LMFDB - Embedded newform 546.2.by.a.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (of order $12$, degree $4$, 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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.4
Character	$\chi$	$=$	546.19
Dual form			546.2.by.a.115.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(3.74075 - 1.00233i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-2.20451 + 1.46293i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(3.74075 - 1.00233i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-2.20451 + 1.46293i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -3.87271 q^{10} +(3.02557 + 3.02557i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(3.26846 - 1.52222i) q^{13} +(2.50802 - 0.842511i) q^{14} +(1.00233 + 3.74075i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.792138 - 1.37202i) q^{17} +(0.965926 + 0.258819i) q^{18} +(0.254457 + 0.254457i) q^{19} +(3.74075 + 1.00233i) q^{20} +(-1.46293 - 2.20451i) q^{21} +(-2.13940 - 3.70555i) q^{22} +(-6.12520 + 3.53639i) q^{23} +(0.707107 - 0.707107i) q^{24} +(8.65839 - 4.99892i) q^{25} +(-3.55107 + 0.624415i) q^{26} -1.00000i q^{27} +(-2.64062 + 0.164680i) q^{28} +(-2.17009 + 3.75870i) q^{29} -3.87271i q^{30} +(0.968081 - 3.61293i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-3.02557 + 3.02557i) q^{33} +(-1.12025 + 1.12025i) q^{34} +(-6.78016 + 7.68208i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-0.503317 + 1.87840i) q^{37} +(-0.179928 - 0.311645i) q^{38} +(1.52222 + 3.26846i) q^{39} +(-3.35386 - 1.93635i) q^{40} +(5.14204 - 1.37781i) q^{41} +(0.842511 + 2.50802i) q^{42} +(7.57309 - 4.37232i) q^{43} +(1.10743 + 4.13300i) q^{44} +(-3.74075 + 1.00233i) q^{45} +(6.83178 - 1.83057i) q^{46} +(0.515596 + 1.92423i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(2.71969 - 6.45006i) q^{49} +(-9.65718 + 2.58763i) q^{50} +(1.37202 + 0.792138i) q^{51} +(3.59168 + 0.315946i) q^{52} +(4.42114 + 7.65764i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(14.3505 + 8.28526i) q^{55} +(2.59327 + 0.524375i) q^{56} +(-0.254457 + 0.254457i) q^{57} +(3.06897 - 3.06897i) q^{58} +(2.31356 + 8.63432i) q^{59} +(-1.00233 + 3.74075i) q^{60} +5.95308i q^{61} +(-1.87019 + 3.23926i) q^{62} +(2.20451 - 1.46293i) q^{63} +1.00000i q^{64} +(10.7007 - 8.97033i) q^{65} +(3.70555 - 2.13940i) q^{66} +(-8.80073 + 8.80073i) q^{67} +(1.37202 - 0.792138i) q^{68} +(-3.53639 - 6.12520i) q^{69} +(8.53740 - 5.66549i) q^{70} +(4.41410 + 1.18275i) q^{71} +(0.707107 + 0.707107i) q^{72} +(-8.88186 - 2.37989i) q^{73} +(0.972333 - 1.68413i) q^{74} +(4.99892 + 8.65839i) q^{75} +(0.0931378 + 0.347595i) q^{76} +(-11.0961 - 2.24369i) q^{77} +(-0.624415 - 3.55107i) q^{78} +(8.16932 - 14.1497i) q^{79} +(2.73842 + 2.73842i) q^{80} +1.00000 q^{81} -5.32344 q^{82} +(-9.65709 - 9.65709i) q^{83} +(-0.164680 - 2.64062i) q^{84} +(1.58797 - 5.92637i) q^{85} +(-8.44668 + 2.26328i) q^{86} +(-3.75870 - 2.17009i) q^{87} -4.27880i q^{88} +(-15.8111 - 4.23657i) q^{89} +3.87271 q^{90} +(-4.97844 + 8.13727i) q^{91} -7.07278 q^{92} +(3.61293 + 0.968081i) q^{93} -1.99211i q^{94} +(1.20691 + 0.696810i) q^{95} +(0.965926 - 0.258819i) q^{96} +(2.68866 - 10.0342i) q^{97} +(-4.29641 + 5.52638i) q^{98} +(-3.02557 - 3.02557i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) $ 32 * q + 8 * q^7 - 32 * q^9	$ 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	3.74075	−	1.00233i	1.67291	−	0.448256i	0.707019	−	0.707195i	$-0.250040\pi$
$5$	3.74075	−	1.00233i	1.67291	−	0.448256i	0.965894	+	0.258939i	$0.0833729\pi$
$6$	0.258819	−	0.965926i	0.105662	−	0.394338i
$7$	−2.20451	+	1.46293i	−0.833225	+	0.552935i
$7$	−2.20451	+	1.46293i	−0.833225	+	0.552935i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	−3.87271			−1.22466
$11$	3.02557	+	3.02557i	0.912243	+	0.912243i	0.996448	−	0.0842056i	$-0.0268353\pi$
$11$	3.02557	+	3.02557i	0.912243	+	0.912243i	−0.0842056	+	0.996448i	$0.526835\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	3.26846	−	1.52222i	0.906508	−	0.422189i
$13$	3.26846	−	1.52222i	0.906508	−	0.422189i
$14$	2.50802	−	0.842511i	0.670297	−	0.225171i
$15$	1.00233	+	3.74075i	0.258800	+	0.965856i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.792138	−	1.37202i	0.192122	−	0.332764i	−0.753832	−	0.657068i	$-0.771797\pi$
$17$	0.792138	−	1.37202i	0.192122	−	0.332764i	0.945953	+	0.324303i	$0.105130\pi$
$18$	0.965926	+	0.258819i	0.227671	+	0.0610042i
$19$	0.254457	+	0.254457i	0.0583765	+	0.0583765i	0.735692	−	0.677316i	$-0.236857\pi$
$19$	0.254457	+	0.254457i	0.0583765	+	0.0583765i	−0.677316	+	0.735692i	$0.736857\pi$
$20$	3.74075	+	1.00233i	0.836456	+	0.224128i
$21$	−1.46293	−	2.20451i	−0.319237	−	0.481062i
$22$	−2.13940	−	3.70555i	−0.456121	−	0.790025i
$23$	−6.12520	+	3.53639i	−1.27719	+	0.737388i	−0.976331	−	0.216280i	$-0.930608\pi$
$23$	−6.12520	+	3.53639i	−1.27719	+	0.737388i	−0.300862	+	0.953668i	$0.597274\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$	8.65839	−	4.99892i	1.73168	−	0.999785i
$26$	−3.55107	+	0.624415i	−0.696422	+	0.122458i
$27$		−	1.00000i		−	0.192450i
$28$	−2.64062	+	0.164680i	−0.499031	+	0.0311215i
$29$	−2.17009	+	3.75870i	−0.402975	+	0.697974i	−0.994084	−	0.108618i	$-0.965357\pi$
$29$	−2.17009	+	3.75870i	−0.402975	+	0.697974i	0.591108	+	0.806592i	$0.298691\pi$
$30$		−	3.87271i		−	0.707056i
$31$	0.968081	−	3.61293i	0.173873	−	0.648901i	−0.822868	−	0.568232i	$-0.807628\pi$
$31$	0.968081	−	3.61293i	0.173873	−	0.648901i	0.996741	−	0.0806691i	$-0.0257057\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−3.02557	+	3.02557i	−0.526684	+	0.526684i
$34$	−1.12025	+	1.12025i	−0.192122	+	0.192122i
$35$	−6.78016	+	7.68208i	−1.14606	+	1.29851i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	−0.503317	+	1.87840i	−0.0827447	+	0.308808i	−0.994878	−	0.101087i	$-0.967768\pi$
$37$	−0.503317	+	1.87840i	−0.0827447	+	0.308808i	0.912133	+	0.409895i	$0.134435\pi$
$38$	−0.179928	−	0.311645i	−0.0291882	−	0.0505555i
$39$	1.52222	+	3.26846i	0.243751	+	0.523373i
$40$	−3.35386	−	1.93635i	−0.530292	−	0.306164i
$41$	5.14204	−	1.37781i	0.803052	−	0.215177i	0.166129	−	0.986104i	$-0.446873\pi$
$41$	5.14204	−	1.37781i	0.803052	−	0.215177i	0.636924	+	0.770927i	$0.280207\pi$
$42$	0.842511	+	2.50802i	0.130002	+	0.386996i
$43$	7.57309	−	4.37232i	1.15488	−	0.666773i	0.204812	−	0.978801i	$-0.434342\pi$
$43$	7.57309	−	4.37232i	1.15488	−	0.666773i	0.950073	+	0.312028i	$0.101008\pi$
$44$	1.10743	+	4.13300i	0.166952	+	0.623073i
$45$	−3.74075	+	1.00233i	−0.557637	+	0.149419i
$46$	6.83178	−	1.83057i	1.00729	−	0.269903i
$47$	0.515596	+	1.92423i	0.0752074	+	0.280678i	0.993280	−	0.115734i	$-0.0369220\pi$
$47$	0.515596	+	1.92423i	0.0752074	+	0.280678i	−0.918073	+	0.396412i	$0.870255\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	2.71969	−	6.45006i	0.388527	−	0.921437i
$50$	−9.65718	+	2.58763i	−1.36573	+	0.365947i
$51$	1.37202	+	0.792138i	0.192122	+	0.110921i
$52$	3.59168	+	0.315946i	0.498077	+	0.0438138i
$53$	4.42114	+	7.65764i	0.607290	+	1.05186i	0.991685	+	0.128689i	$0.0410767\pi$
$53$	4.42114	+	7.65764i	0.607290	+	1.05186i	−0.384395	+	0.923169i	$0.625590\pi$
$54$	−0.258819	+	0.965926i	−0.0352208	+	0.131446i
$55$	14.3505	+	8.28526i	1.93502	+	1.11718i
$56$	2.59327	+	0.524375i	0.346540	+	0.0700725i
$57$	−0.254457	+	0.254457i	−0.0337037	+	0.0337037i
$58$	3.06897	−	3.06897i	0.402975	−	0.402975i
$59$	2.31356	+	8.63432i	0.301200	+	1.12409i	0.936167	+	0.351554i	$0.114347\pi$
$59$	2.31356	+	8.63432i	0.301200	+	1.12409i	−0.634968	+	0.772539i	$0.718987\pi$
$60$	−1.00233	+	3.74075i	−0.129400	+	0.482928i
$61$			5.95308i			0.762214i	0.924531	+	0.381107i	$0.124457\pi$
$61$			5.95308i			0.762214i	−0.924531	+	0.381107i	$0.875543\pi$
$62$	−1.87019	+	3.23926i	−0.237514	+	0.411387i
$63$	2.20451	−	1.46293i	0.277742	−	0.184312i
$64$			1.00000i			0.125000i
$65$	10.7007	−	8.97033i	1.32726	−	1.11263i
$66$	3.70555	−	2.13940i	0.456121	−	0.263342i
$67$	−8.80073	+	8.80073i	−1.07518	+	1.07518i	−0.0782458	+	0.996934i	$0.524932\pi$
$67$	−8.80073	+	8.80073i	−1.07518	+	1.07518i	−0.996934	+	0.0782458i	$0.975068\pi$
$68$	1.37202	−	0.792138i	0.166382	−	0.0960608i
$69$	−3.53639	−	6.12520i	−0.425731	−	0.737388i
$70$	8.53740	−	5.66549i	1.02041	−	0.677155i
$71$	4.41410	+	1.18275i	0.523857	+	0.140367i	0.511050	−	0.859551i	$-0.329257\pi$
$71$	4.41410	+	1.18275i	0.523857	+	0.140367i	0.0128072	+	0.999918i	$0.495923\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	−8.88186	−	2.37989i	−1.03954	−	0.278545i	−0.301619	−	0.953429i	$-0.597527\pi$
$73$	−8.88186	−	2.37989i	−1.03954	−	0.278545i	−0.737924	+	0.674884i	$0.764194\pi$
$74$	0.972333	−	1.68413i	0.113031	−	0.195776i
$75$	4.99892	+	8.65839i	0.577226	+	0.999785i
$76$	0.0931378	+	0.347595i	0.0106836	+	0.0398719i
$77$	−11.0961	−	2.24369i	−1.26451	−	0.255693i
$78$	−0.624415	−	3.55107i	−0.0707011	−	0.402080i
$79$	8.16932	−	14.1497i	0.919120	−	1.59196i	0.118365	−	0.992970i	$-0.462235\pi$
$79$	8.16932	−	14.1497i	0.919120	−	1.59196i	0.800755	−	0.598993i	$-0.204432\pi$
$80$	2.73842	+	2.73842i	0.306164	+	0.306164i
$81$	1.00000			0.111111
$82$	−5.32344			−0.587875
$83$	−9.65709	−	9.65709i	−1.06000	−	1.06000i	−0.998081	−	0.0619219i	$-0.980277\pi$
$83$	−9.65709	−	9.65709i	−1.06000	−	1.06000i	−0.0619219	−	0.998081i	$-0.519723\pi$
$84$	−0.164680	−	2.64062i	−0.0179680	−	0.288115i
$85$	1.58797	−	5.92637i	0.172239	−	0.642805i
$86$	−8.44668	+	2.26328i	−0.910829	+	0.244056i
$87$	−3.75870	−	2.17009i	−0.402975	−	0.232658i
$88$		−	4.27880i		−	0.456121i
$89$	−15.8111	−	4.23657i	−1.67597	−	0.449076i	−0.709262	−	0.704945i	$-0.750972\pi$
$89$	−15.8111	−	4.23657i	−1.67597	−	0.449076i	−0.966712	+	0.255869i	$0.917639\pi$
$90$	3.87271			0.408219
$91$	−4.97844	+	8.13727i	−0.521882	+	0.853018i
$92$	−7.07278			−0.737388
$93$	3.61293	+	0.968081i	0.374643	+	0.100385i
$94$		−	1.99211i		−	0.205470i
$95$	1.20691	+	0.696810i	0.123826	+	0.0714912i
$96$	0.965926	−	0.258819i	0.0985844	−	0.0264156i
$97$	2.68866	−	10.0342i	0.272992	−	1.01882i	−0.684183	−	0.729310i	$-0.739841\pi$
$97$	2.68866	−	10.0342i	0.272992	−	1.01882i	0.957175	−	0.289510i	$-0.0934923\pi$
$98$	−4.29641	+	5.52638i	−0.434003	+	0.558248i
$99$	−3.02557	−	3.02557i	−0.304081	−	0.304081i
$100$	9.99785			0.999785
$101$	12.4787			1.24168			0.620840	−	0.783938i	$-0.286792\pi$
$101$	12.4787			1.24168			0.620840	+	0.783938i	$0.286792\pi$
$102$	−1.12025	−	1.12025i	−0.110921	−	0.110921i
$103$	0.784555	−	1.35889i	0.0773045	−	0.133895i	−0.824782	−	0.565451i	$-0.808702\pi$
$103$	0.784555	−	1.35889i	0.0773045	−	0.133895i	0.902086	+	0.431556i	$0.142035\pi$
$104$	−3.38753	−	1.23478i	−0.332174	−	0.121080i
$105$	−7.68208	−	6.78016i	−0.749694	−	0.661676i
$106$	−2.28855	−	8.54098i	−0.222284	−	0.829574i
$107$	−4.32759	−	7.49560i	−0.418364	−	0.724627i	0.577411	−	0.816453i	$-0.304063\pi$
$107$	−4.32759	−	7.49560i	−0.418364	−	0.724627i	−0.995775	+	0.0918261i	$0.970730\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−9.65675	−	2.58752i	−0.924949	−	0.247839i	−0.235249	−	0.971935i	$-0.575591\pi$
$109$	−9.65675	−	2.58752i	−0.924949	−	0.247839i	−0.689699	+	0.724096i	$0.742257\pi$
$110$	−11.7171	−	11.7171i	−1.11718	−	1.11718i
$111$	−1.87840	−	0.503317i	−0.178290	−	0.0477727i
$112$	−2.36918	−	1.17769i	−0.223867	−	0.111282i
$113$	−1.11853	−	1.93735i	−0.105223	−	0.182251i	0.808607	−	0.588350i	$-0.200222\pi$
$113$	−1.11853	−	1.93735i	−0.105223	−	0.182251i	−0.913829	+	0.406099i	$0.866889\pi$
$114$	0.311645	−	0.179928i	0.0291882	−	0.0168518i
$115$	−19.3682	+	19.3682i	−1.80609	+	1.80609i
$116$	−3.75870	+	2.17009i	−0.348987	+	0.201488i
$117$	−3.26846	+	1.52222i	−0.302169	+	0.140730i
$118$		−	8.93891i		−	0.822893i
$119$	0.260898	+	4.18347i	0.0239165	+	0.383498i
$120$	1.93635	−	3.35386i	0.176764	−	0.306164i
$121$			7.30811i			0.664374i
$122$	1.54077	−	5.75024i	0.139495	−	0.520602i
$123$	1.37781	+	5.14204i	0.124233	+	0.463642i
$124$	2.64485	−	2.64485i	0.237514	−	0.237514i
$125$	13.6862	−	13.6862i	1.22413	−	1.22413i
$126$	−2.50802	+	0.842511i	−0.223432	+	0.0750569i
$127$	−16.0382	−	9.25967i	−1.42316	−	0.821662i	−0.426593	−	0.904444i	$-0.640286\pi$
$127$	−16.0382	−	9.25967i	−1.42316	−	0.821662i	−0.996568	+	0.0827811i	$0.973620\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	4.37232	+	7.57309i	0.384962	+	0.666773i
$130$	−12.6578	+	5.89512i	−1.11016	+	0.517037i
$131$	11.1843	+	6.45723i	0.977173	+	0.564171i	0.901416	−	0.432955i	$-0.142529\pi$
$131$	11.1843	+	6.45723i	0.977173	+	0.564171i	0.0757577	+	0.997126i	$0.475862\pi$
$132$	−4.13300	+	1.10743i	−0.359732	+	0.0963898i
$133$	−0.933205	−	0.188700i	−0.0809191	−	0.0163624i
$134$	10.7786	−	6.22305i	0.931133	−	0.537590i
$135$	−1.00233	−	3.74075i	−0.0862668	−	0.321952i
$136$	−1.53029	+	0.410041i	−0.131222	+	0.0351607i
$137$	−8.55322	+	2.29183i	−0.730751	+	0.195804i	−0.604963	−	0.796253i	$-0.706812\pi$
$137$	−8.55322	+	2.29183i	−0.730751	+	0.195804i	−0.125787	+	0.992057i	$0.540146\pi$
$138$	1.83057	+	6.83178i	0.155828	+	0.581559i
$139$	−0.440191	+	0.254144i	−0.0373365	+	0.0215562i	−0.518552	−	0.855046i	$-0.673529\pi$
$139$	−0.440191	+	0.254144i	−0.0373365	+	0.0215562i	0.481216	+	0.876602i	$0.340195\pi$
$140$	−9.71283	+	3.26280i	−0.820884	+	0.275757i
$141$	−1.92423	+	0.515596i	−0.162049	+	0.0434210i
$142$	−3.95758	−	2.28491i	−0.332112	−	0.191745i
$143$	14.4945	+	5.28336i	1.21209	+	0.441817i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−4.35029	+	16.2355i	−0.361272	+	1.34829i
$146$	7.96326	+	4.59759i	0.659044	+	0.380499i
$147$	6.45006	+	2.71969i	0.531992	+	0.224316i
$148$	−1.37509	+	1.37509i	−0.113031	+	0.113031i
$149$	−12.3997	+	12.3997i	−1.01582	+	1.01582i	−0.0159487	+	0.999873i	$0.505077\pi$
$149$	−12.3997	+	12.3997i	−1.01582	+	1.01582i	−0.999873	+	0.0159487i	$0.994923\pi$
$150$	−2.58763	−	9.65718i	−0.211279	−	0.788505i
$151$	5.92821	−	22.1244i	0.482431	−	1.80046i	−0.108928	−	0.994050i	$-0.534742\pi$
$151$	5.92821	−	22.1244i	0.482431	−	1.80046i	0.591360	−	0.806408i	$-0.298591\pi$
$152$		−	0.359857i		−	0.0291882i
$153$	−0.792138	+	1.37202i	−0.0640405	+	0.110921i
$154$	10.1373	+	5.03911i	0.816884	+	0.406063i
$155$		−	14.4854i		−	1.16349i
$156$	−0.315946	+	3.59168i	−0.0252959	+	0.287565i
$157$	−0.568262	+	0.328086i	−0.0453523	+	0.0261841i	−0.522505	−	0.852636i	$-0.675002\pi$
$157$	−0.568262	+	0.328086i	−0.0453523	+	0.0261841i	0.477152	+	0.878821i	$0.341669\pi$
$158$	−11.5532	+	11.5532i	−0.919120	+	0.919120i
$159$	−7.65764	+	4.42114i	−0.607290	+	0.350619i
$160$	−1.93635	−	3.35386i	−0.153082	−	0.265146i
$161$	8.32956	−	16.7567i	0.656462	−	1.32061i
$162$	−0.965926	−	0.258819i	−0.0758903	−	0.0203347i
$163$	−13.9241	−	13.9241i	−1.09062	−	1.09062i	−0.995463	−	0.0951546i	$-0.969665\pi$
$163$	−13.9241	−	13.9241i	−1.09062	−	1.09062i	−0.0951546	−	0.995463i	$-0.530335\pi$
$164$	5.14204	+	1.37781i	0.401526	+	0.107589i
$165$	−8.28526	+	14.3505i	−0.645007	+	1.11718i
$166$	6.82859	+	11.8275i	0.530001	+	0.917989i
$167$	−3.53213	−	13.1821i	−0.273325	−	1.02006i	−0.956956	−	0.290234i	$-0.906267\pi$
$167$	−3.53213	−	13.1821i	−0.273325	−	1.02006i	0.683631	−	0.729828i	$-0.260400\pi$
$168$	−0.524375	+	2.59327i	−0.0404564	+	0.200075i
$169$	8.36567	−	9.95066i	0.643513	−	0.765435i
$170$	−3.06772	+	5.31344i	−0.235283	+	0.407522i
$171$	−0.254457	−	0.254457i	−0.0194588	−	0.0194588i
$172$	8.74465			0.666773
$173$	17.6805			1.34422			0.672112	−	0.740450i	$-0.265387\pi$
$173$	17.6805			1.34422			0.672112	+	0.740450i	$0.265387\pi$
$174$	3.06897	+	3.06897i	0.232658	+	0.232658i
$175$	−11.7744	+	23.6867i	−0.890061	+	1.79055i
$176$	−1.10743	+	4.13300i	−0.0834760	+	0.311537i
$177$	−8.63432	+	2.31356i	−0.648996	+	0.173898i
$178$	14.1759	+	8.18443i	1.06252	+	0.613449i
$179$		−	1.47632i		−	0.110345i	−0.998477	−	0.0551726i	$-0.982429\pi$
$179$		−	1.47632i		−	0.110345i	0.998477	−	0.0551726i	$-0.0175709\pi$
$180$	−3.74075	−	1.00233i	−0.278819	−	0.0747093i
$181$	−14.3938			−1.06988			−0.534941	−	0.844889i	$-0.679666\pi$
$181$	−14.3938			−1.06988			−0.534941	+	0.844889i	$0.679666\pi$
$182$	6.91488	−	6.57149i	0.512565	−	0.487111i
$183$	−5.95308			−0.440065
$184$	6.83178	+	1.83057i	0.503645	+	0.134951i
$185$			7.53112i			0.553699i
$186$	−3.23926	−	1.87019i	−0.237514	−	0.137129i
$187$	6.54781	−	1.75448i	0.478824	−	0.128300i
$188$	−0.515596	+	1.92423i	−0.0376037	+	0.140339i
$189$	1.46293	+	2.20451i	0.106412	+	0.160354i
$190$	−0.985438	−	0.985438i	−0.0714912	−	0.0714912i
$191$	0.654823			0.0473813			0.0236907	−	0.999719i	$-0.492458\pi$
$191$	0.654823			0.0473813			0.0236907	+	0.999719i	$0.492458\pi$
$192$	−1.00000			−0.0721688
$193$	−2.35226	−	2.35226i	−0.169319	−	0.169319i	0.617361	−	0.786680i	$-0.288202\pi$
$193$	−2.35226	−	2.35226i	−0.169319	−	0.169319i	−0.786680	+	0.617361i	$0.788202\pi$
$194$	−5.19409	+	8.99643i	−0.372914	+	0.645906i
$195$	8.97033	+	10.7007i	0.642379	+	0.766294i
$196$	5.58035	−	4.22607i	0.398596	−	0.301862i
$197$	−2.47071	−	9.22081i	−0.176031	−	0.656955i	−0.996374	−	0.0850838i	$-0.972884\pi$
$197$	−2.47071	−	9.22081i	−0.176031	−	0.656955i	0.820343	−	0.571872i	$-0.193782\pi$
$198$	2.13940	+	3.70555i	0.152040	+	0.263342i
$199$	−7.92030	+	13.7184i	−0.561455	+	0.972469i	0.435915	+	0.899988i	$0.356425\pi$
$199$	−7.92030	+	13.7184i	−0.561455	+	0.972469i	−0.997370	+	0.0724809i	$0.976908\pi$
$200$	−9.65718	−	2.58763i	−0.682866	−	0.182973i
$201$	−8.80073	−	8.80073i	−0.620755	−	0.620755i
$202$	−12.0535	−	3.22973i	−0.848083	−	0.227243i
$203$	−0.714739	−	11.4608i	−0.0501649	−	0.804388i
$204$	0.792138	+	1.37202i	0.0554607	+	0.0960608i
$205$	17.8541	−	10.3080i	1.24698	−	0.719945i
$206$	−1.10953	+	1.10953i	−0.0773045	+	0.0773045i
$207$	6.12520	−	3.53639i	0.425731	−	0.245796i
$208$	2.95251	+	2.06946i	0.204720	+	0.143491i
$209$			1.53975i			0.106507i
$210$	5.66549	+	8.53740i	0.390956	+	0.589136i
$211$	3.78670	−	6.55876i	0.260687	−	0.451524i	−0.705737	−	0.708473i	$-0.749384\pi$
$211$	3.78670	−	6.55876i	0.260687	−	0.451524i	0.966425	+	0.256950i	$0.0827175\pi$
$212$			8.84228i			0.607290i
$213$	−1.18275	+	4.41410i	−0.0810410	+	0.302449i
$214$	2.24012	+	8.36026i	0.153132	+	0.571496i
$215$	23.9465	−	23.9465i	1.63314	−	1.63314i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	3.15131	+	9.38095i	0.213925	+	0.636820i
$218$	8.65800	+	4.99870i	0.586394	+	0.338555i
$219$	2.37989	−	8.88186i	0.160818	−	0.600180i
$220$	8.28526	+	14.3505i	0.558592	+	0.967510i
$221$	0.500546	−	5.69021i	0.0336703	−	0.382765i
$222$	1.68413	+	0.972333i	0.113031	+	0.0652587i
$223$	13.7367	−	3.68073i	0.919877	−	0.246480i	0.232344	−	0.972634i	$-0.425361\pi$
$223$	13.7367	−	3.68073i	0.919877	−	0.246480i	0.687533	+	0.726154i	$0.258694\pi$
$224$	1.98365	+	1.75076i	0.132538	+	0.116977i
$225$	−8.65839	+	4.99892i	−0.577226	+	0.333262i
$226$	0.578994	+	2.16084i	0.0385141	+	0.143737i
$227$	−25.6700	+	6.87826i	−1.70378	+	0.456526i	−0.973887	−	0.227035i	$-0.927097\pi$
$227$	−25.6700	+	6.87826i	−1.70378	+	0.456526i	−0.729893	+	0.683561i	$0.760430\pi$
$228$	−0.347595	+	0.0931378i	−0.0230200	+	0.00616820i
$229$	1.60726	+	5.99836i	0.106211	+	0.396383i	0.998480	−	0.0551208i	$-0.0175544\pi$
$229$	1.60726	+	5.99836i	0.106211	+	0.396383i	−0.892269	+	0.451504i	$0.850888\pi$
$230$	23.7211	−	13.6954i	1.56412	−	0.903047i
$231$	2.24369	−	11.0961i	0.147624	−	0.730067i
$232$	4.19229	−	1.12332i	0.275237	−	0.0737496i
$233$	−15.8168	−	9.13186i	−1.03620	−	0.598248i	−0.117442	−	0.993080i	$-0.537469\pi$
$233$	−15.8168	−	9.13186i	−1.03620	−	0.598248i	−0.918753	+	0.394832i	$0.870803\pi$
$234$	3.55107	−	0.624415i	0.232141	−	0.0408193i
$235$	3.85743	+	6.68126i	0.251631	+	0.435837i
$236$	−2.31356	+	8.63432i	−0.150600	+	0.562047i
$237$	14.1497	+	8.16932i	0.919120	+	0.530654i
$238$	0.830754	−	4.10845i	0.0538498	−	0.266311i
$239$	0.158134	−	0.158134i	0.0102288	−	0.0102288i	−0.701974	−	0.712203i	$-0.747698\pi$
$239$	0.158134	−	0.158134i	0.0102288	−	0.0102288i	0.712203	+	0.701974i	$0.247698\pi$
$240$	−2.73842	+	2.73842i	−0.176764	+	0.176764i
$241$	−3.45246	−	12.8848i	−0.222393	−	0.829981i	−0.983432	−	0.181275i	$-0.941977\pi$
$241$	−3.45246	−	12.8848i	−0.222393	−	0.829981i	0.761040	−	0.648705i	$-0.224689\pi$
$242$	1.89148	−	7.05909i	0.121589	−	0.453776i
$243$			1.00000i			0.0641500i
$244$	−2.97654	+	5.15552i	−0.190554	+	0.330049i
$245$	3.70857	−	26.8541i	0.236932	−	1.71564i
$246$		−	5.32344i		−	0.339410i
$247$	1.21902	+	0.444343i	0.0775647	+	0.0282728i
$248$	−3.23926	+	1.87019i	−0.205693	+	0.118757i
$249$	9.65709	−	9.65709i	0.611993	−	0.611993i
$250$	−16.7621	+	9.67759i	−1.06013	+	0.612065i
$251$	2.49027	+	4.31328i	0.157184	+	0.272252i	0.933852	−	0.357659i	$-0.116425\pi$
$251$	2.49027	+	4.31328i	0.157184	+	0.272252i	−0.776668	+	0.629910i	$0.783092\pi$
$252$	2.64062	−	0.164680i	0.166344	−	0.0103738i
$253$	−29.2318	−	7.83264i	−1.83779	−	0.492434i
$254$	13.0951	+	13.0951i	0.821662	+	0.821662i
$255$	5.92637	+	1.58797i	0.371124	+	0.0994423i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.79093	−	6.56609i	−0.236472	−	0.409581i	0.723228	−	0.690610i	$-0.242658\pi$
$257$	−3.79093	−	6.56609i	−0.236472	−	0.409581i	−0.959699	+	0.281029i	$0.909324\pi$
$258$	−2.26328	−	8.44668i	−0.140906	−	0.525867i
$259$	−1.63840	−	4.87727i	−0.101805	−	0.303059i
$260$	13.7523	−	2.41818i	0.852878	−	0.149969i
$261$	2.17009	−	3.75870i	0.134325	−	0.232658i
$262$	−9.13191	−	9.13191i	−0.564171	−	0.564171i
$263$	−25.9242			−1.59856			−0.799278	−	0.600962i	$-0.794784\pi$
$263$	−25.9242			−1.59856			−0.799278	+	0.600962i	$0.794784\pi$
$264$	4.27880			0.263342
$265$	24.2138	+	24.2138i	1.48744	+	1.48744i
$266$	0.852568	+	0.423801i	0.0522743	+	0.0259849i
$267$	4.23657	−	15.8111i	0.259274	−	0.967624i
$268$	−12.0220	+	3.22129i	−0.734362	+	0.196772i
$269$	8.29785	+	4.79077i	0.505929	+	0.292098i	0.731159	−	0.682207i	$-0.238980\pi$
$269$	8.29785	+	4.79077i	0.505929	+	0.292098i	−0.225230	+	0.974306i	$0.572313\pi$
$270$			3.87271i			0.235685i
$271$	12.5689	+	3.36783i	0.763507	+	0.204581i	0.619501	−	0.784996i	$-0.287335\pi$
$271$	12.5689	+	3.36783i	0.763507	+	0.204581i	0.144006	+	0.989577i	$0.454002\pi$
$272$	1.58428			0.0960608
$273$	−8.13727	−	4.97844i	−0.492490	−	0.301309i
$274$	8.85494			0.534947
$275$	41.3211	+	11.0720i	2.49176	+	0.667664i
$276$		−	7.07278i		−	0.425731i
$277$	−8.14723	−	4.70380i	−0.489519	−	0.282624i	0.234856	−	0.972030i	$-0.424538\pi$
$277$	−8.14723	−	4.70380i	−0.489519	−	0.282624i	−0.724375	+	0.689406i	$0.757872\pi$
$278$	0.490969	−	0.131555i	0.0294464	−	0.00789013i
$279$	−0.968081	+	3.61293i	−0.0579575	+	0.216300i
$280$	10.2263	−	0.637756i	0.611141	−	0.0381132i
$281$	−6.76237	−	6.76237i	−0.403409	−	0.403409i	0.476024	−	0.879433i	$-0.342078\pi$
$281$	−6.76237	−	6.76237i	−0.403409	−	0.403409i	−0.879433	+	0.476024i	$0.842078\pi$
$282$	1.99211			0.118628
$283$	2.35306			0.139875			0.0699375	−	0.997551i	$-0.477720\pi$
$283$	2.35306			0.139875			0.0699375	+	0.997551i	$0.477720\pi$
$284$	3.23135	+	3.23135i	0.191745	+	0.191745i
$285$	−0.696810	+	1.20691i	−0.0412755	+	0.0714912i
$286$	−12.6332	−	8.85479i	−0.747018	−	0.523595i
$287$	−9.32003	+	10.5598i	−0.550144	+	0.623326i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	7.24504	+	12.5488i	0.426179	+	0.738163i
$290$	8.40412	−	14.5564i	0.493507	−	0.854779i
$291$	10.0342	+	2.68866i	0.588216	+	0.157612i
$292$	−6.50197	−	6.50197i	−0.380499	−	0.380499i
$293$	18.0335	+	4.83207i	1.05353	+	0.282292i	0.743710	−	0.668503i	$-0.233065\pi$
$293$	18.0335	+	4.83207i	1.05353	+	0.282292i	0.309820	+	0.950795i	$0.399731\pi$
$294$	−5.52638	−	4.29641i	−0.322305	−	0.250572i
$295$	17.3089	+	29.9799i	1.00776	+	1.74550i
$296$	1.68413	−	0.972333i	0.0978881	−	0.0565157i
$297$	3.02557	−	3.02557i	0.175561	−	0.175561i
$298$	15.1864	−	8.76790i	0.879727	−	0.507911i
$299$	−14.6368	+	20.8825i	−0.846469	+	1.20766i
$300$			9.99785i			0.577226i
$301$	−10.2985	+	20.7177i	−0.593597	+	1.19415i
$302$	−11.4524	+	19.8362i	−0.659013	+	1.14144i
$303$			12.4787i			0.716884i
$304$	−0.0931378	+	0.347595i	−0.00534182	+	0.0199359i
$305$	5.96695	+	22.2690i	0.341667	+	1.27512i
$306$	1.12025	−	1.12025i	0.0640405	−	0.0640405i
$307$	−1.49765	+	1.49765i	−0.0854756	+	0.0854756i	−0.748552	−	0.663076i	$-0.769250\pi$
$307$	−1.49765	+	1.49765i	−0.0854756	+	0.0854756i	0.663076	+	0.748552i	$0.269250\pi$
$308$	−8.48763	−	7.49113i	−0.483627	−	0.426847i
$309$	1.35889	+	0.784555i	0.0773045	+	0.0446317i
$310$	−3.74909	+	13.9918i	−0.212934	+	0.794681i
$311$	7.75912	+	13.4392i	0.439979	+	0.762066i	0.997687	−	0.0679709i	$-0.0216525\pi$
$311$	7.75912	+	13.4392i	0.439979	+	0.762066i	−0.557708	+	0.830037i	$0.688319\pi$
$312$	1.23478	−	3.38753i	0.0699054	−	0.191781i
$313$	−1.50320	−	0.867872i	−0.0849658	−	0.0490550i	0.456915	−	0.889510i	$-0.348954\pi$
$313$	−1.50320	−	0.867872i	−0.0849658	−	0.0490550i	−0.541881	+	0.840455i	$0.682288\pi$
$314$	0.633814	−	0.169830i	0.0357682	−	0.00958406i
$315$	6.78016	−	7.68208i	0.382019	−	0.432836i
$316$	14.1497	−	8.16932i	0.795981	−	0.459560i
$317$	8.77234	+	32.7388i	0.492703	+	1.83879i	0.542530	+	0.840036i	$0.317466\pi$
$317$	8.77234	+	32.7388i	0.492703	+	1.83879i	−0.0498267	+	0.998758i	$0.515867\pi$
$318$	8.54098	−	2.28855i	0.478955	−	0.128335i
$319$	−17.9380	+	4.80646i	−1.00433	+	0.269110i
$320$	1.00233	+	3.74075i	0.0560319	+	0.209114i
$321$	7.49560	−	4.32759i	0.418364	−	0.241542i
$322$	−12.3827	+	14.0299i	−0.690061	+	0.781855i
$323$	0.550686	−	0.147556i	0.0306410	−	0.00821023i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$	20.6901	−	29.5188i	1.14768	−	1.63741i
$326$	9.84580	+	17.0534i	0.545309	+	0.944502i
$327$	2.58752	−	9.65675i	0.143090	−	0.534019i
$328$	−4.61023	−	2.66172i	−0.254557	−	0.146969i
$329$	−3.95164	−	3.48770i	−0.217861	−	0.192283i
$330$	11.7171	−	11.7171i	0.645007	−	0.645007i
$331$	6.04854	−	6.04854i	0.332458	−	0.332458i	−0.521061	−	0.853519i	$-0.674464\pi$
$331$	6.04854	−	6.04854i	0.332458	−	0.332458i	0.853519	+	0.521061i	$0.174464\pi$
$332$	−3.53474	−	13.1918i	−0.193994	−	0.723995i
$333$	0.503317	−	1.87840i	0.0275816	−	0.102936i
$334$			13.6471i			0.746737i
$335$	−24.1001	+	41.7425i	−1.31673	+	2.28064i
$336$	1.17769	−	2.36918i	0.0642485	−	0.129250i
$337$			3.09226i			0.168446i	0.996447	+	0.0842230i	$0.0268408\pi$
$337$			3.09226i			0.168446i	−0.996447	+	0.0842230i	$0.973159\pi$
$338$	−10.6560	+	7.44640i	−0.579612	+	0.405031i
$339$	1.93735	−	1.11853i	0.105223	−	0.0607503i
$340$	4.33841	−	4.33841i	0.235283	−	0.235283i
$341$	13.8602	−	8.00216i	0.750569	−	0.433341i
$342$	0.179928	+	0.311645i	0.00972942	+	0.0168518i
$343$	3.44041	+	18.1979i	0.185765	+	0.982594i
$344$	−8.44668	−	2.26328i	−0.455414	−	0.122028i
$345$	−19.3682	−	19.3682i	−1.04275	−	1.04275i
$346$	−17.0781	−	4.57605i	−0.918122	−	0.246010i
$347$	4.19762	−	7.27048i	0.225340	−	0.390300i	−0.731082	−	0.682290i	$-0.760984\pi$
$347$	4.19762	−	7.27048i	0.225340	−	0.390300i	0.956421	+	0.291990i	$0.0943174\pi$
$348$	−2.17009	−	3.75870i	−0.116329	−	0.201488i
$349$	−4.98005	−	18.5858i	−0.266576	−	0.994874i	−0.961279	−	0.275578i	$-0.911131\pi$
$349$	−4.98005	−	18.5858i	−0.266576	−	0.994874i	0.694703	−	0.719297i	$-0.255536\pi$
$350$	17.5038	−	19.8322i	0.935616	−	1.06008i
$351$	−1.52222	−	3.26846i	−0.0812503	−	0.174458i
$352$	2.13940	−	3.70555i	0.114030	−	0.197506i
$353$	−1.22448	−	1.22448i	−0.0651727	−	0.0651727i	0.673769	−	0.738942i	$-0.264674\pi$
$353$	−1.22448	−	1.22448i	−0.0651727	−	0.0651727i	−0.738942	+	0.673769i	$0.764674\pi$
$354$	8.93891			0.475098
$355$	17.6975			0.939288
$356$	−11.5745	−	11.5745i	−0.613449	−	0.613449i
$357$	−4.18347	+	0.260898i	−0.221413	+	0.0138082i
$358$	−0.382099	+	1.42601i	−0.0201946	+	0.0753671i
$359$	9.75266	−	2.61322i	0.514726	−	0.137920i	0.00789978	−	0.999969i	$-0.497485\pi$
$359$	9.75266	−	2.61322i	0.514726	−	0.137920i	0.506826	+	0.862048i	$0.330819\pi$
$360$	3.35386	+	1.93635i	0.176764	+	0.102055i
$361$		−	18.8705i		−	0.993184i
$362$	13.9033	+	3.72539i	0.730744	+	0.195802i
$363$	−7.30811			−0.383576
$364$	−8.38009	+	4.55787i	−0.439236	+	0.238897i
$365$	−35.6102			−1.86392
$366$	5.75024	+	1.54077i	0.300570	+	0.0805374i
$367$			7.11196i			0.371241i	0.982621	+	0.185621i	$0.0594296\pi$
$367$			7.11196i			0.371241i	−0.982621	+	0.185621i	$0.940570\pi$
$368$	−6.12520	−	3.53639i	−0.319298	−	0.184347i
$369$	−5.14204	+	1.37781i	−0.267684	+	0.0717257i
$370$	1.94920	−	7.27450i	0.101334	−	0.378183i
$371$	−20.9490	−	10.4135i	−1.08762	−	0.540642i
$372$	2.64485	+	2.64485i	0.137129	+	0.137129i
$373$	33.0514			1.71134			0.855668	−	0.517524i	$-0.173146\pi$
$373$	33.0514			1.71134			0.855668	+	0.517524i	$0.173146\pi$
$374$	−6.77880			−0.350523
$375$	13.6862	+	13.6862i	0.706751	+	0.706751i
$376$	0.996055	−	1.72522i	0.0513676	−	0.0889713i
$377$	−1.37126	+	15.5885i	−0.0706236	+	0.802851i
$378$	−0.842511	−	2.50802i	−0.0433341	−	0.128999i
$379$	8.08095	+	30.1585i	0.415091	+	1.54914i	0.784654	+	0.619934i	$0.212841\pi$
$379$	8.08095	+	30.1585i	0.415091	+	1.54914i	−0.369563	+	0.929206i	$0.620493\pi$
$380$	0.696810	+	1.20691i	0.0357456	+	0.0619132i
$381$	9.25967	−	16.0382i	0.474387	−	0.821662i
$382$	−0.632510	−	0.169481i	−0.0323620	−	0.00867138i
$383$	9.00186	+	9.00186i	0.459973	+	0.459973i	0.898647	−	0.438673i	$-0.144551\pi$
$383$	9.00186	+	9.00186i	0.459973	+	0.459973i	−0.438673	+	0.898647i	$0.644551\pi$
$384$	0.965926	+	0.258819i	0.0492922	+	0.0132078i
$385$	−43.7565	+	2.72883i	−2.23004	+	0.139074i
$386$	1.66330	+	2.88091i	0.0846595	+	0.146635i
$387$	−7.57309	+	4.37232i	−0.384962	+	0.222258i
$388$	7.34555	−	7.34555i	0.372914	−	0.372914i
$389$	19.2107	−	11.0913i	0.974019	−	0.562350i	0.0735598	−	0.997291i	$-0.476564\pi$
$389$	19.2107	−	11.0913i	0.974019	−	0.562350i	0.900459	+	0.434941i	$0.143231\pi$
$390$	−5.89512	−	12.6578i	−0.298511	−	0.640952i
$391$			11.2052i			0.566673i
$392$	−6.48399	+	2.63777i	−0.327491	+	0.133228i
$393$	−6.45723	+	11.1843i	−0.325724	+	0.564171i
$394$			9.54608i			0.480925i
$395$	16.3767	−	61.1187i	0.824001	−	3.07521i
$396$	−1.10743	−	4.13300i	−0.0556507	−	0.207691i
$397$	−3.59656	+	3.59656i	−0.180506	+	0.180506i	−0.791576	−	0.611070i	$-0.790739\pi$
$397$	−3.59656	+	3.59656i	−0.180506	+	0.180506i	0.611070	+	0.791576i	$0.290739\pi$
$398$	11.2010	−	11.2010i	0.561455	−	0.561455i
$399$	0.188700	−	0.933205i	0.00944681	−	0.0467187i
$400$	8.65839	+	4.99892i	0.432919	+	0.249946i
$401$	0.949113	−	3.54214i	0.0473965	−	0.176886i	−0.938170	−	0.346175i	$-0.887480\pi$
$401$	0.949113	−	3.54214i	0.0473965	−	0.176886i	0.985566	+	0.169289i	$0.0541471\pi$
$402$	6.22305	+	10.7786i	0.310378	+	0.537590i
$403$	−2.33555	−	13.2823i	−0.116342	−	0.661641i
$404$	10.8069	+	6.23936i	0.537663	+	0.310420i
$405$	3.74075	−	1.00233i	0.185879	−	0.0498062i
$406$	−2.27588	+	11.2552i	−0.112950	+	0.558588i
$407$	−7.20605	+	4.16042i	−0.357191	+	0.206224i
$408$	−0.410041	−	1.53029i	−0.0203000	−	0.0757608i
$409$	−16.5375	+	4.43122i	−0.817728	+	0.219110i	−0.643353	−	0.765570i	$-0.722457\pi$
$409$	−16.5375	+	4.43122i	−0.817728	+	0.219110i	−0.174375	+	0.984679i	$0.555791\pi$
$410$	−19.9136	+	5.33584i	−0.983464	+	0.263518i
$411$	−2.29183	−	8.55322i	−0.113048	−	0.421899i
$412$	1.35889	−	0.784555i	0.0669476	−	0.0386522i
$413$	−17.7316	−	15.6498i	−0.872517	−	0.770078i
$414$	−6.83178	+	1.83057i	−0.335764	+	0.0899676i
$415$	−45.8043	−	26.4451i	−2.24844	−	1.29814i
$416$	−2.31630	−	2.76311i	−0.113566	−	0.135473i
$417$	−0.254144	−	0.440191i	−0.0124455	−	0.0215562i
$418$	0.398518	−	1.48729i	0.0194921	−	0.0727457i
$419$	1.19774	+	0.691514i	0.0585133	+	0.0337827i	0.528971	−	0.848640i	$-0.322578\pi$
$419$	1.19774	+	0.691514i	0.0585133	+	0.0337827i	−0.470458	+	0.882422i	$0.655911\pi$
$420$	−3.26280	−	9.71283i	−0.159208	−	0.473938i
$421$	−19.8508	+	19.8508i	−0.967469	+	0.967469i	−0.999487	−	0.0320178i	$-0.989807\pi$
$421$	−19.8508	+	19.8508i	−0.967469	+	0.967469i	0.0320178	+	0.999487i	$0.489807\pi$
$422$	−5.35521	+	5.35521i	−0.260687	+	0.260687i
$423$	−0.515596	−	1.92423i	−0.0250691	−	0.0935593i
$424$	2.28855	−	8.54098i	0.111142	−	0.414787i
$425$		−	15.8393i		−	0.768321i
$426$	2.28491	−	3.95758i	0.110704	−	0.191745i
$427$	−8.70893	−	13.1236i	−0.421455	−	0.635096i
$428$		−	8.65518i		−	0.418364i
$429$	−5.28336	+	14.4945i	−0.255083	+	0.699803i
$430$	−29.3283	+	16.9327i	−1.41434	+	0.816568i
$431$	4.87258	−	4.87258i	0.234704	−	0.234704i	−0.579949	−	0.814653i	$-0.696928\pi$
$431$	4.87258	−	4.87258i	0.234704	−	0.234704i	0.814653	+	0.579949i	$0.196928\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	3.30247	+	5.72004i	0.158706	+	0.274888i	0.934402	−	0.356219i	$-0.115934\pi$
$433$	3.30247	+	5.72004i	0.158706	+	0.274888i	−0.775696	+	0.631107i	$0.782601\pi$
$434$	−0.615965	−	9.87692i	−0.0295672	−	0.474107i
$435$	−16.2355	−	4.35029i	−0.778433	−	0.208580i
$436$	−7.06923	−	7.06923i	−0.338555	−	0.338555i
$437$	−2.45846	−	0.658743i	−0.117604	−	0.0315119i
$438$	−4.59759	+	7.96326i	−0.219681	+	0.380499i
$439$	5.58357	+	9.67104i	0.266489	+	0.461573i	0.967953	−	0.251132i	$-0.0808029\pi$
$439$	5.58357	+	9.67104i	0.266489	+	0.461573i	−0.701463	+	0.712706i	$0.747470\pi$
$440$	−4.28877	−	16.0059i	−0.204459	−	0.763051i
$441$	−2.71969	+	6.45006i	−0.129509	+	0.307146i
$442$	−1.95623	+	5.36677i	−0.0930482	+	0.255271i
$443$	5.10413	−	8.84062i	0.242505	−	0.420030i	−0.718922	−	0.695090i	$-0.755364\pi$
$443$	5.10413	−	8.84062i	0.242505	−	0.420030i	0.961427	+	0.275060i	$0.0886977\pi$
$444$	−1.37509	−	1.37509i	−0.0652587	−	0.0652587i
$445$	−63.3918			−3.00506
$446$	−14.2213			−0.673396
$447$	−12.3997	−	12.3997i	−0.586485	−	0.586485i
$448$	−1.46293	−	2.20451i	−0.0691168	−	0.104153i
$449$	7.99914	−	29.8532i	0.377503	−	1.40886i	−0.472151	−	0.881518i	$-0.656522\pi$
$449$	7.99914	−	29.8532i	0.377503	−	1.40886i	0.849653	−	0.527342i	$-0.176811\pi$
$450$	9.65718	−	2.58763i	0.455244	−	0.121982i
$451$	19.7262	+	11.3890i	0.928873	+	0.536285i
$452$		−	2.23706i		−	0.105223i
$453$	22.1244	+	5.92821i	1.03949	+	0.278532i
$454$	26.5756			1.24725
$455$	−10.4668	+	35.4295i	−0.490693	+	1.66096i
$456$	0.359857			0.0168518
$457$	−19.7641	−	5.29578i	−0.924526	−	0.247726i	−0.235007	−	0.971994i	$-0.575511\pi$
$457$	−19.7641	−	5.29578i	−0.924526	−	0.247726i	−0.689519	+	0.724268i	$0.742178\pi$
$458$		−	6.20996i		−	0.290172i
$459$	−1.37202	−	0.792138i	−0.0640405	−	0.0369738i
$460$	−26.4575	+	7.08925i	−1.23359	+	0.330538i
$461$	−2.42182	+	9.03836i	−0.112795	+	0.420958i	−0.999113	−	0.0421206i	$-0.986589\pi$
$461$	−2.42182	+	9.03836i	−0.112795	+	0.420958i	0.886317	+	0.463079i	$0.153255\pi$
$462$	−5.03911	+	10.1373i	−0.234441	+	0.471628i
$463$	17.9800	+	17.9800i	0.835601	+	0.835601i	0.988276	−	0.152675i	$-0.0487888\pi$
$463$	17.9800	+	17.9800i	0.835601	+	0.835601i	−0.152675	+	0.988276i	$0.548789\pi$
$464$	−4.34018			−0.201488
$465$	14.4854			0.671744
$466$	12.9144	+	12.9144i	0.598248	+	0.598248i
$467$	−8.49550	+	14.7146i	−0.393125	+	0.680912i	−0.992860	−	0.119287i	$-0.961939\pi$
$467$	−8.49550	+	14.7146i	−0.393125	+	0.680912i	0.599735	+	0.800199i	$0.295273\pi$
$468$	−3.59168	−	0.315946i	−0.166026	−	0.0146046i
$469$	6.52642	−	32.2761i	0.301362	−	1.49037i
$470$	−1.99675	−	7.45198i	−0.0921033	−	0.343734i
$471$	−0.328086	−	0.568262i	−0.0151174	−	0.0261841i
$472$	4.46945	−	7.74132i	0.205723	−	0.356323i
$473$	36.1416	+	9.68412i	1.66179	+	0.445276i
$474$	−11.5532	−	11.5532i	−0.530654	−	0.530654i
$475$	3.47520	+	0.931178i	0.159453	+	0.0427254i
$476$	−1.86579	+	3.75344i	−0.0855184	+	0.172039i
$477$	−4.42114	−	7.65764i	−0.202430	−	0.350619i
$478$	−0.193674	+	0.111818i	−0.00885843	+	0.00511442i
$479$	−30.2968	+	30.2968i	−1.38430	+	1.38430i	−0.547472	+	0.836824i	$0.684410\pi$
$479$	−30.2968	+	30.2968i	−1.38430	+	1.38430i	−0.836824	+	0.547472i	$0.815590\pi$
$480$	3.35386	−	1.93635i	0.153082	−	0.0883820i
$481$	1.21428	+	6.90565i	0.0553664	+	0.314870i
$482$			13.3393i			0.607588i
$483$	16.7567	+	8.32956i	0.762457	+	0.379008i
$484$	−3.65406	+	6.32901i	−0.166093	+	0.287682i
$485$		−	40.2304i		−	1.82677i
$486$	0.258819	−	0.965926i	0.0117403	−	0.0438153i
$487$	0.222519	+	0.830450i	0.0100833	+	0.0376313i	0.970784	−	0.239954i	$-0.0771325\pi$
$487$	0.222519	+	0.830450i	0.0100833	+	0.0376313i	−0.960701	+	0.277586i	$0.910466\pi$
$488$	4.20947	−	4.20947i	0.190554	−	0.190554i
$489$	13.9241	−	13.9241i	0.629668	−	0.629668i
$490$	−10.5325	+	24.9792i	−0.475812	+	1.12844i
$491$	4.74663	+	2.74047i	0.214212	+	0.123675i	0.603267	−	0.797539i	$-0.293865\pi$
$491$	4.74663	+	2.74047i	0.214212	+	0.123675i	−0.389055	+	0.921214i	$0.627198\pi$
$492$	−1.37781	+	5.14204i	−0.0621163	+	0.231821i
$493$	3.43802	+	5.95482i	0.154841	+	0.268192i
$494$	−1.06248	−	0.744709i	−0.0478034	−	0.0335060i
$495$	−14.3505	−	8.28526i	−0.645007	−	0.372395i
$496$	3.61293	−	0.968081i	0.162225	−	0.0434681i
$497$	−11.4612	+	3.85012i	−0.514105	+	0.172702i
$498$	−11.8275	+	6.82859i	−0.530001	+	0.305996i
$499$	−4.12370	−	15.3898i	−0.184602	−	0.688944i	−0.994715	−	0.102671i	$-0.967261\pi$
$499$	−4.12370	−	15.3898i	−0.184602	−	0.688944i	0.810113	−	0.586273i	$-0.199405\pi$
$500$	18.6957	−	5.00949i	0.836096	−	0.224031i
$501$	13.1821	−	3.53213i	0.588933	−	0.157804i
$502$	−1.28906	−	4.81083i	−0.0575335	−	0.214718i
$503$	−16.5880	+	9.57711i	−0.739624	+	0.427022i	−0.821933	−	0.569585i	$-0.807104\pi$
$503$	−16.5880	+	9.57711i	−0.739624	+	0.427022i	0.0823084	+	0.996607i	$0.473771\pi$
$504$	−2.59327	−	0.524375i	−0.115513	−	0.0233575i
$505$	46.6797	−	12.5078i	2.07722	−	0.556590i
$506$	26.2085	+	15.1315i	1.16511	+	0.672677i
$507$	9.95066	+	8.36567i	0.441924	+	0.371532i
$508$	−9.25967	−	16.0382i	−0.410831	−	0.711581i
$509$	4.10886	−	15.3345i	0.182122	−	0.679689i	−0.813106	−	0.582115i	$-0.802225\pi$
$509$	4.10886	−	15.3345i	0.182122	−	0.679689i	0.995228	−	0.0975737i	$-0.0311082\pi$
$510$	−5.31344	−	3.06772i	−0.235283	−	0.135841i
$511$	23.0617	−	7.74704i	1.02019	−	0.342709i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	0.254457	−	0.254457i	0.0112346	−	0.0112346i
$514$	1.96233	+	7.32352i	0.0865547	+	0.323027i
$515$	1.57276	−	5.86964i	0.0693043	−	0.258647i
$516$			8.74465i			0.384962i
$517$	−4.26192	+	7.38186i	−0.187439	+	0.324654i
$518$	0.320247	+	5.13513i	0.0140709	+	0.225625i
$519$			17.6805i			0.776088i
$520$	−13.9095	−	1.22357i	−0.609973	−	0.0536569i
$521$	10.3862	−	5.99650i	0.455030	−	0.262712i	−0.254922	−	0.966962i	$-0.582050\pi$
$521$	10.3862	−	5.99650i	0.455030	−	0.262712i	0.709952	+	0.704250i	$0.248717\pi$
$522$	−3.06897	+	3.06897i	−0.134325	+	0.134325i
$523$	21.3404	−	12.3209i	0.933150	−	0.538754i	0.0453435	−	0.998971i	$-0.485562\pi$
$523$	21.3404	−	12.3209i	0.933150	−	0.538754i	0.887806	+	0.460217i	$0.152228\pi$
$524$	6.45723	+	11.1843i	0.282086	+	0.488587i
$525$	−23.6867	−	11.7744i	−1.03377	−	0.513877i
$526$	25.0409	+	6.70968i	1.09183	+	0.292556i
$527$	−4.19017	−	4.19017i	−0.182527	−	0.182527i
$528$	−4.13300	−	1.10743i	−0.179866	−	0.0481949i
$529$	13.5121	−	23.4036i	0.587482	−	1.01755i
$530$	−17.1218	−	29.6558i	−0.743722	−	1.28816i
$531$	−2.31356	−	8.63432i	−0.100400	−	0.374698i
$532$	−0.713829	−	0.630021i	−0.0309484	−	0.0273149i
$533$	14.7092	−	12.3306i	0.637128	−	0.534100i
$534$	−8.18443	+	14.1759i	−0.354175	+	0.613449i
$535$	−23.7015	−	23.7015i	−1.02470	−	1.02470i
$536$	12.4461			0.537590
$537$	1.47632			0.0637078
$538$	−6.77517	−	6.77517i	−0.292098	−	0.292098i
$539$	27.7437	−	11.2865i	1.19501	−	0.486144i
$540$	1.00233	−	3.74075i	0.0431334	−	0.160976i
$541$	−30.7831	+	8.24830i	−1.32347	+	0.354622i	−0.850276	−	0.526337i	$-0.823565\pi$
$541$	−30.7831	+	8.24830i	−1.32347	+	0.354622i	−0.473192	+	0.880959i	$0.656898\pi$
$542$	−11.2690	−	6.50615i	−0.484044	−	0.279463i
$543$		−	14.3938i		−	0.617697i
$544$	−1.53029	−	0.410041i	−0.0656108	−	0.0175803i
$545$	−38.7170			−1.65845
$546$	6.57149	+	6.91488i	0.281234	+	0.295930i
$547$	16.4490			0.703307			0.351653	−	0.936130i	$-0.385620\pi$
$547$	16.4490			0.703307			0.351653	+	0.936130i	$0.385620\pi$
$548$	−8.55322	−	2.29183i	−0.365375	−	0.0979020i
$549$		−	5.95308i		−	0.254071i
$550$	−37.0475	−	21.3894i	−1.57971	−	0.912046i
$551$	−1.50862	+	0.404235i	−0.0642696	+	0.0172210i
$552$	−1.83057	+	6.83178i	−0.0779142	+	0.290780i
$553$	2.69064	+	43.1441i	0.114418	+	1.83468i
$554$	6.65218	+	6.65218i	0.282624	+	0.282624i
$555$	−7.53112			−0.319678
$556$	−0.508288			−0.0215562
$557$	18.8769	+	18.8769i	0.799838	+	0.799838i	0.983070	−	0.183232i	$-0.0586559\pi$
$557$	18.8769	+	18.8769i	0.799838	+	0.799838i	−0.183232	+	0.983070i	$0.558656\pi$
$558$	1.87019	−	3.23926i	0.0791714	−	0.137129i
$559$	18.0967	−	25.8187i	0.765408	−	1.09201i
$560$	−10.0430	−	2.03075i	−0.424392	−	0.0858148i
$561$	1.75448	+	6.54781i	0.0740743	+	0.276449i
$562$	4.78172	+	8.28217i	0.201704	+	0.349362i
$563$	4.27970	−	7.41266i	0.180368	−	0.312406i	−0.761638	−	0.648003i	$-0.775605\pi$
$563$	4.27970	−	7.41266i	0.180368	−	0.312406i	0.942006	+	0.335597i	$0.108938\pi$
$564$	−1.92423	−	0.515596i	−0.0810247	−	0.0217105i
$565$	−6.12601	−	6.12601i	−0.257723	−	0.257723i
$566$	−2.27288	−	0.609017i	−0.0955363	−	0.0255989i
$567$	−2.20451	+	1.46293i	−0.0925805	+	0.0614372i
$568$	−2.28491	−	3.95758i	−0.0958726	−	0.166056i
$569$	33.4365	−	19.3045i	1.40173	−	0.809289i	0.407159	−	0.913357i	$-0.366519\pi$
$569$	33.4365	−	19.3045i	1.40173	−	0.809289i	0.994570	+	0.104069i	$0.0331861\pi$
$570$	0.985438	−	0.985438i	0.0412755	−	0.0412755i
$571$	−20.6559	+	11.9257i	−0.864423	+	0.499075i	−0.865491	−	0.500925i	$-0.832993\pi$
$571$	−20.6559	+	11.9257i	−0.864423	+	0.499075i	0.00106798	+	0.999999i	$0.499660\pi$
$572$	9.91096	+	11.8228i	0.414398	+	0.494336i
$573$			0.654823i			0.0273556i
$574$	11.7355	−	7.78780i	0.489832	−	0.325056i
$575$	−35.3563	+	61.2388i	−1.47446	+	2.55384i
$576$		−	1.00000i		−	0.0416667i
$577$	−8.42837	+	31.4551i	−0.350877	+	1.30949i	0.534716	+	0.845032i	$0.320419\pi$
$577$	−8.42837	+	31.4551i	−0.350877	+	1.30949i	−0.885594	+	0.464461i	$0.846248\pi$
$578$	−3.75031	−	13.9963i	−0.155992	−	0.582171i
$579$	2.35226	−	2.35226i	0.0977564	−	0.0977564i
$580$	−11.8852	+	11.8852i	−0.493507	+	0.493507i
$581$	35.4167	+	7.16148i	1.46933	+	0.297108i
$582$	−8.99643	−	5.19409i	−0.372914	−	0.215302i
$583$	−9.79224	+	36.5451i	−0.405553	+	1.51355i
$584$	4.59759	+	7.96326i	0.190250	+	0.329522i
$585$	−10.7007	+	8.97033i	−0.442420	+	0.370877i
$586$	−16.1684	−	9.33484i	−0.667911	−	0.385619i
$587$	−26.2589	+	7.03605i	−1.08382	+	0.290409i	−0.756160	−	0.654387i	$-0.772927\pi$
$587$	−26.2589	+	7.03605i	−1.08382	+	0.290409i	−0.327660	+	0.944796i	$0.606260\pi$
$588$	4.22607	+	5.58035i	0.174280	+	0.230130i
$589$	1.16567	−	0.673001i	0.0480306	−	0.0277305i
$590$	−8.95974	−	33.4382i	−0.368867	−	1.37663i
$591$	9.22081	−	2.47071i	0.379293	−	0.101631i
$592$	−1.87840	+	0.503317i	−0.0772019	+	0.0206862i
$593$	12.0362	+	44.9198i	0.494269	+	1.84464i	0.534089	+	0.845428i	$0.320655\pi$
$593$	12.0362	+	44.9198i	0.494269	+	1.84464i	−0.0398202	+	0.999207i	$0.512679\pi$
$594$	−3.70555	+	2.13940i	−0.152040	+	0.0877806i
$595$	5.16917	+	15.3878i	0.211915	+	0.630838i
$596$	−16.9383	+	4.53860i	−0.693819	+	0.185908i
$597$	−13.7184	−	7.92030i	−0.561455	−	0.324156i
$598$	19.5429	−	16.3826i	0.799167	−	0.669936i
$599$	−12.2342	−	21.1903i	−0.499877	−	0.865813i	0.500123	−	0.865955i	$-0.333288\pi$
$599$	−12.2342	−	21.1903i	−0.499877	−	0.865813i	−1.00000		0.000141679i	$0.999955\pi$
$600$	2.58763	−	9.65718i	0.105640	−	0.394253i
$601$	15.8703	+	9.16272i	0.647363	+	0.373755i	0.787445	−	0.616385i	$-0.211403\pi$
$601$	15.8703	+	9.16272i	0.647363	+	0.373755i	−0.140082	+	0.990140i	$0.544737\pi$
$602$	15.3097	−	17.3463i	0.623978	−	0.706982i
$603$	8.80073	−	8.80073i	0.358393	−	0.358393i
$604$	16.1962	−	16.1962i	0.659013	−	0.659013i
$605$	7.32514	+	27.3378i	0.297809	+	1.11144i
$606$	3.22973	−	12.0535i	0.131199	−	0.489641i
$607$		−	33.9749i		−	1.37900i	−0.724286	−	0.689500i	$-0.757830\pi$
$607$		−	33.9749i		−	1.37900i	0.724286	−	0.689500i	$-0.242170\pi$
$608$	0.179928	−	0.311645i	0.00729706	−	0.0126389i
$609$	11.4608	−	0.714739i	0.464414	−	0.0289627i
$610$		−	23.0545i		−	0.933451i
$611$	4.61431	+	5.50442i	0.186675	+	0.222685i
$612$	−1.37202	+	0.792138i	−0.0554607	+	0.0320203i
$613$	7.83114	−	7.83114i	0.316297	−	0.316297i	−0.531046	−	0.847343i	$-0.678201\pi$
$613$	7.83114	−	7.83114i	0.316297	−	0.316297i	0.847343	+	0.531046i	$0.178201\pi$
$614$	1.83424	−	1.05900i	0.0740240	−	0.0427378i
$615$	10.3080	+	17.8541i	0.415661	+	0.719945i
$616$	6.25957	+	9.43263i	0.252205	+	0.380052i
$617$	−32.1486	−	8.61418i	−1.29425	−	0.346794i	−0.454979	−	0.890502i	$-0.650353\pi$
$617$	−32.1486	−	8.61418i	−1.29425	−	0.346794i	−0.839274	+	0.543708i	$0.817020\pi$
$618$	−1.10953	−	1.10953i	−0.0446317	−	0.0446317i
$619$	3.70436	+	0.992581i	0.148891	+	0.0398952i	0.332495	−	0.943105i	$-0.392110\pi$
$619$	3.70436	+	0.992581i	0.148891	+	0.0398952i	−0.183604	+	0.983000i	$0.558776\pi$
$620$	7.24269	−	12.5447i	0.290874	−	0.503808i
$621$	3.53639	+	6.12520i	0.141910	+	0.245796i
$622$	−4.01641	−	14.9895i	−0.161044	−	0.601023i
$623$	41.0535	−	13.7910i	1.64477	−	0.552523i
$624$	−2.06946	+	2.95251i	−0.0828446	+	0.118195i
$625$	12.4838	−	21.6227i	0.499354	−	0.864906i
$626$	1.22736	+	1.22736i	0.0490550	+	0.0490550i
$627$	−1.53975			−0.0614919
$628$	−0.656173			−0.0261841
$629$	2.17852	+	2.17852i	0.0868631	+	0.0868631i
$630$	−8.53740	+	5.66549i	−0.340138	+	0.225718i
$631$	4.45622	−	16.6308i	0.177399	−	0.662063i	−0.818731	−	0.574177i	$-0.805322\pi$
$631$	4.45622	−	16.6308i	0.177399	−	0.662063i	0.996131	−	0.0878860i	$-0.0280111\pi$
$632$	−15.7819	+	4.22875i	−0.627771	+	0.168211i
$633$	6.55876	+	3.78670i	0.260687	+	0.150508i
$634$		−	33.8937i		−	1.34609i
$635$	−69.2761	−	18.5625i	−2.74914	−	0.736630i
$636$	−8.84228			−0.350619
$637$	−0.929249	−	25.2217i	−0.0368182	−	0.999322i
$638$	18.5707			0.735223
$639$	−4.41410	−	1.18275i	−0.174619	−	0.0467891i
$640$		−	3.87271i		−	0.153082i
$641$	−19.5916	−	11.3112i	−0.773821	−	0.446766i	0.0604148	−	0.998173i	$-0.480758\pi$
$641$	−19.5916	−	11.3112i	−0.773821	−	0.446766i	−0.834236	+	0.551407i	$0.814091\pi$
$642$	−8.36026	+	2.24012i	−0.329953	+	0.0884107i
$643$	9.23701	−	34.4730i	0.364272	−	1.35948i	−0.504133	−	0.863626i	$-0.668188\pi$
$643$	9.23701	−	34.4730i	0.364272	−	1.35948i	0.868405	−	0.495855i	$-0.165145\pi$
$644$	15.5920	−	10.3470i	0.614410	−	0.407727i
$645$	23.9465	+	23.9465i	0.942892	+	0.942892i
$646$	−0.570113			−0.0224308
$647$	13.1666			0.517634			0.258817	−	0.965926i	$-0.416667\pi$
$647$	13.1666			0.517634			0.258817	+	0.965926i	$0.416667\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	−19.1239	+	33.1236i	−0.750679	+	1.30021i
$650$	−27.6251	+	23.1580i	−1.08355	+	0.908330i
$651$	−9.38095	+	3.15131i	−0.367668	+	0.123510i
$652$	−5.09656	−	19.0206i	−0.199597	−	0.744905i
$653$	21.0542	+	36.4670i	0.823916	+	1.42707i	0.902745	+	0.430177i	$0.141549\pi$
$653$	21.0542	+	36.4670i	0.823916	+	1.42707i	−0.0788282	+	0.996888i	$0.525118\pi$
$654$	−4.99870	+	8.65800i	−0.195465	+	0.338555i
$655$	48.3098	+	12.9446i	1.88762	+	0.505786i
$656$	3.76424	+	3.76424i	0.146969	+	0.146969i
$657$	8.88186	+	2.37989i	0.346514	+	0.0928482i
$658$	2.91431	+	4.39162i	0.113612	+	0.171203i
$659$	−10.1803	−	17.6328i	−0.396569	−	0.686878i	0.596731	−	0.802441i	$-0.296466\pi$
$659$	−10.1803	−	17.6328i	−0.396569	−	0.686878i	−0.993300	+	0.115564i	$0.963133\pi$
$660$	−14.3505	+	8.28526i	−0.558592	+	0.322503i
$661$	−20.4387	+	20.4387i	−0.794975	+	0.794975i	−0.982298	−	0.187324i	$-0.940019\pi$
$661$	−20.4387	+	20.4387i	−0.794975	+	0.794975i	0.187324	+	0.982298i	$0.440019\pi$
$662$	−7.40792	+	4.27697i	−0.287917	+	0.166229i
$663$	5.69021	+	0.500546i	0.220990	+	0.0194396i
$664$			13.6572i			0.530001i
$665$	−3.68002	+	0.229501i	−0.142705	+	0.00889966i
$666$	−0.972333	+	1.68413i	−0.0376771	+	0.0652587i
$667$		−	30.6971i		−	1.18860i
$668$	3.53213	−	13.1821i	0.136662	−	0.510031i
$669$	3.68073	+	13.7367i	0.142305	+	0.531091i
$670$	34.0826	−	34.0826i	1.31673	−	1.31673i
$671$	−18.0115	+	18.0115i	−0.695325	+	0.695325i
$672$	−1.75076	+	1.98365i	−0.0675368	+	0.0765209i
$673$	6.17376	+	3.56442i	0.237981	+	0.137398i	0.614248	−	0.789113i	$-0.289459\pi$
$673$	6.17376	+	3.56442i	0.237981	+	0.137398i	−0.376267	+	0.926511i	$0.622793\pi$
$674$	0.800335	−	2.98689i	0.0308278	−	0.115051i
$675$	−4.99892	−	8.65839i	−0.192409	−	0.333262i
$676$	12.2202	−	4.43469i	0.470008	−	0.170565i
$677$	37.1749	+	21.4629i	1.42875	+	0.824888i	0.997022	−	0.0771168i	$-0.0245714\pi$
$677$	37.1749	+	21.4629i	1.42875	+	0.824888i	0.431726	+	0.902005i	$0.357905\pi$
$678$	−2.16084	+	0.578994i	−0.0829864	+	0.0222361i
$679$	8.75216	+	26.0538i	0.335877	+	0.999853i
$680$	−5.31344	+	3.06772i	−0.203761	+	0.117642i
$681$	−6.87826	−	25.6700i	−0.263576	−	0.983678i
$682$	−15.4590	+	4.14222i	−0.591955	+	0.158614i
$683$	−27.7411	+	7.43322i	−1.06149	+	0.284424i	−0.746990	−	0.664835i	$-0.768502\pi$
$683$	−27.7411	+	7.43322i	−1.06149	+	0.284424i	−0.314495	+	0.949259i	$0.601835\pi$
$684$	−0.0931378	−	0.347595i	−0.00356121	−	0.0132906i
$685$	−29.6982	+	17.1463i	−1.13471	+	0.655126i
$686$	1.38678	−	18.4683i	0.0529476	−	0.705122i
$687$	−5.99836	+	1.60726i	−0.228852	+	0.0613207i
$688$	7.57309	+	4.37232i	0.288721	+	0.166693i
$689$	26.1070	+	18.2987i	0.994596	+	0.697126i
$690$	13.6954	+	23.7211i	0.521375	+	0.903047i
$691$	12.2052	−	45.5503i	0.464307	−	1.73282i	−0.194871	−	0.980829i	$-0.562429\pi$
$691$	12.2052	−	45.5503i	0.464307	−	1.73282i	0.659178	−	0.751987i	$-0.270904\pi$
$692$	15.3118	+	8.84025i	0.582066	+	0.336056i
$693$	11.0961	+	2.24369i	0.421505	+	0.0852309i
$694$	−5.93632	+	5.93632i	−0.225340	+	0.225340i
$695$	−1.39191	+	1.39191i	−0.0527980	+	0.0527980i
$696$	1.12332	+	4.19229i	0.0425794	+	0.158908i
$697$	2.18283	−	8.14641i	0.0826804	−	0.308567i
$698$			19.2414i			0.728298i
$699$	9.13186	−	15.8168i	0.345398	−	0.598248i
$700$	−22.0403	+	14.6261i	−0.833045	+	0.552816i
$701$			6.01200i			0.227070i	0.993534	+	0.113535i	$0.0362174\pi$
$701$			6.01200i			0.227070i	−0.993534	+	0.113535i	$0.963783\pi$
$702$	0.624415	+	3.55107i	0.0235670	+	0.134027i
$703$	−0.606046	+	0.349901i	−0.0228575	+	0.0131968i
$704$	−3.02557	+	3.02557i	−0.114030	+	0.114030i
$705$	−6.68126	+	3.85743i	−0.251631	+	0.145279i
$706$	0.865841	+	1.49968i	0.0325863	+	0.0564412i
$707$	−27.5094	+	18.2555i	−1.03460	+	0.686568i
$708$	−8.63432	−	2.31356i	−0.324498	−	0.0869489i
$709$	4.93912	+	4.93912i	0.185493	+	0.185493i	0.793744	−	0.608252i	$-0.208129\pi$
$709$	4.93912	+	4.93912i	0.185493	+	0.185493i	−0.608252	+	0.793744i	$0.708129\pi$
$710$	−17.0945	−	4.58046i	−0.641546	−	0.171902i
$711$	−8.16932	+	14.1497i	−0.306373	+	0.530654i
$712$	8.18443	+	14.1759i	0.306725	+	0.531262i
$713$	6.84702	+	25.5534i	0.256423	+	0.956984i
$714$	4.10845	+	0.830754i	0.153755	+	0.0310902i
$715$	59.5160	+	5.23539i	2.22577	+	0.195792i
$716$	0.738159	−	1.27853i	0.0275863	−	0.0477809i
$717$	0.158134	+	0.158134i	0.00590562	+	0.00590562i
$718$	−10.0967			−0.376805
$719$	16.6351			0.620383			0.310191	−	0.950674i	$-0.399607\pi$
$719$	16.6351			0.620383			0.310191	+	0.950674i	$0.399607\pi$
$720$	−2.73842	−	2.73842i	−0.102055	−	0.102055i
$721$	0.258400	+	4.14342i	0.00962334	+	0.154309i
$722$	−4.88405	+	18.2275i	−0.181765	+	0.678358i
$723$	12.8848	−	3.45246i	0.479190	−	0.128398i
$724$	−12.4654	−	7.19690i	−0.463273	−	0.267471i
$725$			43.3924i			1.61155i
$726$	7.05909	+	1.89148i	0.261988	+	0.0701994i
$727$	−27.7026			−1.02743			−0.513716	−	0.857960i	$-0.671732\pi$
$727$	−27.7026			−1.02743			−0.513716	+	0.857960i	$0.671732\pi$
$728$	9.27421	−	2.23363i	0.343725	−	0.0827840i
$729$	−1.00000			−0.0370370
$730$	34.3968	+	9.21660i	1.27308	+	0.341122i
$731$		−	13.8539i		−	0.512406i
$732$	−5.15552	−	2.97654i	−0.190554	−	0.110016i
$733$	−7.85783	+	2.10550i	−0.290236	+	0.0777684i	−0.400999	−	0.916078i	$-0.631337\pi$
$733$	−7.85783	+	2.10550i	−0.290236	+	0.0777684i	0.110764	+	0.993847i	$0.464670\pi$
$734$	1.84071	−	6.86963i	0.0679419	−	0.253563i
$735$	26.8541	+	3.70857i	0.990527	+	0.136793i
$736$	5.00121	+	5.00121i	0.184347	+	0.184347i
$737$	−53.2544			−1.96165
$738$	5.32344			0.195958
$739$	26.0807	+	26.0807i	0.959395	+	0.959395i	0.999207	−	0.0398124i	$-0.0126760\pi$
$739$	26.0807	+	26.0807i	0.959395	+	0.959395i	−0.0398124	+	0.999207i	$0.512676\pi$
$740$	−3.76556	+	6.52214i	−0.138425	+	0.239759i
$741$	−0.444343	+	1.21902i	−0.0163233	+	0.0447820i
$742$	17.5400	+	15.4807i	0.643912	+	0.568313i
$743$	−6.26734	−	23.3900i	−0.229926	−	0.858097i	−0.980371	−	0.197163i	$-0.936827\pi$
$743$	−6.26734	−	23.3900i	−0.229926	−	0.858097i	0.750444	−	0.660934i	$-0.229840\pi$
$744$	−1.87019	−	3.23926i	−0.0685645	−	0.118757i
$745$	−33.9555	+	58.8126i	−1.24403	+	2.15473i
$746$	−31.9252	−	8.55433i	−1.16886	−	0.313196i
$747$	9.65709	+	9.65709i	0.353334	+	0.353334i
$748$	6.54781	+	1.75448i	0.239412	+	0.0641502i
$749$	20.5057	+	10.1931i	0.749262	+	0.372450i
$750$	−9.67759	−	16.7621i	−0.353376	−	0.612065i
$751$	−20.5726	+	11.8776i	−0.750703	+	0.433419i	−0.825948	−	0.563746i	$-0.809360\pi$
$751$	−20.5726	+	11.8776i	−0.750703	+	0.433419i	0.0752446	+	0.997165i	$0.476026\pi$
$752$	−1.40863	+	1.40863i	−0.0513676	+	0.0513676i
$753$	−4.31328	+	2.49027i	−0.157184	+	0.0907505i
$754$	5.35915	−	14.7025i	0.195169	−	0.535432i
$755$		−	88.7038i		−	3.22826i
$756$	0.164680	+	2.64062i	0.00598934	+	0.0960385i
$757$	9.11505	−	15.7877i	0.331292	−	0.573815i	−0.651473	−	0.758671i	$-0.725849\pi$
$757$	9.11505	−	15.7877i	0.331292	−	0.573815i	0.982765	+	0.184857i	$0.0591821\pi$
$758$		−	31.2224i		−	1.13405i
$759$	7.83264	−	29.2318i	0.284307	−	1.06105i
$760$	−0.360695	−	1.34613i	−0.0130838	−	0.0488294i
$761$	1.13498	−	1.13498i	0.0411430	−	0.0411430i	−0.686236	−	0.727379i	$-0.740738\pi$
$761$	1.13498	−	1.13498i	0.0411430	−	0.0411430i	0.727379	+	0.686236i	$0.240738\pi$
$762$	−13.0951	+	13.0951i	−0.474387	+	0.474387i
$763$	25.0737	−	8.42293i	0.907729	−	0.304930i
$764$	0.567093	+	0.327411i	0.0205167	+	0.0118453i
$765$	−1.58797	+	5.92637i	−0.0574131	+	0.214268i
$766$	−6.36527	−	11.0250i	−0.229987	−	0.398349i
$767$	20.7052	+	24.6992i	0.747620	+	0.891836i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−29.4787	+	7.89880i	−1.06303	+	0.284838i	−0.747627	−	0.664119i	$-0.768807\pi$
$769$	−29.4787	+	7.89880i	−1.06303	+	0.284838i	−0.315404	+	0.948957i	$0.602140\pi$
$770$	42.9718	+	8.68916i	1.54860	+	0.313136i
$771$	6.56609	−	3.79093i	0.236472	−	0.136527i
$772$	−0.860985	−	3.21324i	−0.0309875	−	0.115647i
$773$	−11.1177	+	2.97898i	−0.399876	+	0.107146i	−0.453152	−	0.891433i	$-0.649700\pi$
$773$	−11.1177	+	2.97898i	−0.399876	+	0.107146i	0.0532757	+	0.998580i	$0.483034\pi$
$774$	8.44668	−	2.26328i	0.303610	−	0.0813520i
$775$	−9.67873	−	36.1215i	−0.347670	−	1.29752i
$776$	−8.99643	+	5.19409i	−0.322953	+	0.186457i
$777$	4.87727	−	1.63840i	0.174971	−	0.0587774i
$778$	−21.4267	+	5.74127i	−0.768184	+	0.205834i
$779$	1.65902	+	0.957837i	0.0594407	+	0.0343181i
$780$	2.41818	+	13.7523i	0.0865846	+	0.492410i
$781$	9.77666	+	16.9337i	0.349836	+	0.605934i
$782$	2.90013	−	10.8234i	0.103708	−	0.387045i
$783$	3.75870	+	2.17009i	0.134325	+	0.0775527i
$784$	6.94576	−	0.869714i	0.248063	−	0.0310612i
$785$	−1.79687	+	1.79687i	−0.0641332	+	0.0641332i
$786$	9.13191	−	9.13191i	0.325724	−	0.325724i
$787$	−4.24357	−	15.8372i	−0.151267	−	0.564535i	−0.999396	−	0.0347462i	$-0.988938\pi$
$787$	−4.24357	−	15.8372i	−0.151267	−	0.564535i	0.848129	−	0.529789i	$-0.177729\pi$
$788$	2.47071	−	9.22081i	0.0880153	−	0.328478i
$789$		−	25.9242i		−	0.922926i
$790$	−31.6374	+	54.7975i	−1.12561	+	1.94961i
$791$	5.30002	+	2.63458i	0.188447	+	0.0936747i
$792$			4.27880i			0.152040i
$793$	9.06193	+	19.4574i	0.321798	+	0.690953i
$794$	4.40487	−	2.54315i	0.156323	−	0.0902531i
$795$	−24.2138	+	24.2138i	−0.858776	+	0.858776i
$796$	−13.7184	+	7.92030i	−0.486234	+	0.280728i
$797$	18.9373	+	32.8004i	0.670794	+	1.16185i	0.977679	+	0.210102i	$0.0673797\pi$
$797$	18.9373	+	32.8004i	0.670794	+	1.16185i	−0.306886	+	0.951746i	$0.599287\pi$
$798$	−0.423801	+	0.852568i	−0.0150024	+	0.0301806i
$799$	3.04851	+	0.816846i	0.107849	+	0.0288979i
$800$	−7.06954	−	7.06954i	−0.249946	−	0.249946i
$801$	15.8111	+	4.23657i	0.558658	+	0.149692i
$802$	−1.83355	+	3.17579i	−0.0647448	+	0.112141i
$803$	−19.6722	−	34.0732i	−0.694215	−	1.20242i
$804$	−3.22129	−	12.0220i	−0.113606	−	0.423984i
$805$	14.3630	−	71.0316i	0.506230	−	2.50353i
$806$	−1.18176	+	13.4342i	−0.0416256	+	0.473201i
$807$	−4.79077	+	8.29785i	−0.168643	+	0.292098i
$808$	−8.82379	−	8.82379i	−0.310420	−	0.310420i
$809$	−26.4503			−0.929943			−0.464972	−	0.885326i	$-0.653935\pi$
$809$	−26.4503			−0.929943			−0.464972	+	0.885326i	$0.653935\pi$
$810$	−3.87271			−0.136073
$811$	16.2954	+	16.2954i	0.572208	+	0.572208i	0.932745	−	0.360537i	$-0.117407\pi$
$811$	16.2954	+	16.2954i	0.572208	+	0.572208i	−0.360537	+	0.932745i	$0.617407\pi$
$812$	5.11140	−	10.2827i	0.179375	−	0.360852i
$813$	−3.36783	+	12.5689i	−0.118115	+	0.440811i
$814$	8.03731	−	2.15359i	0.281708	−	0.0754833i
$815$	−66.0429	−	38.1299i	−2.31338	−	1.33563i
$816$			1.58428i			0.0554607i
$817$	3.03960	+	0.814457i	0.106342	+	0.0284943i
$818$	17.1209			0.598619
$819$	4.97844	−	8.13727i	0.173961	−	0.284339i
$820$	20.6161			0.719945
$821$	35.8503	+	9.60605i	1.25118	+	0.335254i	0.822794	−	0.568340i	$-0.192414\pi$
$821$	35.8503	+	9.60605i	1.25118	+	0.335254i	0.428390	+	0.903594i	$0.359081\pi$
$822$			8.85494i			0.308852i
$823$	−7.52800	−	4.34629i	−0.262410	−	0.151502i	0.363024	−	0.931780i	$-0.381744\pi$
$823$	−7.52800	−	4.34629i	−0.262410	−	0.151502i	−0.625433	+	0.780278i	$0.715078\pi$
$824$	−1.51564	+	0.406115i	−0.0527999	+	0.0141477i
$825$	−11.0720	+	41.3211i	−0.385476	+	1.43862i
$826$	13.0770	+	19.7059i	0.455006	+	0.685655i
$827$	12.9002	+	12.9002i	0.448584	+	0.448584i	0.894884	−	0.446300i	$-0.147258\pi$
$827$	12.9002	+	12.9002i	0.448584	+	0.448584i	−0.446300	+	0.894884i	$0.647258\pi$
$828$	7.07278			0.245796
$829$	−23.7209			−0.823861			−0.411931	−	0.911215i	$-0.635145\pi$
$829$	−23.7209			−0.823861			−0.411931	+	0.911215i	$0.635145\pi$
$830$	37.3990	+	37.3990i	1.29814	+	1.29814i
$831$	4.70380	−	8.14723i	0.163173	−	0.282624i
$832$	1.52222	+	3.26846i	0.0527736	+	0.113313i
$833$	−6.69527	−	8.84081i	−0.231977	−	0.306316i
$834$	0.131555	+	0.490969i	0.00455537	+	0.0170009i
$835$	−26.4256	−	45.7705i	−0.914496	−	1.58395i
$836$	−0.769877	+	1.33347i	−0.0266268	+	0.0461189i
$837$	−3.61293	−	0.968081i	−0.124881	−	0.0334618i
$838$	−0.977948	−	0.977948i	−0.0337827	−	0.0337827i
$839$	−36.7821	−	9.85572i	−1.26986	−	0.340257i	−0.439881	−	0.898056i	$-0.644979\pi$
$839$	−36.7821	−	9.85572i	−1.26986	−	0.340257i	−0.829976	+	0.557799i	$0.811646\pi$
$840$	0.637756	+	10.2263i	0.0220047	+	0.352843i
$841$	5.08143	+	8.80129i	0.175222	+	0.303493i
$842$	24.3122	−	14.0366i	0.837853	−	0.483735i
$843$	6.76237	−	6.76237i	0.232908	−	0.232908i
$844$	6.55876	−	3.78670i	0.225762	−	0.130344i
$845$	21.3200	−	45.6080i	0.733431	−	1.56896i
$846$			1.99211i			0.0684901i
$847$	−10.6912	−	16.1108i	−0.367355	−	0.553573i
$848$	−4.42114	+	7.65764i	−0.151823	+	0.262964i
$849$			2.35306i			0.0807568i
$850$	−4.09952	+	15.2996i	−0.140613	+	0.524773i
$851$	−3.55985	−	13.2855i	−0.122030	−	0.455422i
$852$	−3.23135	+	3.23135i	−0.110704	+	0.110704i
$853$	8.19249	−	8.19249i	0.280505	−	0.280505i	−0.552805	−	0.833311i	$-0.686443\pi$
$853$	8.19249	−	8.19249i	0.280505	−	0.280505i	0.833311	+	0.552805i	$0.186443\pi$
$854$	5.01554	+	14.9305i	0.171628	+	0.510910i
$855$	−1.20691	−	0.696810i	−0.0412755	−	0.0238304i
$856$	−2.24012	+	8.36026i	−0.0765659	+	0.285748i
$857$	−3.89354	−	6.74381i	−0.133001	−	0.230364i	0.791831	−	0.610740i	$-0.209128\pi$
$857$	−3.89354	−	6.74381i	−0.133001	−	0.230364i	−0.924832	+	0.380376i	$0.875795\pi$
$858$	8.85479	−	12.6332i	0.302298	−	0.431291i
$859$	40.9958	+	23.6689i	1.39876	+	0.807573i	0.994263	−	0.106967i	$-0.0341139\pi$
$859$	40.9958	+	23.6689i	1.39876	+	0.807573i	0.404495	+	0.914540i	$0.367447\pi$
$860$	32.7115	−	8.76502i	1.11545	−	0.298885i
$861$	−10.5598	−	9.32003i	−0.359878	−	0.317626i
$862$	−5.96766	+	3.44543i	−0.203259	+	0.117352i
$863$	9.68771	+	36.1550i	0.329774	+	1.23073i	0.909425	+	0.415868i	$0.136522\pi$
$863$	9.68771	+	36.1550i	0.329774	+	1.23073i	−0.579652	+	0.814864i	$0.696811\pi$
$864$	−0.965926	+	0.258819i	−0.0328615	+	0.00880520i
$865$	66.1383	−	17.7217i	2.24877	−	0.602556i
$866$	−1.70948	−	6.37988i	−0.0580906	−	0.216797i
$867$	−12.5488	+	7.24504i	−0.426179	+	0.246054i
$868$	−1.96136	+	9.69980i	−0.0665729	+	0.329233i
$869$	67.5276	−	18.0940i	2.29072	−	0.613796i
$870$	14.5564	+	8.40412i	0.493507	+	0.284926i
$871$	−15.3682	+	42.1615i	−0.520730	+	1.42859i
$872$	4.99870	+	8.65800i	0.169277	+	0.293197i
$873$	−2.68866	+	10.0342i	−0.0909973	+	0.339607i
$874$	2.20420	+	1.27259i	0.0745581	+	0.0430461i
$875$	−10.1494	+	50.1932i	−0.343111	+	1.69684i
$876$	6.50197	−	6.50197i	0.219681	−	0.219681i
$877$	8.74056	−	8.74056i	0.295148	−	0.295148i	−0.543962	−	0.839110i	$-0.683076\pi$
$877$	8.74056	−	8.74056i	0.295148	−	0.295148i	0.839110	+	0.543962i	$0.183076\pi$
$878$	−2.89027	−	10.7866i	−0.0975419	−	0.364031i
$879$	−4.83207	+	18.0335i	−0.162982	+	0.608256i
$880$			16.5705i			0.558592i
$881$	8.46718	−	14.6656i	0.285267	−	0.494096i	−0.687407	−	0.726272i	$-0.741251\pi$
$881$	8.46718	−	14.6656i	0.285267	−	0.494096i	0.972674	+	0.232176i	$0.0745845\pi$
$882$	4.29641	−	5.52638i	0.144668	−	0.186083i
$883$			14.3982i			0.484537i	0.970209	+	0.242268i	$0.0778914\pi$
$883$			14.3982i			0.484537i	−0.970209	+	0.242268i	$0.922109\pi$
$884$	3.27859	−	4.67760i	0.110271	−	0.157325i
$885$	−29.9799	+	17.3089i	−1.00776	+	0.581832i
$886$	−7.21834	+	7.21834i	−0.242505	+	0.242505i
$887$	−37.1566	+	21.4524i	−1.24760	+	0.720300i	−0.970629	−	0.240580i	$-0.922662\pi$
$887$	−37.1566	+	21.4524i	−1.24760	+	0.720300i	−0.276966	+	0.960880i	$0.589329\pi$
$888$	0.972333	+	1.68413i	0.0326294	+	0.0565157i
$889$	48.9025	−	3.04976i	1.64014	−	0.102286i
$890$	61.2318	+	16.4070i	2.05249	+	0.549964i
$891$	3.02557	+	3.02557i	0.101360	+	0.101360i
$892$	13.7367	+	3.68073i	0.459938	+	0.123240i
$893$	−0.358437	+	0.620831i	−0.0119946	+	0.0207753i
$894$	8.76790	+	15.1864i	0.293242	+	0.507911i
$895$	−1.47976	−	5.52253i	−0.0494628	−	0.184598i
$896$	0.842511	+	2.50802i	0.0281463	+	0.0837871i
$897$	−20.8825	−	14.6368i	−0.697246	−	0.488709i
$898$	−15.4532	+	26.7656i	−0.515678	+	0.893181i
$899$	11.4791	+	11.4791i	0.382850	+	0.382850i
$900$	−9.99785			−0.333262
$901$	14.0086			0.466694
$902$	−16.1064	−	16.1064i	−0.536285	−	0.536285i
$903$	−20.7177	−	10.2985i	−0.689441	−	0.342713i
$904$	−0.578994	+	2.16084i	−0.0192571	+	0.0718684i
$905$	−53.8436	+	14.4273i	−1.78982	+	0.479581i
$906$	−19.8362	−	11.4524i	−0.659013	−	0.380481i
$907$		−	49.7264i		−	1.65114i	−0.564301	−	0.825569i	$-0.690854\pi$
$907$		−	49.7264i		−	1.65114i	0.564301	−	0.825569i	$-0.309146\pi$
$908$	−25.6700	−	6.87826i	−0.851890	−	0.228263i
$909$	−12.4787			−0.413893
$910$	19.2800	−	31.5133i	0.639126	−	1.04465i
$911$	0.604437			0.0200259			0.0100129	−	0.999950i	$-0.496813\pi$
$911$	0.604437			0.0200259			0.0100129	+	0.999950i	$0.496813\pi$
$912$	−0.347595	−	0.0931378i	−0.0115100	−	0.00308410i
$913$		−	58.4363i		−	1.93396i
$914$	17.7200	+	10.2307i	0.586126	+	0.338400i
$915$	−22.2690	+	5.96695i	−0.736190	+	0.197261i
$916$	−1.60726	+	5.99836i	−0.0531053	+	0.198191i
$917$	−34.1022	+	2.12675i	−1.12615	+	0.0702315i
$918$	1.12025	+	1.12025i	0.0369738	+	0.0369738i
$919$	34.1289			1.12581			0.562905	−	0.826522i	$-0.309684\pi$
$919$	34.1289			1.12581			0.562905	+	0.826522i	$0.309684\pi$
$920$	27.3908			0.903047
$921$	−1.49765	−	1.49765i	−0.0493493	−	0.0493493i
$922$	4.67860	−	8.10357i	0.154081	−	0.266877i
$923$	16.2277	−	2.85346i	0.534142	−	0.0939228i
$924$	7.49113	−	8.48763i	0.246440	−	0.279222i
$925$	5.03208	+	18.7800i	0.165454	+	0.617482i
$926$	−12.7138	−	22.0209i	−0.417801	−	0.723652i
$927$	−0.784555	+	1.35889i	−0.0257682	+	0.0446317i
$928$	4.19229	+	1.12332i	0.137619	+	0.0368748i
$929$	−4.47695	−	4.47695i	−0.146884	−	0.146884i	0.629840	−	0.776725i	$-0.283120\pi$
$929$	−4.47695	−	4.47695i	−0.146884	−	0.146884i	−0.776725	+	0.629840i	$0.783120\pi$
$930$	−13.9918	−	3.74909i	−0.458809	−	0.122938i
$931$	2.33331	−	0.949221i	0.0764711	−	0.0311095i
$932$	−9.13186	−	15.8168i	−0.299124	−	0.518098i
$933$	−13.4392	+	7.75912i	−0.439979	+	0.254022i
$934$	12.0144	−	12.0144i	0.393125	−	0.393125i
$935$	22.7351	−	13.1261i	0.743519	−	0.429271i
$936$	3.38753	+	1.23478i	0.110725	+	0.0403599i
$937$		−	58.3352i		−	1.90573i	−0.303398	−	0.952864i	$-0.598121\pi$
$937$		−	58.3352i		−	1.90573i	0.303398	−	0.952864i	$-0.401879\pi$
$938$	−14.6577	+	29.4871i	−0.478591	+	0.962789i
$939$	0.867872	−	1.50320i	0.0283219	−	0.0490550i
$940$			7.71485i			0.251631i
$941$	−9.84700	+	36.7495i	−0.321003	+	1.19800i	0.597266	+	0.802043i	$0.296253\pi$
$941$	−9.84700	+	36.7495i	−0.321003	+	1.19800i	−0.918269	+	0.395956i	$0.870413\pi$
$942$	0.169830	+	0.633814i	0.00553336	+	0.0206508i
$943$	−26.6236	+	26.6236i	−0.866984	+	0.866984i
$944$	−6.32076	+	6.32076i	−0.205723	+	0.205723i
$945$	7.68208	+	6.78016i	0.249898	+	0.220559i
$946$	−32.4037	−	18.7083i	−1.05354	−	0.608259i
$947$	−5.48121	+	20.4561i	−0.178115	+	0.664735i	0.817885	+	0.575382i	$0.195147\pi$
$947$	−5.48121	+	20.4561i	−0.178115	+	0.664735i	−0.996000	+	0.0893532i	$0.971520\pi$
$948$	8.16932	+	14.1497i	0.265327	+	0.459560i
$949$	−32.6527	+	5.74161i	−1.05995	+	0.186381i
$950$	−3.11578	−	1.79890i	−0.101089	−	0.0583639i
$951$	−32.7388	+	8.77234i	−1.06163	+	0.284462i
$952$	2.77368	−	3.14264i	0.0898954	−	0.101854i
$953$	35.7121	−	20.6184i	1.15683	−	0.667895i	0.206287	−	0.978492i	$-0.433862\pi$
$953$	35.7121	−	20.6184i	1.15683	−	0.667895i	0.950542	+	0.310596i	$0.100529\pi$
$954$	2.28855	+	8.54098i	0.0740945	+	0.276525i
$955$	2.44953	−	0.656349i	0.0792648	−	0.0212389i
$956$	0.216015	−	0.0578810i	0.00698642	−	0.00187201i
$957$	−4.80646	−	17.9380i	−0.155371	−	0.579852i
$958$	37.1058	−	21.4231i	1.19884	−	0.692148i
$959$	15.5028	−	17.5651i	0.500613	−	0.567206i
$960$	−3.74075	+	1.00233i	−0.120732	+	0.0323501i
$961$	14.7307	+	8.50478i	0.475184	+	0.274348i
$962$	0.614409	−	6.98462i	0.0198094	−	0.225193i
$963$	4.32759	+	7.49560i	0.139455	+	0.241542i
$964$	3.45246	−	12.8848i	0.111196	−	0.414990i
$965$	−11.1569	−	6.44145i	−0.359154	−	0.207358i
$966$	−14.0299	−	12.3827i	−0.451404	−	0.398407i
$967$	−23.8026	+	23.8026i	−0.765439	+	0.765439i	−0.977300	−	0.211861i	$-0.932048\pi$
$967$	−23.8026	+	23.8026i	−0.765439	+	0.765439i	0.211861	+	0.977300i	$0.432048\pi$
$968$	5.16762	−	5.16762i	0.166093	−	0.166093i
$969$	0.147556	+	0.550686i	0.00474018	+	0.0176906i
$970$	−10.4124	+	38.8596i	−0.334322	+	1.24771i
$971$		−	5.73070i		−	0.183907i	−0.995763	−	0.0919534i	$-0.970689\pi$
$971$		−	5.73070i		−	0.183907i	0.995763	−	0.0919534i	$-0.0293111\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	0.598608	−	1.20423i	0.0191905	−	0.0386058i
$974$		−	0.859746i		−	0.0275480i
$975$	29.5188	+	20.6901i	0.945358	+	0.662614i
$976$	−5.15552	+	2.97654i	−0.165024	+	0.0952768i
$977$	21.9031	−	21.9031i	0.700741	−	0.700741i	−0.263828	−	0.964570i	$-0.584985\pi$
$977$	21.9031	−	21.9031i	0.700741	−	0.700741i	0.964570	+	0.263828i	$0.0849852\pi$
$978$	−17.0534	+	9.84580i	−0.545309	+	0.314834i
$979$	−35.0195	−	60.6556i	−1.11923	−	1.93856i
$980$	16.6387	−	21.4020i	0.531505	−	0.683663i
$981$	9.65675	+	2.58752i	0.308316	+	0.0826131i
$982$	−3.87560	−	3.87560i	−0.123675	−	0.123675i
$983$	8.82392	+	2.36436i	0.281439	+	0.0754114i	0.396777	−	0.917915i	$-0.370128\pi$
$983$	8.82392	+	2.36436i	0.281439	+	0.0754114i	−0.115338	+	0.993326i	$0.536795\pi$
$984$	2.66172	−	4.61023i	0.0848525	−	0.146969i
$985$	−18.4846	−	32.0162i	−0.588968	−	1.02012i
$986$	−1.77965	−	6.64174i	−0.0566756	−	0.211516i
$987$	3.48770	−	3.95164i	0.111015	−	0.125782i
$988$	0.833535	+	0.994324i	0.0265183	+	0.0316337i
$989$	−30.9245	+	53.5627i	−0.983341	+	1.70320i
$990$	11.7171	+	11.7171i	0.372395	+	0.372395i
$991$	24.5403			0.779547			0.389773	−	0.920911i	$-0.372553\pi$
$991$	24.5403			0.779547			0.389773	+	0.920911i	$0.372553\pi$
$992$	−3.74038			−0.118757
$993$	6.04854	+	6.04854i	0.191945	+	0.191945i
$994$	12.0671	−	0.752556i	0.382747	−	0.0238696i
$995$	−15.8775	+	59.2557i	−0.503351	+	1.87853i
$996$	13.1918	−	3.53474i	0.417999	−	0.112002i
$997$	6.79694	+	3.92421i	0.215261	+	0.124281i	0.603754	−	0.797171i	$-0.293671\pi$
$997$	6.79694	+	3.92421i	0.215261	+	0.124281i	−0.388493	+	0.921452i	$0.627004\pi$
$998$			15.9327i			0.504342i
$999$	1.87840	+	0.503317i	0.0594301	+	0.0159242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.a.19.4	✓	32
7.3	odd	6		546.2.cg.a.409.8	yes	32
13.11	odd	12		546.2.cg.a.271.8	yes	32
91.24	even	12	inner	546.2.by.a.115.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.a.19.4	✓	32	1.1	even	1	trivial
546.2.by.a.115.4	yes	32	91.24	even	12	inner
546.2.cg.a.271.8	yes	32	13.11	odd	12
546.2.cg.a.409.8	yes	32	7.3	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.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(3.74075 - 1.00233i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-2.20451 + 1.46293i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(3.74075 - 1.00233i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-2.20451 + 1.46293i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -3.87271 q^{10} +(3.02557 + 3.02557i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(3.26846 - 1.52222i) q^{13} +(2.50802 - 0.842511i) q^{14} +(1.00233 + 3.74075i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.792138 - 1.37202i) q^{17} +(0.965926 + 0.258819i) q^{18} +(0.254457 + 0.254457i) q^{19} +(3.74075 + 1.00233i) q^{20} +(-1.46293 - 2.20451i) q^{21} +(-2.13940 - 3.70555i) q^{22} +(-6.12520 + 3.53639i) q^{23} +(0.707107 - 0.707107i) q^{24} +(8.65839 - 4.99892i) q^{25} +(-3.55107 + 0.624415i) q^{26} -1.00000i q^{27} +(-2.64062 + 0.164680i) q^{28} +(-2.17009 + 3.75870i) q^{29} -3.87271i q^{30} +(0.968081 - 3.61293i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-3.02557 + 3.02557i) q^{33} +(-1.12025 + 1.12025i) q^{34} +(-6.78016 + 7.68208i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-0.503317 + 1.87840i) q^{37} +(-0.179928 - 0.311645i) q^{38} +(1.52222 + 3.26846i) q^{39} +(-3.35386 - 1.93635i) q^{40} +(5.14204 - 1.37781i) q^{41} +(0.842511 + 2.50802i) q^{42} +(7.57309 - 4.37232i) q^{43} +(1.10743 + 4.13300i) q^{44} +(-3.74075 + 1.00233i) q^{45} +(6.83178 - 1.83057i) q^{46} +(0.515596 + 1.92423i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(2.71969 - 6.45006i) q^{49} +(-9.65718 + 2.58763i) q^{50} +(1.37202 + 0.792138i) q^{51} +(3.59168 + 0.315946i) q^{52} +(4.42114 + 7.65764i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(14.3505 + 8.28526i) q^{55} +(2.59327 + 0.524375i) q^{56} +(-0.254457 + 0.254457i) q^{57} +(3.06897 - 3.06897i) q^{58} +(2.31356 + 8.63432i) q^{59} +(-1.00233 + 3.74075i) q^{60} +5.95308i q^{61} +(-1.87019 + 3.23926i) q^{62} +(2.20451 - 1.46293i) q^{63} +1.00000i q^{64} +(10.7007 - 8.97033i) q^{65} +(3.70555 - 2.13940i) q^{66} +(-8.80073 + 8.80073i) q^{67} +(1.37202 - 0.792138i) q^{68} +(-3.53639 - 6.12520i) q^{69} +(8.53740 - 5.66549i) q^{70} +(4.41410 + 1.18275i) q^{71} +(0.707107 + 0.707107i) q^{72} +(-8.88186 - 2.37989i) q^{73} +(0.972333 - 1.68413i) q^{74} +(4.99892 + 8.65839i) q^{75} +(0.0931378 + 0.347595i) q^{76} +(-11.0961 - 2.24369i) q^{77} +(-0.624415 - 3.55107i) q^{78} +(8.16932 - 14.1497i) q^{79} +(2.73842 + 2.73842i) q^{80} +1.00000 q^{81} -5.32344 q^{82} +(-9.65709 - 9.65709i) q^{83} +(-0.164680 - 2.64062i) q^{84} +(1.58797 - 5.92637i) q^{85} +(-8.44668 + 2.26328i) q^{86} +(-3.75870 - 2.17009i) q^{87} -4.27880i q^{88} +(-15.8111 - 4.23657i) q^{89} +3.87271 q^{90} +(-4.97844 + 8.13727i) q^{91} -7.07278 q^{92} +(3.61293 + 0.968081i) q^{93} -1.99211i q^{94} +(1.20691 + 0.696810i) q^{95} +(0.965926 - 0.258819i) q^{96} +(2.68866 - 10.0342i) q^{97} +(-4.29641 + 5.52638i) q^{98} +(-3.02557 - 3.02557i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) \) 32 * q + 8 * q^7 - 32 * q^9	\( 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

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