LMFDB - Embedded newform 546.2.k.d.445.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(373,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("546.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.k (of order $3$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.6498455769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} + 3x^{5} + 25x^{4} - 3x^{3} + 6x^{2} + x + 1 $ x^8 - x^7 + 6x^6 + 3x^5 + 25x^4 - 3x^3 + 6*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			445.2
Root			$-0.922415 - 1.59767i$ of defining polynomial
Character	$\chi$	$=$	546.445
Dual form			546.2.k.d.373.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.15139 - 1.99426i) q^{5} +(0.500000 - 0.866025i) q^{6} +(2.61586 - 0.396592i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.15139 - 1.99426i) q^{5} +(0.500000 - 0.866025i) q^{6} +(2.61586 - 0.396592i) q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.30278 q^{10} -0.357320 q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.73997 - 2.34362i) q^{13} +(0.964471 - 2.46370i) q^{14} +(-1.15139 - 1.99426i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.12412 - 3.67908i) q^{17} +(0.500000 - 0.866025i) q^{18} +6.79924 q^{19} +(-1.15139 + 1.99426i) q^{20} +(2.61586 - 0.396592i) q^{21} +(-0.178660 + 0.309448i) q^{22} +(-1.77550 + 3.07526i) q^{23} -1.00000 q^{24} +(-0.151388 + 0.262211i) q^{25} +(-3.39962 + 1.20108i) q^{26} +1.00000 q^{27} +(-1.65139 - 2.06710i) q^{28} +(-0.624116 - 1.08100i) q^{29} -2.30278 q^{30} +(-0.124116 + 0.214975i) q^{31} +(0.500000 + 0.866025i) q^{32} -0.357320 q^{33} -4.24823 q^{34} +(-3.80278 - 4.76008i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-4.72096 + 8.17694i) q^{37} +(3.39962 - 5.88831i) q^{38} +(-2.73997 - 2.34362i) q^{39} +(1.15139 + 1.99426i) q^{40} +(-2.95621 - 5.12031i) q^{41} +(0.964471 - 2.46370i) q^{42} +(2.63282 - 4.56018i) q^{43} +(0.178660 + 0.309448i) q^{44} +(-1.15139 - 1.99426i) q^{45} +(1.77550 + 3.07526i) q^{46} +(4.19414 + 7.26446i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(6.68543 - 2.07486i) q^{49} +(0.151388 + 0.262211i) q^{50} +(-2.12412 - 3.67908i) q^{51} +(-0.659645 + 3.54470i) q^{52} +(-0.605101 + 1.04807i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.411414 + 0.712590i) q^{55} +(-2.61586 + 0.396592i) q^{56} +6.79924 q^{57} -1.24823 q^{58} +(3.58033 + 6.20131i) q^{59} +(-1.15139 + 1.99426i) q^{60} +13.7076 q^{61} +(0.124116 + 0.214975i) q^{62} +(2.61586 - 0.396592i) q^{63} +1.00000 q^{64} +(-1.51901 + 8.16264i) q^{65} +(-0.178660 + 0.309448i) q^{66} -2.81985 q^{67} +(-2.12412 + 3.67908i) q^{68} +(-1.77550 + 3.07526i) q^{69} +(-6.02373 + 0.913262i) q^{70} +(0.794068 - 1.37537i) q^{71} -1.00000 q^{72} +(0.407877 - 0.706463i) q^{73} +(4.72096 + 8.17694i) q^{74} +(-0.151388 + 0.262211i) q^{75} +(-3.39962 - 5.88831i) q^{76} +(-0.934698 + 0.141710i) q^{77} +(-3.39962 + 1.20108i) q^{78} +(5.77345 + 9.99992i) q^{79} +2.30278 q^{80} +1.00000 q^{81} -5.91243 q^{82} -1.24823 q^{83} +(-1.65139 - 2.06710i) q^{84} +(-4.89136 + 8.47209i) q^{85} +(-2.63282 - 4.56018i) q^{86} +(-0.624116 - 1.08100i) q^{87} +0.357320 q^{88} +(-0.367627 + 0.636749i) q^{89} -2.30278 q^{90} +(-8.09684 - 5.04392i) q^{91} +3.55101 q^{92} +(-0.124116 + 0.214975i) q^{93} +8.38827 q^{94} +(-7.82856 - 13.5595i) q^{95} +(0.500000 + 0.866025i) q^{96} +(-3.63237 + 6.29145i) q^{97} +(1.54584 - 6.82718i) q^{98} -0.357320 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 8 q^{3} - 4 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 8 * q^3 - 4 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q + 4 q^{2} + 8 q^{3} - 4 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} + 8 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} + 7 q^{13} - 3 q^{14} - 2 q^{15} - 4 q^{16} - 6 q^{17} + 4 q^{18} - 4 q^{19} - 2 q^{20} + 3 q^{21} + 2 q^{22} + 4 q^{23} - 8 q^{24} + 6 q^{25} + 2 q^{26} + 8 q^{27} - 6 q^{28} + 6 q^{29} - 4 q^{30} + 10 q^{31} + 4 q^{32} + 4 q^{33} - 12 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{37} - 2 q^{38} + 7 q^{39} + 2 q^{40} - 6 q^{41} - 3 q^{42} - 4 q^{43} - 2 q^{44} - 2 q^{45} - 4 q^{46} - 17 q^{47} - 4 q^{48} + 17 q^{49} - 6 q^{50} - 6 q^{51} - 5 q^{52} + 3 q^{53} + 4 q^{54} + 25 q^{55} - 3 q^{56} - 4 q^{57} + 12 q^{58} - 2 q^{60} + 8 q^{61} - 10 q^{62} + 3 q^{63} + 8 q^{64} - 9 q^{65} + 2 q^{66} + 14 q^{67} - 6 q^{68} + 4 q^{69} - 8 q^{70} + 6 q^{71} - 8 q^{72} - 19 q^{73} + 12 q^{74} + 6 q^{75} + 2 q^{76} - 10 q^{77} + 2 q^{78} + 24 q^{79} + 4 q^{80} + 8 q^{81} - 12 q^{82} + 12 q^{83} - 6 q^{84} - 3 q^{85} + 4 q^{86} + 6 q^{87} - 4 q^{88} - 7 q^{89} - 4 q^{90} - 50 q^{91} - 8 q^{92} + 10 q^{93} - 34 q^{94} - 12 q^{95} + 4 q^{96} - 25 q^{97} + 34 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 8 * q^3 - 4 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 + 8 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 + 7 * q^13 - 3 * q^14 - 2 * q^15 - 4 * q^16 - 6 * q^17 + 4 * q^18 - 4 * q^19 - 2 * q^20 + 3 * q^21 + 2 * q^22 + 4 * q^23 - 8 * q^24 + 6 * q^25 + 2 * q^26 + 8 * q^27 - 6 * q^28 + 6 * q^29 - 4 * q^30 + 10 * q^31 + 4 * q^32 + 4 * q^33 - 12 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^37 - 2 * q^38 + 7 * q^39 + 2 * q^40 - 6 * q^41 - 3 * q^42 - 4 * q^43 - 2 * q^44 - 2 * q^45 - 4 * q^46 - 17 * q^47 - 4 * q^48 + 17 * q^49 - 6 * q^50 - 6 * q^51 - 5 * q^52 + 3 * q^53 + 4 * q^54 + 25 * q^55 - 3 * q^56 - 4 * q^57 + 12 * q^58 - 2 * q^60 + 8 * q^61 - 10 * q^62 + 3 * q^63 + 8 * q^64 - 9 * q^65 + 2 * q^66 + 14 * q^67 - 6 * q^68 + 4 * q^69 - 8 * q^70 + 6 * q^71 - 8 * q^72 - 19 * q^73 + 12 * q^74 + 6 * q^75 + 2 * q^76 - 10 * q^77 + 2 * q^78 + 24 * q^79 + 4 * q^80 + 8 * q^81 - 12 * q^82 + 12 * q^83 - 6 * q^84 - 3 * q^85 + 4 * q^86 + 6 * q^87 - 4 * q^88 - 7 * q^89 - 4 * q^90 - 50 * q^91 - 8 * q^92 + 10 * q^93 - 34 * q^94 - 12 * q^95 + 4 * q^96 - 25 * q^97 + 34 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.15139	−	1.99426i	−0.514916	−	0.891861i	−0.999850	−	0.0173104i	$-0.994490\pi$
$5$	−1.15139	−	1.99426i	−0.514916	−	0.891861i	0.484934	−	0.874551i	$-0.338844\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	2.61586	−	0.396592i	0.988702	−	0.149898i
$7$	2.61586	−	0.396592i	0.988702	−	0.149898i
$8$	−1.00000			−0.353553
$9$	1.00000			0.333333
$10$	−2.30278			−0.728202
$11$	−0.357320			−0.107736			−0.0538680	−	0.998548i	$-0.517155\pi$
$11$	−0.357320			−0.107736			−0.0538680	+	0.998548i	$0.517155\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−2.73997	−	2.34362i	−0.759932	−	0.650003i
$13$	−2.73997	−	2.34362i	−0.759932	−	0.650003i
$14$	0.964471	−	2.46370i	0.257766	−	0.658450i
$15$	−1.15139	−	1.99426i	−0.297287	−	0.514916i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.12412	−	3.67908i	−0.515174	−	0.892307i	−0.999845	−	0.0176106i	$-0.994394\pi$
$17$	−2.12412	−	3.67908i	−0.515174	−	0.892307i	0.484671	−	0.874696i	$-0.338939\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	6.79924			1.55985			0.779926	−	0.625872i	$-0.215257\pi$
$19$	6.79924			1.55985			0.779926	+	0.625872i	$0.215257\pi$
$20$	−1.15139	+	1.99426i	−0.257458	+	0.445931i
$21$	2.61586	−	0.396592i	0.570827	−	0.0865434i
$22$	−0.178660	+	0.309448i	−0.0380904	+	0.0659746i
$23$	−1.77550	+	3.07526i	−0.370218	+	0.641237i	−0.989599	−	0.143854i	$-0.954050\pi$
$23$	−1.77550	+	3.07526i	−0.370218	+	0.641237i	0.619381	+	0.785091i	$0.287384\pi$
$24$	−1.00000			−0.204124
$25$	−0.151388	+	0.262211i	−0.0302776	+	0.0524423i
$26$	−3.39962	+	1.20108i	−0.666720	+	0.235551i
$27$	1.00000			0.192450
$28$	−1.65139	−	2.06710i	−0.312083	−	0.390646i
$29$	−0.624116	−	1.08100i	−0.115895	−	0.200737i	0.802242	−	0.596999i	$-0.203640\pi$
$29$	−0.624116	−	1.08100i	−0.115895	−	0.200737i	−0.918137	+	0.396262i	$0.870307\pi$
$30$	−2.30278			−0.420427
$31$	−0.124116	+	0.214975i	−0.0222918	+	0.0386106i	−0.876956	−	0.480570i	$-0.840430\pi$
$31$	−0.124116	+	0.214975i	−0.0222918	+	0.0386106i	0.854664	+	0.519181i	$0.173763\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.357320			−0.0622014
$34$	−4.24823			−0.728566
$35$	−3.80278	−	4.76008i	−0.642786	−	0.804600i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−4.72096	+	8.17694i	−0.776121	+	1.34428i	0.158041	+	0.987432i	$0.449482\pi$
$37$	−4.72096	+	8.17694i	−0.776121	+	1.34428i	−0.934162	+	0.356848i	$0.883851\pi$
$38$	3.39962	−	5.88831i	0.551491	−	0.955211i
$39$	−2.73997	−	2.34362i	−0.438747	−	0.375279i
$40$	1.15139	+	1.99426i	0.182050	+	0.315321i
$41$	−2.95621	−	5.12031i	−0.461683	−	0.799658i	0.537362	−	0.843352i	$-0.319421\pi$
$41$	−2.95621	−	5.12031i	−0.461683	−	0.799658i	−0.999045	+	0.0436934i	$0.986088\pi$
$42$	0.964471	−	2.46370i	0.148821	−	0.380157i
$43$	2.63282	−	4.56018i	0.401502	−	0.695422i	−0.592406	−	0.805640i	$-0.701822\pi$
$43$	2.63282	−	4.56018i	0.401502	−	0.695422i	0.993907	+	0.110218i	$0.0351550\pi$
$44$	0.178660	+	0.309448i	0.0269340	+	0.0466511i
$45$	−1.15139	−	1.99426i	−0.171639	−	0.297287i
$46$	1.77550	+	3.07526i	0.261784	+	0.453423i
$47$	4.19414	+	7.26446i	0.611778	+	1.05963i	0.990941	+	0.134300i	$0.0428787\pi$
$47$	4.19414	+	7.26446i	0.611778	+	1.05963i	−0.379163	+	0.925330i	$0.623788\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	6.68543	−	2.07486i	0.955061	−	0.296408i
$50$	0.151388	+	0.262211i	0.0214095	+	0.0370823i
$51$	−2.12412	−	3.67908i	−0.297436	−	0.515174i
$52$	−0.659645	+	3.54470i	−0.0914763	+	0.491561i
$53$	−0.605101	+	1.04807i	−0.0831170	+	0.143963i	−0.904587	−	0.426288i	$-0.859821\pi$
$53$	−0.605101	+	1.04807i	−0.0831170	+	0.143963i	0.821470	+	0.570251i	$0.193154\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	0.411414	+	0.712590i	0.0554750	+	0.0960856i
$56$	−2.61586	+	0.396592i	−0.349559	+	0.0529968i
$57$	6.79924			0.900581
$58$	−1.24823			−0.163901
$59$	3.58033	+	6.20131i	0.466119	+	0.807342i	0.999251	−	0.0386900i	$-0.0123185\pi$
$59$	3.58033	+	6.20131i	0.466119	+	0.807342i	−0.533132	+	0.846032i	$0.678985\pi$
$60$	−1.15139	+	1.99426i	−0.148644	+	0.257458i
$61$	13.7076			1.75507			0.877537	−	0.479509i	$-0.159185\pi$
$61$	13.7076			1.75507			0.877537	+	0.479509i	$0.159185\pi$
$62$	0.124116	+	0.214975i	0.0157627	+	0.0273018i
$63$	2.61586	−	0.396592i	0.329567	−	0.0499659i
$64$	1.00000			0.125000
$65$	−1.51901	+	8.16264i	−0.188411	+	1.01245i
$66$	−0.178660	+	0.309448i	−0.0219915	+	0.0380904i
$67$	−2.81985			−0.344500			−0.172250	−	0.985053i	$-0.555104\pi$
$67$	−2.81985			−0.344500			−0.172250	+	0.985053i	$0.555104\pi$
$68$	−2.12412	+	3.67908i	−0.257587	+	0.446154i
$69$	−1.77550	+	3.07526i	−0.213746	+	0.370218i
$70$	−6.02373	+	0.913262i	−0.719974	+	0.109156i
$71$	0.794068	−	1.37537i	0.0942385	−	0.163226i	−0.815052	−	0.579388i	$-0.803292\pi$
$71$	0.794068	−	1.37537i	0.0942385	−	0.163226i	0.909291	+	0.416162i	$0.136625\pi$
$72$	−1.00000			−0.117851
$73$	0.407877	−	0.706463i	0.0477383	−	0.0826852i	−0.841169	−	0.540773i	$-0.818132\pi$
$73$	0.407877	−	0.706463i	0.0477383	−	0.0826852i	0.888907	+	0.458087i	$0.151465\pi$
$74$	4.72096	+	8.17694i	0.548800	+	0.950550i
$75$	−0.151388	+	0.262211i	−0.0174808	+	0.0302776i
$76$	−3.39962	−	5.88831i	−0.389963	−	0.675436i
$77$	−0.934698	+	0.141710i	−0.106519	+	0.0161494i
$78$	−3.39962	+	1.20108i	−0.384931	+	0.135995i
$79$	5.77345	+	9.99992i	0.649564	+	1.12508i	0.983227	+	0.182386i	$0.0583820\pi$
$79$	5.77345	+	9.99992i	0.649564	+	1.12508i	−0.333663	+	0.942693i	$0.608285\pi$
$80$	2.30278			0.257458
$81$	1.00000			0.111111
$82$	−5.91243			−0.652918
$83$	−1.24823			−0.137011			−0.0685056	−	0.997651i	$-0.521823\pi$
$83$	−1.24823			−0.137011			−0.0685056	+	0.997651i	$0.521823\pi$
$84$	−1.65139	−	2.06710i	−0.180181	−	0.225540i
$85$	−4.89136	+	8.47209i	−0.530543	+	0.918927i
$86$	−2.63282	−	4.56018i	−0.283905	−	0.491737i
$87$	−0.624116	−	1.08100i	−0.0669122	−	0.115895i
$88$	0.357320			0.0380904
$89$	−0.367627	+	0.636749i	−0.0389684	+	0.0674952i	−0.884852	−	0.465873i	$-0.845740\pi$
$89$	−0.367627	+	0.636749i	−0.0389684	+	0.0674952i	0.845883	+	0.533368i	$0.179074\pi$
$90$	−2.30278			−0.242734
$91$	−8.09684	−	5.04392i	−0.848780	−	0.528746i
$92$	3.55101			0.370218
$93$	−0.124116	+	0.214975i	−0.0128702	+	0.0222918i
$94$	8.38827			0.865185
$95$	−7.82856	−	13.5595i	−0.803193	−	1.39117i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−3.63237	+	6.29145i	−0.368812	+	0.638800i	−0.989380	−	0.145352i	$-0.953569\pi$
$97$	−3.63237	+	6.29145i	−0.368812	+	0.638800i	0.620568	+	0.784152i	$0.286902\pi$
$98$	1.54584	−	6.82718i	0.156153	−	0.689649i
$99$	−0.357320			−0.0359120
$100$	0.302776			0.0302776
$101$	15.8682			1.57895			0.789474	−	0.613785i	$-0.210354\pi$
$101$	15.8682			1.57895			0.789474	+	0.613785i	$0.210354\pi$
$102$	−4.24823			−0.420638
$103$	8.14990	+	14.1160i	0.803034	+	1.39089i	0.917611	+	0.397481i	$0.130115\pi$
$103$	8.14990	+	14.1160i	0.803034	+	1.39089i	−0.114577	+	0.993414i	$0.536551\pi$
$104$	2.73997	+	2.34362i	0.268677	+	0.229811i
$105$	−3.80278	−	4.76008i	−0.371113	−	0.464536i
$106$	0.605101	+	1.04807i	0.0587726	+	0.101797i
$107$	3.81308	−	6.60445i	0.368625	−	0.638477i	−0.620726	−	0.784027i	$-0.713162\pi$
$107$	3.81308	−	6.60445i	0.368625	−	0.638477i	0.989351	+	0.145551i	$0.0464955\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	0.472708	+	0.881219i	$0.343277\pi$
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	−0.999512	+	0.0312328i	$0.990057\pi$
$110$	0.822828			0.0784535
$111$	−4.72096	+	8.17694i	−0.448094	+	0.776121i
$112$	−0.964471	+	2.46370i	−0.0911339	+	0.232797i
$113$	−6.46919	+	11.2050i	−0.608570	+	1.05407i	0.382906	+	0.923787i	$0.374923\pi$
$113$	−6.46919	+	11.2050i	−0.608570	+	1.05407i	−0.991476	+	0.130287i	$0.958410\pi$
$114$	3.39962	−	5.88831i	0.318404	−	0.551491i
$115$	8.17717			0.762525
$116$	−0.624116	+	1.08100i	−0.0579477	+	0.100368i
$117$	−2.73997	−	2.34362i	−0.253311	−	0.216668i
$118$	7.16066			0.659192
$119$	−7.01548	−	8.78154i	−0.643108	−	0.805002i
$120$	1.15139	+	1.99426i	0.105107	+	0.182050i
$121$	−10.8723			−0.988393
$122$	6.85378	−	11.8711i	0.620512	−	1.07476i
$123$	−2.95621	−	5.12031i	−0.266553	−	0.461683i
$124$	0.248231			0.0222918
$125$	−10.8167			−0.967471
$126$	0.964471	−	2.46370i	0.0859219	−	0.219483i
$127$	5.47318	+	9.47982i	0.485666	+	0.841198i	0.999864	−	0.0164731i	$-0.00524379\pi$
$127$	5.47318	+	9.47982i	0.485666	+	0.841198i	−0.514198	+	0.857671i	$0.671910\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	2.63282	−	4.56018i	0.231807	−	0.401502i
$130$	6.30955	+	5.39682i	0.553384	+	0.473333i
$131$	−10.1210	−	17.5301i	−0.884278	−	1.53162i	−0.846538	−	0.532328i	$-0.821317\pi$
$131$	−10.1210	−	17.5301i	−0.884278	−	1.53162i	−0.0377399	−	0.999288i	$-0.512016\pi$
$132$	0.178660	+	0.309448i	0.0155504	+	0.0269340i
$133$	17.7858	−	2.69652i	1.54223	−	0.233818i
$134$	−1.40993	+	2.44206i	−0.121799	+	0.210962i
$135$	−1.15139	−	1.99426i	−0.0990957	−	0.171639i
$136$	2.12412	+	3.67908i	0.182141	+	0.315478i
$137$	2.67040	+	4.62527i	0.228148	+	0.395164i	0.957259	−	0.289231i	$-0.0933997\pi$
$137$	2.67040	+	4.62527i	0.228148	+	0.395164i	−0.729111	+	0.684395i	$0.760066\pi$
$138$	1.77550	+	3.07526i	0.151141	+	0.261784i
$139$	4.49174	−	7.77993i	0.380985	−	0.659885i	−0.610219	−	0.792233i	$-0.708918\pi$
$139$	4.49174	−	7.77993i	0.380985	−	0.659885i	0.991203	+	0.132348i	$0.0422517\pi$
$140$	−2.22096	+	5.67334i	−0.187705	+	0.479485i
$141$	4.19414	+	7.26446i	0.353210	+	0.611778i
$142$	−0.794068	−	1.37537i	−0.0666367	−	0.115418i
$143$	0.979047	+	0.837421i	0.0818720	+	0.0700287i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−1.43720	+	2.48930i	−0.119353	+	0.206725i
$146$	−0.407877	−	0.706463i	−0.0337561	−	0.0584673i
$147$	6.68543	−	2.07486i	0.551405	−	0.171131i
$148$	9.44192			0.776121
$149$	8.92074			0.730816			0.365408	−	0.930848i	$-0.380930\pi$
$149$	8.92074			0.730816			0.365408	+	0.930848i	$0.380930\pi$
$150$	0.151388	+	0.262211i	0.0123608	+	0.0214095i
$151$	−8.47995	+	14.6877i	−0.690088	+	1.19527i	0.281720	+	0.959497i	$0.409095\pi$
$151$	−8.47995	+	14.6877i	−0.690088	+	1.19527i	−0.971809	+	0.235772i	$0.924238\pi$
$152$	−6.79924			−0.551491
$153$	−2.12412	−	3.67908i	−0.171725	−	0.297436i
$154$	−0.344625	+	0.880328i	−0.0277706	+	0.0709388i
$155$	0.571621			0.0459137
$156$	−0.659645	+	3.54470i	−0.0528139	+	0.283803i
$157$	3.65861	−	6.33689i	0.291989	−	0.505739i	−0.682291	−	0.731081i	$-0.739016\pi$
$157$	3.65861	−	6.33689i	0.291989	−	0.505739i	0.974280	+	0.225341i	$0.0723497\pi$
$158$	11.5469			0.918623
$159$	−0.605101	+	1.04807i	−0.0479876	+	0.0831170i
$160$	1.15139	−	1.99426i	0.0910252	−	0.157660i
$161$	−3.42484	+	8.74860i	−0.269915	+	0.689486i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−2.28626			−0.179074			−0.0895369	−	0.995984i	$-0.528539\pi$
$163$	−2.28626			−0.179074			−0.0895369	+	0.995984i	$0.528539\pi$
$164$	−2.95621	+	5.12031i	−0.230841	+	0.399829i
$165$	0.411414	+	0.712590i	0.0320285	+	0.0554750i
$166$	−0.624116	+	1.08100i	−0.0484408	+	0.0839019i
$167$	1.95416	+	3.38471i	0.151218	+	0.261917i	0.931675	−	0.363292i	$-0.118347\pi$
$167$	1.95416	+	3.38471i	0.151218	+	0.261917i	−0.780458	+	0.625209i	$0.785014\pi$
$168$	−2.61586	+	0.396592i	−0.201818	+	0.0305977i
$169$	2.01492	+	12.8429i	0.154993	+	0.987915i
$170$	4.89136	+	8.47209i	0.375150	+	0.649779i
$171$	6.79924			0.519951
$172$	−5.26565			−0.401502
$173$	17.8332			1.35583			0.677915	−	0.735140i	$-0.262884\pi$
$173$	17.8332			1.35583			0.677915	+	0.735140i	$0.262884\pi$
$174$	−1.24823			−0.0946282
$175$	−0.292018	+	0.745947i	−0.0220745	+	0.0563883i
$176$	0.178660	−	0.309448i	0.0134670	−	0.0233255i
$177$	3.58033	+	6.20131i	0.269114	+	0.466119i
$178$	0.367627	+	0.636749i	0.0275548	+	0.0477263i
$179$	−5.60145			−0.418672			−0.209336	−	0.977844i	$-0.567130\pi$
$179$	−5.60145			−0.418672			−0.209336	+	0.977844i	$0.567130\pi$
$180$	−1.15139	+	1.99426i	−0.0858194	+	0.148644i
$181$	−7.83227			−0.582168			−0.291084	−	0.956698i	$-0.594016\pi$
$181$	−7.83227			−0.582168			−0.291084	+	0.956698i	$0.594016\pi$
$182$	−8.41658	+	4.49011i	−0.623879	+	0.332829i
$183$	13.7076			1.01329
$184$	1.77550	−	3.07526i	0.130892	−	0.226711i
$185$	21.7426			1.59855
$186$	0.124116	+	0.214975i	0.00910060	+	0.0157627i
$187$	0.758989	+	1.31461i	0.0555028	+	0.0961336i
$188$	4.19414	−	7.26446i	0.305889	−	0.529815i
$189$	2.61586	−	0.396592i	0.190276	−	0.0288478i
$190$	−15.6571			−1.13589
$191$	−13.6436			−0.987215			−0.493607	−	0.869685i	$-0.664322\pi$
$191$	−13.6436			−0.987215			−0.493607	+	0.869685i	$0.664322\pi$
$192$	1.00000			0.0721688
$193$	12.7992			0.921309			0.460655	−	0.887579i	$-0.347615\pi$
$193$	12.7992			0.921309			0.460655	+	0.887579i	$0.347615\pi$
$194$	3.63237	+	6.29145i	0.260789	+	0.451700i
$195$	−1.51901	+	8.16264i	−0.108779	+	0.584539i
$196$	−5.13959	−	4.75232i	−0.367114	−	0.339452i
$197$	−7.84758	−	13.5924i	−0.559117	−	0.968418i	−0.997570	−	0.0696646i	$-0.977807\pi$
$197$	−7.84758	−	13.5924i	−0.559117	−	0.968418i	0.438454	−	0.898754i	$-0.355526\pi$
$198$	−0.178660	+	0.309448i	−0.0126968	+	0.0219915i
$199$	−10.6144	−	18.3846i	−0.752433	−	1.30325i	−0.946641	−	0.322291i	$-0.895547\pi$
$199$	−10.6144	−	18.3846i	−0.752433	−	1.30325i	0.194208	−	0.980960i	$-0.437786\pi$
$200$	0.151388	−	0.262211i	0.0107047	−	0.0185411i
$201$	−2.81985			−0.198897
$202$	7.93411	−	13.7423i	0.558242	−	0.966904i
$203$	−2.06131	−	2.58022i	−0.144676	−	0.181096i
$204$	−2.12412	+	3.67908i	−0.148718	+	0.257587i
$205$	−6.80750	+	11.7909i	−0.475456	+	0.823514i
$206$	16.2998			1.13566
$207$	−1.77550	+	3.07526i	−0.123406	+	0.213746i
$208$	3.39962	−	1.20108i	0.235721	−	0.0832798i
$209$	−2.42950			−0.168052
$210$	−6.02373	+	0.913262i	−0.415677	+	0.0630211i
$211$	−12.0787	−	20.9210i	−0.831534	−	1.44026i	−0.896821	−	0.442393i	$-0.854130\pi$
$211$	−12.0787	−	20.9210i	−0.831534	−	1.44026i	0.0652874	−	0.997867i	$-0.479204\pi$
$212$	1.21020			0.0831170
$213$	0.794068	−	1.37537i	0.0544086	−	0.0942385i
$214$	−3.81308	−	6.60445i	−0.260657	−	0.451471i
$215$	−12.1256			−0.826959
$216$	−1.00000			−0.0680414
$217$	−0.239412	+	0.611567i	−0.0162523	+	0.0415158i
$218$	5.50000	+	9.52628i	0.372507	+	0.645201i
$219$	0.407877	−	0.706463i	0.0275617	−	0.0477383i
$220$	0.411414	−	0.712590i	0.0277375	−	0.0480428i
$221$	−2.80233	+	15.0587i	−0.188505	+	1.01296i
$222$	4.72096	+	8.17694i	0.316850	+	0.548800i
$223$	−3.65611	−	6.33256i	−0.244831	−	0.424060i	0.717253	−	0.696813i	$-0.245399\pi$
$223$	−3.65611	−	6.33256i	−0.244831	−	0.424060i	−0.962084	+	0.272753i	$0.912066\pi$
$224$	1.65139	+	2.06710i	0.110338	+	0.138114i
$225$	−0.151388	+	0.262211i	−0.0100925	+	0.0174808i
$226$	6.46919	+	11.2050i	0.430324	+	0.745343i
$227$	−14.7997	−	25.6338i	−0.982290	−	1.70138i	−0.653410	−	0.757004i	$-0.726662\pi$
$227$	−14.7997	−	25.6338i	−0.982290	−	1.70138i	−0.328880	−	0.944372i	$-0.606671\pi$
$228$	−3.39962	−	5.88831i	−0.225145	−	0.389963i
$229$	−3.62207	−	6.27360i	−0.239353	−	0.414571i	0.721176	−	0.692752i	$-0.243602\pi$
$229$	−3.62207	−	6.27360i	−0.239353	−	0.414571i	−0.960529	+	0.278181i	$0.910269\pi$
$230$	4.08859	−	7.08164i	0.269593	−	0.466949i
$231$	−0.934698	+	0.141710i	−0.0614986	+	0.00932385i
$232$	0.624116	+	1.08100i	0.0409752	+	0.0709711i
$233$	10.2092	+	17.6828i	0.668825	+	1.15844i	0.978233	+	0.207509i	$0.0665356\pi$
$233$	10.2092	+	17.6828i	0.668825	+	1.15844i	−0.309408	+	0.950929i	$0.600131\pi$
$234$	−3.39962	+	1.20108i	−0.222240	+	0.0785170i
$235$	9.65816	−	16.7284i	0.630029	−	1.09124i
$236$	3.58033	−	6.20131i	0.233060	−	0.403671i
$237$	5.77345	+	9.99992i	0.375026	+	0.649564i
$238$	−11.1128	+	1.68481i	−0.720334	+	0.109210i
$239$	−6.02686			−0.389845			−0.194922	−	0.980819i	$-0.562446\pi$
$239$	−6.02686			−0.389845			−0.194922	+	0.980819i	$0.562446\pi$
$240$	2.30278			0.148644
$241$	−5.50472	−	9.53445i	−0.354590	−	0.614168i	0.632458	−	0.774595i	$-0.282046\pi$
$241$	−5.50472	−	9.53445i	−0.354590	−	0.614168i	−0.987048	+	0.160427i	$0.948713\pi$
$242$	−5.43616	+	9.41571i	−0.349450	+	0.605265i
$243$	1.00000			0.0641500
$244$	−6.85378	−	11.8711i	−0.438768	−	0.759969i
$245$	−11.8353	−	10.9435i	−0.756131	−	0.699157i
$246$	−5.91243			−0.376963
$247$	−18.6297	−	15.9348i	−1.18538	−	1.01391i
$248$	0.124116	−	0.214975i	0.00788135	−	0.0136509i
$249$	−1.24823			−0.0791034
$250$	−5.40833	+	9.36750i	−0.342053	+	0.592453i
$251$	12.6772	−	21.9575i	0.800176	−	1.38595i	−0.119324	−	0.992855i	$-0.538073\pi$
$251$	12.6772	−	21.9575i	0.800176	−	1.38595i	0.919500	−	0.393090i	$-0.128594\pi$
$252$	−1.65139	−	2.06710i	−0.104028	−	0.130215i
$253$	0.634423	−	1.09885i	0.0398858	−	0.0690843i
$254$	10.9464			0.686835
$255$	−4.89136	+	8.47209i	−0.306309	+	0.530543i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.5952	+	18.3515i	−0.660913	+	1.14474i	0.319463	+	0.947599i	$0.396498\pi$
$257$	−10.5952	+	18.3515i	−0.660913	+	1.14474i	−0.980376	+	0.197136i	$0.936836\pi$
$258$	−2.63282	−	4.56018i	−0.163912	−	0.283905i
$259$	−9.10645	+	23.2620i	−0.565847	+	1.44543i
$260$	7.82856	−	2.76581i	0.485507	−	0.171529i
$261$	−0.624116	−	1.08100i	−0.0386318	−	0.0669122i
$262$	−20.2421			−1.25056
$263$	−9.13504			−0.563291			−0.281645	−	0.959519i	$-0.590880\pi$
$263$	−9.13504			−0.563291			−0.281645	+	0.959519i	$0.590880\pi$
$264$	0.357320			0.0219915
$265$	2.78682			0.171193
$266$	6.55767	−	16.7513i	0.402076	−	1.02709i
$267$	−0.367627	+	0.636749i	−0.0224984	+	0.0389684i
$268$	1.40993	+	2.44206i	0.0861250	+	0.149173i
$269$	−0.0247720	−	0.0429064i	−0.00151038	−	0.00261605i	0.865269	−	0.501307i	$-0.167147\pi$
$269$	−0.0247720	−	0.0429064i	−0.00151038	−	0.00261605i	−0.866780	+	0.498691i	$0.833814\pi$
$270$	−2.30278			−0.140142
$271$	−0.00665800	+	0.0115320i	−0.000404445	+	0.000700519i	−0.866228	−	0.499650i	$-0.833462\pi$
$271$	−0.00665800	+	0.0115320i	−0.000404445	+	0.000700519i	0.865823	+	0.500350i	$0.166795\pi$
$272$	4.24823			0.257587
$273$	−8.09684	−	5.04392i	−0.490043	−	0.305272i
$274$	5.34081			0.322650
$275$	0.0540939	−	0.0936934i	0.00326198	−	0.00564992i
$276$	3.55101			0.213746
$277$	−11.0725	−	19.1782i	−0.665283	−	1.15230i	−0.979208	−	0.202857i	$-0.934977\pi$
$277$	−11.0725	−	19.1782i	−0.665283	−	1.15230i	0.313925	−	0.949448i	$-0.398356\pi$
$278$	−4.49174	−	7.77993i	−0.269397	−	0.466609i
$279$	−0.124116	+	0.214975i	−0.00743061	+	0.0128702i
$280$	3.80278	+	4.76008i	0.227259	+	0.284469i
$281$	−4.44192			−0.264983			−0.132491	−	0.991184i	$-0.542298\pi$
$281$	−4.44192			−0.264983			−0.132491	+	0.991184i	$0.542298\pi$
$282$	8.38827			0.499515
$283$	20.2122			1.20149			0.600746	−	0.799440i	$-0.294870\pi$
$283$	20.2122			1.20149			0.600746	+	0.799440i	$0.294870\pi$
$284$	−1.58814			−0.0942385
$285$	−7.82856	−	13.5595i	−0.463724	−	0.803193i
$286$	1.21475	−	0.429169i	0.0718298	−	0.0253773i
$287$	−9.76371	−	12.2216i	−0.576334	−	0.721418i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−0.523735	+	0.907135i	−0.0308079	+	0.0533609i
$290$	1.43720	+	2.48930i	0.0843952	+	0.146177i
$291$	−3.63237	+	6.29145i	−0.212933	+	0.368812i
$292$	−0.815753			−0.0477383
$293$	−14.1231	+	24.4619i	−0.825079	+	1.42908i	0.0767798	+	0.997048i	$0.475536\pi$
$293$	−14.1231	+	24.4619i	−0.825079	+	1.42908i	−0.901859	+	0.432031i	$0.857797\pi$
$294$	1.54584	−	6.82718i	0.0901550	−	0.398169i
$295$	8.24469	−	14.2802i	0.480025	−	0.831427i
$296$	4.72096	−	8.17694i	0.274400	−	0.475275i
$297$	−0.357320			−0.0207338
$298$	4.46037	−	7.72559i	0.258382	−	0.447531i
$299$	12.0721	−	4.26504i	0.698146	−	0.246654i
$300$	0.302776			0.0174808
$301$	5.07856	−	12.9730i	0.292723	−	0.747748i
$302$	8.47995	+	14.6877i	0.487966	+	0.845182i
$303$	15.8682			0.911606
$304$	−3.39962	+	5.88831i	−0.194982	+	0.337718i
$305$	−15.7827	−	27.3365i	−0.903716	−	1.56528i
$306$	−4.24823			−0.242855
$307$	−20.3037			−1.15879			−0.579396	−	0.815046i	$-0.696712\pi$
$307$	−20.3037			−1.15879			−0.579396	+	0.815046i	$0.696712\pi$
$308$	0.590074	+	0.738617i	0.0336226	+	0.0420866i
$309$	8.14990	+	14.1160i	0.463632	+	0.803034i
$310$	0.285811	−	0.495038i	0.0162329	−	0.0281163i
$311$	−11.7028	+	20.2699i	−0.663607	+	1.14940i	0.316053	+	0.948741i	$0.397642\pi$
$311$	−11.7028	+	20.2699i	−0.663607	+	1.14940i	−0.979661	+	0.200660i	$0.935691\pi$
$312$	2.73997	+	2.34362i	0.155120	+	0.132681i
$313$	−10.8455	−	18.7850i	−0.613025	−	1.06179i	−0.990728	−	0.135864i	$-0.956619\pi$
$313$	−10.8455	−	18.7850i	−0.613025	−	1.06179i	0.377702	−	0.925927i	$-0.376714\pi$
$314$	−3.65861	−	6.33689i	−0.206467	−	0.357612i
$315$	−3.80278	−	4.76008i	−0.214262	−	0.268200i
$316$	5.77345	−	9.99992i	0.324782	−	0.562539i
$317$	13.9135	+	24.0989i	0.781460	+	1.35353i	0.931091	+	0.364786i	$0.118858\pi$
$317$	13.9135	+	24.0989i	0.781460	+	1.35353i	−0.149631	+	0.988742i	$0.547809\pi$
$318$	0.605101	+	1.04807i	0.0339324	+	0.0587726i
$319$	0.223009	+	0.386263i	0.0124861	+	0.0216266i
$320$	−1.15139	−	1.99426i	−0.0643645	−	0.111483i
$321$	3.81308	−	6.60445i	0.212826	−	0.368625i
$322$	5.86409	+	7.34030i	0.326793	+	0.409059i
$323$	−14.4424	−	25.0149i	−0.803595	−	1.39187i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	1.02932	−	0.363657i	0.0570965	−	0.0201721i
$326$	−1.14313	+	1.97996i	−0.0633121	+	0.109660i
$327$	−5.50000	+	9.52628i	−0.304151	+	0.526804i
$328$	2.95621	+	5.12031i	0.163230	+	0.282722i
$329$	13.8523	+	17.3394i	0.763702	+	0.955954i
$330$	0.822828			0.0452952
$331$	−7.24116			−0.398010			−0.199005	−	0.979998i	$-0.563771\pi$
$331$	−7.24116			−0.398010			−0.199005	+	0.979998i	$0.563771\pi$
$332$	0.624116	+	1.08100i	0.0342528	+	0.0593276i
$333$	−4.72096	+	8.17694i	−0.258707	+	0.448094i
$334$	3.90833			0.213854
$335$	3.24674	+	5.62353i	0.177389	+	0.307246i
$336$	−0.964471	+	2.46370i	−0.0526162	+	0.134406i
$337$	−0.380909			−0.0207494			−0.0103747	−	0.999946i	$-0.503302\pi$
$337$	−0.380909			−0.0207494			−0.0103747	+	0.999946i	$0.503302\pi$
$338$	12.1297	+	4.67648i	0.659771	+	0.254367i
$339$	−6.46919	+	11.2050i	−0.351358	+	0.608570i
$340$	9.78272			0.530543
$341$	0.0443490	−	0.0768147i	0.00240163	−	0.00415975i
$342$	3.39962	−	5.88831i	0.183830	−	0.318404i
$343$	16.6653	−	8.07892i	0.899840	−	0.436221i
$344$	−2.63282	+	4.56018i	−0.141952	+	0.245869i
$345$	8.17717			0.440244
$346$	8.91658	−	15.4440i	0.479359	−	0.830273i
$347$	3.95770	+	6.85494i	0.212461	+	0.367992i	0.952484	−	0.304589i	$-0.0985190\pi$
$347$	3.95770	+	6.85494i	0.212461	+	0.367992i	−0.740023	+	0.672581i	$0.765186\pi$
$348$	−0.624116	+	1.08100i	−0.0334561	+	0.0579477i
$349$	−3.90212	−	6.75867i	−0.208876	−	0.361783i	0.742485	−	0.669863i	$-0.233647\pi$
$349$	−3.90212	−	6.75867i	−0.208876	−	0.361783i	−0.951361	+	0.308079i	$0.900314\pi$
$350$	0.500000	+	0.625869i	0.0267261	+	0.0334541i
$351$	−2.73997	−	2.34362i	−0.146249	−	0.125093i
$352$	−0.178660	−	0.309448i	−0.00952261	−	0.0164936i
$353$	13.1864			0.701841			0.350920	−	0.936405i	$-0.385869\pi$
$353$	13.1864			0.701841			0.350920	+	0.936405i	$0.385869\pi$
$354$	7.16066			0.380585
$355$	−3.65712			−0.194100
$356$	0.735254			0.0389684
$357$	−7.01548	−	8.78154i	−0.371298	−	0.464768i
$358$	−2.80073	+	4.85100i	−0.148023	+	0.256383i
$359$	0.580329	+	1.00516i	0.0306286	+	0.0530503i	0.880933	−	0.473240i	$-0.156916\pi$
$359$	0.580329	+	1.00516i	0.0306286	+	0.0530503i	−0.850305	+	0.526291i	$0.823582\pi$
$360$	1.15139	+	1.99426i	0.0606835	+	0.105107i
$361$	27.2296			1.43314
$362$	−3.91613	+	6.78294i	−0.205827	+	0.356504i
$363$	−10.8723			−0.570649
$364$	−0.319741	+	9.53403i	−0.0167590	+	0.499719i
$365$	−1.87850			−0.0983250
$366$	6.85378	−	11.8711i	0.358253	−	0.620512i
$367$	−32.8272			−1.71357			−0.856783	−	0.515676i	$-0.827541\pi$
$367$	−32.8272			−1.71357			−0.856783	+	0.515676i	$0.827541\pi$
$368$	−1.77550	−	3.07526i	−0.0925545	−	0.160309i
$369$	−2.95621	−	5.12031i	−0.153894	−	0.266553i
$370$	10.8713	−	18.8297i	0.565172	−	0.978907i
$371$	−1.16720	+	2.98157i	−0.0605982	+	0.154795i
$372$	0.248231			0.0128702
$373$	−29.4873			−1.52680			−0.763398	−	0.645929i	$-0.776470\pi$
$373$	−29.4873			−1.52680			−0.763398	+	0.645929i	$0.776470\pi$
$374$	1.51798			0.0784928
$375$	−10.8167			−0.558570
$376$	−4.19414	−	7.26446i	−0.216296	−	0.374636i
$377$	−0.823390	+	4.42460i	−0.0424067	+	0.227879i
$378$	0.964471	−	2.46370i	0.0496070	−	0.126719i
$379$	8.57929	+	14.8598i	0.440689	+	0.763295i	0.997741	−	0.0671825i	$-0.0214010\pi$
$379$	8.57929	+	14.8598i	0.440689	+	0.763295i	−0.557052	+	0.830478i	$0.688068\pi$
$380$	−7.82856	+	13.5595i	−0.401597	+	0.695586i
$381$	5.47318	+	9.47982i	0.280399	+	0.485666i
$382$	−6.82179	+	11.8157i	−0.349033	+	0.604543i
$383$	18.9753			0.969592			0.484796	−	0.874627i	$-0.338894\pi$
$383$	18.9753			0.969592			0.484796	+	0.874627i	$0.338894\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	1.35881	+	1.70087i	0.0692512	+	0.0866844i
$386$	6.39962	−	11.0845i	0.325732	−	0.564184i
$387$	2.63282	−	4.56018i	0.133834	−	0.231807i
$388$	7.26475			0.368812
$389$	12.8986	−	22.3410i	0.653984	−	1.13273i	−0.328163	−	0.944621i	$-0.606430\pi$
$389$	12.8986	−	22.3410i	0.653984	−	1.13273i	0.982147	−	0.188113i	$-0.0602370\pi$
$390$	6.30955	+	5.39682i	0.319496	+	0.273279i
$391$	15.0855			0.762906
$392$	−6.68543	+	2.07486i	−0.337665	+	0.104796i
$393$	−10.1210	−	17.5301i	−0.510538	−	0.884278i
$394$	−15.6952			−0.790710
$395$	13.2950	−	23.0276i	0.668942	−	1.15864i
$396$	0.178660	+	0.309448i	0.00897800	+	0.0155504i
$397$	−30.7344			−1.54252			−0.771258	−	0.636522i	$-0.780372\pi$
$397$	−30.7344			−1.54252			−0.771258	+	0.636522i	$0.780372\pi$
$398$	−21.2287			−1.06410
$399$	17.7858	−	2.69652i	0.890406	−	0.134995i
$400$	−0.151388	−	0.262211i	−0.00756939	−	0.0131106i
$401$	−8.17877	+	14.1660i	−0.408428	+	0.707419i	−0.994714	−	0.102686i	$-0.967256\pi$
$401$	−8.17877	+	14.1660i	−0.408428	+	0.707419i	0.586285	+	0.810105i	$0.300590\pi$
$402$	−1.40993	+	2.44206i	−0.0703207	+	0.121799i
$403$	0.843892	−	0.298145i	0.0420373	−	0.0148517i
$404$	−7.93411	−	13.7423i	−0.394737	−	0.683704i
$405$	−1.15139	−	1.99426i	−0.0572129	−	0.0990957i
$406$	−3.26520	+	0.495038i	−0.162049	+	0.0245683i
$407$	1.68689	−	2.92178i	0.0836162	−	0.144827i
$408$	2.12412	+	3.67908i	0.105159	+	0.182141i
$409$	−4.83522	−	8.37484i	−0.239086	−	0.414109i	0.721366	−	0.692554i	$-0.243515\pi$
$409$	−4.83522	−	8.37484i	−0.239086	−	0.414109i	−0.960452	+	0.278444i	$0.910181\pi$
$410$	6.80750	+	11.7909i	0.336198	+	0.582312i
$411$	2.67040	+	4.62527i	0.131721	+	0.228148i
$412$	8.14990	−	14.1160i	0.401517	−	0.695447i
$413$	11.8250	+	14.8018i	0.581871	+	0.728350i
$414$	1.77550	+	3.07526i	0.0872612	+	0.151141i
$415$	1.43720	+	2.48930i	0.0705493	+	0.122195i
$416$	0.659645	−	3.54470i	0.0323418	−	0.173793i
$417$	4.49174	−	7.77993i	0.219962	−	0.380985i
$418$	−1.21475	+	2.10401i	−0.0594154	+	0.102911i
$419$	18.0902	+	31.3332i	0.883765	+	1.53073i	0.847123	+	0.531398i	$0.178333\pi$
$419$	18.0902	+	31.3332i	0.883765	+	1.53073i	0.0366425	+	0.999328i	$0.488334\pi$
$420$	−2.22096	+	5.67334i	−0.108372	+	0.276831i
$421$	32.6170			1.58966			0.794828	−	0.606835i	$-0.207561\pi$
$421$	32.6170			1.58966			0.794828	+	0.606835i	$0.207561\pi$
$422$	−24.1575			−1.17597
$423$	4.19414	+	7.26446i	0.203926	+	0.353210i
$424$	0.605101	−	1.04807i	0.0293863	−	0.0508986i
$425$	1.28626			0.0623928
$426$	−0.794068	−	1.37537i	−0.0384727	−	0.0666367i
$427$	35.8570	−	5.43631i	1.73524	−	0.263081i
$428$	−7.62617			−0.368625
$429$	0.979047	+	0.837421i	0.0472688	+	0.0404311i
$430$	−6.06280	+	10.5011i	−0.292374	+	0.506407i
$431$	−9.06489			−0.436640			−0.218320	−	0.975877i	$-0.570058\pi$
$431$	−9.06489			−0.436640			−0.218320	+	0.975877i	$0.570058\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	13.3558	−	23.1330i	0.641840	−	1.11170i	−0.343181	−	0.939269i	$-0.611505\pi$
$433$	13.3558	−	23.1330i	0.641840	−	1.11170i	0.985022	−	0.172431i	$-0.0551621\pi$
$434$	0.409926	+	0.513120i	0.0196771	+	0.0246305i
$435$	−1.43720	+	2.48930i	−0.0689084	+	0.119353i
$436$	11.0000			0.526804
$437$	−12.0721	+	20.9094i	−0.577485	+	1.00023i
$438$	−0.407877	−	0.706463i	−0.0194891	−	0.0337561i
$439$	9.78949	−	16.9559i	0.467227	−	0.809261i	−0.532072	−	0.846699i	$-0.678586\pi$
$439$	9.78949	−	16.9559i	0.467227	−	0.809261i	0.999299	+	0.0374382i	$0.0119197\pi$
$440$	−0.411414	−	0.712590i	−0.0196134	−	0.0339714i
$441$	6.68543	−	2.07486i	0.318354	−	0.0988027i
$442$	11.6400	+	9.95623i	0.553660	+	0.473570i
$443$	−1.40684	−	2.43672i	−0.0668410	−	0.115772i	0.830668	−	0.556768i	$-0.187959\pi$
$443$	−1.40684	−	2.43672i	−0.0668410	−	0.115772i	−0.897509	+	0.440996i	$0.854625\pi$
$444$	9.44192			0.448094
$445$	1.69312			0.0802618
$446$	−7.31222			−0.346243
$447$	8.92074			0.421937
$448$	2.61586	−	0.396592i	0.123588	−	0.0187372i
$449$	11.0541	−	19.1463i	0.521677	−	0.903570i	−0.478006	−	0.878357i	$-0.658640\pi$
$449$	11.0541	−	19.1463i	0.521677	−	0.903570i	0.999682	−	0.0252135i	$-0.00802654\pi$
$450$	0.151388	+	0.262211i	0.00713649	+	0.0123608i
$451$	1.05631	+	1.82959i	0.0497399	+	0.0861520i
$452$	12.9384			0.608570
$453$	−8.47995	+	14.6877i	−0.398423	+	0.690088i
$454$	−29.5994			−1.38917
$455$	−0.736291	+	21.9547i	−0.0345179	+	1.02925i
$456$	−6.79924			−0.318404
$457$	−15.5382	+	26.9129i	−0.726845	+	1.25893i	0.231365	+	0.972867i	$0.425681\pi$
$457$	−15.5382	+	26.9129i	−0.726845	+	1.25893i	−0.958210	+	0.286066i	$0.907652\pi$
$458$	−7.24413			−0.338496
$459$	−2.12412	−	3.67908i	−0.0991452	−	0.171725i
$460$	−4.08859	−	7.08164i	−0.190631	−	0.330183i
$461$	−19.9244	+	34.5100i	−0.927970	+	1.60729i	−0.141257	+	0.989973i	$0.545114\pi$
$461$	−19.9244	+	34.5100i	−0.927970	+	1.60729i	−0.786713	+	0.617319i	$0.788219\pi$
$462$	−0.344625	+	0.880328i	−0.0160334	+	0.0409565i
$463$	5.91153			0.274732			0.137366	−	0.990520i	$-0.456136\pi$
$463$	5.91153			0.274732			0.137366	+	0.990520i	$0.456136\pi$
$464$	1.24823			0.0579477
$465$	0.571621			0.0265083
$466$	20.4183			0.945861
$467$	−8.15760	−	14.1294i	−0.377488	−	0.653829i	0.613208	−	0.789922i	$-0.289879\pi$
$467$	−8.15760	−	14.1294i	−0.377488	−	0.653829i	−0.990696	+	0.136093i	$0.956546\pi$
$468$	−0.659645	+	3.54470i	−0.0304921	+	0.163854i
$469$	−7.37633	+	1.11833i	−0.340607	+	0.0516397i
$470$	−9.65816	−	16.7284i	−0.445498	−	0.771624i
$471$	3.65861	−	6.33689i	0.168580	−	0.291989i
$472$	−3.58033	−	6.20131i	−0.164798	−	0.285438i
$473$	−0.940760	+	1.62944i	−0.0432562	+	0.0749219i
$474$	11.5469			0.530367
$475$	−1.02932	+	1.78284i	−0.0472285	+	0.0818022i
$476$	−4.09729	+	10.4663i	−0.187799	+	0.479724i
$477$	−0.605101	+	1.04807i	−0.0277057	+	0.0479876i
$478$	−3.01343	+	5.21941i	−0.137831	+	0.238730i
$479$	9.40367			0.429664			0.214832	−	0.976651i	$-0.431080\pi$
$479$	9.40367			0.429664			0.214832	+	0.976651i	$0.431080\pi$
$480$	1.15139	−	1.99426i	0.0525534	−	0.0910252i
$481$	32.0989	−	11.3405i	1.46359	−	0.517082i
$482$	−11.0094			−0.501466
$483$	−3.42484	+	8.74860i	−0.155836	+	0.398075i
$484$	5.43616	+	9.41571i	0.247098	+	0.427987i
$485$	16.7291			0.759628
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	16.7693	+	29.0453i	0.759891	+	1.31617i	0.942906	+	0.333059i	$0.108081\pi$
$487$	16.7693	+	29.0453i	0.759891	+	1.31617i	−0.183015	+	0.983110i	$0.558586\pi$
$488$	−13.7076			−0.620512
$489$	−2.28626			−0.103388
$490$	−15.3950	+	4.77793i	−0.695477	+	0.215845i
$491$	11.7456	+	20.3440i	0.530071	+	0.918110i	0.999385	+	0.0350786i	$0.0111682\pi$
$491$	11.7456	+	20.3440i	0.530071	+	0.918110i	−0.469313	+	0.883032i	$0.655498\pi$
$492$	−2.95621	+	5.12031i	−0.133276	+	0.230841i
$493$	−2.65139	+	4.59234i	−0.119413	+	0.206829i
$494$	−23.1148	+	8.16642i	−1.03998	+	0.367425i
$495$	0.411414	+	0.712590i	0.0184917	+	0.0320285i
$496$	−0.124116	−	0.214975i	−0.00557296	−	0.00965265i
$497$	1.53171	−	3.91268i	0.0687066	−	0.175508i
$498$	−0.624116	+	1.08100i	−0.0279673	+	0.0484408i
$499$	−11.2416	−	19.4710i	−0.503243	−	0.871643i	−0.999993	−	0.00374928i	$-0.998807\pi$
$499$	−11.2416	−	19.4710i	−0.503243	−	0.871643i	0.496750	−	0.867894i	$-0.334527\pi$
$500$	5.40833	+	9.36750i	0.241868	+	0.418927i
$501$	1.95416	+	3.38471i	0.0873056	+	0.151218i
$502$	−12.6772	−	21.9575i	−0.565810	−	0.980011i
$503$	−8.16743	+	14.1464i	−0.364168	+	0.630757i	−0.988642	−	0.150288i	$-0.951980\pi$
$503$	−8.16743	+	14.1464i	−0.364168	+	0.630757i	0.624475	+	0.781045i	$0.285313\pi$
$504$	−2.61586	+	0.396592i	−0.116520	+	0.0176656i
$505$	−18.2705	−	31.6454i	−0.813026	−	1.40820i
$506$	−0.634423	−	1.09885i	−0.0282035	−	0.0488499i
$507$	2.01492	+	12.8429i	0.0894855	+	0.570373i
$508$	5.47318	−	9.47982i	0.242833	−	0.420599i
$509$	2.20905	−	3.82619i	0.0979145	−	0.169593i	−0.812907	−	0.582394i	$-0.802116\pi$
$509$	2.20905	−	3.82619i	0.0979145	−	0.169593i	0.910821	+	0.412801i	$0.135449\pi$
$510$	4.89136	+	8.47209i	0.216593	+	0.375150i
$511$	0.786770	−	2.00977i	0.0348046	−	0.0889069i
$512$	−1.00000			−0.0441942
$513$	6.79924			0.300194
$514$	10.5952	+	18.3515i	0.467336	+	0.809450i
$515$	18.7674	−	32.5061i	0.826990	−	1.43239i
$516$	−5.26565			−0.231807
$517$	−1.49865	−	2.59574i	−0.0659105	−	0.114160i
$518$	15.5923	+	19.5174i	0.685085	+	0.857546i
$519$	17.8332			0.782789
$520$	1.51901	−	8.16264i	0.0666132	−	0.357955i
$521$	−6.51121	+	11.2777i	−0.285261	+	0.494087i	−0.972672	−	0.232181i	$-0.925414\pi$
$521$	−6.51121	+	11.2777i	−0.285261	+	0.494087i	0.687411	+	0.726268i	$0.258747\pi$
$522$	−1.24823			−0.0546336
$523$	2.81620	−	4.87781i	0.123144	−	0.213292i	−0.797862	−	0.602840i	$-0.794036\pi$
$523$	2.81620	−	4.87781i	0.123144	−	0.213292i	0.921006	+	0.389549i	$0.127369\pi$
$524$	−10.1210	+	17.5301i	−0.442139	+	0.765808i
$525$	−0.292018	+	0.745947i	−0.0127447	+	0.0325558i
$526$	−4.56752	+	7.91118i	−0.199153	+	0.344944i
$527$	1.05454			0.0459367
$528$	0.178660	−	0.309448i	0.00777518	−	0.0134670i
$529$	5.19517	+	8.99831i	0.225877	+	0.391231i
$530$	1.39341	−	2.41346i	0.0605259	−	0.104834i
$531$	3.58033	+	6.20131i	0.155373	+	0.269114i
$532$	−11.2282	−	14.0547i	−0.486803	−	0.609350i
$533$	−3.90010	+	20.9578i	−0.168932	+	0.907781i
$534$	0.367627	+	0.636749i	0.0159088	+	0.0275548i
$535$	−17.5613			−0.759243
$536$	2.81985			0.121799
$537$	−5.60145			−0.241720
$538$	−0.0495440			−0.00213599
$539$	−2.38884	+	0.741387i	−0.102895	+	0.0319338i
$540$	−1.15139	+	1.99426i	−0.0495478	+	0.0858194i
$541$	1.39035	+	2.40816i	0.0597758	+	0.103535i	0.894365	−	0.447339i	$-0.147628\pi$
$541$	1.39035	+	2.40816i	0.0597758	+	0.103535i	−0.834589	+	0.550873i	$0.814295\pi$
$542$	0.00665800	+	0.0115320i	0.000285986	+	0.000495341i
$543$	−7.83227			−0.336115
$544$	2.12412	−	3.67908i	0.0910707	−	0.157739i
$545$	25.3305			1.08504
$546$	−8.41658	+	4.49011i	−0.360197	+	0.192159i
$547$	12.7497			0.545138			0.272569	−	0.962136i	$-0.412127\pi$
$547$	12.7497			0.545138			0.272569	+	0.962136i	$0.412127\pi$
$548$	2.67040	−	4.62527i	0.114074	−	0.197582i
$549$	13.7076			0.585025
$550$	−0.0540939	−	0.0936934i	−0.00230657	−	0.00399510i
$551$	−4.24351	−	7.34998i	−0.180780	−	0.313120i
$552$	1.77550	−	3.07526i	0.0755704	−	0.130892i
$553$	19.0684	+	23.8687i	0.810872	+	1.01500i
$554$	−22.1450			−0.940853
$555$	21.7426			0.922923
$556$	−8.98349			−0.380985
$557$	−45.2052			−1.91541			−0.957703	−	0.287757i	$-0.907090\pi$
$557$	−45.2052			−1.91541			−0.957703	+	0.287757i	$0.907090\pi$
$558$	0.124116	+	0.214975i	0.00525424	+	0.00910060i
$559$	−17.9012	+	6.32445i	−0.757140	+	0.267496i
$560$	6.02373	−	0.913262i	0.254549	−	0.0385924i
$561$	0.758989	+	1.31461i	0.0320445	+	0.0555028i
$562$	−2.22096	+	3.84681i	−0.0936855	+	0.162268i
$563$	14.8579	+	25.7347i	0.626188	+	1.08459i	0.988310	+	0.152458i	$0.0487189\pi$
$563$	14.8579	+	25.7347i	0.626188	+	1.08459i	−0.362122	+	0.932131i	$0.617948\pi$
$564$	4.19414	−	7.26446i	0.176605	−	0.305889i
$565$	29.7942			1.25345
$566$	10.1061	−	17.5043i	0.424792	−	0.735761i
$567$	2.61586	−	0.396592i	0.109856	−	0.0166553i
$568$	−0.794068	+	1.37537i	−0.0333183	+	0.0577091i
$569$	7.22922	−	12.5214i	0.303065	−	0.524923i	−0.673764	−	0.738947i	$-0.735324\pi$
$569$	7.22922	−	12.5214i	0.303065	−	0.524923i	0.976829	+	0.214023i	$0.0686569\pi$
$570$	−15.6571			−0.655805
$571$	−10.5516	+	18.2759i	−0.441569	+	0.764821i	−0.997806	−	0.0662032i	$-0.978911\pi$
$571$	−10.5516	+	18.2759i	−0.441569	+	0.764821i	0.556237	+	0.831024i	$0.312245\pi$
$572$	0.235704	−	1.26659i	0.00985529	−	0.0529588i
$573$	−13.6436			−0.569969
$574$	−15.4661	+	2.34482i	−0.645541	+	0.0978709i
$575$	−0.537579	−	0.931114i	−0.0224186	−	0.0388302i
$576$	1.00000			0.0416667
$577$	8.22461	−	14.2454i	0.342395	−	0.593045i	−0.642482	−	0.766301i	$-0.722095\pi$
$577$	8.22461	−	14.2454i	0.342395	−	0.593045i	0.984877	+	0.173255i	$0.0554286\pi$
$578$	0.523735	+	0.907135i	0.0217845	+	0.0377319i
$579$	12.7992			0.531918
$580$	2.87440			0.119353
$581$	−3.26520	+	0.495038i	−0.135463	+	0.0205377i
$582$	3.63237	+	6.29145i	0.150567	+	0.260789i
$583$	0.216215	−	0.374495i	0.00895469	−	0.0155100i
$584$	−0.407877	+	0.706463i	−0.0168781	+	0.0292336i
$585$	−1.51901	+	8.16264i	−0.0628035	+	0.337484i
$586$	14.1231	+	24.4619i	0.583419	+	1.01051i
$587$	20.9559	+	36.2967i	0.864943	+	1.49813i	0.867104	+	0.498127i	$0.165979\pi$
$587$	20.9559	+	36.2967i	0.864943	+	1.49813i	−0.00216095	+	0.999998i	$0.500688\pi$
$588$	−5.13959	−	4.75232i	−0.211953	−	0.195983i
$589$	−0.843892	+	1.46166i	−0.0347720	+	0.0602268i
$590$	−8.24469	−	14.2802i	−0.339429	−	0.587908i
$591$	−7.84758	−	13.5924i	−0.322806	−	0.559117i
$592$	−4.72096	−	8.17694i	−0.194030	−	0.336070i
$593$	13.7451	+	23.8073i	0.564445	+	0.977648i	0.997101	+	0.0760889i	$0.0242433\pi$
$593$	13.7451	+	23.8073i	0.564445	+	0.977648i	−0.432656	+	0.901559i	$0.642423\pi$
$594$	−0.178660	+	0.309448i	−0.00733051	+	0.0126968i
$595$	−9.43515	+	24.1017i	−0.386803	+	0.988072i
$596$	−4.46037	−	7.72559i	−0.182704	−	0.316452i
$597$	−10.6144	−	18.3846i	−0.434417	−	0.752433i
$598$	2.34240	−	12.5872i	0.0957880	−	0.514731i
$599$	17.0294	−	29.4957i	0.695801	−	1.20516i	−0.274109	−	0.961699i	$-0.588383\pi$
$599$	17.0294	−	29.4957i	0.695801	−	1.20516i	0.969910	−	0.243464i	$-0.0782836\pi$
$600$	0.151388	−	0.262211i	0.00618038	−	0.0107047i
$601$	4.40624	+	7.63184i	0.179734	+	0.311309i	0.941790	−	0.336203i	$-0.109143\pi$
$601$	4.40624	+	7.63184i	0.179734	+	0.311309i	−0.762055	+	0.647512i	$0.775809\pi$
$602$	−8.69563	−	10.8846i	−0.354407	−	0.443625i
$603$	−2.81985			−0.114833
$604$	16.9599			0.690088
$605$	12.5183	+	21.6823i	0.508940	+	0.881509i
$606$	7.93411	−	13.7423i	0.322301	−	0.558242i
$607$	−33.7963			−1.37175			−0.685874	−	0.727720i	$-0.740580\pi$
$607$	−33.7963			−1.37175			−0.685874	+	0.727720i	$0.740580\pi$
$608$	3.39962	+	5.88831i	0.137873	+	0.238803i
$609$	−2.06131	−	2.58022i	−0.0835287	−	0.104556i
$610$	−31.5654			−1.27805
$611$	5.53328	−	29.7339i	0.223853	−	1.20290i
$612$	−2.12412	+	3.67908i	−0.0858623	+	0.148718i
$613$	−24.1831			−0.976745			−0.488373	−	0.872635i	$-0.662409\pi$
$613$	−24.1831			−0.976745			−0.488373	+	0.872635i	$0.662409\pi$
$614$	−10.1518	+	17.5835i	−0.409695	+	0.709612i
$615$	−6.80750	+	11.7909i	−0.274505	+	0.475456i
$616$	0.934698	−	0.141710i	0.0376601	−	0.00570967i
$617$	−17.7662	+	30.7720i	−0.715241	+	1.23883i	0.247626	+	0.968856i	$0.420350\pi$
$617$	−17.7662	+	30.7720i	−0.715241	+	1.23883i	−0.962867	+	0.269977i	$0.912984\pi$
$618$	16.2998			0.655674
$619$	−2.12839	+	3.68647i	−0.0855470	+	0.148172i	−0.905624	−	0.424081i	$-0.860597\pi$
$619$	−2.12839	+	3.68647i	−0.0855470	+	0.148172i	0.820077	+	0.572253i	$0.193930\pi$
$620$	−0.285811	−	0.495038i	−0.0114784	−	0.0198812i
$621$	−1.77550	+	3.07526i	−0.0712485	+	0.123406i
$622$	11.7028	+	20.2699i	0.469241	+	0.812750i
$623$	−0.709131	+	1.81144i	−0.0284107	+	0.0725739i
$624$	3.39962	−	1.20108i	0.136094	−	0.0480816i
$625$	13.2111	+	22.8823i	0.528444	+	0.915292i
$626$	−21.6911			−0.866949
$627$	−2.42950			−0.0970250
$628$	−7.31722			−0.291989
$629$	40.1115			1.59935
$630$	−6.02373	+	0.913262i	−0.239991	+	0.0363852i
$631$	−5.15299	+	8.92524i	−0.205137	+	0.355308i	−0.950176	−	0.311713i	$-0.899097\pi$
$631$	−5.15299	+	8.92524i	−0.205137	+	0.355308i	0.745039	+	0.667021i	$0.232431\pi$
$632$	−5.77345	−	9.99992i	−0.229656	−	0.397775i
$633$	−12.0787	−	20.9210i	−0.480086	−	0.831534i
$634$	27.8270			1.10515
$635$	12.6035	−	21.8299i	0.500155	−	0.866293i
$636$	1.21020			0.0479876
$637$	−23.1806	−	9.98304i	−0.918448	−	0.395542i
$638$	0.446018			0.0176580
$639$	0.794068	−	1.37537i	0.0314128	−	0.0544086i
$640$	−2.30278			−0.0910252
$641$	−14.0660	−	24.3631i	−0.555575	−	0.962284i	−0.997859	−	0.0654088i	$-0.979165\pi$
$641$	−14.0660	−	24.3631i	−0.555575	−	0.962284i	0.442284	−	0.896875i	$-0.354168\pi$
$642$	−3.81308	−	6.60445i	−0.150490	−	0.260657i
$643$	12.8349	−	22.2307i	0.506158	−	0.876692i	−0.493816	−	0.869566i	$-0.664399\pi$
$643$	12.8349	−	22.2307i	0.506158	−	0.876692i	0.999975	−	0.00712558i	$-0.00226816\pi$
$644$	9.28893	−	1.40830i	0.366035	−	0.0554948i
$645$	−12.1256			−0.477445
$646$	−28.8847			−1.13645
$647$	−41.1713			−1.61861			−0.809305	−	0.587388i	$-0.800156\pi$
$647$	−41.1713			−1.61861			−0.809305	+	0.587388i	$0.800156\pi$
$648$	−1.00000			−0.0392837
$649$	−1.27932	−	2.21585i	−0.0502178	−	0.0869798i
$650$	0.199724	−	1.07325i	0.00783384	−	0.0420962i
$651$	−0.239412	+	0.611567i	−0.00938329	+	0.0239692i
$652$	1.14313	+	1.97996i	0.0447684	+	0.0775412i
$653$	20.8519	−	36.1165i	0.815997	−	1.41335i	−0.0926127	−	0.995702i	$-0.529522\pi$
$653$	20.8519	−	36.1165i	0.815997	−	1.41335i	0.908610	−	0.417646i	$-0.137145\pi$
$654$	5.50000	+	9.52628i	0.215067	+	0.372507i
$655$	−23.3065	+	40.3680i	−0.910659	+	1.57731i
$656$	5.91243			0.230841
$657$	0.407877	−	0.706463i	0.0159128	−	0.0275617i
$658$	21.9425	−	3.32672i	0.855409	−	0.129689i
$659$	12.0134	−	20.8079i	0.467977	−	0.810559i	−0.531354	−	0.847150i	$-0.678316\pi$
$659$	12.0134	−	20.8079i	0.467977	−	0.810559i	0.999330	+	0.0365907i	$0.0116498\pi$
$660$	0.411414	−	0.712590i	0.0160143	−	0.0277375i
$661$	0.883273			0.0343553			0.0171777	−	0.999852i	$-0.494532\pi$
$661$	0.883273			0.0343553			0.0171777	+	0.999852i	$0.494532\pi$
$662$	−3.62058	+	6.27103i	−0.140718	+	0.243730i
$663$	−2.80233	+	15.0587i	−0.108833	+	0.584831i
$664$	1.24823			0.0484408
$665$	−25.8560	−	32.3649i	−1.00265	−	1.25506i
$666$	4.72096	+	8.17694i	0.182933	+	0.316850i
$667$	4.43248			0.171626
$668$	1.95416	−	3.38471i	0.0756089	−	0.130958i
$669$	−3.65611	−	6.33256i	−0.141353	−	0.244831i
$670$	6.49349			0.250865
$671$	−4.89799			−0.189085
$672$	1.65139	+	2.06710i	0.0637037	+	0.0797403i
$673$	0.585015	+	1.01328i	0.0225507	+	0.0390589i	0.877081	−	0.480343i	$-0.159488\pi$
$673$	0.585015	+	1.01328i	0.0225507	+	0.0390589i	−0.854530	+	0.519402i	$0.826155\pi$
$674$	−0.190455	+	0.329877i	−0.00733604	+	0.0127064i
$675$	−0.151388	+	0.262211i	−0.00582692	+	0.0100925i
$676$	10.1148	−	8.16642i	0.389032	−	0.314093i
$677$	21.8452	+	37.8370i	0.839580	+	1.45420i	0.890246	+	0.455480i	$0.150532\pi$
$677$	21.8452	+	37.8370i	0.839580	+	1.45420i	−0.0506662	+	0.998716i	$0.516134\pi$
$678$	6.46919	+	11.2050i	0.248448	+	0.430324i
$679$	−7.00663	+	17.8981i	−0.268890	+	0.686867i
$680$	4.89136	−	8.47209i	0.187575	−	0.324890i
$681$	−14.7997	−	25.6338i	−0.567125	−	0.982290i
$682$	−0.0443490	−	0.0768147i	−0.00169821	−	0.00294139i
$683$	−4.15611	−	7.19859i	−0.159029	−	0.275446i	0.775490	−	0.631360i	$-0.217503\pi$
$683$	−4.15611	−	7.19859i	−0.159029	−	0.275446i	−0.934519	+	0.355914i	$0.884170\pi$
$684$	−3.39962	−	5.88831i	−0.129988	−	0.225145i
$685$	6.14934	−	10.6510i	0.234954	−	0.406952i
$686$	1.33609	−	18.4720i	0.0510120	−	0.705264i
$687$	−3.62207	−	6.27360i	−0.138190	−	0.239353i
$688$	2.63282	+	4.56018i	0.100375	+	0.173855i
$689$	4.11423	−	1.45355i	0.156739	−	0.0553757i
$690$	4.08859	−	7.08164i	0.155650	−	0.269593i
$691$	−14.0108	+	24.2673i	−0.532994	+	0.923173i	0.466263	+	0.884646i	$0.345600\pi$
$691$	−14.0108	+	24.2673i	−0.532994	+	0.923173i	−0.999258	+	0.0385272i	$0.987733\pi$
$692$	−8.91658	−	15.4440i	−0.338958	−	0.587092i
$693$	−0.934698	+	0.141710i	−0.0355063	+	0.00538312i
$694$	7.91540			0.300465
$695$	−20.6870			−0.784701
$696$	0.624116	+	1.08100i	0.0236570	+	0.0409752i
$697$	−12.5587	+	21.7523i	−0.475694	+	0.823926i
$698$	−7.80424			−0.295395
$699$	10.2092	+	17.6828i	0.386146	+	0.668825i
$700$	0.792018	−	0.120078i	0.0299355	−	0.00453854i
$701$	27.7353			1.04755			0.523773	−	0.851858i	$-0.324524\pi$
$701$	27.7353			1.04755			0.523773	+	0.851858i	$0.324524\pi$
$702$	−3.39962	+	1.20108i	−0.128310	+	0.0453318i
$703$	−32.0989	+	55.5970i	−1.21063	+	2.09688i
$704$	−0.357320			−0.0134670
$705$	9.65816	−	16.7284i	0.363747	−	0.630029i
$706$	6.59319	−	11.4197i	0.248138	−	0.429788i
$707$	41.5090	−	6.29321i	1.56111	−	0.236680i
$708$	3.58033	−	6.20131i	0.134557	−	0.233060i
$709$	−13.0855			−0.491436			−0.245718	−	0.969341i	$-0.579024\pi$
$709$	−13.0855			−0.491436			−0.245718	+	0.969341i	$0.579024\pi$
$710$	−1.82856	+	3.16716i	−0.0686246	+	0.118861i
$711$	5.77345	+	9.99992i	0.216521	+	0.375026i
$712$	0.367627	−	0.636749i	0.0137774	−	0.0238632i
$713$	−0.440736	−	0.763377i	−0.0165057	−	0.0285887i
$714$	−11.1128	+	1.68481i	−0.415885	+	0.0630526i
$715$	0.542774	−	2.91667i	0.0202986	−	0.109077i
$716$	2.80073	+	4.85100i	0.104668	+	0.181290i
$717$	−6.02686			−0.225077
$718$	1.16066			0.0433154
$719$	50.3319			1.87706			0.938531	−	0.345194i	$-0.112187\pi$
$719$	50.3319			1.87706			0.938531	+	0.345194i	$0.112187\pi$
$720$	2.30278			0.0858194
$721$	26.9173	+	33.6934i	1.00245	+	1.25481i
$722$	13.6148	−	23.5816i	0.506691	−	0.877615i
$723$	−5.50472	−	9.53445i	−0.204723	−	0.354590i
$724$	3.91613	+	6.78294i	0.145542	+	0.252086i
$725$	0.377934			0.0140361
$726$	−5.43616	+	9.41571i	−0.201755	+	0.349450i
$727$	36.3505			1.34817			0.674083	−	0.738655i	$-0.264539\pi$
$727$	36.3505			1.34817			0.674083	+	0.738655i	$0.264539\pi$
$728$	8.09684	+	5.04392i	0.300089	+	0.186940i
$729$	1.00000			0.0370370
$730$	−0.939248	+	1.62683i	−0.0347631	+	0.0602115i
$731$	−22.3697			−0.827373
$732$	−6.85378	−	11.8711i	−0.253323	−	0.438768i
$733$	5.18234	+	8.97608i	0.191414	+	0.331539i	0.945719	−	0.324985i	$-0.105359\pi$
$733$	5.18234	+	8.97608i	0.191414	+	0.331539i	−0.754305	+	0.656524i	$0.772026\pi$
$734$	−16.4136	+	28.4292i	−0.605837	+	1.04934i
$735$	−11.8353	−	10.9435i	−0.436553	−	0.403658i
$736$	−3.55101			−0.130892
$737$	1.00759			0.0371150
$738$	−5.91243			−0.217639
$739$	38.8155			1.42785			0.713925	−	0.700222i	$-0.246916\pi$
$739$	38.8155			1.42785			0.713925	+	0.700222i	$0.246916\pi$
$740$	−10.8713	−	18.8297i	−0.399637	−	0.692192i
$741$	−18.6297	−	15.9348i	−0.684380	−	0.585380i
$742$	1.99851	+	2.50161i	0.0733677	+	0.0918371i
$743$	0.231154	+	0.400371i	0.00848024	+	0.0146882i	0.870234	−	0.492638i	$-0.163967\pi$
$743$	0.231154	+	0.400371i	0.00848024	+	0.0146882i	−0.861754	+	0.507326i	$0.830634\pi$
$744$	0.124116	−	0.214975i	0.00455030	−	0.00788135i
$745$	−10.2712	−	17.7903i	−0.376309	−	0.651786i
$746$	−14.7437	+	25.5368i	−0.539804	+	0.934967i
$747$	−1.24823			−0.0456704
$748$	0.758989	−	1.31461i	0.0277514	−	0.0480668i
$749$	7.35521	−	18.7886i	0.268754	−	0.686519i
$750$	−5.40833	+	9.36750i	−0.197484	+	0.342053i
$751$	13.5047	−	23.3908i	0.492793	−	0.853543i	−0.507172	−	0.861845i	$-0.669309\pi$
$751$	13.5047	−	23.3908i	0.492793	−	0.853543i	0.999966	+	0.00830164i	$0.00264252\pi$
$752$	−8.38827			−0.305889
$753$	12.6772	−	21.9575i	0.461982	−	0.800176i
$754$	3.42012	+	2.92538i	0.124553	+	0.106536i
$755$	39.0548			1.42135
$756$	−1.65139	−	2.06710i	−0.0600604	−	0.0751798i
$757$	−15.1344	−	26.2136i	−0.550070	−	0.952749i	−0.998269	−	0.0588153i	$-0.981268\pi$
$757$	−15.1344	−	26.2136i	−0.550070	−	0.952749i	0.448199	−	0.893934i	$-0.352066\pi$
$758$	17.1586			0.623228
$759$	0.634423	−	1.09885i	0.0230281	−	0.0398858i
$760$	7.82856	+	13.5595i	0.283972	+	0.491853i
$761$	−27.9189			−1.01206			−0.506030	−	0.862516i	$-0.668887\pi$
$761$	−27.9189			−1.01206			−0.506030	+	0.862516i	$0.668887\pi$
$762$	10.9464			0.396545
$763$	−10.6092	+	27.1007i	−0.384078	+	0.981110i
$764$	6.82179	+	11.8157i	0.246804	+	0.427477i
$765$	−4.89136	+	8.47209i	−0.176848	+	0.306309i
$766$	9.48764	−	16.4331i	0.342802	−	0.593751i
$767$	4.72349	−	25.3824i	0.170555	−	0.916504i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	3.78741	+	6.55999i	0.136577	+	0.236559i	0.926199	−	0.377035i	$-0.123056\pi$
$769$	3.78741	+	6.55999i	0.136577	+	0.236559i	−0.789621	+	0.613594i	$0.789723\pi$
$770$	2.15240	−	0.326327i	0.0775671	−	0.0117600i
$771$	−10.5952	+	18.3515i	−0.381578	+	0.660913i
$772$	−6.39962	−	11.0845i	−0.230327	−	0.398939i
$773$	−12.4552	−	21.5730i	−0.447982	−	0.775928i	0.550272	−	0.834985i	$-0.314524\pi$
$773$	−12.4552	−	21.5730i	−0.447982	−	0.775928i	−0.998255	+	0.0590570i	$0.981191\pi$
$774$	−2.63282	−	4.56018i	−0.0946349	−	0.163912i
$775$	−0.0375792	−	0.0650891i	−0.00134988	−	0.00233807i
$776$	3.63237	−	6.29145i	0.130395	−	0.225850i
$777$	−9.10645	+	23.2620i	−0.326692	+	0.834520i
$778$	−12.8986	−	22.3410i	−0.462437	−	0.800964i
$779$	−20.1000	−	34.8142i	−0.720157	−	1.24735i
$780$	7.82856	−	2.76581i	0.280307	−	0.0990320i
$781$	−0.283736	+	0.491446i	−0.0101529	+	0.0175853i
$782$	7.54275	−	13.0644i	0.269728	−	0.467183i
$783$	−0.624116	−	1.08100i	−0.0223041	−	0.0386318i
$784$	−1.54584	+	6.82718i	−0.0552084	+	0.243828i
$785$	−16.8499			−0.601399
$786$	−20.2421			−0.722010
$787$	−3.29303	−	5.70370i	−0.117384	−	0.203315i	0.801346	−	0.598201i	$-0.204117\pi$
$787$	−3.29303	−	5.70370i	−0.117384	−	0.203315i	−0.918730	+	0.394886i	$0.870784\pi$
$788$	−7.84758	+	13.5924i	−0.279558	+	0.484209i
$789$	−9.13504			−0.325216
$790$	−13.2950	−	23.0276i	−0.473014	−	0.819284i
$791$	−12.4787	+	31.8762i	−0.443691	+	1.13339i
$792$	0.357320			0.0126968
$793$	−37.5584	−	32.1253i	−1.33374	−	1.14080i
$794$	−15.3672	+	26.6168i	−0.545362	+	0.944595i
$795$	2.78682			0.0988384
$796$	−10.6144	+	18.3846i	−0.376216	+	0.651626i
$797$	21.8104	−	37.7768i	0.772566	−	1.33812i	−0.163587	−	0.986529i	$-0.552306\pi$
$797$	21.8104	−	37.7768i	0.772566	−	1.33812i	0.936153	−	0.351594i	$-0.114360\pi$
$798$	6.55767	−	16.7513i	0.232139	−	0.592988i
$799$	17.8177	−	30.8611i	0.630344	−	1.09179i
$800$	−0.302776			−0.0107047
$801$	−0.367627	+	0.636749i	−0.0129895	+	0.0224984i
$802$	8.17877	+	14.1660i	0.288802	+	0.500221i
$803$	−0.145742	+	0.252433i	−0.00514314	+	0.00890818i
$804$	1.40993	+	2.44206i	0.0497243	+	0.0861250i
$805$	21.3903	−	3.24300i	0.753910	−	0.114301i
$806$	0.163745	−	0.879905i	0.00576766	−	0.0309933i
$807$	−0.0247720	−	0.0429064i	−0.000872016	−	0.00151038i
$808$	−15.8682			−0.558242
$809$	27.8240			0.978238			0.489119	−	0.872217i	$-0.337318\pi$
$809$	27.8240			0.978238			0.489119	+	0.872217i	$0.337318\pi$
$810$	−2.30278			−0.0809113
$811$	−15.9773			−0.561039			−0.280520	−	0.959848i	$-0.590507\pi$
$811$	−15.9773			−0.561039			−0.280520	+	0.959848i	$0.590507\pi$
$812$	−1.20388	+	3.07526i	−0.0422480	+	0.107921i
$813$	−0.00665800	+	0.0115320i	−0.000233506	+	0.000404445i
$814$	−1.68689	−	2.92178i	−0.0591256	−	0.102408i
$815$	2.63237	+	4.55940i	0.0922080	+	0.159709i
$816$	4.24823			0.148718
$817$	17.9012	−	31.0058i	0.626283	−	1.08475i
$818$	−9.67044			−0.338119
$819$	−8.09684	−	5.04392i	−0.282927	−	0.176249i
$820$	13.6150			0.475456
$821$	22.1464	−	38.3586i	0.772913	−	1.33873i	−0.163046	−	0.986618i	$-0.552132\pi$
$821$	22.1464	−	38.3586i	0.772913	−	1.33873i	0.935960	−	0.352107i	$-0.114535\pi$
$822$	5.34081			0.186282
$823$	3.21787	+	5.57352i	0.112168	+	0.194281i	0.916644	−	0.399704i	$-0.130887\pi$
$823$	3.21787	+	5.57352i	0.112168	+	0.194281i	−0.804476	+	0.593985i	$0.797554\pi$
$824$	−8.14990	−	14.1160i	−0.283915	−	0.491756i
$825$	0.0540939	−	0.0936934i	0.00188331	−	0.00326198i
$826$	18.7313	−	2.83986i	0.651744	−	0.0988113i
$827$	16.6468			0.578865			0.289433	−	0.957198i	$-0.406533\pi$
$827$	16.6468			0.578865			0.289433	+	0.957198i	$0.406533\pi$
$828$	3.55101			0.123406
$829$	7.14712			0.248230			0.124115	−	0.992268i	$-0.460391\pi$
$829$	7.14712			0.248230			0.124115	+	0.992268i	$0.460391\pi$
$830$	2.87440			0.0997718
$831$	−11.0725	−	19.1782i	−0.384102	−	0.665283i
$832$	−2.73997	−	2.34362i	−0.0949915	−	0.0812503i
$833$	−21.8342	−	20.1890i	−0.756510	−	0.699506i
$834$	−4.49174	−	7.77993i	−0.155536	−	0.269397i
$835$	4.50000	−	7.79423i	0.155729	−	0.269730i
$836$	1.21475	+	2.10401i	0.0420131	+	0.0727688i
$837$	−0.124116	+	0.214975i	−0.00429007	+	0.00743061i
$838$	36.1804			1.24983
$839$	−9.65080	+	16.7157i	−0.333183	+	0.577089i	−0.983134	−	0.182887i	$-0.941456\pi$
$839$	−9.65080	+	16.7157i	−0.333183	+	0.577089i	0.649951	+	0.759976i	$0.274789\pi$
$840$	3.80278	+	4.76008i	0.131208	+	0.164238i
$841$	13.7210	−	23.7654i	0.473137	−	0.819497i
$842$	16.3085	−	28.2472i	0.562028	−	0.973462i
$843$	−4.44192			−0.152988
$844$	−12.0787	+	20.9210i	−0.415767	+	0.720130i
$845$	23.2922	−	18.8054i	0.801275	−	0.646926i
$846$	8.38827			0.288395
$847$	−28.4405	+	4.31187i	−0.977226	+	0.148158i
$848$	−0.605101	−	1.04807i	−0.0207792	−	0.0359907i
$849$	20.2122			0.693682
$850$	0.643130	−	1.11393i	0.0220592	−	0.0382076i
$851$	−16.7642	−	29.0364i	−0.574668	−	0.995354i
$852$	−1.58814			−0.0544086
$853$	−5.45343			−0.186722			−0.0933610	−	0.995632i	$-0.529761\pi$
$853$	−5.45343			−0.186722			−0.0933610	+	0.995632i	$0.529761\pi$
$854$	13.2205	−	33.7713i	0.452398	−	1.15563i
$855$	−7.82856	−	13.5595i	−0.267731	−	0.463724i
$856$	−3.81308	+	6.60445i	−0.130328	+	0.225736i
$857$	−5.69198	+	9.85879i	−0.194434	+	0.336770i	−0.946715	−	0.322073i	$-0.895620\pi$
$857$	−5.69198	+	9.85879i	−0.194434	+	0.336770i	0.752281	+	0.658843i	$0.228954\pi$
$858$	1.21475	−	0.429169i	0.0414709	−	0.0146516i
$859$	−1.39552	−	2.41711i	−0.0476145	−	0.0824708i	0.841236	−	0.540668i	$-0.181829\pi$
$859$	−1.39552	−	2.41711i	−0.0476145	−	0.0824708i	−0.888850	+	0.458198i	$0.848495\pi$
$860$	6.06280	+	10.5011i	0.206740	+	0.358084i
$861$	−9.76371	−	12.2216i	−0.332746	−	0.416511i
$862$	−4.53244	+	7.85042i	−0.154376	+	0.267386i
$863$	−10.2385	−	17.7336i	−0.348522	−	0.603658i	0.637465	−	0.770479i	$-0.279983\pi$
$863$	−10.2385	−	17.7336i	−0.348522	−	0.603658i	−0.985987	+	0.166821i	$0.946650\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−20.5329	−	35.5640i	−0.698139	−	1.20921i
$866$	−13.3558	−	23.1330i	−0.453850	−	0.786091i
$867$	−0.523735	+	0.907135i	−0.0177870	+	0.0308079i
$868$	0.649338	−	0.0984465i	0.0220400	−	0.00334149i
$869$	−2.06297	−	3.57317i	−0.0699815	−	0.121211i
$870$	1.43720	+	2.48930i	0.0487256	+	0.0843952i
$871$	7.72632	+	6.60866i	0.261796	+	0.223926i
$872$	5.50000	−	9.52628i	0.186254	−	0.322601i
$873$	−3.63237	+	6.29145i	−0.122937	+	0.212933i
$874$	12.0721	+	20.9094i	0.408344	+	0.707272i
$875$	−28.2948	+	4.28980i	−0.956540	+	0.145022i
$876$	−0.815753			−0.0275617
$877$	−2.90630			−0.0981388			−0.0490694	−	0.998795i	$-0.515626\pi$
$877$	−2.90630			−0.0981388			−0.0490694	+	0.998795i	$0.515626\pi$
$878$	−9.78949	−	16.9559i	−0.330379	−	0.572234i
$879$	−14.1231	+	24.4619i	−0.476360	+	0.825079i
$880$	−0.822828			−0.0277375
$881$	−24.6993	−	42.7805i	−0.832141	−	1.44131i	−0.896337	−	0.443373i	$-0.853782\pi$
$881$	−24.6993	−	42.7805i	−0.832141	−	1.44131i	0.0641964	−	0.997937i	$-0.479552\pi$
$882$	1.54584	−	6.82718i	0.0520510	−	0.229883i
$883$	−35.2559			−1.18646			−0.593228	−	0.805034i	$-0.702147\pi$
$883$	−35.2559			−1.18646			−0.593228	+	0.805034i	$0.702147\pi$
$884$	14.4424	−	5.10246i	0.485749	−	0.171614i
$885$	8.24469	−	14.2802i	0.277142	−	0.480025i
$886$	−2.81368			−0.0945274
$887$	−18.1911	+	31.5078i	−0.610796	+	1.05793i	0.380311	+	0.924859i	$0.375817\pi$
$887$	−18.1911	+	31.5078i	−0.610796	+	1.05793i	−0.991107	+	0.133070i	$0.957516\pi$
$888$	4.72096	−	8.17694i	0.158425	−	0.274400i
$889$	18.0767	+	22.6273i	0.606272	+	0.758894i
$890$	0.846562	−	1.46629i	0.0283768	−	0.0491501i
$891$	−0.357320			−0.0119707
$892$	−3.65611	+	6.33256i	−0.122416	+	0.212030i
$893$	28.5169	+	49.3928i	0.954283	+	1.65287i
$894$	4.46037	−	7.72559i	0.149177	−	0.258382i
$895$	6.44944	+	11.1708i	0.215581	+	0.373397i
$896$	0.964471	−	2.46370i	0.0322207	−	0.0823063i
$897$	12.0721	−	4.26504i	0.403075	−	0.142405i
$898$	−11.0541	−	19.1463i	−0.368881	−	0.638921i
$899$	0.309850			0.0103341
$900$	0.302776			0.0100925
$901$	5.14122			0.171279
$902$	2.11263			0.0703428
$903$	5.07856	−	12.9730i	0.169004	−	0.431713i
$904$	6.46919	−	11.2050i	0.215162	−	0.372672i
$905$	9.01798	+	15.6196i	0.299768	+	0.519213i
$906$	8.47995	+	14.6877i	0.281727	+	0.487966i
$907$	4.62353			0.153522			0.0767609	−	0.997050i	$-0.475542\pi$
$907$	4.62353			0.153522			0.0767609	+	0.997050i	$0.475542\pi$
$908$	−14.7997	+	25.6338i	−0.491145	+	0.850688i
$909$	15.8682			0.526316
$910$	18.6452	+	11.6150i	0.618083	+	0.385034i
$911$	−35.1359			−1.16411			−0.582053	−	0.813151i	$-0.697750\pi$
$911$	−35.1359			−1.16411			−0.582053	+	0.813151i	$0.697750\pi$
$912$	−3.39962	+	5.88831i	−0.112573	+	0.194982i
$913$	0.446018			0.0147610
$914$	15.5382	+	26.9129i	0.513957	+	0.890200i
$915$	−15.7827	−	27.3365i	−0.521761	−	0.903716i
$916$	−3.62207	+	6.27360i	−0.119676	+	0.207286i
$917$	−33.4275	−	41.8424i	−1.10387	−	1.38176i
$918$	−4.24823			−0.140213
$919$	−0.725137			−0.0239201			−0.0119600	−	0.999928i	$-0.503807\pi$
$919$	−0.725137			−0.0239201			−0.0119600	+	0.999928i	$0.503807\pi$
$920$	−8.17717			−0.269593
$921$	−20.3037			−0.669029
$922$	19.9244	+	34.5100i	0.656174	+	1.13653i
$923$	−5.39906	+	1.90748i	−0.177712	+	0.0627853i
$924$	0.590074	+	0.738617i	0.0194120	+	0.0242987i
$925$	−1.42939	−	2.47578i	−0.0469981	−	0.0814031i
$926$	2.95576	−	5.11953i	0.0971324	−	0.168238i
$927$	8.14990	+	14.1160i	0.267678	+	0.463632i
$928$	0.624116	−	1.08100i	0.0204876	−	0.0354856i
$929$	−4.87322			−0.159885			−0.0799426	−	0.996799i	$-0.525474\pi$
$929$	−4.87322			−0.159885			−0.0799426	+	0.996799i	$0.525474\pi$
$930$	0.285811	−	0.495038i	0.00937210	−	0.0162329i
$931$	45.4558	−	14.1074i	1.48975	−	0.462353i
$932$	10.2092	−	17.6828i	0.334412	−	0.579219i
$933$	−11.7028	+	20.2699i	−0.383134	+	0.663607i
$934$	−16.3152			−0.533849
$935$	1.74778	−	3.02725i	0.0571585	−	0.0990015i
$936$	2.73997	+	2.34362i	0.0895589	+	0.0766035i
$937$	−54.0847			−1.76687			−0.883435	−	0.468555i	$-0.844775\pi$
$937$	−54.0847			−1.76687			−0.883435	+	0.468555i	$0.844775\pi$
$938$	−2.71966	+	6.94726i	−0.0888002	+	0.226836i
$939$	−10.8455	−	18.7850i	−0.353930	−	0.613025i
$940$	−19.3163			−0.630029
$941$	13.4459	−	23.2890i	0.438324	−	0.759199i	−0.559236	−	0.829008i	$-0.688906\pi$
$941$	13.4459	−	23.2890i	0.438324	−	0.759199i	0.997560	+	0.0698088i	$0.0222389\pi$
$942$	−3.65861	−	6.33689i	−0.119204	−	0.206467i
$943$	20.9951			0.683693
$944$	−7.16066			−0.233060
$945$	−3.80278	−	4.76008i	−0.123704	−	0.154845i
$946$	0.940760	+	1.62944i	0.0305868	+	0.0529778i
$947$	−7.67130	+	13.2871i	−0.249284	+	0.431772i	−0.963327	−	0.268329i	$-0.913529\pi$
$947$	−7.67130	+	13.2871i	−0.249284	+	0.431772i	0.714043	+	0.700101i	$0.246862\pi$
$948$	5.77345	−	9.99992i	0.187513	−	0.324782i
$949$	−2.77325	+	0.979783i	−0.0900235	+	0.0318051i
$950$	1.02932	+	1.78284i	0.0333956	+	0.0578429i
$951$	13.9135	+	24.0989i	0.451176	+	0.781460i
$952$	7.01548	+	8.78154i	0.227373	+	0.284611i
$953$	−23.6107	+	40.8950i	−0.764826	+	1.32472i	0.175512	+	0.984477i	$0.443842\pi$
$953$	−23.6107	+	40.8950i	−0.764826	+	1.32472i	−0.940338	+	0.340241i	$0.889491\pi$
$954$	0.605101	+	1.04807i	0.0195909	+	0.0339324i
$955$	15.7091	+	27.2089i	0.508333	+	0.880459i
$956$	3.01343	+	5.21941i	0.0974612	+	0.168808i
$957$	0.223009	+	0.386263i	0.00720886	+	0.0124861i
$958$	4.70183	−	8.14381i	0.151909	−	0.263115i
$959$	8.81974	+	11.0400i	0.284804	+	0.356500i
$960$	−1.15139	−	1.99426i	−0.0371609	−	0.0643645i
$961$	15.4692	+	26.7934i	0.499006	+	0.864304i
$962$	6.22832	−	33.4687i	0.200809	−	1.07908i
$963$	3.81308	−	6.60445i	0.122875	−	0.212826i
$964$	−5.50472	+	9.53445i	−0.177295	+	0.307084i
$965$	−14.7369	−	25.5250i	−0.474397	−	0.821680i
$966$	5.86409	+	7.34030i	0.188674	+	0.236170i
$967$	−35.8272			−1.15213			−0.576063	−	0.817405i	$-0.695412\pi$
$967$	−35.8272			−1.15213			−0.576063	+	0.817405i	$0.695412\pi$
$968$	10.8723			0.349450
$969$	−14.4424	−	25.0149i	−0.463956	−	0.803595i
$970$	8.36454	−	14.4878i	0.268569	−	0.465175i
$971$	4.61819			0.148205			0.0741024	−	0.997251i	$-0.476391\pi$
$971$	4.61819			0.148205			0.0741024	+	0.997251i	$0.476391\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	8.66431	−	22.1326i	0.277765	−	0.709538i
$974$	33.5387			1.07465
$975$	1.02932	−	0.363657i	0.0329647	−	0.0116464i
$976$	−6.85378	+	11.8711i	−0.219384	+	0.379985i
$977$	−13.1527			−0.420792			−0.210396	−	0.977616i	$-0.567475\pi$
$977$	−13.1527			−0.420792			−0.210396	+	0.977616i	$0.567475\pi$
$978$	−1.14313	+	1.97996i	−0.0365533	+	0.0633121i
$979$	0.131360	−	0.227523i	0.00419830	−	0.00727167i
$980$	−3.55971	+	15.7215i	−0.113711	+	0.502204i
$981$	−5.50000	+	9.52628i	−0.175601	+	0.304151i
$982$	23.4912			0.749634
$983$	−3.44034	+	5.95885i	−0.109730	+	0.190058i	−0.915661	−	0.401952i	$-0.868332\pi$
$983$	−3.44034	+	5.95885i	−0.109730	+	0.190058i	0.805931	+	0.592010i	$0.201665\pi$
$984$	2.95621	+	5.12031i	0.0942406	+	0.163230i
$985$	−18.0712	+	31.3002i	−0.575796	+	0.997309i
$986$	2.65139	+	4.59234i	0.0844374	+	0.146250i
$987$	13.8523	+	17.3394i	0.440923	+	0.551920i
$988$	−4.48508	+	24.1012i	−0.142690	+	0.766762i
$989$	9.34917	+	16.1932i	0.297286	+	0.514915i
$990$	0.822828			0.0261512
$991$	15.4977			0.492301			0.246150	−	0.969232i	$-0.420834\pi$
$991$	15.4977			0.492301			0.246150	+	0.969232i	$0.420834\pi$
$992$	−0.248231			−0.00788135
$993$	−7.24116			−0.229791
$994$	−2.62263	−	3.28284i	−0.0831847	−	0.104125i
$995$	−24.4425	+	42.3357i	−0.774880	+	1.34213i
$996$	0.624116	+	1.08100i	0.0197759	+	0.0342528i
$997$	−22.9565	−	39.7619i	−0.727041	−	1.25927i	−0.958129	−	0.286338i	$-0.907562\pi$
$997$	−22.9565	−	39.7619i	−0.727041	−	1.25927i	0.231088	−	0.972933i	$-0.425771\pi$
$998$	−22.4832			−0.711694
$999$	−4.72096	+	8.17694i	−0.149365	+	0.258707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.k.d.445.2	yes	8
3.2	odd	2		1638.2.p.g.991.4		8
7.2	even	3		546.2.j.b.289.1	✓	8
13.9	even	3		546.2.j.b.529.1	yes	8
21.2	odd	6		1638.2.m.i.289.3		8
39.35	odd	6		1638.2.m.i.1621.3		8
91.9	even	3	inner	546.2.k.d.373.2	yes	8
273.191	odd	6		1638.2.p.g.919.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.b.289.1	✓	8	7.2	even	3
546.2.j.b.529.1	yes	8	13.9	even	3
546.2.k.d.373.2	yes	8	91.9	even	3	inner
546.2.k.d.445.2	yes	8	1.1	even	1	trivial
1638.2.m.i.289.3		8	21.2	odd	6
1638.2.m.i.1621.3		8	39.35	odd	6
1638.2.p.g.919.4		8	273.191	odd	6
1638.2.p.g.991.4		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.15139 - 1.99426i) q^{5} +(0.500000 - 0.866025i) q^{6} +(2.61586 - 0.396592i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.15139 - 1.99426i) q^{5} +(0.500000 - 0.866025i) q^{6} +(2.61586 - 0.396592i) q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.30278 q^{10} -0.357320 q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.73997 - 2.34362i) q^{13} +(0.964471 - 2.46370i) q^{14} +(-1.15139 - 1.99426i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.12412 - 3.67908i) q^{17} +(0.500000 - 0.866025i) q^{18} +6.79924 q^{19} +(-1.15139 + 1.99426i) q^{20} +(2.61586 - 0.396592i) q^{21} +(-0.178660 + 0.309448i) q^{22} +(-1.77550 + 3.07526i) q^{23} -1.00000 q^{24} +(-0.151388 + 0.262211i) q^{25} +(-3.39962 + 1.20108i) q^{26} +1.00000 q^{27} +(-1.65139 - 2.06710i) q^{28} +(-0.624116 - 1.08100i) q^{29} -2.30278 q^{30} +(-0.124116 + 0.214975i) q^{31} +(0.500000 + 0.866025i) q^{32} -0.357320 q^{33} -4.24823 q^{34} +(-3.80278 - 4.76008i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-4.72096 + 8.17694i) q^{37} +(3.39962 - 5.88831i) q^{38} +(-2.73997 - 2.34362i) q^{39} +(1.15139 + 1.99426i) q^{40} +(-2.95621 - 5.12031i) q^{41} +(0.964471 - 2.46370i) q^{42} +(2.63282 - 4.56018i) q^{43} +(0.178660 + 0.309448i) q^{44} +(-1.15139 - 1.99426i) q^{45} +(1.77550 + 3.07526i) q^{46} +(4.19414 + 7.26446i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(6.68543 - 2.07486i) q^{49} +(0.151388 + 0.262211i) q^{50} +(-2.12412 - 3.67908i) q^{51} +(-0.659645 + 3.54470i) q^{52} +(-0.605101 + 1.04807i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.411414 + 0.712590i) q^{55} +(-2.61586 + 0.396592i) q^{56} +6.79924 q^{57} -1.24823 q^{58} +(3.58033 + 6.20131i) q^{59} +(-1.15139 + 1.99426i) q^{60} +13.7076 q^{61} +(0.124116 + 0.214975i) q^{62} +(2.61586 - 0.396592i) q^{63} +1.00000 q^{64} +(-1.51901 + 8.16264i) q^{65} +(-0.178660 + 0.309448i) q^{66} -2.81985 q^{67} +(-2.12412 + 3.67908i) q^{68} +(-1.77550 + 3.07526i) q^{69} +(-6.02373 + 0.913262i) q^{70} +(0.794068 - 1.37537i) q^{71} -1.00000 q^{72} +(0.407877 - 0.706463i) q^{73} +(4.72096 + 8.17694i) q^{74} +(-0.151388 + 0.262211i) q^{75} +(-3.39962 - 5.88831i) q^{76} +(-0.934698 + 0.141710i) q^{77} +(-3.39962 + 1.20108i) q^{78} +(5.77345 + 9.99992i) q^{79} +2.30278 q^{80} +1.00000 q^{81} -5.91243 q^{82} -1.24823 q^{83} +(-1.65139 - 2.06710i) q^{84} +(-4.89136 + 8.47209i) q^{85} +(-2.63282 - 4.56018i) q^{86} +(-0.624116 - 1.08100i) q^{87} +0.357320 q^{88} +(-0.367627 + 0.636749i) q^{89} -2.30278 q^{90} +(-8.09684 - 5.04392i) q^{91} +3.55101 q^{92} +(-0.124116 + 0.214975i) q^{93} +8.38827 q^{94} +(-7.82856 - 13.5595i) q^{95} +(0.500000 + 0.866025i) q^{96} +(-3.63237 + 6.29145i) q^{97} +(1.54584 - 6.82718i) q^{98} -0.357320 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 8 q^{3} - 4 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 8 * q^3 - 4 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q + 4 q^{2} + 8 q^{3} - 4 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} + 8 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} + 7 q^{13} - 3 q^{14} - 2 q^{15} - 4 q^{16} - 6 q^{17} + 4 q^{18} - 4 q^{19} - 2 q^{20} + 3 q^{21} + 2 q^{22} + 4 q^{23} - 8 q^{24} + 6 q^{25} + 2 q^{26} + 8 q^{27} - 6 q^{28} + 6 q^{29} - 4 q^{30} + 10 q^{31} + 4 q^{32} + 4 q^{33} - 12 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{37} - 2 q^{38} + 7 q^{39} + 2 q^{40} - 6 q^{41} - 3 q^{42} - 4 q^{43} - 2 q^{44} - 2 q^{45} - 4 q^{46} - 17 q^{47} - 4 q^{48} + 17 q^{49} - 6 q^{50} - 6 q^{51} - 5 q^{52} + 3 q^{53} + 4 q^{54} + 25 q^{55} - 3 q^{56} - 4 q^{57} + 12 q^{58} - 2 q^{60} + 8 q^{61} - 10 q^{62} + 3 q^{63} + 8 q^{64} - 9 q^{65} + 2 q^{66} + 14 q^{67} - 6 q^{68} + 4 q^{69} - 8 q^{70} + 6 q^{71} - 8 q^{72} - 19 q^{73} + 12 q^{74} + 6 q^{75} + 2 q^{76} - 10 q^{77} + 2 q^{78} + 24 q^{79} + 4 q^{80} + 8 q^{81} - 12 q^{82} + 12 q^{83} - 6 q^{84} - 3 q^{85} + 4 q^{86} + 6 q^{87} - 4 q^{88} - 7 q^{89} - 4 q^{90} - 50 q^{91} - 8 q^{92} + 10 q^{93} - 34 q^{94} - 12 q^{95} + 4 q^{96} - 25 q^{97} + 34 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 8 * q^3 - 4 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 + 8 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 + 7 * q^13 - 3 * q^14 - 2 * q^15 - 4 * q^16 - 6 * q^17 + 4 * q^18 - 4 * q^19 - 2 * q^20 + 3 * q^21 + 2 * q^22 + 4 * q^23 - 8 * q^24 + 6 * q^25 + 2 * q^26 + 8 * q^27 - 6 * q^28 + 6 * q^29 - 4 * q^30 + 10 * q^31 + 4 * q^32 + 4 * q^33 - 12 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^37 - 2 * q^38 + 7 * q^39 + 2 * q^40 - 6 * q^41 - 3 * q^42 - 4 * q^43 - 2 * q^44 - 2 * q^45 - 4 * q^46 - 17 * q^47 - 4 * q^48 + 17 * q^49 - 6 * q^50 - 6 * q^51 - 5 * q^52 + 3 * q^53 + 4 * q^54 + 25 * q^55 - 3 * q^56 - 4 * q^57 + 12 * q^58 - 2 * q^60 + 8 * q^61 - 10 * q^62 + 3 * q^63 + 8 * q^64 - 9 * q^65 + 2 * q^66 + 14 * q^67 - 6 * q^68 + 4 * q^69 - 8 * q^70 + 6 * q^71 - 8 * q^72 - 19 * q^73 + 12 * q^74 + 6 * q^75 + 2 * q^76 - 10 * q^77 + 2 * q^78 + 24 * q^79 + 4 * q^80 + 8 * q^81 - 12 * q^82 + 12 * q^83 - 6 * q^84 - 3 * q^85 + 4 * q^86 + 6 * q^87 - 4 * q^88 - 7 * q^89 - 4 * q^90 - 50 * q^91 - 8 * q^92 + 10 * q^93 - 34 * q^94 - 12 * q^95 + 4 * q^96 - 25 * q^97 + 34 * q^98 + 4 * q^99

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