LMFDB - Embedded newform 546.2.j.b.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(289,546)]

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, 2]))

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

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

chi := DirichletCharacter("546.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.j (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			289.1
Root			$0.271028 - 0.469434i$ of defining polynomial
Character	$\chi$	$=$	546.289
Dual form			546.2.j.b.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-1.15139 + 1.99426i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.964471 - 2.46370i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-1.15139 + 1.99426i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.964471 - 2.46370i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.15139 - 1.99426i) q^{10} +(0.178660 - 0.309448i) 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} +1.00000 q^{16} +4.24823 q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.39962 - 5.88831i) q^{19} +(-1.15139 + 1.99426i) q^{20} +(2.61586 + 0.396592i) q^{21} +(-0.178660 + 0.309448i) q^{22} +3.55101 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.151388 - 0.262211i) q^{25} +(2.73997 + 2.34362i) q^{26} +1.00000 q^{27} +(-0.964471 - 2.46370i) q^{28} +(-0.624116 - 1.08100i) q^{29} +(1.15139 + 1.99426i) q^{30} +(-0.124116 - 0.214975i) q^{31} -1.00000 q^{32} +(0.178660 + 0.309448i) q^{33} -4.24823 q^{34} +(6.02373 + 0.913262i) q^{35} +(-0.500000 - 0.866025i) q^{36} +9.44192 q^{37} +(3.39962 + 5.88831i) q^{38} +(3.39962 - 1.20108i) q^{39} +(1.15139 - 1.99426i) q^{40} +(-2.95621 - 5.12031i) q^{41} +(-2.61586 - 0.396592i) q^{42} +(2.63282 - 4.56018i) q^{43} +(0.178660 - 0.309448i) q^{44} +2.30278 q^{45} -3.55101 q^{46} +(4.19414 - 7.26446i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-5.13959 + 4.75232i) q^{49} +(0.151388 + 0.262211i) q^{50} +(-2.12412 + 3.67908i) q^{51} +(-2.73997 - 2.34362i) q^{52} +(-0.605101 - 1.04807i) q^{53} -1.00000 q^{54} +(0.411414 + 0.712590i) q^{55} +(0.964471 + 2.46370i) q^{56} +6.79924 q^{57} +(0.624116 + 1.08100i) q^{58} -7.16066 q^{59} +(-1.15139 - 1.99426i) q^{60} +(-6.85378 - 11.8711i) q^{61} +(0.124116 + 0.214975i) q^{62} +(-1.65139 + 2.06710i) q^{63} +1.00000 q^{64} +(7.82856 - 2.76581i) q^{65} +(-0.178660 - 0.309448i) q^{66} +(1.40993 - 2.44206i) q^{67} +4.24823 q^{68} +(-1.77550 + 3.07526i) q^{69} +(-6.02373 - 0.913262i) q^{70} +(0.794068 - 1.37537i) q^{71} +(0.500000 + 0.866025i) q^{72} +(0.407877 + 0.706463i) q^{73} -9.44192 q^{74} +0.302776 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} +(-1.15139 + 1.99426i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.95621 + 5.12031i) q^{82} -1.24823 q^{83} +(2.61586 + 0.396592i) q^{84} +(-4.89136 + 8.47209i) q^{85} +(-2.63282 + 4.56018i) q^{86} +1.24823 q^{87} +(-0.178660 + 0.309448i) q^{88} +0.735254 q^{89} -2.30278 q^{90} +(-3.13134 + 9.01081i) q^{91} +3.55101 q^{92} +0.248231 q^{93} +(-4.19414 + 7.26446i) q^{94} +15.6571 q^{95} +(0.500000 - 0.866025i) q^{96} +(-3.63237 + 6.29145i) q^{97} +(5.13959 - 4.75232i) q^{98} -0.357320 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 - 4 * q^9	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 2 q^{11} - 4 q^{12} + 7 q^{13} - 3 q^{14} - 2 q^{15} + 8 q^{16} + 12 q^{17} + 4 q^{18} + 2 q^{19} - 2 q^{20} + 3 q^{21} + 2 q^{22} - 8 q^{23} + 4 q^{24} + 6 q^{25} - 7 q^{26} + 8 q^{27} + 3 q^{28} + 6 q^{29} + 2 q^{30} + 10 q^{31} - 8 q^{32} - 2 q^{33} - 12 q^{34} + 8 q^{35} - 4 q^{36} + 24 q^{37} - 2 q^{38} - 2 q^{39} + 2 q^{40} - 6 q^{41} - 3 q^{42} - 4 q^{43} - 2 q^{44} + 4 q^{45} + 8 q^{46} - 17 q^{47} - 4 q^{48} + 17 q^{49} - 6 q^{50} - 6 q^{51} + 7 q^{52} + 3 q^{53} - 8 q^{54} + 25 q^{55} - 3 q^{56} - 4 q^{57} - 6 q^{58} - 2 q^{60} - 4 q^{61} - 10 q^{62} - 6 q^{63} + 8 q^{64} + 12 q^{65} + 2 q^{66} - 7 q^{67} + 12 q^{68} + 4 q^{69} - 8 q^{70} + 6 q^{71} + 4 q^{72} - 19 q^{73} - 24 q^{74} - 12 q^{75} + 2 q^{76} - 10 q^{77} + 2 q^{78} + 24 q^{79} - 2 q^{80} - 4 q^{81} + 6 q^{82} + 12 q^{83} + 3 q^{84} - 3 q^{85} + 4 q^{86} - 12 q^{87} + 2 q^{88} + 14 q^{89} - 4 q^{90} + 40 q^{91} - 8 q^{92} - 20 q^{93} + 17 q^{94} + 24 q^{95} + 4 q^{96} - 25 q^{97} - 17 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 - 4 * q^9 + 2 * q^10 - 2 * q^11 - 4 * q^12 + 7 * q^13 - 3 * q^14 - 2 * q^15 + 8 * q^16 + 12 * q^17 + 4 * q^18 + 2 * q^19 - 2 * q^20 + 3 * q^21 + 2 * q^22 - 8 * q^23 + 4 * q^24 + 6 * q^25 - 7 * q^26 + 8 * q^27 + 3 * q^28 + 6 * q^29 + 2 * q^30 + 10 * q^31 - 8 * q^32 - 2 * q^33 - 12 * q^34 + 8 * q^35 - 4 * q^36 + 24 * q^37 - 2 * q^38 - 2 * q^39 + 2 * q^40 - 6 * q^41 - 3 * q^42 - 4 * q^43 - 2 * q^44 + 4 * q^45 + 8 * q^46 - 17 * q^47 - 4 * q^48 + 17 * q^49 - 6 * q^50 - 6 * q^51 + 7 * q^52 + 3 * q^53 - 8 * q^54 + 25 * q^55 - 3 * q^56 - 4 * q^57 - 6 * q^58 - 2 * q^60 - 4 * q^61 - 10 * q^62 - 6 * q^63 + 8 * q^64 + 12 * q^65 + 2 * q^66 - 7 * q^67 + 12 * q^68 + 4 * q^69 - 8 * q^70 + 6 * q^71 + 4 * q^72 - 19 * q^73 - 24 * q^74 - 12 * q^75 + 2 * q^76 - 10 * q^77 + 2 * q^78 + 24 * q^79 - 2 * q^80 - 4 * q^81 + 6 * q^82 + 12 * q^83 + 3 * q^84 - 3 * q^85 + 4 * q^86 - 12 * q^87 + 2 * q^88 + 14 * q^89 - 4 * q^90 + 40 * q^91 - 8 * q^92 - 20 * q^93 + 17 * q^94 + 24 * q^95 + 4 * q^96 - 25 * q^97 - 17 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	−1.15139	+	1.99426i	−0.514916	+	0.891861i	0.484934	+	0.874551i	$0.338844\pi$
$5$	−1.15139	+	1.99426i	−0.514916	+	0.891861i	−0.999850	+	0.0173104i	$0.994490\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−0.964471	−	2.46370i	−0.364536	−	0.931189i
$7$	−0.964471	−	2.46370i	−0.364536	−	0.931189i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.15139	−	1.99426i	0.364101	−	0.630641i
$11$	0.178660	−	0.309448i	0.0538680	−	0.0933021i	−0.837834	−	0.545925i	$-0.816178\pi$
$11$	0.178660	−	0.309448i	0.0538680	−	0.0933021i	0.891702	+	0.452623i	$0.149512\pi$
$12$	−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
$16$	1.00000			0.250000
$17$	4.24823			1.03035			0.515174	−	0.857086i	$-0.327727\pi$
$17$	4.24823			1.03035			0.515174	+	0.857086i	$0.327727\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−3.39962	−	5.88831i	−0.779926	−	1.35087i	−0.931984	−	0.362500i	$-0.881923\pi$
$19$	−3.39962	−	5.88831i	−0.779926	−	1.35087i	0.152058	−	0.988372i	$-0.451410\pi$
$20$	−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
$23$	3.55101			0.740436			0.370218	−	0.928945i	$-0.379283\pi$
$23$	3.55101			0.740436			0.370218	+	0.928945i	$0.379283\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.151388	−	0.262211i	−0.0302776	−	0.0524423i
$26$	2.73997	+	2.34362i	0.537353	+	0.459621i
$27$	1.00000			0.192450
$28$	−0.964471	−	2.46370i	−0.182268	−	0.465595i
$29$	−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	$0.870307\pi$
$30$	1.15139	+	1.99426i	0.210214	+	0.364101i
$31$	−0.124116	−	0.214975i	−0.0222918	−	0.0386106i	0.854664	−	0.519181i	$-0.173763\pi$
$31$	−0.124116	−	0.214975i	−0.0222918	−	0.0386106i	−0.876956	+	0.480570i	$0.840430\pi$
$32$	−1.00000			−0.176777
$33$	0.178660	+	0.309448i	0.0311007	+	0.0538680i
$34$	−4.24823			−0.728566
$35$	6.02373	+	0.913262i	1.01820	+	0.154369i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	9.44192			1.55224			0.776121	−	0.630584i	$-0.217185\pi$
$37$	9.44192			1.55224			0.776121	+	0.630584i	$0.217185\pi$
$38$	3.39962	+	5.88831i	0.551491	+	0.955211i
$39$	3.39962	−	1.20108i	0.544375	−	0.192326i
$40$	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	$0.986088\pi$
$42$	−2.61586	−	0.396592i	−0.403636	−	0.0611955i
$43$	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
$45$	2.30278			0.343278
$46$	−3.55101			−0.523567
$47$	4.19414	−	7.26446i	0.611778	−	1.05963i	−0.379163	−	0.925330i	$-0.623788\pi$
$47$	4.19414	−	7.26446i	0.611778	−	1.05963i	0.990941	−	0.134300i	$-0.0428787\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−5.13959	+	4.75232i	−0.734228	+	0.678903i
$50$	0.151388	+	0.262211i	0.0214095	+	0.0370823i
$51$	−2.12412	+	3.67908i	−0.297436	+	0.515174i
$52$	−2.73997	−	2.34362i	−0.379966	−	0.325001i
$53$	−0.605101	−	1.04807i	−0.0831170	−	0.143963i	0.821470	−	0.570251i	$-0.193154\pi$
$53$	−0.605101	−	1.04807i	−0.0831170	−	0.143963i	−0.904587	+	0.426288i	$0.859821\pi$
$54$	−1.00000			−0.136083
$55$	0.411414	+	0.712590i	0.0554750	+	0.0960856i
$56$	0.964471	+	2.46370i	0.128883	+	0.329225i
$57$	6.79924			0.900581
$58$	0.624116	+	1.08100i	0.0819504	+	0.141942i
$59$	−7.16066			−0.932238			−0.466119	−	0.884722i	$-0.654348\pi$
$59$	−7.16066			−0.932238			−0.466119	+	0.884722i	$0.654348\pi$
$60$	−1.15139	−	1.99426i	−0.148644	−	0.257458i
$61$	−6.85378	−	11.8711i	−0.877537	−	1.51994i	−0.854035	−	0.520215i	$-0.825852\pi$
$61$	−6.85378	−	11.8711i	−0.877537	−	1.51994i	−0.0235015	−	0.999724i	$-0.507481\pi$
$62$	0.124116	+	0.214975i	0.0157627	+	0.0273018i
$63$	−1.65139	+	2.06710i	−0.208055	+	0.260431i
$64$	1.00000			0.125000
$65$	7.82856	−	2.76581i	0.971013	−	0.343057i
$66$	−0.178660	−	0.309448i	−0.0219915	−	0.0380904i
$67$	1.40993	−	2.44206i	0.172250	−	0.298346i	−0.766956	−	0.641699i	$-0.778230\pi$
$67$	1.40993	−	2.44206i	0.172250	−	0.298346i	0.939206	+	0.343354i	$0.111563\pi$
$68$	4.24823			0.515174
$69$	−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	$0.136625\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	0.407877	+	0.706463i	0.0477383	+	0.0826852i	0.888907	−	0.458087i	$-0.151465\pi$
$73$	0.407877	+	0.706463i	0.0477383	+	0.0826852i	−0.841169	+	0.540773i	$0.818132\pi$
$74$	−9.44192			−1.09760
$75$	0.302776			0.0349615
$76$	−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	−0.333663	−	0.942693i	$-0.608285\pi$
$79$	5.77345	−	9.99992i	0.649564	−	1.12508i	0.983227	−	0.182386i	$-0.0583820\pi$
$80$	−1.15139	+	1.99426i	−0.128729	+	0.222965i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.95621	+	5.12031i	0.326459	+	0.565444i
$83$	−1.24823			−0.137011			−0.0685056	−	0.997651i	$-0.521823\pi$
$83$	−1.24823			−0.137011			−0.0685056	+	0.997651i	$0.521823\pi$
$84$	2.61586	+	0.396592i	0.285414	+	0.0432717i
$85$	−4.89136	+	8.47209i	−0.530543	+	0.918927i
$86$	−2.63282	+	4.56018i	−0.283905	+	0.491737i
$87$	1.24823			0.133824
$88$	−0.178660	+	0.309448i	−0.0190452	+	0.0329873i
$89$	0.735254			0.0779368			0.0389684	−	0.999240i	$-0.487593\pi$
$89$	0.735254			0.0779368			0.0389684	+	0.999240i	$0.487593\pi$
$90$	−2.30278			−0.242734
$91$	−3.13134	+	9.01081i	−0.328253	+	0.944590i
$92$	3.55101			0.370218
$93$	0.248231			0.0257404
$94$	−4.19414	+	7.26446i	−0.432592	+	0.749272i
$95$	15.6571			1.60639
$96$	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	$0.286902\pi$
$98$	5.13959	−	4.75232i	0.519177	−	0.480057i
$99$	−0.357320			−0.0359120
$100$	−0.151388	−	0.262211i	−0.0151388	−	0.0262211i
$101$	−7.93411	+	13.7423i	−0.789474	+	1.36741i	0.136816	+	0.990596i	$0.456313\pi$
$101$	−7.93411	+	13.7423i	−0.789474	+	1.36741i	−0.926290	+	0.376812i	$0.877020\pi$
$102$	2.12412	−	3.67908i	0.210319	−	0.364283i
$103$	8.14990	−	14.1160i	0.803034	−	1.39089i	−0.114577	−	0.993414i	$-0.536551\pi$
$103$	8.14990	−	14.1160i	0.803034	−	1.39089i	0.917611	−	0.397481i	$-0.130115\pi$
$104$	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
$107$	−7.62617			−0.737249			−0.368625	−	0.929578i	$-0.620171\pi$
$107$	−7.62617			−0.737249			−0.368625	+	0.929578i	$0.620171\pi$
$108$	1.00000			0.0962250
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	−0.999512	−	0.0312328i	$-0.990057\pi$
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	0.472708	−	0.881219i	$-0.343277\pi$
$110$	−0.411414	−	0.712590i	−0.0392268	−	0.0679428i
$111$	−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	$0.958410\pi$
$114$	−6.79924			−0.636807
$115$	−4.08859	+	7.08164i	−0.381263	+	0.660366i
$116$	−0.624116	−	1.08100i	−0.0579477	−	0.100368i
$117$	−0.659645	+	3.54470i	−0.0609842	+	0.327707i
$118$	7.16066			0.659192
$119$	−4.09729	−	10.4663i	−0.375598	−	0.959449i
$120$	1.15139	+	1.99426i	0.105107	+	0.182050i
$121$	5.43616	+	9.41571i	0.494196	+	0.855973i
$122$	6.85378	+	11.8711i	0.620512	+	1.07476i
$123$	5.91243			0.533106
$124$	−0.124116	−	0.214975i	−0.0111459	−	0.0193053i
$125$	−10.8167			−0.967471
$126$	1.65139	−	2.06710i	0.147117	−	0.184152i
$127$	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	$0.671910\pi$
$128$	−1.00000			−0.0883883
$129$	2.63282	+	4.56018i	0.231807	+	0.401502i
$130$	−7.82856	+	2.76581i	−0.686610	+	0.242578i
$131$	−10.1210	+	17.5301i	−0.884278	+	1.53162i	−0.0377399	+	0.999288i	$0.512016\pi$
$131$	−10.1210	+	17.5301i	−0.884278	+	1.53162i	−0.846538	+	0.532328i	$0.821317\pi$
$132$	0.178660	+	0.309448i	0.0155504	+	0.0269340i
$133$	−11.2282	+	14.0547i	−0.973607	+	1.21870i
$134$	−1.40993	+	2.44206i	−0.121799	+	0.210962i
$135$	−1.15139	+	1.99426i	−0.0990957	+	0.171639i
$136$	−4.24823			−0.364283
$137$	−5.34081			−0.456296			−0.228148	−	0.973626i	$-0.573267\pi$
$137$	−5.34081			−0.456296			−0.228148	+	0.973626i	$0.573267\pi$
$138$	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	$0.0422517\pi$
$140$	6.02373	+	0.913262i	0.509099	+	0.0771847i
$141$	4.19414	+	7.26446i	0.353210	+	0.611778i
$142$	−0.794068	+	1.37537i	−0.0666367	+	0.115418i
$143$	−1.21475	+	0.429169i	−0.101583	+	0.0358889i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	2.87440			0.238706
$146$	−0.407877	−	0.706463i	−0.0337561	−	0.0584673i
$147$	−1.54584	−	6.82718i	−0.127498	−	0.563096i
$148$	9.44192			0.776121
$149$	−4.46037	−	7.72559i	−0.365408	−	0.632905i	0.623434	−	0.781876i	$-0.285737\pi$
$149$	−4.46037	−	7.72559i	−0.365408	−	0.632905i	−0.988842	+	0.148971i	$0.952404\pi$
$150$	−0.302776			−0.0247215
$151$	−8.47995	−	14.6877i	−0.690088	−	1.19527i	−0.971809	−	0.235772i	$-0.924238\pi$
$151$	−8.47995	−	14.6877i	−0.690088	−	1.19527i	0.281720	−	0.959497i	$-0.409095\pi$
$152$	3.39962	+	5.88831i	0.275746	+	0.477605i
$153$	−2.12412	−	3.67908i	−0.171725	−	0.297436i
$154$	0.934698	+	0.141710i	0.0753201	+	0.0114193i
$155$	0.571621			0.0459137
$156$	3.39962	−	1.20108i	0.272187	−	0.0961632i
$157$	3.65861	+	6.33689i	0.291989	+	0.505739i	0.974280	−	0.225341i	$-0.0723497\pi$
$157$	3.65861	+	6.33689i	0.291989	+	0.505739i	−0.682291	+	0.731081i	$0.739016\pi$
$158$	−5.77345	+	9.99992i	−0.459311	+	0.795551i
$159$	1.21020			0.0959752
$160$	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
$163$	1.14313	+	1.97996i	0.0895369	+	0.155082i	0.907315	−	0.420451i	$-0.138128\pi$
$163$	1.14313	+	1.97996i	0.0895369	+	0.155082i	−0.817779	+	0.575533i	$0.804795\pi$
$164$	−2.95621	−	5.12031i	−0.230841	−	0.399829i
$165$	−0.822828			−0.0640570
$166$	1.24823			0.0968815
$167$	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
$171$	−3.39962	+	5.88831i	−0.259975	+	0.450291i
$172$	2.63282	−	4.56018i	0.200751	−	0.347711i
$173$	−8.91658	−	15.4440i	−0.677915	−	1.17418i	−0.975608	−	0.219522i	$-0.929550\pi$
$173$	−8.91658	−	15.4440i	−0.677915	−	1.17418i	0.297692	−	0.954662i	$-0.403783\pi$
$174$	−1.24823			−0.0946282
$175$	−0.500000	+	0.625869i	−0.0377964	+	0.0473112i
$176$	0.178660	−	0.309448i	0.0134670	−	0.0233255i
$177$	3.58033	−	6.20131i	0.269114	−	0.466119i
$178$	−0.735254			−0.0551096
$179$	2.80073	−	4.85100i	0.209336	−	0.362581i	−0.742169	−	0.670212i	$-0.766203\pi$
$179$	2.80073	−	4.85100i	0.209336	−	0.362581i	0.951506	+	0.307632i	$0.0995364\pi$
$180$	2.30278			0.171639
$181$	−7.83227			−0.582168			−0.291084	−	0.956698i	$-0.594016\pi$
$181$	−7.83227			−0.582168			−0.291084	+	0.956698i	$0.594016\pi$
$182$	3.13134	−	9.01081i	0.232110	−	0.667926i
$183$	13.7076			1.01329
$184$	−3.55101			−0.261784
$185$	−10.8713	+	18.8297i	−0.799275	+	1.38438i
$186$	−0.248231			−0.0182012
$187$	0.758989	−	1.31461i	0.0555028	−	0.0961336i
$188$	4.19414	−	7.26446i	0.305889	−	0.529815i
$189$	−0.964471	−	2.46370i	−0.0701549	−	0.179207i
$190$	−15.6571			−1.13589
$191$	6.82179	+	11.8157i	0.493607	+	0.854953i	0.999973	−	0.00736584i	$-0.00234464\pi$
$191$	6.82179	+	11.8157i	0.493607	+	0.854953i	−0.506365	+	0.862319i	$0.669011\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−6.39962	+	11.0845i	−0.460655	+	0.797877i	−0.998994	−	0.0448511i	$-0.985719\pi$
$193$	−6.39962	+	11.0845i	−0.460655	+	0.797877i	0.538339	+	0.842728i	$0.319052\pi$
$194$	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	$-0.355526\pi$
$198$	0.357320			0.0253936
$199$	21.2287			1.50487			0.752433	−	0.658669i	$-0.228880\pi$
$199$	21.2287			1.50487			0.752433	+	0.658669i	$0.228880\pi$
$200$	0.151388	+	0.262211i	0.0107047	+	0.0185411i
$201$	1.40993	+	2.44206i	0.0994485	+	0.172250i
$202$	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
$205$	13.6150			0.950912
$206$	−8.14990	+	14.1160i	−0.567830	+	0.983511i
$207$	−1.77550	−	3.07526i	−0.123406	−	0.213746i
$208$	−2.73997	−	2.34362i	−0.189983	−	0.162501i
$209$	−2.42950			−0.168052
$210$	3.80278	−	4.76008i	0.262416	−	0.328476i
$211$	−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	$-0.479204\pi$
$212$	−0.605101	−	1.04807i	−0.0415585	−	0.0719814i
$213$	0.794068	+	1.37537i	0.0544086	+	0.0942385i
$214$	7.62617			0.521314
$215$	6.06280	+	10.5011i	0.413480	+	0.716168i
$216$	−1.00000			−0.0680414
$217$	−0.409926	+	0.513120i	−0.0278276	+	0.0348329i
$218$	5.50000	+	9.52628i	0.372507	+	0.645201i
$219$	−0.815753			−0.0551235
$220$	0.411414	+	0.712590i	0.0277375	+	0.0480428i
$221$	−11.6400	−	9.95623i	−0.782994	−	0.669728i
$222$	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	$0.912066\pi$
$224$	0.964471	+	2.46370i	0.0644414	+	0.164613i
$225$	−0.151388	+	0.262211i	−0.0100925	+	0.0174808i
$226$	6.46919	−	11.2050i	0.430324	−	0.745343i
$227$	29.5994			1.96458			0.982290	−	0.187368i	$-0.0599956\pi$
$227$	29.5994			1.96458			0.982290	+	0.187368i	$0.0599956\pi$
$228$	6.79924			0.450291
$229$	−3.62207	+	6.27360i	−0.239353	+	0.414571i	−0.960529	−	0.278181i	$-0.910269\pi$
$229$	−3.62207	+	6.27360i	−0.239353	+	0.414571i	0.721176	+	0.692752i	$0.243602\pi$
$230$	4.08859	−	7.08164i	0.269593	−	0.466949i
$231$	0.590074	−	0.738617i	0.0388240	−	0.0485975i
$232$	0.624116	+	1.08100i	0.0409752	+	0.0709711i
$233$	10.2092	−	17.6828i	0.668825	−	1.15844i	−0.309408	−	0.950929i	$-0.600131\pi$
$233$	10.2092	−	17.6828i	0.668825	−	1.15844i	0.978233	−	0.207509i	$-0.0665356\pi$
$234$	0.659645	−	3.54470i	0.0431224	−	0.231724i
$235$	9.65816	+	16.7284i	0.630029	+	1.09124i
$236$	−7.16066			−0.466119
$237$	5.77345	+	9.99992i	0.375026	+	0.649564i
$238$	4.09729	+	10.4663i	0.265588	+	0.678433i
$239$	−6.02686			−0.389845			−0.194922	−	0.980819i	$-0.562446\pi$
$239$	−6.02686			−0.389845			−0.194922	+	0.980819i	$0.562446\pi$
$240$	−1.15139	−	1.99426i	−0.0743218	−	0.128729i
$241$	11.0094			0.709180			0.354590	−	0.935022i	$-0.384620\pi$
$241$	11.0094			0.709180			0.354590	+	0.935022i	$0.384620\pi$
$242$	−5.43616	−	9.41571i	−0.349450	−	0.605265i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−6.85378	−	11.8711i	−0.438768	−	0.759969i
$245$	−3.55971	−	15.7215i	−0.227422	−	1.00441i
$246$	−5.91243			−0.376963
$247$	−4.48508	+	24.1012i	−0.285379	+	1.53352i
$248$	0.124116	+	0.214975i	0.00788135	+	0.0136509i
$249$	0.624116	−	1.08100i	0.0395517	−	0.0685056i
$250$	10.8167			0.684105
$251$	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
$254$	−5.47318	−	9.47982i	−0.343418	−	0.594817i
$255$	−4.89136	−	8.47209i	−0.306309	−	0.530543i
$256$	1.00000			0.0625000
$257$	21.1905			1.32183			0.660913	−	0.750462i	$-0.270169\pi$
$257$	21.1905			1.32183			0.660913	+	0.750462i	$0.270169\pi$
$258$	−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
$262$	10.1210	−	17.5301i	0.625279	−	1.08302i
$263$	4.56752	−	7.91118i	0.281645	−	0.487824i	−0.690145	−	0.723671i	$-0.742453\pi$
$263$	4.56752	−	7.91118i	0.281645	−	0.487824i	0.971790	+	0.235847i	$0.0757865\pi$
$264$	−0.178660	−	0.309448i	−0.0109958	−	0.0190452i
$265$	2.78682			0.171193
$266$	11.2282	−	14.0547i	0.688444	−	0.861751i
$267$	−0.367627	+	0.636749i	−0.0224984	+	0.0389684i
$268$	1.40993	−	2.44206i	0.0861250	−	0.149173i
$269$	0.0495440			0.00302075			0.00151038	−	0.999999i	$-0.499519\pi$
$269$	0.0495440			0.00302075			0.00151038	+	0.999999i	$0.499519\pi$
$270$	1.15139	−	1.99426i	0.0700712	−	0.121367i
$271$	0.0133160			0.000808889			0.000404445	−	1.00000i	$-0.499871\pi$
$271$	0.0133160			0.000808889			0.000404445		1.00000i	$0.499871\pi$
$272$	4.24823			0.257587
$273$	−6.23792	−	7.21722i	−0.377536	−	0.436806i
$274$	5.34081			0.322650
$275$	−0.108188			−0.00652397
$276$	−1.77550	+	3.07526i	−0.106873	+	0.185109i
$277$	22.1450			1.33057			0.665283	−	0.746591i	$-0.268311\pi$
$277$	22.1450			1.33057			0.665283	+	0.746591i	$0.268311\pi$
$278$	−4.49174	+	7.77993i	−0.269397	+	0.466609i
$279$	−0.124116	+	0.214975i	−0.00743061	+	0.0128702i
$280$	−6.02373	−	0.913262i	−0.359987	−	0.0545779i
$281$	−4.44192			−0.264983			−0.132491	−	0.991184i	$-0.542298\pi$
$281$	−4.44192			−0.264983			−0.132491	+	0.991184i	$0.542298\pi$
$282$	−4.19414	−	7.26446i	−0.249757	−	0.432592i
$283$	−10.1061	+	17.5043i	−0.600746	+	1.04052i	0.391962	+	0.919981i	$0.371796\pi$
$283$	−10.1061	+	17.5043i	−0.600746	+	1.04052i	−0.992708	+	0.120541i	$0.961537\pi$
$284$	0.794068	−	1.37537i	0.0471193	−	0.0816130i
$285$	−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
$289$	1.04747			0.0616159
$290$	−2.87440			−0.168790
$291$	−3.63237	−	6.29145i	−0.212933	−	0.368812i
$292$	0.407877	+	0.706463i	0.0238692	+	0.0413426i
$293$	−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
$296$	−9.44192			−0.548800
$297$	0.178660	−	0.309448i	0.0103669	−	0.0179560i
$298$	4.46037	+	7.72559i	0.258382	+	0.447531i
$299$	−9.72967	−	8.32220i	−0.562681	−	0.481285i
$300$	0.302776			0.0174808
$301$	−13.7742	−	2.08831i	−0.793931	−	0.120368i
$302$	8.47995	+	14.6877i	0.487966	+	0.845182i
$303$	−7.93411	−	13.7423i	−0.455803	−	0.789474i
$304$	−3.39962	−	5.88831i	−0.194982	−	0.337718i
$305$	31.5654			1.80743
$306$	2.12412	+	3.67908i	0.121428	+	0.210319i
$307$	−20.3037			−1.15879			−0.579396	−	0.815046i	$-0.696712\pi$
$307$	−20.3037			−1.15879			−0.579396	+	0.815046i	$0.696712\pi$
$308$	−0.934698	−	0.141710i	−0.0532594	−	0.00807469i
$309$	8.14990	+	14.1160i	0.463632	+	0.803034i
$310$	−0.571621			−0.0324659
$311$	−11.7028	−	20.2699i	−0.663607	−	1.14940i	−0.979661	−	0.200660i	$-0.935691\pi$
$311$	−11.7028	−	20.2699i	−0.663607	−	1.14940i	0.316053	−	0.948741i	$-0.397642\pi$
$312$	−3.39962	+	1.20108i	−0.192466	+	0.0679977i
$313$	−10.8455	+	18.7850i	−0.613025	+	1.06179i	0.377702	+	0.925927i	$0.376714\pi$
$313$	−10.8455	+	18.7850i	−0.613025	+	1.06179i	−0.990728	+	0.135864i	$0.956619\pi$
$314$	−3.65861	−	6.33689i	−0.206467	−	0.357612i
$315$	−2.22096	−	5.67334i	−0.125137	−	0.319656i
$316$	5.77345	−	9.99992i	0.324782	−	0.562539i
$317$	13.9135	−	24.0989i	0.781460	−	1.35353i	−0.149631	−	0.988742i	$-0.547809\pi$
$317$	13.9135	−	24.0989i	0.781460	−	1.35353i	0.931091	−	0.364786i	$-0.118858\pi$
$318$	−1.21020			−0.0678647
$319$	−0.446018			−0.0249722
$320$	−1.15139	+	1.99426i	−0.0643645	+	0.111483i
$321$	3.81308	−	6.60445i	0.212826	−	0.368625i
$322$	3.42484	+	8.74860i	0.190859	+	0.487540i
$323$	−14.4424	−	25.0149i	−0.803595	−	1.39187i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−0.199724	+	1.07325i	−0.0110787	+	0.0595331i
$326$	−1.14313	−	1.97996i	−0.0633121	−	0.109660i
$327$	11.0000			0.608301
$328$	2.95621	+	5.12031i	0.163230	+	0.282722i
$329$	−21.9425	−	3.32672i	−1.20973	−	0.183408i
$330$	0.822828			0.0452952
$331$	3.62058	+	6.27103i	0.199005	+	0.344687i	0.948206	−	0.317656i	$-0.102896\pi$
$331$	3.62058	+	6.27103i	0.199005	+	0.344687i	−0.749201	+	0.662343i	$0.769562\pi$
$332$	−1.24823			−0.0685056
$333$	−4.72096	−	8.17694i	−0.258707	−	0.448094i
$334$	−1.95416	−	3.38471i	−0.106927	−	0.185203i
$335$	3.24674	+	5.62353i	0.177389	+	0.307246i
$336$	2.61586	+	0.396592i	0.142707	+	0.0216359i
$337$	−0.380909			−0.0207494			−0.0103747	−	0.999946i	$-0.503302\pi$
$337$	−0.380909			−0.0207494			−0.0103747	+	0.999946i	$0.503302\pi$
$338$	−2.01492	−	12.8429i	−0.109597	−	0.698562i
$339$	−6.46919	−	11.2050i	−0.351358	−	0.608570i
$340$	−4.89136	+	8.47209i	−0.265271	+	0.459463i
$341$	−0.0886980			−0.00480327
$342$	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
$345$	−4.08859	−	7.08164i	−0.220122	−	0.381263i
$346$	8.91658	+	15.4440i	0.479359	+	0.830273i
$347$	−7.91540			−0.424921			−0.212461	−	0.977170i	$-0.568148\pi$
$347$	−7.91540			−0.424921			−0.212461	+	0.977170i	$0.568148\pi$
$348$	1.24823			0.0669122
$349$	−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
$353$	−6.59319	+	11.4197i	−0.350920	+	0.607812i	−0.986411	−	0.164297i	$-0.947465\pi$
$353$	−6.59319	+	11.4197i	−0.350920	+	0.607812i	0.635491	+	0.772109i	$0.280798\pi$
$354$	−3.58033	+	6.20131i	−0.190292	+	0.329596i
$355$	1.82856	+	3.16716i	0.0970499	+	0.168095i
$356$	0.735254			0.0389684
$357$	11.1128	+	1.68481i	0.588150	+	0.0891698i
$358$	−2.80073	+	4.85100i	−0.148023	+	0.256383i
$359$	0.580329	−	1.00516i	0.0306286	−	0.0530503i	−0.850305	−	0.526291i	$-0.823582\pi$
$359$	0.580329	−	1.00516i	0.0306286	−	0.0530503i	0.880933	+	0.473240i	$0.156916\pi$
$360$	−2.30278			−0.121367
$361$	−13.6148	+	23.5816i	−0.716570	+	1.24113i
$362$	7.83227			0.411655
$363$	−10.8723			−0.570649
$364$	−3.13134	+	9.01081i	−0.164127	+	0.472295i
$365$	−1.87850			−0.0983250
$366$	−13.7076			−0.716506
$367$	16.4136	−	28.4292i	0.856783	−	1.48399i	−0.0181972	−	0.999834i	$-0.505793\pi$
$367$	16.4136	−	28.4292i	0.856783	−	1.48399i	0.874981	−	0.484158i	$-0.160874\pi$
$368$	3.55101			0.185109
$369$	−2.95621	+	5.12031i	−0.153894	+	0.266553i
$370$	10.8713	−	18.8297i	0.565172	−	0.978907i
$371$	−1.99851	+	2.50161i	−0.103758	+	0.129877i
$372$	0.248231			0.0128702
$373$	14.7437	+	25.5368i	0.763398	+	1.32224i	0.941090	+	0.338157i	$0.109804\pi$
$373$	14.7437	+	25.5368i	0.763398	+	1.32224i	−0.177692	+	0.984086i	$0.556863\pi$
$374$	−0.758989	+	1.31461i	−0.0392464	+	0.0679767i
$375$	5.40833	−	9.36750i	0.279285	−	0.483735i
$376$	−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	$0.688068\pi$
$380$	15.6571			0.803193
$381$	−10.9464			−0.560799
$382$	−6.82179	−	11.8157i	−0.349033	−	0.604543i
$383$	−9.48764	−	16.4331i	−0.484796	−	0.839691i	0.515052	−	0.857159i	$-0.327773\pi$
$383$	−9.48764	−	16.4331i	−0.484796	−	0.839691i	−0.999847	+	0.0174681i	$0.994439\pi$
$384$	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
$387$	−5.26565			−0.267668
$388$	−3.63237	+	6.29145i	−0.184406	+	0.319400i
$389$	12.8986	+	22.3410i	0.653984	+	1.13273i	0.982147	+	0.188113i	$0.0602370\pi$
$389$	12.8986	+	22.3410i	0.653984	+	1.13273i	−0.328163	+	0.944621i	$0.606430\pi$
$390$	1.51901	−	8.16264i	0.0769183	−	0.413331i
$391$	15.0855			0.762906
$392$	5.13959	−	4.75232i	0.259589	−	0.240029i
$393$	−10.1210	−	17.5301i	−0.510538	−	0.884278i
$394$	7.84758	+	13.5924i	0.395355	+	0.684775i
$395$	13.2950	+	23.0276i	0.668942	+	1.15864i
$396$	−0.357320			−0.0179560
$397$	15.3672	+	26.6168i	0.771258	+	1.33586i	0.936874	+	0.349668i	$0.113706\pi$
$397$	15.3672	+	26.6168i	0.771258	+	1.33586i	−0.165616	+	0.986190i	$0.552961\pi$
$398$	−21.2287			−1.06410
$399$	−6.55767	−	16.7513i	−0.328294	−	0.838612i
$400$	−0.151388	−	0.262211i	−0.00756939	−	0.0131106i
$401$	16.3575			0.816857			0.408428	−	0.912790i	$-0.366077\pi$
$401$	16.3575			0.816857			0.408428	+	0.912790i	$0.366077\pi$
$402$	−1.40993	−	2.44206i	−0.0703207	−	0.121799i
$403$	−0.163745	+	0.879905i	−0.00815670	+	0.0438312i
$404$	−7.93411	+	13.7423i	−0.394737	+	0.683704i
$405$	−1.15139	−	1.99426i	−0.0572129	−	0.0990957i
$406$	2.06131	−	2.58022i	0.102301	−	0.128054i
$407$	1.68689	−	2.92178i	0.0836162	−	0.144827i
$408$	2.12412	−	3.67908i	0.105159	−	0.182141i
$409$	9.67044			0.478172			0.239086	−	0.970998i	$-0.423152\pi$
$409$	9.67044			0.478172			0.239086	+	0.970998i	$0.423152\pi$
$410$	−13.6150			−0.672396
$411$	2.67040	−	4.62527i	0.131721	−	0.228148i
$412$	8.14990	−	14.1160i	0.401517	−	0.695447i
$413$	6.90624	+	17.6417i	0.339834	+	0.868090i
$414$	1.77550	+	3.07526i	0.0872612	+	0.151141i
$415$	1.43720	−	2.48930i	0.0705493	−	0.122195i
$416$	2.73997	+	2.34362i	0.134338	+	0.114905i
$417$	4.49174	+	7.77993i	0.219962	+	0.380985i
$418$	2.42950			0.118831
$419$	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	$0.488334\pi$
$420$	−3.80278	+	4.76008i	−0.185556	+	0.232268i
$421$	32.6170			1.58966			0.794828	−	0.606835i	$-0.207561\pi$
$421$	32.6170			1.58966			0.794828	+	0.606835i	$0.207561\pi$
$422$	12.0787	+	20.9210i	0.587983	+	1.01842i
$423$	−8.38827			−0.407852
$424$	0.605101	+	1.04807i	0.0293863	+	0.0508986i
$425$	−0.643130	−	1.11393i	−0.0311964	−	0.0540338i
$426$	−0.794068	−	1.37537i	−0.0384727	−	0.0666367i
$427$	−22.6365	+	28.3350i	−1.09546	+	1.37122i
$428$	−7.62617			−0.368625
$429$	0.235704	−	1.26659i	0.0113799	−	0.0611516i
$430$	−6.06280	−	10.5011i	−0.292374	−	0.506407i
$431$	4.53244	−	7.85042i	0.218320	−	0.378141i	−0.735974	−	0.677009i	$-0.763276\pi$
$431$	4.53244	−	7.85042i	0.218320	−	0.378141i	0.954295	+	0.298868i	$0.0966090\pi$
$432$	1.00000			0.0481125
$433$	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
$436$	−5.50000	−	9.52628i	−0.263402	−	0.456226i
$437$	−12.0721	−	20.9094i	−0.577485	−	1.00023i
$438$	0.815753			0.0389782
$439$	−19.5790			−0.934454			−0.467227	−	0.884137i	$-0.654747\pi$
$439$	−19.5790			−0.934454			−0.467227	+	0.884137i	$0.654747\pi$
$440$	−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	−0.897509	−	0.440996i	$-0.854625\pi$
$443$	−1.40684	+	2.43672i	−0.0668410	+	0.115772i	0.830668	+	0.556768i	$0.187959\pi$
$444$	−4.72096	+	8.17694i	−0.224047	+	0.388060i
$445$	−0.846562	+	1.46629i	−0.0401309	+	0.0695088i
$446$	3.65611	+	6.33256i	0.173122	+	0.299856i
$447$	8.92074			0.421937
$448$	−0.964471	−	2.46370i	−0.0455669	−	0.116399i
$449$	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
$451$	−2.11263			−0.0994798
$452$	−6.46919	+	11.2050i	−0.304285	+	0.527037i
$453$	16.9599			0.796845
$454$	−29.5994			−1.38917
$455$	−14.3645	−	16.6196i	−0.673420	−	0.779141i
$456$	−6.79924			−0.318404
$457$	31.0764			1.45369			0.726845	−	0.686801i	$-0.240986\pi$
$457$	31.0764			1.45369			0.726845	+	0.686801i	$0.240986\pi$
$458$	3.62207	−	6.27360i	0.169248	−	0.293146i
$459$	4.24823			0.198290
$460$	−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	$0.788219\pi$
$462$	−0.590074	+	0.738617i	−0.0274527	+	0.0343636i
$463$	5.91153			0.274732			0.137366	−	0.990520i	$-0.456136\pi$
$463$	5.91153			0.274732			0.137366	+	0.990520i	$0.456136\pi$
$464$	−0.624116	−	1.08100i	−0.0289738	−	0.0501842i
$465$	−0.285811	+	0.495038i	−0.0132541	+	0.0229569i
$466$	−10.2092	+	17.6828i	−0.472930	+	0.819140i
$467$	−8.15760	+	14.1294i	−0.377488	+	0.653829i	−0.990696	−	0.136093i	$-0.956546\pi$
$467$	−8.15760	+	14.1294i	−0.377488	+	0.653829i	0.613208	+	0.789922i	$0.289879\pi$
$468$	−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
$471$	−7.31722			−0.337160
$472$	7.16066			0.329596
$473$	−0.940760	−	1.62944i	−0.0432562	−	0.0749219i
$474$	−5.77345	−	9.99992i	−0.265184	−	0.459311i
$475$	−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
$478$	6.02686			0.275662
$479$	−4.70183	+	8.14381i	−0.214832	+	0.372100i	−0.953221	−	0.302275i	$-0.902254\pi$
$479$	−4.70183	+	8.14381i	−0.214832	+	0.372100i	0.738388	+	0.674376i	$0.235587\pi$
$480$	1.15139	+	1.99426i	0.0525534	+	0.0910252i
$481$	−25.8706	−	22.1282i	−1.17960	−	1.00896i
$482$	−11.0094			−0.501466
$483$	9.28893	+	1.40830i	0.422661	+	0.0640799i
$484$	5.43616	+	9.41571i	0.247098	+	0.427987i
$485$	−8.36454	−	14.4878i	−0.379814	−	0.657857i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−33.5387			−1.51978			−0.759891	−	0.650051i	$-0.774748\pi$
$487$	−33.5387			−1.51978			−0.759891	+	0.650051i	$0.774748\pi$
$488$	6.85378	+	11.8711i	0.310256	+	0.537379i
$489$	−2.28626			−0.103388
$490$	3.55971	+	15.7215i	0.160812	+	0.710223i
$491$	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	$0.655498\pi$
$492$	5.91243			0.266553
$493$	−2.65139	−	4.59234i	−0.119413	−	0.206829i
$494$	4.48508	−	24.1012i	0.201793	−	1.08437i
$495$	0.411414	−	0.712590i	0.0184917	−	0.0320285i
$496$	−0.124116	−	0.214975i	−0.00557296	−	0.00965265i
$497$	−4.15434	−	0.629842i	−0.186348	−	0.0282523i
$498$	−0.624116	+	1.08100i	−0.0279673	+	0.0484408i
$499$	−11.2416	+	19.4710i	−0.503243	+	0.871643i	0.496750	+	0.867894i	$0.334527\pi$
$499$	−11.2416	+	19.4710i	−0.503243	+	0.871643i	−0.999993	+	0.00374928i	$0.998807\pi$
$500$	−10.8167			−0.483735
$501$	−3.90833			−0.174611
$502$	−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	$0.285313\pi$
$504$	1.65139	−	2.06710i	0.0735587	−	0.0920761i
$505$	−18.2705	−	31.6454i	−0.813026	−	1.40820i
$506$	−0.634423	+	1.09885i	−0.0282035	+	0.0488499i
$507$	−12.1297	−	4.67648i	−0.538701	−	0.207690i
$508$	5.47318	+	9.47982i	0.242833	+	0.420599i
$509$	−4.41811			−0.195829			−0.0979145	−	0.995195i	$-0.531217\pi$
$509$	−4.41811			−0.195829			−0.0979145	+	0.995195i	$0.531217\pi$
$510$	4.89136	+	8.47209i	0.216593	+	0.375150i
$511$	1.34712	−	1.68625i	0.0595933	−	0.0745951i
$512$	−1.00000			−0.0441942
$513$	−3.39962	−	5.88831i	−0.150097	−	0.259975i
$514$	−21.1905			−0.934672
$515$	18.7674	+	32.5061i	0.826990	+	1.43239i
$516$	2.63282	+	4.56018i	0.115904	+	0.200751i
$517$	−1.49865	−	2.59574i	−0.0659105	−	0.114160i
$518$	9.10645	+	23.2620i	0.400115	+	1.02207i
$519$	17.8332			0.782789
$520$	−7.82856	+	2.76581i	−0.343305	+	0.121289i
$521$	−6.51121	−	11.2777i	−0.285261	−	0.494087i	0.687411	−	0.726268i	$-0.258747\pi$
$521$	−6.51121	−	11.2777i	−0.285261	−	0.494087i	−0.972672	+	0.232181i	$0.925414\pi$
$522$	0.624116	−	1.08100i	0.0273168	−	0.0473141i
$523$	−5.63241			−0.246288			−0.123144	−	0.992389i	$-0.539298\pi$
$523$	−5.63241			−0.246288			−0.123144	+	0.992389i	$0.539298\pi$
$524$	−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
$527$	−0.527272	−	0.913262i	−0.0229683	−	0.0397823i
$528$	0.178660	+	0.309448i	0.00777518	+	0.0134670i
$529$	−10.3903			−0.451754
$530$	−2.78682			−0.121052
$531$	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
$535$	8.78067	−	15.2086i	0.379622	−	0.657524i
$536$	−1.40993	+	2.44206i	−0.0608995	+	0.105481i
$537$	2.80073	+	4.85100i	0.120860	+	0.209336i
$538$	−0.0495440			−0.00213599
$539$	0.552358	+	2.43949i	0.0237918	+	0.105076i
$540$	−1.15139	+	1.99426i	−0.0495478	+	0.0858194i
$541$	1.39035	−	2.40816i	0.0597758	−	0.103535i	−0.834589	−	0.550873i	$-0.814295\pi$
$541$	1.39035	−	2.40816i	0.0597758	−	0.103535i	0.894365	+	0.447339i	$0.147628\pi$
$542$	−0.0133160			−0.000571971
$543$	3.91613	−	6.78294i	0.168057	−	0.291084i
$544$	−4.24823			−0.182141
$545$	25.3305			1.08504
$546$	6.23792	+	7.21722i	0.266959	+	0.308869i
$547$	12.7497			0.545138			0.272569	−	0.962136i	$-0.412127\pi$
$547$	12.7497			0.545138			0.272569	+	0.962136i	$0.412127\pi$
$548$	−5.34081			−0.228148
$549$	−6.85378	+	11.8711i	−0.292512	+	0.506646i
$550$	0.108188			0.00461314
$551$	−4.24351	+	7.34998i	−0.180780	+	0.313120i
$552$	1.77550	−	3.07526i	0.0755704	−	0.130892i
$553$	−30.2051	−	4.57941i	−1.28445	−	0.194736i
$554$	−22.1450			−0.940853
$555$	−10.8713	−	18.8297i	−0.461461	−	0.799275i
$556$	4.49174	−	7.77993i	0.190492	−	0.329942i
$557$	22.6026	−	39.1489i	0.957703	−	1.65879i	0.229646	−	0.973274i	$-0.426243\pi$
$557$	22.6026	−	39.1489i	0.957703	−	1.65879i	0.728057	−	0.685517i	$-0.240424\pi$
$558$	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
$562$	4.44192			0.187371
$563$	−29.7159			−1.25238			−0.626188	−	0.779672i	$-0.715386\pi$
$563$	−29.7159			−1.25238			−0.626188	+	0.779672i	$0.715386\pi$
$564$	4.19414	+	7.26446i	0.176605	+	0.305889i
$565$	−14.8971	−	25.8025i	−0.626725	−	1.08552i
$566$	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
$569$	−14.4584			−0.606129			−0.303065	−	0.952970i	$-0.598010\pi$
$569$	−14.4584			−0.606129			−0.303065	+	0.952970i	$0.598010\pi$
$570$	7.82856	−	13.5595i	0.327902	−	0.567943i
$571$	−10.5516	−	18.2759i	−0.441569	−	0.764821i	0.556237	−	0.831024i	$-0.312245\pi$
$571$	−10.5516	−	18.2759i	−0.441569	−	0.764821i	−0.997806	+	0.0662032i	$0.978911\pi$
$572$	−1.21475	+	0.429169i	−0.0507913	+	0.0179445i
$573$	−13.6436			−0.569969
$574$	9.76371	−	12.2216i	0.407529	−	0.510120i
$575$	−0.537579	−	0.931114i	−0.0224186	−	0.0388302i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	8.22461	+	14.2454i	0.342395	+	0.593045i	0.984877	−	0.173255i	$-0.0554286\pi$
$577$	8.22461	+	14.2454i	0.342395	+	0.593045i	−0.642482	+	0.766301i	$0.722095\pi$
$578$	−1.04747			−0.0435690
$579$	−6.39962	−	11.0845i	−0.265959	−	0.460655i
$580$	2.87440			0.119353
$581$	1.20388	+	3.07526i	0.0499455	+	0.127583i
$582$	3.63237	+	6.29145i	0.150567	+	0.260789i
$583$	−0.432429			−0.0179094
$584$	−0.407877	−	0.706463i	−0.0168781	−	0.0292336i
$585$	−6.30955	−	5.39682i	−0.260868	−	0.223131i
$586$	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	$0.500688\pi$
$588$	−1.54584	−	6.82718i	−0.0637492	−	0.281548i
$589$	−0.843892	+	1.46166i	−0.0347720	+	0.0602268i
$590$	−8.24469	+	14.2802i	−0.339429	+	0.587908i
$591$	15.6952			0.645612
$592$	9.44192			0.388060
$593$	13.7451	−	23.8073i	0.564445	−	0.977648i	−0.432656	−	0.901559i	$-0.642423\pi$
$593$	13.7451	−	23.8073i	0.564445	−	0.977648i	0.997101	−	0.0760889i	$-0.0242433\pi$
$594$	−0.178660	+	0.309448i	−0.00733051	+	0.0126968i
$595$	25.5902	+	3.87975i	1.04910	+	0.159054i
$596$	−4.46037	−	7.72559i	−0.182704	−	0.316452i
$597$	−10.6144	+	18.3846i	−0.434417	+	0.752433i
$598$	9.72967	+	8.32220i	0.397876	+	0.340320i
$599$	17.0294	+	29.4957i	0.695801	+	1.20516i	0.969910	+	0.243464i	$0.0782836\pi$
$599$	17.0294	+	29.4957i	0.695801	+	1.20516i	−0.274109	+	0.961699i	$0.588383\pi$
$600$	−0.302776			−0.0123608
$601$	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	$0.775809\pi$
$602$	13.7742	+	2.08831i	0.561394	+	0.0851133i
$603$	−2.81985			−0.114833
$604$	−8.47995	−	14.6877i	−0.345044	−	0.597634i
$605$	−25.0365			−1.01788
$606$	7.93411	+	13.7423i	0.322301	+	0.558242i
$607$	16.8981	+	29.2684i	0.685874	+	1.18797i	0.973161	+	0.230124i	$0.0739132\pi$
$607$	16.8981	+	29.2684i	0.685874	+	1.18797i	−0.287287	+	0.957844i	$0.592753\pi$
$608$	3.39962	+	5.88831i	0.137873	+	0.238803i
$609$	−1.20388	−	3.07526i	−0.0487838	−	0.124616i
$610$	−31.5654			−1.27805
$611$	−28.5169	+	10.0750i	−1.15367	+	0.407590i
$612$	−2.12412	−	3.67908i	−0.0858623	−	0.148718i
$613$	12.0915	−	20.9432i	0.488373	−	0.845886i	−0.511538	−	0.859261i	$-0.670924\pi$
$613$	12.0915	−	20.9432i	0.488373	−	0.845886i	0.999911	+	0.0133746i	$0.00425738\pi$
$614$	20.3037			0.819390
$615$	−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	$0.912984\pi$
$618$	−8.14990	−	14.1160i	−0.327837	−	0.567830i
$619$	−2.12839	−	3.68647i	−0.0855470	−	0.148172i	0.820077	−	0.572253i	$-0.193930\pi$
$619$	−2.12839	−	3.68647i	−0.0855470	−	0.148172i	−0.905624	+	0.424081i	$0.860597\pi$
$620$	0.571621			0.0229569
$621$	3.55101			0.142497
$622$	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
$626$	10.8455	−	18.7850i	0.433474	−	0.750800i
$627$	1.21475	−	2.10401i	0.0485125	−	0.0840261i
$628$	3.65861	+	6.33689i	0.145994	+	0.252870i
$629$	40.1115			1.59935
$630$	2.22096	+	5.67334i	0.0884851	+	0.226031i
$631$	−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
$633$	24.1575			0.960173
$634$	−13.9135	+	24.0989i	−0.552576	+	0.957089i
$635$	−25.2070			−1.00031
$636$	1.21020			0.0479876
$637$	25.2200	−	0.976004i	0.999252	−	0.0386707i
$638$	0.446018			0.0176580
$639$	−1.58814			−0.0628257
$640$	1.15139	−	1.99426i	0.0455126	−	0.0788301i
$641$	28.1321			1.11115			0.555575	−	0.831466i	$-0.312498\pi$
$641$	28.1321			1.11115			0.555575	+	0.831466i	$0.312498\pi$
$642$	−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	$-0.00226816\pi$
$644$	−3.42484	−	8.74860i	−0.134958	−	0.344743i
$645$	−12.1256			−0.477445
$646$	14.4424	+	25.0149i	0.568227	+	0.984199i
$647$	20.5856	−	35.6554i	0.809305	−	1.40176i	−0.104041	−	0.994573i	$-0.533177\pi$
$647$	20.5856	−	35.6554i	0.809305	−	1.40176i	0.913346	−	0.407185i	$-0.133489\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−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
$653$	−41.7038			−1.63199			−0.815997	−	0.578056i	$-0.803811\pi$
$653$	−41.7038			−1.63199			−0.815997	+	0.578056i	$0.803811\pi$
$654$	−11.0000			−0.430134
$655$	−23.3065	−	40.3680i	−0.910659	−	1.57731i
$656$	−2.95621	−	5.12031i	−0.115421	−	0.199915i
$657$	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	$0.0116498\pi$
$660$	−0.822828			−0.0320285
$661$	−0.441636	+	0.764937i	−0.0171777	+	0.0297526i	−0.874486	−	0.485050i	$-0.838801\pi$
$661$	−0.441636	+	0.764937i	−0.0171777	+	0.0297526i	0.857309	+	0.514803i	$0.172135\pi$
$662$	−3.62058	−	6.27103i	−0.140718	−	0.243730i
$663$	14.4424	−	5.10246i	0.560895	−	0.198163i
$664$	1.24823			0.0484408
$665$	−15.1008	−	38.5744i	−0.585585	−	1.49585i
$666$	4.72096	+	8.17694i	0.182933	+	0.316850i
$667$	−2.21624	−	3.83864i	−0.0858131	−	0.148633i
$668$	1.95416	+	3.38471i	0.0756089	+	0.130958i
$669$	7.31222			0.282707
$670$	−3.24674	−	5.62353i	−0.125433	−	0.217256i
$671$	−4.89799			−0.189085
$672$	−2.61586	−	0.396592i	−0.100909	−	0.0152989i
$673$	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	$0.826155\pi$
$674$	0.380909			0.0146721
$675$	−0.151388	−	0.262211i	−0.00582692	−	0.0100925i
$676$	2.01492	+	12.8429i	0.0774967	+	0.493958i
$677$	21.8452	−	37.8370i	0.839580	−	1.45420i	−0.0506662	−	0.998716i	$-0.516134\pi$
$677$	21.8452	−	37.8370i	0.839580	−	1.45420i	0.890246	−	0.455480i	$-0.150532\pi$
$678$	6.46919	+	11.2050i	0.248448	+	0.430324i
$679$	19.0035	+	2.88114i	0.729289	+	0.110568i
$680$	4.89136	−	8.47209i	0.187575	−	0.324890i
$681$	−14.7997	+	25.6338i	−0.567125	+	0.982290i
$682$	0.0886980			0.00339642
$683$	8.31222			0.318058			0.159029	−	0.987274i	$-0.449164\pi$
$683$	8.31222			0.318058			0.159029	+	0.987274i	$0.449164\pi$
$684$	−3.39962	+	5.88831i	−0.129988	+	0.225145i
$685$	6.14934	−	10.6510i	0.234954	−	0.406952i
$686$	−16.6653	−	8.07892i	−0.636283	−	0.308455i
$687$	−3.62207	−	6.27360i	−0.138190	−	0.239353i
$688$	2.63282	−	4.56018i	0.100375	−	0.173855i
$689$	−0.798304	+	4.28980i	−0.0304130	+	0.163428i
$690$	4.08859	+	7.08164i	0.155650	+	0.269593i
$691$	28.0215			1.06599			0.532994	−	0.846119i	$-0.321067\pi$
$691$	28.0215			1.06599			0.532994	+	0.846119i	$0.321067\pi$
$692$	−8.91658	−	15.4440i	−0.338958	−	0.587092i
$693$	0.344625	+	0.880328i	0.0130912	+	0.0334409i
$694$	7.91540			0.300465
$695$	10.3435	+	17.9154i	0.392350	+	0.679571i
$696$	−1.24823			−0.0473141
$697$	−12.5587	−	21.7523i	−0.475694	−	0.823926i
$698$	3.90212	+	6.75867i	0.147697	+	0.255819i
$699$	10.2092	+	17.6828i	0.386146	+	0.668825i
$700$	−0.500000	+	0.625869i	−0.0188982	+	0.0236556i
$701$	27.7353			1.04755			0.523773	−	0.851858i	$-0.324524\pi$
$701$	27.7353			1.04755			0.523773	+	0.851858i	$0.324524\pi$
$702$	2.73997	+	2.34362i	0.103414	+	0.0884541i
$703$	−32.0989	−	55.5970i	−1.21063	−	2.09688i
$704$	0.178660	−	0.309448i	0.00673350	−	0.0116628i
$705$	−19.3163			−0.727495
$706$	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
$709$	6.54275	+	11.3324i	0.245718	+	0.425596i	0.962333	−	0.271873i	$-0.0876429\pi$
$709$	6.54275	+	11.3324i	0.245718	+	0.425596i	−0.716615	+	0.697469i	$0.754310\pi$
$710$	−1.82856	−	3.16716i	−0.0686246	−	0.118861i
$711$	−11.5469			−0.433043
$712$	−0.735254			−0.0275548
$713$	−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
$717$	3.01343	−	5.21941i	0.112539	−	0.194922i
$718$	−0.580329	+	1.00516i	−0.0216577	+	0.0375122i
$719$	−25.1659	−	43.5887i	−0.938531	−	1.62558i	−0.768213	−	0.640195i	$-0.778854\pi$
$719$	−25.1659	−	43.5887i	−0.938531	−	1.62558i	−0.170318	−	0.985389i	$-0.554480\pi$
$720$	2.30278			0.0858194
$721$	−42.6380	−	6.46437i	−1.58792	−	0.240746i
$722$	13.6148	−	23.5816i	0.506691	−	0.877615i
$723$	−5.50472	+	9.53445i	−0.204723	+	0.354590i
$724$	−7.83227			−0.291084
$725$	−0.188967	+	0.327300i	−0.00701806	+	0.0121556i
$726$	10.8723			0.403510
$727$	36.3505			1.34817			0.674083	−	0.738655i	$-0.264539\pi$
$727$	36.3505			1.34817			0.674083	+	0.738655i	$0.264539\pi$
$728$	3.13134	−	9.01081i	0.116055	−	0.333963i
$729$	1.00000			0.0370370
$730$	1.87850			0.0695263
$731$	11.1848	−	19.3727i	0.413686	−	0.716526i
$732$	13.7076			0.506646
$733$	5.18234	−	8.97608i	0.191414	−	0.331539i	−0.754305	−	0.656524i	$-0.772026\pi$
$733$	5.18234	−	8.97608i	0.191414	−	0.331539i	0.945719	+	0.324985i	$0.105359\pi$
$734$	−16.4136	+	28.4292i	−0.605837	+	1.04934i
$735$	15.3950	+	4.77793i	0.567855	+	0.176237i
$736$	−3.55101			−0.130892
$737$	−0.503795	−	0.872598i	−0.0185575	−	0.0321426i
$738$	2.95621	−	5.12031i	0.108820	−	0.188481i
$739$	−19.4077	+	33.6152i	−0.713925	+	1.23655i	0.249447	+	0.968388i	$0.419751\pi$
$739$	−19.4077	+	33.6152i	−0.713925	+	1.23655i	−0.963373	+	0.268166i	$0.913582\pi$
$740$	−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	$0.830634\pi$
$744$	−0.248231			−0.00910060
$745$	20.5425			0.752618
$746$	−14.7437	−	25.5368i	−0.539804	−	0.934967i
$747$	0.624116	+	1.08100i	0.0228352	+	0.0395517i
$748$	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
$751$	−27.0094			−0.985587			−0.492793	−	0.870146i	$-0.664024\pi$
$751$	−27.0094			−0.985587			−0.492793	+	0.870146i	$0.664024\pi$
$752$	4.19414	−	7.26446i	0.152944	−	0.264908i
$753$	12.6772	+	21.9575i	0.461982	+	0.800176i
$754$	0.823390	−	4.42460i	0.0299861	−	0.161134i
$755$	39.0548			1.42135
$756$	−0.964471	−	2.46370i	−0.0350775	−	0.0896037i
$757$	−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	$-0.352066\pi$
$758$	−8.57929	−	14.8598i	−0.311614	−	0.539731i
$759$	0.634423	+	1.09885i	0.0230281	+	0.0398858i
$760$	−15.6571			−0.567943
$761$	13.9594	+	24.1785i	0.506030	+	0.876469i	0.999976	+	0.00697633i	$0.00222065\pi$
$761$	13.9594	+	24.1785i	0.506030	+	0.876469i	−0.493946	+	0.869492i	$0.664446\pi$
$762$	10.9464			0.396545
$763$	−18.1653	+	22.7381i	−0.657627	+	0.823176i
$764$	6.82179	+	11.8157i	0.246804	+	0.427477i
$765$	9.78272			0.353695
$766$	9.48764	+	16.4331i	0.342802	+	0.593751i
$767$	19.6200	+	16.7818i	0.708438	+	0.605957i
$768$	−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	$0.789723\pi$
$770$	−1.35881	+	1.70087i	−0.0489680	+	0.0612951i
$771$	−10.5952	+	18.3515i	−0.381578	+	0.660913i
$772$	−6.39962	+	11.0845i	−0.230327	+	0.398939i
$773$	24.9104			0.895965			0.447982	−	0.894042i	$-0.352143\pi$
$773$	24.9104			0.895965			0.447982	+	0.894042i	$0.352143\pi$
$774$	5.26565			0.189270
$775$	−0.0375792	+	0.0650891i	−0.00134988	+	0.00233807i
$776$	3.63237	−	6.29145i	0.130395	−	0.225850i
$777$	24.6987	+	3.74459i	0.886062	+	0.134336i
$778$	−12.8986	−	22.3410i	−0.462437	−	0.800964i
$779$	−20.1000	+	34.8142i	−0.720157	+	1.24735i
$780$	−1.51901	+	8.16264i	−0.0543895	+	0.292269i
$781$	−0.283736	−	0.491446i	−0.0101529	−	0.0175853i
$782$	−15.0855			−0.539456
$783$	−0.624116	−	1.08100i	−0.0223041	−	0.0386318i
$784$	−5.13959	+	4.75232i	−0.183557	+	0.169726i
$785$	−16.8499			−0.601399
$786$	10.1210	+	17.5301i	0.361005	+	0.625279i
$787$	6.58606			0.234768			0.117384	−	0.993087i	$-0.462549\pi$
$787$	6.58606			0.234768			0.117384	+	0.993087i	$0.462549\pi$
$788$	−7.84758	−	13.5924i	−0.279558	−	0.484209i
$789$	4.56752	+	7.91118i	0.162608	+	0.281645i
$790$	−13.2950	−	23.0276i	−0.473014	−	0.819284i
$791$	33.8450	+	5.13126i	1.20339	+	0.182446i
$792$	0.357320			0.0126968
$793$	−9.04213	+	48.5891i	−0.321095	+	1.72545i
$794$	−15.3672	−	26.6168i	−0.545362	−	0.944595i
$795$	−1.39341	+	2.41346i	−0.0494192	+	0.0855966i
$796$	21.2287			0.752433
$797$	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
$800$	0.151388	+	0.262211i	0.00535237	+	0.00927057i
$801$	−0.367627	−	0.636749i	−0.0129895	−	0.0224984i
$802$	−16.3575			−0.577605
$803$	0.291485			0.0102863
$804$	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
$808$	7.93411	−	13.7423i	0.279121	−	0.483452i
$809$	−13.9120	+	24.0962i	−0.489119	+	0.847179i	−0.999922	−	0.0125190i	$-0.996015\pi$
$809$	−13.9120	+	24.0962i	−0.489119	+	0.847179i	0.510803	+	0.859698i	$0.329348\pi$
$810$	1.15139	+	1.99426i	0.0404556	+	0.0700712i
$811$	−15.9773			−0.561039			−0.280520	−	0.959848i	$-0.590507\pi$
$811$	−15.9773			−0.561039			−0.280520	+	0.959848i	$0.590507\pi$
$812$	−2.06131	+	2.58022i	−0.0723379	+	0.0905481i
$813$	−0.00665800	+	0.0115320i	−0.000233506	+	0.000404445i
$814$	−1.68689	+	2.92178i	−0.0591256	+	0.102408i
$815$	−5.26475			−0.184416
$816$	−2.12412	+	3.67908i	−0.0743589	+	0.128793i
$817$	−35.8024			−1.25257
$818$	−9.67044			−0.338119
$819$	9.36926	−	1.79359i	0.327388	−	0.0626731i
$820$	13.6150			0.475456
$821$	−44.2927			−1.54583			−0.772913	−	0.634512i	$-0.781201\pi$
$821$	−44.2927			−1.54583			−0.772913	+	0.634512i	$0.781201\pi$
$822$	−2.67040	+	4.62527i	−0.0931410	+	0.161325i
$823$	−6.43574			−0.224336			−0.112168	−	0.993689i	$-0.535779\pi$
$823$	−6.43574			−0.224336			−0.112168	+	0.993689i	$0.535779\pi$
$824$	−8.14990	+	14.1160i	−0.283915	+	0.491756i
$825$	0.0540939	−	0.0936934i	0.00188331	−	0.00326198i
$826$	−6.90624	−	17.6417i	−0.240299	−	0.613833i
$827$	16.6468			0.578865			0.289433	−	0.957198i	$-0.406533\pi$
$827$	16.6468			0.578865			0.289433	+	0.957198i	$0.406533\pi$
$828$	−1.77550	−	3.07526i	−0.0617030	−	0.106873i
$829$	−3.57356	+	6.18959i	−0.124115	+	0.214973i	−0.921387	−	0.388647i	$-0.872942\pi$
$829$	−3.57356	+	6.18959i	−0.124115	+	0.214973i	0.797272	+	0.603621i	$0.206276\pi$
$830$	−1.43720	+	2.48930i	−0.0498859	+	0.0864049i
$831$	−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
$835$	−9.00000			−0.311458
$836$	−2.42950			−0.0840261
$837$	−0.124116	−	0.214975i	−0.00429007	−	0.00743061i
$838$	−18.0902	−	31.3332i	−0.624916	−	1.08239i
$839$	−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
$842$	−32.6170			−1.12406
$843$	2.22096	−	3.84681i	0.0764939	−	0.132491i
$844$	−12.0787	−	20.9210i	−0.415767	−	0.720130i
$845$	−27.9321	−	10.7689i	−0.960892	−	0.370461i
$846$	8.38827			0.288395
$847$	17.9544	−	22.4742i	0.616921	−	0.772223i
$848$	−0.605101	−	1.04807i	−0.0207792	−	0.0359907i
$849$	−10.1061	−	17.5043i	−0.346841	−	0.600746i
$850$	0.643130	+	1.11393i	0.0220592	+	0.0382076i
$851$	33.5283			1.14934
$852$	0.794068	+	1.37537i	0.0272043	+	0.0471193i
$853$	−5.45343			−0.186722			−0.0933610	−	0.995632i	$-0.529761\pi$
$853$	−5.45343			−0.186722			−0.0933610	+	0.995632i	$0.529761\pi$
$854$	22.6365	−	28.3350i	0.774605	−	0.969602i
$855$	−7.82856	−	13.5595i	−0.267731	−	0.463724i
$856$	7.62617			0.260657
$857$	−5.69198	−	9.85879i	−0.194434	−	0.336770i	0.752281	−	0.658843i	$-0.228954\pi$
$857$	−5.69198	−	9.85879i	−0.194434	−	0.336770i	−0.946715	+	0.322073i	$0.895620\pi$
$858$	−0.235704	+	1.26659i	−0.00804681	+	0.0432407i
$859$	−1.39552	+	2.41711i	−0.0476145	+	0.0824708i	−0.888850	−	0.458198i	$-0.848495\pi$
$859$	−1.39552	+	2.41711i	−0.0476145	+	0.0824708i	0.841236	+	0.540668i	$0.181829\pi$
$860$	6.06280	+	10.5011i	0.206740	+	0.358084i
$861$	−5.70236	−	14.5664i	−0.194336	−	0.496422i
$862$	−4.53244	+	7.85042i	−0.154376	+	0.267386i
$863$	−10.2385	+	17.7336i	−0.348522	+	0.603658i	−0.985987	−	0.166821i	$-0.946650\pi$
$863$	−10.2385	+	17.7336i	−0.348522	+	0.603658i	0.637465	+	0.770479i	$0.279983\pi$
$864$	−1.00000			−0.0340207
$865$	41.0658			1.39628
$866$	−13.3558	+	23.1330i	−0.453850	+	0.786091i
$867$	−0.523735	+	0.907135i	−0.0177870	+	0.0308079i
$868$	−0.409926	+	0.513120i	−0.0139138	+	0.0174164i
$869$	−2.06297	−	3.57317i	−0.0699815	−	0.121211i
$870$	1.43720	−	2.48930i	0.0487256	−	0.0843952i
$871$	−9.58642	+	3.38686i	−0.324824	+	0.114760i
$872$	5.50000	+	9.52628i	0.186254	+	0.322601i
$873$	7.26475			0.245874
$874$	12.0721	+	20.9094i	0.408344	+	0.707272i
$875$	10.4323	+	26.6489i	0.352678	+	0.900899i
$876$	−0.815753			−0.0275617
$877$	1.45315	+	2.51693i	0.0490694	+	0.0849907i	0.889517	−	0.456902i	$-0.151041\pi$
$877$	1.45315	+	2.51693i	0.0490694	+	0.0849907i	−0.840447	+	0.541893i	$0.817708\pi$
$878$	19.5790			0.660759
$879$	−14.1231	−	24.4619i	−0.476360	−	0.825079i
$880$	0.411414	+	0.712590i	0.0138688	+	0.0240214i
$881$	−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	$-0.479552\pi$
$882$	−6.68543	−	2.07486i	−0.225110	−	0.0698640i
$883$	−35.2559			−1.18646			−0.593228	−	0.805034i	$-0.702147\pi$
$883$	−35.2559			−1.18646			−0.593228	+	0.805034i	$0.702147\pi$
$884$	−11.6400	−	9.95623i	−0.391497	−	0.334864i
$885$	8.24469	+	14.2802i	0.277142	+	0.480025i
$886$	1.40684	−	2.43672i	0.0472637	−	0.0818631i
$887$	36.3821			1.22159			0.610796	−	0.791788i	$-0.290850\pi$
$887$	36.3821			1.22159			0.610796	+	0.791788i	$0.290850\pi$
$888$	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
$891$	0.178660	+	0.309448i	0.00598533	+	0.0103669i
$892$	−3.65611	−	6.33256i	−0.122416	−	0.212030i
$893$	−57.0339			−1.90857
$894$	−8.92074			−0.298354
$895$	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
$899$	−0.154925	+	0.268338i	−0.00516704	+	0.00894958i
$900$	−0.151388	+	0.262211i	−0.00504626	+	0.00874038i
$901$	−2.57061	−	4.45242i	−0.0856394	−	0.148332i
$902$	2.11263			0.0703428
$903$	8.69563	−	10.8846i	0.289372	−	0.362218i
$904$	6.46919	−	11.2050i	0.215162	−	0.372672i
$905$	9.01798	−	15.6196i	0.299768	−	0.519213i
$906$	−16.9599			−0.563455
$907$	−2.31177	+	4.00410i	−0.0767609	+	0.132954i	−0.901851	−	0.432048i	$-0.857791\pi$
$907$	−2.31177	+	4.00410i	−0.0767609	+	0.132954i	0.825090	+	0.565002i	$0.191124\pi$
$908$	29.5994			0.982290
$909$	15.8682			0.526316
$910$	14.3645	+	16.6196i	0.476180	+	0.550936i
$911$	−35.1359			−1.16411			−0.582053	−	0.813151i	$-0.697750\pi$
$911$	−35.1359			−1.16411			−0.582053	+	0.813151i	$0.697750\pi$
$912$	6.79924			0.225145
$913$	−0.223009	+	0.386263i	−0.00738052	+	0.0127834i
$914$	−31.0764			−1.02791
$915$	−15.7827	+	27.3365i	−0.521761	+	0.903716i
$916$	−3.62207	+	6.27360i	−0.119676	+	0.207286i
$917$	52.9504	+	8.02784i	1.74857	+	0.265102i
$918$	−4.24823			−0.140213
$919$	0.362568	+	0.627987i	0.0119600	+	0.0207154i	0.871943	−	0.489607i	$-0.162860\pi$
$919$	0.362568	+	0.627987i	0.0119600	+	0.0207154i	−0.859983	+	0.510322i	$0.829526\pi$
$920$	4.08859	−	7.08164i	0.134797	−	0.233475i
$921$	10.1518	−	17.5835i	0.334514	−	0.579396i
$922$	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
$926$	−5.91153			−0.194265
$927$	−16.2998			−0.535356
$928$	0.624116	+	1.08100i	0.0204876	+	0.0354856i
$929$	2.43661	+	4.22034i	0.0799426	+	0.138465i	0.903225	−	0.429167i	$-0.141193\pi$
$929$	2.43661	+	4.22034i	0.0799426	+	0.138465i	−0.823282	+	0.567632i	$0.807860\pi$
$930$	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
$933$	23.4057			0.766268
$934$	8.15760	−	14.1294i	0.266925	−	0.462327i
$935$	1.74778	+	3.02725i	0.0571585	+	0.0990015i
$936$	0.659645	−	3.54470i	0.0215612	−	0.115862i
$937$	−54.0847			−1.76687			−0.883435	−	0.468555i	$-0.844775\pi$
$937$	−54.0847			−1.76687			−0.883435	+	0.468555i	$0.844775\pi$
$938$	7.37633	+	1.11833i	0.240846	+	0.0365148i
$939$	−10.8455	−	18.7850i	−0.353930	−	0.613025i
$940$	9.65816	+	16.7284i	0.315014	+	0.545621i
$941$	13.4459	+	23.2890i	0.438324	+	0.759199i	0.997560	−	0.0698088i	$-0.0222389\pi$
$941$	13.4459	+	23.2890i	0.438324	+	0.759199i	−0.559236	+	0.829008i	$0.688906\pi$
$942$	7.31722			0.238408
$943$	−10.4975	−	18.1823i	−0.341847	−	0.592096i
$944$	−7.16066			−0.233060
$945$	6.02373	+	0.913262i	0.195952	+	0.0297084i
$946$	0.940760	+	1.62944i	0.0305868	+	0.0529778i
$947$	15.3426			0.498568			0.249284	−	0.968430i	$-0.419805\pi$
$947$	15.3426			0.498568			0.249284	+	0.968430i	$0.419805\pi$
$948$	5.77345	+	9.99992i	0.187513	+	0.324782i
$949$	0.538108	−	2.89160i	0.0174677	−	0.0938652i
$950$	1.02932	−	1.78284i	0.0333956	−	0.0578429i
$951$	13.9135	+	24.0989i	0.451176	+	0.781460i
$952$	4.09729	+	10.4663i	0.132794	+	0.339216i
$953$	−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
$955$	−31.4181			−1.01667
$956$	−6.02686			−0.194922
$957$	0.223009	−	0.386263i	0.00720886	−	0.0124861i
$958$	4.70183	−	8.14381i	0.151909	−	0.263115i
$959$	5.15105	+	13.1581i	0.166336	+	0.424898i
$960$	−1.15139	−	1.99426i	−0.0371609	−	0.0643645i
$961$	15.4692	−	26.7934i	0.499006	−	0.864304i
$962$	25.8706	+	22.1282i	0.834102	+	0.713443i
$963$	3.81308	+	6.60445i	0.122875	+	0.212826i
$964$	11.0094			0.354590
$965$	−14.7369	−	25.5250i	−0.474397	−	0.821680i
$966$	−9.28893	−	1.40830i	−0.298866	−	0.0453113i
$967$	−35.8272			−1.15213			−0.576063	−	0.817405i	$-0.695412\pi$
$967$	−35.8272			−1.15213			−0.576063	+	0.817405i	$0.695412\pi$
$968$	−5.43616	−	9.41571i	−0.174725	−	0.302632i
$969$	28.8847			0.927911
$970$	8.36454	+	14.4878i	0.268569	+	0.465175i
$971$	−2.30910	−	3.99947i	−0.0741024	−	0.128349i	0.826593	−	0.562800i	$-0.190276\pi$
$971$	−2.30910	−	3.99947i	−0.0741024	−	0.128349i	−0.900696	+	0.434451i	$0.856942\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−23.4995	−	3.56278i	−0.753360	−	0.114217i
$974$	33.5387			1.07465
$975$	−0.829597	−	0.709590i	−0.0265684	−	0.0227251i
$976$	−6.85378	−	11.8711i	−0.219384	−	0.379985i
$977$	6.57634	−	11.3906i	0.210396	−	0.364416i	−0.741443	−	0.671016i	$-0.765858\pi$
$977$	6.57634	−	11.3906i	0.210396	−	0.364416i	0.951838	+	0.306600i	$0.0991914\pi$
$978$	2.28626			0.0731066
$979$	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
$982$	−11.7456	−	20.3440i	−0.374817	−	0.649202i
$983$	−3.44034	−	5.95885i	−0.109730	−	0.190058i	0.805931	−	0.592010i	$-0.201665\pi$
$983$	−3.44034	−	5.95885i	−0.109730	−	0.190058i	−0.915661	+	0.401952i	$0.868332\pi$
$984$	−5.91243			−0.188481
$985$	36.1424			1.15159
$986$	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
$990$	−0.411414	+	0.712590i	−0.0130756	+	0.0226476i
$991$	−7.74885	+	13.4214i	−0.246150	+	0.426345i	−0.962454	−	0.271443i	$-0.912499\pi$
$991$	−7.74885	+	13.4214i	−0.246150	+	0.426345i	0.716304	+	0.697788i	$0.245832\pi$
$992$	0.124116	+	0.214975i	0.00394068	+	0.00682545i
$993$	−7.24116			−0.229791
$994$	4.15434	+	0.629842i	0.131768	+	0.0199774i
$995$	−24.4425	+	42.3357i	−0.774880	+	1.34213i
$996$	0.624116	−	1.08100i	0.0197759	−	0.0342528i
$997$	45.9131			1.45408			0.727041	−	0.686595i	$-0.240895\pi$
$997$	45.9131			1.45408			0.727041	+	0.686595i	$0.240895\pi$
$998$	11.2416	−	19.4710i	0.355847	−	0.616345i
$999$	9.44192			0.298729

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.b.289.1	✓	8	1.1	even	1	trivial
546.2.j.b.529.1	yes	8	91.74	even	3	inner
546.2.k.d.373.2	yes	8	13.9	even	3
546.2.k.d.445.2	yes	8	7.4	even	3
1638.2.m.i.289.3		8	3.2	odd	2
1638.2.m.i.1621.3		8	273.74	odd	6
1638.2.p.g.919.4		8	39.35	odd	6
1638.2.p.g.991.4		8	21.11	odd	6

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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-1.15139 + 1.99426i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.964471 - 2.46370i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-1.15139 + 1.99426i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.964471 - 2.46370i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.15139 - 1.99426i) q^{10} +(0.178660 - 0.309448i) 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} +1.00000 q^{16} +4.24823 q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.39962 - 5.88831i) q^{19} +(-1.15139 + 1.99426i) q^{20} +(2.61586 + 0.396592i) q^{21} +(-0.178660 + 0.309448i) q^{22} +3.55101 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.151388 - 0.262211i) q^{25} +(2.73997 + 2.34362i) q^{26} +1.00000 q^{27} +(-0.964471 - 2.46370i) q^{28} +(-0.624116 - 1.08100i) q^{29} +(1.15139 + 1.99426i) q^{30} +(-0.124116 - 0.214975i) q^{31} -1.00000 q^{32} +(0.178660 + 0.309448i) q^{33} -4.24823 q^{34} +(6.02373 + 0.913262i) q^{35} +(-0.500000 - 0.866025i) q^{36} +9.44192 q^{37} +(3.39962 + 5.88831i) q^{38} +(3.39962 - 1.20108i) q^{39} +(1.15139 - 1.99426i) q^{40} +(-2.95621 - 5.12031i) q^{41} +(-2.61586 - 0.396592i) q^{42} +(2.63282 - 4.56018i) q^{43} +(0.178660 - 0.309448i) q^{44} +2.30278 q^{45} -3.55101 q^{46} +(4.19414 - 7.26446i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-5.13959 + 4.75232i) q^{49} +(0.151388 + 0.262211i) q^{50} +(-2.12412 + 3.67908i) q^{51} +(-2.73997 - 2.34362i) q^{52} +(-0.605101 - 1.04807i) q^{53} -1.00000 q^{54} +(0.411414 + 0.712590i) q^{55} +(0.964471 + 2.46370i) q^{56} +6.79924 q^{57} +(0.624116 + 1.08100i) q^{58} -7.16066 q^{59} +(-1.15139 - 1.99426i) q^{60} +(-6.85378 - 11.8711i) q^{61} +(0.124116 + 0.214975i) q^{62} +(-1.65139 + 2.06710i) q^{63} +1.00000 q^{64} +(7.82856 - 2.76581i) q^{65} +(-0.178660 - 0.309448i) q^{66} +(1.40993 - 2.44206i) q^{67} +4.24823 q^{68} +(-1.77550 + 3.07526i) q^{69} +(-6.02373 - 0.913262i) q^{70} +(0.794068 - 1.37537i) q^{71} +(0.500000 + 0.866025i) q^{72} +(0.407877 + 0.706463i) q^{73} -9.44192 q^{74} +0.302776 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} +(-1.15139 + 1.99426i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.95621 + 5.12031i) q^{82} -1.24823 q^{83} +(2.61586 + 0.396592i) q^{84} +(-4.89136 + 8.47209i) q^{85} +(-2.63282 + 4.56018i) q^{86} +1.24823 q^{87} +(-0.178660 + 0.309448i) q^{88} +0.735254 q^{89} -2.30278 q^{90} +(-3.13134 + 9.01081i) q^{91} +3.55101 q^{92} +0.248231 q^{93} +(-4.19414 + 7.26446i) q^{94} +15.6571 q^{95} +(0.500000 - 0.866025i) q^{96} +(-3.63237 + 6.29145i) q^{97} +(5.13959 - 4.75232i) q^{98} -0.357320 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 - 4 * q^9	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 2 q^{11} - 4 q^{12} + 7 q^{13} - 3 q^{14} - 2 q^{15} + 8 q^{16} + 12 q^{17} + 4 q^{18} + 2 q^{19} - 2 q^{20} + 3 q^{21} + 2 q^{22} - 8 q^{23} + 4 q^{24} + 6 q^{25} - 7 q^{26} + 8 q^{27} + 3 q^{28} + 6 q^{29} + 2 q^{30} + 10 q^{31} - 8 q^{32} - 2 q^{33} - 12 q^{34} + 8 q^{35} - 4 q^{36} + 24 q^{37} - 2 q^{38} - 2 q^{39} + 2 q^{40} - 6 q^{41} - 3 q^{42} - 4 q^{43} - 2 q^{44} + 4 q^{45} + 8 q^{46} - 17 q^{47} - 4 q^{48} + 17 q^{49} - 6 q^{50} - 6 q^{51} + 7 q^{52} + 3 q^{53} - 8 q^{54} + 25 q^{55} - 3 q^{56} - 4 q^{57} - 6 q^{58} - 2 q^{60} - 4 q^{61} - 10 q^{62} - 6 q^{63} + 8 q^{64} + 12 q^{65} + 2 q^{66} - 7 q^{67} + 12 q^{68} + 4 q^{69} - 8 q^{70} + 6 q^{71} + 4 q^{72} - 19 q^{73} - 24 q^{74} - 12 q^{75} + 2 q^{76} - 10 q^{77} + 2 q^{78} + 24 q^{79} - 2 q^{80} - 4 q^{81} + 6 q^{82} + 12 q^{83} + 3 q^{84} - 3 q^{85} + 4 q^{86} - 12 q^{87} + 2 q^{88} + 14 q^{89} - 4 q^{90} + 40 q^{91} - 8 q^{92} - 20 q^{93} + 17 q^{94} + 24 q^{95} + 4 q^{96} - 25 q^{97} - 17 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 - 4 * q^9 + 2 * q^10 - 2 * q^11 - 4 * q^12 + 7 * q^13 - 3 * q^14 - 2 * q^15 + 8 * q^16 + 12 * q^17 + 4 * q^18 + 2 * q^19 - 2 * q^20 + 3 * q^21 + 2 * q^22 - 8 * q^23 + 4 * q^24 + 6 * q^25 - 7 * q^26 + 8 * q^27 + 3 * q^28 + 6 * q^29 + 2 * q^30 + 10 * q^31 - 8 * q^32 - 2 * q^33 - 12 * q^34 + 8 * q^35 - 4 * q^36 + 24 * q^37 - 2 * q^38 - 2 * q^39 + 2 * q^40 - 6 * q^41 - 3 * q^42 - 4 * q^43 - 2 * q^44 + 4 * q^45 + 8 * q^46 - 17 * q^47 - 4 * q^48 + 17 * q^49 - 6 * q^50 - 6 * q^51 + 7 * q^52 + 3 * q^53 - 8 * q^54 + 25 * q^55 - 3 * q^56 - 4 * q^57 - 6 * q^58 - 2 * q^60 - 4 * q^61 - 10 * q^62 - 6 * q^63 + 8 * q^64 + 12 * q^65 + 2 * q^66 - 7 * q^67 + 12 * q^68 + 4 * q^69 - 8 * q^70 + 6 * q^71 + 4 * q^72 - 19 * q^73 - 24 * q^74 - 12 * q^75 + 2 * q^76 - 10 * q^77 + 2 * q^78 + 24 * q^79 - 2 * q^80 - 4 * q^81 + 6 * q^82 + 12 * q^83 + 3 * q^84 - 3 * q^85 + 4 * q^86 - 12 * q^87 + 2 * q^88 + 14 * q^89 - 4 * q^90 + 40 * q^91 - 8 * q^92 - 20 * q^93 + 17 * q^94 + 24 * q^95 + 4 * q^96 - 25 * q^97 - 17 * q^98 + 4 * q^99

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