LMFDB - Embedded newform 546.2.l.h.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(211,546)]

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, 0, 2]))

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

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

chi := DirichletCharacter("546.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.l (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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.211
Dual form			546.2.l.h.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +4.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +4.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.00000 + 3.46410i) q^{10} +(1.50000 + 2.59808i) q^{11} -1.00000 q^{12} +(-2.50000 - 2.59808i) q^{13} -1.00000 q^{14} +(2.00000 + 3.46410i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.50000 - 4.33013i) q^{17} -1.00000 q^{18} +(-1.50000 + 2.59808i) q^{19} +(-2.00000 + 3.46410i) q^{20} -1.00000 q^{21} +(-1.50000 + 2.59808i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +11.0000 q^{25} +(1.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(4.50000 + 7.79423i) q^{29} +(-2.00000 + 3.46410i) q^{30} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +5.00000 q^{34} +(-2.00000 + 3.46410i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-2.00000 - 3.46410i) q^{37} -3.00000 q^{38} +(1.00000 - 3.46410i) q^{39} -4.00000 q^{40} +(-2.50000 - 4.33013i) q^{41} +(-0.500000 - 0.866025i) q^{42} -3.00000 q^{44} +(-2.00000 + 3.46410i) q^{45} +(3.00000 - 5.19615i) q^{46} -3.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(5.50000 + 9.52628i) q^{50} +5.00000 q^{51} +(3.50000 - 0.866025i) q^{52} -11.0000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(6.00000 + 10.3923i) q^{55} +(0.500000 - 0.866025i) q^{56} -3.00000 q^{57} +(-4.50000 + 7.79423i) q^{58} +(-1.00000 + 1.73205i) q^{59} -4.00000 q^{60} +(0.500000 - 0.866025i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(-10.0000 - 10.3923i) q^{65} -3.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +(2.50000 + 4.33013i) q^{68} +(3.00000 - 5.19615i) q^{69} -4.00000 q^{70} +(-3.00000 + 5.19615i) q^{71} +(0.500000 - 0.866025i) q^{72} +12.0000 q^{73} +(2.00000 - 3.46410i) q^{74} +(5.50000 + 9.52628i) q^{75} +(-1.50000 - 2.59808i) q^{76} -3.00000 q^{77} +(3.50000 - 0.866025i) q^{78} +11.0000 q^{79} +(-2.00000 - 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.50000 - 4.33013i) q^{82} +6.00000 q^{83} +(0.500000 - 0.866025i) q^{84} +(10.0000 - 17.3205i) q^{85} +(-4.50000 + 7.79423i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(-3.50000 - 6.06218i) q^{89} -4.00000 q^{90} +(3.50000 - 0.866025i) q^{91} +6.00000 q^{92} +(-2.00000 - 3.46410i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-6.00000 + 10.3923i) q^{95} +1.00000 q^{96} +(6.00000 - 10.3923i) q^{97} +(0.500000 - 0.866025i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} + 8 q^{5} - q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 + 8 * q^5 - q^6 - q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} + 8 q^{5} - q^{6} - q^{7} - 2 q^{8} - q^{9} + 4 q^{10} + 3 q^{11} - 2 q^{12} - 5 q^{13} - 2 q^{14} + 4 q^{15} - q^{16} + 5 q^{17} - 2 q^{18} - 3 q^{19} - 4 q^{20} - 2 q^{21} - 3 q^{22} - 6 q^{23} - q^{24} + 22 q^{25} + 2 q^{26} - 2 q^{27} - q^{28} + 9 q^{29} - 4 q^{30} - 8 q^{31} + q^{32} - 3 q^{33} + 10 q^{34} - 4 q^{35} - q^{36} - 4 q^{37} - 6 q^{38} + 2 q^{39} - 8 q^{40} - 5 q^{41} - q^{42} - 6 q^{44} - 4 q^{45} + 6 q^{46} - 6 q^{47} + q^{48} - q^{49} + 11 q^{50} + 10 q^{51} + 7 q^{52} - 22 q^{53} - q^{54} + 12 q^{55} + q^{56} - 6 q^{57} - 9 q^{58} - 2 q^{59} - 8 q^{60} + q^{61} - 4 q^{62} - q^{63} + 2 q^{64} - 20 q^{65} - 6 q^{66} - 2 q^{67} + 5 q^{68} + 6 q^{69} - 8 q^{70} - 6 q^{71} + q^{72} + 24 q^{73} + 4 q^{74} + 11 q^{75} - 3 q^{76} - 6 q^{77} + 7 q^{78} + 22 q^{79} - 4 q^{80} - q^{81} + 5 q^{82} + 12 q^{83} + q^{84} + 20 q^{85} - 9 q^{87} - 3 q^{88} - 7 q^{89} - 8 q^{90} + 7 q^{91} + 12 q^{92} - 4 q^{93} - 3 q^{94} - 12 q^{95} + 2 q^{96} + 12 q^{97} + q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + 8 * q^5 - q^6 - q^7 - 2 * q^8 - q^9 + 4 * q^10 + 3 * q^11 - 2 * q^12 - 5 * q^13 - 2 * q^14 + 4 * q^15 - q^16 + 5 * q^17 - 2 * q^18 - 3 * q^19 - 4 * q^20 - 2 * q^21 - 3 * q^22 - 6 * q^23 - q^24 + 22 * q^25 + 2 * q^26 - 2 * q^27 - q^28 + 9 * q^29 - 4 * q^30 - 8 * q^31 + q^32 - 3 * q^33 + 10 * q^34 - 4 * q^35 - q^36 - 4 * q^37 - 6 * q^38 + 2 * q^39 - 8 * q^40 - 5 * q^41 - q^42 - 6 * q^44 - 4 * q^45 + 6 * q^46 - 6 * q^47 + q^48 - q^49 + 11 * q^50 + 10 * q^51 + 7 * q^52 - 22 * q^53 - q^54 + 12 * q^55 + q^56 - 6 * q^57 - 9 * q^58 - 2 * q^59 - 8 * q^60 + q^61 - 4 * q^62 - q^63 + 2 * q^64 - 20 * q^65 - 6 * q^66 - 2 * q^67 + 5 * q^68 + 6 * q^69 - 8 * q^70 - 6 * q^71 + q^72 + 24 * q^73 + 4 * q^74 + 11 * q^75 - 3 * q^76 - 6 * q^77 + 7 * q^78 + 22 * q^79 - 4 * q^80 - q^81 + 5 * q^82 + 12 * q^83 + q^84 + 20 * q^85 - 9 * q^87 - 3 * q^88 - 7 * q^89 - 8 * q^90 + 7 * q^91 + 12 * q^92 - 4 * q^93 - 3 * q^94 - 12 * q^95 + 2 * q^96 + 12 * q^97 + q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	4.00000			1.78885			0.894427	−	0.447214i	$-0.147584\pi$
$5$	4.00000			1.78885			0.894427	+	0.447214i	$0.147584\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.00000	+	3.46410i	0.632456	+	1.09545i
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$	−1.00000			−0.288675
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$14$	−1.00000			−0.267261
$15$	2.00000	+	3.46410i	0.516398	+	0.894427i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.50000	−	4.33013i	0.606339	−	1.05021i	−0.385499	−	0.922708i	$-0.625971\pi$
$17$	2.50000	−	4.33013i	0.606339	−	1.05021i	0.991838	−	0.127502i	$-0.0406959\pi$
$18$	−1.00000			−0.235702
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	−0.985194	−	0.171442i	$-0.945157\pi$
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	0.641071	+	0.767482i	$0.278491\pi$
$20$	−2.00000	+	3.46410i	−0.447214	+	0.774597i
$21$	−1.00000			−0.218218
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	11.0000			2.20000
$26$	1.00000	−	3.46410i	0.196116	−	0.679366i
$27$	−1.00000			−0.192450
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	4.50000	+	7.79423i	0.835629	+	1.44735i	0.893517	+	0.449029i	$0.148230\pi$
$29$	4.50000	+	7.79423i	0.835629	+	1.44735i	−0.0578882	+	0.998323i	$0.518437\pi$
$30$	−2.00000	+	3.46410i	−0.365148	+	0.632456i
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$	5.00000			0.857493
$35$	−2.00000	+	3.46410i	−0.338062	+	0.585540i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	0.653476	−	0.756948i	$-0.273310\pi$
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	−0.982274	+	0.187453i	$0.939977\pi$
$38$	−3.00000			−0.486664
$39$	1.00000	−	3.46410i	0.160128	−	0.554700i
$40$	−4.00000			−0.632456
$41$	−2.50000	−	4.33013i	−0.390434	−	0.676252i	0.602072	−	0.798441i	$-0.294342\pi$
$41$	−2.50000	−	4.33013i	−0.390434	−	0.676252i	−0.992507	+	0.122189i	$0.961009\pi$
$42$	−0.500000	−	0.866025i	−0.0771517	−	0.133631i
$43$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$43$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$44$	−3.00000			−0.452267
$45$	−2.00000	+	3.46410i	−0.298142	+	0.516398i
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	5.50000	+	9.52628i	0.777817	+	1.34722i
$51$	5.00000			0.700140
$52$	3.50000	−	0.866025i	0.485363	−	0.120096i
$53$	−11.0000			−1.51097			−0.755483	−	0.655168i	$-0.772598\pi$
$53$	−11.0000			−1.51097			−0.755483	+	0.655168i	$0.772598\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	6.00000	+	10.3923i	0.809040	+	1.40130i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	−3.00000			−0.397360
$58$	−4.50000	+	7.79423i	−0.590879	+	1.02343i
$59$	−1.00000	+	1.73205i	−0.130189	+	0.225494i	−0.923749	−	0.382998i	$-0.874892\pi$
$59$	−1.00000	+	1.73205i	−0.130189	+	0.225494i	0.793560	+	0.608492i	$0.208225\pi$
$60$	−4.00000			−0.516398
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$	−0.500000	−	0.866025i	−0.0629941	−	0.109109i
$64$	1.00000			0.125000
$65$	−10.0000	−	10.3923i	−1.24035	−	1.28901i
$66$	−3.00000			−0.369274
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	2.50000	+	4.33013i	0.303170	+	0.525105i
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$	−4.00000			−0.478091
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	12.0000			1.40449			0.702247	−	0.711934i	$-0.252180\pi$
$73$	12.0000			1.40449			0.702247	+	0.711934i	$0.252180\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$	5.50000	+	9.52628i	0.635085	+	1.10000i
$76$	−1.50000	−	2.59808i	−0.172062	−	0.298020i
$77$	−3.00000			−0.341882
$78$	3.50000	−	0.866025i	0.396297	−	0.0980581i
$79$	11.0000			1.23760			0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000			1.23760			0.618798	+	0.785550i	$0.287620\pi$
$80$	−2.00000	−	3.46410i	−0.223607	−	0.387298i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.50000	−	4.33013i	0.276079	−	0.478183i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	0.500000	−	0.866025i	0.0545545	−	0.0944911i
$85$	10.0000	−	17.3205i	1.08465	−	1.87867i
$86$		0			0
$87$	−4.50000	+	7.79423i	−0.482451	+	0.835629i
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	−3.50000	−	6.06218i	−0.370999	−	0.642590i	0.618720	−	0.785611i	$-0.287651\pi$
$89$	−3.50000	−	6.06218i	−0.370999	−	0.642590i	−0.989720	+	0.143022i	$0.954318\pi$
$90$	−4.00000			−0.421637
$91$	3.50000	−	0.866025i	0.366900	−	0.0907841i
$92$	6.00000			0.625543
$93$	−2.00000	−	3.46410i	−0.207390	−	0.359211i
$94$	−1.50000	−	2.59808i	−0.154713	−	0.267971i
$95$	−6.00000	+	10.3923i	−0.615587	+	1.06623i
$96$	1.00000			0.102062
$97$	6.00000	−	10.3923i	0.609208	−	1.05518i	−0.382164	−	0.924095i	$-0.624821\pi$
$97$	6.00000	−	10.3923i	0.609208	−	1.05518i	0.991371	−	0.131084i	$-0.0418458\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$	−3.00000			−0.301511
$100$	−5.50000	+	9.52628i	−0.550000	+	0.952628i
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	0.502477	−	0.864590i	$-0.332422\pi$
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	−0.999996	+	0.00286291i	$0.999089\pi$
$102$	2.50000	+	4.33013i	0.247537	+	0.428746i
$103$	20.0000			1.97066			0.985329	−	0.170664i	$-0.0545913\pi$
$103$	20.0000			1.97066			0.985329	+	0.170664i	$0.0545913\pi$
$104$	2.50000	+	2.59808i	0.245145	+	0.254762i
$105$	−4.00000			−0.390360
$106$	−5.50000	−	9.52628i	−0.534207	−	0.925274i
$107$	−8.50000	−	14.7224i	−0.821726	−	1.42327i	−0.904396	−	0.426694i	$-0.859678\pi$
$107$	−8.50000	−	14.7224i	−0.821726	−	1.42327i	0.0826699	−	0.996577i	$-0.473655\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−6.00000	+	10.3923i	−0.572078	+	0.990867i
$111$	2.00000	−	3.46410i	0.189832	−	0.328798i
$112$	1.00000			0.0944911
$113$	−6.00000	+	10.3923i	−0.564433	+	0.977626i	0.432670	+	0.901553i	$0.357572\pi$
$113$	−6.00000	+	10.3923i	−0.564433	+	0.977626i	−0.997102	+	0.0760733i	$0.975762\pi$
$114$	−1.50000	−	2.59808i	−0.140488	−	0.243332i
$115$	−12.0000	−	20.7846i	−1.11901	−	1.93817i
$116$	−9.00000			−0.835629
$117$	3.50000	−	0.866025i	0.323575	−	0.0800641i
$118$	−2.00000			−0.184115
$119$	2.50000	+	4.33013i	0.229175	+	0.396942i
$120$	−2.00000	−	3.46410i	−0.182574	−	0.316228i
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	1.00000			0.0905357
$123$	2.50000	−	4.33013i	0.225417	−	0.390434i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	24.0000			2.14663
$126$	0.500000	−	0.866025i	0.0445435	−	0.0771517i
$127$	−4.00000	−	6.92820i	−0.354943	−	0.614779i	0.632166	−	0.774833i	$-0.282166\pi$
$127$	−4.00000	−	6.92820i	−0.354943	−	0.614779i	−0.987108	+	0.160055i	$0.948833\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	4.00000	−	13.8564i	0.350823	−	1.21529i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$	−1.50000	−	2.59808i	−0.130558	−	0.226134i
$133$	−1.50000	−	2.59808i	−0.130066	−	0.225282i
$134$	1.00000	−	1.73205i	0.0863868	−	0.149626i
$135$	−4.00000			−0.344265
$136$	−2.50000	+	4.33013i	−0.214373	+	0.371305i
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	−0.169226	−	0.985577i	$-0.554127\pi$
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	0.938148	−	0.346235i	$-0.112540\pi$
$138$	6.00000			0.510754
$139$	−6.50000	+	11.2583i	−0.551323	+	0.954919i	0.446857	+	0.894606i	$0.352543\pi$
$139$	−6.50000	+	11.2583i	−0.551323	+	0.954919i	−0.998179	+	0.0603135i	$0.980790\pi$
$140$	−2.00000	−	3.46410i	−0.169031	−	0.292770i
$141$	−1.50000	−	2.59808i	−0.126323	−	0.218797i
$142$	−6.00000			−0.503509
$143$	3.00000	−	10.3923i	0.250873	−	0.869048i
$144$	1.00000			0.0833333
$145$	18.0000	+	31.1769i	1.49482	+	2.58910i
$146$	6.00000	+	10.3923i	0.496564	+	0.860073i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$	4.00000			0.328798
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	0.216394	+	0.976306i	$0.430570\pi$
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	−0.953703	+	0.300750i	$0.902763\pi$
$150$	−5.50000	+	9.52628i	−0.449073	+	0.777817i
$151$	−11.0000			−0.895167			−0.447584	−	0.894242i	$-0.647715\pi$
$151$	−11.0000			−0.895167			−0.447584	+	0.894242i	$0.647715\pi$
$152$	1.50000	−	2.59808i	0.121666	−	0.210732i
$153$	2.50000	+	4.33013i	0.202113	+	0.350070i
$154$	−1.50000	−	2.59808i	−0.120873	−	0.209359i
$155$	−16.0000			−1.28515
$156$	2.50000	+	2.59808i	0.200160	+	0.208013i
$157$	−2.00000			−0.159617			−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000			−0.159617			−0.0798087	+	0.996810i	$0.525431\pi$
$158$	5.50000	+	9.52628i	0.437557	+	0.757870i
$159$	−5.50000	−	9.52628i	−0.436178	−	0.755483i
$160$	2.00000	−	3.46410i	0.158114	−	0.273861i
$161$	6.00000			0.472866
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$	5.00000			0.390434
$165$	−6.00000	+	10.3923i	−0.467099	+	0.809040i
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$	8.00000	+	13.8564i	0.619059	+	1.07224i	0.989658	+	0.143448i	$0.0458190\pi$
$167$	8.00000	+	13.8564i	0.619059	+	1.07224i	−0.370599	+	0.928793i	$0.620848\pi$
$168$	1.00000			0.0771517
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$	20.0000			1.53393
$171$	−1.50000	−	2.59808i	−0.114708	−	0.198680i
$172$		0			0
$173$	1.00000	−	1.73205i	0.0760286	−	0.131685i	−0.825505	−	0.564396i	$-0.809109\pi$
$173$	1.00000	−	1.73205i	0.0760286	−	0.131685i	0.901533	+	0.432710i	$0.142443\pi$
$174$	−9.00000			−0.682288
$175$	−5.50000	+	9.52628i	−0.415761	+	0.720119i
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$	−2.00000			−0.150329
$178$	3.50000	−	6.06218i	0.262336	−	0.454379i
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.831408	−	0.555663i	$-0.812464\pi$
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.0655145	−	0.997852i	$-0.520869\pi$
$180$	−2.00000	−	3.46410i	−0.149071	−	0.258199i
$181$	−5.00000			−0.371647			−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000			−0.371647			−0.185824	+	0.982583i	$0.559495\pi$
$182$	2.50000	+	2.59808i	0.185312	+	0.192582i
$183$	1.00000			0.0739221
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$	−8.00000	−	13.8564i	−0.588172	−	1.01874i
$186$	2.00000	−	3.46410i	0.146647	−	0.254000i
$187$	15.0000			1.09691
$188$	1.50000	−	2.59808i	0.109399	−	0.189484i
$189$	0.500000	−	0.866025i	0.0363696	−	0.0629941i
$190$	−12.0000			−0.870572
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−6.50000	−	11.2583i	−0.467880	−	0.810392i	0.531446	−	0.847092i	$-0.321649\pi$
$193$	−6.50000	−	11.2583i	−0.467880	−	0.810392i	−0.999326	+	0.0366998i	$0.988315\pi$
$194$	12.0000			0.861550
$195$	4.00000	−	13.8564i	0.286446	−	0.992278i
$196$	1.00000			0.0714286
$197$	9.50000	+	16.4545i	0.676847	+	1.17233i	0.975925	+	0.218105i	$0.0699875\pi$
$197$	9.50000	+	16.4545i	0.676847	+	1.17233i	−0.299078	+	0.954229i	$0.596679\pi$
$198$	−1.50000	−	2.59808i	−0.106600	−	0.184637i
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	−11.0000			−0.777817
$201$	1.00000	−	1.73205i	0.0705346	−	0.122169i
$202$	5.00000	−	8.66025i	0.351799	−	0.609333i
$203$	−9.00000			−0.631676
$204$	−2.50000	+	4.33013i	−0.175035	+	0.303170i
$205$	−10.0000	−	17.3205i	−0.698430	−	1.20972i
$206$	10.0000	+	17.3205i	0.696733	+	1.20678i
$207$	6.00000			0.417029
$208$	−1.00000	+	3.46410i	−0.0693375	+	0.240192i
$209$	−9.00000			−0.622543
$210$	−2.00000	−	3.46410i	−0.138013	−	0.239046i
$211$	−7.00000	−	12.1244i	−0.481900	−	0.834675i	0.517884	−	0.855451i	$-0.326720\pi$
$211$	−7.00000	−	12.1244i	−0.481900	−	0.834675i	−0.999784	+	0.0207756i	$0.993386\pi$
$212$	5.50000	−	9.52628i	0.377742	−	0.654268i
$213$	−6.00000			−0.411113
$214$	8.50000	−	14.7224i	0.581048	−	1.00640i
$215$		0			0
$216$	1.00000			0.0680414
$217$	2.00000	−	3.46410i	0.135769	−	0.235159i
$218$	−1.00000	−	1.73205i	−0.0677285	−	0.117309i
$219$	6.00000	+	10.3923i	0.405442	+	0.702247i
$220$	−12.0000			−0.809040
$221$	−17.5000	+	4.33013i	−1.17718	+	0.291276i
$222$	4.00000			0.268462
$223$	8.00000	+	13.8564i	0.535720	+	0.927894i	0.999128	+	0.0417488i	$0.0132929\pi$
$223$	8.00000	+	13.8564i	0.535720	+	0.927894i	−0.463409	+	0.886145i	$0.653374\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	−5.50000	+	9.52628i	−0.366667	+	0.635085i
$226$	−12.0000			−0.798228
$227$	−7.00000	+	12.1244i	−0.464606	+	0.804722i	−0.999184	−	0.0403978i	$-0.987137\pi$
$227$	−7.00000	+	12.1244i	−0.464606	+	0.804722i	0.534577	+	0.845120i	$0.320471\pi$
$228$	1.50000	−	2.59808i	0.0993399	−	0.172062i
$229$	−5.00000			−0.330409			−0.165205	−	0.986259i	$-0.552828\pi$
$229$	−5.00000			−0.330409			−0.165205	+	0.986259i	$0.552828\pi$
$230$	12.0000	−	20.7846i	0.791257	−	1.37050i
$231$	−1.50000	−	2.59808i	−0.0986928	−	0.170941i
$232$	−4.50000	−	7.79423i	−0.295439	−	0.511716i
$233$	4.00000			0.262049			0.131024	−	0.991379i	$-0.458173\pi$
$233$	4.00000			0.262049			0.131024	+	0.991379i	$0.458173\pi$
$234$	2.50000	+	2.59808i	0.163430	+	0.169842i
$235$	−12.0000			−0.782794
$236$	−1.00000	−	1.73205i	−0.0650945	−	0.112747i
$237$	5.50000	+	9.52628i	0.357263	+	0.618798i
$238$	−2.50000	+	4.33013i	−0.162051	+	0.280680i
$239$	−26.0000			−1.68180			−0.840900	−	0.541190i	$-0.817974\pi$
$239$	−26.0000			−1.68180			−0.840900	+	0.541190i	$0.817974\pi$
$240$	2.00000	−	3.46410i	0.129099	−	0.223607i
$241$	−6.00000	+	10.3923i	−0.386494	+	0.669427i	−0.991975	−	0.126432i	$-0.959647\pi$
$241$	−6.00000	+	10.3923i	−0.386494	+	0.669427i	0.605481	+	0.795860i	$0.292981\pi$
$242$	2.00000			0.128565
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	0.500000	+	0.866025i	0.0320092	+	0.0554416i
$245$	−2.00000	−	3.46410i	−0.127775	−	0.221313i
$246$	5.00000			0.318788
$247$	10.5000	−	2.59808i	0.668099	−	0.165312i
$248$	4.00000			0.254000
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	12.0000	+	20.7846i	0.758947	+	1.31453i
$251$	−7.00000	+	12.1244i	−0.441836	+	0.765283i	−0.997826	−	0.0659066i	$-0.979006\pi$
$251$	−7.00000	+	12.1244i	−0.441836	+	0.765283i	0.555990	+	0.831189i	$0.312339\pi$
$252$	1.00000			0.0629941
$253$	9.00000	−	15.5885i	0.565825	−	0.980038i
$254$	4.00000	−	6.92820i	0.250982	−	0.434714i
$255$	20.0000			1.25245
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.50000	−	6.06218i	−0.218324	−	0.378148i	0.735972	−	0.677012i	$-0.236726\pi$
$257$	−3.50000	−	6.06218i	−0.218324	−	0.378148i	−0.954296	+	0.298864i	$0.903392\pi$
$258$		0			0
$259$	4.00000			0.248548
$260$	14.0000	−	3.46410i	0.868243	−	0.214834i
$261$	−9.00000			−0.557086
$262$	6.00000	+	10.3923i	0.370681	+	0.642039i
$263$	13.0000	+	22.5167i	0.801614	+	1.38844i	0.918553	+	0.395298i	$0.129359\pi$
$263$	13.0000	+	22.5167i	0.801614	+	1.38844i	−0.116939	+	0.993139i	$0.537308\pi$
$264$	1.50000	−	2.59808i	0.0923186	−	0.159901i
$265$	−44.0000			−2.70290
$266$	1.50000	−	2.59808i	0.0919709	−	0.159298i
$267$	3.50000	−	6.06218i	0.214197	−	0.370999i
$268$	2.00000			0.122169
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	−0.224523	−	0.974469i	$-0.572083\pi$
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	0.956176	−	0.292791i	$-0.0945841\pi$
$270$	−2.00000	−	3.46410i	−0.121716	−	0.210819i
$271$	6.00000	+	10.3923i	0.364474	+	0.631288i	0.988692	−	0.149963i	$-0.0479155\pi$
$271$	6.00000	+	10.3923i	0.364474	+	0.631288i	−0.624218	+	0.781251i	$0.714582\pi$
$272$	−5.00000			−0.303170
$273$	2.50000	+	2.59808i	0.151307	+	0.157243i
$274$	18.0000			1.08742
$275$	16.5000	+	28.5788i	0.994987	+	1.72337i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	−0.995997	−	0.0893846i	$-0.971510\pi$
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	0.575408	+	0.817867i	$0.304843\pi$
$278$	−13.0000			−0.779688
$279$	2.00000	−	3.46410i	0.119737	−	0.207390i
$280$	2.00000	−	3.46410i	0.119523	−	0.207020i
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$	1.50000	−	2.59808i	0.0893237	−	0.154713i
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$	−12.0000			−0.710819
$286$	10.5000	−	2.59808i	0.620878	−	0.153627i
$287$	5.00000			0.295141
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	−18.0000	+	31.1769i	−1.05700	+	1.83077i
$291$	12.0000			0.703452
$292$	−6.00000	+	10.3923i	−0.351123	+	0.608164i
$293$	−12.0000	+	20.7846i	−0.701047	+	1.21425i	0.267052	+	0.963682i	$0.413951\pi$
$293$	−12.0000	+	20.7846i	−0.701047	+	1.21425i	−0.968099	+	0.250568i	$0.919383\pi$
$294$	1.00000			0.0583212
$295$	−4.00000	+	6.92820i	−0.232889	+	0.403376i
$296$	2.00000	+	3.46410i	0.116248	+	0.201347i
$297$	−1.50000	−	2.59808i	−0.0870388	−	0.150756i
$298$	−18.0000			−1.04271
$299$	−6.00000	+	20.7846i	−0.346989	+	1.20201i
$300$	−11.0000			−0.635085
$301$		0			0
$302$	−5.50000	−	9.52628i	−0.316489	−	0.548176i
$303$	5.00000	−	8.66025i	0.287242	−	0.497519i
$304$	3.00000			0.172062
$305$	2.00000	−	3.46410i	0.114520	−	0.198354i
$306$	−2.50000	+	4.33013i	−0.142915	+	0.247537i
$307$	21.0000			1.19853			0.599267	−	0.800549i	$-0.295459\pi$
$307$	21.0000			1.19853			0.599267	+	0.800549i	$0.295459\pi$
$308$	1.50000	−	2.59808i	0.0854704	−	0.148039i
$309$	10.0000	+	17.3205i	0.568880	+	0.985329i
$310$	−8.00000	−	13.8564i	−0.454369	−	0.786991i
$311$	−19.0000			−1.07739			−0.538696	−	0.842500i	$-0.681083\pi$
$311$	−19.0000			−1.07739			−0.538696	+	0.842500i	$0.681083\pi$
$312$	−1.00000	+	3.46410i	−0.0566139	+	0.196116i
$313$	−14.0000			−0.791327			−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000			−0.791327			−0.395663	+	0.918396i	$0.629485\pi$
$314$	−1.00000	−	1.73205i	−0.0564333	−	0.0977453i
$315$	−2.00000	−	3.46410i	−0.112687	−	0.195180i
$316$	−5.50000	+	9.52628i	−0.309399	+	0.535895i
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$	5.50000	−	9.52628i	0.308425	−	0.534207i
$319$	−13.5000	+	23.3827i	−0.755855	+	1.30918i
$320$	4.00000			0.223607
$321$	8.50000	−	14.7224i	0.474424	−	0.821726i
$322$	3.00000	+	5.19615i	0.167183	+	0.289570i
$323$	7.50000	+	12.9904i	0.417311	+	0.722804i
$324$	1.00000			0.0555556
$325$	−27.5000	−	28.5788i	−1.52543	−	1.58527i
$326$	−20.0000			−1.10770
$327$	−1.00000	−	1.73205i	−0.0553001	−	0.0957826i
$328$	2.50000	+	4.33013i	0.138039	+	0.239091i
$329$	1.50000	−	2.59808i	0.0826977	−	0.143237i
$330$	−12.0000			−0.660578
$331$	−1.00000	+	1.73205i	−0.0549650	+	0.0952021i	−0.892199	−	0.451643i	$-0.850838\pi$
$331$	−1.00000	+	1.73205i	−0.0549650	+	0.0952021i	0.837234	+	0.546845i	$0.184171\pi$
$332$	−3.00000	+	5.19615i	−0.164646	+	0.285176i
$333$	4.00000			0.219199
$334$	−8.00000	+	13.8564i	−0.437741	+	0.758189i
$335$	−4.00000	−	6.92820i	−0.218543	−	0.378528i
$336$	0.500000	+	0.866025i	0.0272772	+	0.0472456i
$337$	31.0000			1.68868			0.844339	−	0.535810i	$-0.179994\pi$
$337$	31.0000			1.68868			0.844339	+	0.535810i	$0.179994\pi$
$338$	−11.5000	+	6.06218i	−0.625518	+	0.329739i
$339$	−12.0000			−0.651751
$340$	10.0000	+	17.3205i	0.542326	+	0.939336i
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$	1.50000	−	2.59808i	0.0811107	−	0.140488i
$343$	1.00000			0.0539949
$344$		0			0
$345$	12.0000	−	20.7846i	0.646058	−	1.11901i
$346$	2.00000			0.107521
$347$	−5.50000	+	9.52628i	−0.295255	+	0.511397i	−0.975044	−	0.222010i	$-0.928738\pi$
$347$	−5.50000	+	9.52628i	−0.295255	+	0.511397i	0.679789	+	0.733408i	$0.262071\pi$
$348$	−4.50000	−	7.79423i	−0.241225	−	0.417815i
$349$	17.0000	+	29.4449i	0.909989	+	1.57615i	0.814076	+	0.580758i	$0.197244\pi$
$349$	17.0000	+	29.4449i	0.909989	+	1.57615i	0.0959126	+	0.995390i	$0.469423\pi$
$350$	−11.0000			−0.587975
$351$	2.50000	+	2.59808i	0.133440	+	0.138675i
$352$	3.00000			0.159901
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	0.999711	−	0.0240566i	$-0.00765819\pi$
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	−0.520689	+	0.853746i	$0.674325\pi$
$354$	−1.00000	−	1.73205i	−0.0531494	−	0.0920575i
$355$	−12.0000	+	20.7846i	−0.636894	+	1.10313i
$356$	7.00000			0.370999
$357$	−2.50000	+	4.33013i	−0.132314	+	0.229175i
$358$	12.0000	−	20.7846i	0.634220	−	1.09850i
$359$	−20.0000			−1.05556			−0.527780	−	0.849381i	$-0.676975\pi$
$359$	−20.0000			−1.05556			−0.527780	+	0.849381i	$0.676975\pi$
$360$	2.00000	−	3.46410i	0.105409	−	0.182574i
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$	−2.50000	−	4.33013i	−0.131397	−	0.227586i
$363$	2.00000			0.104973
$364$	−1.00000	+	3.46410i	−0.0524142	+	0.181568i
$365$	48.0000			2.51243
$366$	0.500000	+	0.866025i	0.0261354	+	0.0452679i
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	0.529607	−	0.848243i	$-0.322339\pi$
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	−0.999404	+	0.0345320i	$0.989006\pi$
$368$	−3.00000	+	5.19615i	−0.156386	+	0.270868i
$369$	5.00000			0.260290
$370$	8.00000	−	13.8564i	0.415900	−	0.720360i
$371$	5.50000	−	9.52628i	0.285546	−	0.494580i
$372$	4.00000			0.207390
$373$	−17.0000	+	29.4449i	−0.880227	+	1.52460i	−0.0291379	+	0.999575i	$0.509276\pi$
$373$	−17.0000	+	29.4449i	−0.880227	+	1.52460i	−0.851089	+	0.525022i	$0.824057\pi$
$374$	7.50000	+	12.9904i	0.387816	+	0.671717i
$375$	12.0000	+	20.7846i	0.619677	+	1.07331i
$376$	3.00000			0.154713
$377$	9.00000	−	31.1769i	0.463524	−	1.60569i
$378$	1.00000			0.0514344
$379$	9.00000	+	15.5885i	0.462299	+	0.800725i	0.999075	−	0.0429994i	$-0.0136914\pi$
$379$	9.00000	+	15.5885i	0.462299	+	0.800725i	−0.536776	+	0.843725i	$0.680358\pi$
$380$	−6.00000	−	10.3923i	−0.307794	−	0.533114i
$381$	4.00000	−	6.92820i	0.204926	−	0.354943i
$382$	6.00000			0.306987
$383$	5.50000	−	9.52628i	0.281037	−	0.486770i	−0.690604	−	0.723234i	$-0.742655\pi$
$383$	5.50000	−	9.52628i	0.281037	−	0.486770i	0.971640	+	0.236463i	$0.0759883\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	−12.0000			−0.611577
$386$	6.50000	−	11.2583i	0.330841	−	0.573034i
$387$		0			0
$388$	6.00000	+	10.3923i	0.304604	+	0.527589i
$389$	−26.0000			−1.31825			−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000			−1.31825			−0.659126	+	0.752032i	$0.729074\pi$
$390$	14.0000	−	3.46410i	0.708918	−	0.175412i
$391$	−30.0000			−1.51717
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$	6.00000	+	10.3923i	0.302660	+	0.524222i
$394$	−9.50000	+	16.4545i	−0.478603	+	0.828965i
$395$	44.0000			2.21388
$396$	1.50000	−	2.59808i	0.0753778	−	0.130558i
$397$	11.5000	−	19.9186i	0.577168	−	0.999685i	−0.418634	−	0.908155i	$-0.637491\pi$
$397$	11.5000	−	19.9186i	0.577168	−	0.999685i	0.995802	−	0.0915300i	$-0.0291757\pi$
$398$		0			0
$399$	1.50000	−	2.59808i	0.0750939	−	0.130066i
$400$	−5.50000	−	9.52628i	−0.275000	−	0.476314i
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$	2.00000			0.0997509
$403$	10.0000	+	10.3923i	0.498135	+	0.517678i
$404$	10.0000			0.497519
$405$	−2.00000	−	3.46410i	−0.0993808	−	0.172133i
$406$	−4.50000	−	7.79423i	−0.223331	−	0.386821i
$407$	6.00000	−	10.3923i	0.297409	−	0.515127i
$408$	−5.00000			−0.247537
$409$	1.00000	−	1.73205i	0.0494468	−	0.0856444i	−0.840243	−	0.542211i	$-0.817588\pi$
$409$	1.00000	−	1.73205i	0.0494468	−	0.0856444i	0.889689	+	0.456566i	$0.150921\pi$
$410$	10.0000	−	17.3205i	0.493865	−	0.855399i
$411$	18.0000			0.887875
$412$	−10.0000	+	17.3205i	−0.492665	+	0.853320i
$413$	−1.00000	−	1.73205i	−0.0492068	−	0.0852286i
$414$	3.00000	+	5.19615i	0.147442	+	0.255377i
$415$	24.0000			1.17811
$416$	−3.50000	+	0.866025i	−0.171602	+	0.0424604i
$417$	−13.0000			−0.636613
$418$	−4.50000	−	7.79423i	−0.220102	−	0.381228i
$419$	−9.00000	−	15.5885i	−0.439679	−	0.761546i	0.557986	−	0.829851i	$-0.311574\pi$
$419$	−9.00000	−	15.5885i	−0.439679	−	0.761546i	−0.997665	+	0.0683046i	$0.978241\pi$
$420$	2.00000	−	3.46410i	0.0975900	−	0.169031i
$421$	−18.0000			−0.877266			−0.438633	−	0.898666i	$-0.644537\pi$
$421$	−18.0000			−0.877266			−0.438633	+	0.898666i	$0.644537\pi$
$422$	7.00000	−	12.1244i	0.340755	−	0.590204i
$423$	1.50000	−	2.59808i	0.0729325	−	0.126323i
$424$	11.0000			0.534207
$425$	27.5000	−	47.6314i	1.33395	−	2.31046i
$426$	−3.00000	−	5.19615i	−0.145350	−	0.251754i
$427$	0.500000	+	0.866025i	0.0241967	+	0.0419099i
$428$	17.0000			0.821726
$429$	10.5000	−	2.59808i	0.506945	−	0.125436i
$430$		0			0
$431$	−19.0000	−	32.9090i	−0.915198	−	1.58517i	−0.806611	−	0.591082i	$-0.798701\pi$
$431$	−19.0000	−	32.9090i	−0.915198	−	1.58517i	−0.108586	−	0.994087i	$-0.534632\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−17.0000	+	29.4449i	−0.816968	+	1.41503i	0.0909384	+	0.995857i	$0.471013\pi$
$433$	−17.0000	+	29.4449i	−0.816968	+	1.41503i	−0.907906	+	0.419173i	$0.862320\pi$
$434$	4.00000			0.192006
$435$	−18.0000	+	31.1769i	−0.863034	+	1.49482i
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$	18.0000			0.861057
$438$	−6.00000	+	10.3923i	−0.286691	+	0.496564i
$439$	−20.0000	−	34.6410i	−0.954548	−	1.65333i	−0.735399	−	0.677634i	$-0.763005\pi$
$439$	−20.0000	−	34.6410i	−0.954548	−	1.65333i	−0.219149	−	0.975691i	$-0.570328\pi$
$440$	−6.00000	−	10.3923i	−0.286039	−	0.495434i
$441$	1.00000			0.0476190
$442$	−12.5000	−	12.9904i	−0.594564	−	0.617889i
$443$	−15.0000			−0.712672			−0.356336	−	0.934358i	$-0.615974\pi$
$443$	−15.0000			−0.712672			−0.356336	+	0.934358i	$0.615974\pi$
$444$	2.00000	+	3.46410i	0.0949158	+	0.164399i
$445$	−14.0000	−	24.2487i	−0.663664	−	1.14950i
$446$	−8.00000	+	13.8564i	−0.378811	+	0.656120i
$447$	−18.0000			−0.851371
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	−10.0000	+	17.3205i	−0.471929	+	0.817405i	−0.999484	−	0.0321156i	$-0.989776\pi$
$449$	−10.0000	+	17.3205i	−0.471929	+	0.817405i	0.527555	+	0.849521i	$0.323109\pi$
$450$	−11.0000			−0.518545
$451$	7.50000	−	12.9904i	0.353161	−	0.611693i
$452$	−6.00000	−	10.3923i	−0.282216	−	0.488813i
$453$	−5.50000	−	9.52628i	−0.258413	−	0.447584i
$454$	−14.0000			−0.657053
$455$	14.0000	−	3.46410i	0.656330	−	0.162400i
$456$	3.00000			0.140488
$457$	1.00000	+	1.73205i	0.0467780	+	0.0810219i	0.888466	−	0.458942i	$-0.151771\pi$
$457$	1.00000	+	1.73205i	0.0467780	+	0.0810219i	−0.841688	+	0.539964i	$0.818438\pi$
$458$	−2.50000	−	4.33013i	−0.116817	−	0.202334i
$459$	−2.50000	+	4.33013i	−0.116690	+	0.202113i
$460$	24.0000			1.11901
$461$	16.0000	−	27.7128i	0.745194	−	1.29071i	−0.204910	−	0.978781i	$-0.565690\pi$
$461$	16.0000	−	27.7128i	0.745194	−	1.29071i	0.950104	−	0.311933i	$-0.100977\pi$
$462$	1.50000	−	2.59808i	0.0697863	−	0.120873i
$463$	1.00000			0.0464739			0.0232370	−	0.999730i	$-0.492603\pi$
$463$	1.00000			0.0464739			0.0232370	+	0.999730i	$0.492603\pi$
$464$	4.50000	−	7.79423i	0.208907	−	0.361838i
$465$	−8.00000	−	13.8564i	−0.370991	−	0.642575i
$466$	2.00000	+	3.46410i	0.0926482	+	0.160471i
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$	−1.00000	+	3.46410i	−0.0462250	+	0.160128i
$469$	2.00000			0.0923514
$470$	−6.00000	−	10.3923i	−0.276759	−	0.479361i
$471$	−1.00000	−	1.73205i	−0.0460776	−	0.0798087i
$472$	1.00000	−	1.73205i	0.0460287	−	0.0797241i
$473$		0			0
$474$	−5.50000	+	9.52628i	−0.252623	+	0.437557i
$475$	−16.5000	+	28.5788i	−0.757072	+	1.31129i
$476$	−5.00000			−0.229175
$477$	5.50000	−	9.52628i	0.251828	−	0.436178i
$478$	−13.0000	−	22.5167i	−0.594606	−	1.02989i
$479$	16.5000	+	28.5788i	0.753904	+	1.30580i	0.945917	+	0.324408i	$0.105165\pi$
$479$	16.5000	+	28.5788i	0.753904	+	1.30580i	−0.192013	+	0.981392i	$0.561502\pi$
$480$	4.00000			0.182574
$481$	−4.00000	+	13.8564i	−0.182384	+	0.631798i
$482$	−12.0000			−0.546585
$483$	3.00000	+	5.19615i	0.136505	+	0.236433i
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	24.0000	−	41.5692i	1.08978	−	1.88756i
$486$	1.00000			0.0453609
$487$	10.5000	−	18.1865i	0.475800	−	0.824110i	−0.523815	−	0.851832i	$-0.675492\pi$
$487$	10.5000	−	18.1865i	0.475800	−	0.824110i	0.999616	+	0.0277214i	$0.00882512\pi$
$488$	−0.500000	+	0.866025i	−0.0226339	+	0.0392031i
$489$	−20.0000			−0.904431
$490$	2.00000	−	3.46410i	0.0903508	−	0.156492i
$491$	10.0000	+	17.3205i	0.451294	+	0.781664i	0.998467	−	0.0553560i	$-0.0176294\pi$
$491$	10.0000	+	17.3205i	0.451294	+	0.781664i	−0.547173	+	0.837020i	$0.684296\pi$
$492$	2.50000	+	4.33013i	0.112709	+	0.195217i
$493$	45.0000			2.02670
$494$	7.50000	+	7.79423i	0.337441	+	0.350679i
$495$	−12.0000			−0.539360
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	−3.00000	−	5.19615i	−0.134568	−	0.233079i
$498$	−3.00000	+	5.19615i	−0.134433	+	0.232845i
$499$	40.0000			1.79065			0.895323	−	0.445418i	$-0.146945\pi$
$499$	40.0000			1.79065			0.895323	+	0.445418i	$0.146945\pi$
$500$	−12.0000	+	20.7846i	−0.536656	+	0.929516i
$501$	−8.00000	+	13.8564i	−0.357414	+	0.619059i
$502$	−14.0000			−0.624851
$503$	−8.00000	+	13.8564i	−0.356702	+	0.617827i	−0.987408	−	0.158196i	$-0.949432\pi$
$503$	−8.00000	+	13.8564i	−0.356702	+	0.617827i	0.630705	+	0.776022i	$0.282766\pi$
$504$	0.500000	+	0.866025i	0.0222718	+	0.0385758i
$505$	−20.0000	−	34.6410i	−0.889988	−	1.54150i
$506$	18.0000			0.800198
$507$	−11.5000	+	6.06218i	−0.510733	+	0.269231i
$508$	8.00000			0.354943
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	0.979322	+	0.202306i	$0.0648436\pi$
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	−0.314459	+	0.949271i	$0.601823\pi$
$510$	10.0000	+	17.3205i	0.442807	+	0.766965i
$511$	−6.00000	+	10.3923i	−0.265424	+	0.459728i
$512$	−1.00000			−0.0441942
$513$	1.50000	−	2.59808i	0.0662266	−	0.114708i
$514$	3.50000	−	6.06218i	0.154378	−	0.267391i
$515$	80.0000			3.52522
$516$		0			0
$517$	−4.50000	−	7.79423i	−0.197910	−	0.342790i
$518$	2.00000	+	3.46410i	0.0878750	+	0.152204i
$519$	2.00000			0.0877903
$520$	10.0000	+	10.3923i	0.438529	+	0.455733i
$521$	−5.00000			−0.219054			−0.109527	−	0.993984i	$-0.534934\pi$
$521$	−5.00000			−0.219054			−0.109527	+	0.993984i	$0.534934\pi$
$522$	−4.50000	−	7.79423i	−0.196960	−	0.341144i
$523$	−13.5000	−	23.3827i	−0.590314	−	1.02245i	−0.994190	−	0.107640i	$-0.965671\pi$
$523$	−13.5000	−	23.3827i	−0.590314	−	1.02245i	0.403876	−	0.914814i	$-0.367663\pi$
$524$	−6.00000	+	10.3923i	−0.262111	+	0.453990i
$525$	−11.0000			−0.480079
$526$	−13.0000	+	22.5167i	−0.566827	+	0.981773i
$527$	−10.0000	+	17.3205i	−0.435607	+	0.754493i
$528$	3.00000			0.130558
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	−22.0000	−	38.1051i	−0.955619	−	1.65518i
$531$	−1.00000	−	1.73205i	−0.0433963	−	0.0751646i
$532$	3.00000			0.130066
$533$	−5.00000	+	17.3205i	−0.216574	+	0.750234i
$534$	7.00000			0.302920
$535$	−34.0000	−	58.8897i	−1.46995	−	2.54602i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$	12.0000	−	20.7846i	0.517838	−	0.896922i
$538$	24.0000			1.03471
$539$	1.50000	−	2.59808i	0.0646096	−	0.111907i
$540$	2.00000	−	3.46410i	0.0860663	−	0.149071i
$541$	−2.00000			−0.0859867			−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000			−0.0859867			−0.0429934	+	0.999075i	$0.513689\pi$
$542$	−6.00000	+	10.3923i	−0.257722	+	0.446388i
$543$	−2.50000	−	4.33013i	−0.107285	−	0.185824i
$544$	−2.50000	−	4.33013i	−0.107187	−	0.185653i
$545$	−8.00000			−0.342682
$546$	−1.00000	+	3.46410i	−0.0427960	+	0.148250i
$547$	2.00000			0.0855138			0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000			0.0855138			0.0427569	+	0.999086i	$0.486386\pi$
$548$	9.00000	+	15.5885i	0.384461	+	0.665906i
$549$	0.500000	+	0.866025i	0.0213395	+	0.0369611i
$550$	−16.5000	+	28.5788i	−0.703562	+	1.21861i
$551$	−27.0000			−1.15024
$552$	−3.00000	+	5.19615i	−0.127688	+	0.221163i
$553$	−5.50000	+	9.52628i	−0.233884	+	0.405099i
$554$	−14.0000			−0.594803
$555$	8.00000	−	13.8564i	0.339581	−	0.588172i
$556$	−6.50000	−	11.2583i	−0.275661	−	0.477460i
$557$	−5.50000	−	9.52628i	−0.233042	−	0.403641i	0.725660	−	0.688054i	$-0.241535\pi$
$557$	−5.50000	−	9.52628i	−0.233042	−	0.403641i	−0.958702	+	0.284413i	$0.908201\pi$
$558$	4.00000			0.169334
$559$		0			0
$560$	4.00000			0.169031
$561$	7.50000	+	12.9904i	0.316650	+	0.548454i
$562$	15.0000	+	25.9808i	0.632737	+	1.09593i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$	3.00000			0.126323
$565$	−24.0000	+	41.5692i	−1.00969	+	1.74883i
$566$	−2.00000	+	3.46410i	−0.0840663	+	0.145607i
$567$	1.00000			0.0419961
$568$	3.00000	−	5.19615i	0.125877	−	0.218026i
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	0.796266	−	0.604947i	$-0.206806\pi$
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	−0.922032	+	0.387113i	$0.873472\pi$
$570$	−6.00000	−	10.3923i	−0.251312	−	0.435286i
$571$	38.0000			1.59025			0.795125	−	0.606445i	$-0.207405\pi$
$571$	38.0000			1.59025			0.795125	+	0.606445i	$0.207405\pi$
$572$	7.50000	+	7.79423i	0.313591	+	0.325893i
$573$	6.00000			0.250654
$574$	2.50000	+	4.33013i	0.104348	+	0.180736i
$575$	−33.0000	−	57.1577i	−1.37620	−	2.38364i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−18.0000			−0.749350			−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000			−0.749350			−0.374675	+	0.927156i	$0.622246\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	6.50000	−	11.2583i	0.270131	−	0.467880i
$580$	−36.0000			−1.49482
$581$	−3.00000	+	5.19615i	−0.124461	+	0.215573i
$582$	6.00000	+	10.3923i	0.248708	+	0.430775i
$583$	−16.5000	−	28.5788i	−0.683360	−	1.18361i
$584$	−12.0000			−0.496564
$585$	14.0000	−	3.46410i	0.578829	−	0.143223i
$586$	−24.0000			−0.991431
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	0.962872	−	0.269957i	$-0.0870095\pi$
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	−0.715226	+	0.698893i	$0.753676\pi$
$588$	0.500000	+	0.866025i	0.0206197	+	0.0357143i
$589$	6.00000	−	10.3923i	0.247226	−	0.428207i
$590$	−8.00000			−0.329355
$591$	−9.50000	+	16.4545i	−0.390778	+	0.676847i
$592$	−2.00000	+	3.46410i	−0.0821995	+	0.142374i
$593$	41.0000			1.68367			0.841834	−	0.539736i	$-0.181476\pi$
$593$	41.0000			1.68367			0.841834	+	0.539736i	$0.181476\pi$
$594$	1.50000	−	2.59808i	0.0615457	−	0.106600i
$595$	10.0000	+	17.3205i	0.409960	+	0.710072i
$596$	−9.00000	−	15.5885i	−0.368654	−	0.638528i
$597$		0			0
$598$	−21.0000	+	5.19615i	−0.858754	+	0.212486i
$599$	−30.0000			−1.22577			−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000			−1.22577			−0.612883	+	0.790173i	$0.709990\pi$
$600$	−5.50000	−	9.52628i	−0.224537	−	0.388909i
$601$	22.0000	+	38.1051i	0.897399	+	1.55434i	0.830808	+	0.556560i	$0.187879\pi$
$601$	22.0000	+	38.1051i	0.897399	+	1.55434i	0.0665912	+	0.997780i	$0.478788\pi$
$602$		0			0
$603$	2.00000			0.0814463
$604$	5.50000	−	9.52628i	0.223792	−	0.387619i
$605$	4.00000	−	6.92820i	0.162623	−	0.281672i
$606$	10.0000			0.406222
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	−0.773358	−	0.633970i	$-0.781424\pi$
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	0.935713	+	0.352763i	$0.114758\pi$
$608$	1.50000	+	2.59808i	0.0608330	+	0.105366i
$609$	−4.50000	−	7.79423i	−0.182349	−	0.315838i
$610$	4.00000			0.161955
$611$	7.50000	+	7.79423i	0.303418	+	0.315321i
$612$	−5.00000			−0.202113
$613$	−4.00000	−	6.92820i	−0.161558	−	0.279827i	0.773869	−	0.633345i	$-0.218319\pi$
$613$	−4.00000	−	6.92820i	−0.161558	−	0.279827i	−0.935428	+	0.353518i	$0.884985\pi$
$614$	10.5000	+	18.1865i	0.423746	+	0.733949i
$615$	10.0000	−	17.3205i	0.403239	−	0.698430i
$616$	3.00000			0.120873
$617$	−5.00000	+	8.66025i	−0.201292	+	0.348649i	−0.948945	−	0.315441i	$-0.897847\pi$
$617$	−5.00000	+	8.66025i	−0.201292	+	0.348649i	0.747653	+	0.664090i	$0.231181\pi$
$618$	−10.0000	+	17.3205i	−0.402259	+	0.696733i
$619$	17.0000			0.683288			0.341644	−	0.939829i	$-0.389016\pi$
$619$	17.0000			0.683288			0.341644	+	0.939829i	$0.389016\pi$
$620$	8.00000	−	13.8564i	0.321288	−	0.556487i
$621$	3.00000	+	5.19615i	0.120386	+	0.208514i
$622$	−9.50000	−	16.4545i	−0.380915	−	0.659765i
$623$	7.00000			0.280449
$624$	−3.50000	+	0.866025i	−0.140112	+	0.0346688i
$625$	41.0000			1.64000
$626$	−7.00000	−	12.1244i	−0.279776	−	0.484587i
$627$	−4.50000	−	7.79423i	−0.179713	−	0.311272i
$628$	1.00000	−	1.73205i	0.0399043	−	0.0691164i
$629$	−20.0000			−0.797452
$630$	2.00000	−	3.46410i	0.0796819	−	0.138013i
$631$	6.50000	−	11.2583i	0.258761	−	0.448187i	−0.707149	−	0.707064i	$-0.750019\pi$
$631$	6.50000	−	11.2583i	0.258761	−	0.448187i	0.965910	+	0.258877i	$0.0833525\pi$
$632$	−11.0000			−0.437557
$633$	7.00000	−	12.1244i	0.278225	−	0.481900i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$	−16.0000	−	27.7128i	−0.634941	−	1.09975i
$636$	11.0000			0.436178
$637$	−1.00000	+	3.46410i	−0.0396214	+	0.137253i
$638$	−27.0000			−1.06894
$639$	−3.00000	−	5.19615i	−0.118678	−	0.205557i
$640$	2.00000	+	3.46410i	0.0790569	+	0.136931i
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$	17.0000			0.670936
$643$	8.50000	−	14.7224i	0.335207	−	0.580596i	−0.648317	−	0.761370i	$-0.724527\pi$
$643$	8.50000	−	14.7224i	0.335207	−	0.580596i	0.983525	+	0.180774i	$0.0578603\pi$
$644$	−3.00000	+	5.19615i	−0.118217	+	0.204757i
$645$		0			0
$646$	−7.50000	+	12.9904i	−0.295084	+	0.511100i
$647$	−7.50000	−	12.9904i	−0.294855	−	0.510705i	0.680096	−	0.733123i	$-0.261938\pi$
$647$	−7.50000	−	12.9904i	−0.294855	−	0.510705i	−0.974951	+	0.222419i	$0.928605\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−6.00000			−0.235521
$650$	11.0000	−	38.1051i	0.431455	−	1.49461i
$651$	4.00000			0.156772
$652$	−10.0000	−	17.3205i	−0.391630	−	0.678323i
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	0.999456	+	0.0329874i	$0.0105021\pi$
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	−0.471160	+	0.882048i	$0.656165\pi$
$654$	1.00000	−	1.73205i	0.0391031	−	0.0677285i
$655$	48.0000			1.87552
$656$	−2.50000	+	4.33013i	−0.0976086	+	0.169063i
$657$	−6.00000	+	10.3923i	−0.234082	+	0.405442i
$658$	3.00000			0.116952
$659$	−19.5000	+	33.7750i	−0.759612	+	1.31569i	0.183436	+	0.983032i	$0.441278\pi$
$659$	−19.5000	+	33.7750i	−0.759612	+	1.31569i	−0.943049	+	0.332655i	$0.892055\pi$
$660$	−6.00000	−	10.3923i	−0.233550	−	0.404520i
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	0.946729	−	0.322031i	$-0.104366\pi$
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	−0.752252	+	0.658876i	$0.771032\pi$
$662$	−2.00000			−0.0777322
$663$	−12.5000	−	12.9904i	−0.485460	−	0.504505i
$664$	−6.00000			−0.232845
$665$	−6.00000	−	10.3923i	−0.232670	−	0.402996i
$666$	2.00000	+	3.46410i	0.0774984	+	0.134231i
$667$	27.0000	−	46.7654i	1.04544	−	1.81076i
$668$	−16.0000			−0.619059
$669$	−8.00000	+	13.8564i	−0.309298	+	0.535720i
$670$	4.00000	−	6.92820i	0.154533	−	0.267660i
$671$	3.00000			0.115814
$672$	−0.500000	+	0.866025i	−0.0192879	+	0.0334077i
$673$	−11.5000	−	19.9186i	−0.443292	−	0.767805i	0.554639	−	0.832091i	$-0.312856\pi$
$673$	−11.5000	−	19.9186i	−0.443292	−	0.767805i	−0.997932	+	0.0642860i	$0.979523\pi$
$674$	15.5000	+	26.8468i	0.597038	+	1.03410i
$675$	−11.0000			−0.423390
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	−26.0000			−0.999261			−0.499631	−	0.866239i	$-0.666531\pi$
$677$	−26.0000			−0.999261			−0.499631	+	0.866239i	$0.666531\pi$
$678$	−6.00000	−	10.3923i	−0.230429	−	0.399114i
$679$	6.00000	+	10.3923i	0.230259	+	0.398820i
$680$	−10.0000	+	17.3205i	−0.383482	+	0.664211i
$681$	−14.0000			−0.536481
$682$	6.00000	−	10.3923i	0.229752	−	0.397942i
$683$	10.0000	−	17.3205i	0.382639	−	0.662751i	−0.608799	−	0.793324i	$-0.708349\pi$
$683$	10.0000	−	17.3205i	0.382639	−	0.662751i	0.991439	+	0.130573i	$0.0416818\pi$
$684$	3.00000			0.114708
$685$	36.0000	−	62.3538i	1.37549	−	2.38242i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	−2.50000	−	4.33013i	−0.0953809	−	0.165205i
$688$		0			0
$689$	27.5000	+	28.5788i	1.04767	+	1.08877i
$690$	24.0000			0.913664
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	1.00000	+	1.73205i	0.0380143	+	0.0658427i
$693$	1.50000	−	2.59808i	0.0569803	−	0.0986928i
$694$	−11.0000			−0.417554
$695$	−26.0000	+	45.0333i	−0.986236	+	1.70821i
$696$	4.50000	−	7.79423i	0.170572	−	0.295439i
$697$	−25.0000			−0.946943
$698$	−17.0000	+	29.4449i	−0.643459	+	1.11450i
$699$	2.00000	+	3.46410i	0.0756469	+	0.131024i
$700$	−5.50000	−	9.52628i	−0.207880	−	0.360060i
$701$	−21.0000			−0.793159			−0.396580	−	0.918000i	$-0.629803\pi$
$701$	−21.0000			−0.793159			−0.396580	+	0.918000i	$0.629803\pi$
$702$	−1.00000	+	3.46410i	−0.0377426	+	0.130744i
$703$	12.0000			0.452589
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$	−6.00000	−	10.3923i	−0.225973	−	0.391397i
$706$	−9.00000	+	15.5885i	−0.338719	+	0.586679i
$707$	10.0000			0.376089
$708$	1.00000	−	1.73205i	0.0375823	−	0.0650945i
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	−0.944509	−	0.328484i	$-0.893462\pi$
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	0.756730	+	0.653727i	$0.226796\pi$
$710$	−24.0000			−0.900704
$711$	−5.50000	+	9.52628i	−0.206266	+	0.357263i
$712$	3.50000	+	6.06218i	0.131168	+	0.227190i
$713$	12.0000	+	20.7846i	0.449404	+	0.778390i
$714$	−5.00000			−0.187120
$715$	12.0000	−	41.5692i	0.448775	−	1.55460i
$716$	24.0000			0.896922
$717$	−13.0000	−	22.5167i	−0.485494	−	0.840900i
$718$	−10.0000	−	17.3205i	−0.373197	−	0.646396i
$719$	0.500000	−	0.866025i	0.0186469	−	0.0322973i	−0.856551	−	0.516062i	$-0.827398\pi$
$719$	0.500000	−	0.866025i	0.0186469	−	0.0322973i	0.875198	+	0.483764i	$0.160731\pi$
$720$	4.00000			0.149071
$721$	−10.0000	+	17.3205i	−0.372419	+	0.645049i
$722$	−5.00000	+	8.66025i	−0.186081	+	0.322301i
$723$	−12.0000			−0.446285
$724$	2.50000	−	4.33013i	0.0929118	−	0.160928i
$725$	49.5000	+	85.7365i	1.83838	+	3.18417i
$726$	1.00000	+	1.73205i	0.0371135	+	0.0642824i
$727$	12.0000			0.445055			0.222528	−	0.974926i	$-0.428569\pi$
$727$	12.0000			0.445055			0.222528	+	0.974926i	$0.428569\pi$
$728$	−3.50000	+	0.866025i	−0.129719	+	0.0320970i
$729$	1.00000			0.0370370
$730$	24.0000	+	41.5692i	0.888280	+	1.53855i
$731$		0			0
$732$	−0.500000	+	0.866025i	−0.0184805	+	0.0320092i
$733$	13.0000			0.480166			0.240083	−	0.970752i	$-0.422825\pi$
$733$	13.0000			0.480166			0.240083	+	0.970752i	$0.422825\pi$
$734$	9.00000	−	15.5885i	0.332196	−	0.575380i
$735$	2.00000	−	3.46410i	0.0737711	−	0.127775i
$736$	−6.00000			−0.221163
$737$	3.00000	−	5.19615i	0.110506	−	0.191403i
$738$	2.50000	+	4.33013i	0.0920263	+	0.159394i
$739$	27.0000	+	46.7654i	0.993211	+	1.72029i	0.597347	+	0.801983i	$0.296222\pi$
$739$	27.0000	+	46.7654i	0.993211	+	1.72029i	0.395864	+	0.918309i	$0.370445\pi$
$740$	16.0000			0.588172
$741$	7.50000	+	7.79423i	0.275519	+	0.286328i
$742$	11.0000			0.403823
$743$	−14.0000	−	24.2487i	−0.513610	−	0.889599i	−0.999875	−	0.0157876i	$-0.994974\pi$
$743$	−14.0000	−	24.2487i	−0.513610	−	0.889599i	0.486265	−	0.873811i	$-0.338359\pi$
$744$	2.00000	+	3.46410i	0.0733236	+	0.127000i
$745$	−36.0000	+	62.3538i	−1.31894	+	2.28447i
$746$	−34.0000			−1.24483
$747$	−3.00000	+	5.19615i	−0.109764	+	0.190117i
$748$	−7.50000	+	12.9904i	−0.274227	+	0.474975i
$749$	17.0000			0.621166
$750$	−12.0000	+	20.7846i	−0.438178	+	0.758947i
$751$	−15.5000	−	26.8468i	−0.565603	−	0.979653i	−0.996993	−	0.0774878i	$-0.975310\pi$
$751$	−15.5000	−	26.8468i	−0.565603	−	0.979653i	0.431390	−	0.902165i	$-0.358023\pi$
$752$	1.50000	+	2.59808i	0.0546994	+	0.0947421i
$753$	−14.0000			−0.510188
$754$	31.5000	−	7.79423i	1.14716	−	0.283849i
$755$	−44.0000			−1.60132
$756$	0.500000	+	0.866025i	0.0181848	+	0.0314970i
$757$	−11.0000	−	19.0526i	−0.399802	−	0.692477i	0.593899	−	0.804539i	$-0.297588\pi$
$757$	−11.0000	−	19.0526i	−0.399802	−	0.692477i	−0.993701	+	0.112062i	$0.964254\pi$
$758$	−9.00000	+	15.5885i	−0.326895	+	0.566198i
$759$	18.0000			0.653359
$760$	6.00000	−	10.3923i	0.217643	−	0.376969i
$761$	13.0000	−	22.5167i	0.471250	−	0.816228i	−0.528209	−	0.849114i	$-0.677136\pi$
$761$	13.0000	−	22.5167i	0.471250	−	0.816228i	0.999459	+	0.0328858i	$0.0104698\pi$
$762$	8.00000			0.289809
$763$	1.00000	−	1.73205i	0.0362024	−	0.0627044i
$764$	3.00000	+	5.19615i	0.108536	+	0.187990i
$765$	10.0000	+	17.3205i	0.361551	+	0.626224i
$766$	11.0000			0.397446
$767$	7.00000	−	1.73205i	0.252755	−	0.0625407i
$768$	−1.00000			−0.0360844
$769$	2.00000	+	3.46410i	0.0721218	+	0.124919i	0.899831	−	0.436239i	$-0.143690\pi$
$769$	2.00000	+	3.46410i	0.0721218	+	0.124919i	−0.827709	+	0.561157i	$0.810356\pi$
$770$	−6.00000	−	10.3923i	−0.216225	−	0.374513i
$771$	3.50000	−	6.06218i	0.126049	−	0.218324i
$772$	13.0000			0.467880
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	−0.981250	−	0.192740i	$-0.938263\pi$
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	0.657542	+	0.753418i	$0.271596\pi$
$774$		0			0
$775$	−44.0000			−1.58053
$776$	−6.00000	+	10.3923i	−0.215387	+	0.373062i
$777$	2.00000	+	3.46410i	0.0717496	+	0.124274i
$778$	−13.0000	−	22.5167i	−0.466073	−	0.807261i
$779$	15.0000			0.537431
$780$	10.0000	+	10.3923i	0.358057	+	0.372104i
$781$	−18.0000			−0.644091
$782$	−15.0000	−	25.9808i	−0.536399	−	0.929070i
$783$	−4.50000	−	7.79423i	−0.160817	−	0.278543i
$784$	−0.500000	+	0.866025i	−0.0178571	+	0.0309295i
$785$	−8.00000			−0.285532
$786$	−6.00000	+	10.3923i	−0.214013	+	0.370681i
$787$	5.50000	−	9.52628i	0.196054	−	0.339575i	−0.751192	−	0.660084i	$-0.770521\pi$
$787$	5.50000	−	9.52628i	0.196054	−	0.339575i	0.947245	+	0.320509i	$0.103854\pi$
$788$	−19.0000			−0.676847
$789$	−13.0000	+	22.5167i	−0.462812	+	0.801614i
$790$	22.0000	+	38.1051i	0.782725	+	1.35572i
$791$	−6.00000	−	10.3923i	−0.213335	−	0.369508i
$792$	3.00000			0.106600
$793$	−3.50000	+	0.866025i	−0.124289	+	0.0307535i
$794$	23.0000			0.816239
$795$	−22.0000	−	38.1051i	−0.780260	−	1.35145i
$796$		0			0
$797$	1.00000	−	1.73205i	0.0354218	−	0.0613524i	−0.847771	−	0.530362i	$-0.822056\pi$
$797$	1.00000	−	1.73205i	0.0354218	−	0.0613524i	0.883193	+	0.469010i	$0.155389\pi$
$798$	3.00000			0.106199
$799$	−7.50000	+	12.9904i	−0.265331	+	0.459567i
$800$	5.50000	−	9.52628i	0.194454	−	0.336805i
$801$	7.00000			0.247333
$802$	9.00000	−	15.5885i	0.317801	−	0.550448i
$803$	18.0000	+	31.1769i	0.635206	+	1.10021i
$804$	1.00000	+	1.73205i	0.0352673	+	0.0610847i
$805$	24.0000			0.845889
$806$	−4.00000	+	13.8564i	−0.140894	+	0.488071i
$807$	24.0000			0.844840
$808$	5.00000	+	8.66025i	0.175899	+	0.304667i
$809$	25.0000	+	43.3013i	0.878953	+	1.52239i	0.852491	+	0.522742i	$0.175091\pi$
$809$	25.0000	+	43.3013i	0.878953	+	1.52239i	0.0264621	+	0.999650i	$0.491576\pi$
$810$	2.00000	−	3.46410i	0.0702728	−	0.121716i
$811$	24.0000			0.842754			0.421377	−	0.906886i	$-0.361547\pi$
$811$	24.0000			0.842754			0.421377	+	0.906886i	$0.361547\pi$
$812$	4.50000	−	7.79423i	0.157919	−	0.273524i
$813$	−6.00000	+	10.3923i	−0.210429	+	0.364474i
$814$	12.0000			0.420600
$815$	−40.0000	+	69.2820i	−1.40114	+	2.42684i
$816$	−2.50000	−	4.33013i	−0.0875175	−	0.151585i
$817$		0			0
$818$	2.00000			0.0699284
$819$	−1.00000	+	3.46410i	−0.0349428	+	0.121046i
$820$	20.0000			0.698430
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	0.966708	−	0.255884i	$-0.0823665\pi$
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	−0.704956	+	0.709251i	$0.749033\pi$
$822$	9.00000	+	15.5885i	0.313911	+	0.543710i
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$	−20.0000			−0.696733
$825$	−16.5000	+	28.5788i	−0.574456	+	0.994987i
$826$	1.00000	−	1.73205i	0.0347945	−	0.0602658i
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$	−3.00000	+	5.19615i	−0.104257	+	0.180579i
$829$	−2.50000	−	4.33013i	−0.0868286	−	0.150392i	0.819340	−	0.573307i	$-0.194340\pi$
$829$	−2.50000	−	4.33013i	−0.0868286	−	0.150392i	−0.906169	+	0.422916i	$0.861007\pi$
$830$	12.0000	+	20.7846i	0.416526	+	0.721444i
$831$	−14.0000			−0.485655
$832$	−2.50000	−	2.59808i	−0.0866719	−	0.0900721i
$833$	−5.00000			−0.173240
$834$	−6.50000	−	11.2583i	−0.225077	−	0.389844i
$835$	32.0000	+	55.4256i	1.10741	+	1.91808i
$836$	4.50000	−	7.79423i	0.155636	−	0.269569i
$837$	4.00000			0.138260
$838$	9.00000	−	15.5885i	0.310900	−	0.538494i
$839$	−22.0000	+	38.1051i	−0.759524	+	1.31553i	0.183569	+	0.983007i	$0.441235\pi$
$839$	−22.0000	+	38.1051i	−0.759524	+	1.31553i	−0.943093	+	0.332528i	$0.892098\pi$
$840$	4.00000			0.138013
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$	−9.00000	−	15.5885i	−0.310160	−	0.537214i
$843$	15.0000	+	25.9808i	0.516627	+	0.894825i
$844$	14.0000			0.481900
$845$	−2.00000	+	51.9615i	−0.0688021	+	1.78753i
$846$	3.00000			0.103142
$847$	1.00000	+	1.73205i	0.0343604	+	0.0595140i
$848$	5.50000	+	9.52628i	0.188871	+	0.327134i
$849$	−2.00000	+	3.46410i	−0.0686398	+	0.118888i
$850$	55.0000			1.88648
$851$	−12.0000	+	20.7846i	−0.411355	+	0.712487i
$852$	3.00000	−	5.19615i	0.102778	−	0.178017i
$853$	49.0000			1.67773			0.838864	−	0.544341i	$-0.183220\pi$
$853$	49.0000			1.67773			0.838864	+	0.544341i	$0.183220\pi$
$854$	−0.500000	+	0.866025i	−0.0171096	+	0.0296348i
$855$	−6.00000	−	10.3923i	−0.205196	−	0.355409i
$856$	8.50000	+	14.7224i	0.290524	+	0.503202i
$857$	10.0000			0.341593			0.170797	−	0.985306i	$-0.445366\pi$
$857$	10.0000			0.341593			0.170797	+	0.985306i	$0.445366\pi$
$858$	7.50000	+	7.79423i	0.256046	+	0.266091i
$859$	−5.00000			−0.170598			−0.0852989	−	0.996355i	$-0.527185\pi$
$859$	−5.00000			−0.170598			−0.0852989	+	0.996355i	$0.527185\pi$
$860$		0			0
$861$	2.50000	+	4.33013i	0.0851998	+	0.147570i
$862$	19.0000	−	32.9090i	0.647143	−	1.12088i
$863$	−14.0000			−0.476566			−0.238283	−	0.971196i	$-0.576585\pi$
$863$	−14.0000			−0.476566			−0.238283	+	0.971196i	$0.576585\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	4.00000	−	6.92820i	0.136004	−	0.235566i
$866$	−34.0000			−1.15537
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$	2.00000	+	3.46410i	0.0678844	+	0.117579i
$869$	16.5000	+	28.5788i	0.559724	+	0.969471i
$870$	−36.0000			−1.22051
$871$	−2.00000	+	6.92820i	−0.0677674	+	0.234753i
$872$	2.00000			0.0677285
$873$	6.00000	+	10.3923i	0.203069	+	0.351726i
$874$	9.00000	+	15.5885i	0.304430	+	0.527287i
$875$	−12.0000	+	20.7846i	−0.405674	+	0.702648i
$876$	−12.0000			−0.405442
$877$	−21.0000	+	36.3731i	−0.709120	+	1.22823i	0.256064	+	0.966660i	$0.417574\pi$
$877$	−21.0000	+	36.3731i	−0.709120	+	1.22823i	−0.965184	+	0.261571i	$0.915759\pi$
$878$	20.0000	−	34.6410i	0.674967	−	1.16908i
$879$	−24.0000			−0.809500
$880$	6.00000	−	10.3923i	0.202260	−	0.350325i
$881$	−1.00000	−	1.73205i	−0.0336909	−	0.0583543i	0.848688	−	0.528893i	$-0.177393\pi$
$881$	−1.00000	−	1.73205i	−0.0336909	−	0.0583543i	−0.882379	+	0.470539i	$0.844059\pi$
$882$	0.500000	+	0.866025i	0.0168359	+	0.0291606i
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$	5.00000	−	17.3205i	0.168168	−	0.582552i
$885$	−8.00000			−0.268917
$886$	−7.50000	−	12.9904i	−0.251967	−	0.436420i
$887$	−19.5000	−	33.7750i	−0.654746	−	1.13405i	−0.981957	−	0.189102i	$-0.939442\pi$
$887$	−19.5000	−	33.7750i	−0.654746	−	1.13405i	0.327212	−	0.944951i	$-0.393891\pi$
$888$	−2.00000	+	3.46410i	−0.0671156	+	0.116248i
$889$	8.00000			0.268311
$890$	14.0000	−	24.2487i	0.469281	−	0.812819i
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$	−16.0000			−0.535720
$893$	4.50000	−	7.79423i	0.150587	−	0.260824i
$894$	−9.00000	−	15.5885i	−0.301005	−	0.521356i
$895$	−48.0000	−	83.1384i	−1.60446	−	2.77901i
$896$	−1.00000			−0.0334077
$897$	−21.0000	+	5.19615i	−0.701170	+	0.173494i
$898$	−20.0000			−0.667409
$899$	−18.0000	−	31.1769i	−0.600334	−	1.03981i
$900$	−5.50000	−	9.52628i	−0.183333	−	0.317543i
$901$	−27.5000	+	47.6314i	−0.916158	+	1.58683i
$902$	15.0000			0.499445
$903$		0			0
$904$	6.00000	−	10.3923i	0.199557	−	0.345643i
$905$	−20.0000			−0.664822
$906$	5.50000	−	9.52628i	0.182725	−	0.316489i
$907$	7.00000	+	12.1244i	0.232431	+	0.402583i	0.958523	−	0.285015i	$-0.0919986\pi$
$907$	7.00000	+	12.1244i	0.232431	+	0.402583i	−0.726092	+	0.687598i	$0.758665\pi$
$908$	−7.00000	−	12.1244i	−0.232303	−	0.402361i
$909$	10.0000			0.331679
$910$	10.0000	+	10.3923i	0.331497	+	0.344502i
$911$	−2.00000			−0.0662630			−0.0331315	−	0.999451i	$-0.510548\pi$
$911$	−2.00000			−0.0662630			−0.0331315	+	0.999451i	$0.510548\pi$
$912$	1.50000	+	2.59808i	0.0496700	+	0.0860309i
$913$	9.00000	+	15.5885i	0.297857	+	0.515903i
$914$	−1.00000	+	1.73205i	−0.0330771	+	0.0572911i
$915$	4.00000			0.132236
$916$	2.50000	−	4.33013i	0.0826023	−	0.143071i
$917$	−6.00000	+	10.3923i	−0.198137	+	0.343184i
$918$	−5.00000			−0.165025
$919$	5.50000	−	9.52628i	0.181428	−	0.314243i	−0.760939	−	0.648824i	$-0.775261\pi$
$919$	5.50000	−	9.52628i	0.181428	−	0.314243i	0.942367	+	0.334581i	$0.108595\pi$
$920$	12.0000	+	20.7846i	0.395628	+	0.685248i
$921$	10.5000	+	18.1865i	0.345987	+	0.599267i
$922$	32.0000			1.05386
$923$	21.0000	−	5.19615i	0.691223	−	0.171033i
$924$	3.00000			0.0986928
$925$	−22.0000	−	38.1051i	−0.723356	−	1.25289i
$926$	0.500000	+	0.866025i	0.0164310	+	0.0284594i
$927$	−10.0000	+	17.3205i	−0.328443	+	0.568880i
$928$	9.00000			0.295439
$929$	11.5000	−	19.9186i	0.377303	−	0.653508i	−0.613366	−	0.789799i	$-0.710185\pi$
$929$	11.5000	−	19.9186i	0.377303	−	0.653508i	0.990669	+	0.136291i	$0.0435183\pi$
$930$	8.00000	−	13.8564i	0.262330	−	0.454369i
$931$	3.00000			0.0983210
$932$	−2.00000	+	3.46410i	−0.0655122	+	0.113470i
$933$	−9.50000	−	16.4545i	−0.311016	−	0.538696i
$934$	−6.00000	−	10.3923i	−0.196326	−	0.340047i
$935$	60.0000			1.96221
$936$	−3.50000	+	0.866025i	−0.114401	+	0.0283069i
$937$	44.0000			1.43742			0.718709	−	0.695311i	$-0.244734\pi$
$937$	44.0000			1.43742			0.718709	+	0.695311i	$0.244734\pi$
$938$	1.00000	+	1.73205i	0.0326512	+	0.0565535i
$939$	−7.00000	−	12.1244i	−0.228436	−	0.395663i
$940$	6.00000	−	10.3923i	0.195698	−	0.338960i
$941$	48.0000			1.56476			0.782378	−	0.622804i	$-0.214007\pi$
$941$	48.0000			1.56476			0.782378	+	0.622804i	$0.214007\pi$
$942$	1.00000	−	1.73205i	0.0325818	−	0.0564333i
$943$	−15.0000	+	25.9808i	−0.488467	+	0.846050i
$944$	2.00000			0.0650945
$945$	2.00000	−	3.46410i	0.0650600	−	0.112687i
$946$		0			0
$947$	−1.50000	−	2.59808i	−0.0487435	−	0.0844261i	0.840624	−	0.541619i	$-0.182188\pi$
$947$	−1.50000	−	2.59808i	−0.0487435	−	0.0844261i	−0.889368	+	0.457193i	$0.848855\pi$
$948$	−11.0000			−0.357263
$949$	−30.0000	−	31.1769i	−0.973841	−	1.01205i
$950$	−33.0000			−1.07066
$951$	−9.00000	−	15.5885i	−0.291845	−	0.505490i
$952$	−2.50000	−	4.33013i	−0.0810255	−	0.140340i
$953$	−12.0000	+	20.7846i	−0.388718	+	0.673280i	−0.992277	−	0.124039i	$-0.960415\pi$
$953$	−12.0000	+	20.7846i	−0.388718	+	0.673280i	0.603559	+	0.797318i	$0.293749\pi$
$954$	11.0000			0.356138
$955$	12.0000	−	20.7846i	0.388311	−	0.672574i
$956$	13.0000	−	22.5167i	0.420450	−	0.728241i
$957$	−27.0000			−0.872786
$958$	−16.5000	+	28.5788i	−0.533091	+	0.923340i
$959$	9.00000	+	15.5885i	0.290625	+	0.503378i
$960$	2.00000	+	3.46410i	0.0645497	+	0.111803i
$961$	−15.0000			−0.483871
$962$	−14.0000	+	3.46410i	−0.451378	+	0.111687i
$963$	17.0000			0.547817
$964$	−6.00000	−	10.3923i	−0.193247	−	0.334714i
$965$	−26.0000	−	45.0333i	−0.836970	−	1.44967i
$966$	−3.00000	+	5.19615i	−0.0965234	+	0.167183i
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$	−7.50000	+	12.9904i	−0.240935	+	0.417311i
$970$	48.0000			1.54119
$971$	25.0000	−	43.3013i	0.802288	−	1.38960i	−0.115818	−	0.993270i	$-0.536949\pi$
$971$	25.0000	−	43.3013i	0.802288	−	1.38960i	0.918107	−	0.396333i	$-0.129718\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−6.50000	−	11.2583i	−0.208380	−	0.360925i
$974$	21.0000			0.672883
$975$	11.0000	−	38.1051i	0.352282	−	1.22034i
$976$	−1.00000			−0.0320092
$977$	2.00000	+	3.46410i	0.0639857	+	0.110826i	0.896244	−	0.443562i	$-0.146285\pi$
$977$	2.00000	+	3.46410i	0.0639857	+	0.110826i	−0.832258	+	0.554389i	$0.812952\pi$
$978$	−10.0000	−	17.3205i	−0.319765	−	0.553849i
$979$	10.5000	−	18.1865i	0.335581	−	0.581244i
$980$	4.00000			0.127775
$981$	1.00000	−	1.73205i	0.0319275	−	0.0553001i
$982$	−10.0000	+	17.3205i	−0.319113	+	0.552720i
$983$		0			0			−	1.00000i	$-0.5\pi$
$983$		0			0				1.00000i	$0.5\pi$
$984$	−2.50000	+	4.33013i	−0.0796971	+	0.138039i
$985$	38.0000	+	65.8179i	1.21078	+	2.09713i
$986$	22.5000	+	38.9711i	0.716546	+	1.24109i
$987$	3.00000			0.0954911
$988$	−3.00000	+	10.3923i	−0.0954427	+	0.330623i
$989$		0			0
$990$	−6.00000	−	10.3923i	−0.190693	−	0.330289i
$991$	−16.5000	−	28.5788i	−0.524140	−	0.907837i	−0.999605	−	0.0281022i	$-0.991054\pi$
$991$	−16.5000	−	28.5788i	−0.524140	−	0.907837i	0.475465	−	0.879734i	$-0.342280\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$	−2.00000			−0.0634681
$994$	3.00000	−	5.19615i	0.0951542	−	0.164812i
$995$		0			0
$996$	−6.00000			−0.190117
$997$	6.50000	−	11.2583i	0.205857	−	0.356555i	−0.744548	−	0.667568i	$-0.767335\pi$
$997$	6.50000	−	11.2583i	0.205857	−	0.356555i	0.950405	+	0.311014i	$0.100668\pi$
$998$	20.0000	+	34.6410i	0.633089	+	1.09654i
$999$	2.00000	+	3.46410i	0.0632772	+	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.l.h.211.1	✓	2
3.2	odd	2		1638.2.r.a.757.1		2
13.3	even	3		7098.2.a.g.1.1		1
13.9	even	3	inner	546.2.l.h.295.1	yes	2
13.10	even	6		7098.2.a.q.1.1		1
39.35	odd	6		1638.2.r.a.1387.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.h.211.1	✓	2	1.1	even	1	trivial
546.2.l.h.295.1	yes	2	13.9	even	3	inner
1638.2.r.a.757.1		2	3.2	odd	2
1638.2.r.a.1387.1		2	39.35	odd	6
7098.2.a.g.1.1		1	13.3	even	3
7098.2.a.q.1.1		1	13.10	even	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.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +4.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +4.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.00000 + 3.46410i) q^{10} +(1.50000 + 2.59808i) q^{11} -1.00000 q^{12} +(-2.50000 - 2.59808i) q^{13} -1.00000 q^{14} +(2.00000 + 3.46410i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.50000 - 4.33013i) q^{17} -1.00000 q^{18} +(-1.50000 + 2.59808i) q^{19} +(-2.00000 + 3.46410i) q^{20} -1.00000 q^{21} +(-1.50000 + 2.59808i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +11.0000 q^{25} +(1.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(4.50000 + 7.79423i) q^{29} +(-2.00000 + 3.46410i) q^{30} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +5.00000 q^{34} +(-2.00000 + 3.46410i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-2.00000 - 3.46410i) q^{37} -3.00000 q^{38} +(1.00000 - 3.46410i) q^{39} -4.00000 q^{40} +(-2.50000 - 4.33013i) q^{41} +(-0.500000 - 0.866025i) q^{42} -3.00000 q^{44} +(-2.00000 + 3.46410i) q^{45} +(3.00000 - 5.19615i) q^{46} -3.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(5.50000 + 9.52628i) q^{50} +5.00000 q^{51} +(3.50000 - 0.866025i) q^{52} -11.0000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(6.00000 + 10.3923i) q^{55} +(0.500000 - 0.866025i) q^{56} -3.00000 q^{57} +(-4.50000 + 7.79423i) q^{58} +(-1.00000 + 1.73205i) q^{59} -4.00000 q^{60} +(0.500000 - 0.866025i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(-10.0000 - 10.3923i) q^{65} -3.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +(2.50000 + 4.33013i) q^{68} +(3.00000 - 5.19615i) q^{69} -4.00000 q^{70} +(-3.00000 + 5.19615i) q^{71} +(0.500000 - 0.866025i) q^{72} +12.0000 q^{73} +(2.00000 - 3.46410i) q^{74} +(5.50000 + 9.52628i) q^{75} +(-1.50000 - 2.59808i) q^{76} -3.00000 q^{77} +(3.50000 - 0.866025i) q^{78} +11.0000 q^{79} +(-2.00000 - 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.50000 - 4.33013i) q^{82} +6.00000 q^{83} +(0.500000 - 0.866025i) q^{84} +(10.0000 - 17.3205i) q^{85} +(-4.50000 + 7.79423i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(-3.50000 - 6.06218i) q^{89} -4.00000 q^{90} +(3.50000 - 0.866025i) q^{91} +6.00000 q^{92} +(-2.00000 - 3.46410i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-6.00000 + 10.3923i) q^{95} +1.00000 q^{96} +(6.00000 - 10.3923i) q^{97} +(0.500000 - 0.866025i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} + 8 q^{5} - q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 + 8 * q^5 - q^6 - q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} + 8 q^{5} - q^{6} - q^{7} - 2 q^{8} - q^{9} + 4 q^{10} + 3 q^{11} - 2 q^{12} - 5 q^{13} - 2 q^{14} + 4 q^{15} - q^{16} + 5 q^{17} - 2 q^{18} - 3 q^{19} - 4 q^{20} - 2 q^{21} - 3 q^{22} - 6 q^{23} - q^{24} + 22 q^{25} + 2 q^{26} - 2 q^{27} - q^{28} + 9 q^{29} - 4 q^{30} - 8 q^{31} + q^{32} - 3 q^{33} + 10 q^{34} - 4 q^{35} - q^{36} - 4 q^{37} - 6 q^{38} + 2 q^{39} - 8 q^{40} - 5 q^{41} - q^{42} - 6 q^{44} - 4 q^{45} + 6 q^{46} - 6 q^{47} + q^{48} - q^{49} + 11 q^{50} + 10 q^{51} + 7 q^{52} - 22 q^{53} - q^{54} + 12 q^{55} + q^{56} - 6 q^{57} - 9 q^{58} - 2 q^{59} - 8 q^{60} + q^{61} - 4 q^{62} - q^{63} + 2 q^{64} - 20 q^{65} - 6 q^{66} - 2 q^{67} + 5 q^{68} + 6 q^{69} - 8 q^{70} - 6 q^{71} + q^{72} + 24 q^{73} + 4 q^{74} + 11 q^{75} - 3 q^{76} - 6 q^{77} + 7 q^{78} + 22 q^{79} - 4 q^{80} - q^{81} + 5 q^{82} + 12 q^{83} + q^{84} + 20 q^{85} - 9 q^{87} - 3 q^{88} - 7 q^{89} - 8 q^{90} + 7 q^{91} + 12 q^{92} - 4 q^{93} - 3 q^{94} - 12 q^{95} + 2 q^{96} + 12 q^{97} + q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + 8 * q^5 - q^6 - q^7 - 2 * q^8 - q^9 + 4 * q^10 + 3 * q^11 - 2 * q^12 - 5 * q^13 - 2 * q^14 + 4 * q^15 - q^16 + 5 * q^17 - 2 * q^18 - 3 * q^19 - 4 * q^20 - 2 * q^21 - 3 * q^22 - 6 * q^23 - q^24 + 22 * q^25 + 2 * q^26 - 2 * q^27 - q^28 + 9 * q^29 - 4 * q^30 - 8 * q^31 + q^32 - 3 * q^33 + 10 * q^34 - 4 * q^35 - q^36 - 4 * q^37 - 6 * q^38 + 2 * q^39 - 8 * q^40 - 5 * q^41 - q^42 - 6 * q^44 - 4 * q^45 + 6 * q^46 - 6 * q^47 + q^48 - q^49 + 11 * q^50 + 10 * q^51 + 7 * q^52 - 22 * q^53 - q^54 + 12 * q^55 + q^56 - 6 * q^57 - 9 * q^58 - 2 * q^59 - 8 * q^60 + q^61 - 4 * q^62 - q^63 + 2 * q^64 - 20 * q^65 - 6 * q^66 - 2 * q^67 + 5 * q^68 + 6 * q^69 - 8 * q^70 - 6 * q^71 + q^72 + 24 * q^73 + 4 * q^74 + 11 * q^75 - 3 * q^76 - 6 * q^77 + 7 * q^78 + 22 * q^79 - 4 * q^80 - q^81 + 5 * q^82 + 12 * q^83 + q^84 + 20 * q^85 - 9 * q^87 - 3 * q^88 - 7 * q^89 - 8 * q^90 + 7 * q^91 + 12 * q^92 - 4 * q^93 - 3 * q^94 - 12 * q^95 + 2 * q^96 + 12 * q^97 + q^98 - 6 * q^99

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