i	$-0.939350\pi$
$71$		−	3.19160i		−	0.378773i	0.981903	−	0.189387i	$-0.0606500\pi$
$72$	2.99565	+	0.161416i	0.353041	+	0.0190231i
$73$	7.14647	+	7.14647i	0.836431	+	0.836431i	0.988387	−	0.151956i	$-0.0485572\pi$
$73$	7.14647	+	7.14647i	0.836431	+	0.836431i	−0.151956	+	0.988387i	$0.548557\pi$
$74$	5.39241			0.626855
$75$	−7.57154	−	4.20377i	−0.874287	−	0.485410i
$76$	5.28003			0.605661
$77$	12.7210	+	12.7210i	1.44969	+	1.44969i
$78$	−2.88638	+	6.47009i	−0.326818	+	0.732594i
$79$			3.97142i			0.446820i	0.974725	+	0.223410i	$0.0717189\pi$
$79$			3.97142i			0.446820i	−0.974725	+	0.223410i	$0.928281\pi$
$80$	2.23394	+	0.0974809i	0.249762	+	0.0108987i
$81$	−0.967094	+	8.94789i	−0.107455	+	0.994210i
$82$	2.14806	−	2.14806i	0.237214	−	0.237214i
$83$	3.62800	−	3.62800i	0.398225	−	0.398225i	−0.479382	−	0.877607i	$-0.659139\pi$
$83$	3.62800	−	3.62800i	0.398225	−	0.398225i	0.877607	+	0.479382i	$0.159139\pi$
$84$	2.85580	+	7.45600i	0.311593	+	0.813516i
$85$	1.51071	+	1.64857i	0.163859	+	0.178812i
$86$			5.18310i			0.558908i
$87$	2.87794	+	1.28388i	0.308547	+	0.137646i
$88$	−2.75962	−	2.75962i	−0.294177	−	0.294177i
$89$	−7.98362			−0.846262			−0.423131	−	0.906068i	$-0.639069\pi$
$89$	−7.98362			−0.846262			−0.423131	+	0.906068i	$0.639069\pi$
$90$	−0.652613	+	6.67638i	−0.0687915	+	0.703753i
$91$	−18.8553			−1.97657
$92$	1.08718	+	1.08718i	0.113347	+	0.113347i
$93$	−11.8163	−	5.27138i	−1.22529	−	0.546617i
$94$		−	5.37118i		−	0.553995i
$95$	−0.514702	+	11.7953i	−0.0528073	+	1.21017i
$96$	−0.619522	−	1.61746i	−0.0632297	−	0.165082i
$97$	9.40927	−	9.40927i	0.955366	−	0.955366i	−0.0436795	−	0.999046i	$-0.513908\pi$
$97$	9.40927	−	9.40927i	0.955366	−	0.955366i	0.999046	+	0.0436795i	$0.0139080\pi$
$98$	−10.0757	+	10.0757i	−1.01780	+	1.01780i
$99$	8.71232	−	7.82142i	0.875621	−	0.786083i
$100$	−0.435533	+	4.98099i	−0.0435533	+	0.498099i
$101$			16.9895i			1.69052i	0.534355	+	0.845260i	$0.320555\pi$
$101$			16.9895i			1.69052i	−0.534355	+	0.845260i	$0.679445\pi$
$102$	0.705653	−	1.58179i	0.0698700	−	0.156620i
$103$	−2.46916	−	2.46916i	−0.243294	−	0.243294i	0.574918	−	0.818211i	$-0.305034\pi$
$103$	−2.46916	−	2.46916i	−0.243294	−	0.243294i	−0.818211	+	0.574918i	$0.805034\pi$
$104$	4.09037			0.401093
$105$	−16.9347	+	5.65287i	−1.65265	+	0.551664i
$106$	−12.4518			−1.20942
$107$	−6.82347	−	6.82347i	−0.659650	−	0.659650i	0.295647	−	0.955297i	$-0.404465\pi$
$107$	−6.82347	−	6.82347i	−0.659650	−	0.659650i	−0.955297	+	0.295647i	$0.904465\pi$
$108$	4.94537	−	1.59479i	0.475868	−	0.153459i
$109$		−	4.73409i		−	0.453444i	−0.973960	−	0.226722i	$-0.927199\pi$
$109$		−	4.73409i		−	0.453444i	0.973960	−	0.226722i	$-0.0728008\pi$
$110$	6.43384	−	5.89582i	0.613443	−	0.562145i
$111$	8.72203	−	3.34071i	0.827858	−	0.317086i
$112$	3.25954	−	3.25954i	0.307997	−	0.307997i
$113$	−8.88951	+	8.88951i	−0.836255	+	0.836255i	−0.988364	−	0.152109i	$-0.951394\pi$
$113$	−8.88951	+	8.88951i	−0.836255	+	0.836255i	0.152109	+	0.988364i	$0.451394\pi$
$114$	8.54027	−	3.27109i	0.799869	−	0.306366i
$115$	−2.53468	+	2.32272i	−0.236360	+	0.216595i
$116$		−	1.81942i		−	0.168929i
$117$	−0.660251	+	12.2533i	−0.0610402	+	1.13282i
$118$	−5.99443	−	5.99443i	−0.551832	−	0.551832i
$119$	4.60968			0.422569
$120$	3.67371	−	1.22630i	0.335363	−	0.111946i
$121$	−4.23102			−0.384638
$122$	−7.15371	−	7.15371i	−0.647666	−	0.647666i
$123$	2.14365	−	4.80519i	0.193286	−	0.433270i
$124$			7.47022i			0.670846i
$125$	−11.0848	−	1.45851i	−0.991455	−	0.130453i
$126$	9.23831	+	10.2906i	0.823014	+	0.916759i
$127$	−1.01172	+	1.01172i	−0.0897759	+	0.0897759i	−0.750569	−	0.660793i	$-0.770220\pi$
$127$	−1.01172	+	1.01172i	−0.0897759	+	0.0897759i	0.660793	+	0.750569i	$0.270220\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	3.21104	+	8.38348i	0.282717	+	0.738124i
$130$	−0.398732	+	9.13764i	−0.0349712	+	0.801424i
$131$			11.3118i			0.988318i	0.869371	+	0.494159i	$0.164524\pi$
$131$			11.3118i			0.988318i	−0.869371	+	0.494159i	$0.835476\pi$
$132$	−6.17324	−	2.75395i	−0.537311	−	0.239700i
$133$	17.2105	+	17.2105i	1.49234	+	1.49234i
$134$	−6.06935			−0.524312
$135$	3.08058	+	11.2031i	0.265135	+	0.964211i
$136$	−1.00000			−0.0857493
$137$	11.6612	+	11.6612i	0.996280	+	0.996280i	0.999993	−	0.00371269i	$-0.00118179\pi$
$137$	11.6612	+	11.6612i	0.996280	+	0.996280i	−0.00371269	+	0.999993i	$0.501182\pi$
$138$	2.43201	+	1.08495i	0.207027	+	0.0923568i
$139$			7.67749i			0.651197i	0.945508	+	0.325598i	$0.105566\pi$
$139$			7.67749i			0.651197i	−0.945508	+	0.325598i	$0.894434\pi$
$140$	6.96388	+	7.59936i	0.588555	+	0.642263i
$141$	−3.32756	−	8.68769i	−0.280231	−	0.731636i
$142$	−2.25680	+	2.25680i	−0.189387	+	0.189387i
$143$	11.2879	−	11.2879i	0.943938	−	0.943938i
$144$	−2.00411	−	2.23239i	−0.167009	−	0.186032i
$145$	4.06448	+	0.177359i	0.337536	+	0.0147288i
$146$		−	10.1066i		−	0.836431i
$147$	−10.0550	+	22.5392i	−0.829320	+	1.85900i
$148$	−3.81301	−	3.81301i	−0.313427	−	0.313427i
$149$	−2.13276			−0.174722			−0.0873612	−	0.996177i	$-0.527843\pi$
$149$	−2.13276			−0.174722			−0.0873612	+	0.996177i	$0.527843\pi$
$150$	2.38137	+	8.32641i	0.194438	+	0.679848i
$151$	13.8184			1.12453			0.562263	−	0.826958i	$-0.309931\pi$
$151$	13.8184			1.12453			0.562263	+	0.826958i	$0.309931\pi$
$152$	−3.73355	−	3.73355i	−0.302831	−	0.302831i
$153$	0.161416	−	2.99565i	0.0130497	−	0.242184i
$154$		−	17.9902i		−	1.44969i
$155$	−16.6880	−	0.728204i	−1.34042	−	0.0584908i
$156$	6.61602	−	2.53407i	0.529706	−	0.202888i
$157$	5.24511	−	5.24511i	0.418605	−	0.418605i	−0.466118	−	0.884723i	$-0.654348\pi$
$157$	5.24511	−	5.24511i	0.418605	−	0.418605i	0.884723	+	0.466118i	$0.154348\pi$
$158$	2.80822	−	2.80822i	0.223410	−	0.223410i
$159$	−20.1403	+	7.71415i	−1.59723	+	0.611772i
$160$	−1.51071	−	1.64857i	−0.119432	−	0.130331i
$161$			7.08743i			0.558568i
$162$	7.01095	−	5.64327i	0.550832	−	0.443378i
$163$	−16.2607	−	16.2607i	−1.27364	−	1.27364i	−0.944164	−	0.329476i	$-0.893128\pi$
$163$	−16.2607	−	16.2607i	−1.27364	−	1.27364i	−0.329476	−	0.944164i	$-0.606872\pi$
$164$	−3.03782			−0.237214
$165$	6.75393	−	13.5222i	0.525793	−	1.05270i
$166$	−5.13077			−0.398225
$167$	−10.1271	−	10.1271i	−0.783659	−	0.783659i	0.196787	−	0.980446i	$-0.436949\pi$
$167$	−10.1271	−	10.1271i	−0.783659	−	0.783659i	−0.980446	+	0.196787i	$0.936949\pi$
$168$	3.25283	−	7.29154i	0.250962	−	0.562555i
$169$			3.73109i			0.287007i
$170$	0.0974809	−	2.23394i	0.00747644	−	0.171336i
$171$	11.7871	−	10.5818i	0.901380	−	0.809208i
$172$	3.66501	−	3.66501i	0.279454	−	0.279454i
$173$	17.0581	−	17.0581i	1.29691	−	1.29691i	0.366480	−	0.930426i	$-0.380563\pi$
$173$	17.0581	−	17.0581i	1.29691	−	1.29691i	0.930426	−	0.366480i	$-0.119437\pi$
$174$	−1.12717	−	2.94285i	−0.0854505	−	0.223097i
$175$	−17.6554	+	14.8161i	−1.33462	+	1.11999i
$176$			3.90269i			0.294177i
$177$	−13.4095	−	5.98210i	−1.00792	−	0.449642i
$178$	5.64527	+	5.64527i	0.423131	+	0.423131i
$179$	−9.08118			−0.678759			−0.339380	−	0.940649i	$-0.610217\pi$
$179$	−9.08118			−0.678759			−0.339380	+	0.940649i	$0.610217\pi$
$180$	5.18238	−	4.25945i	0.386272	−	0.317481i
$181$	14.9787			1.11336			0.556681	−	0.830727i	$-0.312075\pi$
$181$	14.9787			1.11336			0.556681	+	0.830727i	$0.312075\pi$
$182$	13.3327	+	13.3327i	0.988286	+	0.988286i
$183$	−16.0028	−	7.13900i	−1.18296	−	0.527730i
$184$		−	1.53751i		−	0.113347i
$185$	8.88973	−	8.14634i	0.653586	−	0.598931i
$186$	4.62797	+	12.0828i	0.339339	+	0.885956i
$187$	−2.75962	+	2.75962i	−0.201803	+	0.201803i
$188$	−3.79800	+	3.79800i	−0.276997	+	0.276997i
$189$	21.3179	+	10.9213i	1.55065	+	0.794411i
$190$	8.70448	−	7.97658i	0.631489	−	0.578682i
$191$		−	15.3084i		−	1.10767i	−0.832625	−	0.553837i	$-0.813163\pi$
$191$		−	15.3084i		−	1.10767i	0.832625	−	0.553837i	$-0.186837\pi$
$192$	−0.705653	+	1.58179i	−0.0509261	+	0.114156i
$193$	−9.92832	−	9.92832i	−0.714656	−	0.714656i	0.252849	−	0.967506i	$-0.418632\pi$
$193$	−9.92832	−	9.92832i	−0.714656	−	0.714656i	−0.967506	+	0.252849i	$0.918632\pi$
$194$	−13.3067			−0.955366
$195$	5.01603	+	15.0268i	0.359205	+	1.07609i
$196$	14.2492			1.01780
$197$	−7.73048	−	7.73048i	−0.550774	−	0.550774i	0.375890	−	0.926664i	$-0.377337\pi$
$197$	−7.73048	−	7.73048i	−0.550774	−	0.550774i	−0.926664	+	0.375890i	$0.877337\pi$
$198$	−11.6911	−	0.629958i	−0.830852	−	0.0447691i
$199$		−	8.35422i		−	0.592215i	−0.955155	−	0.296107i	$-0.904311\pi$
$199$		−	8.35422i		−	0.592215i	0.955155	−	0.296107i	$-0.0956886\pi$
$200$	3.83006	−	3.21413i	0.270826	−	0.227273i
$201$	−9.81696	+	3.76009i	−0.692435	+	0.265217i
$202$	12.0134	−	12.0134i	0.845260	−	0.845260i
$203$	5.93046	−	5.93046i	0.416237	−	0.416237i
$204$	−1.61746	+	0.619522i	−0.113245	+	0.0433752i
$205$	0.296130	−	6.78632i	0.0206826	−	0.473977i
$206$			3.49192i			0.243294i
$207$	4.60585	+	0.248179i	0.320128	+	0.0172496i
$208$	−2.89233	−	2.89233i	−0.200547	−	0.200547i
$209$	−20.6063			−1.42537
$210$	15.9718	+	7.97743i	1.10216	+	0.550495i
$211$	19.1998			1.32177			0.660883	−	0.750489i	$-0.270182\pi$
$211$	19.1998			1.32177			0.660883	+	0.750489i	$0.270182\pi$
$212$	8.80475	+	8.80475i	0.604712	+	0.604712i
$213$	−2.25216	+	5.04844i	−0.154316	+	0.345913i
$214$			9.64984i			0.659650i
$215$	7.83014	+	8.54468i	0.534011	+	0.582742i
$216$	−4.62459	−	2.36922i	−0.314663	−	0.161205i
$217$	−24.3495	+	24.3495i	−1.65295	+	1.65295i
$218$	−3.34751	+	3.34751i	−0.226722	+	0.226722i
$219$	−6.26128	−	16.3471i	−0.423098	−	1.10464i
$220$	−8.71839	−	0.380438i	−0.587794	−	0.0256491i
$221$		−	4.09037i		−	0.275148i
$222$	−8.52965	−	3.80517i	−0.572472	−	0.255386i
$223$	−0.420157	−	0.420157i	−0.0281358	−	0.0281358i	0.692899	−	0.721035i	$-0.256333\pi$
$223$	−0.420157	−	0.420157i	−0.0281358	−	0.0281358i	−0.721035	+	0.692899i	$0.756333\pi$
$224$	−4.60968			−0.307997
$225$	9.01018	+	11.9924i	0.600679	+	0.799491i
$226$	12.5717			0.836255
$227$	1.51258	+	1.51258i	0.100393	+	0.100393i	0.755519	−	0.655126i	$-0.227385\pi$
$227$	1.51258	+	1.51258i	0.100393	+	0.100393i	−0.655126	+	0.755519i	$0.727385\pi$
$228$	−8.35189	−	3.72587i	−0.553118	−	0.246752i
$229$			8.99545i			0.594436i	0.954810	+	0.297218i	$0.0960588\pi$
$229$			8.99545i			0.594436i	−0.954810	+	0.297218i	$0.903941\pi$
$230$	3.43471	+	0.149878i	0.226478	+	0.00988265i
$231$	−11.1453	−	29.0985i	−0.733307	−	1.91454i
$232$	−1.28652	+	1.28652i	−0.0844644	+	0.0844644i
$233$	18.1089	−	18.1089i	1.18635	−	1.18635i	0.208284	−	0.978068i	$-0.433212\pi$
$233$	18.1089	−	18.1089i	1.18635	−	1.18635i	0.978068	−	0.208284i	$-0.0667877\pi$
$234$	9.13127	−	8.19754i	0.596930	−	0.535890i
$235$	−8.11427	−	8.85473i	−0.529317	−	0.577619i
$236$			8.47740i			0.551832i
$237$	2.80244	−	6.28195i	0.182038	−	0.408057i
$238$	−3.25954	−	3.25954i	−0.211284	−	0.211284i
$239$	−5.44845			−0.352431			−0.176215	−	0.984352i	$-0.556386\pi$
$239$	−5.44845			−0.352431			−0.176215	+	0.984352i	$0.556386\pi$
$240$	−3.46484	−	1.73058i	−0.223654	−	0.111709i
$241$	−25.8531			−1.66534			−0.832671	−	0.553768i	$-0.813189\pi$
$241$	−25.8531			−1.66534			−0.832671	+	0.553768i	$0.813189\pi$
$242$	2.99178	+	2.99178i	0.192319	+	0.192319i
$243$	7.84384	−	13.4712i	0.503182	−	0.864180i
$244$			10.1169i			0.647666i
$245$	−1.38902	+	31.8318i	−0.0887414	+	2.03366i
$246$	−4.91357	+	1.88200i	−0.313278	+	0.119992i
$247$	15.2716	−	15.2716i	0.971707	−	0.971707i
$248$	5.28225	−	5.28225i	0.335423	−	0.335423i
$249$	−8.29884	+	3.17862i	−0.525918	+	0.201437i
$250$	6.80682	+	8.86946i	0.430501	+	0.560954i
$251$		−	0.996953i		−	0.0629271i	−0.999505	−	0.0314636i	$-0.989983\pi$
$251$		−	0.996953i		−	0.0629271i	0.999505	−	0.0314636i	$-0.0100168\pi$
$252$	0.744077	−	13.8090i	0.0468724	−	0.869886i
$253$	−4.24294	−	4.24294i	−0.266751	−	0.266751i
$254$	1.43079			0.0897759
$255$	−1.22630	−	3.67371i	−0.0767941	−	0.230057i
$256$	1.00000			0.0625000
$257$	3.90745	+	3.90745i	0.243740	+	0.243740i	0.818395	−	0.574655i	$-0.194864\pi$
$257$	3.90745	+	3.90745i	0.243740	+	0.243740i	−0.574655	+	0.818395i	$0.694864\pi$
$258$	3.65747	−	8.19857i	0.227704	−	0.510421i
$259$		−	24.8573i		−	1.54456i
$260$	6.74323	−	6.17934i	0.418198	−	0.383226i
$261$	−3.64631	−	4.06164i	−0.225701	−	0.251409i
$262$	7.99866	−	7.99866i	0.494159	−	0.494159i
$263$	−6.86457	+	6.86457i	−0.423287	+	0.423287i	−0.886334	−	0.463047i	$-0.846756\pi$
$263$	−6.86457	+	6.86457i	−0.423287	+	0.423287i	0.463047	+	0.886334i	$0.346756\pi$
$264$	2.41780	+	6.31247i	0.148805	+	0.388506i
$265$	−20.5276	+	18.8110i	−1.26100	+	1.15555i
$266$		−	24.3393i		−	1.49234i
$267$	12.6284	+	5.63366i	0.772846	+	0.344775i
$268$	4.29168	+	4.29168i	0.262156	+	0.262156i
$269$	15.5623			0.948852			0.474426	−	0.880296i	$-0.342656\pi$
$269$	15.5623			0.948852			0.474426	+	0.880296i	$0.342656\pi$
$270$	5.74350	−	10.1001i	0.349538	−	0.614673i
$271$	−5.75713			−0.349721			−0.174860	−	0.984593i	$-0.555947\pi$
$271$	−5.75713			−0.349721			−0.174860	+	0.984593i	$0.555947\pi$
$272$	0.707107	+	0.707107i	0.0428746	+	0.0428746i
$273$	29.8251	+	13.3053i	1.80510	+	0.805272i
$274$		−	16.4914i		−	0.996280i
$275$	1.69975	−	19.4393i	0.102499	−	1.17223i
$276$	−0.952520	−	2.48687i	−0.0573350	−	0.149692i
$277$	9.17605	−	9.17605i	0.551335	−	0.551335i	−0.375491	−	0.926826i	$-0.622526\pi$
$277$	9.17605	−	9.17605i	0.551335	−	0.551335i	0.926826	+	0.375491i	$0.122526\pi$
$278$	5.42881	−	5.42881i	0.325598	−	0.325598i
$279$	14.9711	+	16.6764i	0.896299	+	0.998391i
$280$	0.449356	−	10.2978i	0.0268542	−	0.615409i
$281$		−	15.4358i		−	0.920821i	−0.887706	−	0.460410i	$-0.847702\pi$
$281$		−	15.4358i		−	0.920821i	0.887706	−	0.460410i	$-0.152298\pi$
$282$	−3.79018	+	8.49607i	−0.225702	+	0.505933i
$283$	19.7777	+	19.7777i	1.17566	+	1.17566i	0.980838	+	0.194827i	$0.0624146\pi$
$283$	19.7777	+	19.7777i	1.17566	+	1.17566i	0.194827	+	0.980838i	$0.437585\pi$
$284$	3.19160			0.189387
$285$	9.13752	−	18.2944i	0.541260	−	1.08367i
$286$	−15.9634			−0.943938
$287$	−9.90190	−	9.90190i	−0.584491	−	0.584491i
$288$	−0.161416	+	2.99565i	−0.00951154	+	0.176521i
$289$			1.00000i			0.0588235i
$290$	−2.74861	−	2.99943i	−0.161404	−	0.176133i
$291$	−21.5231	+	8.24379i	−1.26171	+	0.483260i
$292$	−7.14647	+	7.14647i	−0.418216	+	0.418216i
$293$	−19.2480	+	19.2480i	−1.12448	+	1.12448i	−0.133420	+	0.991060i	$0.542596\pi$
$293$	−19.2480	+	19.2480i	−1.12448	+	1.12448i	−0.991060	+	0.133420i	$0.957404\pi$
$294$	23.0475	−	8.82767i	1.34416	−	0.514840i
$295$	−18.9380	−	0.826385i	−1.10261	−	0.0481140i
$296$			5.39241i			0.313427i
$297$	−19.3003	+	6.22397i	−1.11991	+	0.361151i
$298$	1.50809	+	1.50809i	0.0873612	+	0.0873612i
$299$	6.28897			0.363701
$300$	4.20377	−	7.57154i	0.242705	−	0.437143i
$301$	23.8924			1.37714
$302$	−9.77109	−	9.77109i	−0.562263	−	0.562263i
$303$	11.9887	−	26.8738i	0.688733	−	1.54386i
$304$			5.28003i			0.302831i
$305$	−22.6005	−	0.986202i	−1.29410	−	0.0564697i
$306$	−2.23239	+	2.00411i	−0.127617	+	0.114567i
$307$	5.92844	−	5.92844i	0.338354	−	0.338354i	−0.517394	−	0.855748i	$-0.673098\pi$
$307$	5.92844	−	5.92844i	0.338354	−	0.338354i	0.855748	+	0.517394i	$0.173098\pi$
$308$	−12.7210	+	12.7210i	−0.724845	+	0.724845i
$309$	2.16332	+	5.64806i	0.123067	+	0.321307i
$310$	11.2853	+	12.3152i	0.640963	+	0.699454i
$311$			4.17394i			0.236682i	0.992973	+	0.118341i	$0.0377576\pi$
$311$			4.17394i			0.236682i	−0.992973	+	0.118341i	$0.962242\pi$
$312$	−6.47009	−	2.88638i	−0.366297	−	0.163409i
$313$	10.9767	+	10.9767i	0.620441	+	0.620441i	0.945644	−	0.325203i	$-0.105433\pi$
$313$	10.9767	+	10.9767i	0.620441	+	0.620441i	−0.325203	+	0.945644i	$0.605433\pi$
$314$	−7.41770			−0.418605
$315$	30.7760	+	3.00834i	1.73403	+	0.169501i
$316$	−3.97142			−0.223410
$317$	1.86935	+	1.86935i	0.104993	+	0.104993i	0.757652	−	0.652659i	$-0.226346\pi$
$317$	1.86935	+	1.86935i	0.104993	+	0.104993i	−0.652659	+	0.757652i	$0.726346\pi$
$318$	19.6961	+	8.78664i	1.10450	+	0.492730i
$319$			7.10063i			0.397559i
$320$	−0.0974809	+	2.23394i	−0.00544935	+	0.124881i
$321$	5.97829	+	15.6083i	0.333675	+	0.871170i
$322$	5.01157	−	5.01157i	0.279284	−	0.279284i
$323$	−3.73355	+	3.73355i	−0.207740	+	0.207740i
$324$	−8.94789	−	0.967094i	−0.497105	−	0.0537274i
$325$	13.1470	+	15.6664i	0.729262	+	0.869013i
$326$			22.9962i			1.27364i
$327$	−3.34062	+	7.48833i	−0.184737	+	0.414106i
$328$	2.14806	+	2.14806i	0.118607	+	0.118607i
$329$	−24.7594			−1.36503
$330$	−14.3374	+	4.78589i	−0.789247	+	0.263454i
$331$	1.88295			0.103496			0.0517481	−	0.998660i	$-0.483521\pi$
$331$	1.88295			0.103496			0.0517481	+	0.998660i	$0.483521\pi$
$332$	3.62800	+	3.62800i	0.199112	+	0.199112i
$333$	−16.1538	−	0.870421i	−0.885222	−	0.0476988i
$334$			14.3219i			0.783659i
$335$	−10.0057	+	9.16900i	−0.546671	+	0.500956i
$336$	−7.45600	+	2.85580i	−0.406758	+	0.155797i
$337$	24.0957	−	24.0957i	1.31258	−	1.31258i	0.393067	−	0.919510i	$-0.371414\pi$
$337$	24.0957	−	24.0957i	1.31258	−	1.31258i	0.919510	−	0.393067i	$-0.128586\pi$
$338$	2.63828	−	2.63828i	0.143503	−	0.143503i
$339$	20.3342	−	7.78842i	1.10440	−	0.423009i
$340$	−1.64857	+	1.51071i	−0.0894060	+	0.0819295i
$341$		−	29.1540i		−	1.57878i
$342$	−15.8172	−	0.852282i	−0.855294	−	0.0460861i
$343$	23.6290	+	23.6290i	1.27584	+	1.27584i
$344$	−5.18310			−0.279454
$345$	5.64837	−	1.88545i	0.304098	−	0.101509i
$346$	−24.1238			−1.29691
$347$	6.50876	+	6.50876i	0.349409	+	0.349409i	0.859889	−	0.510481i	$-0.170532\pi$
$347$	6.50876	+	6.50876i	0.349409	+	0.349409i	−0.510481	+	0.859889i	$0.670532\pi$
$348$	−1.28388	+	2.87794i	−0.0688230	+	0.154274i
$349$		−	22.5261i		−	1.20580i	−0.797819	−	0.602898i	$-0.794013\pi$
$349$		−	22.5261i		−	1.20580i	0.797819	−	0.602898i	$-0.205987\pi$
$350$	22.9608	+	2.00767i	1.22731	+	0.107315i
$351$	9.69096	−	18.9163i	0.517265	−	1.00967i
$352$	2.75962	−	2.75962i	0.147088	−	0.147088i
$353$	8.14941	−	8.14941i	0.433749	−	0.433749i	−0.456152	−	0.889902i	$-0.650773\pi$
$353$	8.14941	−	8.14941i	0.433749	−	0.433749i	0.889902	+	0.456152i	$0.150773\pi$
$354$	5.25193	+	13.7119i	0.279137	+	0.728779i
$355$	−0.311120	+	7.12985i	−0.0165125	+	0.378413i
$356$		−	7.98362i		−	0.423131i
$357$	−7.29154	−	3.25283i	−0.385909	−	0.172158i
$358$	6.42136	+	6.42136i	0.339380	+	0.339380i
$359$	−35.3639			−1.86643			−0.933216	−	0.359315i	$-0.883010\pi$
$359$	−35.3639			−1.86643			−0.933216	+	0.359315i	$0.883010\pi$
$360$	−6.67638	−	0.652613i	−0.351876	−	0.0343957i
$361$	−8.87874			−0.467302
$362$	−10.5916	−	10.5916i	−0.556681	−	0.556681i
$363$	6.69257	+	2.98563i	0.351269	+	0.156705i
$364$		−	18.8553i		−	0.988286i
$365$	−15.2682	−	16.6615i	−0.799172	−	0.872100i
$366$	6.26762	+	16.3637i	0.327614	+	0.855344i
$367$	17.3116	−	17.3116i	0.903657	−	0.903657i	−0.0920930	−	0.995750i	$-0.529356\pi$
$367$	17.3116	−	17.3116i	0.903657	−	0.903657i	0.995750	+	0.0920930i	$0.0293557\pi$
$368$	−1.08718	+	1.08718i	−0.0566733	+	0.0566733i
$369$	−6.78159	+	6.08813i	−0.353036	+	0.316935i
$370$	−12.0463	−	0.525657i	−0.626259	−	0.0273276i
$371$			57.3988i			2.98000i
$372$	5.27138	−	11.8163i	0.273308	−	0.612647i
$373$	−3.76040	−	3.76040i	−0.194706	−	0.194706i	0.603020	−	0.797726i	$-0.293964\pi$
$373$	−3.76040	−	3.76040i	−0.194706	−	0.194706i	−0.797726	+	0.603020i	$0.793964\pi$
$374$	3.90269			0.201803
$375$	16.5046	+	10.1291i	0.852294	+	0.523063i
$376$	5.37118			0.276997
$377$	−5.26235	−	5.26235i	−0.271025	−	0.271025i
$378$	−7.35147	−	22.7966i	−0.378119	−	1.17253i
$379$		−	7.87559i		−	0.404542i	−0.979330	−	0.202271i	$-0.935168\pi$
$379$		−	7.87559i		−	0.404542i	0.979330	−	0.202271i	$-0.0648321\pi$
$380$	−11.7953	−	0.514702i	−0.605085	−	0.0264037i
$381$	2.31426	−	0.886407i	0.118563	−	0.0454120i
$382$	−10.8246	+	10.8246i	−0.553837	+	0.553837i
$383$	−6.96499	+	6.96499i	−0.355895	+	0.355895i	−0.862297	−	0.506403i	$-0.830975\pi$
$383$	−6.96499	+	6.96499i	−0.355895	+	0.355895i	0.506403	+	0.862297i	$0.330975\pi$
$384$	1.61746	−	0.619522i	0.0825409	−	0.0316148i
$385$	−27.1779	−	29.6580i	−1.38511	−	1.51151i
$386$			14.0408i			0.714656i
$387$	0.836636	−	15.5268i	0.0425286	−	0.789270i
$388$	9.40927	+	9.40927i	0.477683	+	0.477683i
$389$	17.8089			0.902947			0.451474	−	0.892285i	$-0.350899\pi$
$389$	17.8089			0.902947			0.451474	+	0.892285i	$0.350899\pi$
$390$	7.07871	−	14.1724i	0.358444	−	0.717650i
$391$	−1.53751			−0.0777552
$392$	−10.0757	−	10.0757i	−0.508899	−	0.508899i
$393$	7.98221	−	17.8929i	0.402649	−	0.902578i
$394$			10.9325i			0.550774i
$395$	0.387138	−	8.87193i	0.0194790	−	0.446395i
$396$	7.82142	+	8.71232i	0.393041	+	0.437810i
$397$	−17.8589	+	17.8589i	−0.896311	+	0.896311i	−0.995108	−	0.0987970i	$-0.968501\pi$
$397$	−17.8589	+	17.8589i	−0.896311	+	0.896311i	0.0987970	+	0.995108i	$0.468501\pi$
$398$	−5.90732	+	5.90732i	−0.296107	+	0.296107i
$399$	−15.0787	−	39.3679i	−0.754880	−	1.97086i
$400$	−4.98099	−	0.435533i	−0.249050	−	0.0217767i
$401$			6.95303i			0.347218i	0.984815	+	0.173609i	$0.0555429\pi$
$401$			6.95303i			0.347218i	−0.984815	+	0.173609i	$0.944457\pi$
$402$	9.60043	+	4.28285i	0.478826	+	0.213609i
$403$	21.6063	+	21.6063i	1.07629	+	1.07629i
$404$	−16.9895			−0.845260
$405$	3.03268	−	19.8948i	0.150695	−	0.988580i
$406$	−8.38694			−0.416237
$407$	14.8810	+	14.8810i	0.737624	+	0.737624i
$408$	1.58179	+	0.705653i	0.0783102	+	0.0349350i
$409$			5.76172i			0.284899i	0.989802	+	0.142449i	$0.0454978\pi$
$409$			5.76172i			0.284899i	−0.989802	+	0.142449i	$0.954502\pi$
$410$	−5.00805	+	4.58926i	−0.247330	+	0.226647i
$411$	−10.2168	−	26.6742i	−0.503956	−	1.31574i
$412$	2.46916	−	2.46916i	0.121647	−	0.121647i
$413$	−27.6324	+	27.6324i	−1.35970	+	1.35970i
$414$	−3.08134	−	3.43231i	−0.151439	−	0.168689i
$415$	−8.45841	+	7.75108i	−0.415207	+	0.380486i
$416$			4.09037i			0.200547i
$417$	5.41764	−	12.1442i	0.265303	−	0.594703i
$418$	14.5709	+	14.5709i	0.712685	+	0.712685i
$419$	27.5481			1.34581			0.672907	−	0.739727i	$-0.265045\pi$
$419$	27.5481			1.34581			0.672907	+	0.739727i	$0.265045\pi$
$420$	−5.65287	−	16.9347i	−0.275832	−	0.826327i
$421$	−22.9481			−1.11842			−0.559210	−	0.829026i	$-0.688895\pi$
$421$	−22.9481			−1.11842			−0.559210	+	0.829026i	$0.688895\pi$
$422$	−13.5763	−	13.5763i	−0.660883	−	0.660883i
$423$	−0.866994	+	16.0902i	−0.0421547	+	0.782332i
$424$		−	12.4518i		−	0.604712i
$425$	−3.21413	−	3.83006i	−0.155908	−	0.185785i
$426$	5.16230	−	1.97727i	0.250114	−	0.0957988i
$427$	−32.9763	+	32.9763i	−1.59584	+	1.59584i
$428$	6.82347	−	6.82347i	0.329825	−	0.329825i
$429$	−25.8203	+	9.88970i	−1.24662	+	0.477479i
$430$	0.505253	−	11.5787i	0.0243655	−	0.558377i
$431$		−	5.39650i		−	0.259940i	−0.991518	−	0.129970i	$-0.958512\pi$
$431$		−	5.39650i		−	0.259940i	0.991518	−	0.129970i	$-0.0414882\pi$
$432$	1.59479	+	4.94537i	0.0767293	+	0.237934i
$433$	−4.51012	−	4.51012i	−0.216743	−	0.216743i	0.590382	−	0.807124i	$-0.298977\pi$
$433$	−4.51012	−	4.51012i	−0.216743	−	0.216743i	−0.807124	+	0.590382i	$0.798977\pi$
$434$	34.4354			1.65295
$435$	−6.30399	−	3.14865i	−0.302253	−	0.150966i
$436$	4.73409			0.226722
$437$	−5.74036	−	5.74036i	−0.274599	−	0.274599i
$438$	−7.13178	+	15.9866i	−0.340769	+	0.763868i
$439$			6.51713i			0.311046i	0.987832	+	0.155523i	$0.0497062\pi$
$439$			6.51713i			0.311046i	−0.987832	+	0.155523i	$0.950294\pi$
$440$	5.89582	+	6.43384i	0.281072	+	0.306721i
$441$	31.8097	−	28.5569i	1.51475	−	1.35985i
$442$	−2.89233	+	2.89233i	−0.137574	+	0.137574i
$443$	−10.5407	+	10.5407i	−0.500803	+	0.500803i	−0.911687	−	0.410885i	$-0.865220\pi$
$443$	−10.5407	+	10.5407i	−0.500803	+	0.500803i	0.410885	+	0.911687i	$0.365220\pi$
$444$	3.34071	+	8.72203i	0.158543	+	0.413929i
$445$	17.8350	+	0.778251i	0.845458	+	0.0368926i
$446$			0.594192i			0.0281358i
$447$	3.37357	+	1.50499i	0.159565	+	0.0711835i
$448$	3.25954	+	3.25954i	0.153999	+	0.153999i
$449$	36.5410			1.72448			0.862238	−	0.506503i	$-0.169062\pi$
$449$	36.5410			1.72448			0.862238	+	0.506503i	$0.169062\pi$
$450$	2.10872	−	14.8510i	0.0994060	−	0.700085i
$451$	11.8557			0.558263
$452$	−8.88951	−	8.88951i	−0.418128	−	0.418128i
$453$	−21.8578	−	9.75099i	−1.02697	−	0.458142i
$454$		−	2.13911i		−	0.100393i
$455$	42.1216	+	1.83803i	1.97469	+	0.0861682i
$456$	3.27109	+	8.54027i	0.153183	+	0.399935i
$457$	−17.2432	+	17.2432i	−0.806603	+	0.806603i	−0.984118	−	0.177515i	$-0.943194\pi$
$457$	−17.2432	+	17.2432i	−0.806603	+	0.806603i	0.177515	+	0.984118i	$0.443194\pi$
$458$	6.36075	−	6.36075i	0.297218	−	0.297218i
$459$	−2.36922	+	4.62459i	−0.110586	+	0.215857i
$460$	−2.32272	−	2.53468i	−0.108298	−	0.118180i
$461$		−	3.61206i		−	0.168231i	−0.996456	−	0.0841153i	$-0.973194\pi$
$461$		−	3.61206i		−	0.168231i	0.996456	−	0.0841153i	$-0.0268064\pi$
$462$	−12.6948	+	28.4567i	−0.590616	+	1.32392i
$463$	21.4799	+	21.4799i	0.998255	+	0.998255i	0.999998	−	0.00174346i	$-0.000554961\pi$
$463$	21.4799	+	21.4799i	0.998255	+	0.998255i	−0.00174346	+	0.999998i	$0.500555\pi$
$464$	1.81942			0.0844644
$465$	25.8831	+	12.9278i	1.20030	+	0.599514i
$466$	−25.6098			−1.18635
$467$	19.8768	+	19.8768i	0.919787	+	0.919787i	0.997014	−	0.0772267i	$-0.0246065\pi$
$467$	19.8768	+	19.8768i	0.919787	+	0.919787i	−0.0772267	+	0.997014i	$0.524607\pi$
$468$	−12.2533	−	0.660251i	−0.566410	−	0.0305201i
$469$			27.9778i			1.29189i
$470$	−0.523587	+	11.9989i	−0.0241513	+	0.553468i
$471$	−11.9979	+	4.59543i	−0.552833	+	0.211746i
$472$	5.99443	−	5.99443i	0.275916	−	0.275916i
$473$	−14.3034	+	14.3034i	−0.657671	+	0.657671i
$474$	−6.42364	+	2.46038i	−0.295047	+	0.113009i
$475$	2.29963	−	26.2998i	0.105514	−	1.20672i
$476$			4.60968i			0.211284i
$477$	37.3013	+	2.00992i	1.70791	+	0.0920279i
$478$	3.85263	+	3.85263i	0.176215	+	0.176215i
$479$	−2.36428			−0.108027			−0.0540133	−	0.998540i	$-0.517201\pi$
$479$	−2.36428			−0.108027			−0.0540133	+	0.998540i	$0.517201\pi$
$480$	1.22630	+	3.67371i	0.0559728	+	0.167681i
$481$	−22.0569			−1.00571
$482$	18.2809	+	18.2809i	0.832671	+	0.832671i
$483$	5.00126	−	11.2108i	0.227565	−	0.510110i
$484$		−	4.23102i		−	0.192319i
$485$	−21.9370	+	20.1025i	−0.996107	+	0.912809i
$486$	−15.0720	+	3.97917i	−0.683681	+	0.180499i
$487$	−27.7336	+	27.7336i	−1.25673	+	1.25673i	−0.304083	+	0.952646i	$0.598350\pi$
$487$	−27.7336	+	27.7336i	−1.25673	+	1.25673i	−0.952646	+	0.304083i	$0.901650\pi$
$488$	7.15371	−	7.15371i	0.323833	−	0.323833i
$489$	14.2466	+	37.1955i	0.644254	+	1.68204i
$490$	23.4907	−	21.5263i	1.06120	−	0.972460i
$491$			15.6906i			0.708108i	0.935225	+	0.354054i	$0.115197\pi$
$491$			15.6906i			0.708108i	−0.935225	+	0.354054i	$0.884803\pi$
$492$	4.80519	+	2.14365i	0.216635	+	0.0966431i
$493$	1.28652	+	1.28652i	0.0579421	+	0.0579421i
$494$	−21.5973			−0.971707
$495$	−20.2253	+	16.6233i	−0.909058	+	0.747163i
$496$	−7.47022			−0.335423
$497$	10.4031	+	10.4031i	0.466645	+	0.466645i
$498$	8.11579	+	3.62054i	0.363677	+	0.162240i
$499$			5.93860i			0.265848i	0.991126	+	0.132924i	$0.0424367\pi$
$499$			5.93860i			0.265848i	−0.991126	+	0.132924i	$0.957563\pi$
$500$	1.45851	−	11.0848i	0.0652265	−	0.495727i
$501$	8.87272	+	23.1651i	0.396404	+	1.03494i
$502$	−0.704952	+	0.704952i	−0.0314636	+	0.0314636i
$503$	−8.99427	+	8.99427i	−0.401034	+	0.401034i	−0.878597	−	0.477563i	$-0.841520\pi$
$503$	−8.99427	+	8.99427i	−0.401034	+	0.401034i	0.477563	+	0.878597i	$0.341520\pi$
$504$	−10.2906	+	9.23831i	−0.458379	+	0.411507i
$505$	1.65615	−	37.9536i	0.0736979	−	1.68891i
$506$			6.00043i			0.266751i
$507$	2.63285	−	5.90179i	0.116929	−	0.262108i
$508$	−1.01172	−	1.01172i	−0.0448880	−	0.0448880i
$509$	33.6344			1.49082			0.745410	−	0.666607i	$-0.232254\pi$
$509$	33.6344			1.49082			0.745410	+	0.666607i	$0.232254\pi$
$510$	−1.73058	+	3.46484i	−0.0766314	+	0.153426i
$511$	−46.5884			−2.06095
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−26.1117	+	8.42053i	−1.15286	+	0.371776i
$514$		−	5.52597i		−	0.243740i
$515$	5.27527	+	5.75666i	0.232456	+	0.253669i
$516$	−8.38348	+	3.21104i	−0.369062	+	0.141358i
$517$	14.8224	−	14.8224i	0.651889	−	0.651889i
$518$	−17.5768	+	17.5768i	−0.772278	+	0.772278i
$519$	−39.0195	+	14.9452i	−1.71276	+	0.656023i
$520$	−9.13764	−	0.398732i	−0.400712	−	0.0174856i
$521$		−	36.1197i		−	1.58243i	−0.611536	−	0.791216i	$-0.709448\pi$
$521$		−	36.1197i		−	1.58243i	0.611536	−	0.791216i	$-0.290552\pi$
$522$	−0.293683	+	5.45035i	−0.0128542	+	0.238555i
$523$	0.00754156	+	0.00754156i	0.000329770	+	0.000329770i	0.707272	−	0.706942i	$-0.249926\pi$
$523$	0.00754156	+	0.00754156i	0.000329770	+	0.000329770i	−0.706942	+	0.707272i	$0.749926\pi$
$524$	−11.3118			−0.494159
$525$	38.3821	−	10.9774i	1.67513	−	0.479092i
$526$	9.70796			0.423287
$527$	−5.28225	−	5.28225i	−0.230098	−	0.230098i
$528$	2.75395	−	6.17324i	0.119850	−	0.268656i
$529$			20.6361i			0.897220i
$530$	27.8166	+	1.21381i	1.20828	+	0.0527246i
$531$	16.9896	+	18.9248i	0.737287	+	0.821268i
$532$	−17.2105	+	17.2105i	−0.746168	+	0.746168i
$533$	−8.78637	+	8.78637i	−0.380580	+	0.380580i
$534$	−4.94603	−	12.9132i	−0.214036	−	0.558810i
$535$	14.5781	+	15.9084i	0.630265	+	0.687780i
$536$		−	6.06935i		−	0.262156i
$537$	14.3645	+	6.40816i	0.619874	+	0.276532i
$538$	−11.0042	−	11.0042i	−0.474426	−	0.474426i
$539$	−55.6102			−2.39530
$540$	−11.2031	+	3.08058i	−0.482106	+	0.132567i
$541$	2.19623			0.0944231			0.0472116	−	0.998885i	$-0.484967\pi$
$541$	2.19623			0.0944231			0.0472116	+	0.998885i	$0.484967\pi$
$542$	4.07091	+	4.07091i	0.174860	+	0.174860i
$543$	−23.6932	−	10.5698i	−1.01677	−	0.453593i
$544$		−	1.00000i		−	0.0428746i
$545$	−0.461483	+	10.5757i	−0.0197678	+	0.453013i
$546$	−11.6813	−	30.4978i	−0.499912	−	1.30518i
$547$	21.9578	−	21.9578i	0.938846	−	0.938846i	−0.0593890	−	0.998235i	$-0.518915\pi$
$547$	21.9578	−	21.9578i	0.938846	−	0.938846i	0.998235	+	0.0593890i	$0.0189152\pi$
$548$	−11.6612	+	11.6612i	−0.498140	+	0.498140i
$549$	20.2753	+	22.5848i	0.865329	+	0.963894i
$550$	−14.9476	+	12.5438i	−0.637366	+	0.534867i
$551$			9.60659i			0.409254i
$552$	−1.08495	+	2.43201i	−0.0461784	+	0.103513i
$553$	−12.9450	−	12.9450i	−0.550478	−	0.550478i
$554$	−12.9769			−0.551335
$555$	−19.8102	+	6.61273i	−0.840895	+	0.280695i
$556$	−7.67749			−0.325598
$557$	−23.7672	−	23.7672i	−1.00705	−	1.00705i	−0.999975	−	0.00707190i	$-0.997749\pi$
$557$	−23.7672	−	23.7672i	−1.00705	−	1.00705i	−0.00707190	−	0.999975i	$-0.502251\pi$
$558$	1.20581	−	22.3782i	0.0510462	−	0.947345i
$559$		−	21.2008i		−	0.896697i
$560$	−7.59936	+	6.96388i	−0.321132	+	0.294277i
$561$	6.31247	−	2.41780i	0.266513	−	0.102080i
$562$	−10.9147	+	10.9147i	−0.460410	+	0.460410i
$563$	17.6870	−	17.6870i	0.745420	−	0.745420i	−0.228195	−	0.973615i	$-0.573283\pi$
$563$	17.6870	−	17.6870i	0.745420	−	0.745420i	0.973615	+	0.228195i	$0.0732825\pi$
$564$	8.68769	−	3.32756i	0.365818	−	0.140116i
$565$	20.7252	−	18.9921i	0.871916	−	0.799004i
$566$		−	27.9700i		−	1.17566i
$567$	−26.0137	−	32.3183i	−1.09247	−	1.35724i
$568$	−2.25680	−	2.25680i	−0.0946933	−	0.0946933i
$569$	17.4609			0.731999			0.365999	−	0.930615i	$-0.380727\pi$
$569$	17.4609			0.731999			0.365999	+	0.930615i	$0.380727\pi$
$570$	−19.3973	+	6.47492i	−0.812465	+	0.271205i
$571$	10.9552			0.458459			0.229230	−	0.973372i	$-0.426379\pi$
$571$	10.9552			0.458459			0.229230	+	0.973372i	$0.426379\pi$
$572$	11.2879	+	11.2879i	0.471969	+	0.471969i
$573$	−10.8024	+	24.2146i	−0.451276	+	1.01158i
$574$			14.0034i			0.584491i
$575$	5.88876	−	4.94175i	0.245578	−	0.206085i
$576$	2.23239	−	2.00411i	0.0930161	−	0.0835045i
$577$	15.7139	−	15.7139i	0.654178	−	0.654178i	−0.299818	−	0.953996i	$-0.596926\pi$
$577$	15.7139	−	15.7139i	0.654178	−	0.654178i	0.953996	+	0.299818i	$0.0969259\pi$
$578$	0.707107	−	0.707107i	0.0294118	−	0.0294118i
$579$	8.69856	+	22.7105i	0.361500	+	0.943814i
$580$	−0.177359	+	4.06448i	−0.00736441	+	0.168768i
$581$			23.6512i			0.981218i
$582$	21.0484	+	9.38991i	0.872484	+	0.389224i
$583$	−34.3622	−	34.3622i	−1.42314	−	1.42314i
$584$	10.1066			0.418216
$585$	2.66943	−	27.3088i	0.110367	−	1.12908i
$586$	27.2208			1.12448
$587$	−19.6039	−	19.6039i	−0.809141	−	0.809141i	0.175363	−	0.984504i	$-0.443890\pi$
$587$	−19.6039	−	19.6039i	−0.809141	−	0.809141i	−0.984504	+	0.175363i	$0.943890\pi$
$588$	−22.5392	−	10.0550i	−0.929500	−	0.414660i
$589$		−	39.4430i		−	1.62522i
$590$	12.8069	+	13.9755i	0.527250	+	0.575364i
$591$	6.77295	+	17.6830i	0.278602	+	0.727382i
$592$	3.81301	−	3.81301i	0.156714	−	0.156714i
$593$	2.88370	−	2.88370i	0.118419	−	0.118419i	−0.645414	−	0.763833i	$-0.723315\pi$
$593$	2.88370	−	2.88370i	0.118419	−	0.118419i	0.763833	+	0.645414i	$0.223315\pi$
$594$	18.0483	+	9.24633i	0.740533	+	0.379381i
$595$	−10.2978	−	0.449356i	−0.422167	−	0.0184218i
$596$		−	2.13276i		−	0.0873612i
$597$	−5.89517	+	13.2146i	−0.241273	+	0.540838i
$598$	−4.44698	−	4.44698i	−0.181850	−	0.181850i
$599$	10.8202			0.442103			0.221052	−	0.975262i	$-0.429051\pi$
$599$	10.8202			0.442103			0.221052	+	0.975262i	$0.429051\pi$
$600$	−8.32641	+	2.38137i	−0.339924	+	0.0972192i
$601$	−42.3666			−1.72817			−0.864085	−	0.503345i	$-0.832102\pi$
$601$	−42.3666			−1.72817			−0.864085	+	0.503345i	$0.832102\pi$
$602$	−16.8945	−	16.8945i	−0.688569	−	0.688569i
$603$	18.1817	+	0.979691i	0.740415	+	0.0398961i
$604$			13.8184i			0.562263i
$605$	9.45185	+	0.412443i	0.384272	+	0.0167682i
$606$	−27.4800	+	10.5254i	−1.11630	+	0.427564i
$607$	−7.50184	+	7.50184i	−0.304490	+	0.304490i	−0.842768	−	0.538277i	$-0.819075\pi$
$607$	−7.50184	+	7.50184i	−0.304490	+	0.304490i	0.538277	+	0.842768i	$0.319075\pi$
$608$	3.73355	−	3.73355i	0.151415	−	0.151415i
$609$	−13.5656	+	5.19589i	−0.549705	+	0.210548i
$610$	15.2836	+	16.6783i	0.618816	+	0.675286i
$611$			21.9701i			0.888814i
$612$	2.99565	+	0.161416i	0.121092	+	0.00652486i
$613$	−11.5598	−	11.5598i	−0.466897	−	0.466897i	0.434011	−	0.900908i	$-0.357098\pi$
$613$	−11.5598	−	11.5598i	−0.466897	−	0.466897i	−0.900908	+	0.434011i	$0.857098\pi$
$614$	−8.38408			−0.338354
$615$	−5.25720	+	10.5256i	−0.211991	+	0.424431i
$616$	17.9902			0.724845
$617$	13.0778	+	13.0778i	0.526492	+	0.526492i	0.919525	−	0.393032i	$-0.128574\pi$
$617$	13.0778	+	13.0778i	0.526492	+	0.526492i	−0.393032	+	0.919525i	$0.628574\pi$
$618$	2.46408	−	5.52348i	0.0991200	−	0.222187i
$619$			0.359349i			0.0144435i	0.999974	+	0.00722173i	$0.00229877\pi$
$619$			0.359349i			0.0144435i	−0.999974	+	0.00722173i	$0.997701\pi$
$620$	0.728204	−	16.6880i	0.0292454	−	0.670208i
$621$	−7.11035	−	3.64269i	−0.285328	−	0.146176i
$622$	2.95142	−	2.95142i	0.118341	−	0.118341i
$623$	26.0229	−	26.0229i	1.04259	−	1.04259i
$624$	2.53407	+	6.61602i	0.101444	+	0.264853i
$625$	24.6206	+	4.33878i	0.984825	+	0.173551i
$626$		−	15.5234i		−	0.620441i
$627$	32.5949	+	14.5409i	1.30171	+	0.580708i
$628$	5.24511	+	5.24511i	0.209303	+	0.209303i
$629$	5.39241			0.215009
$630$	−19.6347	−	23.8891i	−0.782265	−	0.951766i
$631$	16.4627			0.655370			0.327685	−	0.944787i	$-0.393731\pi$
$631$	16.4627			0.655370			0.327685	+	0.944787i	$0.393731\pi$
$632$	2.80822	+	2.80822i	0.111705	+	0.111705i
$633$	−30.3700	−	13.5484i	−1.20710	−	0.538499i
$634$		−	2.64367i		−	0.104993i
$635$	2.35875	−	2.16151i	0.0936043	−	0.0857768i
$636$	−7.71415	−	20.1403i	−0.305886	−	0.798616i
$637$	41.2132	−	41.2132i	1.63293	−	1.63293i
$638$	5.02091	−	5.02091i	0.198780	−	0.198780i
$639$	7.12489	−	6.39632i	0.281856	−	0.253034i
$640$	1.64857	−	1.51071i	0.0651653	−	0.0597159i
$641$		−	31.7919i		−	1.25571i	−0.778332	−	0.627853i	$-0.783934\pi$
$641$		−	31.7919i		−	1.25571i	0.778332	−	0.627853i	$-0.216066\pi$
$642$	6.80944	−	15.2640i	0.268747	−	0.602423i
$643$	18.8832	+	18.8832i	0.744679	+	0.744679i	0.973475	−	0.228795i	$-0.0734786\pi$
$643$	18.8832	+	18.8832i	0.744679	+	0.744679i	−0.228795	+	0.973475i	$0.573479\pi$
$644$	−7.08743			−0.279284
$645$	−6.35605	−	19.0412i	−0.250269	−	0.749748i
$646$	5.28003			0.207740
$647$	18.3944	+	18.3944i	0.723157	+	0.723157i	0.969247	−	0.246090i	$-0.0791459\pi$
$647$	18.3944	+	18.3944i	0.723157	+	0.723157i	−0.246090	+	0.969247i	$0.579146\pi$
$648$	5.64327	+	7.01095i	0.221689	+	0.275416i
$649$		−	33.0847i		−	1.29869i
$650$	1.78149	−	20.3741i	0.0698758	−	0.799138i
$651$	55.6980	−	21.3335i	2.18298	−	0.836124i
$652$	16.2607	−	16.2607i	0.636820	−	0.636820i
$653$	8.36925	−	8.36925i	0.327514	−	0.327514i	−0.524126	−	0.851641i	$-0.675608\pi$
$653$	8.36925	−	8.36925i	0.327514	−	0.327514i	0.851641	+	0.524126i	$0.175608\pi$
$654$	7.65723	−	2.93287i	0.299421	−	0.114684i
$655$	1.10269	−	25.2700i	0.0430855	−	0.987379i
$656$		−	3.03782i		−	0.118607i
$657$	−1.63137	+	30.2760i	−0.0636460	+	1.18118i
$658$	17.5076	+	17.5076i	0.682516	+	0.682516i
$659$	−34.0877			−1.32787			−0.663933	−	0.747792i	$-0.731114\pi$
$659$	−34.0877			−1.32787			−0.663933	+	0.747792i	$0.731114\pi$
$660$	13.5222	+	6.75393i	0.526351	+	0.262896i
$661$	33.6922			1.31047			0.655237	−	0.755424i	$-0.272569\pi$
$661$	33.6922			1.31047			0.655237	+	0.755424i	$0.272569\pi$
$662$	−1.33144	−	1.33144i	−0.0517481	−	0.0517481i
$663$	−2.88638	+	6.47009i	−0.112098	+	0.251278i
$664$		−	5.13077i		−	0.199112i
$665$	−36.7695	−	40.1249i	−1.42586	−	1.55598i
$666$	10.8070	+	12.0379i	0.418762	+	0.466460i
$667$	−1.97804	+	1.97804i	−0.0765901	+	0.0765901i
$668$	10.1271	−	10.1271i	0.391829	−	0.391829i
$669$	0.368115	+	0.961084i	0.0142321	+	0.0371577i
$670$	13.5586	+	0.591646i	0.523813	+	0.0228573i
$671$		−	39.4831i		−	1.52423i
$672$	7.29154	+	3.25283i	0.281277	+	0.125481i
$673$	18.3125	+	18.3125i	0.705895	+	0.705895i	0.965669	−	0.259775i	$-0.0836483\pi$
$673$	18.3125	+	18.3125i	0.705895	+	0.705895i	−0.259775	+	0.965669i	$0.583648\pi$
$674$	−34.0765			−1.31258
$675$	−5.78976	−	25.3274i	−0.222848	−	0.974853i
$676$	−3.73109			−0.143503
$677$	18.3319	+	18.3319i	0.704553	+	0.704553i	0.965384	−	0.260831i	$-0.0839966\pi$
$677$	18.3319	+	18.3319i	0.704553	+	0.704553i	−0.260831	+	0.965384i	$0.583997\pi$
$678$	−19.8857	−	8.87123i	−0.763707	−	0.340698i
$679$			61.3397i			2.35400i
$680$	2.23394	+	0.0974809i	0.0856678	+	0.00373822i
$681$	−1.32522	−	3.45993i	−0.0507826	−	0.132585i
$682$	−20.6150	+	20.6150i	−0.789389	+	0.789389i
$683$	11.9231	−	11.9231i	0.456226	−	0.456226i	−0.441189	−	0.897414i	$-0.645443\pi$
$683$	11.9231	−	11.9231i	0.456226	−	0.456226i	0.897414	+	0.441189i	$0.145443\pi$
$684$	10.5818	+	11.7871i	0.404604	+	0.450690i
$685$	−24.9136	−	27.1871i	−0.951901	−	1.03877i
$686$		−	33.4164i		−	1.27584i
$687$	6.34766	−	14.2289i	0.242178	−	0.542866i
$688$	3.66501	+	3.66501i	0.139727	+	0.139727i
$689$	50.9324			1.94037
$690$	−5.32722	−	2.66078i	−0.202804	−	0.101294i
$691$	−49.4748			−1.88211			−0.941056	−	0.338252i	$-0.890164\pi$
$691$	−49.4748			−1.88211			−0.941056	+	0.338252i	$0.890164\pi$
$692$	17.0581	+	17.0581i	0.648453	+	0.648453i
$693$	−2.90390	+	53.8924i	−0.110310	+	2.04720i
$694$		−	9.20478i		−	0.349409i
$695$	0.748409	−	17.1511i	0.0283888	−	0.650577i
$696$	2.94285	−	1.12717i	0.111548	−	0.0427252i
$697$	2.14806	−	2.14806i	0.0813638	−	0.0813638i
$698$	−15.9284	+	15.9284i	−0.602898	+	0.602898i
$699$	−41.4230	+	15.8658i	−1.56676	+	0.600101i
$700$	−14.8161	−	17.6554i	−0.559996	−	0.667311i
$701$			30.3819i			1.14751i	0.819028	+	0.573753i	$0.194513\pi$
$701$			30.3819i			1.14751i	−0.819028	+	0.573753i	$0.805487\pi$
$702$	−20.2284	+	6.52326i	−0.763470	+	0.246205i
$703$	20.1328	+	20.1328i	0.759323	+	0.759323i
$704$	−3.90269			−0.147088
$705$	6.58669	+	19.7322i	0.248069	+	0.743157i
$706$	−11.5250			−0.433749
$707$	−55.3780	−	55.3780i	−2.08270	−	2.08270i
$708$	5.98210	−	13.4095i	0.224821	−	0.503958i
$709$		−	14.1717i		−	0.532230i	−0.963941	−	0.266115i	$-0.914260\pi$
$709$		−	14.1717i		−	0.532230i	0.963941	−	0.266115i	$-0.0857401\pi$
$710$	5.26156	−	4.82157i	0.197463	−	0.180950i
$711$	−8.86575	+	7.95917i	−0.332492	+	0.298492i
$712$	−5.64527	+	5.64527i	−0.211566	+	0.211566i
$713$	8.12150	−	8.12150i	0.304153	−	0.304153i
$714$	2.85580	+	7.45600i	0.106876	+	0.279034i
$715$	−26.3168	+	24.1161i	−0.984191	+	0.901890i
$716$		−	9.08118i		−	0.339380i
$717$	8.61829	+	3.84471i	0.321856	+	0.143583i
$718$	25.0060	+	25.0060i	0.933216	+	0.933216i
$719$	7.39087			0.275633			0.137817	−	0.990458i	$-0.455992\pi$
$719$	7.39087			0.275633			0.137817	+	0.990458i	$0.455992\pi$
$720$	4.25945	+	5.18238i	0.158740	+	0.193136i
$721$	16.0967			0.599471
$722$	6.27822	+	6.27822i	0.233651	+	0.233651i
$723$	40.8941	+	18.2433i	1.52087	+	0.678475i
$724$			14.9787i			0.556681i
$725$	−9.06251	−	0.792417i	−0.336573	−	0.0294296i
$726$	−2.62121	−	6.84352i	−0.0972821	−	0.253987i
$727$	13.8500	−	13.8500i	0.513668	−	0.513668i	−0.401980	−	0.915648i	$-0.631678\pi$
$727$	13.8500	−	13.8500i	0.513668	−	0.513668i	0.915648	+	0.401980i	$0.131678\pi$
$728$	−13.3327	+	13.3327i	−0.494143	+	0.494143i
$729$	−21.9133	+	15.7736i	−0.811604	+	0.584208i
$730$	−0.985204	+	22.5776i	−0.0364640	+	0.835636i
$731$			5.18310i			0.191704i
$732$	7.13900	−	16.0028i	0.263865	−	0.591479i
$733$	−19.3721	−	19.3721i	−0.715523	−	0.715523i	0.252162	−	0.967685i	$-0.418858\pi$
$733$	−19.3721	−	19.3721i	−0.715523	−	0.715523i	−0.967685	+	0.252162i	$0.918858\pi$
$734$	−24.4823			−0.903657
$735$	24.6594	−	49.3711i	0.909574	−	1.82108i
$736$	1.53751			0.0566733
$737$	−16.7491	−	16.7491i	−0.616961	−	0.616961i
$738$	9.10027	+	0.490353i	0.334985	+	0.0180502i
$739$		−	13.7133i		−	0.504451i	−0.967669	−	0.252225i	$-0.918838\pi$
$739$		−	13.7133i		−	0.504451i	0.967669	−	0.252225i	$-0.0811624\pi$
$740$	8.14634	+	8.88973i	0.299465	+	0.326793i
$741$	−34.9328	+	13.3800i	−1.28329	+	0.491526i
$742$	40.5871	−	40.5871i	1.49000	−	1.49000i
$743$	−21.8424	+	21.8424i	−0.801319	+	0.801319i	−0.983302	−	0.181983i	$-0.941748\pi$
$743$	−21.8424	+	21.8424i	−0.801319	+	0.801319i	0.181983	+	0.983302i	$0.441748\pi$
$744$	−12.0828	+	4.62797i	−0.442978	+	0.169669i
$745$	4.76446	+	0.207903i	0.174556	+	0.00761699i
$746$			5.31801i			0.194706i
$747$	15.3700	+	0.828189i	0.562359	+	0.0303018i
$748$	−2.75962	−	2.75962i	−0.100902	−	0.100902i
$749$	44.4827			1.62536
$750$	−4.50819	−	18.8329i	−0.164616	−	0.687678i
$751$	−27.4426			−1.00139			−0.500697	−	0.865622i	$-0.666923\pi$
$751$	−27.4426			−1.00139			−0.500697	+	0.865622i	$0.666923\pi$
$752$	−3.79800	−	3.79800i	−0.138499	−	0.138499i
$753$	−0.703502	+	1.57697i	−0.0256371	+	0.0574679i
$754$			7.44209i			0.271025i
$755$	−30.8695	−	1.34703i	−1.12346	−	0.0490235i
$756$	−10.9213	+	21.3179i	−0.397205	+	0.775324i
$757$	−1.69517	+	1.69517i	−0.0616121	+	0.0616121i	−0.737241	−	0.675629i	$-0.763872\pi$
$757$	−1.69517	+	1.69517i	−0.0616121	+	0.0616121i	0.675629	+	0.737241i	$0.263872\pi$
$758$	−5.56888	+	5.56888i	−0.202271	+	0.202271i
$759$	3.71739	+	9.70548i	0.134933	+	0.352287i
$760$	7.97658	+	8.70448i	0.289341	+	0.315745i
$761$		−	2.02486i		−	0.0734012i	−0.999326	−	0.0367006i	$-0.988315\pi$
$761$		−	2.02486i		−	0.0734012i	0.999326	−	0.0367006i	$-0.0116848\pi$
$762$	−2.26321	−	1.00964i	−0.0819875	−	0.0365755i
$763$	15.4309	+	15.4309i	0.558638	+	0.558638i
$764$	15.3084			0.553837
$765$	−0.652613	+	6.67638i	−0.0235953	+	0.241385i
$766$	9.84999			0.355895
$767$	24.5194	+	24.5194i	0.885344	+	0.885344i
$768$	−1.58179	−	0.705653i	−0.0570779	−	0.0254630i
$769$		−	2.81119i		−	0.101374i	−0.998715	−	0.0506871i	$-0.983859\pi$
$769$		−	2.81119i		−	0.101374i	0.998715	−	0.0506871i	$-0.0161411\pi$
$770$	−1.75370	+	40.1890i	−0.0631989	+	1.44831i
$771$	−3.42346	−	8.93806i	−0.123293	−	0.321896i
$772$	9.92832	−	9.92832i	0.357328	−	0.357328i
$773$	9.30098	−	9.30098i	0.334533	−	0.334533i	−0.519772	−	0.854305i	$-0.673983\pi$
$773$	9.30098	−	9.30098i	0.334533	−	0.334533i	0.854305	+	0.519772i	$0.173983\pi$
$774$	−11.5707	+	10.3875i	−0.415899	+	0.373371i
$775$	37.2091	+	3.25353i	1.33659	+	0.116870i
$776$		−	13.3067i		−	0.477683i
$777$	−17.5406	+	39.3190i	−0.629266	+	1.41056i
$778$	−12.5928	−	12.5928i	−0.451474	−	0.451474i
$779$	16.0398			0.574686
$780$	−15.0268	+	5.01603i	−0.538047	+	0.179603i
$781$	−12.4558			−0.445705
$782$	1.08718	+	1.08718i	0.0388776	+	0.0388776i
$783$	2.90159	+	8.99769i	0.103694	+	0.321551i
$784$			14.2492i			0.508899i
$785$	−12.2286	+	11.2060i	−0.436456	+	0.399958i
$786$	−18.2965	+	7.00792i	−0.652614	+	0.249964i
$787$	−15.0478	+	15.0478i	−0.536397	+	0.536397i	−0.922469	−	0.386072i	$-0.873832\pi$
$787$	−15.0478	+	15.0478i	−0.536397	+	0.536397i	0.386072	+	0.922469i	$0.373832\pi$
$788$	7.73048	−	7.73048i	0.275387	−	0.275387i
$789$	15.7023	−	6.01429i	0.559016	−	0.214115i
$790$	−6.54715	+	5.99965i	−0.232937	+	0.213458i
$791$		−	57.9514i		−	2.06051i
$792$	0.629958	−	11.6911i	0.0223846	−	0.415426i
$793$	29.2613	+	29.2613i	1.03910	+	1.03910i
$794$	25.2562			0.896311
$795$	45.7443	−	15.2697i	1.62238	−	0.541560i
$796$	8.35422			0.296107
$797$	−4.65701	−	4.65701i	−0.164960	−	0.164960i	0.619800	−	0.784760i	$-0.287214\pi$
$797$	−4.65701	−	4.65701i	−0.164960	−	0.164960i	−0.784760	+	0.619800i	$0.787214\pi$
$798$	−17.1751	+	38.4996i	−0.607991	+	1.36287i
$799$		−	5.37118i		−	0.190019i
$800$	3.21413	+	3.83006i	0.113637	+	0.135413i
$801$	−16.0001	−	17.8225i	−0.565334	−	0.629728i
$802$	4.91654	−	4.91654i	0.173609	−	0.173609i
$803$	27.8905	−	27.8905i	0.984234	−	0.984234i
$804$	−3.76009	−	9.81696i	−0.132608	−	0.346217i
$805$	0.690889	−	15.8329i	0.0243506	−	0.558037i
$806$		−	30.5559i		−	1.07629i
$807$	−24.6163	−	10.9816i	−0.866535	−	0.386570i
$808$	12.0134	+	12.0134i	0.422630	+	0.422630i
$809$	17.6568			0.620781			0.310391	−	0.950609i	$-0.399540\pi$
$809$	17.6568			0.620781			0.310391	+	0.950609i	$0.399540\pi$
$810$	−16.2122	+	11.9233i	−0.569638	+	0.418943i
$811$	−18.2740			−0.641687			−0.320843	−	0.947132i	$-0.603966\pi$
$811$	−18.2740			−0.641687			−0.320843	+	0.947132i	$0.603966\pi$
$812$	5.93046	+	5.93046i	0.208118	+	0.208118i
$813$	9.10656	+	4.06253i	0.319381	+	0.142479i
$814$		−	21.0449i		−	0.737624i
$815$	34.7404	+	37.9107i	1.21690	+	1.32795i
$816$	−0.619522	−	1.61746i	−0.0216876	−	0.0566226i
$817$	−19.3513	+	19.3513i	−0.677018	+	0.677018i
$818$	4.07415	−	4.07415i	0.142449	−	0.142449i
$819$	−37.7881	−	42.0923i	−1.32042	−	1.47082i
$820$	6.78632	+	0.296130i	0.236989	+	0.0103413i
$821$			12.6502i			0.441494i	0.975331	+	0.220747i	$0.0708495\pi$
$821$			12.6502i			0.441494i	−0.975331	+	0.220747i	$0.929150\pi$
$822$	−11.6372	+	26.0859i	−0.405893	+	0.909849i
$823$	−16.6310	−	16.6310i	−0.579720	−	0.579720i	0.355106	−	0.934826i	$-0.384445\pi$
$823$	−16.6310	−	16.6310i	−0.579720	−	0.579720i	−0.934826	+	0.355106i	$0.884445\pi$
$824$	−3.49192			−0.121647
$825$	−16.4060	+	29.5494i	−0.571185	+	1.02878i
$826$	39.0781			1.35970
$827$	17.7163	+	17.7163i	0.616055	+	0.616055i	0.944517	−	0.328462i	$-0.106530\pi$
$827$	17.7163	+	17.7163i	0.616055	+	0.616055i	−0.328462	+	0.944517i	$0.606530\pi$
$828$	−0.248179	+	4.60585i	−0.00862481	+	0.160064i
$829$		−	6.98698i		−	0.242668i	−0.992612	−	0.121334i	$-0.961283\pi$
$829$		−	6.98698i		−	0.242668i	0.992612	−	0.121334i	$-0.0387172\pi$
$830$	11.4618	+	0.500152i	0.397846	+	0.0173605i
$831$	−20.9897	+	8.03946i	−0.728123	+	0.278886i
$832$	2.89233	−	2.89233i	0.100273	−	0.100273i
$833$	−10.0757	+	10.0757i	−0.349102	+	0.349102i
$834$	−12.4181	+	4.75637i	−0.430003	+	0.164700i
$835$	21.6362	+	23.6106i	0.748750	+	0.817077i
$836$		−	20.6063i		−	0.712685i
$837$	−11.9134	−	36.9430i	−0.411788	−	1.27694i
$838$	−19.4795	−	19.4795i	−0.672907	−	0.672907i
$839$	29.2981			1.01148			0.505741	−	0.862685i	$-0.331219\pi$
$839$	29.2981			1.01148			0.505741	+	0.862685i	$0.331219\pi$
$840$	−7.97743	+	15.9718i	−0.275247	+	0.551079i
$841$	−25.6897			−0.885852
$842$	16.2267	+	16.2267i	0.559210	+	0.559210i
$843$	−10.8923	+	24.4161i	−0.375150	+	0.840936i
$844$			19.1998i			0.660883i
$845$	0.363710	−	8.33504i	0.0125120	−	0.286734i
$846$	11.9905	−	10.7644i	0.412243	−	0.370089i
$847$	13.7912	−	13.7912i	0.473870	−	0.473870i
$848$	−8.80475	+	8.80475i	−0.302356	+	0.302356i
$849$	−17.3280	−	45.2404i	−0.594695	−	1.55265i
$850$	−0.435533	+	4.98099i	−0.0149387	+	0.170847i
$851$			8.29087i			0.284208i
$852$	−5.04844	−	2.25216i	−0.172957	−	0.0771578i
$853$	0.563629	+	0.563629i	0.0192983	+	0.0192983i	0.716690	−	0.697392i	$-0.245656\pi$
$853$	0.563629	+	0.563629i	0.0192983	+	0.0192983i	−0.697392	+	0.716690i	$0.745656\pi$
$854$	46.6356			1.59584
$855$	−27.3632	+	22.4900i	−0.935800	+	0.769143i
$856$	−9.64984			−0.329825
$857$	22.0419	+	22.0419i	0.752938	+	0.752938i	0.975027	−	0.222088i	$-0.0712874\pi$
$857$	22.0419	+	22.0419i	0.752938	+	0.752938i	−0.222088	+	0.975027i	$0.571287\pi$
$858$	25.2508	+	11.2646i	0.862048	+	0.384569i
$859$			11.0071i			0.375556i	0.982211	+	0.187778i	$0.0601286\pi$
$859$			11.0071i			0.375556i	−0.982211	+	0.187778i	$0.939871\pi$
$860$	−8.54468	+	7.83014i	−0.291371	+	0.267006i
$861$	8.67541	+	22.6500i	0.295657	+	0.771910i
$862$	−3.81590	+	3.81590i	−0.129970	+	0.129970i
$863$	26.4047	−	26.4047i	0.898825	−	0.898825i	−0.0965074	−	0.995332i	$-0.530767\pi$
$863$	26.4047	−	26.4047i	0.898825	−	0.898825i	0.995332	+	0.0965074i	$0.0307671\pi$
$864$	2.36922	−	4.62459i	0.0806024	−	0.157332i
$865$	−39.7697	+	36.4440i	−1.35221	+	1.23913i
$866$			6.37828i			0.216743i
$867$	0.705653	−	1.58179i	0.0239652	−	0.0537204i
$868$	−24.3495	−	24.3495i	−0.826475	−	0.826475i
$869$	15.4992			0.525776
$870$	2.23116	+	6.68402i	0.0756434	+	0.226610i
$871$	24.8259			0.841192
$872$	−3.34751	−	3.34751i	−0.113361	−	0.113361i
$873$	39.8623	+	2.14792i	1.34913	+	0.0726960i
$874$			8.11810i			0.274599i
$875$	40.8854	−	31.3773i	1.38218	−	1.06074i
$876$	16.3471	−	6.26128i	0.552319	−	0.211549i
$877$	20.8103	−	20.8103i	0.702715	−	0.702715i	−0.262277	−	0.964993i	$-0.584473\pi$
$877$	20.8103	−	20.8103i	0.702715	−	0.702715i	0.964993	+	0.262277i	$0.0844734\pi$
$878$	4.60831	−	4.60831i	0.155523	−	0.155523i
$879$	44.0286	−	16.8639i	1.48505	−	0.568804i
$880$	0.380438	−	8.71839i	0.0128246	−	0.293897i
$881$		−	53.3751i		−	1.79825i	−0.437688	−	0.899127i	$-0.644202\pi$
$881$		−	53.3751i		−	1.79825i	0.437688	−	0.899127i	$-0.355798\pi$
$882$	−42.6856	−	2.30005i	−1.43730	−	0.0774466i
$883$	−27.8731	−	27.8731i	−0.938004	−	0.938004i	0.0601829	−	0.998187i	$-0.480832\pi$
$883$	−27.8731	−	27.8731i	−0.938004	−	0.938004i	−0.998187	+	0.0601829i	$0.980832\pi$
$884$	4.09037			0.137574
$885$	29.3728	+	14.6708i	0.987356	+	0.493154i
$886$	14.9068			0.500803
$887$	30.8955	+	30.8955i	1.03737	+	1.03737i	0.999274	+	0.0380949i	$0.0121289\pi$
$887$	30.8955	+	30.8955i	1.03737	+	1.03737i	0.0380949	+	0.999274i	$0.487871\pi$
$888$	3.80517	−	8.52965i	0.127693	−	0.286236i
$889$		−	6.59550i		−	0.221206i
$890$	−12.0609	−	13.1615i	−0.404283	−	0.441175i
$891$	34.9209	+	3.77427i	1.16989	+	0.126443i
$892$	0.420157	−	0.420157i	0.0140679	−	0.0140679i
$893$	20.0535	−	20.0535i	0.671066	−	0.671066i
$894$	−1.32129	−	3.44966i	−0.0441906	−	0.115374i
$895$	20.2868	+	0.885242i	0.678114	+	0.0295904i
$896$		−	4.60968i		−	0.153999i
$897$	−9.94783	−	4.43783i	−0.332148	−	0.148175i
$898$	−25.8384	−	25.8384i	−0.862238	−	0.862238i
$899$	−13.5915			−0.453301
$900$	−11.9924	+	9.01018i	−0.399745	+	0.300339i
$901$	−12.4518			−0.414829
$902$	−8.38324	−	8.38324i	−0.279131	−	0.279131i
$903$	−37.7928	−	16.8598i	−1.25767	−	0.561058i
$904$			12.5717i			0.418128i
$905$	−33.4616	−	1.46014i	−1.11230	−	0.0485367i
$906$	8.56080	+	22.3508i	0.284414	+	0.742555i
$907$	−25.6343	+	25.6343i	−0.851172	+	0.851172i	−0.990278	−	0.139106i	$-0.955577\pi$
$907$	−25.6343	+	25.6343i	−0.851172	+	0.851172i	0.139106	+	0.990278i	$0.455577\pi$
$908$	−1.51258	+	1.51258i	−0.0501966	+	0.0501966i
$909$	−37.9272	+	34.0489i	−1.25796	+	1.12933i
$910$	−28.4848	−	31.0842i	−0.944262	−	1.03043i
$911$			32.9517i			1.09174i	0.837871	+	0.545869i	$0.183800\pi$
$911$			32.9517i			1.09174i	−0.837871	+	0.545869i	$0.816200\pi$
$912$	3.72587	−	8.35189i	0.123376	−	0.276559i
$913$	−14.1590	−	14.1590i	−0.468594	−	0.468594i
$914$	24.3856			0.806603
$915$	35.0533	+	17.5081i	1.15883	+	0.578799i
$916$	−8.99545			−0.297218
$917$	−36.8713	−	36.8713i	−1.21760	−	1.21760i
$918$	4.94537	−	1.59479i	0.163221	−	0.0526358i
$919$			23.4665i			0.774087i	0.922061	+	0.387044i	$0.126504\pi$
$919$			23.4665i			0.774087i	−0.922061	+	0.387044i	$0.873496\pi$
$920$	−0.149878	+	3.43471i	−0.00494132	+	0.113239i
$921$	−13.5610	+	5.19412i	−0.446849	+	0.171152i
$922$	−2.55411	+	2.55411i	−0.0841153	+	0.0841153i
$923$	9.23115	−	9.23115i	0.303847	−	0.303847i
$924$	29.0985	−	11.1453i	0.957270	−	0.366654i
$925$	−20.6533	+	17.3319i	−0.679075	+	0.569869i
$926$		−	30.3771i		−	0.998255i
$927$	0.563653	−	10.4606i	0.0185128	−	0.343571i
$928$	−1.28652	−	1.28652i	−0.0422322	−	0.0422322i
$929$	9.57033			0.313992			0.156996	−	0.987599i	$-0.449819\pi$
$929$	9.57033			0.313992			0.156996	+	0.987599i	$0.449819\pi$
$930$	−9.16076	−	27.4435i	−0.300393	−	0.899907i
$931$	−75.2361			−2.46576
$932$	18.1089	+	18.1089i	0.593176	+	0.593176i
$933$	2.94535	−	6.60229i	0.0964264	−	0.216149i
$934$		−	28.1100i		−	0.919787i
$935$	6.43384	−	5.89582i	0.210409	−	0.192814i
$936$	8.19754	+	9.13127i	0.267945	+	0.298465i
$937$	9.07827	−	9.07827i	0.296574	−	0.296574i	−0.543096	−	0.839670i	$-0.682748\pi$
$937$	9.07827	−	9.07827i	0.296574	−	0.296574i	0.839670	+	0.543096i	$0.182748\pi$
$938$	19.7833	−	19.7833i	0.645947	−	0.645947i
$939$	−9.61711	−	25.1086i	−0.313842	−	0.819389i
$940$	8.85473	−	8.11427i	0.288810	−	0.264658i
$941$		−	12.2228i		−	0.398453i	−0.979953	−	0.199227i	$-0.936157\pi$
$941$		−	12.2228i		−	0.398453i	0.979953	−	0.199227i	$-0.0638430\pi$
$942$	11.7332	+	5.23432i	0.382289	+	0.170543i
$943$	3.30267	+	3.30267i	0.107550	+	0.107550i
$944$	−8.47740			−0.275916
$945$	−46.5583	−	26.4757i	−1.51454	−	0.861255i
$946$	20.2281			0.657671
$947$	−33.9481	−	33.9481i	−1.10316	−	1.10316i	−0.994027	−	0.109138i	$-0.965191\pi$
$947$	−33.9481	−	33.9481i	−1.10316	−	1.10316i	−0.109138	−	0.994027i	$-0.534809\pi$
$948$	6.28195	+	2.80244i	0.204028	+	0.0910192i
$949$			41.3398i			1.34195i
$950$	−20.2229	+	16.9707i	−0.656116	+	0.550602i
$951$	−1.63781	−	4.27604i	−0.0531096	−	0.138660i
$952$	3.25954	−	3.25954i	0.105642	−	0.105642i
$953$	−28.0165	+	28.0165i	−0.907544	+	0.907544i	−0.996074	−	0.0885292i	$-0.971783\pi$
$953$	−28.0165	+	28.0165i	−0.907544	+	0.907544i	0.0885292	+	0.996074i	$0.471783\pi$
$954$	−24.9547	−	27.7972i	−0.807940	−	0.899968i
$955$	−1.49227	+	34.1980i	−0.0482888	+	1.10662i
$956$		−	5.44845i		−	0.176215i
$957$	5.01058	−	11.2317i	0.161969	−	0.363069i
$958$	1.67180	+	1.67180i	0.0540133	+	0.0540133i
$959$	−76.0200			−2.45481
$960$	1.73058	−	3.46484i	0.0558543	−	0.111827i
$961$	24.8042			0.800137
$962$	15.5966	+	15.5966i	0.502854	+	0.502854i
$963$	1.55764	−	28.9076i	0.0501943	−	0.931534i
$964$		−	25.8531i		−	0.832671i
$965$	21.2115	+	23.1471i	0.682822	+	0.745132i
$966$	−11.4637	+	4.39082i	−0.368837	+	0.141272i
$967$	17.3419	−	17.3419i	0.557677	−	0.557677i	−0.370969	−	0.928645i	$-0.620974\pi$
$967$	17.3419	−	17.3419i	0.557677	−	0.557677i	0.928645	+	0.370969i	$0.120974\pi$
$968$	−2.99178	+	2.99178i	−0.0961595	+	0.0961595i
$969$	8.54027	−	3.27109i	0.274353	−	0.105083i
$970$	29.7264	+	1.29715i	0.954458	+	0.0416490i
$971$			4.24446i			0.136211i	0.997678	+	0.0681055i	$0.0216955\pi$
$971$			4.24446i			0.136211i	−0.997678	+	0.0681055i	$0.978305\pi$
$972$	13.4712	+	7.84384i	0.432090	+	0.251591i
$973$	−25.0251	−	25.0251i	−0.802267	−	0.802267i
$974$	39.2212			1.25673
$975$	−9.74069	−	34.0580i	−0.311952	−	1.09073i
$976$	−10.1169			−0.323833
$977$	12.7973	+	12.7973i	0.409422	+	0.409422i	0.881537	−	0.472115i	$-0.156509\pi$
$977$	12.7973	+	12.7973i	0.409422	+	0.409422i	−0.472115	+	0.881537i	$0.656509\pi$
$978$	16.2273	−	36.3751i	0.518892	−	1.16315i
$979$			31.1576i			0.995802i
$980$	−31.8318	−	1.38902i	−1.01683	−	0.0443707i
$981$	10.5683	−	9.48763i	0.337420	−	0.302917i
$982$	11.0949	−	11.0949i	0.354054	−	0.354054i
$983$	−39.4370	+	39.4370i	−1.25785	+	1.25785i	−0.305726	+	0.952120i	$0.598899\pi$
$983$	−39.4370	+	39.4370i	−1.25785	+	1.25785i	−0.952120	+	0.305726i	$0.901101\pi$
$984$	−1.88200	−	4.91357i	−0.0599959	−	0.156639i
$985$	16.5159	+	18.0230i	0.526239	+	0.574261i
$986$		−	1.81942i		−	0.0579421i
$987$	39.1642	+	17.4715i	1.24661	+	0.556126i
$988$	15.2716	+	15.2716i	0.485853	+	0.485853i
$989$	−7.96906			−0.253401
$990$	26.0559	+	2.54695i	0.828110	+	0.0809474i
$991$	56.6961			1.80101			0.900505	−	0.434845i	$-0.143197\pi$
$991$	56.6961			1.80101			0.900505	+	0.434845i	$0.143197\pi$
$992$	5.28225	+	5.28225i	0.167711	+	0.167711i
$993$	−2.97842	−	1.32871i	−0.0945174	−	0.0421652i
$994$		−	14.7123i		−	0.466645i
$995$	−0.814377	+	18.6628i	−0.0258175	+	0.591652i
$996$	−3.17862	−	8.29884i	−0.100718	−	0.262959i
$997$	19.2446	−	19.2446i	0.609481	−	0.609481i	−0.333329	−	0.942810i	$-0.608172\pi$
$997$	19.2446	−	19.2446i	0.609481	−	0.609481i	0.942810	+	0.333329i	$0.108172\pi$
$998$	4.19923	−	4.19923i	0.132924	−	0.132924i
$999$	24.9377	+	12.7758i	0.788993	+	0.404208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.l.g.443.2	yes	28
3.2	odd	2	inner	510.2.l.g.443.10	yes	28
5.2	odd	4	inner	510.2.l.g.137.10	yes	28
15.2	even	4	inner	510.2.l.g.137.2	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.l.g.137.2	✓	28	15.2	even	4	inner
510.2.l.g.137.10	yes	28	5.2	odd	4	inner
510.2.l.g.443.2	yes	28	1.1	even	1	trivial
510.2.l.g.443.10	yes	28	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.58179 - 0.705653i) q^{3} +1.00000i q^{4} +(-2.23394 - 0.0974809i) q^{5} +(0.619522 + 1.61746i) q^{6} +(-3.25954 + 3.25954i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.00411 + 2.23239i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.58179 - 0.705653i) q^{3} +1.00000i q^{4} +(-2.23394 - 0.0974809i) q^{5} +(0.619522 + 1.61746i) q^{6} +(-3.25954 + 3.25954i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.00411 + 2.23239i) q^{9} +(1.51071 + 1.64857i) q^{10} -3.90269i q^{11} +(0.705653 - 1.58179i) q^{12} +(2.89233 + 2.89233i) q^{13} +4.60968 q^{14} +(3.46484 + 1.73058i) q^{15} -1.00000 q^{16} +(-0.707107 - 0.707107i) q^{17} +(0.161416 - 2.99565i) q^{18} -5.28003i q^{19} +(0.0974809 - 2.23394i) q^{20} +(7.45600 - 2.85580i) q^{21} +(-2.75962 + 2.75962i) q^{22} +(1.08718 - 1.08718i) q^{23} +(-1.61746 + 0.619522i) q^{24} +(4.98099 + 0.435533i) q^{25} -4.09037i q^{26} +(-1.59479 - 4.94537i) q^{27} +(-3.25954 - 3.25954i) q^{28} -1.81942 q^{29} +(-1.22630 - 3.67371i) q^{30} +7.47022 q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.75395 + 6.17324i) q^{33} +1.00000i q^{34} +(7.59936 - 6.96388i) q^{35} +(-2.23239 + 2.00411i) q^{36} +(-3.81301 + 3.81301i) q^{37} +(-3.73355 + 3.73355i) q^{38} +(-2.53407 - 6.61602i) q^{39} +(-1.64857 + 1.51071i) q^{40} +3.03782i q^{41} +(-7.29154 - 3.25283i) q^{42} +(-3.66501 - 3.66501i) q^{43} +3.90269 q^{44} +(-4.25945 - 5.18238i) q^{45} -1.53751 q^{46} +(3.79800 + 3.79800i) q^{47} +(1.58179 + 0.705653i) q^{48} -14.2492i q^{49} +(-3.21413 - 3.83006i) q^{50} +(0.619522 + 1.61746i) q^{51} +(-2.89233 + 2.89233i) q^{52} +(8.80475 - 8.80475i) q^{53} +(-2.36922 + 4.62459i) q^{54} +(-0.380438 + 8.71839i) q^{55} +4.60968i q^{56} +(-3.72587 + 8.35189i) q^{57} +(1.28652 + 1.28652i) q^{58} +8.47740 q^{59} +(-1.73058 + 3.46484i) q^{60} +10.1169 q^{61} +(-5.28225 - 5.28225i) q^{62} +(-13.8090 - 0.744077i) q^{63} -1.00000i q^{64} +(-6.17934 - 6.74323i) q^{65} +(6.31247 - 2.41780i) q^{66} +(4.29168 - 4.29168i) q^{67} +(0.707107 - 0.707107i) q^{68} +(-2.48687 + 0.952520i) q^{69} +(-10.2978 - 0.449356i) q^{70} -3.19160i q^{71} +(2.99565 + 0.161416i) q^{72} +(7.14647 + 7.14647i) q^{73} +5.39241 q^{74} +(-7.57154 - 4.20377i) q^{75} +5.28003 q^{76} +(12.7210 + 12.7210i) q^{77} +(-2.88638 + 6.47009i) q^{78} +3.97142i q^{79} +(2.23394 + 0.0974809i) q^{80} +(-0.967094 + 8.94789i) q^{81} +(2.14806 - 2.14806i) q^{82} +(3.62800 - 3.62800i) q^{83} +(2.85580 + 7.45600i) q^{84} +(1.51071 + 1.64857i) q^{85} +5.18310i q^{86} +(2.87794 + 1.28388i) q^{87} +(-2.75962 - 2.75962i) q^{88} -7.98362 q^{89} +(-0.652613 + 6.67638i) q^{90} -18.8553 q^{91} +(1.08718 + 1.08718i) q^{92} +(-11.8163 - 5.27138i) q^{93} -5.37118i q^{94} +(-0.514702 + 11.7953i) q^{95} +(-0.619522 - 1.61746i) q^{96} +(9.40927 - 9.40927i) q^{97} +(-10.0757 + 10.0757i) q^{98} +(8.71232 - 7.82142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{7}+O(q^{10}) \) 28 * q + 4 * q^7	\( 28 q + 4 q^{7} - 12 q^{10} - 8 q^{13} + 8 q^{15} - 28 q^{16} - 16 q^{18} + 48 q^{21} + 20 q^{22} + 40 q^{25} - 36 q^{27} + 4 q^{28} - 12 q^{30} + 16 q^{31} + 8 q^{33} + 8 q^{37} - 8 q^{40} - 48 q^{42} + 48 q^{43} + 36 q^{45} - 64 q^{46} + 8 q^{52} - 36 q^{55} - 32 q^{57} + 20 q^{58} + 12 q^{60} - 16 q^{61} - 56 q^{63} + 32 q^{66} + 112 q^{67} - 28 q^{70} + 16 q^{72} + 12 q^{73} + 16 q^{75} - 8 q^{76} - 32 q^{78} - 48 q^{81} + 24 q^{82} - 12 q^{85} - 44 q^{87} + 20 q^{88} - 20 q^{90} - 80 q^{91} + 28 q^{93} + 60 q^{97}+O(q^{100}) \) 28 * q + 4 * q^7 - 12 * q^10 - 8 * q^13 + 8 * q^15 - 28 * q^16 - 16 * q^18 + 48 * q^21 + 20 * q^22 + 40 * q^25 - 36 * q^27 + 4 * q^28 - 12 * q^30 + 16 * q^31 + 8 * q^33 + 8 * q^37 - 8 * q^40 - 48 * q^42 + 48 * q^43 + 36 * q^45 - 64 * q^46 + 8 * q^52 - 36 * q^55 - 32 * q^57 + 20 * q^58 + 12 * q^60 - 16 * q^61 - 56 * q^63 + 32 * q^66 + 112 * q^67 - 28 * q^70 + 16 * q^72 + 12 * q^73 + 16 * q^75 - 8 * q^76 - 32 * q^78 - 48 * q^81 + 24 * q^82 - 12 * q^85 - 44 * q^87 + 20 * q^88 - 20 * q^90 - 80 * q^91 + 28 * q^93 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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