LMFDB - Embedded newform 546.2.bn.b.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(101,546)]

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([3, 1, 5]))

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

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

chi := DirichletCharacter("546.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bn (of order $6$, 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:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.101
Dual form			546.2.bn.b.173.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.00000 + 1.73205i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.00000 + 1.73205i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} -3.00000 q^{9} -3.46410i q^{10} +6.00000 q^{11} +(-1.50000 + 0.866025i) q^{12} +(2.50000 - 2.59808i) q^{13} +(0.500000 - 2.59808i) q^{14} +(3.00000 + 5.19615i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{18} +5.00000 q^{19} +(3.00000 + 1.73205i) q^{20} +(1.50000 + 4.33013i) q^{21} +(-3.00000 + 5.19615i) q^{22} +(3.00000 + 1.73205i) q^{23} -1.73205i q^{24} +(3.50000 - 6.06218i) q^{25} +(1.00000 + 3.46410i) q^{26} +5.19615i q^{27} +(2.00000 + 1.73205i) q^{28} +(-6.00000 + 3.46410i) q^{29} -6.00000 q^{30} +(4.00000 - 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} -10.3923i q^{33} +(6.00000 - 6.92820i) q^{35} +(1.50000 + 2.59808i) q^{36} +(7.50000 + 4.33013i) q^{37} +(-2.50000 + 4.33013i) q^{38} +(-4.50000 - 4.33013i) q^{39} +(-3.00000 + 1.73205i) q^{40} +(9.00000 - 5.19615i) q^{41} +(-4.50000 - 0.866025i) q^{42} +(-0.500000 + 0.866025i) q^{43} +(-3.00000 - 5.19615i) q^{44} +(9.00000 - 5.19615i) q^{45} +(-3.00000 + 1.73205i) q^{46} +(-6.00000 + 3.46410i) q^{47} +(1.50000 + 0.866025i) q^{48} +(5.50000 - 4.33013i) q^{49} +(3.50000 + 6.06218i) q^{50} +(-3.50000 - 0.866025i) q^{52} +(3.00000 + 1.73205i) q^{53} +(-4.50000 - 2.59808i) q^{54} +(-18.0000 + 10.3923i) q^{55} +(-2.50000 + 0.866025i) q^{56} -8.66025i q^{57} -6.92820i q^{58} +(3.00000 - 5.19615i) q^{60} -5.19615i q^{61} +(4.00000 + 6.92820i) q^{62} +(7.50000 - 2.59808i) q^{63} +1.00000 q^{64} +(-3.00000 + 12.1244i) q^{65} +(9.00000 + 5.19615i) q^{66} +3.46410i q^{67} +(3.00000 - 5.19615i) q^{69} +(3.00000 + 8.66025i) q^{70} -3.00000 q^{72} +(-3.50000 + 6.06218i) q^{73} +(-7.50000 + 4.33013i) q^{74} +(-10.5000 - 6.06218i) q^{75} +(-2.50000 - 4.33013i) q^{76} +(-15.0000 + 5.19615i) q^{77} +(6.00000 - 1.73205i) q^{78} +(4.00000 + 6.92820i) q^{79} -3.46410i q^{80} +9.00000 q^{81} +10.3923i q^{82} +3.46410i q^{83} +(3.00000 - 3.46410i) q^{84} +(-0.500000 - 0.866025i) q^{86} +(6.00000 + 10.3923i) q^{87} +6.00000 q^{88} +(-3.00000 - 1.73205i) q^{89} +10.3923i q^{90} +(-4.00000 + 8.66025i) q^{91} -3.46410i q^{92} +(-12.0000 - 6.92820i) q^{93} -6.92820i q^{94} +(-15.0000 + 8.66025i) q^{95} +(-1.50000 + 0.866025i) q^{96} +(3.50000 - 6.06218i) q^{97} +(1.00000 + 6.92820i) q^{98} -18.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q - q^2 - q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 2 * q^8 - 6 * q^9	$ 2 q - q^{2} - q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9} + 12 q^{11} - 3 q^{12} + 5 q^{13} + q^{14} + 6 q^{15} - q^{16} + 3 q^{18} + 10 q^{19} + 6 q^{20} + 3 q^{21} - 6 q^{22} + 6 q^{23} + 7 q^{25} + 2 q^{26} + 4 q^{28} - 12 q^{29} - 12 q^{30} + 8 q^{31} - q^{32} + 12 q^{35} + 3 q^{36} + 15 q^{37} - 5 q^{38} - 9 q^{39} - 6 q^{40} + 18 q^{41} - 9 q^{42} - q^{43} - 6 q^{44} + 18 q^{45} - 6 q^{46} - 12 q^{47} + 3 q^{48} + 11 q^{49} + 7 q^{50} - 7 q^{52} + 6 q^{53} - 9 q^{54} - 36 q^{55} - 5 q^{56} + 6 q^{60} + 8 q^{62} + 15 q^{63} + 2 q^{64} - 6 q^{65} + 18 q^{66} + 6 q^{69} + 6 q^{70} - 6 q^{72} - 7 q^{73} - 15 q^{74} - 21 q^{75} - 5 q^{76} - 30 q^{77} + 12 q^{78} + 8 q^{79} + 18 q^{81} + 6 q^{84} - q^{86} + 12 q^{87} + 12 q^{88} - 6 q^{89} - 8 q^{91} - 24 q^{93} - 30 q^{95} - 3 q^{96} + 7 q^{97} + 2 q^{98} - 36 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 2 * q^8 - 6 * q^9 + 12 * q^11 - 3 * q^12 + 5 * q^13 + q^14 + 6 * q^15 - q^16 + 3 * q^18 + 10 * q^19 + 6 * q^20 + 3 * q^21 - 6 * q^22 + 6 * q^23 + 7 * q^25 + 2 * q^26 + 4 * q^28 - 12 * q^29 - 12 * q^30 + 8 * q^31 - q^32 + 12 * q^35 + 3 * q^36 + 15 * q^37 - 5 * q^38 - 9 * q^39 - 6 * q^40 + 18 * q^41 - 9 * q^42 - q^43 - 6 * q^44 + 18 * q^45 - 6 * q^46 - 12 * q^47 + 3 * q^48 + 11 * q^49 + 7 * q^50 - 7 * q^52 + 6 * q^53 - 9 * q^54 - 36 * q^55 - 5 * q^56 + 6 * q^60 + 8 * q^62 + 15 * q^63 + 2 * q^64 - 6 * q^65 + 18 * q^66 + 6 * q^69 + 6 * q^70 - 6 * q^72 - 7 * q^73 - 15 * q^74 - 21 * q^75 - 5 * q^76 - 30 * q^77 + 12 * q^78 + 8 * q^79 + 18 * q^81 + 6 * q^84 - q^86 + 12 * q^87 + 12 * q^88 - 6 * q^89 - 8 * q^91 - 24 * q^93 - 30 * q^95 - 3 * q^96 + 7 * q^97 + 2 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		−	1.73205i		−	1.00000i
$3$		−	1.73205i		−	1.00000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−3.00000	+	1.73205i	−1.34164	+	0.774597i	−0.987048	−	0.160424i	$-0.948714\pi$
$5$	−3.00000	+	1.73205i	−1.34164	+	0.774597i	−0.354593	+	0.935021i	$0.615380\pi$
$6$	1.50000	+	0.866025i	0.612372	+	0.353553i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	1.00000			0.353553
$9$	−3.00000			−1.00000
$10$		−	3.46410i		−	1.09545i
$11$	6.00000			1.80907			0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000			1.80907			0.904534	+	0.426401i	$0.140219\pi$
$12$	−1.50000	+	0.866025i	−0.433013	+	0.250000i
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$14$	0.500000	−	2.59808i	0.133631	−	0.694365i
$15$	3.00000	+	5.19615i	0.774597	+	1.34164i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	1.50000	−	2.59808i	0.353553	−	0.612372i
$19$	5.00000			1.14708			0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000			1.14708			0.573539	+	0.819178i	$0.305570\pi$
$20$	3.00000	+	1.73205i	0.670820	+	0.387298i
$21$	1.50000	+	4.33013i	0.327327	+	0.944911i
$22$	−3.00000	+	5.19615i	−0.639602	+	1.10782i
$23$	3.00000	+	1.73205i	0.625543	+	0.361158i	0.779024	−	0.626994i	$-0.215715\pi$
$23$	3.00000	+	1.73205i	0.625543	+	0.361158i	−0.153481	+	0.988152i	$0.549048\pi$
$24$		−	1.73205i		−	0.353553i
$25$	3.50000	−	6.06218i	0.700000	−	1.21244i
$26$	1.00000	+	3.46410i	0.196116	+	0.679366i
$27$			5.19615i			1.00000i
$28$	2.00000	+	1.73205i	0.377964	+	0.327327i
$29$	−6.00000	+	3.46410i	−1.11417	+	0.643268i	−0.939907	−	0.341431i	$-0.889088\pi$
$29$	−6.00000	+	3.46410i	−1.11417	+	0.643268i	−0.174265	+	0.984699i	$0.555755\pi$
$30$	−6.00000			−1.09545
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		−	10.3923i		−	1.80907i
$34$		0			0
$35$	6.00000	−	6.92820i	1.01419	−	1.17108i
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	7.50000	+	4.33013i	1.23299	+	0.711868i	0.967653	−	0.252286i	$-0.0811825\pi$
$37$	7.50000	+	4.33013i	1.23299	+	0.711868i	0.265340	+	0.964155i	$0.414516\pi$
$38$	−2.50000	+	4.33013i	−0.405554	+	0.702439i
$39$	−4.50000	−	4.33013i	−0.720577	−	0.693375i
$40$	−3.00000	+	1.73205i	−0.474342	+	0.273861i
$41$	9.00000	−	5.19615i	1.40556	−	0.811503i	0.410608	−	0.911812i	$-0.365317\pi$
$41$	9.00000	−	5.19615i	1.40556	−	0.811503i	0.994956	+	0.100309i	$0.0319833\pi$
$42$	−4.50000	−	0.866025i	−0.694365	−	0.133631i
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	0.825380	+	0.564578i	$0.190961\pi$
$44$	−3.00000	−	5.19615i	−0.452267	−	0.783349i
$45$	9.00000	−	5.19615i	1.34164	−	0.774597i
$46$	−3.00000	+	1.73205i	−0.442326	+	0.255377i
$47$	−6.00000	+	3.46410i	−0.875190	+	0.505291i	−0.869069	−	0.494690i	$-0.835282\pi$
$47$	−6.00000	+	3.46410i	−0.875190	+	0.505291i	−0.00612051	+	0.999981i	$0.501948\pi$
$48$	1.50000	+	0.866025i	0.216506	+	0.125000i
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	3.50000	+	6.06218i	0.494975	+	0.857321i
$51$		0			0
$52$	−3.50000	−	0.866025i	−0.485363	−	0.120096i
$53$	3.00000	+	1.73205i	0.412082	+	0.237915i	0.691684	−	0.722200i	$-0.256869\pi$
$53$	3.00000	+	1.73205i	0.412082	+	0.237915i	−0.279602	+	0.960116i	$0.590203\pi$
$54$	−4.50000	−	2.59808i	−0.612372	−	0.353553i
$55$	−18.0000	+	10.3923i	−2.42712	+	1.40130i
$56$	−2.50000	+	0.866025i	−0.334077	+	0.115728i
$57$		−	8.66025i		−	1.14708i
$58$		−	6.92820i		−	0.909718i
$59$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$59$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$60$	3.00000	−	5.19615i	0.387298	−	0.670820i
$61$		−	5.19615i		−	0.665299i	−0.943051	−	0.332650i	$-0.892057\pi$
$61$		−	5.19615i		−	0.665299i	0.943051	−	0.332650i	$-0.107943\pi$
$62$	4.00000	+	6.92820i	0.508001	+	0.879883i
$63$	7.50000	−	2.59808i	0.944911	−	0.327327i
$64$	1.00000			0.125000
$65$	−3.00000	+	12.1244i	−0.372104	+	1.50384i
$66$	9.00000	+	5.19615i	1.10782	+	0.639602i
$67$			3.46410i			0.423207i	0.977356	+	0.211604i	$0.0678686\pi$
$67$			3.46410i			0.423207i	−0.977356	+	0.211604i	$0.932131\pi$
$68$		0			0
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$	3.00000	+	8.66025i	0.358569	+	1.03510i
$71$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$71$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$72$	−3.00000			−0.353553
$73$	−3.50000	+	6.06218i	−0.409644	+	0.709524i	−0.994850	−	0.101361i	$-0.967680\pi$
$73$	−3.50000	+	6.06218i	−0.409644	+	0.709524i	0.585206	+	0.810885i	$0.301014\pi$
$74$	−7.50000	+	4.33013i	−0.871857	+	0.503367i
$75$	−10.5000	−	6.06218i	−1.21244	−	0.700000i
$76$	−2.50000	−	4.33013i	−0.286770	−	0.496700i
$77$	−15.0000	+	5.19615i	−1.70941	+	0.592157i
$78$	6.00000	−	1.73205i	0.679366	−	0.196116i
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	0.998388	−	0.0567635i	$-0.0180781\pi$
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	−0.548352	+	0.836247i	$0.684745\pi$
$80$		−	3.46410i		−	0.387298i
$81$	9.00000			1.00000
$82$			10.3923i			1.14764i
$83$			3.46410i			0.380235i	0.981761	+	0.190117i	$0.0608868\pi$
$83$			3.46410i			0.380235i	−0.981761	+	0.190117i	$0.939113\pi$
$84$	3.00000	−	3.46410i	0.327327	−	0.377964i
$85$		0			0
$86$	−0.500000	−	0.866025i	−0.0539164	−	0.0933859i
$87$	6.00000	+	10.3923i	0.643268	+	1.11417i
$88$	6.00000			0.639602
$89$	−3.00000	−	1.73205i	−0.317999	−	0.183597i	0.332501	−	0.943103i	$-0.392107\pi$
$89$	−3.00000	−	1.73205i	−0.317999	−	0.183597i	−0.650500	+	0.759506i	$0.725441\pi$
$90$			10.3923i			1.09545i
$91$	−4.00000	+	8.66025i	−0.419314	+	0.907841i
$92$		−	3.46410i		−	0.361158i
$93$	−12.0000	−	6.92820i	−1.24434	−	0.718421i
$94$		−	6.92820i		−	0.714590i
$95$	−15.0000	+	8.66025i	−1.53897	+	0.888523i
$96$	−1.50000	+	0.866025i	−0.153093	+	0.0883883i
$97$	3.50000	−	6.06218i	0.355371	−	0.615521i	−0.631810	−	0.775123i	$-0.717688\pi$
$97$	3.50000	−	6.06218i	0.355371	−	0.615521i	0.987181	+	0.159602i	$0.0510211\pi$
$98$	1.00000	+	6.92820i	0.101015	+	0.699854i
$99$	−18.0000			−1.80907
$100$	−7.00000			−0.700000
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$		0			0
$103$	4.50000	−	2.59808i	0.443398	−	0.255996i	−0.261640	−	0.965166i	$-0.584263\pi$
$103$	4.50000	−	2.59808i	0.443398	−	0.255996i	0.705038	+	0.709170i	$0.250930\pi$
$104$	2.50000	−	2.59808i	0.245145	−	0.254762i
$105$	−12.0000	−	10.3923i	−1.17108	−	1.01419i
$106$	−3.00000	+	1.73205i	−0.291386	+	0.168232i
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$	10.5000	+	6.06218i	1.00572	+	0.580651i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	10.5000	+	6.06218i	1.00572	+	0.580651i	0.0957826	+	0.995402i	$0.469465\pi$
$110$		−	20.7846i		−	1.98173i
$111$	7.50000	−	12.9904i	0.711868	−	1.23299i
$112$	0.500000	−	2.59808i	0.0472456	−	0.245495i
$113$	6.00000	+	3.46410i	0.564433	+	0.325875i	0.754923	−	0.655814i	$-0.227674\pi$
$113$	6.00000	+	3.46410i	0.564433	+	0.325875i	−0.190490	+	0.981689i	$0.561008\pi$
$114$	7.50000	+	4.33013i	0.702439	+	0.405554i
$115$	−12.0000			−1.11901
$116$	6.00000	+	3.46410i	0.557086	+	0.321634i
$117$	−7.50000	+	7.79423i	−0.693375	+	0.720577i
$118$		0			0
$119$		0			0
$120$	3.00000	+	5.19615i	0.273861	+	0.474342i
$121$	25.0000			2.27273
$122$	4.50000	+	2.59808i	0.407411	+	0.235219i
$123$	−9.00000	−	15.5885i	−0.811503	−	1.40556i
$124$	−8.00000			−0.718421
$125$			6.92820i			0.619677i
$126$	−1.50000	+	7.79423i	−0.133631	+	0.694365i
$127$	−0.500000	−	0.866025i	−0.0443678	−	0.0768473i	0.842989	−	0.537931i	$-0.180794\pi$
$127$	−0.500000	−	0.866025i	−0.0443678	−	0.0768473i	−0.887357	+	0.461084i	$0.847461\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	1.50000	+	0.866025i	0.132068	+	0.0762493i
$130$	−9.00000	−	8.66025i	−0.789352	−	0.759555i
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	−0.928199	−	0.372084i	$-0.878643\pi$
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	0.141865	−	0.989886i	$-0.454690\pi$
$132$	−9.00000	+	5.19615i	−0.783349	+	0.452267i
$133$	−12.5000	+	4.33013i	−1.08389	+	0.375470i
$134$	−3.00000	−	1.73205i	−0.259161	−	0.149626i
$135$	−9.00000	−	15.5885i	−0.774597	−	1.34164i
$136$		0			0
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	0.965250	−	0.261329i	$-0.0841608\pi$
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	−0.708942	+	0.705266i	$0.750827\pi$
$138$	3.00000	+	5.19615i	0.255377	+	0.442326i
$139$	3.00000	+	1.73205i	0.254457	+	0.146911i	0.621803	−	0.783174i	$-0.286400\pi$
$139$	3.00000	+	1.73205i	0.254457	+	0.146911i	−0.367347	+	0.930084i	$0.619734\pi$
$140$	−9.00000	−	1.73205i	−0.760639	−	0.146385i
$141$	6.00000	+	10.3923i	0.505291	+	0.875190i
$142$		0			0
$143$	15.0000	−	15.5885i	1.25436	−	1.30357i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	12.0000	−	20.7846i	0.996546	−	1.72607i
$146$	−3.50000	−	6.06218i	−0.289662	−	0.501709i
$147$	−7.50000	−	9.52628i	−0.618590	−	0.785714i
$148$		−	8.66025i		−	0.711868i
$149$	18.0000			1.47462			0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000			1.47462			0.737309	+	0.675556i	$0.236096\pi$
$150$	10.5000	−	6.06218i	0.857321	−	0.494975i
$151$	−3.00000	−	1.73205i	−0.244137	−	0.140952i	0.372940	−	0.927855i	$-0.378350\pi$
$151$	−3.00000	−	1.73205i	−0.244137	−	0.140952i	−0.617076	+	0.786903i	$0.711683\pi$
$152$	5.00000			0.405554
$153$		0			0
$154$	3.00000	−	15.5885i	0.241747	−	1.25615i
$155$			27.7128i			2.22595i
$156$	−1.50000	+	6.06218i	−0.120096	+	0.485363i
$157$	−16.5000	−	9.52628i	−1.31684	−	0.760280i	−0.333624	−	0.942706i	$-0.608272\pi$
$157$	−16.5000	−	9.52628i	−1.31684	−	0.760280i	−0.983220	+	0.182426i	$0.941605\pi$
$158$	−8.00000			−0.636446
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$	3.00000	+	1.73205i	0.237171	+	0.136931i
$161$	−9.00000	−	1.73205i	−0.709299	−	0.136505i
$162$	−4.50000	+	7.79423i	−0.353553	+	0.612372i
$163$			1.73205i			0.135665i	0.997697	+	0.0678323i	$0.0216083\pi$
$163$			1.73205i			0.135665i	−0.997697	+	0.0678323i	$0.978392\pi$
$164$	−9.00000	−	5.19615i	−0.702782	−	0.405751i
$165$	18.0000	+	31.1769i	1.40130	+	2.42712i
$166$	−3.00000	−	1.73205i	−0.232845	−	0.134433i
$167$	−3.00000	+	1.73205i	−0.232147	+	0.134030i	−0.611562	−	0.791196i	$-0.709459\pi$
$167$	−3.00000	+	1.73205i	−0.232147	+	0.134030i	0.379415	+	0.925227i	$0.376125\pi$
$168$	1.50000	+	4.33013i	0.115728	+	0.334077i
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	−15.0000			−1.14708
$172$	1.00000			0.0762493
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$	−12.0000			−0.909718
$175$	−3.50000	+	18.1865i	−0.264575	+	1.37477i
$176$	−3.00000	+	5.19615i	−0.226134	+	0.391675i
$177$		0			0
$178$	3.00000	−	1.73205i	0.224860	−	0.129823i
$179$		−	24.2487i		−	1.81243i	−0.422813	−	0.906217i	$-0.638957\pi$
$179$		−	24.2487i		−	1.81243i	0.422813	−	0.906217i	$-0.361043\pi$
$180$	−9.00000	−	5.19615i	−0.670820	−	0.387298i
$181$		−	15.5885i		−	1.15868i	−0.815086	−	0.579340i	$-0.803310\pi$
$181$		−	15.5885i		−	1.15868i	0.815086	−	0.579340i	$-0.196690\pi$
$182$	−5.50000	−	7.79423i	−0.407687	−	0.577747i
$183$	−9.00000			−0.665299
$184$	3.00000	+	1.73205i	0.221163	+	0.127688i
$185$	−30.0000			−2.20564
$186$	12.0000	−	6.92820i	0.879883	−	0.508001i
$187$		0			0
$188$	6.00000	+	3.46410i	0.437595	+	0.252646i
$189$	−4.50000	−	12.9904i	−0.327327	−	0.944911i
$190$		−	17.3205i		−	1.25656i
$191$			20.7846i			1.50392i	0.659208	+	0.751961i	$0.270892\pi$
$191$			20.7846i			1.50392i	−0.659208	+	0.751961i	$0.729108\pi$
$192$		−	1.73205i		−	0.125000i
$193$			5.19615i			0.374027i	0.982357	+	0.187014i	$0.0598809\pi$
$193$			5.19615i			0.374027i	−0.982357	+	0.187014i	$0.940119\pi$
$194$	3.50000	+	6.06218i	0.251285	+	0.435239i
$195$	21.0000	+	5.19615i	1.50384	+	0.372104i
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$	−6.00000	−	10.3923i	−0.427482	−	0.740421i	0.569166	−	0.822222i	$-0.307266\pi$
$197$	−6.00000	−	10.3923i	−0.427482	−	0.740421i	−0.996649	+	0.0818013i	$0.973933\pi$
$198$	9.00000	−	15.5885i	0.639602	−	1.10782i
$199$	−13.5000	+	7.79423i	−0.956990	+	0.552518i	−0.895245	−	0.445574i	$-0.853000\pi$
$199$	−13.5000	+	7.79423i	−0.956990	+	0.552518i	−0.0617444	+	0.998092i	$0.519666\pi$
$200$	3.50000	−	6.06218i	0.247487	−	0.428661i
$201$	6.00000			0.423207
$202$	3.00000	−	5.19615i	0.211079	−	0.365600i
$203$	12.0000	−	13.8564i	0.842235	−	0.972529i
$204$		0			0
$205$	−18.0000	+	31.1769i	−1.25717	+	2.17749i
$206$			5.19615i			0.362033i
$207$	−9.00000	−	5.19615i	−0.625543	−	0.361158i
$208$	1.00000	+	3.46410i	0.0693375	+	0.240192i
$209$	30.0000			2.07514
$210$	15.0000	−	5.19615i	1.03510	−	0.358569i
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	0.767049	−	0.641588i	$-0.221724\pi$
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	−0.939156	+	0.343490i	$0.888391\pi$
$212$		−	3.46410i		−	0.237915i
$213$		0			0
$214$		0			0
$215$		−	3.46410i		−	0.236250i
$216$			5.19615i			0.353553i
$217$	−4.00000	+	20.7846i	−0.271538	+	1.41095i
$218$	−10.5000	+	6.06218i	−0.711150	+	0.410582i
$219$	10.5000	+	6.06218i	0.709524	+	0.409644i
$220$	18.0000	+	10.3923i	1.21356	+	0.700649i
$221$		0			0
$222$	7.50000	+	12.9904i	0.503367	+	0.871857i
$223$	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	$0.653374\pi$
$224$	2.00000	+	1.73205i	0.133631	+	0.115728i
$225$	−10.5000	+	18.1865i	−0.700000	+	1.21244i
$226$	−6.00000	+	3.46410i	−0.399114	+	0.230429i
$227$	9.00000	−	5.19615i	0.597351	−	0.344881i	−0.170648	−	0.985332i	$-0.554586\pi$
$227$	9.00000	−	5.19615i	0.597351	−	0.344881i	0.767999	+	0.640451i	$0.221253\pi$
$228$	−7.50000	+	4.33013i	−0.496700	+	0.286770i
$229$	14.5000	+	25.1147i	0.958187	+	1.65963i	0.726900	+	0.686743i	$0.240960\pi$
$229$	14.5000	+	25.1147i	0.958187	+	1.65963i	0.231287	+	0.972886i	$0.425707\pi$
$230$	6.00000	−	10.3923i	0.395628	−	0.685248i
$231$	9.00000	+	25.9808i	0.592157	+	1.70941i
$232$	−6.00000	+	3.46410i	−0.393919	+	0.227429i
$233$	−6.00000	+	3.46410i	−0.393073	+	0.226941i	−0.683491	−	0.729959i	$-0.739539\pi$
$233$	−6.00000	+	3.46410i	−0.393073	+	0.226941i	0.290418	+	0.956900i	$0.406206\pi$
$234$	−3.00000	−	10.3923i	−0.196116	−	0.679366i
$235$	12.0000	−	20.7846i	0.782794	−	1.35584i
$236$		0			0
$237$	12.0000	−	6.92820i	0.779484	−	0.450035i
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$	−6.00000			−0.387298
$241$	13.0000	+	22.5167i	0.837404	+	1.45043i	0.892058	+	0.451920i	$0.149261\pi$
$241$	13.0000	+	22.5167i	0.837404	+	1.45043i	−0.0546547	+	0.998505i	$0.517406\pi$
$242$	−12.5000	+	21.6506i	−0.803530	+	1.39176i
$243$		−	15.5885i		−	1.00000i
$244$	−4.50000	+	2.59808i	−0.288083	+	0.166325i
$245$	−9.00000	+	22.5167i	−0.574989	+	1.43854i
$246$	18.0000			1.14764
$247$	12.5000	−	12.9904i	0.795356	−	0.826558i
$248$	4.00000	−	6.92820i	0.254000	−	0.439941i
$249$	6.00000			0.380235
$250$	−6.00000	−	3.46410i	−0.379473	−	0.219089i
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	−0.990876	−	0.134778i	$-0.956968\pi$
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	0.612159	+	0.790735i	$0.290301\pi$
$252$	−6.00000	−	5.19615i	−0.377964	−	0.327327i
$253$	18.0000	+	10.3923i	1.13165	+	0.653359i
$254$	1.00000			0.0627456
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$	−1.50000	+	0.866025i	−0.0933859	+	0.0539164i
$259$	−22.5000	−	4.33013i	−1.39808	−	0.269061i
$260$	12.0000	−	3.46410i	0.744208	−	0.214834i
$261$	18.0000	−	10.3923i	1.11417	−	0.643268i
$262$	18.0000			1.11204
$263$			13.8564i			0.854423i	0.904152	+	0.427211i	$0.140504\pi$
$263$			13.8564i			0.854423i	−0.904152	+	0.427211i	$0.859496\pi$
$264$		−	10.3923i		−	0.639602i
$265$	−12.0000			−0.737154
$266$	2.50000	−	12.9904i	0.153285	−	0.796491i
$267$	−3.00000	+	5.19615i	−0.183597	+	0.317999i
$268$	3.00000	−	1.73205i	0.183254	−	0.105802i
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	0.623082	−	0.782157i	$-0.285880\pi$
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	−0.988908	+	0.148527i	$0.952547\pi$
$270$	18.0000			1.09545
$271$	0.500000	−	0.866025i	0.0303728	−	0.0526073i	−0.850439	−	0.526073i	$-0.823664\pi$
$271$	0.500000	−	0.866025i	0.0303728	−	0.0526073i	0.880812	+	0.473466i	$0.156997\pi$
$272$		0			0
$273$	15.0000	+	6.92820i	0.907841	+	0.419314i
$274$	−6.00000			−0.362473
$275$	21.0000	−	36.3731i	1.26635	−	2.19338i
$276$	−6.00000			−0.361158
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	−0.999923	−	0.0124177i	$-0.996047\pi$
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	0.489207	−	0.872167i	$-0.337286\pi$
$278$	−3.00000	+	1.73205i	−0.179928	+	0.103882i
$279$	−12.0000	+	20.7846i	−0.718421	+	1.24434i
$280$	6.00000	−	6.92820i	0.358569	−	0.414039i
$281$	12.0000			0.715860			0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000			0.715860			0.357930	+	0.933748i	$0.383483\pi$
$282$	−12.0000			−0.714590
$283$		−	1.73205i		−	0.102960i	−0.998674	−	0.0514799i	$-0.983606\pi$
$283$		−	1.73205i		−	0.102960i	0.998674	−	0.0514799i	$-0.0163938\pi$
$284$		0			0
$285$	15.0000	+	25.9808i	0.888523	+	1.53897i
$286$	6.00000	+	20.7846i	0.354787	+	1.22902i
$287$	−18.0000	+	20.7846i	−1.06251	+	1.22688i
$288$	1.50000	+	2.59808i	0.0883883	+	0.153093i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	12.0000	+	20.7846i	0.704664	+	1.22051i
$291$	−10.5000	−	6.06218i	−0.615521	−	0.355371i
$292$	7.00000			0.409644
$293$	6.00000	+	3.46410i	0.350524	+	0.202375i	0.664916	−	0.746918i	$-0.268467\pi$
$293$	6.00000	+	3.46410i	0.350524	+	0.202375i	−0.314392	+	0.949293i	$0.601801\pi$
$294$	12.0000	−	1.73205i	0.699854	−	0.101015i
$295$		0			0
$296$	7.50000	+	4.33013i	0.435929	+	0.251684i
$297$			31.1769i			1.80907i
$298$	−9.00000	+	15.5885i	−0.521356	+	0.903015i
$299$	12.0000	−	3.46410i	0.693978	−	0.200334i
$300$			12.1244i			0.700000i
$301$	0.500000	−	2.59808i	0.0288195	−	0.149751i
$302$	3.00000	−	1.73205i	0.172631	−	0.0996683i
$303$			10.3923i			0.597022i
$304$	−2.50000	+	4.33013i	−0.143385	+	0.248350i
$305$	9.00000	+	15.5885i	0.515339	+	0.892592i
$306$		0			0
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$	12.0000	+	10.3923i	0.683763	+	0.592157i
$309$	−4.50000	−	7.79423i	−0.255996	−	0.443398i
$310$	−24.0000	−	13.8564i	−1.36311	−	0.786991i
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	−0.768345	−	0.640036i	$-0.778920\pi$
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	0.938460	+	0.345389i	$0.112253\pi$
$312$	−4.50000	−	4.33013i	−0.254762	−	0.245145i
$313$	−28.5000	+	16.4545i	−1.61092	+	0.930062i	−0.621757	+	0.783210i	$0.713581\pi$
$313$	−28.5000	+	16.4545i	−1.61092	+	0.930062i	−0.989158	+	0.146852i	$0.953086\pi$
$314$	16.5000	−	9.52628i	0.931149	−	0.537599i
$315$	−18.0000	+	20.7846i	−1.01419	+	1.17108i
$316$	4.00000	−	6.92820i	0.225018	−	0.389742i
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	−0.999980	−	0.00635137i	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$	3.00000	+	5.19615i	0.168232	+	0.291386i
$319$	−36.0000	+	20.7846i	−2.01561	+	1.16371i
$320$	−3.00000	+	1.73205i	−0.167705	+	0.0968246i
$321$		0			0
$322$	6.00000	−	6.92820i	0.334367	−	0.386094i
$323$		0			0
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	−7.00000	−	24.2487i	−0.388290	−	1.34508i
$326$	−1.50000	−	0.866025i	−0.0830773	−	0.0479647i
$327$	10.5000	−	18.1865i	0.580651	−	1.00572i
$328$	9.00000	−	5.19615i	0.496942	−	0.286910i
$329$	12.0000	−	13.8564i	0.661581	−	0.763928i
$330$	−36.0000			−1.98173
$331$		−	19.0526i		−	1.04722i	−0.851957	−	0.523612i	$-0.824584\pi$
$331$		−	19.0526i		−	1.04722i	0.851957	−	0.523612i	$-0.175416\pi$
$332$	3.00000	−	1.73205i	0.164646	−	0.0950586i
$333$	−22.5000	−	12.9904i	−1.23299	−	0.711868i
$334$		−	3.46410i		−	0.189547i
$335$	−6.00000	−	10.3923i	−0.327815	−	0.567792i
$336$	−4.50000	−	0.866025i	−0.245495	−	0.0472456i
$337$	5.00000			0.272367			0.136184	−	0.990684i	$-0.456516\pi$
$337$	5.00000			0.272367			0.136184	+	0.990684i	$0.456516\pi$
$338$	11.5000	+	6.06218i	0.625518	+	0.329739i
$339$	6.00000	−	10.3923i	0.325875	−	0.564433i
$340$		0			0
$341$	24.0000	−	41.5692i	1.29967	−	2.25110i
$342$	7.50000	−	12.9904i	0.405554	−	0.702439i
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−0.500000	+	0.866025i	−0.0269582	+	0.0466930i
$345$			20.7846i			1.11901i
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$	6.00000	−	10.3923i	0.321634	−	0.557086i
$349$	5.50000	+	9.52628i	0.294408	+	0.509930i	0.974847	−	0.222875i	$-0.0715441\pi$
$349$	5.50000	+	9.52628i	0.294408	+	0.509930i	−0.680439	+	0.732805i	$0.738211\pi$
$350$	−14.0000	−	12.1244i	−0.748331	−	0.648074i
$351$	13.5000	+	12.9904i	0.720577	+	0.693375i
$352$	−3.00000	−	5.19615i	−0.159901	−	0.276956i
$353$		−	10.3923i		−	0.553127i	−0.960996	−	0.276563i	$-0.910804\pi$
$353$		−	10.3923i		−	0.553127i	0.960996	−	0.276563i	$-0.0891955\pi$
$354$		0			0
$355$		0			0
$356$			3.46410i			0.183597i
$357$		0			0
$358$	21.0000	+	12.1244i	1.10988	+	0.640792i
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	−0.986865	−	0.161546i	$-0.948352\pi$
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	0.353529	−	0.935423i	$-0.384981\pi$
$360$	9.00000	−	5.19615i	0.474342	−	0.273861i
$361$	6.00000			0.315789
$362$	13.5000	+	7.79423i	0.709544	+	0.409656i
$363$		−	43.3013i		−	2.27273i
$364$	9.50000	−	0.866025i	0.497935	−	0.0453921i
$365$		−	24.2487i		−	1.26924i
$366$	4.50000	−	7.79423i	0.235219	−	0.407411i
$367$			1.73205i			0.0904123i	0.998978	+	0.0452062i	$0.0143945\pi$
$367$			1.73205i			0.0904123i	−0.998978	+	0.0452062i	$0.985606\pi$
$368$	−3.00000	+	1.73205i	−0.156386	+	0.0902894i
$369$	−27.0000	+	15.5885i	−1.40556	+	0.811503i
$370$	15.0000	−	25.9808i	0.779813	−	1.35068i
$371$	−9.00000	−	1.73205i	−0.467257	−	0.0899236i
$372$			13.8564i			0.718421i
$373$	−2.00000			−0.103556			−0.0517780	−	0.998659i	$-0.516489\pi$
$373$	−2.00000			−0.103556			−0.0517780	+	0.998659i	$0.516489\pi$
$374$		0			0
$375$	12.0000			0.619677
$376$	−6.00000	+	3.46410i	−0.309426	+	0.178647i
$377$	−6.00000	+	24.2487i	−0.309016	+	1.24887i
$378$	13.5000	+	2.59808i	0.694365	+	0.133631i
$379$	−15.0000	+	8.66025i	−0.770498	+	0.444847i	−0.833052	−	0.553194i	$-0.813409\pi$
$379$	−15.0000	+	8.66025i	−0.770498	+	0.444847i	0.0625541	+	0.998042i	$0.480075\pi$
$380$	15.0000	+	8.66025i	0.769484	+	0.444262i
$381$	−1.50000	+	0.866025i	−0.0768473	+	0.0443678i
$382$	−18.0000	−	10.3923i	−0.920960	−	0.531717i
$383$			20.7846i			1.06204i	0.847358	+	0.531022i	$0.178192\pi$
$383$			20.7846i			1.06204i	−0.847358	+	0.531022i	$0.821808\pi$
$384$	1.50000	+	0.866025i	0.0765466	+	0.0441942i
$385$	36.0000	−	41.5692i	1.83473	−	2.11856i
$386$	−4.50000	−	2.59808i	−0.229044	−	0.132239i
$387$	1.50000	−	2.59808i	0.0762493	−	0.132068i
$388$	−7.00000			−0.355371
$389$	−9.00000	−	5.19615i	−0.456318	−	0.263455i	0.254177	−	0.967158i	$-0.418196\pi$
$389$	−9.00000	−	5.19615i	−0.456318	−	0.263455i	−0.710495	+	0.703702i	$0.751529\pi$
$390$	−15.0000	+	15.5885i	−0.759555	+	0.789352i
$391$		0			0
$392$	5.50000	−	4.33013i	0.277792	−	0.218704i
$393$	−27.0000	+	15.5885i	−1.36197	+	0.786334i
$394$	12.0000			0.604551
$395$	−24.0000	−	13.8564i	−1.20757	−	0.697191i
$396$	9.00000	+	15.5885i	0.452267	+	0.783349i
$397$	11.0000			0.552074			0.276037	−	0.961147i	$-0.410979\pi$
$397$	11.0000			0.552074			0.276037	+	0.961147i	$0.410979\pi$
$398$		−	15.5885i		−	0.781379i
$399$	7.50000	+	21.6506i	0.375470	+	1.08389i
$400$	3.50000	+	6.06218i	0.175000	+	0.303109i
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$	−3.00000	+	5.19615i	−0.149626	+	0.259161i
$403$	−8.00000	−	27.7128i	−0.398508	−	1.38047i
$404$	3.00000	+	5.19615i	0.149256	+	0.258518i
$405$	−27.0000	+	15.5885i	−1.34164	+	0.774597i
$406$	6.00000	+	17.3205i	0.297775	+	0.859602i
$407$	45.0000	+	25.9808i	2.23057	+	1.28782i
$408$		0			0
$409$	9.50000	+	16.4545i	0.469745	+	0.813622i	0.999402	−	0.0345902i	$-0.0110126\pi$
$409$	9.50000	+	16.4545i	0.469745	+	0.813622i	−0.529657	+	0.848212i	$0.677679\pi$
$410$	−18.0000	−	31.1769i	−0.888957	−	1.53972i
$411$	9.00000	−	5.19615i	0.443937	−	0.256307i
$412$	−4.50000	−	2.59808i	−0.221699	−	0.127998i
$413$		0			0
$414$	9.00000	−	5.19615i	0.442326	−	0.255377i
$415$	−6.00000	−	10.3923i	−0.294528	−	0.510138i
$416$	−3.50000	−	0.866025i	−0.171602	−	0.0424604i
$417$	3.00000	−	5.19615i	0.146911	−	0.254457i
$418$	−15.0000	+	25.9808i	−0.733674	+	1.27076i
$419$	15.0000	+	25.9808i	0.732798	+	1.26924i	0.955683	+	0.294398i	$0.0951193\pi$
$419$	15.0000	+	25.9808i	0.732798	+	1.26924i	−0.222885	+	0.974845i	$0.571547\pi$
$420$	−3.00000	+	15.5885i	−0.146385	+	0.760639i
$421$			27.7128i			1.35064i	0.737525	+	0.675320i	$0.235994\pi$
$421$			27.7128i			1.35064i	−0.737525	+	0.675320i	$0.764006\pi$
$422$	5.00000			0.243396
$423$	18.0000	−	10.3923i	0.875190	−	0.505291i
$424$	3.00000	+	1.73205i	0.145693	+	0.0841158i
$425$		0			0
$426$		0			0
$427$	4.50000	+	12.9904i	0.217770	+	0.628649i
$428$		0			0
$429$	−27.0000	−	25.9808i	−1.30357	−	1.25436i
$430$	3.00000	+	1.73205i	0.144673	+	0.0835269i
$431$	−18.0000			−0.867029			−0.433515	−	0.901146i	$-0.642727\pi$
$431$	−18.0000			−0.867029			−0.433515	+	0.901146i	$0.642727\pi$
$432$	−4.50000	−	2.59808i	−0.216506	−	0.125000i
$433$	−18.0000	−	10.3923i	−0.865025	−	0.499422i	0.000666943	−	1.00000i	$-0.499788\pi$
$433$	−18.0000	−	10.3923i	−0.865025	−	0.499422i	−0.865692	+	0.500577i	$0.833121\pi$
$434$	−16.0000	−	13.8564i	−0.768025	−	0.665129i
$435$	−36.0000	−	20.7846i	−1.72607	−	0.996546i
$436$		−	12.1244i		−	0.580651i
$437$	15.0000	+	8.66025i	0.717547	+	0.414276i
$438$	−10.5000	+	6.06218i	−0.501709	+	0.289662i
$439$	10.5000	+	6.06218i	0.501138	+	0.289332i	0.729183	−	0.684318i	$-0.239900\pi$
$439$	10.5000	+	6.06218i	0.501138	+	0.289332i	−0.228046	+	0.973650i	$0.573234\pi$
$440$	−18.0000	+	10.3923i	−0.858116	+	0.495434i
$441$	−16.5000	+	12.9904i	−0.785714	+	0.618590i
$442$		0			0
$443$	−33.0000	+	19.0526i	−1.56788	+	0.905214i	−0.571461	+	0.820629i	$0.693623\pi$
$443$	−33.0000	+	19.0526i	−1.56788	+	0.905214i	−0.996416	+	0.0845852i	$0.973043\pi$
$444$	−15.0000			−0.711868
$445$	12.0000			0.568855
$446$	−16.0000			−0.757622
$447$		−	31.1769i		−	1.47462i
$448$	−2.50000	+	0.866025i	−0.118114	+	0.0409159i
$449$	15.0000	−	25.9808i	0.707894	−	1.22611i	−0.257743	−	0.966213i	$-0.582979\pi$
$449$	15.0000	−	25.9808i	0.707894	−	1.22611i	0.965637	−	0.259895i	$-0.0836878\pi$
$450$	−10.5000	−	18.1865i	−0.494975	−	0.857321i
$451$	54.0000	−	31.1769i	2.54276	−	1.46806i
$452$		−	6.92820i		−	0.325875i
$453$	−3.00000	+	5.19615i	−0.140952	+	0.244137i
$454$			10.3923i			0.487735i
$455$	−3.00000	−	32.9090i	−0.140642	−	1.54280i
$456$		−	8.66025i		−	0.405554i
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$	−29.0000			−1.35508
$459$		0			0
$460$	6.00000	+	10.3923i	0.279751	+	0.484544i
$461$	−18.0000	−	10.3923i	−0.838344	−	0.484018i	0.0183573	−	0.999831i	$-0.494156\pi$
$461$	−18.0000	−	10.3923i	−0.838344	−	0.484018i	−0.856701	+	0.515814i	$0.827490\pi$
$462$	−27.0000	−	5.19615i	−1.25615	−	0.241747i
$463$			19.0526i			0.885448i	0.896658	+	0.442724i	$0.145988\pi$
$463$			19.0526i			0.885448i	−0.896658	+	0.442724i	$0.854012\pi$
$464$		−	6.92820i		−	0.321634i
$465$	48.0000			2.22595
$466$		−	6.92820i		−	0.320943i
$467$	9.00000	+	15.5885i	0.416470	+	0.721348i	0.995582	−	0.0939008i	$-0.0299336\pi$
$467$	9.00000	+	15.5885i	0.416470	+	0.721348i	−0.579111	+	0.815249i	$0.696600\pi$
$468$	10.5000	+	2.59808i	0.485363	+	0.120096i
$469$	−3.00000	−	8.66025i	−0.138527	−	0.399893i
$470$	12.0000	+	20.7846i	0.553519	+	0.958723i
$471$	−16.5000	+	28.5788i	−0.760280	+	1.31684i
$472$		0			0
$473$	−3.00000	+	5.19615i	−0.137940	+	0.238919i
$474$			13.8564i			0.636446i
$475$	17.5000	−	30.3109i	0.802955	−	1.39076i
$476$		0			0
$477$	−9.00000	−	5.19615i	−0.412082	−	0.237915i
$478$	3.00000	−	5.19615i	0.137217	−	0.237666i
$479$		−	6.92820i		−	0.316558i	−0.987394	−	0.158279i	$-0.949406\pi$
$479$		−	6.92820i		−	0.316558i	0.987394	−	0.158279i	$-0.0505945\pi$
$480$	3.00000	−	5.19615i	0.136931	−	0.237171i
$481$	30.0000	−	8.66025i	1.36788	−	0.394874i
$482$	−26.0000			−1.18427
$483$	−3.00000	+	15.5885i	−0.136505	+	0.709299i
$484$	−12.5000	−	21.6506i	−0.568182	−	0.984120i
$485$			24.2487i			1.10108i
$486$	13.5000	+	7.79423i	0.612372	+	0.353553i
$487$	−13.5000	+	7.79423i	−0.611743	+	0.353190i	−0.773647	−	0.633616i	$-0.781570\pi$
$487$	−13.5000	+	7.79423i	−0.611743	+	0.353190i	0.161904	+	0.986807i	$0.448236\pi$
$488$		−	5.19615i		−	0.235219i
$489$	3.00000			0.135665
$490$	−15.0000	−	19.0526i	−0.677631	−	0.860707i
$491$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$491$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$492$	−9.00000	+	15.5885i	−0.405751	+	0.702782i
$493$		0			0
$494$	5.00000	+	17.3205i	0.224961	+	0.779287i
$495$	54.0000	−	31.1769i	2.42712	−	1.40130i
$496$	4.00000	+	6.92820i	0.179605	+	0.311086i
$497$		0			0
$498$	−3.00000	+	5.19615i	−0.134433	+	0.232845i
$499$	7.50000	−	4.33013i	0.335746	−	0.193843i	−0.322643	−	0.946521i	$-0.604571\pi$
$499$	7.50000	−	4.33013i	0.335746	−	0.193843i	0.658389	+	0.752678i	$0.271238\pi$
$500$	6.00000	−	3.46410i	0.268328	−	0.154919i
$501$	3.00000	+	5.19615i	0.134030	+	0.232147i
$502$	−6.00000	−	10.3923i	−0.267793	−	0.463831i
$503$	15.0000	−	25.9808i	0.668817	−	1.15842i	−0.309418	−	0.950926i	$-0.600134\pi$
$503$	15.0000	−	25.9808i	0.668817	−	1.15842i	0.978235	−	0.207499i	$-0.0665323\pi$
$504$	7.50000	−	2.59808i	0.334077	−	0.115728i
$505$	18.0000	−	10.3923i	0.800989	−	0.462451i
$506$	−18.0000	+	10.3923i	−0.800198	+	0.461994i
$507$	−22.5000	+	0.866025i	−0.999260	+	0.0384615i
$508$	−0.500000	+	0.866025i	−0.0221839	+	0.0384237i
$509$	−21.0000	−	12.1244i	−0.930809	−	0.537403i	−0.0437414	−	0.999043i	$-0.513928\pi$
$509$	−21.0000	−	12.1244i	−0.930809	−	0.537403i	−0.887067	+	0.461640i	$0.847261\pi$
$510$		0			0
$511$	3.50000	−	18.1865i	0.154831	−	0.804525i
$512$	1.00000			0.0441942
$513$			25.9808i			1.14708i
$514$	9.00000	+	15.5885i	0.396973	+	0.687577i
$515$	−9.00000	+	15.5885i	−0.396587	+	0.686909i
$516$		−	1.73205i		−	0.0762493i
$517$	−36.0000	+	20.7846i	−1.58328	+	0.914106i
$518$	15.0000	−	17.3205i	0.659062	−	0.761019i
$519$		−	10.3923i		−	0.456172i
$520$	−3.00000	+	12.1244i	−0.131559	+	0.531688i
$521$	−6.00000	+	10.3923i	−0.262865	+	0.455295i	−0.967002	−	0.254769i	$-0.918001\pi$
$521$	−6.00000	+	10.3923i	−0.262865	+	0.455295i	0.704137	+	0.710064i	$0.251334\pi$
$522$			20.7846i			0.909718i
$523$	7.50000	+	4.33013i	0.327952	+	0.189343i	0.654932	−	0.755688i	$-0.272697\pi$
$523$	7.50000	+	4.33013i	0.327952	+	0.189343i	−0.326979	+	0.945031i	$0.606031\pi$
$524$	−9.00000	+	15.5885i	−0.393167	+	0.680985i
$525$	31.5000	+	6.06218i	1.37477	+	0.264575i
$526$	−12.0000	−	6.92820i	−0.523225	−	0.302084i
$527$		0			0
$528$	9.00000	+	5.19615i	0.391675	+	0.226134i
$529$	−5.50000	−	9.52628i	−0.239130	−	0.414186i
$530$	6.00000	−	10.3923i	0.260623	−	0.451413i
$531$		0			0
$532$	10.0000	+	8.66025i	0.433555	+	0.375470i
$533$	9.00000	−	36.3731i	0.389833	−	1.57549i
$534$	−3.00000	−	5.19615i	−0.129823	−	0.224860i
$535$		0			0
$536$			3.46410i			0.149626i
$537$	−42.0000			−1.81243
$538$	12.0000			0.517357
$539$	33.0000	−	25.9808i	1.42141	−	1.11907i
$540$	−9.00000	+	15.5885i	−0.387298	+	0.670820i
$541$	−1.50000	+	0.866025i	−0.0644900	+	0.0372333i	−0.531898	−	0.846808i	$-0.678521\pi$
$541$	−1.50000	+	0.866025i	−0.0644900	+	0.0372333i	0.467408	+	0.884042i	$0.345188\pi$
$542$	0.500000	+	0.866025i	0.0214768	+	0.0371990i
$543$	−27.0000			−1.15868
$544$		0			0
$545$	−42.0000			−1.79908
$546$	−13.5000	+	9.52628i	−0.577747	+	0.407687i
$547$	−25.0000			−1.06892			−0.534461	−	0.845193i	$-0.679486\pi$
$547$	−25.0000			−1.06892			−0.534461	+	0.845193i	$0.679486\pi$
$548$	3.00000	−	5.19615i	0.128154	−	0.221969i
$549$			15.5885i			0.665299i
$550$	21.0000	+	36.3731i	0.895443	+	1.55095i
$551$	−30.0000	+	17.3205i	−1.27804	+	0.737878i
$552$	3.00000	−	5.19615i	0.127688	−	0.221163i
$553$	−16.0000	−	13.8564i	−0.680389	−	0.589234i
$554$	17.0000			0.722261
$555$			51.9615i			2.20564i
$556$		−	3.46410i		−	0.146911i
$557$	−18.0000			−0.762684			−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000			−0.762684			−0.381342	+	0.924434i	$0.624538\pi$
$558$	−12.0000	−	20.7846i	−0.508001	−	0.879883i
$559$	1.00000	+	3.46410i	0.0422955	+	0.146516i
$560$	3.00000	+	8.66025i	0.126773	+	0.365963i
$561$		0			0
$562$	−6.00000	+	10.3923i	−0.253095	+	0.438373i
$563$	9.00000	+	15.5885i	0.379305	+	0.656975i	0.990961	−	0.134148i	$-0.0428299\pi$
$563$	9.00000	+	15.5885i	0.379305	+	0.656975i	−0.611656	+	0.791123i	$0.709497\pi$
$564$	6.00000	−	10.3923i	0.252646	−	0.437595i
$565$	−24.0000			−1.00969
$566$	1.50000	+	0.866025i	0.0630497	+	0.0364018i
$567$	−22.5000	+	7.79423i	−0.944911	+	0.327327i
$568$		0			0
$569$	24.0000	+	13.8564i	1.00613	+	0.580891i	0.910057	−	0.414483i	$-0.136038\pi$
$569$	24.0000	+	13.8564i	1.00613	+	0.580891i	0.0960754	+	0.995374i	$0.469371\pi$
$570$	−30.0000			−1.25656
$571$	−9.50000	+	16.4545i	−0.397563	+	0.688599i	−0.993425	−	0.114488i	$-0.963477\pi$
$571$	−9.50000	+	16.4545i	−0.397563	+	0.688599i	0.595862	+	0.803087i	$0.296811\pi$
$572$	−21.0000	−	5.19615i	−0.878054	−	0.217262i
$573$	36.0000			1.50392
$574$	−9.00000	−	25.9808i	−0.375653	−	1.08442i
$575$	21.0000	−	12.1244i	0.875761	−	0.505621i
$576$	−3.00000			−0.125000
$577$	18.5000	−	32.0429i	0.770165	−	1.33397i	−0.167307	−	0.985905i	$-0.553507\pi$
$577$	18.5000	−	32.0429i	0.770165	−	1.33397i	0.937472	−	0.348060i	$-0.113160\pi$
$578$	8.50000	+	14.7224i	0.353553	+	0.612372i
$579$	9.00000			0.374027
$580$	−24.0000			−0.996546
$581$	−3.00000	−	8.66025i	−0.124461	−	0.359288i
$582$	10.5000	−	6.06218i	0.435239	−	0.251285i
$583$	18.0000	+	10.3923i	0.745484	+	0.430405i
$584$	−3.50000	+	6.06218i	−0.144831	+	0.250855i
$585$	9.00000	−	36.3731i	0.372104	−	1.50384i
$586$	−6.00000	+	3.46410i	−0.247858	+	0.143101i
$587$	−39.0000	+	22.5167i	−1.60970	+	0.929362i	−0.620266	+	0.784391i	$0.712975\pi$
$587$	−39.0000	+	22.5167i	−1.60970	+	0.929362i	−0.989436	+	0.144971i	$0.953691\pi$
$588$	−4.50000	+	11.2583i	−0.185577	+	0.464286i
$589$	20.0000	−	34.6410i	0.824086	−	1.42736i
$590$		0			0
$591$	−18.0000	+	10.3923i	−0.740421	+	0.427482i
$592$	−7.50000	+	4.33013i	−0.308248	+	0.177967i
$593$	−6.00000	+	3.46410i	−0.246390	+	0.142254i	−0.618110	−	0.786091i	$-0.712102\pi$
$593$	−6.00000	+	3.46410i	−0.246390	+	0.142254i	0.371720	+	0.928345i	$0.378768\pi$
$594$	−27.0000	−	15.5885i	−1.10782	−	0.639602i
$595$		0			0
$596$	−9.00000	−	15.5885i	−0.368654	−	0.638528i
$597$	13.5000	+	23.3827i	0.552518	+	0.956990i
$598$	−3.00000	+	12.1244i	−0.122679	+	0.495802i
$599$	24.0000	+	13.8564i	0.980613	+	0.566157i	0.902455	−	0.430784i	$-0.141763\pi$
$599$	24.0000	+	13.8564i	0.980613	+	0.566157i	0.0781581	+	0.996941i	$0.475096\pi$
$600$	−10.5000	−	6.06218i	−0.428661	−	0.247487i
$601$	−1.50000	+	0.866025i	−0.0611863	+	0.0353259i	−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−1.50000	+	0.866025i	−0.0611863	+	0.0353259i	0.469095	+	0.883148i	$0.344580\pi$
$602$	2.00000	+	1.73205i	0.0815139	+	0.0705931i
$603$		−	10.3923i		−	0.423207i
$604$			3.46410i			0.140952i
$605$	−75.0000	+	43.3013i	−3.04918	+	1.76045i
$606$	−9.00000	−	5.19615i	−0.365600	−	0.211079i
$607$			15.5885i			0.632716i	0.948640	+	0.316358i	$0.102460\pi$
$607$			15.5885i			0.632716i	−0.948640	+	0.316358i	$0.897540\pi$
$608$	−2.50000	−	4.33013i	−0.101388	−	0.175610i
$609$	−24.0000	−	20.7846i	−0.972529	−	0.842235i
$610$	−18.0000			−0.728799
$611$	−6.00000	+	24.2487i	−0.242734	+	0.980998i
$612$		0			0
$613$		−	25.9808i		−	1.04935i	−0.851302	−	0.524677i	$-0.824186\pi$
$613$		−	25.9808i		−	1.04935i	0.851302	−	0.524677i	$-0.175814\pi$
$614$	−2.00000	+	3.46410i	−0.0807134	+	0.139800i
$615$	54.0000	+	31.1769i	2.17749	+	1.25717i
$616$	−15.0000	+	5.19615i	−0.604367	+	0.209359i
$617$	−18.0000	+	31.1769i	−0.724653	+	1.25514i	0.234464	+	0.972125i	$0.424666\pi$
$617$	−18.0000	+	31.1769i	−0.724653	+	1.25514i	−0.959117	+	0.283011i	$0.908667\pi$
$618$	9.00000			0.362033
$619$	−8.50000	+	14.7224i	−0.341644	+	0.591744i	−0.984738	−	0.174042i	$-0.944317\pi$
$619$	−8.50000	+	14.7224i	−0.341644	+	0.591744i	0.643094	+	0.765787i	$0.277650\pi$
$620$	24.0000	−	13.8564i	0.963863	−	0.556487i
$621$	−9.00000	+	15.5885i	−0.361158	+	0.625543i
$622$	3.00000	+	5.19615i	0.120289	+	0.208347i
$623$	9.00000	+	1.73205i	0.360577	+	0.0693932i
$624$	6.00000	−	1.73205i	0.240192	−	0.0693375i
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$		−	32.9090i		−	1.31531i
$627$		−	51.9615i		−	2.07514i
$628$			19.0526i			0.760280i
$629$		0			0
$630$	−9.00000	−	25.9808i	−0.358569	−	1.03510i
$631$	22.5000	+	12.9904i	0.895711	+	0.517139i	0.875806	−	0.482663i	$-0.160330\pi$
$631$	22.5000	+	12.9904i	0.895711	+	0.517139i	0.0199047	+	0.999802i	$0.493664\pi$
$632$	4.00000	+	6.92820i	0.159111	+	0.275589i
$633$	−7.50000	+	4.33013i	−0.298098	+	0.172107i
$634$	18.0000			0.714871
$635$	3.00000	+	1.73205i	0.119051	+	0.0687343i
$636$	−6.00000			−0.237915
$637$	2.50000	−	25.1147i	0.0990536	−	0.995082i
$638$		−	41.5692i		−	1.64574i
$639$		0			0
$640$		−	3.46410i		−	0.136931i
$641$	33.0000	−	19.0526i	1.30342	−	0.752531i	0.322432	−	0.946593i	$-0.395500\pi$
$641$	33.0000	−	19.0526i	1.30342	−	0.752531i	0.980989	+	0.194062i	$0.0621662\pi$
$642$		0			0
$643$	5.50000	−	9.52628i	0.216899	−	0.375680i	−0.736959	−	0.675937i	$-0.763739\pi$
$643$	5.50000	−	9.52628i	0.216899	−	0.375680i	0.953858	+	0.300257i	$0.0970725\pi$
$644$	3.00000	+	8.66025i	0.118217	+	0.341262i
$645$	−6.00000			−0.236250
$646$		0			0
$647$	−36.0000			−1.41531			−0.707653	−	0.706560i	$-0.750246\pi$
$647$	−36.0000			−1.41531			−0.707653	+	0.706560i	$0.750246\pi$
$648$	9.00000			0.353553
$649$		0			0
$650$	24.5000	+	6.06218i	0.960969	+	0.237778i
$651$	36.0000	+	6.92820i	1.41095	+	0.271538i
$652$	1.50000	−	0.866025i	0.0587445	−	0.0339162i
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$	10.5000	+	18.1865i	0.410582	+	0.711150i
$655$	54.0000	+	31.1769i	2.10995	+	1.21818i
$656$			10.3923i			0.405751i
$657$	10.5000	−	18.1865i	0.409644	−	0.709524i
$658$	6.00000	+	17.3205i	0.233904	+	0.675224i
$659$	−24.0000	−	13.8564i	−0.934907	−	0.539769i	−0.0465470	−	0.998916i	$-0.514822\pi$
$659$	−24.0000	−	13.8564i	−0.934907	−	0.539769i	−0.888360	+	0.459147i	$0.848155\pi$
$660$	18.0000	−	31.1769i	0.700649	−	1.21356i
$661$	−50.0000			−1.94477			−0.972387	−	0.233373i	$-0.925024\pi$
$661$	−50.0000			−1.94477			−0.972387	+	0.233373i	$0.925024\pi$
$662$	16.5000	+	9.52628i	0.641291	+	0.370249i
$663$		0			0
$664$			3.46410i			0.134433i
$665$	30.0000	−	34.6410i	1.16335	−	1.34332i
$666$	22.5000	−	12.9904i	0.871857	−	0.503367i
$667$	−24.0000			−0.929284
$668$	3.00000	+	1.73205i	0.116073	+	0.0670151i
$669$	24.0000	−	13.8564i	0.927894	−	0.535720i
$670$	12.0000			0.463600
$671$		−	31.1769i		−	1.20357i
$672$	3.00000	−	3.46410i	0.115728	−	0.133631i
$673$	−0.500000	−	0.866025i	−0.0192736	−	0.0333828i	0.856228	−	0.516599i	$-0.172802\pi$
$673$	−0.500000	−	0.866025i	−0.0192736	−	0.0333828i	−0.875501	+	0.483216i	$0.839469\pi$
$674$	−2.50000	+	4.33013i	−0.0962964	+	0.166790i
$675$	31.5000	+	18.1865i	1.21244	+	0.700000i
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$	9.00000	+	15.5885i	0.345898	+	0.599113i	0.985517	−	0.169580i	$-0.0542410\pi$
$677$	9.00000	+	15.5885i	0.345898	+	0.599113i	−0.639618	+	0.768693i	$0.720908\pi$
$678$	6.00000	+	10.3923i	0.230429	+	0.399114i
$679$	−3.50000	+	18.1865i	−0.134318	+	0.697935i
$680$		0			0
$681$	−9.00000	−	15.5885i	−0.344881	−	0.597351i
$682$	24.0000	+	41.5692i	0.919007	+	1.59177i
$683$	9.00000	+	15.5885i	0.344375	+	0.596476i	0.985240	−	0.171178i	$-0.0547574\pi$
$683$	9.00000	+	15.5885i	0.344375	+	0.596476i	−0.640865	+	0.767654i	$0.721424\pi$
$684$	7.50000	+	12.9904i	0.286770	+	0.496700i
$685$	−18.0000	−	10.3923i	−0.687745	−	0.397070i
$686$	−8.50000	−	16.4545i	−0.324532	−	0.628235i
$687$	43.5000	−	25.1147i	1.65963	−	0.958187i
$688$	−0.500000	−	0.866025i	−0.0190623	−	0.0330169i
$689$	12.0000	−	3.46410i	0.457164	−	0.131972i
$690$	−18.0000	−	10.3923i	−0.685248	−	0.395628i
$691$	−8.50000	+	14.7224i	−0.323355	+	0.560068i	−0.981178	−	0.193105i	$-0.938144\pi$
$691$	−8.50000	+	14.7224i	−0.323355	+	0.560068i	0.657823	+	0.753173i	$0.271478\pi$
$692$	−3.00000	−	5.19615i	−0.114043	−	0.197528i
$693$	45.0000	−	15.5885i	1.70941	−	0.592157i
$694$		0			0
$695$	−12.0000			−0.455186
$696$	6.00000	+	10.3923i	0.227429	+	0.393919i
$697$		0			0
$698$	−11.0000			−0.416356
$699$	6.00000	+	10.3923i	0.226941	+	0.393073i
$700$	17.5000	−	6.06218i	0.661438	−	0.229129i
$701$			13.8564i			0.523349i	0.965156	+	0.261675i	$0.0842747\pi$
$701$			13.8564i			0.523349i	−0.965156	+	0.261675i	$0.915725\pi$
$702$	−18.0000	+	5.19615i	−0.679366	+	0.196116i
$703$	37.5000	+	21.6506i	1.41434	+	0.816569i
$704$	6.00000			0.226134
$705$	−36.0000	−	20.7846i	−1.35584	−	0.782794i
$706$	9.00000	+	5.19615i	0.338719	+	0.195560i
$707$	15.0000	−	5.19615i	0.564133	−	0.195421i
$708$		0			0
$709$		−	39.8372i		−	1.49612i	−0.663633	−	0.748058i	$-0.730986\pi$
$709$		−	39.8372i		−	1.49612i	0.663633	−	0.748058i	$-0.269014\pi$
$710$		0			0
$711$	−12.0000	−	20.7846i	−0.450035	−	0.779484i
$712$	−3.00000	−	1.73205i	−0.112430	−	0.0649113i
$713$	24.0000	−	13.8564i	0.898807	−	0.518927i
$714$		0			0
$715$	−18.0000	+	72.7461i	−0.673162	+	2.72055i
$716$	−21.0000	+	12.1244i	−0.784807	+	0.453108i
$717$			10.3923i			0.388108i
$718$	24.0000			0.895672
$719$	30.0000			1.11881			0.559406	−	0.828894i	$-0.311029\pi$
$719$	30.0000			1.11881			0.559406	+	0.828894i	$0.311029\pi$
$720$			10.3923i			0.387298i
$721$	−9.00000	+	10.3923i	−0.335178	+	0.387030i
$722$	−3.00000	+	5.19615i	−0.111648	+	0.193381i
$723$	39.0000	−	22.5167i	1.45043	−	0.837404i
$724$	−13.5000	+	7.79423i	−0.501724	+	0.289670i
$725$			48.4974i			1.80115i
$726$	37.5000	+	21.6506i	1.39176	+	0.803530i
$727$			10.3923i			0.385429i	0.981255	+	0.192715i	$0.0617292\pi$
$727$			10.3923i			0.385429i	−0.981255	+	0.192715i	$0.938271\pi$
$728$	−4.00000	+	8.66025i	−0.148250	+	0.320970i
$729$	−27.0000			−1.00000
$730$	21.0000	+	12.1244i	0.777245	+	0.448743i
$731$		0			0
$732$	4.50000	+	7.79423i	0.166325	+	0.288083i
$733$	−23.0000	−	39.8372i	−0.849524	−	1.47142i	−0.881633	−	0.471935i	$-0.843556\pi$
$733$	−23.0000	−	39.8372i	−0.849524	−	1.47142i	0.0321090	−	0.999484i	$-0.489778\pi$
$734$	−1.50000	−	0.866025i	−0.0553660	−	0.0319656i
$735$	39.0000	+	15.5885i	1.43854	+	0.574989i
$736$		−	3.46410i		−	0.127688i
$737$			20.7846i			0.765611i
$738$		−	31.1769i		−	1.14764i
$739$			32.9090i			1.21058i	0.796007	+	0.605288i	$0.206942\pi$
$739$			32.9090i			1.21058i	−0.796007	+	0.605288i	$0.793058\pi$
$740$	15.0000	+	25.9808i	0.551411	+	0.955072i
$741$	−22.5000	−	21.6506i	−0.826558	−	0.795356i
$742$	6.00000	−	6.92820i	0.220267	−	0.254342i
$743$	−15.0000	−	25.9808i	−0.550297	−	0.953142i	−0.998253	−	0.0590862i	$-0.981181\pi$
$743$	−15.0000	−	25.9808i	−0.550297	−	0.953142i	0.447956	−	0.894055i	$-0.352152\pi$
$744$	−12.0000	−	6.92820i	−0.439941	−	0.254000i
$745$	−54.0000	+	31.1769i	−1.97841	+	1.14223i
$746$	1.00000	−	1.73205i	0.0366126	−	0.0634149i
$747$		−	10.3923i		−	0.380235i
$748$		0			0
$749$		0			0
$750$	−6.00000	+	10.3923i	−0.219089	+	0.379473i
$751$	8.50000	−	14.7224i	0.310169	−	0.537229i	−0.668229	−	0.743955i	$-0.732948\pi$
$751$	8.50000	−	14.7224i	0.310169	−	0.537229i	0.978399	+	0.206726i	$0.0662809\pi$
$752$		−	6.92820i		−	0.252646i
$753$	18.0000	+	10.3923i	0.655956	+	0.378717i
$754$	−18.0000	−	17.3205i	−0.655521	−	0.630776i
$755$	12.0000			0.436725
$756$	−9.00000	+	10.3923i	−0.327327	+	0.377964i
$757$	−19.0000	−	32.9090i	−0.690567	−	1.19610i	−0.971652	−	0.236414i	$-0.924028\pi$
$757$	−19.0000	−	32.9090i	−0.690567	−	1.19610i	0.281086	−	0.959683i	$-0.409305\pi$
$758$		−	17.3205i		−	0.629109i
$759$	18.0000	−	31.1769i	0.653359	−	1.13165i
$760$	−15.0000	+	8.66025i	−0.544107	+	0.314140i
$761$		−	3.46410i		−	0.125574i	−0.998027	−	0.0627868i	$-0.980001\pi$
$761$		−	3.46410i		−	0.125574i	0.998027	−	0.0627868i	$-0.0199988\pi$
$762$		−	1.73205i		−	0.0627456i
$763$	−31.5000	−	6.06218i	−1.14038	−	0.219466i
$764$	18.0000	−	10.3923i	0.651217	−	0.375980i
$765$		0			0
$766$	−18.0000	−	10.3923i	−0.650366	−	0.375489i
$767$		0			0
$768$	−1.50000	+	0.866025i	−0.0541266	+	0.0312500i
$769$	−0.500000	−	0.866025i	−0.0180305	−	0.0312297i	0.856869	−	0.515534i	$-0.172406\pi$
$769$	−0.500000	−	0.866025i	−0.0180305	−	0.0312297i	−0.874900	+	0.484304i	$0.839073\pi$
$770$	18.0000	+	51.9615i	0.648675	+	1.87256i
$771$	−27.0000	−	15.5885i	−0.972381	−	0.561405i
$772$	4.50000	−	2.59808i	0.161959	−	0.0935068i
$773$	36.0000	−	20.7846i	1.29483	−	0.747570i	0.315324	−	0.948984i	$-0.397887\pi$
$773$	36.0000	−	20.7846i	1.29483	−	0.747570i	0.979506	+	0.201414i	$0.0645536\pi$
$774$	1.50000	+	2.59808i	0.0539164	+	0.0933859i
$775$	−28.0000	−	48.4974i	−1.00579	−	1.74208i
$776$	3.50000	−	6.06218i	0.125643	−	0.217620i
$777$	−7.50000	+	38.9711i	−0.269061	+	1.39808i
$778$	9.00000	−	5.19615i	0.322666	−	0.186291i
$779$	45.0000	−	25.9808i	1.61229	−	0.930857i
$780$	−6.00000	−	20.7846i	−0.214834	−	0.744208i
$781$		0			0
$782$		0			0
$783$	−18.0000	−	31.1769i	−0.643268	−	1.11417i
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$	66.0000			2.35564
$786$		−	31.1769i		−	1.11204i
$787$	−26.5000	−	45.8993i	−0.944623	−	1.63614i	−0.756504	−	0.653989i	$-0.773094\pi$
$787$	−26.5000	−	45.8993i	−0.944623	−	1.63614i	−0.188119	−	0.982146i	$-0.560239\pi$
$788$	−6.00000	+	10.3923i	−0.213741	+	0.370211i
$789$	24.0000			0.854423
$790$	24.0000	−	13.8564i	0.853882	−	0.492989i
$791$	−18.0000	−	3.46410i	−0.640006	−	0.123169i
$792$	−18.0000			−0.639602
$793$	−13.5000	−	12.9904i	−0.479399	−	0.461302i
$794$	−5.50000	+	9.52628i	−0.195188	+	0.338075i
$795$			20.7846i			0.737154i
$796$	13.5000	+	7.79423i	0.478495	+	0.276259i
$797$	−9.00000	+	15.5885i	−0.318796	+	0.552171i	−0.980237	−	0.197826i	$-0.936612\pi$
$797$	−9.00000	+	15.5885i	−0.318796	+	0.552171i	0.661441	+	0.749997i	$0.269945\pi$
$798$	−22.5000	−	4.33013i	−0.796491	−	0.153285i
$799$		0			0
$800$	−7.00000			−0.247487
$801$	9.00000	+	5.19615i	0.317999	+	0.183597i
$802$	3.00000	+	5.19615i	0.105934	+	0.183483i
$803$	−21.0000	+	36.3731i	−0.741074	+	1.28358i
$804$	−3.00000	−	5.19615i	−0.105802	−	0.183254i
$805$	30.0000	−	10.3923i	1.05736	−	0.366281i
$806$	28.0000	+	6.92820i	0.986258	+	0.244036i
$807$	−18.0000	+	10.3923i	−0.633630	+	0.365826i
$808$	−6.00000			−0.211079
$809$			6.92820i			0.243583i	0.992556	+	0.121791i	$0.0388639\pi$
$809$			6.92820i			0.243583i	−0.992556	+	0.121791i	$0.961136\pi$
$810$		−	31.1769i		−	1.09545i
$811$	1.00000			0.0351147			0.0175574	−	0.999846i	$-0.494411\pi$
$811$	1.00000			0.0351147			0.0175574	+	0.999846i	$0.494411\pi$
$812$	−18.0000	−	3.46410i	−0.631676	−	0.121566i
$813$	−1.50000	−	0.866025i	−0.0526073	−	0.0303728i
$814$	−45.0000	+	25.9808i	−1.57725	+	0.910625i
$815$	−3.00000	−	5.19615i	−0.105085	−	0.182013i
$816$		0			0
$817$	−2.50000	+	4.33013i	−0.0874639	+	0.151492i
$818$	−19.0000			−0.664319
$819$	12.0000	−	25.9808i	0.419314	−	0.907841i
$820$	36.0000			1.25717
$821$	27.0000	−	46.7654i	0.942306	−	1.63212i	0.181250	−	0.983437i	$-0.441986\pi$
$821$	27.0000	−	46.7654i	0.942306	−	1.63212i	0.761056	−	0.648686i	$-0.224681\pi$
$822$			10.3923i			0.362473i
$823$	−28.0000	−	48.4974i	−0.976019	−	1.69051i	−0.676532	−	0.736413i	$-0.736518\pi$
$823$	−28.0000	−	48.4974i	−0.976019	−	1.69051i	−0.299487	−	0.954100i	$-0.596815\pi$
$824$	4.50000	−	2.59808i	0.156765	−	0.0905083i
$825$	−63.0000	−	36.3731i	−2.19338	−	1.26635i
$826$		0			0
$827$	−48.0000			−1.66912			−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000			−1.66912			−0.834562	+	0.550914i	$0.814279\pi$
$828$			10.3923i			0.361158i
$829$		−	1.73205i		−	0.0601566i	−0.999548	−	0.0300783i	$-0.990424\pi$
$829$		−	1.73205i		−	0.0601566i	0.999548	−	0.0300783i	$-0.00957567\pi$
$830$	12.0000			0.416526
$831$	−25.5000	+	14.7224i	−0.884585	+	0.510716i
$832$	2.50000	−	2.59808i	0.0866719	−	0.0900721i
$833$		0			0
$834$	3.00000	+	5.19615i	0.103882	+	0.179928i
$835$	6.00000	−	10.3923i	0.207639	−	0.359641i
$836$	−15.0000	−	25.9808i	−0.518786	−	0.898563i
$837$	36.0000	+	20.7846i	1.24434	+	0.718421i
$838$	−30.0000			−1.03633
$839$	−18.0000	−	10.3923i	−0.621429	−	0.358782i	0.155996	−	0.987758i	$-0.450141\pi$
$839$	−18.0000	−	10.3923i	−0.621429	−	0.358782i	−0.777425	+	0.628975i	$0.783475\pi$
$840$	−12.0000	−	10.3923i	−0.414039	−	0.358569i
$841$	9.50000	−	16.4545i	0.327586	−	0.567396i
$842$	−24.0000	−	13.8564i	−0.827095	−	0.477523i
$843$		−	20.7846i		−	0.715860i
$844$	−2.50000	+	4.33013i	−0.0860535	+	0.149049i
$845$	24.0000	+	38.1051i	0.825625	+	1.31086i
$846$			20.7846i			0.714590i
$847$	−62.5000	+	21.6506i	−2.14753	+	0.743925i
$848$	−3.00000	+	1.73205i	−0.103020	+	0.0594789i
$849$	−3.00000			−0.102960
$850$		0			0
$851$	15.0000	+	25.9808i	0.514193	+	0.890609i
$852$		0			0
$853$	−10.0000			−0.342393			−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000			−0.342393			−0.171197	+	0.985237i	$0.554763\pi$
$854$	−13.5000	−	2.59808i	−0.461960	−	0.0889043i
$855$	45.0000	−	25.9808i	1.53897	−	0.888523i
$856$		0			0
$857$	−12.0000	+	20.7846i	−0.409912	+	0.709989i	−0.994880	−	0.101068i	$-0.967774\pi$
$857$	−12.0000	+	20.7846i	−0.409912	+	0.709989i	0.584967	+	0.811057i	$0.301107\pi$
$858$	36.0000	−	10.3923i	1.22902	−	0.354787i
$859$	−1.50000	+	0.866025i	−0.0511793	+	0.0295484i	−0.525371	−	0.850873i	$-0.676074\pi$
$859$	−1.50000	+	0.866025i	−0.0511793	+	0.0295484i	0.474192	+	0.880421i	$0.342740\pi$
$860$	−3.00000	+	1.73205i	−0.102299	+	0.0590624i
$861$	36.0000	+	31.1769i	1.22688	+	1.06251i
$862$	9.00000	−	15.5885i	0.306541	−	0.530945i
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	0.912558	−	0.408946i	$-0.134104\pi$
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	−0.810437	+	0.585826i	$0.800770\pi$
$864$	4.50000	−	2.59808i	0.153093	−	0.0883883i
$865$	−18.0000	+	10.3923i	−0.612018	+	0.353349i
$866$	18.0000	−	10.3923i	0.611665	−	0.353145i
$867$	−25.5000	−	14.7224i	−0.866025	−	0.500000i
$868$	20.0000	−	6.92820i	0.678844	−	0.235159i
$869$	24.0000	+	41.5692i	0.814144	+	1.41014i
$870$	36.0000	−	20.7846i	1.22051	−	0.704664i
$871$	9.00000	+	8.66025i	0.304953	+	0.293442i
$872$	10.5000	+	6.06218i	0.355575	+	0.205291i
$873$	−10.5000	+	18.1865i	−0.355371	+	0.615521i
$874$	−15.0000	+	8.66025i	−0.507383	+	0.292937i
$875$	−6.00000	−	17.3205i	−0.202837	−	0.585540i
$876$		−	12.1244i		−	0.409644i
$877$			27.7128i			0.935795i	0.883783	+	0.467898i	$0.154988\pi$
$877$			27.7128i			0.935795i	−0.883783	+	0.467898i	$0.845012\pi$
$878$	−10.5000	+	6.06218i	−0.354358	+	0.204589i
$879$	6.00000	−	10.3923i	0.202375	−	0.350524i
$880$		−	20.7846i		−	0.700649i
$881$	−18.0000	−	31.1769i	−0.606435	−	1.05038i	−0.991823	−	0.127622i	$-0.959266\pi$
$881$	−18.0000	−	31.1769i	−0.606435	−	1.05038i	0.385387	−	0.922755i	$-0.374068\pi$
$882$	−3.00000	−	20.7846i	−0.101015	−	0.699854i
$883$	−19.0000			−0.639401			−0.319700	−	0.947519i	$-0.603582\pi$
$883$	−19.0000			−0.639401			−0.319700	+	0.947519i	$0.603582\pi$
$884$		0			0
$885$		0			0
$886$		−	38.1051i		−	1.28017i
$887$	3.00000	−	5.19615i	0.100730	−	0.174470i	−0.811256	−	0.584692i	$-0.801215\pi$
$887$	3.00000	−	5.19615i	0.100730	−	0.174470i	0.911986	+	0.410222i	$0.134549\pi$
$888$	7.50000	−	12.9904i	0.251684	−	0.435929i
$889$	2.00000	+	1.73205i	0.0670778	+	0.0580911i
$890$	−6.00000	+	10.3923i	−0.201120	+	0.348351i
$891$	54.0000			1.80907
$892$	8.00000	−	13.8564i	0.267860	−	0.463947i
$893$	−30.0000	+	17.3205i	−1.00391	+	0.579609i
$894$	27.0000	+	15.5885i	0.903015	+	0.521356i
$895$	42.0000	+	72.7461i	1.40391	+	2.43164i
$896$	0.500000	−	2.59808i	0.0167038	−	0.0867956i
$897$	−6.00000	−	20.7846i	−0.200334	−	0.693978i
$898$	15.0000	+	25.9808i	0.500556	+	0.866989i
$899$			55.4256i			1.84855i
$900$	21.0000			0.700000
$901$		0			0
$902$			62.3538i			2.07616i
$903$	−4.50000	−	0.866025i	−0.149751	−	0.0288195i
$904$	6.00000	+	3.46410i	0.199557	+	0.115214i
$905$	27.0000	+	46.7654i	0.897510	+	1.55453i
$906$	−3.00000	−	5.19615i	−0.0996683	−	0.172631i
$907$	−1.00000			−0.0332045			−0.0166022	−	0.999862i	$-0.505285\pi$
$907$	−1.00000			−0.0332045			−0.0166022	+	0.999862i	$0.505285\pi$
$908$	−9.00000	−	5.19615i	−0.298675	−	0.172440i
$909$	18.0000			0.597022
$910$	30.0000	+	13.8564i	0.994490	+	0.459335i
$911$			13.8564i			0.459083i	0.973299	+	0.229542i	$0.0737227\pi$
$911$			13.8564i			0.459083i	−0.973299	+	0.229542i	$0.926277\pi$
$912$	7.50000	+	4.33013i	0.248350	+	0.143385i
$913$			20.7846i			0.687870i
$914$		0			0
$915$	27.0000	−	15.5885i	0.892592	−	0.515339i
$916$	14.5000	−	25.1147i	0.479093	−	0.829814i
$917$	36.0000	+	31.1769i	1.18882	+	1.02955i
$918$		0			0
$919$	35.0000			1.15454			0.577272	−	0.816552i	$-0.304117\pi$
$919$	35.0000			1.15454			0.577272	+	0.816552i	$0.304117\pi$
$920$	−12.0000			−0.395628
$921$		−	6.92820i		−	0.228292i
$922$	18.0000	−	10.3923i	0.592798	−	0.342252i
$923$		0			0
$924$	18.0000	−	20.7846i	0.592157	−	0.683763i
$925$	52.5000	−	30.3109i	1.72619	−	0.996616i
$926$	−16.5000	−	9.52628i	−0.542224	−	0.313053i
$927$	−13.5000	+	7.79423i	−0.443398	+	0.255996i
$928$	6.00000	+	3.46410i	0.196960	+	0.113715i
$929$			27.7128i			0.909228i	0.890689	+	0.454614i	$0.150223\pi$
$929$			27.7128i			0.909228i	−0.890689	+	0.454614i	$0.849777\pi$
$930$	−24.0000	+	41.5692i	−0.786991	+	1.36311i
$931$	27.5000	−	21.6506i	0.901276	−	0.709571i
$932$	6.00000	+	3.46410i	0.196537	+	0.113470i
$933$	−9.00000	−	5.19615i	−0.294647	−	0.170114i
$934$	−18.0000			−0.588978
$935$		0			0
$936$	−7.50000	+	7.79423i	−0.245145	+	0.254762i
$937$		−	8.66025i		−	0.282918i	−0.989944	−	0.141459i	$-0.954821\pi$
$937$		−	8.66025i		−	0.282918i	0.989944	−	0.141459i	$-0.0451794\pi$
$938$	9.00000	+	1.73205i	0.293860	+	0.0565535i
$939$	28.5000	+	49.3634i	0.930062	+	1.61092i
$940$	−24.0000			−0.782794
$941$	−12.0000	−	6.92820i	−0.391189	−	0.225853i	0.291486	−	0.956575i	$-0.405850\pi$
$941$	−12.0000	−	6.92820i	−0.391189	−	0.225853i	−0.682675	+	0.730722i	$0.739184\pi$
$942$	−16.5000	−	28.5788i	−0.537599	−	0.931149i
$943$	36.0000			1.17232
$944$		0			0
$945$	36.0000	+	31.1769i	1.17108	+	1.01419i
$946$	−3.00000	−	5.19615i	−0.0975384	−	0.168941i
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	0.152106	+	0.988364i	$0.451394\pi$
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	−0.932002	+	0.362454i	$0.881939\pi$
$948$	−12.0000	−	6.92820i	−0.389742	−	0.225018i
$949$	7.00000	+	24.2487i	0.227230	+	0.787146i
$950$	17.5000	+	30.3109i	0.567775	+	0.983415i
$951$	−27.0000	+	15.5885i	−0.875535	+	0.505490i
$952$		0			0
$953$	−33.0000	−	19.0526i	−1.06897	−	0.617173i	−0.141074	−	0.989999i	$-0.545055\pi$
$953$	−33.0000	−	19.0526i	−1.06897	−	0.617173i	−0.927901	+	0.372826i	$0.878389\pi$
$954$	9.00000	−	5.19615i	0.291386	−	0.168232i
$955$	−36.0000	−	62.3538i	−1.16493	−	2.01772i
$956$	3.00000	+	5.19615i	0.0970269	+	0.168056i
$957$	36.0000	+	62.3538i	1.16371	+	2.01561i
$958$	6.00000	+	3.46410i	0.193851	+	0.111920i
$959$	−12.0000	−	10.3923i	−0.387500	−	0.335585i
$960$	3.00000	+	5.19615i	0.0968246	+	0.167705i
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	−7.50000	+	30.3109i	−0.241810	+	0.977262i
$963$		0			0
$964$	13.0000	−	22.5167i	0.418702	−	0.725213i
$965$	−9.00000	−	15.5885i	−0.289720	−	0.501810i
$966$	−12.0000	−	10.3923i	−0.386094	−	0.334367i
$967$			8.66025i			0.278495i	0.990258	+	0.139247i	$0.0444684\pi$
$967$			8.66025i			0.278495i	−0.990258	+	0.139247i	$0.955532\pi$
$968$	25.0000			0.803530
$969$		0			0
$970$	−21.0000	−	12.1244i	−0.674269	−	0.389290i
$971$	6.00000			0.192549			0.0962746	−	0.995355i	$-0.469307\pi$
$971$	6.00000			0.192549			0.0962746	+	0.995355i	$0.469307\pi$
$972$	−13.5000	+	7.79423i	−0.433013	+	0.250000i
$973$	−9.00000	−	1.73205i	−0.288527	−	0.0555270i
$974$		−	15.5885i		−	0.499486i
$975$	−42.0000	+	12.1244i	−1.34508	+	0.388290i
$976$	4.50000	+	2.59808i	0.144041	+	0.0831624i
$977$	36.0000			1.15174			0.575871	−	0.817541i	$-0.304663\pi$
$977$	36.0000			1.15174			0.575871	+	0.817541i	$0.304663\pi$
$978$	−1.50000	+	2.59808i	−0.0479647	+	0.0830773i
$979$	−18.0000	−	10.3923i	−0.575282	−	0.332140i
$980$	24.0000	−	3.46410i	0.766652	−	0.110657i
$981$	−31.5000	−	18.1865i	−1.00572	−	0.580651i
$982$		0			0
$983$	30.0000	+	17.3205i	0.956851	+	0.552438i	0.895203	−	0.445659i	$-0.147031\pi$
$983$	30.0000	+	17.3205i	0.956851	+	0.552438i	0.0616488	+	0.998098i	$0.480364\pi$
$984$	−9.00000	−	15.5885i	−0.286910	−	0.496942i
$985$	36.0000	+	20.7846i	1.14706	+	0.662253i
$986$		0			0
$987$	−24.0000	−	20.7846i	−0.763928	−	0.661581i
$988$	−17.5000	−	4.33013i	−0.556749	−	0.137760i
$989$	−3.00000	+	1.73205i	−0.0953945	+	0.0550760i
$990$			62.3538i			1.98173i
$991$	55.0000			1.74713			0.873566	−	0.486705i	$-0.161801\pi$
$991$	55.0000			1.74713			0.873566	+	0.486705i	$0.161801\pi$
$992$	−8.00000			−0.254000
$993$	−33.0000			−1.04722
$994$		0			0
$995$	27.0000	−	46.7654i	0.855958	−	1.48256i
$996$	−3.00000	−	5.19615i	−0.0950586	−	0.164646i
$997$	37.5000	−	21.6506i	1.18764	−	0.685682i	0.229868	−	0.973222i	$-0.426171\pi$
$997$	37.5000	−	21.6506i	1.18764	−	0.685682i	0.957769	+	0.287539i	$0.0928372\pi$
$998$			8.66025i			0.274136i
$999$	−22.5000	+	38.9711i	−0.711868	+	1.23299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.b.101.1	yes	2
3.2	odd	2		546.2.bn.c.101.1	yes	2
7.5	odd	6		546.2.bi.c.257.1	yes	2
13.4	even	6		546.2.bi.a.17.1	✓	2
21.5	even	6		546.2.bi.a.257.1	yes	2
39.17	odd	6		546.2.bi.c.17.1	yes	2
91.82	odd	6		546.2.bn.c.173.1	yes	2
273.173	even	6	inner	546.2.bn.b.173.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.a.17.1	✓	2	13.4	even	6
546.2.bi.a.257.1	yes	2	21.5	even	6
546.2.bi.c.17.1	yes	2	39.17	odd	6
546.2.bi.c.257.1	yes	2	7.5	odd	6
546.2.bn.b.101.1	yes	2	1.1	even	1	trivial
546.2.bn.b.173.1	yes	2	273.173	even	6	inner
546.2.bn.c.101.1	yes	2	3.2	odd	2
546.2.bn.c.173.1	yes	2	91.82	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.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.00000 + 1.73205i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.00000 + 1.73205i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} -3.00000 q^{9} -3.46410i q^{10} +6.00000 q^{11} +(-1.50000 + 0.866025i) q^{12} +(2.50000 - 2.59808i) q^{13} +(0.500000 - 2.59808i) q^{14} +(3.00000 + 5.19615i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{18} +5.00000 q^{19} +(3.00000 + 1.73205i) q^{20} +(1.50000 + 4.33013i) q^{21} +(-3.00000 + 5.19615i) q^{22} +(3.00000 + 1.73205i) q^{23} -1.73205i q^{24} +(3.50000 - 6.06218i) q^{25} +(1.00000 + 3.46410i) q^{26} +5.19615i q^{27} +(2.00000 + 1.73205i) q^{28} +(-6.00000 + 3.46410i) q^{29} -6.00000 q^{30} +(4.00000 - 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} -10.3923i q^{33} +(6.00000 - 6.92820i) q^{35} +(1.50000 + 2.59808i) q^{36} +(7.50000 + 4.33013i) q^{37} +(-2.50000 + 4.33013i) q^{38} +(-4.50000 - 4.33013i) q^{39} +(-3.00000 + 1.73205i) q^{40} +(9.00000 - 5.19615i) q^{41} +(-4.50000 - 0.866025i) q^{42} +(-0.500000 + 0.866025i) q^{43} +(-3.00000 - 5.19615i) q^{44} +(9.00000 - 5.19615i) q^{45} +(-3.00000 + 1.73205i) q^{46} +(-6.00000 + 3.46410i) q^{47} +(1.50000 + 0.866025i) q^{48} +(5.50000 - 4.33013i) q^{49} +(3.50000 + 6.06218i) q^{50} +(-3.50000 - 0.866025i) q^{52} +(3.00000 + 1.73205i) q^{53} +(-4.50000 - 2.59808i) q^{54} +(-18.0000 + 10.3923i) q^{55} +(-2.50000 + 0.866025i) q^{56} -8.66025i q^{57} -6.92820i q^{58} +(3.00000 - 5.19615i) q^{60} -5.19615i q^{61} +(4.00000 + 6.92820i) q^{62} +(7.50000 - 2.59808i) q^{63} +1.00000 q^{64} +(-3.00000 + 12.1244i) q^{65} +(9.00000 + 5.19615i) q^{66} +3.46410i q^{67} +(3.00000 - 5.19615i) q^{69} +(3.00000 + 8.66025i) q^{70} -3.00000 q^{72} +(-3.50000 + 6.06218i) q^{73} +(-7.50000 + 4.33013i) q^{74} +(-10.5000 - 6.06218i) q^{75} +(-2.50000 - 4.33013i) q^{76} +(-15.0000 + 5.19615i) q^{77} +(6.00000 - 1.73205i) q^{78} +(4.00000 + 6.92820i) q^{79} -3.46410i q^{80} +9.00000 q^{81} +10.3923i q^{82} +3.46410i q^{83} +(3.00000 - 3.46410i) q^{84} +(-0.500000 - 0.866025i) q^{86} +(6.00000 + 10.3923i) q^{87} +6.00000 q^{88} +(-3.00000 - 1.73205i) q^{89} +10.3923i q^{90} +(-4.00000 + 8.66025i) q^{91} -3.46410i q^{92} +(-12.0000 - 6.92820i) q^{93} -6.92820i q^{94} +(-15.0000 + 8.66025i) q^{95} +(-1.50000 + 0.866025i) q^{96} +(3.50000 - 6.06218i) q^{97} +(1.00000 + 6.92820i) q^{98} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q - q^2 - q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 2 * q^8 - 6 * q^9	\( 2 q - q^{2} - q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9} + 12 q^{11} - 3 q^{12} + 5 q^{13} + q^{14} + 6 q^{15} - q^{16} + 3 q^{18} + 10 q^{19} + 6 q^{20} + 3 q^{21} - 6 q^{22} + 6 q^{23} + 7 q^{25} + 2 q^{26} + 4 q^{28} - 12 q^{29} - 12 q^{30} + 8 q^{31} - q^{32} + 12 q^{35} + 3 q^{36} + 15 q^{37} - 5 q^{38} - 9 q^{39} - 6 q^{40} + 18 q^{41} - 9 q^{42} - q^{43} - 6 q^{44} + 18 q^{45} - 6 q^{46} - 12 q^{47} + 3 q^{48} + 11 q^{49} + 7 q^{50} - 7 q^{52} + 6 q^{53} - 9 q^{54} - 36 q^{55} - 5 q^{56} + 6 q^{60} + 8 q^{62} + 15 q^{63} + 2 q^{64} - 6 q^{65} + 18 q^{66} + 6 q^{69} + 6 q^{70} - 6 q^{72} - 7 q^{73} - 15 q^{74} - 21 q^{75} - 5 q^{76} - 30 q^{77} + 12 q^{78} + 8 q^{79} + 18 q^{81} + 6 q^{84} - q^{86} + 12 q^{87} + 12 q^{88} - 6 q^{89} - 8 q^{91} - 24 q^{93} - 30 q^{95} - 3 q^{96} + 7 q^{97} + 2 q^{98} - 36 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 2 * q^8 - 6 * q^9 + 12 * q^11 - 3 * q^12 + 5 * q^13 + q^14 + 6 * q^15 - q^16 + 3 * q^18 + 10 * q^19 + 6 * q^20 + 3 * q^21 - 6 * q^22 + 6 * q^23 + 7 * q^25 + 2 * q^26 + 4 * q^28 - 12 * q^29 - 12 * q^30 + 8 * q^31 - q^32 + 12 * q^35 + 3 * q^36 + 15 * q^37 - 5 * q^38 - 9 * q^39 - 6 * q^40 + 18 * q^41 - 9 * q^42 - q^43 - 6 * q^44 + 18 * q^45 - 6 * q^46 - 12 * q^47 + 3 * q^48 + 11 * q^49 + 7 * q^50 - 7 * q^52 + 6 * q^53 - 9 * q^54 - 36 * q^55 - 5 * q^56 + 6 * q^60 + 8 * q^62 + 15 * q^63 + 2 * q^64 - 6 * q^65 + 18 * q^66 + 6 * q^69 + 6 * q^70 - 6 * q^72 - 7 * q^73 - 15 * q^74 - 21 * q^75 - 5 * q^76 - 30 * q^77 + 12 * q^78 + 8 * q^79 + 18 * q^81 + 6 * q^84 - q^86 + 12 * q^87 + 12 * q^88 - 6 * q^89 - 8 * q^91 - 24 * q^93 - 30 * q^95 - 3 * q^96 + 7 * q^97 + 2 * q^98 - 36 * q^99

Introduction

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