LMFDB - Embedded newform 1110.2.bb.a.1009.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1009,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1110.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.bb (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 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			1009.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1110.1009
Dual form			1110.2.bb.a.1099.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.133975 - 2.23205i) q^{5} +1.00000 q^{6} +(3.46410 - 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.133975 - 2.23205i) q^{5} +1.00000 q^{6} +(3.46410 - 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.00000 + 2.00000i) q^{10} +1.00000 q^{11} +(-0.866025 - 0.500000i) q^{12} +(2.59808 - 1.50000i) q^{13} -4.00000 q^{14} +(1.23205 + 1.86603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(5.19615 + 3.00000i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(2.50000 + 4.33013i) q^{19} +(1.86603 - 1.23205i) q^{20} +(-2.00000 + 3.46410i) q^{21} +(-0.866025 - 0.500000i) q^{22} -7.00000i q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.96410 + 0.598076i) q^{25} -3.00000 q^{26} +1.00000i q^{27} +(3.46410 + 2.00000i) q^{28} -10.0000 q^{29} +(-0.133975 - 2.23205i) q^{30} +(0.866025 - 0.500000i) q^{32} +(-0.866025 + 0.500000i) q^{33} +(-3.00000 - 5.19615i) q^{34} +(-4.92820 - 7.46410i) q^{35} +1.00000 q^{36} +(6.06218 - 0.500000i) q^{37} -5.00000i q^{38} +(-1.50000 + 2.59808i) q^{39} +(-2.23205 + 0.133975i) q^{40} +(1.00000 + 1.73205i) q^{41} +(3.46410 - 2.00000i) q^{42} +6.00000i q^{43} +(0.500000 + 0.866025i) q^{44} +(-2.00000 - 1.00000i) q^{45} +(-3.50000 + 6.06218i) q^{46} +3.00000i q^{47} -1.00000i q^{48} +(4.50000 - 7.79423i) q^{49} +(4.59808 + 1.96410i) q^{50} -6.00000 q^{51} +(2.59808 + 1.50000i) q^{52} +(1.73205 + 1.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.133975 - 2.23205i) q^{55} +(-2.00000 - 3.46410i) q^{56} +(-4.33013 - 2.50000i) q^{57} +(8.66025 + 5.00000i) q^{58} +(5.50000 - 9.52628i) q^{59} +(-1.00000 + 2.00000i) q^{60} +(6.00000 + 10.3923i) q^{61} -4.00000i q^{63} -1.00000 q^{64} +(-3.69615 - 5.59808i) q^{65} +1.00000 q^{66} +(8.66025 - 5.00000i) q^{67} +6.00000i q^{68} +(3.50000 + 6.06218i) q^{69} +(0.535898 + 8.92820i) q^{70} +(-3.00000 - 5.19615i) q^{71} +(-0.866025 - 0.500000i) q^{72} -14.0000i q^{73} +(-5.50000 - 2.59808i) q^{74} +(4.00000 - 3.00000i) q^{75} +(-2.50000 + 4.33013i) q^{76} +(3.46410 - 2.00000i) q^{77} +(2.59808 - 1.50000i) q^{78} +(-4.00000 - 6.92820i) q^{79} +(2.00000 + 1.00000i) q^{80} +(-0.500000 - 0.866025i) q^{81} -2.00000i q^{82} +(-8.66025 - 5.00000i) q^{83} -4.00000 q^{84} +(6.00000 - 12.0000i) q^{85} +(3.00000 - 5.19615i) q^{86} +(8.66025 - 5.00000i) q^{87} -1.00000i q^{88} +(2.50000 - 4.33013i) q^{89} +(1.23205 + 1.86603i) q^{90} +(6.00000 - 10.3923i) q^{91} +(6.06218 - 3.50000i) q^{92} +(1.50000 - 2.59808i) q^{94} +(9.33013 - 6.16025i) q^{95} +(-0.500000 + 0.866025i) q^{96} +18.0000i q^{97} +(-7.79423 + 4.50000i) q^{98} +(0.500000 - 0.866025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{9} - 4 q^{10} + 4 q^{11} - 16 q^{14} - 2 q^{15} - 2 q^{16} + 10 q^{19} + 4 q^{20} - 8 q^{21} + 2 q^{24} - 6 q^{25} - 12 q^{26} - 40 q^{29} - 4 q^{30} - 12 q^{34} + 8 q^{35} + 4 q^{36} - 6 q^{39} - 2 q^{40} + 4 q^{41} + 2 q^{44} - 8 q^{45} - 14 q^{46} + 18 q^{49} + 8 q^{50} - 24 q^{51} + 2 q^{54} - 4 q^{55} - 8 q^{56} + 22 q^{59} - 4 q^{60} + 24 q^{61} - 4 q^{64} + 6 q^{65} + 4 q^{66} + 14 q^{69} + 16 q^{70} - 12 q^{71} - 22 q^{74} + 16 q^{75} - 10 q^{76} - 16 q^{79} + 8 q^{80} - 2 q^{81} - 16 q^{84} + 24 q^{85} + 12 q^{86} + 10 q^{89} - 2 q^{90} + 24 q^{91} + 6 q^{94} + 20 q^{95} - 2 q^{96} + 2 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^9 - 4 * q^10 + 4 * q^11 - 16 * q^14 - 2 * q^15 - 2 * q^16 + 10 * q^19 + 4 * q^20 - 8 * q^21 + 2 * q^24 - 6 * q^25 - 12 * q^26 - 40 * q^29 - 4 * q^30 - 12 * q^34 + 8 * q^35 + 4 * q^36 - 6 * q^39 - 2 * q^40 + 4 * q^41 + 2 * q^44 - 8 * q^45 - 14 * q^46 + 18 * q^49 + 8 * q^50 - 24 * q^51 + 2 * q^54 - 4 * q^55 - 8 * q^56 + 22 * q^59 - 4 * q^60 + 24 * q^61 - 4 * q^64 + 6 * q^65 + 4 * q^66 + 14 * q^69 + 16 * q^70 - 12 * q^71 - 22 * q^74 + 16 * q^75 - 10 * q^76 - 16 * q^79 + 8 * q^80 - 2 * q^81 - 16 * q^84 + 24 * q^85 + 12 * q^86 + 10 * q^89 - 2 * q^90 + 24 * q^91 + 6 * q^94 + 20 * q^95 - 2 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.133975	−	2.23205i	−0.0599153	−	0.998203i
$5$	−0.133975	−	2.23205i	−0.0599153	−	0.998203i
$6$	1.00000			0.408248
$7$	3.46410	−	2.00000i	1.30931	−	0.755929i	0.327327	−	0.944911i	$-0.393852\pi$
$7$	3.46410	−	2.00000i	1.30931	−	0.755929i	0.981981	+	0.188982i	$0.0605189\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.00000	+	2.00000i	−0.316228	+	0.632456i
$11$	1.00000			0.301511			0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000			0.301511			0.150756	+	0.988571i	$0.451829\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	2.59808	−	1.50000i	0.720577	−	0.416025i	−0.0943882	−	0.995535i	$-0.530089\pi$
$13$	2.59808	−	1.50000i	0.720577	−	0.416025i	0.814965	+	0.579510i	$0.196756\pi$
$14$	−4.00000			−1.06904
$15$	1.23205	+	1.86603i	0.318114	+	0.481806i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	5.19615	+	3.00000i	1.26025	+	0.727607i	0.973123	−	0.230285i	$-0.0739659\pi$
$17$	5.19615	+	3.00000i	1.26025	+	0.727607i	0.287129	+	0.957892i	$0.407299\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$	1.86603	−	1.23205i	0.417256	−	0.275495i
$21$	−2.00000	+	3.46410i	−0.436436	+	0.755929i
$22$	−0.866025	−	0.500000i	−0.184637	−	0.106600i
$23$		−	7.00000i		−	1.45960i	−0.683660	−	0.729800i	$-0.739613\pi$
$23$		−	7.00000i		−	1.45960i	0.683660	−	0.729800i	$-0.260387\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$	−3.00000			−0.588348
$27$			1.00000i			0.192450i
$28$	3.46410	+	2.00000i	0.654654	+	0.377964i
$29$	−10.0000			−1.85695			−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−10.0000			−1.85695			−0.928477	+	0.371391i	$0.878881\pi$
$30$	−0.133975	−	2.23205i	−0.0244603	−	0.407515i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.866025	+	0.500000i	−0.150756	+	0.0870388i
$34$	−3.00000	−	5.19615i	−0.514496	−	0.891133i
$35$	−4.92820	−	7.46410i	−0.833018	−	1.26166i
$36$	1.00000			0.166667
$37$	6.06218	−	0.500000i	0.996616	−	0.0821995i
$37$	6.06218	−	0.500000i	0.996616	−	0.0821995i
$38$		−	5.00000i		−	0.811107i
$39$	−1.50000	+	2.59808i	−0.240192	+	0.416025i
$40$	−2.23205	+	0.133975i	−0.352918	+	0.0211832i
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	0.933486	−	0.358614i	$-0.116751\pi$
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	−0.777312	+	0.629115i	$0.783417\pi$
$42$	3.46410	−	2.00000i	0.534522	−	0.308607i
$43$			6.00000i			0.914991i	0.889212	+	0.457496i	$0.151253\pi$
$43$			6.00000i			0.914991i	−0.889212	+	0.457496i	$0.848747\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$	−2.00000	−	1.00000i	−0.298142	−	0.149071i
$46$	−3.50000	+	6.06218i	−0.516047	+	0.893819i
$47$			3.00000i			0.437595i	0.975770	+	0.218797i	$0.0702134\pi$
$47$			3.00000i			0.437595i	−0.975770	+	0.218797i	$0.929787\pi$
$48$		−	1.00000i		−	0.144338i
$49$	4.50000	−	7.79423i	0.642857	−	1.11346i
$50$	4.59808	+	1.96410i	0.650266	+	0.277766i
$51$	−6.00000			−0.840168
$52$	2.59808	+	1.50000i	0.360288	+	0.208013i
$53$	1.73205	+	1.00000i	0.237915	+	0.137361i	0.614218	−	0.789136i	$-0.289471\pi$
$53$	1.73205	+	1.00000i	0.237915	+	0.137361i	−0.376303	+	0.926497i	$0.622805\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−0.133975	−	2.23205i	−0.0180651	−	0.300970i
$56$	−2.00000	−	3.46410i	−0.267261	−	0.462910i
$57$	−4.33013	−	2.50000i	−0.573539	−	0.331133i
$58$	8.66025	+	5.00000i	1.13715	+	0.656532i
$59$	5.50000	−	9.52628i	0.716039	−	1.24022i	−0.246518	−	0.969138i	$-0.579287\pi$
$59$	5.50000	−	9.52628i	0.716039	−	1.24022i	0.962557	−	0.271078i	$-0.0873801\pi$
$60$	−1.00000	+	2.00000i	−0.129099	+	0.258199i
$61$	6.00000	+	10.3923i	0.768221	+	1.33060i	0.938527	+	0.345207i	$0.112191\pi$
$61$	6.00000	+	10.3923i	0.768221	+	1.33060i	−0.170305	+	0.985391i	$0.554475\pi$
$62$		0			0
$63$		−	4.00000i		−	0.503953i
$64$	−1.00000			−0.125000
$65$	−3.69615	−	5.59808i	−0.458451	−	0.694356i
$66$	1.00000			0.123091
$67$	8.66025	−	5.00000i	1.05802	−	0.610847i	0.133135	−	0.991098i	$-0.457496\pi$
$67$	8.66025	−	5.00000i	1.05802	−	0.610847i	0.924883	+	0.380251i	$0.124162\pi$
$68$			6.00000i			0.727607i
$69$	3.50000	+	6.06218i	0.421350	+	0.729800i
$70$	0.535898	+	8.92820i	0.0640521	+	1.06712i
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$		−	14.0000i		−	1.63858i	−0.573382	−	0.819288i	$-0.694369\pi$
$73$		−	14.0000i		−	1.63858i	0.573382	−	0.819288i	$-0.305631\pi$
$74$	−5.50000	−	2.59808i	−0.639362	−	0.302020i
$75$	4.00000	−	3.00000i	0.461880	−	0.346410i
$76$	−2.50000	+	4.33013i	−0.286770	+	0.496700i
$77$	3.46410	−	2.00000i	0.394771	−	0.227921i
$78$	2.59808	−	1.50000i	0.294174	−	0.169842i
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	2.00000	+	1.00000i	0.223607	+	0.111803i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		−	2.00000i		−	0.220863i
$83$	−8.66025	−	5.00000i	−0.950586	−	0.548821i	−0.0573233	−	0.998356i	$-0.518257\pi$
$83$	−8.66025	−	5.00000i	−0.950586	−	0.548821i	−0.893263	+	0.449534i	$0.851590\pi$
$84$	−4.00000			−0.436436
$85$	6.00000	−	12.0000i	0.650791	−	1.30158i
$86$	3.00000	−	5.19615i	0.323498	−	0.560316i
$87$	8.66025	−	5.00000i	0.928477	−	0.536056i
$88$		−	1.00000i		−	0.106600i
$89$	2.50000	−	4.33013i	0.264999	−	0.458993i	−0.702564	−	0.711621i	$-0.747962\pi$
$89$	2.50000	−	4.33013i	0.264999	−	0.458993i	0.967563	+	0.252628i	$0.0812949\pi$
$90$	1.23205	+	1.86603i	0.129870	+	0.196696i
$91$	6.00000	−	10.3923i	0.628971	−	1.08941i
$92$	6.06218	−	3.50000i	0.632026	−	0.364900i
$93$		0			0
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$	9.33013	−	6.16025i	0.957251	−	0.632029i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$			18.0000i			1.82762i	0.406138	+	0.913812i	$0.366875\pi$
$97$			18.0000i			1.82762i	−0.406138	+	0.913812i	$0.633125\pi$
$98$	−7.79423	+	4.50000i	−0.787336	+	0.454569i
$99$	0.500000	−	0.866025i	0.0502519	−	0.0870388i
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$	12.0000			1.19404			0.597022	−	0.802225i	$-0.296350\pi$
$101$	12.0000			1.19404			0.597022	+	0.802225i	$0.296350\pi$
$102$	5.19615	+	3.00000i	0.514496	+	0.297044i
$103$		−	13.0000i		−	1.28093i	−0.767988	−	0.640464i	$-0.778742\pi$
$103$		−	13.0000i		−	1.28093i	0.767988	−	0.640464i	$-0.221258\pi$
$104$	−1.50000	−	2.59808i	−0.147087	−	0.254762i
$105$	8.00000	+	4.00000i	0.780720	+	0.390360i
$106$	−1.00000	−	1.73205i	−0.0971286	−	0.168232i
$107$	−13.8564	+	8.00000i	−1.33955	+	0.773389i	−0.986740	−	0.162306i	$-0.948107\pi$
$107$	−13.8564	+	8.00000i	−1.33955	+	0.773389i	−0.352809	+	0.935695i	$0.614773\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$	−1.00000	+	2.00000i	−0.0953463	+	0.190693i
$111$	−5.00000	+	3.46410i	−0.474579	+	0.328798i
$112$			4.00000i			0.377964i
$113$	−5.19615	−	3.00000i	−0.488813	−	0.282216i	0.235269	−	0.971930i	$-0.424403\pi$
$113$	−5.19615	−	3.00000i	−0.488813	−	0.282216i	−0.724082	+	0.689714i	$0.757736\pi$
$114$	2.50000	+	4.33013i	0.234146	+	0.405554i
$115$	−15.6244	+	0.937822i	−1.45698	+	0.0874524i
$116$	−5.00000	−	8.66025i	−0.464238	−	0.804084i
$117$		−	3.00000i		−	0.277350i
$118$	−9.52628	+	5.50000i	−0.876965	+	0.506316i
$119$	24.0000			2.20008
$120$	1.86603	−	1.23205i	0.170344	−	0.112470i
$121$	−10.0000			−0.909091
$122$		−	12.0000i		−	1.08643i
$123$	−1.73205	−	1.00000i	−0.156174	−	0.0901670i
$124$		0			0
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	−2.00000	+	3.46410i	−0.178174	+	0.308607i
$127$	−4.33013	−	2.50000i	−0.384237	−	0.221839i	0.295423	−	0.955366i	$-0.404539\pi$
$127$	−4.33013	−	2.50000i	−0.384237	−	0.221839i	−0.679660	+	0.733527i	$0.737873\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−3.00000	−	5.19615i	−0.264135	−	0.457496i
$130$	0.401924	+	6.69615i	0.0352510	+	0.587291i
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$	−0.866025	−	0.500000i	−0.0753778	−	0.0435194i
$133$	17.3205	+	10.0000i	1.50188	+	0.867110i
$134$	−10.0000			−0.863868
$135$	2.23205	−	0.133975i	0.192104	−	0.0115307i
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$		−	6.00000i		−	0.512615i	−0.966595	−	0.256307i	$-0.917494\pi$
$137$		−	6.00000i		−	0.512615i	0.966595	−	0.256307i	$-0.0825059\pi$
$138$		−	7.00000i		−	0.595880i
$139$	−6.50000	+	11.2583i	−0.551323	+	0.954919i	0.446857	+	0.894606i	$0.352543\pi$
$139$	−6.50000	+	11.2583i	−0.551323	+	0.954919i	−0.998179	+	0.0603135i	$0.980790\pi$
$140$	4.00000	−	8.00000i	0.338062	−	0.676123i
$141$	−1.50000	−	2.59808i	−0.126323	−	0.218797i
$142$			6.00000i			0.503509i
$143$	2.59808	−	1.50000i	0.217262	−	0.125436i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	1.33975	+	22.3205i	0.111260	+	1.85362i
$146$	−7.00000	+	12.1244i	−0.579324	+	1.00342i
$147$			9.00000i			0.742307i
$148$	3.46410	+	5.00000i	0.284747	+	0.410997i
$149$	8.00000			0.655386			0.327693	−	0.944784i	$-0.393729\pi$
$149$	8.00000			0.655386			0.327693	+	0.944784i	$0.393729\pi$
$150$	−4.96410	+	0.598076i	−0.405317	+	0.0488327i
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	−0.996600	−	0.0823900i	$-0.973745\pi$
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	0.426948	−	0.904276i	$-0.359589\pi$
$152$	4.33013	−	2.50000i	0.351220	−	0.202777i
$153$	5.19615	−	3.00000i	0.420084	−	0.242536i
$154$	−4.00000			−0.322329
$155$		0			0
$156$	−3.00000			−0.240192
$157$	−0.866025	−	0.500000i	−0.0691164	−	0.0399043i	0.465044	−	0.885288i	$-0.346039\pi$
$157$	−0.866025	−	0.500000i	−0.0691164	−	0.0399043i	−0.534160	+	0.845383i	$0.679372\pi$
$158$			8.00000i			0.636446i
$159$	−2.00000			−0.158610
$160$	−1.23205	−	1.86603i	−0.0974022	−	0.147522i
$161$	−14.0000	−	24.2487i	−1.10335	−	1.91107i
$162$			1.00000i			0.0785674i
$163$	12.1244	+	7.00000i	0.949653	+	0.548282i	0.892973	−	0.450110i	$-0.148615\pi$
$163$	12.1244	+	7.00000i	0.949653	+	0.548282i	0.0566798	+	0.998392i	$0.481949\pi$
$164$	−1.00000	+	1.73205i	−0.0780869	+	0.135250i
$165$	1.23205	+	1.86603i	0.0959150	+	0.145270i
$166$	5.00000	+	8.66025i	0.388075	+	0.672166i
$167$	13.8564	−	8.00000i	1.07224	−	0.619059i	0.143448	−	0.989658i	$-0.454181\pi$
$167$	13.8564	−	8.00000i	1.07224	−	0.619059i	0.928793	+	0.370599i	$0.120848\pi$
$168$	3.46410	+	2.00000i	0.267261	+	0.154303i
$169$	−2.00000	+	3.46410i	−0.153846	+	0.266469i
$170$	−11.1962	+	7.39230i	−0.858706	+	0.566964i
$171$	5.00000			0.382360
$172$	−5.19615	+	3.00000i	−0.396203	+	0.228748i
$173$	−18.1865	−	10.5000i	−1.38270	−	0.798300i	−0.390218	−	0.920722i	$-0.627601\pi$
$173$	−18.1865	−	10.5000i	−1.38270	−	0.798300i	−0.992478	+	0.122422i	$0.960934\pi$
$174$	−10.0000			−0.758098
$175$	−16.0000	+	12.0000i	−1.20949	+	0.907115i
$176$	−0.500000	+	0.866025i	−0.0376889	+	0.0652791i
$177$			11.0000i			0.826811i
$178$	−4.33013	+	2.50000i	−0.324557	+	0.187383i
$179$	3.00000			0.224231			0.112115	−	0.993695i	$-0.464237\pi$
$179$	3.00000			0.224231			0.112115	+	0.993695i	$0.464237\pi$
$180$	−0.133975	−	2.23205i	−0.00998588	−	0.166367i
$181$	−6.00000	−	10.3923i	−0.445976	−	0.772454i	0.552143	−	0.833749i	$-0.313810\pi$
$181$	−6.00000	−	10.3923i	−0.445976	−	0.772454i	−0.998120	+	0.0612954i	$0.980477\pi$
$182$	−10.3923	+	6.00000i	−0.770329	+	0.444750i
$183$	−10.3923	−	6.00000i	−0.768221	−	0.443533i
$184$	−7.00000			−0.516047
$185$	−1.92820	−	13.4641i	−0.141764	−	0.989900i
$186$		0			0
$187$	5.19615	+	3.00000i	0.379980	+	0.219382i
$188$	−2.59808	+	1.50000i	−0.189484	+	0.109399i
$189$	2.00000	+	3.46410i	0.145479	+	0.251976i
$190$	−11.1603	+	0.669873i	−0.809650	+	0.0485977i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$		−	4.00000i		−	0.287926i	−0.989583	−	0.143963i	$-0.954015\pi$
$193$		−	4.00000i		−	0.287926i	0.989583	−	0.143963i	$-0.0459847\pi$
$194$	9.00000	−	15.5885i	0.646162	−	1.11919i
$195$	6.00000	+	3.00000i	0.429669	+	0.214834i
$196$	9.00000			0.642857
$197$	15.5885	+	9.00000i	1.11063	+	0.641223i	0.938993	−	0.343937i	$-0.111761\pi$
$197$	15.5885	+	9.00000i	1.11063	+	0.641223i	0.171639	+	0.985160i	$0.445094\pi$
$198$	−0.866025	+	0.500000i	−0.0615457	+	0.0355335i
$199$	−10.0000			−0.708881			−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000			−0.708881			−0.354441	+	0.935079i	$0.615329\pi$
$200$	0.598076	+	4.96410i	0.0422904	+	0.351015i
$201$	−5.00000	+	8.66025i	−0.352673	+	0.610847i
$202$	−10.3923	−	6.00000i	−0.731200	−	0.422159i
$203$	−34.6410	+	20.0000i	−2.43132	+	1.40372i
$204$	−3.00000	−	5.19615i	−0.210042	−	0.363803i
$205$	3.73205	−	2.46410i	0.260658	−	0.172100i
$206$	−6.50000	+	11.2583i	−0.452876	+	0.784405i
$207$	−6.06218	−	3.50000i	−0.421350	−	0.243267i
$208$			3.00000i			0.208013i
$209$	2.50000	+	4.33013i	0.172929	+	0.299521i
$210$	−4.92820	−	7.46410i	−0.340078	−	0.515072i
$211$	−9.00000			−0.619586			−0.309793	−	0.950804i	$-0.600260\pi$
$211$	−9.00000			−0.619586			−0.309793	+	0.950804i	$0.600260\pi$
$212$			2.00000i			0.137361i
$213$	5.19615	+	3.00000i	0.356034	+	0.205557i
$214$	16.0000			1.09374
$215$	13.3923	−	0.803848i	0.913348	−	0.0548219i
$216$	1.00000			0.0680414
$217$		0			0
$218$	−1.73205	+	1.00000i	−0.117309	+	0.0677285i
$219$	7.00000	+	12.1244i	0.473016	+	0.819288i
$220$	1.86603	−	1.23205i	0.125807	−	0.0830648i
$221$	18.0000			1.21081
$222$	6.06218	−	0.500000i	0.406867	−	0.0335578i
$223$		−	7.00000i		−	0.468755i	−0.972146	−	0.234377i	$-0.924695\pi$
$223$		−	7.00000i		−	0.468755i	0.972146	−	0.234377i	$-0.0753051\pi$
$224$	2.00000	−	3.46410i	0.133631	−	0.231455i
$225$	−1.96410	+	4.59808i	−0.130940	+	0.306538i
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	10.3923	−	6.00000i	0.689761	−	0.398234i	−0.113761	−	0.993508i	$-0.536290\pi$
$227$	10.3923	−	6.00000i	0.689761	−	0.398234i	0.803523	+	0.595274i	$0.202957\pi$
$228$		−	5.00000i		−	0.331133i
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	0.999088	−	0.0426906i	$-0.0135930\pi$
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	−0.536515	+	0.843891i	$0.680260\pi$
$230$	14.0000	+	7.00000i	0.923133	+	0.461566i
$231$	−2.00000	+	3.46410i	−0.131590	+	0.227921i
$232$			10.0000i			0.656532i
$233$			6.00000i			0.393073i	0.980497	+	0.196537i	$0.0629694\pi$
$233$			6.00000i			0.393073i	−0.980497	+	0.196537i	$0.937031\pi$
$234$	−1.50000	+	2.59808i	−0.0980581	+	0.169842i
$235$	6.69615	−	0.401924i	0.436809	−	0.0262186i
$236$	11.0000			0.716039
$237$	6.92820	+	4.00000i	0.450035	+	0.259828i
$238$	−20.7846	−	12.0000i	−1.34727	−	0.777844i
$239$	−8.00000	+	13.8564i	−0.517477	+	0.896296i	0.482317	+	0.875997i	$0.339795\pi$
$239$	−8.00000	+	13.8564i	−0.517477	+	0.896296i	−0.999794	+	0.0202996i	$0.993538\pi$
$240$	−2.23205	+	0.133975i	−0.144078	+	0.00864802i
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	0.916159	+	0.400815i	$0.131273\pi$
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	−0.110963	+	0.993825i	$0.535394\pi$
$242$	8.66025	+	5.00000i	0.556702	+	0.321412i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−6.00000	+	10.3923i	−0.384111	+	0.665299i
$245$	−18.0000	−	9.00000i	−1.14998	−	0.574989i
$246$	1.00000	+	1.73205i	0.0637577	+	0.110432i
$247$	12.9904	+	7.50000i	0.826558	+	0.477214i
$248$		0			0
$249$	10.0000			0.633724
$250$	3.76795	−	10.5263i	0.238306	−	0.665740i
$251$	−21.0000			−1.32551			−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000			−1.32551			−0.662754	+	0.748837i	$0.730613\pi$
$252$	3.46410	−	2.00000i	0.218218	−	0.125988i
$253$		−	7.00000i		−	0.440086i
$254$	2.50000	+	4.33013i	0.156864	+	0.271696i
$255$	0.803848	+	13.3923i	0.0503389	+	0.838659i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.92820	+	4.00000i	0.432169	+	0.249513i	0.700270	−	0.713878i	$-0.253063\pi$
$257$	6.92820	+	4.00000i	0.432169	+	0.249513i	−0.268101	+	0.963391i	$0.586396\pi$
$258$			6.00000i			0.373544i
$259$	20.0000	−	13.8564i	1.24274	−	0.860995i
$260$	3.00000	−	6.00000i	0.186052	−	0.372104i
$261$	−5.00000	+	8.66025i	−0.309492	+	0.536056i
$262$	10.3923	−	6.00000i	0.642039	−	0.370681i
$263$	−25.1147	+	14.5000i	−1.54864	+	0.894108i	−0.550395	+	0.834904i	$0.685523\pi$
$263$	−25.1147	+	14.5000i	−1.54864	+	0.894108i	−0.998246	+	0.0592040i	$0.981144\pi$
$264$	0.500000	+	0.866025i	0.0307729	+	0.0533002i
$265$	2.00000	−	4.00000i	0.122859	−	0.245718i
$266$	−10.0000	−	17.3205i	−0.613139	−	1.06199i
$267$			5.00000i			0.305995i
$268$	8.66025	+	5.00000i	0.529009	+	0.305424i
$269$	22.0000			1.34136			0.670682	−	0.741745i	$-0.266002\pi$
$269$	22.0000			1.34136			0.670682	+	0.741745i	$0.266002\pi$
$270$	−2.00000	−	1.00000i	−0.121716	−	0.0608581i
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	−0.384201	−	0.923249i	$-0.625523\pi$
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	0.991658	−	0.128897i	$-0.0411435\pi$
$272$	−5.19615	+	3.00000i	−0.315063	+	0.181902i
$273$			12.0000i			0.726273i
$274$	−3.00000	+	5.19615i	−0.181237	+	0.313911i
$275$	−4.96410	+	0.598076i	−0.299347	+	0.0360654i
$276$	−3.50000	+	6.06218i	−0.210675	+	0.364900i
$277$	−8.66025	+	5.00000i	−0.520344	+	0.300421i	−0.737075	−	0.675810i	$-0.763794\pi$
$277$	−8.66025	+	5.00000i	−0.520344	+	0.300421i	0.216731	+	0.976231i	$0.430460\pi$
$278$	11.2583	−	6.50000i	0.675230	−	0.389844i
$279$		0			0
$280$	−7.46410	+	4.92820i	−0.446065	+	0.294516i
$281$	−4.50000	+	7.79423i	−0.268447	+	0.464965i	−0.968461	−	0.249165i	$-0.919844\pi$
$281$	−4.50000	+	7.79423i	−0.268447	+	0.464965i	0.700014	+	0.714130i	$0.253177\pi$
$282$			3.00000i			0.178647i
$283$	−24.2487	+	14.0000i	−1.44144	+	0.832214i	−0.997946	−	0.0640654i	$-0.979593\pi$
$283$	−24.2487	+	14.0000i	−1.44144	+	0.832214i	−0.443491	+	0.896279i	$0.646260\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$	−5.00000	+	10.0000i	−0.296174	+	0.592349i
$286$	−3.00000			−0.177394
$287$	6.92820	+	4.00000i	0.408959	+	0.236113i
$288$		−	1.00000i		−	0.0589256i
$289$	9.50000	+	16.4545i	0.558824	+	0.967911i
$290$	10.0000	−	20.0000i	0.587220	−	1.17444i
$291$	−9.00000	−	15.5885i	−0.527589	−	0.913812i
$292$	12.1244	−	7.00000i	0.709524	−	0.409644i
$293$	−4.33013	+	2.50000i	−0.252969	+	0.146052i	−0.621123	−	0.783713i	$-0.713323\pi$
$293$	−4.33013	+	2.50000i	−0.252969	+	0.146052i	0.368154	+	0.929765i	$0.379990\pi$
$294$	4.50000	−	7.79423i	0.262445	−	0.454569i
$295$	−22.0000	−	11.0000i	−1.28089	−	0.640445i
$296$	−0.500000	−	6.06218i	−0.0290619	−	0.352357i
$297$			1.00000i			0.0580259i
$298$	−6.92820	−	4.00000i	−0.401340	−	0.231714i
$299$	−10.5000	−	18.1865i	−0.607231	−	1.05175i
$300$	4.59808	+	1.96410i	0.265470	+	0.113397i
$301$	12.0000	+	20.7846i	0.691669	+	1.19800i
$302$			14.0000i			0.805609i
$303$	−10.3923	+	6.00000i	−0.597022	+	0.344691i
$304$	−5.00000			−0.286770
$305$	22.3923	−	14.7846i	1.28218	−	0.846564i
$306$	−6.00000			−0.342997
$307$		−	32.0000i		−	1.82634i	−0.407583	−	0.913168i	$-0.633628\pi$
$307$		−	32.0000i		−	1.82634i	0.407583	−	0.913168i	$-0.366372\pi$
$308$	3.46410	+	2.00000i	0.197386	+	0.113961i
$309$	6.50000	+	11.2583i	0.369772	+	0.640464i
$310$		0			0
$311$	−10.0000	+	17.3205i	−0.567048	+	0.982156i	0.429808	+	0.902920i	$0.358581\pi$
$311$	−10.0000	+	17.3205i	−0.567048	+	0.982156i	−0.996856	+	0.0792356i	$0.974752\pi$
$312$	2.59808	+	1.50000i	0.147087	+	0.0849208i
$313$	6.92820	+	4.00000i	0.391605	+	0.226093i	0.682855	−	0.730554i	$-0.260738\pi$
$313$	6.92820	+	4.00000i	0.391605	+	0.226093i	−0.291250	+	0.956647i	$0.594071\pi$
$314$	0.500000	+	0.866025i	0.0282166	+	0.0488726i
$315$	−8.92820	+	0.535898i	−0.503047	+	0.0301945i
$316$	4.00000	−	6.92820i	0.225018	−	0.389742i
$317$	14.7224	+	8.50000i	0.826894	+	0.477408i	0.852788	−	0.522257i	$-0.174910\pi$
$317$	14.7224	+	8.50000i	0.826894	+	0.477408i	−0.0258939	+	0.999665i	$0.508243\pi$
$318$	1.73205	+	1.00000i	0.0971286	+	0.0560772i
$319$	−10.0000			−0.559893
$320$	0.133975	+	2.23205i	0.00748941	+	0.124775i
$321$	8.00000	−	13.8564i	0.446516	−	0.773389i
$322$			28.0000i			1.56038i
$323$			30.0000i			1.66924i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−12.0000	+	9.00000i	−0.665640	+	0.499230i
$326$	−7.00000	−	12.1244i	−0.387694	−	0.671506i
$327$			2.00000i			0.110600i
$328$	1.73205	−	1.00000i	0.0956365	−	0.0552158i
$329$	6.00000	+	10.3923i	0.330791	+	0.572946i
$330$	−0.133975	−	2.23205i	−0.00737506	−	0.122870i
$331$	−9.50000	+	16.4545i	−0.522167	+	0.904420i	0.477500	+	0.878632i	$0.341543\pi$
$331$	−9.50000	+	16.4545i	−0.522167	+	0.904420i	−0.999667	+	0.0257885i	$0.991790\pi$
$332$		−	10.0000i		−	0.548821i
$333$	2.59808	−	5.50000i	0.142374	−	0.301398i
$334$	−16.0000			−0.875481
$335$	−12.3205	−	18.6603i	−0.673141	−	1.01952i
$336$	−2.00000	−	3.46410i	−0.109109	−	0.188982i
$337$	−6.92820	+	4.00000i	−0.377403	+	0.217894i	−0.676688	−	0.736270i	$-0.736585\pi$
$337$	−6.92820	+	4.00000i	−0.377403	+	0.217894i	0.299285	+	0.954164i	$0.403252\pi$
$338$	3.46410	−	2.00000i	0.188422	−	0.108786i
$339$	6.00000			0.325875
$340$	13.3923	−	0.803848i	0.726300	−	0.0435948i
$341$		0			0
$342$	−4.33013	−	2.50000i	−0.234146	−	0.135185i
$343$		−	8.00000i		−	0.431959i
$344$	6.00000			0.323498
$345$	13.0622	−	8.62436i	0.703244	−	0.464320i
$346$	10.5000	+	18.1865i	0.564483	+	0.977714i
$347$		−	22.0000i		−	1.18102i	−0.807030	−	0.590511i	$-0.798926\pi$
$347$		−	22.0000i		−	1.18102i	0.807030	−	0.590511i	$-0.201074\pi$
$348$	8.66025	+	5.00000i	0.464238	+	0.268028i
$349$	−11.0000	+	19.0526i	−0.588817	+	1.01986i	0.405571	+	0.914063i	$0.367073\pi$
$349$	−11.0000	+	19.0526i	−0.588817	+	1.01986i	−0.994388	+	0.105797i	$0.966261\pi$
$350$	19.8564	−	2.39230i	1.06137	−	0.127874i
$351$	1.50000	+	2.59808i	0.0800641	+	0.138675i
$352$	0.866025	−	0.500000i	0.0461593	−	0.0266501i
$353$	22.5167	+	13.0000i	1.19844	+	0.691920i	0.960207	−	0.279288i	$-0.0900983\pi$
$353$	22.5167	+	13.0000i	1.19844	+	0.691920i	0.238233	+	0.971208i	$0.423432\pi$
$354$	5.50000	−	9.52628i	0.292322	−	0.506316i
$355$	−11.1962	+	7.39230i	−0.594230	+	0.392343i
$356$	5.00000			0.264999
$357$	−20.7846	+	12.0000i	−1.10004	+	0.635107i
$358$	−2.59808	−	1.50000i	−0.137313	−	0.0792775i
$359$	−18.0000			−0.950004			−0.475002	−	0.879985i	$-0.657553\pi$
$359$	−18.0000			−0.950004			−0.475002	+	0.879985i	$0.657553\pi$
$360$	−1.00000	+	2.00000i	−0.0527046	+	0.105409i
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$			12.0000i			0.630706i
$363$	8.66025	−	5.00000i	0.454545	−	0.262432i
$364$	12.0000			0.628971
$365$	−31.2487	+	1.87564i	−1.63563	+	0.0981757i
$366$	6.00000	+	10.3923i	0.313625	+	0.543214i
$367$	6.06218	−	3.50000i	0.316443	−	0.182699i	−0.333363	−	0.942799i	$-0.608183\pi$
$367$	6.06218	−	3.50000i	0.316443	−	0.182699i	0.649806	+	0.760100i	$0.274850\pi$
$368$	6.06218	+	3.50000i	0.316013	+	0.182450i
$369$	2.00000			0.104116
$370$	−5.06218	+	12.6244i	−0.263170	+	0.656309i
$371$	8.00000			0.415339
$372$		0			0
$373$	16.4545	−	9.50000i	0.851981	−	0.491891i	−0.00933789	−	0.999956i	$-0.502972\pi$
$373$	16.4545	−	9.50000i	0.851981	−	0.491891i	0.861319	+	0.508065i	$0.169639\pi$
$374$	−3.00000	−	5.19615i	−0.155126	−	0.268687i
$375$	−7.23205	−	8.52628i	−0.373461	−	0.440295i
$376$	3.00000			0.154713
$377$	−25.9808	+	15.0000i	−1.33808	+	0.772539i
$378$		−	4.00000i		−	0.205738i
$379$	−4.00000	+	6.92820i	−0.205466	+	0.355878i	−0.950281	−	0.311393i	$-0.899204\pi$
$379$	−4.00000	+	6.92820i	−0.205466	+	0.355878i	0.744815	+	0.667271i	$0.232538\pi$
$380$	10.0000	+	5.00000i	0.512989	+	0.256495i
$381$	5.00000			0.256158
$382$		0			0
$383$	−12.9904	+	7.50000i	−0.663777	+	0.383232i	−0.793715	−	0.608290i	$-0.791856\pi$
$383$	−12.9904	+	7.50000i	−0.663777	+	0.383232i	0.129937	+	0.991522i	$0.458522\pi$
$384$	−1.00000			−0.0510310
$385$	−4.92820	−	7.46410i	−0.251164	−	0.380406i
$386$	−2.00000	+	3.46410i	−0.101797	+	0.176318i
$387$	5.19615	+	3.00000i	0.264135	+	0.152499i
$388$	−15.5885	+	9.00000i	−0.791384	+	0.456906i
$389$	12.0000	+	20.7846i	0.608424	+	1.05382i	0.991500	+	0.130105i	$0.0415314\pi$
$389$	12.0000	+	20.7846i	0.608424	+	1.05382i	−0.383076	+	0.923717i	$0.625135\pi$
$390$	−3.69615	−	5.59808i	−0.187162	−	0.283470i
$391$	21.0000	−	36.3731i	1.06202	−	1.83947i
$392$	−7.79423	−	4.50000i	−0.393668	−	0.227284i
$393$		−	12.0000i		−	0.605320i
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$	−14.9282	+	9.85641i	−0.751119	+	0.495930i
$396$	1.00000			0.0502519
$397$		−	33.0000i		−	1.65622i	−0.560564	−	0.828111i	$-0.689416\pi$
$397$		−	33.0000i		−	1.65622i	0.560564	−	0.828111i	$-0.310584\pi$
$398$	8.66025	+	5.00000i	0.434099	+	0.250627i
$399$	−20.0000			−1.00125
$400$	1.96410	−	4.59808i	0.0982051	−	0.229904i
$401$	5.00000			0.249688			0.124844	−	0.992176i	$-0.460157\pi$
$401$	5.00000			0.249688			0.124844	+	0.992176i	$0.460157\pi$
$402$	8.66025	−	5.00000i	0.431934	−	0.249377i
$403$		0			0
$404$	6.00000	+	10.3923i	0.298511	+	0.517036i
$405$	−1.86603	+	1.23205i	−0.0927235	+	0.0612211i
$406$	40.0000			1.98517
$407$	6.06218	−	0.500000i	0.300491	−	0.0247841i
$408$			6.00000i			0.297044i
$409$	1.00000	−	1.73205i	0.0494468	−	0.0856444i	−0.840243	−	0.542211i	$-0.817588\pi$
$409$	1.00000	−	1.73205i	0.0494468	−	0.0856444i	0.889689	+	0.456566i	$0.150921\pi$
$410$	−4.46410	+	0.267949i	−0.220466	+	0.0132331i
$411$	3.00000	+	5.19615i	0.147979	+	0.256307i
$412$	11.2583	−	6.50000i	0.554658	−	0.320232i
$413$		−	44.0000i		−	2.16510i
$414$	3.50000	+	6.06218i	0.172016	+	0.297940i
$415$	−10.0000	+	20.0000i	−0.490881	+	0.981761i
$416$	1.50000	−	2.59808i	0.0735436	−	0.127381i
$417$		−	13.0000i		−	0.636613i
$418$		−	5.00000i		−	0.244558i
$419$	−10.5000	+	18.1865i	−0.512959	+	0.888470i	0.486928	+	0.873442i	$0.338117\pi$
$419$	−10.5000	+	18.1865i	−0.512959	+	0.888470i	−0.999887	+	0.0150285i	$0.995216\pi$
$420$	0.535898	+	8.92820i	0.0261492	+	0.435652i
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$	7.79423	+	4.50000i	0.379417	+	0.219057i
$423$	2.59808	+	1.50000i	0.126323	+	0.0729325i
$424$	1.00000	−	1.73205i	0.0485643	−	0.0841158i
$425$	−27.5885	−	11.7846i	−1.33824	−	0.571638i
$426$	−3.00000	−	5.19615i	−0.145350	−	0.251754i
$427$	41.5692	+	24.0000i	2.01168	+	1.16144i
$428$	−13.8564	−	8.00000i	−0.669775	−	0.386695i
$429$	−1.50000	+	2.59808i	−0.0724207	+	0.125436i
$430$	−12.0000	−	6.00000i	−0.578691	−	0.289346i
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	0.973574	−	0.228373i	$-0.0733406\pi$
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	−0.684564	+	0.728953i	$0.740007\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$		−	14.0000i		−	0.672797i	−0.941720	−	0.336399i	$-0.890791\pi$
$433$		−	14.0000i		−	0.672797i	0.941720	−	0.336399i	$-0.109209\pi$
$434$		0			0
$435$	−12.3205	−	18.6603i	−0.590723	−	0.894691i
$436$	2.00000			0.0957826
$437$	30.3109	−	17.5000i	1.44997	−	0.837139i
$438$		−	14.0000i		−	0.668946i
$439$	−13.0000	−	22.5167i	−0.620456	−	1.07466i	−0.989401	−	0.145210i	$-0.953614\pi$
$439$	−13.0000	−	22.5167i	−0.620456	−	1.07466i	0.368945	−	0.929451i	$-0.379719\pi$
$440$	−2.23205	+	0.133975i	−0.106409	+	0.00638699i
$441$	−4.50000	−	7.79423i	−0.214286	−	0.371154i
$442$	−15.5885	−	9.00000i	−0.741467	−	0.428086i
$443$			14.0000i			0.665160i	0.943075	+	0.332580i	$0.107919\pi$
$443$			14.0000i			0.665160i	−0.943075	+	0.332580i	$0.892081\pi$
$444$	−5.50000	−	2.59808i	−0.261018	−	0.123299i
$445$	−10.0000	−	5.00000i	−0.474045	−	0.237023i
$446$	−3.50000	+	6.06218i	−0.165730	+	0.287052i
$447$	−6.92820	+	4.00000i	−0.327693	+	0.189194i
$448$	−3.46410	+	2.00000i	−0.163663	+	0.0944911i
$449$	−3.00000	−	5.19615i	−0.141579	−	0.245222i	0.786513	−	0.617574i	$-0.211885\pi$
$449$	−3.00000	−	5.19615i	−0.141579	−	0.245222i	−0.928091	+	0.372353i	$0.878551\pi$
$450$	4.00000	−	3.00000i	0.188562	−	0.141421i
$451$	1.00000	+	1.73205i	0.0470882	+	0.0815591i
$452$		−	6.00000i		−	0.282216i
$453$	12.1244	+	7.00000i	0.569652	+	0.328889i
$454$	−12.0000			−0.563188
$455$	−24.0000	−	12.0000i	−1.12514	−	0.562569i
$456$	−2.50000	+	4.33013i	−0.117073	+	0.202777i
$457$	1.73205	−	1.00000i	0.0810219	−	0.0467780i	−0.458942	−	0.888466i	$-0.651771\pi$
$457$	1.73205	−	1.00000i	0.0810219	−	0.0467780i	0.539964	+	0.841688i	$0.318438\pi$
$458$		−	14.0000i		−	0.654177i
$459$	−3.00000	+	5.19615i	−0.140028	+	0.242536i
$460$	−8.62436	−	13.0622i	−0.402113	−	0.609027i
$461$	−12.0000	+	20.7846i	−0.558896	+	0.968036i	0.438693	+	0.898637i	$0.355441\pi$
$461$	−12.0000	+	20.7846i	−0.558896	+	0.968036i	−0.997589	+	0.0693989i	$0.977892\pi$
$462$	3.46410	−	2.00000i	0.161165	−	0.0930484i
$463$	13.8564	−	8.00000i	0.643962	−	0.371792i	−0.142177	−	0.989841i	$-0.545410\pi$
$463$	13.8564	−	8.00000i	0.643962	−	0.371792i	0.786139	+	0.618050i	$0.212077\pi$
$464$	5.00000	−	8.66025i	0.232119	−	0.402042i
$465$		0			0
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$			34.0000i			1.57333i	0.617379	+	0.786666i	$0.288195\pi$
$467$			34.0000i			1.57333i	−0.617379	+	0.786666i	$0.711805\pi$
$468$	2.59808	−	1.50000i	0.120096	−	0.0693375i
$469$	20.0000	−	34.6410i	0.923514	−	1.59957i
$470$	−6.00000	−	3.00000i	−0.276759	−	0.138380i
$471$	1.00000			0.0460776
$472$	−9.52628	−	5.50000i	−0.438483	−	0.253158i
$473$			6.00000i			0.275880i
$474$	−4.00000	−	6.92820i	−0.183726	−	0.318223i
$475$	−15.0000	−	20.0000i	−0.688247	−	0.917663i
$476$	12.0000	+	20.7846i	0.550019	+	0.952661i
$477$	1.73205	−	1.00000i	0.0793052	−	0.0457869i
$478$	13.8564	−	8.00000i	0.633777	−	0.365911i
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	−0.583803	−	0.811895i	$-0.698436\pi$
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	0.995023	+	0.0996406i	$0.0317693\pi$
$480$	2.00000	+	1.00000i	0.0912871	+	0.0456435i
$481$	15.0000	−	10.3923i	0.683941	−	0.473848i
$482$		−	25.0000i		−	1.13872i
$483$	24.2487	+	14.0000i	1.10335	+	0.637022i
$484$	−5.00000	−	8.66025i	−0.227273	−	0.393648i
$485$	40.1769	−	2.41154i	1.82434	−	0.109503i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$		−	32.0000i		−	1.45006i	−0.688718	−	0.725029i	$-0.741826\pi$
$487$		−	32.0000i		−	1.45006i	0.688718	−	0.725029i	$-0.258174\pi$
$488$	10.3923	−	6.00000i	0.470438	−	0.271607i
$489$	−14.0000			−0.633102
$490$	11.0885	+	16.7942i	0.500925	+	0.758686i
$491$	35.0000			1.57953			0.789764	−	0.613411i	$-0.210203\pi$
$491$	35.0000			1.57953			0.789764	+	0.613411i	$0.210203\pi$
$492$		−	2.00000i		−	0.0901670i
$493$	−51.9615	−	30.0000i	−2.34023	−	1.35113i
$494$	−7.50000	−	12.9904i	−0.337441	−	0.584465i
$495$	−2.00000	−	1.00000i	−0.0898933	−	0.0449467i
$496$		0			0
$497$	−20.7846	−	12.0000i	−0.932317	−	0.538274i
$498$	−8.66025	−	5.00000i	−0.388075	−	0.224055i
$499$	6.00000	+	10.3923i	0.268597	+	0.465223i	0.968500	−	0.249015i	$-0.0801067\pi$
$499$	6.00000	+	10.3923i	0.268597	+	0.465223i	−0.699903	+	0.714238i	$0.746773\pi$
$500$	−8.52628	+	7.23205i	−0.381307	+	0.323427i
$501$	−8.00000	+	13.8564i	−0.357414	+	0.619059i
$502$	18.1865	+	10.5000i	0.811705	+	0.468638i
$503$	27.7128	+	16.0000i	1.23565	+	0.713405i	0.968203	−	0.250167i	$-0.0804855\pi$
$503$	27.7128	+	16.0000i	1.23565	+	0.713405i	0.267451	+	0.963572i	$0.413819\pi$
$504$	−4.00000			−0.178174
$505$	−1.60770	−	26.7846i	−0.0715415	−	1.19190i
$506$	−3.50000	+	6.06218i	−0.155594	+	0.269497i
$507$		−	4.00000i		−	0.177646i
$508$		−	5.00000i		−	0.221839i
$509$	−18.0000	+	31.1769i	−0.797836	+	1.38189i	0.123187	+	0.992384i	$0.460689\pi$
$509$	−18.0000	+	31.1769i	−0.797836	+	1.38189i	−0.921023	+	0.389509i	$0.872645\pi$
$510$	6.00000	−	12.0000i	0.265684	−	0.531369i
$511$	−28.0000	−	48.4974i	−1.23865	−	2.14540i
$512$			1.00000i			0.0441942i
$513$	−4.33013	+	2.50000i	−0.191180	+	0.110378i
$514$	−4.00000	−	6.92820i	−0.176432	−	0.305590i
$515$	−29.0167	+	1.74167i	−1.27863	+	0.0767471i
$516$	3.00000	−	5.19615i	0.132068	−	0.228748i
$517$			3.00000i			0.131940i
$518$	−24.2487	+	2.00000i	−1.06543	+	0.0878750i
$519$	21.0000			0.921798
$520$	−5.59808	+	3.69615i	−0.245492	+	0.162087i
$521$	−4.50000	−	7.79423i	−0.197149	−	0.341471i	0.750454	−	0.660922i	$-0.229835\pi$
$521$	−4.50000	−	7.79423i	−0.197149	−	0.341471i	−0.947603	+	0.319451i	$0.896501\pi$
$522$	8.66025	−	5.00000i	0.379049	−	0.218844i
$523$	−17.3205	+	10.0000i	−0.757373	+	0.437269i	−0.828352	−	0.560208i	$-0.810721\pi$
$523$	−17.3205	+	10.0000i	−0.757373	+	0.437269i	0.0709788	+	0.997478i	$0.477388\pi$
$524$	−12.0000			−0.524222
$525$	7.85641	−	18.3923i	0.342882	−	0.802706i
$526$	29.0000			1.26446
$527$		0			0
$528$		−	1.00000i		−	0.0435194i
$529$	−26.0000			−1.13043
$530$	−3.73205	+	2.46410i	−0.162110	+	0.107034i
$531$	−5.50000	−	9.52628i	−0.238680	−	0.413405i
$532$			20.0000i			0.867110i
$533$	5.19615	+	3.00000i	0.225070	+	0.129944i
$534$	2.50000	−	4.33013i	0.108186	−	0.187383i
$535$	19.7128	+	29.8564i	0.852259	+	1.29081i
$536$	−5.00000	−	8.66025i	−0.215967	−	0.374066i
$537$	−2.59808	+	1.50000i	−0.112115	+	0.0647298i
$538$	−19.0526	−	11.0000i	−0.821414	−	0.474244i
$539$	4.50000	−	7.79423i	0.193829	−	0.335721i
$540$	1.23205	+	1.86603i	0.0530190	+	0.0803009i
$541$	−8.00000			−0.343947			−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000			−0.343947			−0.171973	+	0.985102i	$0.555014\pi$
$542$	−17.3205	+	10.0000i	−0.743980	+	0.429537i
$543$	10.3923	+	6.00000i	0.445976	+	0.257485i
$544$	6.00000			0.257248
$545$	−4.00000	−	2.00000i	−0.171341	−	0.0856706i
$546$	6.00000	−	10.3923i	0.256776	−	0.444750i
$547$			10.0000i			0.427569i	0.976881	+	0.213785i	$0.0685791\pi$
$547$			10.0000i			0.427569i	−0.976881	+	0.213785i	$0.931421\pi$
$548$	5.19615	−	3.00000i	0.221969	−	0.128154i
$549$	12.0000			0.512148
$550$	4.59808	+	1.96410i	0.196063	+	0.0837496i
$551$	−25.0000	−	43.3013i	−1.06504	−	1.84470i
$552$	6.06218	−	3.50000i	0.258023	−	0.148970i
$553$	−27.7128	−	16.0000i	−1.17847	−	0.680389i
$554$	10.0000			0.424859
$555$	8.40192	+	10.6962i	0.356642	+	0.454026i
$556$	−13.0000			−0.551323
$557$	26.8468	+	15.5000i	1.13753	+	0.656756i	0.945819	−	0.324694i	$-0.105261\pi$
$557$	26.8468	+	15.5000i	1.13753	+	0.656756i	0.191716	+	0.981450i	$0.438595\pi$
$558$		0			0
$559$	9.00000	+	15.5885i	0.380659	+	0.659321i
$560$	8.92820	−	0.535898i	0.377285	−	0.0226458i
$561$	−6.00000			−0.253320
$562$	7.79423	−	4.50000i	0.328780	−	0.189821i
$563$			8.00000i			0.337160i	0.985688	+	0.168580i	$0.0539181\pi$
$563$			8.00000i			0.337160i	−0.985688	+	0.168580i	$0.946082\pi$
$564$	1.50000	−	2.59808i	0.0631614	−	0.109399i
$565$	−6.00000	+	12.0000i	−0.252422	+	0.504844i
$566$	28.0000			1.17693
$567$	−3.46410	−	2.00000i	−0.145479	−	0.0839921i
$568$	−5.19615	+	3.00000i	−0.218026	+	0.125877i
$569$	−17.0000			−0.712677			−0.356339	−	0.934357i	$-0.615975\pi$
$569$	−17.0000			−0.712677			−0.356339	+	0.934357i	$0.615975\pi$
$570$	9.33013	−	6.16025i	0.390796	−	0.258025i
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	−0.595862	−	0.803087i	$-0.703189\pi$
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	0.993425	+	0.114488i	$0.0365228\pi$
$572$	2.59808	+	1.50000i	0.108631	+	0.0627182i
$573$		0			0
$574$	−4.00000	−	6.92820i	−0.166957	−	0.289178i
$575$	4.18653	+	34.7487i	0.174591	+	1.44912i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−17.3205	−	10.0000i	−0.721062	−	0.416305i	0.0940813	−	0.995565i	$-0.470009\pi$
$577$	−17.3205	−	10.0000i	−0.721062	−	0.416305i	−0.815144	+	0.579259i	$0.803342\pi$
$578$		−	19.0000i		−	0.790296i
$579$	2.00000	+	3.46410i	0.0831172	+	0.143963i
$580$	−18.6603	+	12.3205i	−0.774825	+	0.511581i
$581$	−40.0000			−1.65948
$582$			18.0000i			0.746124i
$583$	1.73205	+	1.00000i	0.0717342	+	0.0414158i
$584$	−14.0000			−0.579324
$585$	−6.69615	+	0.401924i	−0.276852	+	0.0166175i
$586$	5.00000			0.206548
$587$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$587$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$588$	−7.79423	+	4.50000i	−0.321429	+	0.185577i
$589$		0			0
$590$	13.5526	+	20.5263i	0.557950	+	0.845054i
$591$	−18.0000			−0.740421
$592$	−2.59808	+	5.50000i	−0.106780	+	0.226049i
$593$			6.00000i			0.246390i	0.992382	+	0.123195i	$0.0393141\pi$
$593$			6.00000i			0.246390i	−0.992382	+	0.123195i	$0.960686\pi$
$594$	0.500000	−	0.866025i	0.0205152	−	0.0355335i
$595$	−3.21539	−	53.5692i	−0.131818	−	2.19612i
$596$	4.00000	+	6.92820i	0.163846	+	0.283790i
$597$	8.66025	−	5.00000i	0.354441	−	0.204636i
$598$			21.0000i			0.858754i
$599$	−5.00000	−	8.66025i	−0.204294	−	0.353848i	0.745613	−	0.666379i	$-0.232157\pi$
$599$	−5.00000	−	8.66025i	−0.204294	−	0.353848i	−0.949908	+	0.312531i	$0.898823\pi$
$600$	−3.00000	−	4.00000i	−0.122474	−	0.163299i
$601$	−18.5000	+	32.0429i	−0.754631	+	1.30706i	0.190927	+	0.981604i	$0.438851\pi$
$601$	−18.5000	+	32.0429i	−0.754631	+	1.30706i	−0.945558	+	0.325455i	$0.894483\pi$
$602$		−	24.0000i		−	0.978167i
$603$		−	10.0000i		−	0.407231i
$604$	7.00000	−	12.1244i	0.284826	−	0.493333i
$605$	1.33975	+	22.3205i	0.0544684	+	0.907458i
$606$	12.0000			0.487467
$607$	13.8564	+	8.00000i	0.562414	+	0.324710i	0.754114	−	0.656744i	$-0.228067\pi$
$607$	13.8564	+	8.00000i	0.562414	+	0.324710i	−0.191700	+	0.981454i	$0.561400\pi$
$608$	4.33013	+	2.50000i	0.175610	+	0.101388i
$609$	20.0000	−	34.6410i	0.810441	−	1.40372i
$610$	−26.7846	+	1.60770i	−1.08448	+	0.0650937i
$611$	4.50000	+	7.79423i	0.182051	+	0.315321i
$612$	5.19615	+	3.00000i	0.210042	+	0.121268i
$613$	23.3827	+	13.5000i	0.944418	+	0.545260i	0.891342	−	0.453331i	$-0.149764\pi$
$613$	23.3827	+	13.5000i	0.944418	+	0.545260i	0.0530754	+	0.998591i	$0.483098\pi$
$614$	−16.0000	+	27.7128i	−0.645707	+	1.11840i
$615$	−2.00000	+	4.00000i	−0.0806478	+	0.161296i
$616$	−2.00000	−	3.46410i	−0.0805823	−	0.139573i
$617$	19.0526	+	11.0000i	0.767027	+	0.442843i	0.831813	−	0.555056i	$-0.187303\pi$
$617$	19.0526	+	11.0000i	0.767027	+	0.442843i	−0.0647859	+	0.997899i	$0.520636\pi$
$618$		−	13.0000i		−	0.522937i
$619$	−20.0000			−0.803868			−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000			−0.803868			−0.401934	+	0.915669i	$0.631662\pi$
$620$		0			0
$621$	7.00000			0.280900
$622$	17.3205	−	10.0000i	0.694489	−	0.400963i
$623$		−	20.0000i		−	0.801283i
$624$	−1.50000	−	2.59808i	−0.0600481	−	0.104006i
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	−4.00000	−	6.92820i	−0.159872	−	0.276907i
$627$	−4.33013	−	2.50000i	−0.172929	−	0.0998404i
$628$		−	1.00000i		−	0.0399043i
$629$	33.0000	+	15.5885i	1.31580	+	0.621552i
$630$	8.00000	+	4.00000i	0.318728	+	0.159364i
$631$	−3.00000	+	5.19615i	−0.119428	+	0.206856i	−0.919541	−	0.392994i	$-0.871439\pi$
$631$	−3.00000	+	5.19615i	−0.119428	+	0.206856i	0.800113	+	0.599849i	$0.204773\pi$
$632$	−6.92820	+	4.00000i	−0.275589	+	0.159111i
$633$	7.79423	−	4.50000i	0.309793	−	0.178859i
$634$	−8.50000	−	14.7224i	−0.337578	−	0.584702i
$635$	−5.00000	+	10.0000i	−0.198419	+	0.396838i
$636$	−1.00000	−	1.73205i	−0.0396526	−	0.0686803i
$637$		−	27.0000i		−	1.06978i
$638$	8.66025	+	5.00000i	0.342863	+	0.197952i
$639$	−6.00000			−0.237356
$640$	1.00000	−	2.00000i	0.0395285	−	0.0790569i
$641$	−3.50000	+	6.06218i	−0.138242	+	0.239442i	−0.926831	−	0.375478i	$-0.877478\pi$
$641$	−3.50000	+	6.06218i	−0.138242	+	0.239442i	0.788589	+	0.614920i	$0.210812\pi$
$642$	−13.8564	+	8.00000i	−0.546869	+	0.315735i
$643$		−	4.00000i		−	0.157745i	−0.996885	−	0.0788723i	$-0.974868\pi$
$643$		−	4.00000i		−	0.157745i	0.996885	−	0.0788723i	$-0.0251319\pi$
$644$	14.0000	−	24.2487i	0.551677	−	0.955533i
$645$	−11.1962	+	7.39230i	−0.440848	+	0.291072i
$646$	15.0000	−	25.9808i	0.590167	−	1.02220i
$647$	−12.9904	+	7.50000i	−0.510705	+	0.294855i	−0.733123	−	0.680096i	$-0.761938\pi$
$647$	−12.9904	+	7.50000i	−0.510705	+	0.294855i	0.222419	+	0.974951i	$0.428605\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	5.50000	−	9.52628i	0.215894	−	0.373939i
$650$	14.8923	−	1.79423i	0.584124	−	0.0703754i
$651$		0			0
$652$			14.0000i			0.548282i
$653$	33.7750	−	19.5000i	1.32172	−	0.763094i	0.337715	−	0.941248i	$-0.390346\pi$
$653$	33.7750	−	19.5000i	1.32172	−	0.763094i	0.984003	+	0.178154i	$0.0570127\pi$
$654$	1.00000	−	1.73205i	0.0391031	−	0.0677285i
$655$	24.0000	+	12.0000i	0.937758	+	0.468879i
$656$	−2.00000			−0.0780869
$657$	−12.1244	−	7.00000i	−0.473016	−	0.273096i
$658$		−	12.0000i		−	0.467809i
$659$	3.50000	+	6.06218i	0.136341	+	0.236149i	0.926109	−	0.377257i	$-0.123133\pi$
$659$	3.50000	+	6.06218i	0.136341	+	0.236149i	−0.789768	+	0.613405i	$0.789799\pi$
$660$	−1.00000	+	2.00000i	−0.0389249	+	0.0778499i
$661$	10.0000	+	17.3205i	0.388955	+	0.673690i	0.992309	−	0.123784i	$-0.0395028\pi$
$661$	10.0000	+	17.3205i	0.388955	+	0.673690i	−0.603354	+	0.797473i	$0.706170\pi$
$662$	16.4545	−	9.50000i	0.639522	−	0.369228i
$663$	−15.5885	+	9.00000i	−0.605406	+	0.349531i
$664$	−5.00000	+	8.66025i	−0.194038	+	0.336083i
$665$	20.0000	−	40.0000i	0.775567	−	1.55113i
$666$	−5.00000	+	3.46410i	−0.193746	+	0.134231i
$667$			70.0000i			2.71041i
$668$	13.8564	+	8.00000i	0.536120	+	0.309529i
$669$	3.50000	+	6.06218i	0.135318	+	0.234377i
$670$	1.33975	+	22.3205i	0.0517589	+	0.862316i
$671$	6.00000	+	10.3923i	0.231627	+	0.401190i
$672$			4.00000i			0.154303i
$673$	13.8564	−	8.00000i	0.534125	−	0.308377i	−0.208569	−	0.978008i	$-0.566881\pi$
$673$	13.8564	−	8.00000i	0.534125	−	0.308377i	0.742695	+	0.669630i	$0.233547\pi$
$674$	8.00000			0.308148
$675$	−0.598076	−	4.96410i	−0.0230200	−	0.191068i
$676$	−4.00000			−0.153846
$677$		−	27.0000i		−	1.03769i	−0.854867	−	0.518847i	$-0.826361\pi$
$677$		−	27.0000i		−	1.03769i	0.854867	−	0.518847i	$-0.173639\pi$
$678$	−5.19615	−	3.00000i	−0.199557	−	0.115214i
$679$	36.0000	+	62.3538i	1.38155	+	2.39292i
$680$	−12.0000	−	6.00000i	−0.460179	−	0.230089i
$681$	−6.00000	+	10.3923i	−0.229920	+	0.398234i
$682$		0			0
$683$	8.66025	+	5.00000i	0.331375	+	0.191320i	0.656452	−	0.754368i	$-0.272057\pi$
$683$	8.66025	+	5.00000i	0.331375	+	0.191320i	−0.325076	+	0.945688i	$0.605390\pi$
$684$	2.50000	+	4.33013i	0.0955899	+	0.165567i
$685$	−13.3923	+	0.803848i	−0.511694	+	0.0307134i
$686$	−4.00000	+	6.92820i	−0.152721	+	0.264520i
$687$	−12.1244	−	7.00000i	−0.462573	−	0.267067i
$688$	−5.19615	−	3.00000i	−0.198101	−	0.114374i
$689$	6.00000			0.228582
$690$	−15.6244	+	0.937822i	−0.594809	+	0.0357023i
$691$	24.0000	−	41.5692i	0.913003	−	1.58137i	0.103204	−	0.994660i	$-0.467091\pi$
$691$	24.0000	−	41.5692i	0.913003	−	1.58137i	0.809799	−	0.586707i	$-0.199576\pi$
$692$		−	21.0000i		−	0.798300i
$693$		−	4.00000i		−	0.151947i
$694$	−11.0000	+	19.0526i	−0.417554	+	0.723225i
$695$	26.0000	+	13.0000i	0.986236	+	0.493118i
$696$	−5.00000	−	8.66025i	−0.189525	−	0.328266i
$697$			12.0000i			0.454532i
$698$	19.0526	−	11.0000i	0.721150	−	0.416356i
$699$	−3.00000	−	5.19615i	−0.113470	−	0.196537i
$700$	−18.3923	−	7.85641i	−0.695164	−	0.296944i
$701$	−6.00000	+	10.3923i	−0.226617	+	0.392512i	−0.956803	−	0.290736i	$-0.906100\pi$
$701$	−6.00000	+	10.3923i	−0.226617	+	0.392512i	0.730186	+	0.683248i	$0.239433\pi$
$702$		−	3.00000i		−	0.113228i
$703$	17.3205	+	25.0000i	0.653255	+	0.942893i
$704$	−1.00000			−0.0376889
$705$	−5.59808	+	3.69615i	−0.210836	+	0.139205i
$706$	−13.0000	−	22.5167i	−0.489261	−	0.847426i
$707$	41.5692	−	24.0000i	1.56337	−	0.902613i
$708$	−9.52628	+	5.50000i	−0.358020	+	0.206703i
$709$	−12.0000			−0.450669			−0.225335	−	0.974281i	$-0.572348\pi$
$709$	−12.0000			−0.450669			−0.225335	+	0.974281i	$0.572348\pi$
$710$	13.3923	−	0.803848i	0.502604	−	0.0301679i
$711$	−8.00000			−0.300023
$712$	−4.33013	−	2.50000i	−0.162278	−	0.0936915i
$713$		0			0
$714$	24.0000			0.898177
$715$	−3.69615	−	5.59808i	−0.138228	−	0.209356i
$716$	1.50000	+	2.59808i	0.0560576	+	0.0970947i
$717$		−	16.0000i		−	0.597531i
$718$	15.5885	+	9.00000i	0.581756	+	0.335877i
$719$	15.0000	−	25.9808i	0.559406	−	0.968919i	−0.438141	−	0.898906i	$-0.644363\pi$
$719$	15.0000	−	25.9808i	0.559406	−	0.968919i	0.997546	−	0.0700124i	$-0.0223039\pi$
$720$	1.86603	−	1.23205i	0.0695427	−	0.0459158i
$721$	−26.0000	−	45.0333i	−0.968291	−	1.67713i
$722$	5.19615	−	3.00000i	0.193381	−	0.111648i
$723$	−21.6506	−	12.5000i	−0.805196	−	0.464880i
$724$	6.00000	−	10.3923i	0.222988	−	0.386227i
$725$	49.6410	−	5.98076i	1.84362	−	0.222120i
$726$	−10.0000			−0.371135
$727$	−40.7032	+	23.5000i	−1.50960	+	0.871567i	−0.509661	+	0.860376i	$0.670229\pi$
$727$	−40.7032	+	23.5000i	−1.50960	+	0.871567i	−0.999937	+	0.0111912i	$0.996438\pi$
$728$	−10.3923	−	6.00000i	−0.385164	−	0.222375i
$729$	−1.00000			−0.0370370
$730$	28.0000	+	14.0000i	1.03633	+	0.518163i
$731$	−18.0000	+	31.1769i	−0.665754	+	1.15312i
$732$		−	12.0000i		−	0.443533i
$733$	−19.9186	+	11.5000i	−0.735710	+	0.424762i	−0.820507	−	0.571636i	$-0.806309\pi$
$733$	−19.9186	+	11.5000i	−0.735710	+	0.424762i	0.0847976	+	0.996398i	$0.472976\pi$
$734$	−7.00000			−0.258375
$735$	20.0885	−	1.20577i	0.740974	−	0.0444755i
$736$	−3.50000	−	6.06218i	−0.129012	−	0.223455i
$737$	8.66025	−	5.00000i	0.319005	−	0.184177i
$738$	−1.73205	−	1.00000i	−0.0637577	−	0.0368105i
$739$	−23.0000			−0.846069			−0.423034	−	0.906114i	$-0.639035\pi$
$739$	−23.0000			−0.846069			−0.423034	+	0.906114i	$0.639035\pi$
$740$	10.6962	−	8.40192i	0.393198	−	0.308861i
$741$	−15.0000			−0.551039
$742$	−6.92820	−	4.00000i	−0.254342	−	0.146845i
$743$	0.866025	−	0.500000i	0.0317714	−	0.0183432i	−0.484030	−	0.875051i	$-0.660828\pi$
$743$	0.866025	−	0.500000i	0.0317714	−	0.0183432i	0.515802	+	0.856708i	$0.327494\pi$
$744$		0			0
$745$	−1.07180	−	17.8564i	−0.0392676	−	0.654208i
$746$	−19.0000			−0.695639
$747$	−8.66025	+	5.00000i	−0.316862	+	0.182940i
$748$			6.00000i			0.219382i
$749$	−32.0000	+	55.4256i	−1.16925	+	2.02521i
$750$	2.00000	+	11.0000i	0.0730297	+	0.401663i
$751$	46.0000			1.67856			0.839282	−	0.543696i	$-0.182976\pi$
$751$	46.0000			1.67856			0.839282	+	0.543696i	$0.182976\pi$
$752$	−2.59808	−	1.50000i	−0.0947421	−	0.0546994i
$753$	18.1865	−	10.5000i	0.662754	−	0.382641i
$754$	30.0000			1.09254
$755$	−26.1244	+	17.2487i	−0.950763	+	0.627745i
$756$	−2.00000	+	3.46410i	−0.0727393	+	0.125988i
$757$	14.7224	+	8.50000i	0.535096	+	0.308938i	0.743089	−	0.669193i	$-0.233360\pi$
$757$	14.7224	+	8.50000i	0.535096	+	0.308938i	−0.207993	+	0.978130i	$0.566693\pi$
$758$	6.92820	−	4.00000i	0.251644	−	0.145287i
$759$	3.50000	+	6.06218i	0.127042	+	0.220043i
$760$	−6.16025	−	9.33013i	−0.223456	−	0.338439i
$761$	9.50000	−	16.4545i	0.344375	−	0.596475i	−0.640865	−	0.767653i	$-0.721424\pi$
$761$	9.50000	−	16.4545i	0.344375	−	0.596475i	0.985240	+	0.171179i	$0.0547576\pi$
$762$	−4.33013	−	2.50000i	−0.156864	−	0.0905654i
$763$		−	8.00000i		−	0.289619i
$764$		0			0
$765$	−7.39230	−	11.1962i	−0.267269	−	0.404798i
$766$	15.0000			0.541972
$767$		−	33.0000i		−	1.19156i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	10.0000			0.360609			0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000			0.360609			0.180305	+	0.983611i	$0.442292\pi$
$770$	0.535898	+	8.92820i	0.0193124	+	0.321750i
$771$	−8.00000			−0.288113
$772$	3.46410	−	2.00000i	0.124676	−	0.0719816i
$773$	−19.9186	+	11.5000i	−0.716422	+	0.413626i	−0.813434	−	0.581657i	$-0.802405\pi$
$773$	−19.9186	+	11.5000i	−0.716422	+	0.413626i	0.0970125	+	0.995283i	$0.469071\pi$
$774$	−3.00000	−	5.19615i	−0.107833	−	0.186772i
$775$		0			0
$776$	18.0000			0.646162
$777$	−10.3923	+	22.0000i	−0.372822	+	0.789246i
$778$		−	24.0000i		−	0.860442i
$779$	−5.00000	+	8.66025i	−0.179144	+	0.310286i
$780$	0.401924	+	6.69615i	0.0143912	+	0.239761i
$781$	−3.00000	−	5.19615i	−0.107348	−	0.185933i
$782$	−36.3731	+	21.0000i	−1.30070	+	0.750958i
$783$		−	10.0000i		−	0.357371i
$784$	4.50000	+	7.79423i	0.160714	+	0.278365i
$785$	−1.00000	+	2.00000i	−0.0356915	+	0.0713831i
$786$	−6.00000	+	10.3923i	−0.214013	+	0.370681i
$787$		−	34.0000i		−	1.21197i	−0.795476	−	0.605985i	$-0.792779\pi$
$787$		−	34.0000i		−	1.21197i	0.795476	−	0.605985i	$-0.207221\pi$
$788$			18.0000i			0.641223i
$789$	14.5000	−	25.1147i	0.516214	−	0.894108i
$790$	17.8564	−	1.07180i	0.635302	−	0.0381328i
$791$	−24.0000			−0.853342
$792$	−0.866025	−	0.500000i	−0.0307729	−	0.0177667i
$793$	31.1769	+	18.0000i	1.10712	+	0.639199i
$794$	−16.5000	+	28.5788i	−0.585563	+	1.01423i
$795$	0.267949	+	4.46410i	0.00950318	+	0.158325i
$796$	−5.00000	−	8.66025i	−0.177220	−	0.306955i
$797$	−12.9904	−	7.50000i	−0.460143	−	0.265664i	0.251961	−	0.967737i	$-0.418924\pi$
$797$	−12.9904	−	7.50000i	−0.460143	−	0.265664i	−0.712104	+	0.702074i	$0.752258\pi$
$798$	17.3205	+	10.0000i	0.613139	+	0.353996i
$799$	−9.00000	+	15.5885i	−0.318397	+	0.551480i
$800$	−4.00000	+	3.00000i	−0.141421	+	0.106066i
$801$	−2.50000	−	4.33013i	−0.0883332	−	0.152998i
$802$	−4.33013	−	2.50000i	−0.152902	−	0.0882781i
$803$		−	14.0000i		−	0.494049i
$804$	−10.0000			−0.352673
$805$	−52.2487	+	34.4974i	−1.84153	+	1.21587i
$806$		0			0
$807$	−19.0526	+	11.0000i	−0.670682	+	0.387218i
$808$		−	12.0000i		−	0.422159i
$809$	7.50000	+	12.9904i	0.263686	+	0.456717i	0.967219	−	0.253946i	$-0.0817284\pi$
$809$	7.50000	+	12.9904i	0.263686	+	0.456717i	−0.703533	+	0.710663i	$0.748395\pi$
$810$	2.23205	−	0.133975i	0.0784263	−	0.00470739i
$811$	12.5000	+	21.6506i	0.438934	+	0.760257i	0.997608	−	0.0691313i	$-0.0220227\pi$
$811$	12.5000	+	21.6506i	0.438934	+	0.760257i	−0.558673	+	0.829388i	$0.688689\pi$
$812$	−34.6410	−	20.0000i	−1.21566	−	0.701862i
$813$			20.0000i			0.701431i
$814$	−5.50000	−	2.59808i	−0.192775	−	0.0910625i
$815$	14.0000	−	28.0000i	0.490399	−	0.980797i
$816$	3.00000	−	5.19615i	0.105021	−	0.181902i
$817$	−25.9808	+	15.0000i	−0.908952	+	0.524784i
$818$	−1.73205	+	1.00000i	−0.0605597	+	0.0349642i
$819$	−6.00000	−	10.3923i	−0.209657	−	0.363137i
$820$	4.00000	+	2.00000i	0.139686	+	0.0698430i
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$		−	6.00000i		−	0.209274i
$823$	20.7846	+	12.0000i	0.724506	+	0.418294i	0.816409	−	0.577474i	$-0.195962\pi$
$823$	20.7846	+	12.0000i	0.724506	+	0.418294i	−0.0919029	+	0.995768i	$0.529295\pi$
$824$	−13.0000			−0.452876
$825$	4.00000	−	3.00000i	0.139262	−	0.104447i
$826$	−22.0000	+	38.1051i	−0.765478	+	1.32585i
$827$	−3.46410	+	2.00000i	−0.120459	+	0.0695468i	−0.559019	−	0.829155i	$-0.688822\pi$
$827$	−3.46410	+	2.00000i	−0.120459	+	0.0695468i	0.438560	+	0.898702i	$0.355489\pi$
$828$		−	7.00000i		−	0.243267i
$829$	−2.00000	+	3.46410i	−0.0694629	+	0.120313i	−0.898665	−	0.438636i	$-0.855462\pi$
$829$	−2.00000	+	3.46410i	−0.0694629	+	0.120313i	0.829202	+	0.558949i	$0.188795\pi$
$830$	18.6603	−	12.3205i	0.647707	−	0.427651i
$831$	5.00000	−	8.66025i	0.173448	−	0.300421i
$832$	−2.59808	+	1.50000i	−0.0900721	+	0.0520031i
$833$	46.7654	−	27.0000i	1.62032	−	0.935495i
$834$	−6.50000	+	11.2583i	−0.225077	+	0.389844i
$835$	−19.7128	−	29.8564i	−0.682190	−	1.03322i
$836$	−2.50000	+	4.33013i	−0.0864643	+	0.149761i
$837$		0			0
$838$	18.1865	−	10.5000i	0.628243	−	0.362716i
$839$	12.0000	−	20.7846i	0.414286	−	0.717564i	−0.581067	−	0.813856i	$-0.697365\pi$
$839$	12.0000	−	20.7846i	0.414286	−	0.717564i	0.995353	+	0.0962912i	$0.0306980\pi$
$840$	4.00000	−	8.00000i	0.138013	−	0.276026i
$841$	71.0000			2.44828
$842$	−19.0526	−	11.0000i	−0.656595	−	0.379085i
$843$		−	9.00000i		−	0.309976i
$844$	−4.50000	−	7.79423i	−0.154896	−	0.268288i
$845$	8.00000	+	4.00000i	0.275208	+	0.137604i
$846$	−1.50000	−	2.59808i	−0.0515711	−	0.0893237i
$847$	−34.6410	+	20.0000i	−1.19028	+	0.687208i
$848$	−1.73205	+	1.00000i	−0.0594789	+	0.0343401i
$849$	14.0000	−	24.2487i	0.480479	−	0.832214i
$850$	18.0000	+	24.0000i	0.617395	+	0.823193i
$851$	−3.50000	−	42.4352i	−0.119978	−	1.45466i
$852$			6.00000i			0.205557i
$853$	−28.5788	−	16.5000i	−0.978521	−	0.564949i	−0.0766976	−	0.997054i	$-0.524438\pi$
$853$	−28.5788	−	16.5000i	−0.978521	−	0.564949i	−0.901823	+	0.432105i	$0.857771\pi$
$854$	−24.0000	−	41.5692i	−0.821263	−	1.42247i
$855$	−0.669873	−	11.1603i	−0.0229092	−	0.381673i
$856$	8.00000	+	13.8564i	0.273434	+	0.473602i
$857$			6.00000i			0.204956i	0.994735	+	0.102478i	$0.0326771\pi$
$857$			6.00000i			0.204956i	−0.994735	+	0.102478i	$0.967323\pi$
$858$	2.59808	−	1.50000i	0.0886969	−	0.0512092i
$859$	−27.0000			−0.921228			−0.460614	−	0.887601i	$-0.652371\pi$
$859$	−27.0000			−0.921228			−0.460614	+	0.887601i	$0.652371\pi$
$860$	7.39230	+	11.1962i	0.252076	+	0.381786i
$861$	−8.00000			−0.272639
$862$		−	12.0000i		−	0.408722i
$863$	30.3109	+	17.5000i	1.03179	+	0.595707i	0.917498	−	0.397740i	$-0.130205\pi$
$863$	30.3109	+	17.5000i	1.03179	+	0.595707i	0.114296	+	0.993447i	$0.463539\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−21.0000	+	42.0000i	−0.714021	+	1.42804i
$866$	−7.00000	+	12.1244i	−0.237870	+	0.412002i
$867$	−16.4545	−	9.50000i	−0.558824	−	0.322637i
$868$		0			0
$869$	−4.00000	−	6.92820i	−0.135691	−	0.235023i
$870$	1.33975	+	22.3205i	0.0454216	+	0.756736i
$871$	15.0000	−	25.9808i	0.508256	−	0.880325i
$872$	−1.73205	−	1.00000i	−0.0586546	−	0.0338643i
$873$	15.5885	+	9.00000i	0.527589	+	0.304604i
$874$	−35.0000			−1.18389
$875$	28.9282	+	34.1051i	0.977952	+	1.15296i
$876$	−7.00000	+	12.1244i	−0.236508	+	0.409644i
$877$		−	7.00000i		−	0.236373i	−0.992991	−	0.118187i	$-0.962292\pi$
$877$		−	7.00000i		−	0.236373i	0.992991	−	0.118187i	$-0.0377081\pi$
$878$			26.0000i			0.877457i
$879$	2.50000	−	4.33013i	0.0843229	−	0.146052i
$880$	2.00000	+	1.00000i	0.0674200	+	0.0337100i
$881$	9.50000	+	16.4545i	0.320063	+	0.554366i	0.980501	−	0.196515i	$-0.0629625\pi$
$881$	9.50000	+	16.4545i	0.320063	+	0.554366i	−0.660438	+	0.750881i	$0.729629\pi$
$882$			9.00000i			0.303046i
$883$	1.73205	−	1.00000i	0.0582882	−	0.0336527i	−0.470573	−	0.882361i	$-0.655953\pi$
$883$	1.73205	−	1.00000i	0.0582882	−	0.0336527i	0.528861	+	0.848709i	$0.322619\pi$
$884$	9.00000	+	15.5885i	0.302703	+	0.524297i
$885$	24.5526	−	1.47372i	0.825325	−	0.0495386i
$886$	7.00000	−	12.1244i	0.235170	−	0.407326i
$887$		0			0		1.00000			$0$
$887$		0			0		−1.00000			$\pi$
$888$	3.46410	+	5.00000i	0.116248	+	0.167789i
$889$	−20.0000			−0.670778
$890$	6.16025	+	9.33013i	0.206492	+	0.312747i
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	6.06218	−	3.50000i	0.202977	−	0.117189i
$893$	−12.9904	+	7.50000i	−0.434707	+	0.250978i
$894$	8.00000			0.267560
$895$	−0.401924	−	6.69615i	−0.0134348	−	0.223828i
$896$	4.00000			0.133631
$897$	18.1865	+	10.5000i	0.607231	+	0.350585i
$898$			6.00000i			0.200223i
$899$		0			0
$900$	−4.96410	+	0.598076i	−0.165470	+	0.0199359i
$901$	6.00000	+	10.3923i	0.199889	+	0.346218i
$902$		−	2.00000i		−	0.0665927i
$903$	−20.7846	−	12.0000i	−0.691669	−	0.399335i
$904$	−3.00000	+	5.19615i	−0.0997785	+	0.172821i
$905$	−22.3923	+	14.7846i	−0.744345	+	0.491457i
$906$	−7.00000	−	12.1244i	−0.232559	−	0.402805i
$907$	34.6410	−	20.0000i	1.15024	−	0.664089i	0.201291	−	0.979531i	$-0.435486\pi$
$907$	34.6410	−	20.0000i	1.15024	−	0.664089i	0.948945	+	0.315442i	$0.102153\pi$
$908$	10.3923	+	6.00000i	0.344881	+	0.199117i
$909$	6.00000	−	10.3923i	0.199007	−	0.344691i
$910$	14.7846	+	22.3923i	0.490105	+	0.742298i
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$	4.33013	−	2.50000i	0.143385	−	0.0827833i
$913$	−8.66025	−	5.00000i	−0.286613	−	0.165476i
$914$	−2.00000			−0.0661541
$915$	−12.0000	+	24.0000i	−0.396708	+	0.793416i
$916$	−7.00000	+	12.1244i	−0.231287	+	0.400600i
$917$			48.0000i			1.58510i
$918$	5.19615	−	3.00000i	0.171499	−	0.0990148i
$919$	38.0000			1.25350			0.626752	−	0.779219i	$-0.284384\pi$
$919$	38.0000			1.25350			0.626752	+	0.779219i	$0.284384\pi$
$920$	0.937822	+	15.6244i	0.0309191	+	0.515120i
$921$	16.0000	+	27.7128i	0.527218	+	0.913168i
$922$	20.7846	−	12.0000i	0.684505	−	0.395199i
$923$	−15.5885	−	9.00000i	−0.513100	−	0.296239i
$924$	−4.00000			−0.131590
$925$	−29.7942	+	6.10770i	−0.979628	+	0.200820i
$926$	−16.0000			−0.525793
$927$	−11.2583	−	6.50000i	−0.369772	−	0.213488i
$928$	−8.66025	+	5.00000i	−0.284287	+	0.164133i
$929$	0.500000	+	0.866025i	0.0164045	+	0.0284134i	0.874111	−	0.485726i	$-0.161445\pi$
$929$	0.500000	+	0.866025i	0.0164045	+	0.0284134i	−0.857707	+	0.514139i	$0.828111\pi$
$930$		0			0
$931$	45.0000			1.47482
$932$	−5.19615	+	3.00000i	−0.170206	+	0.0982683i
$933$		−	20.0000i		−	0.654771i
$934$	17.0000	−	29.4449i	0.556257	−	0.963465i
$935$	6.00000	−	12.0000i	0.196221	−	0.392442i
$936$	−3.00000			−0.0980581
$937$	−25.9808	−	15.0000i	−0.848755	−	0.490029i	0.0114759	−	0.999934i	$-0.496347\pi$
$937$	−25.9808	−	15.0000i	−0.848755	−	0.490029i	−0.860230	+	0.509906i	$0.829680\pi$
$938$	−34.6410	+	20.0000i	−1.13107	+	0.653023i
$939$	−8.00000			−0.261070
$940$	3.69615	+	5.59808i	0.120555	+	0.182589i
$941$	−30.0000	+	51.9615i	−0.977972	+	1.69390i	−0.308215	+	0.951317i	$0.599732\pi$
$941$	−30.0000	+	51.9615i	−0.977972	+	1.69390i	−0.669757	+	0.742581i	$0.733602\pi$
$942$	−0.866025	−	0.500000i	−0.0282166	−	0.0162909i
$943$	12.1244	−	7.00000i	0.394823	−	0.227951i
$944$	5.50000	+	9.52628i	0.179010	+	0.310054i
$945$	7.46410	−	4.92820i	0.242807	−	0.160314i
$946$	3.00000	−	5.19615i	0.0975384	−	0.168941i
$947$	−5.19615	−	3.00000i	−0.168852	−	0.0974869i	0.413192	−	0.910644i	$-0.364414\pi$
$947$	−5.19615	−	3.00000i	−0.168852	−	0.0974869i	−0.582045	+	0.813157i	$0.697747\pi$
$948$			8.00000i			0.259828i
$949$	−21.0000	−	36.3731i	−0.681689	−	1.18072i
$950$	2.99038	+	24.8205i	0.0970208	+	0.805284i
$951$	−17.0000			−0.551263
$952$		−	24.0000i		−	0.777844i
$953$	−38.1051	−	22.0000i	−1.23435	−	0.712650i	−0.266413	−	0.963859i	$-0.585838\pi$
$953$	−38.1051	−	22.0000i	−1.23435	−	0.712650i	−0.967933	+	0.251209i	$0.919172\pi$
$954$	−2.00000			−0.0647524
$955$		0			0
$956$	−16.0000			−0.517477
$957$	8.66025	−	5.00000i	0.279946	−	0.161627i
$958$	−15.5885	+	9.00000i	−0.503640	+	0.290777i
$959$	−12.0000	−	20.7846i	−0.387500	−	0.671170i
$960$	−1.23205	−	1.86603i	−0.0397643	−	0.0602257i
$961$	−31.0000			−1.00000
$962$	−18.1865	+	1.50000i	−0.586357	+	0.0483619i
$963$			16.0000i			0.515593i
$964$	−12.5000	+	21.6506i	−0.402598	+	0.697320i
$965$	−8.92820	+	0.535898i	−0.287409	+	0.0172512i
$966$	−14.0000	−	24.2487i	−0.450443	−	0.780189i
$967$	−25.1147	+	14.5000i	−0.807635	+	0.466289i	−0.846134	−	0.532970i	$-0.821076\pi$
$967$	−25.1147	+	14.5000i	−0.807635	+	0.466289i	0.0384986	+	0.999259i	$0.487742\pi$
$968$			10.0000i			0.321412i
$969$	−15.0000	−	25.9808i	−0.481869	−	0.834622i
$970$	−36.0000	−	18.0000i	−1.15589	−	0.577945i
$971$	11.5000	−	19.9186i	0.369053	−	0.639218i	−0.620365	−	0.784313i	$-0.713016\pi$
$971$	11.5000	−	19.9186i	0.369053	−	0.639218i	0.989418	+	0.145095i	$0.0463489\pi$
$972$			1.00000i			0.0320750i
$973$			52.0000i			1.66704i
$974$	−16.0000	+	27.7128i	−0.512673	+	0.887976i
$975$	5.89230	−	13.7942i	0.188705	−	0.441769i
$976$	−12.0000			−0.384111
$977$	6.92820	+	4.00000i	0.221653	+	0.127971i	0.606715	−	0.794919i	$-0.292487\pi$
$977$	6.92820	+	4.00000i	0.221653	+	0.127971i	−0.385063	+	0.922890i	$0.625820\pi$
$978$	12.1244	+	7.00000i	0.387694	+	0.223835i
$979$	2.50000	−	4.33013i	0.0799003	−	0.138391i
$980$	−1.20577	−	20.0885i	−0.0385170	−	0.641702i
$981$	−1.00000	−	1.73205i	−0.0319275	−	0.0553001i
$982$	−30.3109	−	17.5000i	−0.967259	−	0.558447i
$983$	7.79423	+	4.50000i	0.248597	+	0.143528i	0.619122	−	0.785295i	$-0.287489\pi$
$983$	7.79423	+	4.50000i	0.248597	+	0.143528i	−0.370525	+	0.928823i	$0.620822\pi$
$984$	−1.00000	+	1.73205i	−0.0318788	+	0.0552158i
$985$	18.0000	−	36.0000i	0.573528	−	1.14706i
$986$	30.0000	+	51.9615i	0.955395	+	1.65479i
$987$	−10.3923	−	6.00000i	−0.330791	−	0.190982i
$988$			15.0000i			0.477214i
$989$	42.0000			1.33552
$990$	1.23205	+	1.86603i	0.0391571	+	0.0593062i
$991$	34.0000			1.08005			0.540023	−	0.841650i	$-0.318416\pi$
$991$	34.0000			1.08005			0.540023	+	0.841650i	$0.318416\pi$
$992$		0			0
$993$		−	19.0000i		−	0.602947i
$994$	12.0000	+	20.7846i	0.380617	+	0.659248i
$995$	1.33975	+	22.3205i	0.0424728	+	0.707608i
$996$	5.00000	+	8.66025i	0.158431	+	0.274411i
$997$	2.59808	+	1.50000i	0.0822819	+	0.0475055i	0.540576	−	0.841295i	$-0.318206\pi$
$997$	2.59808	+	1.50000i	0.0822819	+	0.0475055i	−0.458295	+	0.888800i	$0.651540\pi$
$998$		−	12.0000i		−	0.379853i
$999$	0.500000	+	6.06218i	0.0158193	+	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.bb.a.1009.1	✓	4
5.4	even	2	inner	1110.2.bb.a.1009.2	yes	4
37.26	even	3	inner	1110.2.bb.a.1099.2	yes	4
185.174	even	6	inner	1110.2.bb.a.1099.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.a.1009.1	✓	4	1.1	even	1	trivial
1110.2.bb.a.1009.2	yes	4	5.4	even	2	inner
1110.2.bb.a.1099.1	yes	4	185.174	even	6	inner
1110.2.bb.a.1099.2	yes	4	37.26	even	3	inner

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.133975 - 2.23205i) q^{5} +1.00000 q^{6} +(3.46410 - 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.133975 - 2.23205i) q^{5} +1.00000 q^{6} +(3.46410 - 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.00000 + 2.00000i) q^{10} +1.00000 q^{11} +(-0.866025 - 0.500000i) q^{12} +(2.59808 - 1.50000i) q^{13} -4.00000 q^{14} +(1.23205 + 1.86603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(5.19615 + 3.00000i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(2.50000 + 4.33013i) q^{19} +(1.86603 - 1.23205i) q^{20} +(-2.00000 + 3.46410i) q^{21} +(-0.866025 - 0.500000i) q^{22} -7.00000i q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.96410 + 0.598076i) q^{25} -3.00000 q^{26} +1.00000i q^{27} +(3.46410 + 2.00000i) q^{28} -10.0000 q^{29} +(-0.133975 - 2.23205i) q^{30} +(0.866025 - 0.500000i) q^{32} +(-0.866025 + 0.500000i) q^{33} +(-3.00000 - 5.19615i) q^{34} +(-4.92820 - 7.46410i) q^{35} +1.00000 q^{36} +(6.06218 - 0.500000i) q^{37} -5.00000i q^{38} +(-1.50000 + 2.59808i) q^{39} +(-2.23205 + 0.133975i) q^{40} +(1.00000 + 1.73205i) q^{41} +(3.46410 - 2.00000i) q^{42} +6.00000i q^{43} +(0.500000 + 0.866025i) q^{44} +(-2.00000 - 1.00000i) q^{45} +(-3.50000 + 6.06218i) q^{46} +3.00000i q^{47} -1.00000i q^{48} +(4.50000 - 7.79423i) q^{49} +(4.59808 + 1.96410i) q^{50} -6.00000 q^{51} +(2.59808 + 1.50000i) q^{52} +(1.73205 + 1.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.133975 - 2.23205i) q^{55} +(-2.00000 - 3.46410i) q^{56} +(-4.33013 - 2.50000i) q^{57} +(8.66025 + 5.00000i) q^{58} +(5.50000 - 9.52628i) q^{59} +(-1.00000 + 2.00000i) q^{60} +(6.00000 + 10.3923i) q^{61} -4.00000i q^{63} -1.00000 q^{64} +(-3.69615 - 5.59808i) q^{65} +1.00000 q^{66} +(8.66025 - 5.00000i) q^{67} +6.00000i q^{68} +(3.50000 + 6.06218i) q^{69} +(0.535898 + 8.92820i) q^{70} +(-3.00000 - 5.19615i) q^{71} +(-0.866025 - 0.500000i) q^{72} -14.0000i q^{73} +(-5.50000 - 2.59808i) q^{74} +(4.00000 - 3.00000i) q^{75} +(-2.50000 + 4.33013i) q^{76} +(3.46410 - 2.00000i) q^{77} +(2.59808 - 1.50000i) q^{78} +(-4.00000 - 6.92820i) q^{79} +(2.00000 + 1.00000i) q^{80} +(-0.500000 - 0.866025i) q^{81} -2.00000i q^{82} +(-8.66025 - 5.00000i) q^{83} -4.00000 q^{84} +(6.00000 - 12.0000i) q^{85} +(3.00000 - 5.19615i) q^{86} +(8.66025 - 5.00000i) q^{87} -1.00000i q^{88} +(2.50000 - 4.33013i) q^{89} +(1.23205 + 1.86603i) q^{90} +(6.00000 - 10.3923i) q^{91} +(6.06218 - 3.50000i) q^{92} +(1.50000 - 2.59808i) q^{94} +(9.33013 - 6.16025i) q^{95} +(-0.500000 + 0.866025i) q^{96} +18.0000i q^{97} +(-7.79423 + 4.50000i) q^{98} +(0.500000 - 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{9} - 4 q^{10} + 4 q^{11} - 16 q^{14} - 2 q^{15} - 2 q^{16} + 10 q^{19} + 4 q^{20} - 8 q^{21} + 2 q^{24} - 6 q^{25} - 12 q^{26} - 40 q^{29} - 4 q^{30} - 12 q^{34} + 8 q^{35} + 4 q^{36} - 6 q^{39} - 2 q^{40} + 4 q^{41} + 2 q^{44} - 8 q^{45} - 14 q^{46} + 18 q^{49} + 8 q^{50} - 24 q^{51} + 2 q^{54} - 4 q^{55} - 8 q^{56} + 22 q^{59} - 4 q^{60} + 24 q^{61} - 4 q^{64} + 6 q^{65} + 4 q^{66} + 14 q^{69} + 16 q^{70} - 12 q^{71} - 22 q^{74} + 16 q^{75} - 10 q^{76} - 16 q^{79} + 8 q^{80} - 2 q^{81} - 16 q^{84} + 24 q^{85} + 12 q^{86} + 10 q^{89} - 2 q^{90} + 24 q^{91} + 6 q^{94} + 20 q^{95} - 2 q^{96} + 2 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^9 - 4 * q^10 + 4 * q^11 - 16 * q^14 - 2 * q^15 - 2 * q^16 + 10 * q^19 + 4 * q^20 - 8 * q^21 + 2 * q^24 - 6 * q^25 - 12 * q^26 - 40 * q^29 - 4 * q^30 - 12 * q^34 + 8 * q^35 + 4 * q^36 - 6 * q^39 - 2 * q^40 + 4 * q^41 + 2 * q^44 - 8 * q^45 - 14 * q^46 + 18 * q^49 + 8 * q^50 - 24 * q^51 + 2 * q^54 - 4 * q^55 - 8 * q^56 + 22 * q^59 - 4 * q^60 + 24 * q^61 - 4 * q^64 + 6 * q^65 + 4 * q^66 + 14 * q^69 + 16 * q^70 - 12 * q^71 - 22 * q^74 + 16 * q^75 - 10 * q^76 - 16 * q^79 + 8 * q^80 - 2 * q^81 - 16 * q^84 + 24 * q^85 + 12 * q^86 + 10 * q^89 - 2 * q^90 + 24 * q^91 + 6 * q^94 + 20 * q^95 - 2 * q^96 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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