LMFDB - Embedded newform 546.2.i.f.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(79,546)]

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, 0]))

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

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

chi := DirichletCharacter("546.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.i (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			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.79
Dual form			546.2.i.f.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} -1.00000 q^{13} +(2.00000 + 1.73205i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(0.500000 + 0.866025i) q^{18} +1.00000 q^{20} +(-2.50000 + 0.866025i) q^{21} +3.00000 q^{22} +(-3.00000 + 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-0.500000 + 0.866025i) q^{26} -1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} +9.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} +(-2.50000 - 4.33013i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +2.00000 q^{34} +(-2.00000 - 1.73205i) q^{35} +1.00000 q^{36} +(4.00000 - 6.92820i) q^{37} +(-0.500000 - 0.866025i) q^{39} +(0.500000 - 0.866025i) q^{40} -4.00000 q^{41} +(-0.500000 + 2.59808i) q^{42} +(1.50000 - 2.59808i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(3.00000 + 5.19615i) q^{46} -1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +4.00000 q^{50} +(-1.00000 + 1.73205i) q^{51} +(0.500000 + 0.866025i) q^{52} +(-0.500000 - 0.866025i) q^{53} +(-0.500000 + 0.866025i) q^{54} -3.00000 q^{55} +(0.500000 - 2.59808i) q^{56} +(4.50000 - 7.79423i) q^{58} +(3.50000 + 6.06218i) q^{59} +(0.500000 + 0.866025i) q^{60} +(2.00000 - 3.46410i) q^{61} -5.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(1.50000 + 2.59808i) q^{66} +(2.00000 + 3.46410i) q^{67} +(1.00000 - 1.73205i) q^{68} -6.00000 q^{69} +(-2.50000 + 0.866025i) q^{70} +6.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-3.00000 - 5.19615i) q^{73} +(-4.00000 - 6.92820i) q^{74} +(-2.00000 + 3.46410i) q^{75} +(-7.50000 + 2.59808i) q^{77} -1.00000 q^{78} +(6.50000 - 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.00000 + 3.46410i) q^{82} -3.00000 q^{83} +(2.00000 + 1.73205i) q^{84} -2.00000 q^{85} +(4.50000 + 7.79423i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(4.00000 - 6.92820i) q^{89} -1.00000 q^{90} +(0.500000 - 2.59808i) q^{91} +6.00000 q^{92} +(2.50000 - 4.33013i) q^{93} +(-0.500000 + 0.866025i) q^{96} -15.0000 q^{97} +(-5.50000 + 4.33013i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 - q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - q^{7} - 2 q^{8} - q^{9} + q^{10} + 3 q^{11} + q^{12} - 2 q^{13} + 4 q^{14} - 2 q^{15} - q^{16} + 2 q^{17} + q^{18} + 2 q^{20} - 5 q^{21} + 6 q^{22} - 6 q^{23} - q^{24} + 4 q^{25} - q^{26} - 2 q^{27} + 5 q^{28} + 18 q^{29} - q^{30} - 5 q^{31} + q^{32} - 3 q^{33} + 4 q^{34} - 4 q^{35} + 2 q^{36} + 8 q^{37} - q^{39} + q^{40} - 8 q^{41} - q^{42} + 3 q^{44} - q^{45} + 6 q^{46} - 2 q^{48} - 13 q^{49} + 8 q^{50} - 2 q^{51} + q^{52} - q^{53} - q^{54} - 6 q^{55} + q^{56} + 9 q^{58} + 7 q^{59} + q^{60} + 4 q^{61} - 10 q^{62} - 4 q^{63} + 2 q^{64} + q^{65} + 3 q^{66} + 4 q^{67} + 2 q^{68} - 12 q^{69} - 5 q^{70} + 12 q^{71} + q^{72} - 6 q^{73} - 8 q^{74} - 4 q^{75} - 15 q^{77} - 2 q^{78} + 13 q^{79} - q^{80} - q^{81} - 4 q^{82} - 6 q^{83} + 4 q^{84} - 4 q^{85} + 9 q^{87} - 3 q^{88} + 8 q^{89} - 2 q^{90} + q^{91} + 12 q^{92} + 5 q^{93} - q^{96} - 30 q^{97} - 11 q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 - q^7 - 2 * q^8 - q^9 + q^10 + 3 * q^11 + q^12 - 2 * q^13 + 4 * q^14 - 2 * q^15 - q^16 + 2 * q^17 + q^18 + 2 * q^20 - 5 * q^21 + 6 * q^22 - 6 * q^23 - q^24 + 4 * q^25 - q^26 - 2 * q^27 + 5 * q^28 + 18 * q^29 - q^30 - 5 * q^31 + q^32 - 3 * q^33 + 4 * q^34 - 4 * q^35 + 2 * q^36 + 8 * q^37 - q^39 + q^40 - 8 * q^41 - q^42 + 3 * q^44 - q^45 + 6 * q^46 - 2 * q^48 - 13 * q^49 + 8 * q^50 - 2 * q^51 + q^52 - q^53 - q^54 - 6 * q^55 + q^56 + 9 * q^58 + 7 * q^59 + q^60 + 4 * q^61 - 10 * q^62 - 4 * q^63 + 2 * q^64 + q^65 + 3 * q^66 + 4 * q^67 + 2 * q^68 - 12 * q^69 - 5 * q^70 + 12 * q^71 + q^72 - 6 * q^73 - 8 * q^74 - 4 * q^75 - 15 * q^77 - 2 * q^78 + 13 * q^79 - q^80 - q^81 - 4 * q^82 - 6 * q^83 + 4 * q^84 - 4 * q^85 + 9 * q^87 - 3 * q^88 + 8 * q^89 - 2 * q^90 + q^91 + 12 * q^92 + 5 * q^93 - q^96 - 30 * q^97 - 11 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	1.00000			0.408248
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	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	$0.683949\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	2.00000	+	1.73205i	0.534522	+	0.462910i
$15$	−1.00000			−0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$	1.00000			0.223607
$21$	−2.50000	+	0.866025i	−0.545545	+	0.188982i
$22$	3.00000			0.639602
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	−1.00000			−0.192450
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$	9.00000			1.67126			0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000			1.67126			0.835629	+	0.549294i	$0.185103\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$	2.00000			0.342997
$35$	−2.00000	−	1.73205i	−0.338062	−	0.292770i
$36$	1.00000			0.166667
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	−0.323640	−	0.946180i	$-0.604907\pi$
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	0.981236	−	0.192809i	$-0.0617599\pi$
$38$		0			0
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−4.00000			−0.624695			−0.312348	−	0.949968i	$-0.601115\pi$
$41$	−4.00000			−0.624695			−0.312348	+	0.949968i	$0.601115\pi$
$42$	−0.500000	+	2.59808i	−0.0771517	+	0.400892i
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	−1.00000			−0.144338
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	4.00000			0.565685
$51$	−1.00000	+	1.73205i	−0.140028	+	0.242536i
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	−0.500000	−	0.866025i	−0.0686803	−	0.118958i	0.829640	−	0.558298i	$-0.188546\pi$
$53$	−0.500000	−	0.866025i	−0.0686803	−	0.118958i	−0.898321	+	0.439340i	$0.855212\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−3.00000			−0.404520
$56$	0.500000	−	2.59808i	0.0668153	−	0.347183i
$57$		0			0
$58$	4.50000	−	7.79423i	0.590879	−	1.02343i
$59$	3.50000	+	6.06218i	0.455661	+	0.789228i	0.998726	−	0.0504625i	$-0.0160695\pi$
$59$	3.50000	+	6.06218i	0.455661	+	0.789228i	−0.543065	+	0.839691i	$0.682736\pi$
$60$	0.500000	+	0.866025i	0.0645497	+	0.111803i
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	−0.709113	−	0.705095i	$-0.750904\pi$
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	0.965187	+	0.261562i	$0.0842377\pi$
$62$	−5.00000			−0.635001
$63$	−2.00000	−	1.73205i	−0.251976	−	0.218218i
$64$	1.00000			0.125000
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$	1.50000	+	2.59808i	0.184637	+	0.319801i
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$	−6.00000			−0.722315
$70$	−2.50000	+	0.866025i	−0.298807	+	0.103510i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	0.635323	−	0.772246i	$-0.280867\pi$
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	−0.986447	+	0.164083i	$0.947534\pi$
$74$	−4.00000	−	6.92820i	−0.464991	−	0.805387i
$75$	−2.00000	+	3.46410i	−0.230940	+	0.400000i
$76$		0			0
$77$	−7.50000	+	2.59808i	−0.854704	+	0.296078i
$78$	−1.00000			−0.113228
$79$	6.50000	−	11.2583i	0.731307	−	1.26666i	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	6.50000	−	11.2583i	0.731307	−	1.26666i	0.956325	−	0.292306i	$-0.0944227\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.00000	+	3.46410i	−0.220863	+	0.382546i
$83$	−3.00000			−0.329293			−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000			−0.329293			−0.164646	+	0.986353i	$0.552648\pi$
$84$	2.00000	+	1.73205i	0.218218	+	0.188982i
$85$	−2.00000			−0.216930
$86$		0			0
$87$	4.50000	+	7.79423i	0.482451	+	0.835629i
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	4.00000	−	6.92820i	0.423999	−	0.734388i	−0.572327	−	0.820025i	$-0.693959\pi$
$89$	4.00000	−	6.92820i	0.423999	−	0.734388i	0.996326	+	0.0856373i	$0.0272926\pi$
$90$	−1.00000			−0.105409
$91$	0.500000	−	2.59808i	0.0524142	−	0.272352i
$92$	6.00000			0.625543
$93$	2.50000	−	4.33013i	0.259238	−	0.449013i
$94$		0			0
$95$		0			0
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−15.0000			−1.52302			−0.761510	−	0.648154i	$-0.775541\pi$
$97$	−15.0000			−1.52302			−0.761510	+	0.648154i	$0.775541\pi$
$98$	−5.50000	+	4.33013i	−0.555584	+	0.437409i
$99$	−3.00000			−0.301511
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	0.911479	−	0.411346i	$-0.134941\pi$
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	−0.811976	+	0.583691i	$0.801608\pi$
$102$	1.00000	+	1.73205i	0.0990148	+	0.171499i
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	−0.138767	−	0.990325i	$-0.544314\pi$
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	0.927030	−	0.374987i	$-0.122353\pi$
$104$	1.00000			0.0980581
$105$	0.500000	−	2.59808i	0.0487950	−	0.253546i
$106$	−1.00000			−0.0971286
$107$	−8.50000	+	14.7224i	−0.821726	+	1.42327i	0.0826699	+	0.996577i	$0.473655\pi$
$107$	−8.50000	+	14.7224i	−0.821726	+	1.42327i	−0.904396	+	0.426694i	$0.859678\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−8.00000	−	13.8564i	−0.766261	−	1.32720i	−0.939577	−	0.342337i	$-0.888782\pi$
$109$	−8.00000	−	13.8564i	−0.766261	−	1.32720i	0.173316	−	0.984866i	$-0.444552\pi$
$110$	−1.50000	+	2.59808i	−0.143019	+	0.247717i
$111$	8.00000			0.759326
$112$	−2.00000	−	1.73205i	−0.188982	−	0.163663i
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$		0			0
$115$	−3.00000	−	5.19615i	−0.279751	−	0.484544i
$116$	−4.50000	−	7.79423i	−0.417815	−	0.723676i
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$	7.00000			0.644402
$119$	−5.00000	+	1.73205i	−0.458349	+	0.158777i
$120$	1.00000			0.0912871
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−2.00000	−	3.46410i	−0.181071	−	0.313625i
$123$	−2.00000	−	3.46410i	−0.180334	−	0.312348i
$124$	−2.50000	+	4.33013i	−0.224507	+	0.388857i
$125$	−9.00000			−0.804984
$126$	−2.50000	+	0.866025i	−0.222718	+	0.0771517i
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.500000	−	0.866025i	−0.0438529	−	0.0759555i
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	0.326546	+	0.945181i	$0.394115\pi$
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	−0.981824	+	0.189794i	$0.939218\pi$
$132$	3.00000			0.261116
$133$		0			0
$134$	4.00000			0.345547
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$	−3.00000	+	5.19615i	−0.255377	+	0.442326i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$	−0.500000	+	2.59808i	−0.0422577	+	0.219578i
$141$		0			0
$142$	3.00000	−	5.19615i	0.251754	−	0.436051i
$143$	−1.50000	−	2.59808i	−0.125436	−	0.217262i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−4.50000	+	7.79423i	−0.373705	+	0.647275i
$146$	−6.00000			−0.496564
$147$	−1.00000	−	6.92820i	−0.0824786	−	0.571429i
$148$	−8.00000			−0.657596
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	2.00000	+	3.46410i	0.163299	+	0.282843i
$151$	5.50000	+	9.52628i	0.447584	+	0.775238i	0.998228	−	0.0595022i	$-0.0189513\pi$
$151$	5.50000	+	9.52628i	0.447584	+	0.775238i	−0.550645	+	0.834740i	$0.685618\pi$
$152$		0			0
$153$	−2.00000			−0.161690
$154$	−1.50000	+	7.79423i	−0.120873	+	0.628077i
$155$	5.00000			0.401610
$156$	−0.500000	+	0.866025i	−0.0400320	+	0.0693375i
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	0.997609	+	0.0691164i	$0.0220180\pi$
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	−0.438948	+	0.898513i	$0.644649\pi$
$158$	−6.50000	−	11.2583i	−0.517112	−	0.895665i
$159$	0.500000	−	0.866025i	0.0396526	−	0.0686803i
$160$	−1.00000			−0.0790569
$161$	−12.0000	−	10.3923i	−0.945732	−	0.819028i
$162$	−1.00000			−0.0785674
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$	2.00000	+	3.46410i	0.156174	+	0.270501i
$165$	−1.50000	−	2.59808i	−0.116775	−	0.202260i
$166$	−1.50000	+	2.59808i	−0.116423	+	0.201650i
$167$	−4.00000			−0.309529			−0.154765	−	0.987951i	$-0.549462\pi$
$167$	−4.00000			−0.309529			−0.154765	+	0.987951i	$0.549462\pi$
$168$	2.50000	−	0.866025i	0.192879	−	0.0668153i
$169$	1.00000			0.0769231
$170$	−1.00000	+	1.73205i	−0.0766965	+	0.132842i
$171$		0			0
$172$		0			0
$173$	7.00000	−	12.1244i	0.532200	−	0.921798i	−0.467093	−	0.884208i	$-0.654699\pi$
$173$	7.00000	−	12.1244i	0.532200	−	0.921798i	0.999293	−	0.0375896i	$-0.0119679\pi$
$174$	9.00000			0.682288
$175$	−10.0000	+	3.46410i	−0.755929	+	0.261861i
$176$	−3.00000			−0.226134
$177$	−3.50000	+	6.06218i	−0.263076	+	0.455661i
$178$	−4.00000	−	6.92820i	−0.299813	−	0.519291i
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	0.549825	−	0.835280i	$-0.314694\pi$
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	−0.998286	+	0.0585225i	$0.981361\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	−8.00000			−0.594635			−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000			−0.594635			−0.297318	+	0.954779i	$0.596092\pi$
$182$	−2.00000	−	1.73205i	−0.148250	−	0.128388i
$183$	4.00000			0.295689
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$	4.00000	+	6.92820i	0.294086	+	0.509372i
$186$	−2.50000	−	4.33013i	−0.183309	−	0.317500i
$187$	−3.00000	+	5.19615i	−0.219382	+	0.379980i
$188$		0			0
$189$	0.500000	−	2.59808i	0.0363696	−	0.188982i
$190$		0			0
$191$	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
$193$	−9.50000	−	16.4545i	−0.683825	−	1.18442i	−0.973805	−	0.227387i	$-0.926982\pi$
$193$	−9.50000	−	16.4545i	−0.683825	−	1.18442i	0.289980	−	0.957033i	$-0.406351\pi$
$194$	−7.50000	+	12.9904i	−0.538469	+	0.932655i
$195$	1.00000			0.0716115
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	−22.0000			−1.56744			−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000			−1.56744			−0.783718	+	0.621117i	$0.786679\pi$
$198$	−1.50000	+	2.59808i	−0.106600	+	0.184637i
$199$	12.0000	+	20.7846i	0.850657	+	1.47338i	0.880616	+	0.473831i	$0.157129\pi$
$199$	12.0000	+	20.7846i	0.850657	+	1.47338i	−0.0299585	+	0.999551i	$0.509538\pi$
$200$	−2.00000	−	3.46410i	−0.141421	−	0.244949i
$201$	−2.00000	+	3.46410i	−0.141069	+	0.244339i
$202$	2.00000			0.140720
$203$	−4.50000	+	23.3827i	−0.315838	+	1.64114i
$204$	2.00000			0.140028
$205$	2.00000	−	3.46410i	0.139686	−	0.241943i
$206$	−8.00000	−	13.8564i	−0.557386	−	0.965422i
$207$	−3.00000	−	5.19615i	−0.208514	−	0.361158i
$208$	0.500000	−	0.866025i	0.0346688	−	0.0600481i
$209$		0			0
$210$	−2.00000	−	1.73205i	−0.138013	−	0.119523i
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$	−0.500000	+	0.866025i	−0.0343401	+	0.0594789i
$213$	3.00000	+	5.19615i	0.205557	+	0.356034i
$214$	8.50000	+	14.7224i	0.581048	+	1.00640i
$215$		0			0
$216$	1.00000			0.0680414
$217$	12.5000	−	4.33013i	0.848555	−	0.293948i
$218$	−16.0000			−1.08366
$219$	3.00000	−	5.19615i	0.202721	−	0.351123i
$220$	1.50000	+	2.59808i	0.101130	+	0.175162i
$221$	−1.00000	−	1.73205i	−0.0672673	−	0.116510i
$222$	4.00000	−	6.92820i	0.268462	−	0.464991i
$223$	−1.00000			−0.0669650			−0.0334825	−	0.999439i	$-0.510660\pi$
$223$	−1.00000			−0.0669650			−0.0334825	+	0.999439i	$0.510660\pi$
$224$	−2.50000	+	0.866025i	−0.167038	+	0.0578638i
$225$	−4.00000			−0.266667
$226$	6.00000	−	10.3923i	0.399114	−	0.691286i
$227$	6.50000	+	11.2583i	0.431420	+	0.747242i	0.996996	−	0.0774548i	$-0.0246793\pi$
$227$	6.50000	+	11.2583i	0.431420	+	0.747242i	−0.565576	+	0.824696i	$0.691346\pi$
$228$		0			0
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	−0.536515	−	0.843891i	$-0.680260\pi$
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	0.999088	+	0.0426906i	$0.0135930\pi$
$230$	−6.00000			−0.395628
$231$	−6.00000	−	5.19615i	−0.394771	−	0.341882i
$232$	−9.00000			−0.590879
$233$	7.00000	−	12.1244i	0.458585	−	0.794293i	−0.540301	−	0.841472i	$-0.681690\pi$
$233$	7.00000	−	12.1244i	0.458585	−	0.794293i	0.998886	+	0.0471787i	$0.0150230\pi$
$234$	−0.500000	−	0.866025i	−0.0326860	−	0.0566139i
$235$		0			0
$236$	3.50000	−	6.06218i	0.227831	−	0.394614i
$237$	13.0000			0.844441
$238$	−1.00000	+	5.19615i	−0.0648204	+	0.336817i
$239$	22.0000			1.42306			0.711531	−	0.702655i	$-0.248002\pi$
$239$	22.0000			1.42306			0.711531	+	0.702655i	$0.248002\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	13.5000	+	23.3827i	0.869611	+	1.50621i	0.862394	+	0.506237i	$0.168964\pi$
$241$	13.5000	+	23.3827i	0.869611	+	1.50621i	0.00721719	+	0.999974i	$0.497703\pi$
$242$	−1.00000	−	1.73205i	−0.0642824	−	0.111340i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−4.00000			−0.256074
$245$	5.50000	−	4.33013i	0.351382	−	0.276642i
$246$	−4.00000			−0.255031
$247$		0			0
$248$	2.50000	+	4.33013i	0.158750	+	0.274963i
$249$	−1.50000	−	2.59808i	−0.0950586	−	0.164646i
$250$	−4.50000	+	7.79423i	−0.284605	+	0.492950i
$251$	23.0000			1.45175			0.725874	−	0.687828i	$-0.241436\pi$
$251$	23.0000			1.45175			0.725874	+	0.687828i	$0.241436\pi$
$252$	−0.500000	+	2.59808i	−0.0314970	+	0.163663i
$253$	−18.0000			−1.13165
$254$	2.50000	−	4.33013i	0.156864	−	0.271696i
$255$	−1.00000	−	1.73205i	−0.0626224	−	0.108465i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.0000	−	22.5167i	0.810918	−	1.40455i	−0.101305	−	0.994855i	$-0.532302\pi$
$257$	13.0000	−	22.5167i	0.810918	−	1.40455i	0.912222	−	0.409695i	$-0.134365\pi$
$258$		0			0
$259$	16.0000	+	13.8564i	0.994192	+	0.860995i
$260$	−1.00000			−0.0620174
$261$	−4.50000	+	7.79423i	−0.278543	+	0.482451i
$262$	7.50000	+	12.9904i	0.463352	+	0.802548i
$263$	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
$265$	1.00000			0.0614295
$266$		0			0
$267$	8.00000			0.489592
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	0.908124	−	0.418701i	$-0.137514\pi$
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	−0.816668	+	0.577108i	$0.804181\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	−4.50000	+	7.79423i	−0.273356	+	0.473466i	−0.969719	−	0.244224i	$-0.921467\pi$
$271$	−4.50000	+	7.79423i	−0.273356	+	0.473466i	0.696363	+	0.717689i	$0.254800\pi$
$272$	−2.00000			−0.121268
$273$	2.50000	−	0.866025i	0.151307	−	0.0524142i
$274$	12.0000			0.724947
$275$	−6.00000	+	10.3923i	−0.361814	+	0.626680i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	11.0000	+	19.0526i	0.660926	+	1.14476i	0.980373	+	0.197153i	$0.0631696\pi$
$277$	11.0000	+	19.0526i	0.660926	+	1.14476i	−0.319447	+	0.947604i	$0.603497\pi$
$278$	2.00000	−	3.46410i	0.119952	−	0.207763i
$279$	5.00000			0.299342
$280$	2.00000	+	1.73205i	0.119523	+	0.103510i
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$		0			0
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	0.579437	−	0.815017i	$-0.303272\pi$
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	−0.995544	+	0.0942988i	$0.969939\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$		0			0
$286$	−3.00000			−0.177394
$287$	2.00000	−	10.3923i	0.118056	−	0.613438i
$288$	−1.00000			−0.0589256
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	4.50000	+	7.79423i	0.264249	+	0.457693i
$291$	−7.50000	−	12.9904i	−0.439658	−	0.761510i
$292$	−3.00000	+	5.19615i	−0.175562	+	0.304082i
$293$	15.0000			0.876309			0.438155	−	0.898900i	$-0.355632\pi$
$293$	15.0000			0.876309			0.438155	+	0.898900i	$0.355632\pi$
$294$	−6.50000	−	2.59808i	−0.379088	−	0.151523i
$295$	−7.00000			−0.407556
$296$	−4.00000	+	6.92820i	−0.232495	+	0.402694i
$297$	−1.50000	−	2.59808i	−0.0870388	−	0.150756i
$298$	−3.00000	−	5.19615i	−0.173785	−	0.301005i
$299$	3.00000	−	5.19615i	0.173494	−	0.300501i
$300$	4.00000			0.230940
$301$		0			0
$302$	11.0000			0.632979
$303$	−1.00000	+	1.73205i	−0.0574485	+	0.0995037i
$304$		0			0
$305$	2.00000	+	3.46410i	0.114520	+	0.198354i
$306$	−1.00000	+	1.73205i	−0.0571662	+	0.0990148i
$307$	−18.0000			−1.02731			−0.513657	−	0.857996i	$-0.671710\pi$
$307$	−18.0000			−1.02731			−0.513657	+	0.857996i	$0.671710\pi$
$308$	6.00000	+	5.19615i	0.341882	+	0.296078i
$309$	16.0000			0.910208
$310$	2.50000	−	4.33013i	0.141990	−	0.245935i
$311$	−1.00000	−	1.73205i	−0.0567048	−	0.0982156i	0.836280	−	0.548303i	$-0.184726\pi$
$311$	−1.00000	−	1.73205i	−0.0567048	−	0.0982156i	−0.892984	+	0.450088i	$0.851393\pi$
$312$	0.500000	+	0.866025i	0.0283069	+	0.0490290i
$313$	−6.50000	+	11.2583i	−0.367402	+	0.636358i	−0.989158	−	0.146852i	$-0.953086\pi$
$313$	−6.50000	+	11.2583i	−0.367402	+	0.636358i	0.621757	+	0.783210i	$0.286419\pi$
$314$	14.0000			0.790066
$315$	2.50000	−	0.866025i	0.140859	−	0.0487950i
$316$	−13.0000			−0.731307
$317$	−1.50000	+	2.59808i	−0.0842484	+	0.145922i	−0.905071	−	0.425261i	$-0.860182\pi$
$317$	−1.50000	+	2.59808i	−0.0842484	+	0.145922i	0.820822	+	0.571184i	$0.193516\pi$
$318$	−0.500000	−	0.866025i	−0.0280386	−	0.0485643i
$319$	13.5000	+	23.3827i	0.755855	+	1.30918i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−17.0000			−0.948847
$322$	−15.0000	+	5.19615i	−0.835917	+	0.289570i
$323$		0			0
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−2.00000	−	3.46410i	−0.110940	−	0.192154i
$326$	−2.00000	−	3.46410i	−0.110770	−	0.191859i
$327$	8.00000	−	13.8564i	0.442401	−	0.766261i
$328$	4.00000			0.220863
$329$		0			0
$330$	−3.00000			−0.165145
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	−0.954765	−	0.297361i	$-0.903893\pi$
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	0.734905	+	0.678170i	$0.237227\pi$
$332$	1.50000	+	2.59808i	0.0823232	+	0.142588i
$333$	4.00000	+	6.92820i	0.219199	+	0.379663i
$334$	−2.00000	+	3.46410i	−0.109435	+	0.189547i
$335$	−4.00000			−0.218543
$336$	0.500000	−	2.59808i	0.0272772	−	0.141737i
$337$	1.00000			0.0544735			0.0272367	−	0.999629i	$-0.491329\pi$
$337$	1.00000			0.0544735			0.0272367	+	0.999629i	$0.491329\pi$
$338$	0.500000	−	0.866025i	0.0271964	−	0.0471056i
$339$	6.00000	+	10.3923i	0.325875	+	0.564433i
$340$	1.00000	+	1.73205i	0.0542326	+	0.0939336i
$341$	7.50000	−	12.9904i	0.406148	−	0.703469i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$		0			0
$345$	3.00000	−	5.19615i	0.161515	−	0.279751i
$346$	−7.00000	−	12.1244i	−0.376322	−	0.651809i
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	0.947067	+	0.321037i	$0.104031\pi$
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	−0.195507	+	0.980702i	$0.562635\pi$
$348$	4.50000	−	7.79423i	0.241225	−	0.417815i
$349$	−34.0000			−1.81998			−0.909989	−	0.414632i	$-0.863910\pi$
$349$	−34.0000			−1.81998			−0.909989	+	0.414632i	$0.863910\pi$
$350$	−2.00000	+	10.3923i	−0.106904	+	0.555492i
$351$	1.00000			0.0533761
$352$	−1.50000	+	2.59808i	−0.0799503	+	0.138478i
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	0.775077	−	0.631867i	$-0.217711\pi$
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	−0.934751	+	0.355303i	$0.884378\pi$
$354$	3.50000	+	6.06218i	0.186023	+	0.322201i
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$	−8.00000			−0.423999
$357$	−4.00000	−	3.46410i	−0.211702	−	0.183340i
$358$	−12.0000			−0.634220
$359$	1.00000	−	1.73205i	0.0527780	−	0.0914141i	−0.838429	−	0.545010i	$-0.816526\pi$
$359$	1.00000	−	1.73205i	0.0527780	−	0.0914141i	0.891207	+	0.453596i	$0.149859\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	−4.00000	+	6.92820i	−0.210235	+	0.364138i
$363$	2.00000			0.104973
$364$	−2.50000	+	0.866025i	−0.131036	+	0.0453921i
$365$	6.00000			0.314054
$366$	2.00000	−	3.46410i	0.104542	−	0.181071i
$367$	1.50000	+	2.59808i	0.0782994	+	0.135618i	0.902516	−	0.430656i	$-0.141718\pi$
$367$	1.50000	+	2.59808i	0.0782994	+	0.135618i	−0.824217	+	0.566274i	$0.808384\pi$
$368$	−3.00000	−	5.19615i	−0.156386	−	0.270868i
$369$	2.00000	−	3.46410i	0.104116	−	0.180334i
$370$	8.00000			0.415900
$371$	2.50000	−	0.866025i	0.129794	−	0.0449618i
$372$	−5.00000			−0.259238
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	−0.303902	−	0.952703i	$-0.598289\pi$
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	0.977016	−	0.213165i	$-0.0683772\pi$
$374$	3.00000	+	5.19615i	0.155126	+	0.268687i
$375$	−4.50000	−	7.79423i	−0.232379	−	0.402492i
$376$		0			0
$377$	−9.00000			−0.463524
$378$	−2.00000	−	1.73205i	−0.102869	−	0.0890871i
$379$	−24.0000			−1.23280			−0.616399	−	0.787434i	$-0.711409\pi$
$379$	−24.0000			−1.23280			−0.616399	+	0.787434i	$0.711409\pi$
$380$		0			0
$381$	2.50000	+	4.33013i	0.128079	+	0.221839i
$382$	−3.00000	−	5.19615i	−0.153493	−	0.265858i
$383$	13.0000	−	22.5167i	0.664269	−	1.15055i	−0.315214	−	0.949021i	$-0.602076\pi$
$383$	13.0000	−	22.5167i	0.664269	−	1.15055i	0.979483	−	0.201527i	$-0.0645904\pi$
$384$	1.00000			0.0510310
$385$	1.50000	−	7.79423i	0.0764471	−	0.397231i
$386$	−19.0000			−0.967075
$387$		0			0
$388$	7.50000	+	12.9904i	0.380755	+	0.659487i
$389$	−17.0000	−	29.4449i	−0.861934	−	1.49291i	−0.870059	−	0.492947i	$-0.835920\pi$
$389$	−17.0000	−	29.4449i	−0.861934	−	1.49291i	0.00812520	−	0.999967i	$-0.497414\pi$
$390$	0.500000	−	0.866025i	0.0253185	−	0.0438529i
$391$	−12.0000			−0.606866
$392$	6.50000	+	2.59808i	0.328300	+	0.131223i
$393$	−15.0000			−0.756650
$394$	−11.0000	+	19.0526i	−0.554172	+	0.959854i
$395$	6.50000	+	11.2583i	0.327050	+	0.566468i
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	−17.0000	+	29.4449i	−0.853206	+	1.47780i	0.0250943	+	0.999685i	$0.492011\pi$
$397$	−17.0000	+	29.4449i	−0.853206	+	1.47780i	−0.878300	+	0.478110i	$0.841322\pi$
$398$	24.0000			1.20301
$399$		0			0
$400$	−4.00000			−0.200000
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	−0.931158	−	0.364615i	$-0.881200\pi$
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	0.781345	+	0.624099i	$0.214534\pi$
$402$	2.00000	+	3.46410i	0.0997509	+	0.172774i
$403$	2.50000	+	4.33013i	0.124534	+	0.215699i
$404$	1.00000	−	1.73205i	0.0497519	−	0.0861727i
$405$	1.00000			0.0496904
$406$	18.0000	+	15.5885i	0.893325	+	0.773642i
$407$	24.0000			1.18964
$408$	1.00000	−	1.73205i	0.0495074	−	0.0857493i
$409$	5.50000	+	9.52628i	0.271957	+	0.471044i	0.969363	−	0.245633i	$-0.0789957\pi$
$409$	5.50000	+	9.52628i	0.271957	+	0.471044i	−0.697406	+	0.716677i	$0.745662\pi$
$410$	−2.00000	−	3.46410i	−0.0987730	−	0.171080i
$411$	−6.00000	+	10.3923i	−0.295958	+	0.512615i
$412$	−16.0000			−0.788263
$413$	−17.5000	+	6.06218i	−0.861119	+	0.298300i
$414$	−6.00000			−0.294884
$415$	1.50000	−	2.59808i	0.0736321	−	0.127535i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	2.00000	+	3.46410i	0.0979404	+	0.169638i
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	−2.50000	+	0.866025i	−0.121988	+	0.0422577i
$421$	−12.0000			−0.584844			−0.292422	−	0.956289i	$-0.594461\pi$
$421$	−12.0000			−0.584844			−0.292422	+	0.956289i	$0.594461\pi$
$422$	10.0000	−	17.3205i	0.486792	−	0.843149i
$423$		0			0
$424$	0.500000	+	0.866025i	0.0242821	+	0.0420579i
$425$	−4.00000	+	6.92820i	−0.194029	+	0.336067i
$426$	6.00000			0.290701
$427$	8.00000	+	6.92820i	0.387147	+	0.335279i
$428$	17.0000			0.821726
$429$	1.50000	−	2.59808i	0.0724207	−	0.125436i
$430$		0			0
$431$	−13.0000	−	22.5167i	−0.626188	−	1.08459i	−0.988310	−	0.152459i	$-0.951281\pi$
$431$	−13.0000	−	22.5167i	−0.626188	−	1.08459i	0.362122	−	0.932131i	$-0.382052\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−38.0000			−1.82616			−0.913082	−	0.407777i	$-0.866304\pi$
$433$	−38.0000			−1.82616			−0.913082	+	0.407777i	$0.866304\pi$
$434$	2.50000	−	12.9904i	0.120004	−	0.623558i
$435$	−9.00000			−0.431517
$436$	−8.00000	+	13.8564i	−0.383131	+	0.663602i
$437$		0			0
$438$	−3.00000	−	5.19615i	−0.143346	−	0.248282i
$439$	14.5000	−	25.1147i	0.692047	−	1.19866i	−0.279119	−	0.960257i	$-0.590042\pi$
$439$	14.5000	−	25.1147i	0.692047	−	1.19866i	0.971166	−	0.238404i	$-0.0766244\pi$
$440$	3.00000			0.143019
$441$	5.50000	−	4.33013i	0.261905	−	0.206197i
$442$	−2.00000			−0.0951303
$443$	−19.5000	+	33.7750i	−0.926473	+	1.60470i	−0.137298	+	0.990530i	$0.543842\pi$
$443$	−19.5000	+	33.7750i	−0.926473	+	1.60470i	−0.789175	+	0.614168i	$0.789492\pi$
$444$	−4.00000	−	6.92820i	−0.189832	−	0.328798i
$445$	4.00000	+	6.92820i	0.189618	+	0.328428i
$446$	−0.500000	+	0.866025i	−0.0236757	+	0.0410075i
$447$	6.00000			0.283790
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$	8.00000			0.377543			0.188772	−	0.982021i	$-0.439549\pi$
$449$	8.00000			0.377543			0.188772	+	0.982021i	$0.439549\pi$
$450$	−2.00000	+	3.46410i	−0.0942809	+	0.163299i
$451$	−6.00000	−	10.3923i	−0.282529	−	0.489355i
$452$	−6.00000	−	10.3923i	−0.282216	−	0.488813i
$453$	−5.50000	+	9.52628i	−0.258413	+	0.447584i
$454$	13.0000			0.610120
$455$	2.00000	+	1.73205i	0.0937614	+	0.0811998i
$456$		0			0
$457$	−0.500000	+	0.866025i	−0.0233890	+	0.0405110i	−0.877483	−	0.479608i	$-0.840779\pi$
$457$	−0.500000	+	0.866025i	−0.0233890	+	0.0405110i	0.854094	+	0.520119i	$0.174112\pi$
$458$	−7.00000	−	12.1244i	−0.327089	−	0.566534i
$459$	−1.00000	−	1.73205i	−0.0466760	−	0.0808452i
$460$	−3.00000	+	5.19615i	−0.139876	+	0.242272i
$461$	−26.0000			−1.21094			−0.605470	−	0.795868i	$-0.707015\pi$
$461$	−26.0000			−1.21094			−0.605470	+	0.795868i	$0.707015\pi$
$462$	−7.50000	+	2.59808i	−0.348932	+	0.120873i
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$	−4.50000	+	7.79423i	−0.208907	+	0.361838i
$465$	2.50000	+	4.33013i	0.115935	+	0.200805i
$466$	−7.00000	−	12.1244i	−0.324269	−	0.561650i
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	−0.970799	−	0.239892i	$-0.922888\pi$
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	0.693153	+	0.720791i	$0.256221\pi$
$468$	−1.00000			−0.0462250
$469$	−10.0000	+	3.46410i	−0.461757	+	0.159957i
$470$		0			0
$471$	−7.00000	+	12.1244i	−0.322543	+	0.558661i
$472$	−3.50000	−	6.06218i	−0.161101	−	0.279034i
$473$		0			0
$474$	6.50000	−	11.2583i	0.298555	−	0.517112i
$475$		0			0
$476$	4.00000	+	3.46410i	0.183340	+	0.158777i
$477$	1.00000			0.0457869
$478$	11.0000	−	19.0526i	0.503128	−	0.871444i
$479$	−15.0000	−	25.9808i	−0.685367	−	1.18709i	−0.973321	−	0.229447i	$-0.926308\pi$
$479$	−15.0000	−	25.9808i	−0.685367	−	1.18709i	0.287954	−	0.957644i	$-0.407025\pi$
$480$	−0.500000	−	0.866025i	−0.0228218	−	0.0395285i
$481$	−4.00000	+	6.92820i	−0.182384	+	0.315899i
$482$	27.0000			1.22982
$483$	3.00000	−	15.5885i	0.136505	−	0.709299i
$484$	−2.00000			−0.0909091
$485$	7.50000	−	12.9904i	0.340557	−	0.589863i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	4.50000	+	7.79423i	0.203914	+	0.353190i	0.949786	−	0.312899i	$-0.101300\pi$
$487$	4.50000	+	7.79423i	0.203914	+	0.353190i	−0.745872	+	0.666089i	$0.767967\pi$
$488$	−2.00000	+	3.46410i	−0.0905357	+	0.156813i
$489$	4.00000			0.180886
$490$	−1.00000	−	6.92820i	−0.0451754	−	0.312984i
$491$	−29.0000			−1.30875			−0.654376	−	0.756169i	$-0.727069\pi$
$491$	−29.0000			−1.30875			−0.654376	+	0.756169i	$0.727069\pi$
$492$	−2.00000	+	3.46410i	−0.0901670	+	0.156174i
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$		0			0
$495$	1.50000	−	2.59808i	0.0674200	−	0.116775i
$496$	5.00000			0.224507
$497$	−3.00000	+	15.5885i	−0.134568	+	0.699238i
$498$	−3.00000			−0.134433
$499$	−8.00000	+	13.8564i	−0.358129	+	0.620298i	−0.987648	−	0.156687i	$-0.949919\pi$
$499$	−8.00000	+	13.8564i	−0.358129	+	0.620298i	0.629519	+	0.776985i	$0.283252\pi$
$500$	4.50000	+	7.79423i	0.201246	+	0.348569i
$501$	−2.00000	−	3.46410i	−0.0893534	−	0.154765i
$502$	11.5000	−	19.9186i	0.513270	−	0.889010i
$503$	−26.0000			−1.15928			−0.579641	−	0.814872i	$-0.696807\pi$
$503$	−26.0000			−1.15928			−0.579641	+	0.814872i	$0.696807\pi$
$504$	2.00000	+	1.73205i	0.0890871	+	0.0771517i
$505$	−2.00000			−0.0889988
$506$	−9.00000	+	15.5885i	−0.400099	+	0.692991i
$507$	0.500000	+	0.866025i	0.0222058	+	0.0384615i
$508$	−2.50000	−	4.33013i	−0.110920	−	0.192118i
$509$	10.5000	−	18.1865i	0.465404	−	0.806104i	−0.533815	−	0.845601i	$-0.679242\pi$
$509$	10.5000	−	18.1865i	0.465404	−	0.806104i	0.999220	+	0.0394971i	$0.0125756\pi$
$510$	−2.00000			−0.0885615
$511$	15.0000	−	5.19615i	0.663561	−	0.229864i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−13.0000	−	22.5167i	−0.573405	−	0.993167i
$515$	8.00000	+	13.8564i	0.352522	+	0.610586i
$516$		0			0
$517$		0			0
$518$	20.0000	−	6.92820i	0.878750	−	0.304408i
$519$	14.0000			0.614532
$520$	−0.500000	+	0.866025i	−0.0219265	+	0.0379777i
$521$	−14.0000	−	24.2487i	−0.613351	−	1.06236i	−0.990671	−	0.136272i	$-0.956488\pi$
$521$	−14.0000	−	24.2487i	−0.613351	−	1.06236i	0.377320	−	0.926083i	$-0.376846\pi$
$522$	4.50000	+	7.79423i	0.196960	+	0.341144i
$523$	6.00000	−	10.3923i	0.262362	−	0.454424i	−0.704507	−	0.709697i	$-0.748832\pi$
$523$	6.00000	−	10.3923i	0.262362	−	0.454424i	0.966869	+	0.255273i	$0.0821653\pi$
$524$	15.0000			0.655278
$525$	−8.00000	−	6.92820i	−0.349149	−	0.302372i
$526$	26.0000			1.13365
$527$	5.00000	−	8.66025i	0.217803	−	0.377247i
$528$	−1.50000	−	2.59808i	−0.0652791	−	0.113067i
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	0.500000	−	0.866025i	0.0217186	−	0.0376177i
$531$	−7.00000			−0.303774
$532$		0			0
$533$	4.00000			0.173259
$534$	4.00000	−	6.92820i	0.173097	−	0.299813i
$535$	−8.50000	−	14.7224i	−0.367487	−	0.636506i
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$	6.00000	−	10.3923i	0.258919	−	0.448461i
$538$	3.00000			0.129339
$539$	−3.00000	−	20.7846i	−0.129219	−	0.895257i
$540$	−1.00000			−0.0430331
$541$	16.0000	−	27.7128i	0.687894	−	1.19147i	−0.284624	−	0.958639i	$-0.591869\pi$
$541$	16.0000	−	27.7128i	0.687894	−	1.19147i	0.972518	−	0.232828i	$-0.0747978\pi$
$542$	4.50000	+	7.79423i	0.193292	+	0.334791i
$543$	−4.00000	−	6.92820i	−0.171656	−	0.297318i
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$	16.0000			0.685365
$546$	0.500000	−	2.59808i	0.0213980	−	0.111187i
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	6.00000	−	10.3923i	0.256307	−	0.443937i
$549$	2.00000	+	3.46410i	0.0853579	+	0.147844i
$550$	6.00000	+	10.3923i	0.255841	+	0.443129i
$551$		0			0
$552$	6.00000			0.255377
$553$	26.0000	+	22.5167i	1.10563	+	0.957506i
$554$	22.0000			0.934690
$555$	−4.00000	+	6.92820i	−0.169791	+	0.294086i
$556$	−2.00000	−	3.46410i	−0.0848189	−	0.146911i
$557$	−8.50000	−	14.7224i	−0.360157	−	0.623809i	0.627830	−	0.778351i	$-0.283943\pi$
$557$	−8.50000	−	14.7224i	−0.360157	−	0.623809i	−0.987986	+	0.154541i	$0.950610\pi$
$558$	2.50000	−	4.33013i	0.105833	−	0.183309i
$559$		0			0
$560$	2.50000	−	0.866025i	0.105644	−	0.0365963i
$561$	−6.00000			−0.253320
$562$		0			0
$563$	−1.50000	−	2.59808i	−0.0632175	−	0.109496i	0.832684	−	0.553748i	$-0.186803\pi$
$563$	−1.50000	−	2.59808i	−0.0632175	−	0.109496i	−0.895902	+	0.444252i	$0.853470\pi$
$564$		0			0
$565$	−6.00000	+	10.3923i	−0.252422	+	0.437208i
$566$	−14.0000			−0.588464
$567$	2.50000	−	0.866025i	0.104990	−	0.0363696i
$568$	−6.00000			−0.251754
$569$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$569$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	−1.50000	+	2.59808i	−0.0627182	+	0.108631i
$573$	6.00000			0.250654
$574$	−8.00000	−	6.92820i	−0.333914	−	0.289178i
$575$	−24.0000			−1.00087
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	1.50000	+	2.59808i	0.0624458	+	0.108159i	0.895558	−	0.444945i	$-0.146777\pi$
$577$	1.50000	+	2.59808i	0.0624458	+	0.108159i	−0.833112	+	0.553104i	$0.813443\pi$
$578$	−6.50000	−	11.2583i	−0.270364	−	0.468285i
$579$	9.50000	−	16.4545i	0.394807	−	0.683825i
$580$	9.00000			0.373705
$581$	1.50000	−	7.79423i	0.0622305	−	0.323359i
$582$	−15.0000			−0.621770
$583$	1.50000	−	2.59808i	0.0621237	−	0.107601i
$584$	3.00000	+	5.19615i	0.124141	+	0.215018i
$585$	0.500000	+	0.866025i	0.0206725	+	0.0358057i
$586$	7.50000	−	12.9904i	0.309822	−	0.536628i
$587$	−9.00000			−0.371470			−0.185735	−	0.982600i	$-0.559467\pi$
$587$	−9.00000			−0.371470			−0.185735	+	0.982600i	$0.559467\pi$
$588$	−5.50000	+	4.33013i	−0.226816	+	0.178571i
$589$		0			0
$590$	−3.50000	+	6.06218i	−0.144093	+	0.249576i
$591$	−11.0000	−	19.0526i	−0.452480	−	0.783718i
$592$	4.00000	+	6.92820i	0.164399	+	0.284747i
$593$	20.0000	−	34.6410i	0.821302	−	1.42254i	−0.0834118	−	0.996515i	$-0.526582\pi$
$593$	20.0000	−	34.6410i	0.821302	−	1.42254i	0.904713	−	0.426021i	$-0.140085\pi$
$594$	−3.00000			−0.123091
$595$	1.00000	−	5.19615i	0.0409960	−	0.213021i
$596$	−6.00000			−0.245770
$597$	−12.0000	+	20.7846i	−0.491127	+	0.850657i
$598$	−3.00000	−	5.19615i	−0.122679	−	0.212486i
$599$	−9.00000	−	15.5885i	−0.367730	−	0.636927i	0.621480	−	0.783430i	$-0.286532\pi$
$599$	−9.00000	−	15.5885i	−0.367730	−	0.636927i	−0.989210	+	0.146503i	$0.953198\pi$
$600$	2.00000	−	3.46410i	0.0816497	−	0.141421i
$601$	19.0000			0.775026			0.387513	−	0.921864i	$-0.373334\pi$
$601$	19.0000			0.775026			0.387513	+	0.921864i	$0.373334\pi$
$602$		0			0
$603$	−4.00000			−0.162893
$604$	5.50000	−	9.52628i	0.223792	−	0.387619i
$605$	1.00000	+	1.73205i	0.0406558	+	0.0704179i
$606$	1.00000	+	1.73205i	0.0406222	+	0.0703598i
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	−0.875994	−	0.482322i	$-0.839794\pi$
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	0.855700	+	0.517472i	$0.173127\pi$
$608$		0			0
$609$	−22.5000	+	7.79423i	−0.911746	+	0.315838i
$610$	4.00000			0.161955
$611$		0			0
$612$	1.00000	+	1.73205i	0.0404226	+	0.0700140i
$613$	14.0000	+	24.2487i	0.565455	+	0.979396i	0.997007	+	0.0773084i	$0.0246326\pi$
$613$	14.0000	+	24.2487i	0.565455	+	0.979396i	−0.431553	+	0.902088i	$0.642034\pi$
$614$	−9.00000	+	15.5885i	−0.363210	+	0.629099i
$615$	4.00000			0.161296
$616$	7.50000	−	2.59808i	0.302184	−	0.104679i
$617$	4.00000			0.161034			0.0805170	−	0.996753i	$-0.474343\pi$
$617$	4.00000			0.161034			0.0805170	+	0.996753i	$0.474343\pi$
$618$	8.00000	−	13.8564i	0.321807	−	0.557386i
$619$	−16.0000	−	27.7128i	−0.643094	−	1.11387i	−0.984738	−	0.174042i	$-0.944317\pi$
$619$	−16.0000	−	27.7128i	−0.643094	−	1.11387i	0.341644	−	0.939829i	$-0.389016\pi$
$620$	−2.50000	−	4.33013i	−0.100402	−	0.173902i
$621$	3.00000	−	5.19615i	0.120386	−	0.208514i
$622$	−2.00000			−0.0801927
$623$	16.0000	+	13.8564i	0.641026	+	0.555145i
$624$	1.00000			0.0400320
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	6.50000	+	11.2583i	0.259792	+	0.449973i
$627$		0			0
$628$	7.00000	−	12.1244i	0.279330	−	0.483814i
$629$	16.0000			0.637962
$630$	0.500000	−	2.59808i	0.0199205	−	0.103510i
$631$	−13.0000			−0.517522			−0.258761	−	0.965941i	$-0.583314\pi$
$631$	−13.0000			−0.517522			−0.258761	+	0.965941i	$0.583314\pi$
$632$	−6.50000	+	11.2583i	−0.258556	+	0.447832i
$633$	10.0000	+	17.3205i	0.397464	+	0.688428i
$634$	1.50000	+	2.59808i	0.0595726	+	0.103183i
$635$	−2.50000	+	4.33013i	−0.0992095	+	0.171836i
$636$	−1.00000			−0.0396526
$637$	6.50000	+	2.59808i	0.257539	+	0.102940i
$638$	27.0000			1.06894
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	0.722862	−	0.690992i	$-0.242826\pi$
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	−0.959848	+	0.280521i	$0.909493\pi$
$642$	−8.50000	+	14.7224i	−0.335468	+	0.581048i
$643$	−32.0000			−1.26196			−0.630978	−	0.775800i	$-0.717346\pi$
$643$	−32.0000			−1.26196			−0.630978	+	0.775800i	$0.717346\pi$
$644$	−3.00000	+	15.5885i	−0.118217	+	0.614271i
$645$		0			0
$646$		0			0
$647$	−18.0000	−	31.1769i	−0.707653	−	1.22569i	−0.965726	−	0.259565i	$-0.916421\pi$
$647$	−18.0000	−	31.1769i	−0.707653	−	1.22569i	0.258073	−	0.966126i	$-0.416913\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−10.5000	+	18.1865i	−0.412161	+	0.713884i
$650$	−4.00000			−0.156893
$651$	10.0000	+	8.66025i	0.391931	+	0.339422i
$652$	−4.00000			−0.156652
$653$	−19.5000	+	33.7750i	−0.763094	+	1.32172i	0.178154	+	0.984003i	$0.442987\pi$
$653$	−19.5000	+	33.7750i	−0.763094	+	1.32172i	−0.941248	+	0.337715i	$0.890346\pi$
$654$	−8.00000	−	13.8564i	−0.312825	−	0.541828i
$655$	−7.50000	−	12.9904i	−0.293049	−	0.507576i
$656$	2.00000	−	3.46410i	0.0780869	−	0.135250i
$657$	6.00000			0.234082
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$	−1.50000	+	2.59808i	−0.0583874	+	0.101130i
$661$	−13.0000	−	22.5167i	−0.505641	−	0.875797i	−0.999979	−	0.00652642i	$-0.997923\pi$
$661$	−13.0000	−	22.5167i	−0.505641	−	0.875797i	0.494337	−	0.869270i	$-0.335411\pi$
$662$	4.00000	+	6.92820i	0.155464	+	0.269272i
$663$	1.00000	−	1.73205i	0.0388368	−	0.0672673i
$664$	3.00000			0.116423
$665$		0			0
$666$	8.00000			0.309994
$667$	−27.0000	+	46.7654i	−1.04544	+	1.81076i
$668$	2.00000	+	3.46410i	0.0773823	+	0.134030i
$669$	−0.500000	−	0.866025i	−0.0193311	−	0.0334825i
$670$	−2.00000	+	3.46410i	−0.0772667	+	0.133830i
$671$	12.0000			0.463255
$672$	−2.00000	−	1.73205i	−0.0771517	−	0.0668153i
$673$	17.0000			0.655302			0.327651	−	0.944799i	$-0.393743\pi$
$673$	17.0000			0.655302			0.327651	+	0.944799i	$0.393743\pi$
$674$	0.500000	−	0.866025i	0.0192593	−	0.0333581i
$675$	−2.00000	−	3.46410i	−0.0769800	−	0.133333i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−15.5000	+	26.8468i	−0.595713	+	1.03181i	0.397732	+	0.917501i	$0.369797\pi$
$677$	−15.5000	+	26.8468i	−0.595713	+	1.03181i	−0.993446	+	0.114304i	$0.963536\pi$
$678$	12.0000			0.460857
$679$	7.50000	−	38.9711i	0.287824	−	1.49558i
$680$	2.00000			0.0766965
$681$	−6.50000	+	11.2583i	−0.249081	+	0.431420i
$682$	−7.50000	−	12.9904i	−0.287190	−	0.497427i
$683$	20.5000	+	35.5070i	0.784411	+	1.35864i	0.929350	+	0.369199i	$0.120368\pi$
$683$	20.5000	+	35.5070i	0.784411	+	1.35864i	−0.144940	+	0.989440i	$0.546299\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$	−8.50000	−	16.4545i	−0.324532	−	0.628235i
$687$	14.0000			0.534133
$688$		0			0
$689$	0.500000	+	0.866025i	0.0190485	+	0.0329929i
$690$	−3.00000	−	5.19615i	−0.114208	−	0.197814i
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	0.779857	+	0.625958i	$0.215292\pi$
$692$	−14.0000			−0.532200
$693$	1.50000	−	7.79423i	0.0569803	−	0.296078i
$694$	28.0000			1.06287
$695$	−2.00000	+	3.46410i	−0.0758643	+	0.131401i
$696$	−4.50000	−	7.79423i	−0.170572	−	0.295439i
$697$	−4.00000	−	6.92820i	−0.151511	−	0.262424i
$698$	−17.0000	+	29.4449i	−0.643459	+	1.11450i
$699$	14.0000			0.529529
$700$	8.00000	+	6.92820i	0.302372	+	0.261861i
$701$	−39.0000			−1.47301			−0.736505	−	0.676432i	$-0.763525\pi$
$701$	−39.0000			−1.47301			−0.736505	+	0.676432i	$0.763525\pi$
$702$	0.500000	−	0.866025i	0.0188713	−	0.0326860i
$703$		0			0
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$		0			0
$706$	−6.00000			−0.225813
$707$	−5.00000	+	1.73205i	−0.188044	+	0.0651405i
$708$	7.00000			0.263076
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	−0.511683	−	0.859174i	$-0.670978\pi$
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	0.999908	+	0.0135434i	$0.00431112\pi$
$710$	3.00000	+	5.19615i	0.112588	+	0.195008i
$711$	6.50000	+	11.2583i	0.243769	+	0.422220i
$712$	−4.00000	+	6.92820i	−0.149906	+	0.259645i
$713$	30.0000			1.12351
$714$	−5.00000	+	1.73205i	−0.187120	+	0.0648204i
$715$	3.00000			0.112194
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$	11.0000	+	19.0526i	0.410803	+	0.711531i
$718$	−1.00000	−	1.73205i	−0.0373197	−	0.0646396i
$719$	−1.00000	+	1.73205i	−0.0372937	+	0.0645946i	−0.884070	−	0.467355i	$-0.845207\pi$
$719$	−1.00000	+	1.73205i	−0.0372937	+	0.0645946i	0.846776	+	0.531949i	$0.178540\pi$
$720$	1.00000			0.0372678
$721$	32.0000	+	27.7128i	1.19174	+	1.03208i
$722$	19.0000			0.707107
$723$	−13.5000	+	23.3827i	−0.502070	+	0.869611i
$724$	4.00000	+	6.92820i	0.148659	+	0.257485i
$725$	18.0000	+	31.1769i	0.668503	+	1.15788i
$726$	1.00000	−	1.73205i	0.0371135	−	0.0642824i
$727$	−9.00000			−0.333792			−0.166896	−	0.985975i	$-0.553374\pi$
$727$	−9.00000			−0.333792			−0.166896	+	0.985975i	$0.553374\pi$
$728$	−0.500000	+	2.59808i	−0.0185312	+	0.0962911i
$729$	1.00000			0.0370370
$730$	3.00000	−	5.19615i	0.111035	−	0.192318i
$731$		0			0
$732$	−2.00000	−	3.46410i	−0.0739221	−	0.128037i
$733$	−11.0000	+	19.0526i	−0.406294	+	0.703722i	−0.994471	−	0.105010i	$-0.966513\pi$
$733$	−11.0000	+	19.0526i	−0.406294	+	0.703722i	0.588177	+	0.808732i	$0.299846\pi$
$734$	3.00000			0.110732
$735$	6.50000	+	2.59808i	0.239756	+	0.0958315i
$736$	−6.00000			−0.221163
$737$	−6.00000	+	10.3923i	−0.221013	+	0.382805i
$738$	−2.00000	−	3.46410i	−0.0736210	−	0.127515i
$739$	9.00000	+	15.5885i	0.331070	+	0.573431i	0.982722	−	0.185088i	$-0.0592569\pi$
$739$	9.00000	+	15.5885i	0.331070	+	0.573431i	−0.651652	+	0.758518i	$0.725924\pi$
$740$	4.00000	−	6.92820i	0.147043	−	0.254686i
$741$		0			0
$742$	0.500000	−	2.59808i	0.0183556	−	0.0953784i
$743$	−20.0000			−0.733729			−0.366864	−	0.930274i	$-0.619569\pi$
$743$	−20.0000			−0.733729			−0.366864	+	0.930274i	$0.619569\pi$
$744$	−2.50000	+	4.33013i	−0.0916544	+	0.158750i
$745$	3.00000	+	5.19615i	0.109911	+	0.190372i
$746$	−13.0000	−	22.5167i	−0.475964	−	0.824394i
$747$	1.50000	−	2.59808i	0.0548821	−	0.0950586i
$748$	6.00000			0.219382
$749$	−34.0000	−	29.4449i	−1.24233	−	1.07589i
$750$	−9.00000			−0.328634
$751$	−6.50000	+	11.2583i	−0.237188	+	0.410822i	−0.959906	−	0.280321i	$-0.909559\pi$
$751$	−6.50000	+	11.2583i	−0.237188	+	0.410822i	0.722718	+	0.691143i	$0.242893\pi$
$752$		0			0
$753$	11.5000	+	19.9186i	0.419083	+	0.725874i
$754$	−4.50000	+	7.79423i	−0.163880	+	0.283849i
$755$	−11.0000			−0.400331
$756$	−2.50000	+	0.866025i	−0.0909241	+	0.0314970i
$757$	22.0000			0.799604			0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000			0.799604			0.399802	+	0.916602i	$0.369079\pi$
$758$	−12.0000	+	20.7846i	−0.435860	+	0.754931i
$759$	−9.00000	−	15.5885i	−0.326679	−	0.565825i
$760$		0			0
$761$	16.0000	−	27.7128i	0.580000	−	1.00459i	−0.415479	−	0.909603i	$-0.636386\pi$
$761$	16.0000	−	27.7128i	0.580000	−	1.00459i	0.995479	−	0.0949859i	$-0.0302806\pi$
$762$	5.00000			0.181131
$763$	40.0000	−	13.8564i	1.44810	−	0.501636i
$764$	−6.00000			−0.217072
$765$	1.00000	−	1.73205i	0.0361551	−	0.0626224i
$766$	−13.0000	−	22.5167i	−0.469709	−	0.813560i
$767$	−3.50000	−	6.06218i	−0.126378	−	0.218893i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−13.0000			−0.468792			−0.234396	−	0.972141i	$-0.575311\pi$
$769$	−13.0000			−0.468792			−0.234396	+	0.972141i	$0.575311\pi$
$770$	−6.00000	−	5.19615i	−0.216225	−	0.187256i
$771$	26.0000			0.936367
$772$	−9.50000	+	16.4545i	−0.341912	+	0.592210i
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	0.657542	−	0.753418i	$-0.271596\pi$
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	−0.981250	+	0.192740i	$0.938263\pi$
$774$		0			0
$775$	10.0000	−	17.3205i	0.359211	−	0.622171i
$776$	15.0000			0.538469
$777$	−4.00000	+	20.7846i	−0.143499	+	0.745644i
$778$	−34.0000			−1.21896
$779$		0			0
$780$	−0.500000	−	0.866025i	−0.0179029	−	0.0310087i
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$	−6.00000	+	10.3923i	−0.214560	+	0.371628i
$783$	−9.00000			−0.321634
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$	−14.0000			−0.499681
$786$	−7.50000	+	12.9904i	−0.267516	+	0.463352i
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	0.500953	−	0.865474i	$-0.332983\pi$
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	−0.999999	+	0.00110111i	$0.999650\pi$
$788$	11.0000	+	19.0526i	0.391859	+	0.678719i
$789$	−13.0000	+	22.5167i	−0.462812	+	0.801614i
$790$	13.0000			0.462519
$791$	−6.00000	+	31.1769i	−0.213335	+	1.10852i
$792$	3.00000			0.106600
$793$	−2.00000	+	3.46410i	−0.0710221	+	0.123014i
$794$	17.0000	+	29.4449i	0.603307	+	1.04496i
$795$	0.500000	+	0.866025i	0.0177332	+	0.0307148i
$796$	12.0000	−	20.7846i	0.425329	−	0.736691i
$797$	7.00000			0.247953			0.123976	−	0.992285i	$-0.460435\pi$
$797$	7.00000			0.247953			0.123976	+	0.992285i	$0.460435\pi$
$798$		0			0
$799$		0			0
$800$	−2.00000	+	3.46410i	−0.0707107	+	0.122474i
$801$	4.00000	+	6.92820i	0.141333	+	0.244796i
$802$	3.00000	+	5.19615i	0.105934	+	0.183483i
$803$	9.00000	−	15.5885i	0.317603	−	0.550105i
$804$	4.00000			0.141069
$805$	15.0000	−	5.19615i	0.528681	−	0.183140i
$806$	5.00000			0.176117
$807$	−1.50000	+	2.59808i	−0.0528025	+	0.0914566i
$808$	−1.00000	−	1.73205i	−0.0351799	−	0.0609333i
$809$	−2.00000	−	3.46410i	−0.0703163	−	0.121791i	0.828724	−	0.559658i	$-0.189068\pi$
$809$	−2.00000	−	3.46410i	−0.0703163	−	0.121791i	−0.899040	+	0.437867i	$0.855734\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	36.0000			1.26413			0.632065	−	0.774915i	$-0.282207\pi$
$811$	36.0000			1.26413			0.632065	+	0.774915i	$0.282207\pi$
$812$	22.5000	−	7.79423i	0.789595	−	0.273524i
$813$	−9.00000			−0.315644
$814$	12.0000	−	20.7846i	0.420600	−	0.728500i
$815$	2.00000	+	3.46410i	0.0700569	+	0.121342i
$816$	−1.00000	−	1.73205i	−0.0350070	−	0.0606339i
$817$		0			0
$818$	11.0000			0.384606
$819$	2.00000	+	1.73205i	0.0698857	+	0.0605228i
$820$	−4.00000			−0.139686
$821$	−1.50000	+	2.59808i	−0.0523504	+	0.0906735i	−0.891013	−	0.453978i	$-0.850005\pi$
$821$	−1.50000	+	2.59808i	−0.0523504	+	0.0906735i	0.838663	+	0.544651i	$0.183338\pi$
$822$	6.00000	+	10.3923i	0.209274	+	0.362473i
$823$	−10.0000	−	17.3205i	−0.348578	−	0.603755i	0.637419	−	0.770517i	$-0.280002\pi$
$823$	−10.0000	−	17.3205i	−0.348578	−	0.603755i	−0.985997	+	0.166762i	$0.946669\pi$
$824$	−8.00000	+	13.8564i	−0.278693	+	0.482711i
$825$	−12.0000			−0.417786
$826$	−3.50000	+	18.1865i	−0.121781	+	0.632790i
$827$	−27.0000			−0.938882			−0.469441	−	0.882964i	$-0.655545\pi$
$827$	−27.0000			−0.938882			−0.469441	+	0.882964i	$0.655545\pi$
$828$	−3.00000	+	5.19615i	−0.104257	+	0.180579i
$829$	−19.0000	−	32.9090i	−0.659897	−	1.14298i	−0.980642	−	0.195810i	$-0.937266\pi$
$829$	−19.0000	−	32.9090i	−0.659897	−	1.14298i	0.320745	−	0.947166i	$-0.396067\pi$
$830$	−1.50000	−	2.59808i	−0.0520658	−	0.0901805i
$831$	−11.0000	+	19.0526i	−0.381586	+	0.660926i
$832$	−1.00000			−0.0346688
$833$	−2.00000	−	13.8564i	−0.0692959	−	0.480096i
$834$	4.00000			0.138509
$835$	2.00000	−	3.46410i	0.0692129	−	0.119880i
$836$		0			0
$837$	2.50000	+	4.33013i	0.0864126	+	0.149671i
$838$		0			0
$839$	44.0000			1.51905			0.759524	−	0.650479i	$-0.225432\pi$
$839$	44.0000			1.51905			0.759524	+	0.650479i	$0.225432\pi$
$840$	−0.500000	+	2.59808i	−0.0172516	+	0.0896421i
$841$	52.0000			1.79310
$842$	−6.00000	+	10.3923i	−0.206774	+	0.358142i
$843$		0			0
$844$	−10.0000	−	17.3205i	−0.344214	−	0.596196i
$845$	−0.500000	+	0.866025i	−0.0172005	+	0.0297922i
$846$		0			0
$847$	4.00000	+	3.46410i	0.137442	+	0.119028i
$848$	1.00000			0.0343401
$849$	7.00000	−	12.1244i	0.240239	−	0.416107i
$850$	4.00000	+	6.92820i	0.137199	+	0.237635i
$851$	24.0000	+	41.5692i	0.822709	+	1.42497i
$852$	3.00000	−	5.19615i	0.102778	−	0.178017i
$853$	58.0000			1.98588			0.992941	−	0.118609i	$-0.0378434\pi$
$853$	58.0000			1.98588			0.992941	+	0.118609i	$0.0378434\pi$
$854$	10.0000	−	3.46410i	0.342193	−	0.118539i
$855$		0			0
$856$	8.50000	−	14.7224i	0.290524	−	0.503202i
$857$	25.0000	+	43.3013i	0.853984	+	1.47914i	0.877585	+	0.479422i	$0.159154\pi$
$857$	25.0000	+	43.3013i	0.853984	+	1.47914i	−0.0236009	+	0.999721i	$0.507513\pi$
$858$	−1.50000	−	2.59808i	−0.0512092	−	0.0886969i
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	0.291858	+	0.956462i	$0.405727\pi$
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	−0.974249	+	0.225475i	$0.927607\pi$
$860$		0			0
$861$	10.0000	−	3.46410i	0.340799	−	0.118056i
$862$	−26.0000			−0.885564
$863$	−20.0000	+	34.6410i	−0.680808	+	1.17919i	0.293927	+	0.955828i	$0.405038\pi$
$863$	−20.0000	+	34.6410i	−0.680808	+	1.17919i	−0.974735	+	0.223366i	$0.928296\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	7.00000	+	12.1244i	0.238007	+	0.412240i
$866$	−19.0000	+	32.9090i	−0.645646	+	1.11829i
$867$	13.0000			0.441503
$868$	−10.0000	−	8.66025i	−0.339422	−	0.293948i
$869$	39.0000			1.32298
$870$	−4.50000	+	7.79423i	−0.152564	+	0.264249i
$871$	−2.00000	−	3.46410i	−0.0677674	−	0.117377i
$872$	8.00000	+	13.8564i	0.270914	+	0.469237i
$873$	7.50000	−	12.9904i	0.253837	−	0.439658i
$874$		0			0
$875$	4.50000	−	23.3827i	0.152128	−	0.790479i
$876$	−6.00000			−0.202721
$877$	9.00000	−	15.5885i	0.303908	−	0.526385i	−0.673109	−	0.739543i	$-0.735042\pi$
$877$	9.00000	−	15.5885i	0.303908	−	0.526385i	0.977018	+	0.213158i	$0.0683750\pi$
$878$	−14.5000	−	25.1147i	−0.489351	−	0.847581i
$879$	7.50000	+	12.9904i	0.252969	+	0.438155i
$880$	1.50000	−	2.59808i	0.0505650	−	0.0875811i
$881$	50.0000			1.68454			0.842271	−	0.539054i	$-0.181218\pi$
$881$	50.0000			1.68454			0.842271	+	0.539054i	$0.181218\pi$
$882$	−1.00000	−	6.92820i	−0.0336718	−	0.233285i
$883$	10.0000			0.336527			0.168263	−	0.985742i	$-0.446184\pi$
$883$	10.0000			0.336527			0.168263	+	0.985742i	$0.446184\pi$
$884$	−1.00000	+	1.73205i	−0.0336336	+	0.0582552i
$885$	−3.50000	−	6.06218i	−0.117651	−	0.203778i
$886$	19.5000	+	33.7750i	0.655115	+	1.13469i
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	−0.994077	−	0.108678i	$-0.965338\pi$
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	0.591156	+	0.806557i	$0.298672\pi$
$888$	−8.00000			−0.268462
$889$	−2.50000	+	12.9904i	−0.0838473	+	0.435683i
$890$	8.00000			0.268161
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$	0.500000	+	0.866025i	0.0167412	+	0.0289967i
$893$		0			0
$894$	3.00000	−	5.19615i	0.100335	−	0.173785i
$895$	12.0000			0.401116
$896$	2.00000	+	1.73205i	0.0668153	+	0.0578638i
$897$	6.00000			0.200334
$898$	4.00000	−	6.92820i	0.133482	−	0.231197i
$899$	−22.5000	−	38.9711i	−0.750417	−	1.29976i
$900$	2.00000	+	3.46410i	0.0666667	+	0.115470i
$901$	1.00000	−	1.73205i	0.0333148	−	0.0577030i
$902$	−12.0000			−0.399556
$903$		0			0
$904$	−12.0000			−0.399114
$905$	4.00000	−	6.92820i	0.132964	−	0.230301i
$906$	5.50000	+	9.52628i	0.182725	+	0.316489i
$907$	4.00000	+	6.92820i	0.132818	+	0.230047i	0.924762	−	0.380547i	$-0.124264\pi$
$907$	4.00000	+	6.92820i	0.132818	+	0.230047i	−0.791944	+	0.610594i	$0.790931\pi$
$908$	6.50000	−	11.2583i	0.215710	−	0.373621i
$909$	−2.00000			−0.0663358
$910$	2.50000	−	0.866025i	0.0828742	−	0.0287085i
$911$	−50.0000			−1.65657			−0.828287	−	0.560304i	$-0.810684\pi$
$911$	−50.0000			−1.65657			−0.828287	+	0.560304i	$0.810684\pi$
$912$		0			0
$913$	−4.50000	−	7.79423i	−0.148928	−	0.257951i
$914$	0.500000	+	0.866025i	0.0165385	+	0.0286456i
$915$	−2.00000	+	3.46410i	−0.0661180	+	0.114520i
$916$	−14.0000			−0.462573
$917$	−30.0000	−	25.9808i	−0.990687	−	0.857960i
$918$	−2.00000			−0.0660098
$919$	28.0000	−	48.4974i	0.923635	−	1.59978i	0.129893	−	0.991528i	$-0.458537\pi$
$919$	28.0000	−	48.4974i	0.923635	−	1.59978i	0.793742	−	0.608254i	$-0.208130\pi$
$920$	3.00000	+	5.19615i	0.0989071	+	0.171312i
$921$	−9.00000	−	15.5885i	−0.296560	−	0.513657i
$922$	−13.0000	+	22.5167i	−0.428132	+	0.741547i
$923$	−6.00000			−0.197492
$924$	−1.50000	+	7.79423i	−0.0493464	+	0.256411i
$925$	32.0000			1.05215
$926$	−4.00000	+	6.92820i	−0.131448	+	0.227675i
$927$	8.00000	+	13.8564i	0.262754	+	0.455104i
$928$	4.50000	+	7.79423i	0.147720	+	0.255858i
$929$	−14.0000	+	24.2487i	−0.459325	+	0.795574i	−0.998925	−	0.0463469i	$-0.985242\pi$
$929$	−14.0000	+	24.2487i	−0.459325	+	0.795574i	0.539600	+	0.841921i	$0.318575\pi$
$930$	5.00000			0.163956
$931$		0			0
$932$	−14.0000			−0.458585
$933$	1.00000	−	1.73205i	0.0327385	−	0.0567048i
$934$	6.00000	+	10.3923i	0.196326	+	0.340047i
$935$	−3.00000	−	5.19615i	−0.0981105	−	0.169932i
$936$	−0.500000	+	0.866025i	−0.0163430	+	0.0283069i
$937$	−37.0000			−1.20874			−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000			−1.20874			−0.604369	+	0.796705i	$0.706575\pi$
$938$	−2.00000	+	10.3923i	−0.0653023	+	0.339321i
$939$	−13.0000			−0.424239
$940$		0			0
$941$	19.5000	+	33.7750i	0.635682	+	1.10103i	0.986370	+	0.164541i	$0.0526143\pi$
$941$	19.5000	+	33.7750i	0.635682	+	1.10103i	−0.350688	+	0.936492i	$0.614052\pi$
$942$	7.00000	+	12.1244i	0.228072	+	0.395033i
$943$	12.0000	−	20.7846i	0.390774	−	0.676840i
$944$	−7.00000			−0.227831
$945$	2.00000	+	1.73205i	0.0650600	+	0.0563436i
$946$		0			0
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	−0.946892	−	0.321552i	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$	−6.50000	−	11.2583i	−0.211110	−	0.365654i
$949$	3.00000	+	5.19615i	0.0973841	+	0.168674i
$950$		0			0
$951$	−3.00000			−0.0972817
$952$	5.00000	−	1.73205i	0.162051	−	0.0561361i
$953$	12.0000			0.388718			0.194359	−	0.980930i	$-0.437737\pi$
$953$	12.0000			0.388718			0.194359	+	0.980930i	$0.437737\pi$
$954$	0.500000	−	0.866025i	0.0161881	−	0.0280386i
$955$	3.00000	+	5.19615i	0.0970777	+	0.168144i
$956$	−11.0000	−	19.0526i	−0.355765	−	0.616204i
$957$	−13.5000	+	23.3827i	−0.436393	+	0.755855i
$958$	−30.0000			−0.969256
$959$	−30.0000	+	10.3923i	−0.968751	+	0.335585i
$960$	−1.00000			−0.0322749
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$	4.00000	+	6.92820i	0.128965	+	0.223374i
$963$	−8.50000	−	14.7224i	−0.273909	−	0.474424i
$964$	13.5000	−	23.3827i	0.434806	−	0.753106i
$965$	19.0000			0.611632
$966$	−12.0000	−	10.3923i	−0.386094	−	0.334367i
$967$	21.0000			0.675314			0.337657	−	0.941269i	$-0.390366\pi$
$967$	21.0000			0.675314			0.337657	+	0.941269i	$0.390366\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$		0			0
$970$	−7.50000	−	12.9904i	−0.240810	−	0.417096i
$971$	−6.50000	+	11.2583i	−0.208595	+	0.361297i	−0.951272	−	0.308353i	$-0.900222\pi$
$971$	−6.50000	+	11.2583i	−0.208595	+	0.361297i	0.742677	+	0.669650i	$0.233556\pi$
$972$	−1.00000			−0.0320750
$973$	−2.00000	+	10.3923i	−0.0641171	+	0.333162i
$974$	9.00000			0.288379
$975$	2.00000	−	3.46410i	0.0640513	−	0.110940i
$976$	2.00000	+	3.46410i	0.0640184	+	0.110883i
$977$	11.0000	+	19.0526i	0.351921	+	0.609545i	0.986586	−	0.163242i	$-0.0521952\pi$
$977$	11.0000	+	19.0526i	0.351921	+	0.609545i	−0.634665	+	0.772787i	$0.718862\pi$
$978$	2.00000	−	3.46410i	0.0639529	−	0.110770i
$979$	24.0000			0.767043
$980$	−6.50000	−	2.59808i	−0.207635	−	0.0829925i
$981$	16.0000			0.510841
$982$	−14.5000	+	25.1147i	−0.462714	+	0.801443i
$983$	−3.00000	−	5.19615i	−0.0956851	−	0.165732i	0.814209	−	0.580572i	$-0.197171\pi$
$983$	−3.00000	−	5.19615i	−0.0956851	−	0.165732i	−0.909894	+	0.414840i	$0.863838\pi$
$984$	2.00000	+	3.46410i	0.0637577	+	0.110432i
$985$	11.0000	−	19.0526i	0.350489	−	0.607065i
$986$	18.0000			0.573237
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−1.50000	−	2.59808i	−0.0476731	−	0.0825723i
$991$	−7.50000	−	12.9904i	−0.238245	−	0.412653i	0.721966	−	0.691929i	$-0.243239\pi$
$991$	−7.50000	−	12.9904i	−0.238245	−	0.412653i	−0.960211	+	0.279276i	$0.909906\pi$
$992$	2.50000	−	4.33013i	0.0793751	−	0.137482i
$993$	−8.00000			−0.253872
$994$	12.0000	+	10.3923i	0.380617	+	0.329624i
$995$	−24.0000			−0.760851
$996$	−1.50000	+	2.59808i	−0.0475293	+	0.0823232i
$997$	−4.00000	−	6.92820i	−0.126681	−	0.219418i	0.795708	−	0.605681i	$-0.207099\pi$
$997$	−4.00000	−	6.92820i	−0.126681	−	0.219418i	−0.922389	+	0.386263i	$0.873766\pi$
$998$	8.00000	+	13.8564i	0.253236	+	0.438617i
$999$	−4.00000	+	6.92820i	−0.126554	+	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.i.f.79.1	✓	2
3.2	odd	2		1638.2.j.e.1171.1		2
7.2	even	3		3822.2.a.f.1.1		1
7.4	even	3	inner	546.2.i.f.235.1	yes	2
7.5	odd	6		3822.2.a.l.1.1		1
21.11	odd	6		1638.2.j.e.235.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.f.79.1	✓	2	1.1	even	1	trivial
546.2.i.f.235.1	yes	2	7.4	even	3	inner
1638.2.j.e.235.1		2	21.11	odd	6
1638.2.j.e.1171.1		2	3.2	odd	2
3822.2.a.f.1.1		1	7.2	even	3
3822.2.a.l.1.1		1	7.5	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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} -1.00000 q^{13} +(2.00000 + 1.73205i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(0.500000 + 0.866025i) q^{18} +1.00000 q^{20} +(-2.50000 + 0.866025i) q^{21} +3.00000 q^{22} +(-3.00000 + 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-0.500000 + 0.866025i) q^{26} -1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} +9.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} +(-2.50000 - 4.33013i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +2.00000 q^{34} +(-2.00000 - 1.73205i) q^{35} +1.00000 q^{36} +(4.00000 - 6.92820i) q^{37} +(-0.500000 - 0.866025i) q^{39} +(0.500000 - 0.866025i) q^{40} -4.00000 q^{41} +(-0.500000 + 2.59808i) q^{42} +(1.50000 - 2.59808i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(3.00000 + 5.19615i) q^{46} -1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +4.00000 q^{50} +(-1.00000 + 1.73205i) q^{51} +(0.500000 + 0.866025i) q^{52} +(-0.500000 - 0.866025i) q^{53} +(-0.500000 + 0.866025i) q^{54} -3.00000 q^{55} +(0.500000 - 2.59808i) q^{56} +(4.50000 - 7.79423i) q^{58} +(3.50000 + 6.06218i) q^{59} +(0.500000 + 0.866025i) q^{60} +(2.00000 - 3.46410i) q^{61} -5.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(1.50000 + 2.59808i) q^{66} +(2.00000 + 3.46410i) q^{67} +(1.00000 - 1.73205i) q^{68} -6.00000 q^{69} +(-2.50000 + 0.866025i) q^{70} +6.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-3.00000 - 5.19615i) q^{73} +(-4.00000 - 6.92820i) q^{74} +(-2.00000 + 3.46410i) q^{75} +(-7.50000 + 2.59808i) q^{77} -1.00000 q^{78} +(6.50000 - 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.00000 + 3.46410i) q^{82} -3.00000 q^{83} +(2.00000 + 1.73205i) q^{84} -2.00000 q^{85} +(4.50000 + 7.79423i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(4.00000 - 6.92820i) q^{89} -1.00000 q^{90} +(0.500000 - 2.59808i) q^{91} +6.00000 q^{92} +(2.50000 - 4.33013i) q^{93} +(-0.500000 + 0.866025i) q^{96} -15.0000 q^{97} +(-5.50000 + 4.33013i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 - q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - q^{7} - 2 q^{8} - q^{9} + q^{10} + 3 q^{11} + q^{12} - 2 q^{13} + 4 q^{14} - 2 q^{15} - q^{16} + 2 q^{17} + q^{18} + 2 q^{20} - 5 q^{21} + 6 q^{22} - 6 q^{23} - q^{24} + 4 q^{25} - q^{26} - 2 q^{27} + 5 q^{28} + 18 q^{29} - q^{30} - 5 q^{31} + q^{32} - 3 q^{33} + 4 q^{34} - 4 q^{35} + 2 q^{36} + 8 q^{37} - q^{39} + q^{40} - 8 q^{41} - q^{42} + 3 q^{44} - q^{45} + 6 q^{46} - 2 q^{48} - 13 q^{49} + 8 q^{50} - 2 q^{51} + q^{52} - q^{53} - q^{54} - 6 q^{55} + q^{56} + 9 q^{58} + 7 q^{59} + q^{60} + 4 q^{61} - 10 q^{62} - 4 q^{63} + 2 q^{64} + q^{65} + 3 q^{66} + 4 q^{67} + 2 q^{68} - 12 q^{69} - 5 q^{70} + 12 q^{71} + q^{72} - 6 q^{73} - 8 q^{74} - 4 q^{75} - 15 q^{77} - 2 q^{78} + 13 q^{79} - q^{80} - q^{81} - 4 q^{82} - 6 q^{83} + 4 q^{84} - 4 q^{85} + 9 q^{87} - 3 q^{88} + 8 q^{89} - 2 q^{90} + q^{91} + 12 q^{92} + 5 q^{93} - q^{96} - 30 q^{97} - 11 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 - q^7 - 2 * q^8 - q^9 + q^10 + 3 * q^11 + q^12 - 2 * q^13 + 4 * q^14 - 2 * q^15 - q^16 + 2 * q^17 + q^18 + 2 * q^20 - 5 * q^21 + 6 * q^22 - 6 * q^23 - q^24 + 4 * q^25 - q^26 - 2 * q^27 + 5 * q^28 + 18 * q^29 - q^30 - 5 * q^31 + q^32 - 3 * q^33 + 4 * q^34 - 4 * q^35 + 2 * q^36 + 8 * q^37 - q^39 + q^40 - 8 * q^41 - q^42 + 3 * q^44 - q^45 + 6 * q^46 - 2 * q^48 - 13 * q^49 + 8 * q^50 - 2 * q^51 + q^52 - q^53 - q^54 - 6 * q^55 + q^56 + 9 * q^58 + 7 * q^59 + q^60 + 4 * q^61 - 10 * q^62 - 4 * q^63 + 2 * q^64 + q^65 + 3 * q^66 + 4 * q^67 + 2 * q^68 - 12 * q^69 - 5 * q^70 + 12 * q^71 + q^72 - 6 * q^73 - 8 * q^74 - 4 * q^75 - 15 * q^77 - 2 * q^78 + 13 * q^79 - q^80 - q^81 - 4 * q^82 - 6 * q^83 + 4 * q^84 - 4 * q^85 + 9 * q^87 - 3 * q^88 + 8 * q^89 - 2 * q^90 + q^91 + 12 * q^92 + 5 * q^93 - q^96 - 30 * q^97 - 11 * q^98 - 6 * q^99

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