LMFDB - Embedded newform 546.2.bb.a.269.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(269,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 4]))

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

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

chi := DirichletCharacter("546.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.17
Character	$\chi$	$=$	546.269
Dual form			546.2.bb.a.341.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.63536 - 0.570612i) q^{3} -1.00000 q^{4} +(-1.99252 - 3.45115i) q^{5} +(-0.570612 - 1.63536i) q^{6} +(2.09752 - 1.61258i) q^{7} +1.00000i q^{8} +(2.34880 - 1.86631i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.63536 - 0.570612i) q^{3} -1.00000 q^{4} +(-1.99252 - 3.45115i) q^{5} +(-0.570612 - 1.63536i) q^{6} +(2.09752 - 1.61258i) q^{7} +1.00000i q^{8} +(2.34880 - 1.86631i) q^{9} +(-3.45115 + 1.99252i) q^{10} +(-3.18471 + 1.83869i) q^{11} +(-1.63536 + 0.570612i) q^{12} +(-3.60330 + 0.127442i) q^{13} +(-1.61258 - 2.09752i) q^{14} +(-5.22776 - 4.50691i) q^{15} +1.00000 q^{16} +2.34449 q^{17} +(-1.86631 - 2.34880i) q^{18} +(3.64245 + 2.10297i) q^{19} +(1.99252 + 3.45115i) q^{20} +(2.51004 - 3.83402i) q^{21} +(1.83869 + 3.18471i) q^{22} -2.14586i q^{23} +(0.570612 + 1.63536i) q^{24} +(-5.44029 + 9.42285i) q^{25} +(0.127442 + 3.60330i) q^{26} +(2.77620 - 4.39235i) q^{27} +(-2.09752 + 1.61258i) q^{28} +(3.39215 + 1.95846i) q^{29} +(-4.50691 + 5.22776i) q^{30} +(-7.42132 - 4.28470i) q^{31} -1.00000i q^{32} +(-4.15896 + 4.82416i) q^{33} -2.34449i q^{34} +(-9.74460 - 4.02576i) q^{35} +(-2.34880 + 1.86631i) q^{36} +6.89376 q^{37} +(2.10297 - 3.64245i) q^{38} +(-5.81997 + 2.26450i) q^{39} +(3.45115 - 1.99252i) q^{40} +(1.55096 - 2.68634i) q^{41} +(-3.83402 - 2.51004i) q^{42} +(2.70900 + 4.69212i) q^{43} +(3.18471 - 1.83869i) q^{44} +(-11.1210 - 4.38740i) q^{45} -2.14586 q^{46} +(-5.81511 - 10.0721i) q^{47} +(1.63536 - 0.570612i) q^{48} +(1.79918 - 6.76483i) q^{49} +(9.42285 + 5.44029i) q^{50} +(3.83408 - 1.33779i) q^{51} +(3.60330 - 0.127442i) q^{52} +(1.81528 + 1.04805i) q^{53} +(-4.39235 - 2.77620i) q^{54} +(12.6912 + 7.32727i) q^{55} +(1.61258 + 2.09752i) q^{56} +(7.15670 + 1.36069i) q^{57} +(1.95846 - 3.39215i) q^{58} +9.71836 q^{59} +(5.22776 + 4.50691i) q^{60} +(-0.239694 - 0.138387i) q^{61} +(-4.28470 + 7.42132i) q^{62} +(1.91709 - 7.70226i) q^{63} -1.00000 q^{64} +(7.61947 + 12.1816i) q^{65} +(4.82416 + 4.15896i) q^{66} +(-5.35441 - 9.27410i) q^{67} -2.34449 q^{68} +(-1.22445 - 3.50925i) q^{69} +(-4.02576 + 9.74460i) q^{70} +(-3.24128 + 1.87136i) q^{71} +(1.86631 + 2.34880i) q^{72} +(-0.474423 - 0.273908i) q^{73} -6.89376i q^{74} +(-3.52003 + 18.5140i) q^{75} +(-3.64245 - 2.10297i) q^{76} +(-3.71496 + 8.99228i) q^{77} +(2.26450 + 5.81997i) q^{78} +(1.56372 + 2.70844i) q^{79} +(-1.99252 - 3.45115i) q^{80} +(2.03376 - 8.76720i) q^{81} +(-2.68634 - 1.55096i) q^{82} +13.0428 q^{83} +(-2.51004 + 3.83402i) q^{84} +(-4.67144 - 8.09117i) q^{85} +(4.69212 - 2.70900i) q^{86} +(6.66491 + 1.26718i) q^{87} +(-1.83869 - 3.18471i) q^{88} +1.91893 q^{89} +(-4.38740 + 11.1210i) q^{90} +(-7.35248 + 6.07791i) q^{91} +2.14586i q^{92} +(-14.5814 - 2.77233i) q^{93} +(-10.0721 + 5.81511i) q^{94} -16.7609i q^{95} +(-0.570612 - 1.63536i) q^{96} +(2.07811 - 1.19980i) q^{97} +(-6.76483 - 1.79918i) q^{98} +(-4.04868 + 10.2624i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.63536	−	0.570612i	0.944175	−	0.329443i
$3$	1.63536	−	0.570612i	0.944175	−	0.329443i
$4$	−1.00000			−0.500000
$5$	−1.99252	−	3.45115i	−0.891083	−	1.54340i	−0.838579	−	0.544780i	$-0.816613\pi$
$5$	−1.99252	−	3.45115i	−0.891083	−	1.54340i	−0.0525039	−	0.998621i	$-0.516720\pi$
$6$	−0.570612	−	1.63536i	−0.232951	−	0.667633i
$7$	2.09752	−	1.61258i	0.792788	−	0.609497i
$7$	2.09752	−	1.61258i	0.792788	−	0.609497i
$8$			1.00000i			0.353553i
$9$	2.34880	−	1.86631i	0.782935	−	0.622104i
$10$	−3.45115	+	1.99252i	−1.09135	+	0.630091i
$11$	−3.18471	+	1.83869i	−0.960226	+	0.554386i	−0.896242	−	0.443565i	$-0.853714\pi$
$11$	−3.18471	+	1.83869i	−0.960226	+	0.554386i	−0.0639831	+	0.997951i	$0.520380\pi$
$12$	−1.63536	+	0.570612i	−0.472088	+	0.164722i
$13$	−3.60330	+	0.127442i	−0.999375	+	0.0353462i
$13$	−3.60330	+	0.127442i	−0.999375	+	0.0353462i
$14$	−1.61258	−	2.09752i	−0.430980	−	0.560586i
$15$	−5.22776	−	4.50691i	−1.34980	−	1.16368i
$16$	1.00000			0.250000
$17$	2.34449			0.568622			0.284311	−	0.958732i	$-0.408235\pi$
$17$	2.34449			0.568622			0.284311	+	0.958732i	$0.408235\pi$
$18$	−1.86631	−	2.34880i	−0.439894	−	0.553618i
$19$	3.64245	+	2.10297i	0.835635	+	0.482454i	0.855778	−	0.517343i	$-0.173079\pi$
$19$	3.64245	+	2.10297i	0.835635	+	0.482454i	−0.0201428	+	0.999797i	$0.506412\pi$
$20$	1.99252	+	3.45115i	0.445541	+	0.771700i
$21$	2.51004	−	3.83402i	0.547737	−	0.836651i
$22$	1.83869	+	3.18471i	0.392010	+	0.678982i
$23$		−	2.14586i		−	0.447442i	−0.974653	−	0.223721i	$-0.928180\pi$
$23$		−	2.14586i		−	0.447442i	0.974653	−	0.223721i	$-0.0718205\pi$
$24$	0.570612	+	1.63536i	0.116476	+	0.333816i
$25$	−5.44029	+	9.42285i	−1.08806	+	1.88457i
$26$	0.127442	+	3.60330i	0.0249935	+	0.706665i
$27$	2.77620	−	4.39235i	0.534280	−	0.845308i
$28$	−2.09752	+	1.61258i	−0.396394	+	0.304749i
$29$	3.39215	+	1.95846i	0.629906	+	0.363677i	0.780716	−	0.624886i	$-0.214855\pi$
$29$	3.39215	+	1.95846i	0.629906	+	0.363677i	−0.150809	+	0.988563i	$0.548188\pi$
$30$	−4.50691	+	5.22776i	−0.822846	+	0.954454i
$31$	−7.42132	−	4.28470i	−1.33291	−	0.769555i	−0.347163	−	0.937805i	$-0.612855\pi$
$31$	−7.42132	−	4.28470i	−1.33291	−	0.769555i	−0.985744	+	0.168250i	$0.946188\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−4.15896	+	4.82416i	−0.723983	+	0.839778i
$34$		−	2.34449i		−	0.402076i
$35$	−9.74460	−	4.02576i	−1.64714	−	0.680478i
$36$	−2.34880	+	1.86631i	−0.391467	+	0.311052i
$37$	6.89376			1.13333			0.566664	−	0.823949i	$-0.308234\pi$
$37$	6.89376			1.13333			0.566664	+	0.823949i	$0.308234\pi$
$38$	2.10297	−	3.64245i	0.341147	−	0.590884i
$39$	−5.81997	+	2.26450i	−0.931941	+	0.362610i
$40$	3.45115	−	1.99252i	0.545675	−	0.315045i
$41$	1.55096	−	2.68634i	0.242219	−	0.419536i	−0.719127	−	0.694879i	$-0.755458\pi$
$41$	1.55096	−	2.68634i	0.242219	−	0.419536i	0.961346	+	0.275343i	$0.0887913\pi$
$42$	−3.83402	−	2.51004i	−0.591601	−	0.387308i
$43$	2.70900	+	4.69212i	0.413118	+	0.715541i	0.995229	−	0.0975681i	$-0.0311064\pi$
$43$	2.70900	+	4.69212i	0.413118	+	0.715541i	−0.582111	+	0.813109i	$0.697773\pi$
$44$	3.18471	−	1.83869i	0.480113	−	0.277193i
$45$	−11.1210	−	4.38740i	−1.65782	−	0.654036i
$46$	−2.14586			−0.316389
$47$	−5.81511	−	10.0721i	−0.848220	−	1.46916i	−0.882795	−	0.469759i	$-0.844341\pi$
$47$	−5.81511	−	10.0721i	−0.848220	−	1.46916i	0.0345746	−	0.999402i	$-0.488992\pi$
$48$	1.63536	−	0.570612i	0.236044	−	0.0823608i
$49$	1.79918	−	6.76483i	0.257026	−	0.966404i
$50$	9.42285	+	5.44029i	1.33259	+	0.769373i
$51$	3.83408	−	1.33779i	0.536878	−	0.187328i
$52$	3.60330	−	0.127442i	0.499688	−	0.0176731i
$53$	1.81528	+	1.04805i	0.249348	+	0.143961i	0.619466	−	0.785024i	$-0.287349\pi$
$53$	1.81528	+	1.04805i	0.249348	+	0.143961i	−0.370118	+	0.928985i	$0.620683\pi$
$54$	−4.39235	−	2.77620i	−0.597723	−	0.377793i
$55$	12.6912	+	7.32727i	1.71128	+	0.988009i
$56$	1.61258	+	2.09752i	0.215490	+	0.280293i
$57$	7.15670	+	1.36069i	0.947928	+	0.180227i
$58$	1.95846	−	3.39215i	0.257158	−	0.445411i
$59$	9.71836			1.26522			0.632612	−	0.774469i	$-0.281983\pi$
$59$	9.71836			1.26522			0.632612	+	0.774469i	$0.281983\pi$
$60$	5.22776	+	4.50691i	0.674901	+	0.581840i
$61$	−0.239694	−	0.138387i	−0.0306896	−	0.0177187i	0.484577	−	0.874749i	$-0.338974\pi$
$61$	−0.239694	−	0.138387i	−0.0306896	−	0.0177187i	−0.515266	+	0.857030i	$0.672307\pi$
$62$	−4.28470	+	7.42132i	−0.544157	+	0.942508i
$63$	1.91709	−	7.70226i	0.241531	−	0.970393i
$64$	−1.00000			−0.125000
$65$	7.61947	+	12.1816i	0.945079	+	1.51094i
$66$	4.82416	+	4.15896i	0.593813	+	0.511933i
$67$	−5.35441	−	9.27410i	−0.654145	−	1.13301i	−0.982107	−	0.188321i	$-0.939695\pi$
$67$	−5.35441	−	9.27410i	−0.654145	−	1.13301i	0.327963	−	0.944691i	$-0.393638\pi$
$68$	−2.34449			−0.284311
$69$	−1.22445	−	3.50925i	−0.147407	−	0.422464i
$70$	−4.02576	+	9.74460i	−0.481170	+	1.16470i
$71$	−3.24128	+	1.87136i	−0.384670	+	0.222089i	−0.679848	−	0.733353i	$-0.737954\pi$
$71$	−3.24128	+	1.87136i	−0.384670	+	0.222089i	0.295178	+	0.955442i	$0.404621\pi$
$72$	1.86631	+	2.34880i	0.219947	+	0.276809i
$73$	−0.474423	−	0.273908i	−0.0555270	−	0.0320586i	0.471979	−	0.881610i	$-0.343540\pi$
$73$	−0.474423	−	0.273908i	−0.0555270	−	0.0320586i	−0.527507	+	0.849551i	$0.676873\pi$
$74$		−	6.89376i		−	0.801383i
$75$	−3.52003	+	18.5140i	−0.406458	+	2.13782i
$76$	−3.64245	−	2.10297i	−0.417818	−	0.241227i
$77$	−3.71496	+	8.99228i	−0.423359	+	1.02477i
$78$	2.26450	+	5.81997i	0.256404	+	0.658982i
$79$	1.56372	+	2.70844i	0.175932	+	0.304723i	0.940483	−	0.339840i	$-0.110373\pi$
$79$	1.56372	+	2.70844i	0.175932	+	0.304723i	−0.764552	+	0.644563i	$0.777039\pi$
$80$	−1.99252	−	3.45115i	−0.222771	−	0.385850i
$81$	2.03376	−	8.76720i	0.225973	−	0.974134i
$82$	−2.68634	−	1.55096i	−0.296657	−	0.171275i
$83$	13.0428			1.43163			0.715817	−	0.698287i	$-0.246054\pi$
$83$	13.0428			1.43163			0.715817	+	0.698287i	$0.246054\pi$
$84$	−2.51004	+	3.83402i	−0.273868	+	0.418325i
$85$	−4.67144	−	8.09117i	−0.506689	−	0.877611i
$86$	4.69212	−	2.70900i	0.505964	−	0.292118i
$87$	6.66491	+	1.26718i	0.714553	+	0.135856i
$88$	−1.83869	−	3.18471i	−0.196005	−	0.339491i
$89$	1.91893			0.203406			0.101703	−	0.994815i	$-0.467571\pi$
$89$	1.91893			0.203406			0.101703	+	0.994815i	$0.467571\pi$
$90$	−4.38740	+	11.1210i	−0.462473	+	1.17225i
$91$	−7.35248	+	6.07791i	−0.770749	+	0.637138i
$92$			2.14586i			0.223721i
$93$	−14.5814	−	2.77233i	−1.51202	−	0.287477i
$94$	−10.0721	+	5.81511i	−1.03885	+	0.599782i
$95$		−	16.7609i		−	1.71963i
$96$	−0.570612	−	1.63536i	−0.0582378	−	0.166908i
$97$	2.07811	−	1.19980i	0.211000	−	0.121821i	−0.390776	−	0.920486i	$-0.627793\pi$
$97$	2.07811	−	1.19980i	0.211000	−	0.121821i	0.601776	+	0.798665i	$0.294460\pi$
$98$	−6.76483	−	1.79918i	−0.683351	−	0.181745i
$99$	−4.04868	+	10.2624i	−0.406908	+	1.03141i
$100$	5.44029	−	9.42285i	0.544029	−	0.942285i
$101$	3.76758	+	6.52563i	0.374888	+	0.649325i	0.990310	−	0.138873i	$-0.0443479\pi$
$101$	3.76758	+	6.52563i	0.374888	+	0.649325i	−0.615422	+	0.788198i	$0.711015\pi$
$102$	−1.33779	−	3.83408i	−0.132461	−	0.379630i
$103$	7.80371	−	4.50547i	0.768922	−	0.443938i	−0.0635677	−	0.997978i	$-0.520248\pi$
$103$	7.80371	−	4.50547i	0.768922	−	0.443938i	0.832490	+	0.554040i	$0.186915\pi$
$104$	−0.127442	−	3.60330i	−0.0124968	−	0.353332i
$105$	−18.2331	−	1.02318i	−1.77937	−	0.0998519i
$106$	1.04805	−	1.81528i	0.101796	−	0.176315i
$107$			13.2524i			1.28116i	0.767892	+	0.640580i	$0.221306\pi$
$107$			13.2524i			1.28116i	−0.767892	+	0.640580i	$0.778694\pi$
$108$	−2.77620	+	4.39235i	−0.267140	+	0.422654i
$109$	−4.23287	+	7.33155i	−0.405436	+	0.702235i	−0.994372	−	0.105944i	$-0.966213\pi$
$109$	−4.23287	+	7.33155i	−0.405436	+	0.702235i	0.588936	+	0.808179i	$0.299547\pi$
$110$	7.32727	−	12.6912i	0.698628	−	1.21006i
$111$	11.2738	−	3.93366i	1.07006	−	0.373367i
$112$	2.09752	−	1.61258i	0.198197	−	0.152374i
$113$	10.1766	−	5.87547i	0.957335	−	0.552717i	0.0619829	−	0.998077i	$-0.480258\pi$
$113$	10.1766	−	5.87547i	0.957335	−	0.552717i	0.895352	+	0.445360i	$0.146924\pi$
$114$	1.36069	−	7.15670i	0.127440	−	0.670286i
$115$	−7.40567	+	4.27567i	−0.690583	+	0.398708i
$116$	−3.39215	−	1.95846i	−0.314953	−	0.181838i
$117$	−8.22559	+	7.02422i	−0.760456	+	0.649389i
$118$		−	9.71836i		−	0.894648i
$119$	4.91761	−	3.78067i	0.450796	−	0.346573i
$120$	4.50691	−	5.22776i	0.411423	−	0.477227i
$121$	1.26158	−	2.18511i	0.114689	−	0.198647i
$122$	−0.138387	+	0.239694i	−0.0125290	+	0.0217009i
$123$	1.00352	−	5.27814i	0.0904843	−	0.475914i
$124$	7.42132	+	4.28470i	0.666454	+	0.384777i
$125$	23.4343			2.09603
$126$	−7.70226	−	1.91709i	−0.686172	−	0.170788i
$127$	0.726767	−	1.25880i	0.0644901	−	0.111700i	−0.831978	−	0.554809i	$-0.812791\pi$
$127$	0.726767	−	1.25880i	0.0644901	−	0.111700i	0.896468	+	0.443109i	$0.146125\pi$
$128$			1.00000i			0.0883883i
$129$	7.10756	+	6.12752i	0.625786	+	0.539498i
$130$	12.1816	−	7.61947i	1.06840	−	0.668272i
$131$	8.82931	+	15.2928i	0.771421	+	1.33614i	0.936784	+	0.349907i	$0.113787\pi$
$131$	8.82931	+	15.2928i	0.771421	+	1.33614i	−0.165364	+	0.986233i	$0.552880\pi$
$132$	4.15896	−	4.82416i	0.361991	−	0.419889i
$133$	11.0313	−	1.46271i	0.956537	−	0.126833i
$134$	−9.27410	+	5.35441i	−0.801161	+	0.462550i
$135$	−20.6903	−	0.829229i	−1.78074	−	0.0713687i
$136$			2.34449i			0.201038i
$137$			12.5570i			1.07281i	0.843960	+	0.536407i	$0.180219\pi$
$137$			12.5570i			1.07281i	−0.843960	+	0.536407i	$0.819781\pi$
$138$	−3.50925	+	1.22445i	−0.298727	+	0.104232i
$139$	−13.3742	+	7.72159i	−1.13438	+	0.654937i	−0.945034	−	0.326973i	$-0.893971\pi$
$139$	−13.3742	+	7.72159i	−1.13438	+	0.654937i	−0.189350	+	0.981910i	$0.560638\pi$
$140$	9.74460	+	4.02576i	0.823569	+	0.340239i
$141$	−15.2570	−	13.1533i	−1.28487	−	1.10771i
$142$	1.87136	+	3.24128i	0.157041	+	0.272002i
$143$	11.2411	−	7.03122i	0.940030	−	0.587980i
$144$	2.34880	−	1.86631i	0.195734	−	0.155526i
$145$		−	15.6091i		−	1.29626i
$146$	−0.273908	+	0.474423i	−0.0226688	+	0.0392635i
$147$	−0.917779	−	12.0896i	−0.0756972	−	0.997131i
$148$	−6.89376			−0.566664
$149$	−3.50132	−	2.02149i	−0.286839	−	0.165607i	0.349676	−	0.936871i	$-0.386292\pi$
$149$	−3.50132	−	2.02149i	−0.286839	−	0.165607i	−0.636516	+	0.771264i	$0.719625\pi$
$150$	18.5140	+	3.52003i	1.51167	+	0.287410i
$151$	4.77604	−	8.27235i	0.388669	−	0.673194i	−0.603602	−	0.797286i	$-0.706268\pi$
$151$	4.77604	−	8.27235i	0.388669	−	0.673194i	0.992271	+	0.124092i	$0.0396017\pi$
$152$	−2.10297	+	3.64245i	−0.170573	+	0.295442i
$153$	5.50674	−	4.37554i	0.445193	−	0.353742i
$154$	8.99228	+	3.71496i	0.724619	+	0.299360i
$155$			34.1494i			2.74295i
$156$	5.81997	−	2.26450i	0.465970	−	0.181305i
$157$	17.0665	+	9.85334i	1.36205	+	0.786383i	0.989897	−	0.141787i	$-0.0452849\pi$
$157$	17.0665	+	9.85334i	1.36205	+	0.786383i	0.372157	+	0.928170i	$0.378618\pi$
$158$	2.70844	−	1.56372i	0.215472	−	0.124403i
$159$	3.56667	+	0.678122i	0.282855	+	0.0537786i
$160$	−3.45115	+	1.99252i	−0.272837	+	0.157523i
$161$	−3.46036	−	4.50098i	−0.272715	−	0.354727i
$162$	−8.76720	−	2.03376i	−0.688816	−	0.159787i
$163$	0.179871	−	0.311545i	0.0140886	−	0.0244021i	−0.858895	−	0.512151i	$-0.828849\pi$
$163$	0.179871	−	0.311545i	0.0140886	−	0.0244021i	0.872984	+	0.487749i	$0.162182\pi$
$164$	−1.55096	+	2.68634i	−0.121110	+	0.209768i
$165$	24.9357	+	4.74097i	1.94124	+	0.369084i
$166$		−	13.0428i		−	1.01232i
$167$	−1.89219	+	3.27738i	−0.146422	+	0.253611i	−0.929903	−	0.367806i	$-0.880109\pi$
$167$	−1.89219	+	3.27738i	−0.146422	+	0.253611i	0.783480	+	0.621417i	$0.213443\pi$
$168$	3.83402	+	2.51004i	0.295801	+	0.193654i
$169$	12.9675	−	0.918426i	0.997501	−	0.0706481i
$170$	−8.09117	+	4.67144i	−0.620565	+	0.358283i
$171$	12.4802	−	1.85849i	0.954385	−	0.142122i
$172$	−2.70900	−	4.69212i	−0.206559	−	0.357771i
$173$	10.7432	−	18.6077i	0.816789	−	1.41472i	−0.0912480	−	0.995828i	$-0.529086\pi$
$173$	10.7432	−	18.6077i	0.816789	−	1.41472i	0.908037	−	0.418891i	$-0.137581\pi$
$174$	1.26718	−	6.66491i	0.0960649	−	0.505265i
$175$	3.78397	+	28.5375i	0.286041	+	2.15723i
$176$	−3.18471	+	1.83869i	−0.240056	+	0.138597i
$177$	15.8930	−	5.54541i	1.19459	−	0.416819i
$178$		−	1.91893i		−	0.143830i
$179$	−13.3321	+	7.69731i	−0.996490	+	0.575324i	−0.907208	−	0.420683i	$-0.861791\pi$
$179$	−13.3321	+	7.69731i	−0.996490	+	0.575324i	−0.0892820	+	0.996006i	$0.528457\pi$
$180$	11.1210	+	4.38740i	0.828908	+	0.327018i
$181$		−	23.9027i		−	1.77668i	−0.459189	−	0.888339i	$-0.651860\pi$
$181$		−	23.9027i		−	1.77668i	0.459189	−	0.888339i	$-0.348140\pi$
$182$	6.07791	+	7.35248i	0.450525	+	0.545002i
$183$	−0.470951	−	0.0895408i	−0.0348137	−	0.00661905i
$184$	2.14586			0.158195
$185$	−13.7360	−	23.7914i	−1.00989	−	1.74918i
$186$	−2.77233	+	14.5814i	−0.203277	+	1.06916i
$187$	−7.46650	+	4.31079i	−0.546005	+	0.315236i
$188$	5.81511	+	10.0721i	0.424110	+	0.734580i
$189$	−1.25987	−	13.6899i	−0.0916419	−	0.995792i
$190$	−16.7609			−1.21596
$191$	−13.2220	−	7.63375i	−0.956713	−	0.552359i	−0.0615532	−	0.998104i	$-0.519605\pi$
$191$	−13.2220	−	7.63375i	−0.956713	−	0.552359i	−0.895160	+	0.445745i	$0.852939\pi$
$192$	−1.63536	+	0.570612i	−0.118022	+	0.0411804i
$193$	−8.35541	−	14.4720i	−0.601436	−	1.04172i	−0.992604	−	0.121398i	$-0.961262\pi$
$193$	−8.35541	−	14.4720i	−0.601436	−	1.04172i	0.391168	−	0.920319i	$-0.372071\pi$
$194$	−1.19980	−	2.07811i	−0.0861405	−	0.149200i
$195$	19.4115	+	15.5735i	1.39009	+	1.11524i
$196$	−1.79918	+	6.76483i	−0.128513	+	0.483202i
$197$	1.81961	+	1.05055i	0.129642	+	0.0748488i	0.563418	−	0.826172i	$-0.309486\pi$
$197$	1.81961	+	1.05055i	0.129642	+	0.0748488i	−0.433776	+	0.901021i	$0.642819\pi$
$198$	10.2624	+	4.04868i	0.729316	+	0.287727i
$199$			15.1451i			1.07361i	0.843708	+	0.536803i	$0.180368\pi$
$199$			15.1451i			1.07361i	−0.843708	+	0.536803i	$0.819632\pi$
$200$	−9.42285	−	5.44029i	−0.666296	−	0.384686i
$201$	−14.0483	−	12.1112i	−0.990890	−	0.854259i
$202$	6.52563	−	3.76758i	0.459142	−	0.265086i
$203$	10.2733	−	1.36220i	0.721042	−	0.0956076i
$204$	−3.83408	+	1.33779i	−0.268439	+	0.0936642i
$205$	−12.3613			−0.863351
$206$	−4.50547	−	7.80371i	−0.313911	−	0.543710i
$207$	−4.00484	−	5.04020i	−0.278356	−	0.350318i
$208$	−3.60330	+	0.127442i	−0.249844	+	0.00883654i
$209$	−15.4669			−1.06986
$210$	−1.02318	+	18.2331i	−0.0706060	+	1.25820i
$211$	−7.97522	+	13.8135i	−0.549037	+	0.950960i	0.449304	+	0.893379i	$0.351672\pi$
$211$	−7.97522	+	13.8135i	−0.549037	+	0.950960i	−0.998341	+	0.0575808i	$0.981661\pi$
$212$	−1.81528	−	1.04805i	−0.124674	−	0.0719805i
$213$	−4.23285	+	4.90986i	−0.290030	+	0.336418i
$214$	13.2524			0.905917
$215$	10.7955	−	18.6983i	0.736245	−	1.27521i
$216$	4.39235	+	2.77620i	0.298861	+	0.188896i
$217$	−22.4758	+	2.98021i	−1.52575	+	0.202310i
$218$	7.33155	+	4.23287i	0.496555	+	0.286686i
$219$	−0.932148	−	0.177227i	−0.0629887	−	0.0119759i
$220$	−12.6912	−	7.32727i	−0.855641	−	0.494004i
$221$	−8.44788	+	0.298787i	−0.568266	+	0.0200986i
$222$	−3.93366	−	11.2738i	−0.264010	−	0.756647i
$223$	15.9530	+	9.21049i	1.06829	+	0.616780i	0.927715	−	0.373289i	$-0.121770\pi$
$223$	15.9530	+	9.21049i	1.06829	+	0.616780i	0.140580	+	0.990069i	$0.455103\pi$
$224$	−1.61258	−	2.09752i	−0.107745	−	0.140146i
$225$	4.80782	+	32.2857i	0.320521	+	2.15238i
$226$	−5.87547	−	10.1766i	−0.390830	−	0.676938i
$227$	−9.78852			−0.649687			−0.324843	−	0.945768i	$-0.605312\pi$
$227$	−9.78852			−0.649687			−0.324843	+	0.945768i	$0.605312\pi$
$228$	−7.15670	−	1.36069i	−0.473964	−	0.0901137i
$229$	−3.72044	+	2.14800i	−0.245853	+	0.141944i	−0.617864	−	0.786285i	$-0.712002\pi$
$229$	−3.72044	+	2.14800i	−0.245853	+	0.141944i	0.372011	+	0.928228i	$0.378668\pi$
$230$	4.27567	+	7.40567i	0.281929	+	0.488316i
$231$	−0.944185	+	16.8254i	−0.0621228	+	1.10703i
$232$	−1.95846	+	3.39215i	−0.128579	+	0.222706i
$233$	8.68795	−	5.01599i	0.569167	−	0.328609i	−0.187650	−	0.982236i	$-0.560087\pi$
$233$	8.68795	−	5.01599i	0.569167	−	0.328609i	0.756817	+	0.653627i	$0.226754\pi$
$234$	7.02422	+	8.22559i	0.459187	+	0.537724i
$235$	−23.1735	+	40.1376i	−1.51167	+	2.61829i
$236$	−9.71836			−0.632612
$237$	4.10271	+	3.53699i	0.266499	+	0.229752i
$238$	−3.78067	−	4.91761i	−0.245064	−	0.318761i
$239$			11.8430i			0.766060i	0.923736	+	0.383030i	$0.125119\pi$
$239$			11.8430i			0.766060i	−0.923736	+	0.383030i	$0.874881\pi$
$240$	−5.22776	−	4.50691i	−0.337450	−	0.290920i
$241$			0.945386i			0.0608976i	0.999536	+	0.0304488i	$0.00969366\pi$
$241$			0.945386i			0.0608976i	−0.999536	+	0.0304488i	$0.990306\pi$
$242$	−2.18511	−	1.26158i	−0.140464	−	0.0810972i
$243$	−1.67674	−	15.4980i	−0.107563	−	0.994198i
$244$	0.239694	+	0.138387i	0.0153448	+	0.00885934i
$245$	−26.9314	+	7.26982i	−1.72058	+	0.464452i
$246$	−5.27814	−	1.00352i	−0.336522	−	0.0639821i
$247$	−13.3928	−	7.11342i	−0.852166	−	0.452616i
$248$	4.28470	−	7.42132i	0.272079	−	0.471254i
$249$	21.3297	−	7.44239i	1.35171	−	0.471642i
$250$		−	23.4343i		−	1.48212i
$251$	−7.94764	−	13.7657i	−0.501650	−	0.868884i	−0.999998	−	0.00190672i	$-0.999393\pi$
$251$	−7.94764	−	13.7657i	−0.501650	−	0.868884i	0.498348	−	0.866977i	$-0.333940\pi$
$252$	−1.91709	+	7.70226i	−0.120765	+	0.485197i
$253$	3.94557	+	6.83393i	0.248056	+	0.429645i
$254$	−1.25880	−	0.726767i	−0.0789839	−	0.0456014i
$255$	−12.2564	−	10.5664i	−0.767526	−	0.661694i
$256$	1.00000			0.0625000
$257$	−20.1972			−1.25987			−0.629933	−	0.776650i	$-0.716917\pi$
$257$	−20.1972			−1.25987			−0.629933	+	0.776650i	$0.716917\pi$
$258$	6.12752	−	7.10756i	0.381482	−	0.442497i
$259$	14.4598	−	11.1167i	0.898489	−	0.690760i
$260$	−7.61947	−	12.1816i	−0.472540	−	0.755470i
$261$	11.6226	−	1.73077i	0.719420	−	0.107132i
$262$	15.2928	−	8.82931i	0.944794	−	0.545477i
$263$	−25.8844	+	14.9444i	−1.59610	+	0.921509i	−0.603872	+	0.797082i	$0.706376\pi$
$263$	−25.8844	+	14.9444i	−1.59610	+	0.921509i	−0.992229	+	0.124428i	$0.960291\pi$
$264$	−4.82416	−	4.15896i	−0.296906	−	0.255967i
$265$		−	8.35306i		−	0.513125i
$266$	−1.46271	−	11.0313i	−0.0896847	−	0.676373i
$267$	3.13814	−	1.09496i	0.192051	−	0.0670107i
$268$	5.35441	+	9.27410i	0.327072	+	0.566506i
$269$	−12.8056			−0.780770			−0.390385	−	0.920652i	$-0.627658\pi$
$269$	−12.8056			−0.780770			−0.390385	+	0.920652i	$0.627658\pi$
$270$	−0.829229	+	20.6903i	−0.0504653	+	1.25917i
$271$			31.5846i			1.91863i	0.282343	+	0.959313i	$0.408888\pi$
$271$			31.5846i			1.91863i	−0.282343	+	0.959313i	$0.591112\pi$
$272$	2.34449			0.142155
$273$	−8.55582	+	14.1350i	−0.517822	+	0.855488i
$274$	12.5570			0.758594
$275$		−	40.0120i		−	2.41282i
$276$	1.22445	+	3.50925i	0.0737034	+	0.211232i
$277$	16.2877			0.978634			0.489317	−	0.872106i	$-0.337246\pi$
$277$	16.2877			0.978634			0.489317	+	0.872106i	$0.337246\pi$
$278$	7.72159	+	13.3742i	0.463110	+	0.802130i
$279$	−25.4278	+	3.78657i	−1.52232	+	0.226696i
$280$	4.02576	−	9.74460i	0.240585	−	0.582351i
$281$		−	13.4422i		−	0.801897i	−0.916101	−	0.400948i	$-0.868681\pi$
$281$		−	13.4422i		−	0.801897i	0.916101	−	0.400948i	$-0.131319\pi$
$282$	−13.1533	+	15.2570i	−0.783266	+	0.908543i
$283$	11.2215	−	6.47874i	0.667050	−	0.385121i	−0.127908	−	0.991786i	$-0.540826\pi$
$283$	11.2215	−	6.47874i	0.667050	−	0.385121i	0.794958	+	0.606665i	$0.207493\pi$
$284$	3.24128	−	1.87136i	0.192335	−	0.111045i
$285$	−9.56394	−	27.4100i	−0.566519	−	1.62363i
$286$	−7.03122	−	11.2411i	−0.415765	−	0.664702i
$287$	−1.07877	−	8.13571i	−0.0636775	−	0.480236i
$288$	−1.86631	−	2.34880i	−0.109973	−	0.138405i
$289$	−11.5034			−0.676670
$290$	−15.6091			−0.916597
$291$	2.71384	−	3.14790i	0.159088	−	0.184533i
$292$	0.474423	+	0.273908i	0.0277635	+	0.0160293i
$293$	12.9609	+	22.4489i	0.757182	+	1.31148i	0.944282	+	0.329136i	$0.106758\pi$
$293$	12.9609	+	22.4489i	0.757182	+	1.31148i	−0.187101	+	0.982341i	$0.559909\pi$
$294$	−12.0896	+	0.917779i	−0.705078	+	0.0535260i
$295$	−19.3641	−	33.5395i	−1.12742	−	1.95275i
$296$			6.89376i			0.400692i
$297$	−0.765210	+	19.0929i	−0.0444020	+	1.10788i
$298$	−2.02149	+	3.50132i	−0.117102	+	0.202826i
$299$	0.273473	+	7.73216i	0.0158154	+	0.447163i
$300$	3.52003	−	18.5140i	0.203229	−	1.06891i
$301$	13.2486	+	5.47335i	0.763635	+	0.315478i
$302$	−8.27235	−	4.77604i	−0.476020	−	0.274830i
$303$	9.88495	+	8.52194i	0.567876	+	0.489572i
$304$	3.64245	+	2.10297i	0.208909	+	0.120614i
$305$			1.10296i			0.0631552i
$306$	−4.37554	−	5.50674i	−0.250133	−	0.314799i
$307$			20.1696i			1.15114i	0.817753	+	0.575569i	$0.195219\pi$
$307$			20.1696i			1.15114i	−0.817753	+	0.575569i	$0.804781\pi$
$308$	3.71496	−	8.99228i	0.211679	−	0.512383i
$309$	10.1910	−	11.8210i	0.579746	−	0.672471i
$310$	34.1494			1.93956
$311$	12.0287	−	20.8342i	0.682082	−	1.18140i	−0.292262	−	0.956338i	$-0.594408\pi$
$311$	12.0287	−	20.8342i	0.682082	−	1.18140i	0.974344	−	0.225063i	$-0.0722588\pi$
$312$	−2.26450	−	5.81997i	−0.128202	−	0.329491i
$313$	−6.85676	+	3.95875i	−0.387567	+	0.223762i	−0.681105	−	0.732185i	$-0.738500\pi$
$313$	−6.85676	+	3.95875i	−0.387567	+	0.223762i	0.293539	+	0.955947i	$0.405167\pi$
$314$	9.85334	−	17.0665i	0.556056	−	0.963118i
$315$	−30.4015	+	8.73075i	−1.71293	+	0.491922i
$316$	−1.56372	−	2.70844i	−0.0879659	−	0.152361i
$317$	−23.9291	+	13.8155i	−1.34399	+	0.775954i	−0.987391	−	0.158302i	$-0.949398\pi$
$317$	−23.9291	+	13.8155i	−1.34399	+	0.775954i	−0.356601	+	0.934257i	$0.616065\pi$
$318$	0.678122	−	3.56667i	0.0380272	−	0.200009i
$319$	−14.4040			−0.806470
$320$	1.99252	+	3.45115i	0.111385	+	0.192925i
$321$	7.56199	+	21.6725i	0.422069	+	1.20964i
$322$	−4.50098	+	3.46036i	−0.250830	+	0.192838i
$323$	8.53968	+	4.93038i	0.475160	+	0.274334i
$324$	−2.03376	+	8.76720i	−0.112987	+	0.487067i
$325$	18.4021	−	34.6467i	1.02077	−	1.92185i
$326$	−0.311545	−	0.179871i	−0.0172549	−	0.00996211i
$327$	−2.73880	+	14.4050i	−0.151456	+	0.796601i
$328$	2.68634	+	1.55096i	0.148329	+	0.0856375i
$329$	−28.4393	−	11.7490i	−1.56791	−	0.647745i
$330$	4.74097	−	24.9357i	0.260982	−	1.37267i
$331$	−6.66281	+	11.5403i	−0.366221	+	0.634313i	−0.988971	−	0.148107i	$-0.952682\pi$
$331$	−6.66281	+	11.5403i	−0.366221	+	0.634313i	0.622750	+	0.782421i	$0.286015\pi$
$332$	−13.0428			−0.715817
$333$	16.1921	−	12.8659i	0.887321	−	0.705047i
$334$	3.27738	+	1.89219i	0.179330	+	0.103536i
$335$	−21.3375	+	36.9577i	−1.16579	+	2.01922i
$336$	2.51004	−	3.83402i	0.136934	−	0.209163i
$337$	6.30526			0.343469			0.171735	−	0.985143i	$-0.445063\pi$
$337$	6.30526			0.343469			0.171735	+	0.985143i	$0.445063\pi$
$338$	−0.918426	−	12.9675i	−0.0499558	−	0.705340i
$339$	13.2898	−	15.4154i	0.721803	−	0.837249i
$340$	4.67144	+	8.09117i	0.253344	+	0.438805i
$341$	31.5130			1.70652
$342$	−1.85849	−	12.4802i	−0.100495	−	0.674852i
$343$	−7.13499	−	17.0907i	−0.385253	−	0.922811i
$344$	−4.69212	+	2.70900i	−0.252982	+	0.146059i
$345$	−9.67120	+	11.2180i	−0.520680	+	0.603958i
$346$	−18.6077	−	10.7432i	−1.00036	−	0.577557i
$347$			14.8278i			0.796001i	0.917385	+	0.398000i	$0.130296\pi$
$347$			14.8278i			0.796001i	−0.917385	+	0.398000i	$0.869704\pi$
$348$	−6.66491	−	1.26718i	−0.357276	−	0.0679281i
$349$	2.57029	+	1.48396i	0.137584	+	0.0794343i	0.567212	−	0.823572i	$-0.308022\pi$
$349$	2.57029	+	1.48396i	0.137584	+	0.0794343i	−0.429628	+	0.903006i	$0.641355\pi$
$350$	28.5375	−	3.78397i	1.52539	−	0.202262i
$351$	−9.44370	+	16.1807i	−0.504068	+	0.863664i
$352$	1.83869	+	3.18471i	0.0980026	+	0.169745i
$353$	−4.30346	−	7.45381i	−0.229050	−	0.396727i	0.728477	−	0.685071i	$-0.240229\pi$
$353$	−4.30346	−	7.45381i	−0.229050	−	0.396727i	−0.957527	+	0.288344i	$0.906895\pi$
$354$	−5.54541	−	15.8930i	−0.294735	−	0.844704i
$355$	12.9167	+	7.45744i	0.685545	+	0.395800i
$356$	−1.91893			−0.101703
$357$	5.88477	−	8.98880i	0.311455	−	0.475738i
$358$	7.69731	+	13.3321i	0.406815	+	0.704625i
$359$	6.89926	−	3.98329i	0.364129	−	0.210230i	−0.306761	−	0.951786i	$-0.599245\pi$
$359$	6.89926	−	3.98329i	0.364129	−	0.210230i	0.670891	+	0.741556i	$0.265912\pi$
$360$	4.38740	−	11.1210i	0.231237	−	0.586126i
$361$	−0.655036	−	1.13456i	−0.0344756	−	0.0597134i
$362$	−23.9027			−1.25630
$363$	0.816278	−	4.29332i	0.0428435	−	0.225341i
$364$	7.35248	−	6.07791i	0.385375	−	0.318569i
$365$			2.18307i			0.114267i
$366$	−0.0895408	+	0.470951i	−0.00468037	+	0.0246170i
$367$	−19.7318	+	11.3921i	−1.02999	+	0.594665i	−0.916982	−	0.398929i	$-0.869382\pi$
$367$	−19.7318	+	11.3921i	−1.02999	+	0.594665i	−0.113008	+	0.993594i	$0.536049\pi$
$368$		−	2.14586i		−	0.111861i
$369$	−1.37065	−	9.20427i	−0.0713533	−	0.479155i
$370$	−23.7914	+	13.7360i	−1.23686	+	0.714099i
$371$	5.49765	−	0.728969i	0.285424	−	0.0378462i
$372$	14.5814	+	2.77233i	0.756011	+	0.143739i
$373$	−10.4632	+	18.1228i	−0.541765	+	0.938364i	0.457038	+	0.889447i	$0.348910\pi$
$373$	−10.4632	+	18.1228i	−0.541765	+	0.938364i	−0.998803	+	0.0489171i	$0.984423\pi$
$374$	4.31079	+	7.46650i	0.222906	+	0.386084i
$375$	38.3236	−	13.3719i	1.97902	−	0.690523i
$376$	10.0721	−	5.81511i	0.519427	−	0.299891i
$377$	−12.4725	−	6.62461i	−0.642367	−	0.341185i
$378$	−13.6899	+	1.25987i	−0.704131	+	0.0648006i
$379$	0.0758760	−	0.131421i	0.00389749	−	0.00675064i	−0.864070	−	0.503372i	$-0.832093\pi$
$379$	0.0758760	−	0.131421i	0.00389749	−	0.00675064i	0.867968	+	0.496621i	$0.165426\pi$
$380$			16.7609i			0.859814i
$381$	0.470240	−	2.47329i	0.0240911	−	0.126710i
$382$	−7.63375	+	13.2220i	−0.390576	+	0.676498i
$383$	−5.67502	+	9.82943i	−0.289980	+	0.502260i	−0.973805	−	0.227386i	$-0.926982\pi$
$383$	−5.67502	+	9.82943i	−0.289980	+	0.502260i	0.683825	+	0.729647i	$0.260315\pi$
$384$	0.570612	+	1.63536i	0.0291189	+	0.0834541i
$385$	38.4358	−	5.09646i	1.95887	−	0.259739i
$386$	−14.4720	+	8.35541i	−0.736605	+	0.425279i
$387$	15.1199	+	5.96503i	0.768585	+	0.303220i
$388$	−2.07811	+	1.19980i	−0.105500	+	0.0609105i
$389$	18.4814	+	10.6702i	0.937043	+	0.541002i	0.889032	−	0.457845i	$-0.151378\pi$
$389$	18.4814	+	10.6702i	0.937043	+	0.541002i	0.0480112	+	0.998847i	$0.484712\pi$
$390$	15.5735	−	19.4115i	0.788596	−	0.982942i
$391$		−	5.03093i		−	0.254425i
$392$	6.76483	+	1.79918i	0.341676	+	0.0908725i
$393$	23.1654	+	19.9712i	1.16854	+	1.00741i
$394$	1.05055	−	1.81961i	0.0529261	−	0.0916707i
$395$	6.23148	−	10.7932i	0.313540	−	0.543067i
$396$	4.04868	−	10.2624i	0.203454	−	0.515704i
$397$	14.1516	+	8.17044i	0.710249	+	0.410063i	0.811153	−	0.584834i	$-0.198840\pi$
$397$	14.1516	+	8.17044i	0.710249	+	0.410063i	−0.100904	+	0.994896i	$0.532174\pi$
$398$	15.1451			0.759154
$399$	17.2055	−	8.68667i	0.861354	−	0.434877i
$400$	−5.44029	+	9.42285i	−0.272014	+	0.471143i
$401$			27.9807i			1.39729i	0.715470	+	0.698644i	$0.246213\pi$
$401$			27.9807i			1.39729i	−0.715470	+	0.698644i	$0.753787\pi$
$402$	−12.1112	+	14.0483i	−0.604052	+	0.700665i
$403$	27.2873	+	14.4933i	1.35928	+	0.721960i
$404$	−3.76758	−	6.52563i	−0.187444	−	0.324662i
$405$	−34.3092	+	10.4500i	−1.70484	+	0.519267i
$406$	−1.36220	−	10.2733i	−0.0676048	−	0.509854i
$407$	−21.9546	+	12.6755i	−1.08825	+	0.628301i
$408$	1.33779	+	3.83408i	0.0662306	+	0.189815i
$409$		−	29.9985i		−	1.48333i	−0.670771	−	0.741664i	$-0.734037\pi$
$409$		−	29.9985i		−	1.48333i	0.670771	−	0.741664i	$-0.265963\pi$
$410$			12.3613i			0.610481i
$411$	7.16515	+	20.5352i	0.353431	+	1.01292i
$412$	−7.80371	+	4.50547i	−0.384461	+	0.221969i
$413$	20.3845	−	15.6716i	1.00305	−	0.771150i
$414$	−5.04020	+	4.00484i	−0.247712	+	0.196827i
$415$	−25.9881	−	45.0127i	−1.27571	−	2.20959i
$416$	0.127442	+	3.60330i	0.00624838	+	0.176666i
$417$	−17.4656	+	20.2590i	−0.855293	+	0.992090i
$418$			15.4669i			0.756509i
$419$	12.1211	−	20.9944i	0.592155	−	1.02564i	−0.401787	−	0.915733i	$-0.631611\pi$
$419$	12.1211	−	20.9944i	0.592155	−	1.02564i	0.993942	−	0.109909i	$-0.0350559\pi$
$420$	18.2331	+	1.02318i	0.889683	+	0.0499260i
$421$	6.28451			0.306288			0.153144	−	0.988204i	$-0.451060\pi$
$421$	6.28451			0.306288			0.153144	+	0.988204i	$0.451060\pi$
$422$	13.8135	+	7.97522i	0.672430	+	0.388228i
$423$	−32.4561	−	12.8045i	−1.57807	−	0.622575i
$424$	−1.04805	+	1.81528i	−0.0508979	+	0.0881577i
$425$	−12.7547	+	22.0918i	−0.618693	+	1.07161i
$426$	4.90986	+	4.23285i	0.237883	+	0.205082i
$427$	−0.725923	+	0.0962548i	−0.0351299	+	0.00465809i
$428$		−	13.2524i		−	0.640580i
$429$	14.3712	−	17.9129i	0.693847	−	0.864843i
$430$	−18.6983	−	10.7955i	−0.901712	−	0.520604i
$431$	12.5883	−	7.26788i	0.606359	−	0.350081i	−0.165180	−	0.986263i	$-0.552821\pi$
$431$	12.5883	−	7.26788i	0.606359	−	0.350081i	0.771539	+	0.636182i	$0.219487\pi$
$432$	2.77620	−	4.39235i	0.133570	−	0.211327i
$433$	14.4330	−	8.33288i	0.693604	−	0.400453i	−0.111357	−	0.993781i	$-0.535520\pi$
$433$	14.4330	−	8.33288i	0.693604	−	0.400453i	0.804961	+	0.593328i	$0.202186\pi$
$434$	2.98021	+	22.4758i	0.143054	+	1.07887i
$435$	−8.90673	−	25.5265i	−0.427045	−	1.22390i
$436$	4.23287	−	7.33155i	0.202718	−	0.351118i
$437$	4.51267	−	7.81618i	0.215870	−	0.373899i
$438$	−0.177227	+	0.932148i	−0.00846824	+	0.0445398i
$439$			2.49431i			0.119047i	0.998227	+	0.0595234i	$0.0189581\pi$
$439$			2.49431i			0.119047i	−0.998227	+	0.0595234i	$0.981042\pi$
$440$	−7.32727	+	12.6912i	−0.349314	+	0.605029i
$441$	−8.39935	−	19.2471i	−0.399969	−	0.916529i
$442$	0.298787	+	8.44788i	0.0142118	+	0.401825i
$443$	0.249840	−	0.144245i	0.0118703	−	0.00685329i	−0.494053	−	0.869432i	$-0.664485\pi$
$443$	0.249840	−	0.144245i	0.0118703	−	0.00685329i	0.505923	+	0.862578i	$0.331152\pi$
$444$	−11.2738	+	3.93366i	−0.535030	+	0.186683i
$445$	−3.82351	−	6.62251i	−0.181252	−	0.313937i
$446$	9.21049	−	15.9530i	0.436129	−	0.755398i
$447$	−6.87940	−	1.30796i	−0.325385	−	0.0618646i
$448$	−2.09752	+	1.61258i	−0.0990985	+	0.0761871i
$449$	−3.87035	+	2.23455i	−0.182653	+	0.105455i	−0.588539	−	0.808469i	$-0.700296\pi$
$449$	−3.87035	+	2.23455i	−0.182653	+	0.105455i	0.405886	+	0.913924i	$0.366963\pi$
$450$	32.2857	−	4.80782i	1.52196	−	0.226643i
$451$			11.4070i			0.537133i
$452$	−10.1766	+	5.87547i	−0.478667	+	0.276359i
$453$	3.09025	−	16.2535i	0.145192	−	0.763658i
$454$			9.78852i			0.459398i
$455$	35.6258	+	13.2641i	1.67016	+	0.621832i
$456$	−1.36069	+	7.15670i	−0.0637200	+	0.335143i
$457$	−32.2831			−1.51014			−0.755069	−	0.655645i	$-0.772397\pi$
$457$	−32.2831			−1.51014			−0.755069	+	0.655645i	$0.772397\pi$
$458$	2.14800	+	3.72044i	0.100369	+	0.173845i
$459$	6.50876	−	10.2978i	0.303803	−	0.480660i
$460$	7.40567	−	4.27567i	0.345291	−	0.199354i
$461$	−19.3508	−	33.5166i	−0.901257	−	1.56102i	−0.825864	−	0.563869i	$-0.809312\pi$
$461$	−19.3508	−	33.5166i	−0.901257	−	1.56102i	−0.0753926	−	0.997154i	$-0.524021\pi$
$462$	16.8254	+	0.944185i	0.782789	+	0.0439274i
$463$	3.56780			0.165810			0.0829048	−	0.996557i	$-0.473580\pi$
$463$	3.56780			0.165810			0.0829048	+	0.996557i	$0.473580\pi$
$464$	3.39215	+	1.95846i	0.157477	+	0.0909191i
$465$	19.4861	+	55.8466i	0.903645	+	2.58982i
$466$	−5.01599	−	8.68795i	−0.232361	−	0.402462i
$467$	−18.2961	−	31.6897i	−0.846641	−	1.46643i	−0.884188	−	0.467131i	$-0.845288\pi$
$467$	−18.2961	−	31.6897i	−0.846641	−	1.46643i	0.0375470	−	0.999295i	$-0.488046\pi$
$468$	8.22559	−	7.02422i	0.380228	−	0.324695i
$469$	−26.1862	−	10.8182i	−1.20917	−	0.499539i
$470$	40.1376	+	23.1735i	1.85141	+	1.06891i
$471$	33.5323	+	6.37542i	1.54509	+	0.293764i
$472$			9.71836i			0.447324i
$473$	−17.2547	−	9.96202i	−0.793373	−	0.458054i
$474$	3.53699	−	4.10271i	0.162459	−	0.188444i
$475$	−39.6320	+	22.8815i	−1.81844	+	1.04988i
$476$	−4.91761	+	3.78067i	−0.225398	+	0.173287i
$477$	6.21973	−	0.926209i	0.284782	−	0.0424082i
$478$	11.8430			0.541687
$479$	−1.03916	−	1.79988i	−0.0474806	−	0.0822388i	0.841308	−	0.540555i	$-0.181786\pi$
$479$	−1.03916	−	1.79988i	−0.0474806	−	0.0822388i	−0.888789	+	0.458317i	$0.848453\pi$
$480$	−4.50691	+	5.22776i	−0.205712	+	0.238613i
$481$	−24.8403	+	0.878557i	−1.13262	+	0.0400588i
$482$	0.945386			0.0430611
$483$	−8.22725	−	5.38620i	−0.374353	−	0.245080i
$484$	−1.26158	+	2.18511i	−0.0573444	+	0.0993233i
$485$	−8.28136	−	4.78125i	−0.376037	−	0.217105i
$486$	−15.4980	+	1.67674i	−0.703004	+	0.0760586i
$487$	21.7401			0.985139			0.492569	−	0.870273i	$-0.336058\pi$
$487$	21.7401			0.985139			0.492569	+	0.870273i	$0.336058\pi$
$488$	0.138387	−	0.239694i	0.00626450	−	0.0108504i
$489$	0.116382	−	0.612125i	0.00526297	−	0.0276812i
$490$	7.26982	+	26.9314i	0.328417	+	1.21663i
$491$	1.43244	+	0.827022i	0.0646453	+	0.0373230i	0.531974	−	0.846761i	$-0.321450\pi$
$491$	1.43244	+	0.827022i	0.0646453	+	0.0373230i	−0.467329	+	0.884083i	$0.654784\pi$
$492$	−1.00352	+	5.27814i	−0.0452422	+	0.237957i
$493$	7.95285	+	4.59158i	0.358178	+	0.206794i
$494$	−7.11342	+	13.3928i	−0.320048	+	0.602573i
$495$	43.4841	−	6.47543i	1.95447	−	0.291049i
$496$	−7.42132	−	4.28470i	−0.333227	−	0.192389i
$497$	−3.78095	+	9.15203i	−0.169599	+	0.410525i
$498$	−7.44239	−	21.3297i	−0.333501	−	0.955807i
$499$	20.1576	+	34.9140i	0.902378	+	1.56296i	0.824399	+	0.566009i	$0.191513\pi$
$499$	20.1576	+	34.9140i	0.902378	+	1.56296i	0.0779790	+	0.996955i	$0.475153\pi$
$500$	−23.4343			−1.04802
$501$	−1.22431	+	6.43940i	−0.0546980	+	0.287691i
$502$	−13.7657	+	7.94764i	−0.614394	+	0.354720i
$503$	−6.12895	−	10.6156i	−0.273276	−	0.473328i	0.696423	−	0.717632i	$-0.254774\pi$
$503$	−6.12895	−	10.6156i	−0.273276	−	0.473328i	−0.969699	+	0.244304i	$0.921441\pi$
$504$	7.70226	+	1.91709i	0.343086	+	0.0853940i
$505$	15.0140	−	26.0049i	0.668112	−	1.15720i
$506$	6.83393	−	3.94557i	0.303805	−	0.175402i
$507$	20.6825	−	8.90138i	0.918542	−	0.395324i
$508$	−0.726767	+	1.25880i	−0.0322451	+	0.0558501i
$509$	20.4558			0.906689			0.453344	−	0.891335i	$-0.350231\pi$
$509$	20.4558			0.906689			0.453344	+	0.891335i	$0.350231\pi$
$510$	−10.5664	+	12.2564i	−0.467888	+	0.542723i
$511$	−1.43681	+	0.190516i	−0.0635608	+	0.00842793i
$512$		−	1.00000i		−	0.0441942i
$513$	19.3491	−	10.1606i	0.854286	−	0.448603i
$514$			20.1972i			0.890859i
$515$	−31.0981	−	17.9545i	−1.37035	−	0.791170i
$516$	−7.10756	−	6.12752i	−0.312893	−	0.269749i
$517$	37.0388	+	21.3844i	1.62897	+	0.940484i
$518$	−11.1167	−	14.4598i	−0.488441	−	0.635327i
$519$	6.95117	−	36.5605i	0.305122	−	1.60483i
$520$	−12.1816	+	7.61947i	−0.534198	+	0.334136i
$521$	−1.32358	+	2.29252i	−0.0579873	+	0.100437i	−0.893562	−	0.448940i	$-0.851802\pi$
$521$	−1.32358	+	2.29252i	−0.0579873	+	0.100437i	0.835575	+	0.549377i	$0.185135\pi$
$522$	−1.73077	−	11.6226i	−0.0757540	−	0.508707i
$523$			7.10822i			0.310821i	0.987850	+	0.155410i	$0.0496700\pi$
$523$			7.10822i			0.310821i	−0.987850	+	0.155410i	$0.950330\pi$
$524$	−8.82931	−	15.2928i	−0.385710	−	0.668070i
$525$	22.4720	+	44.5099i	0.980759	+	1.94257i
$526$	14.9444	+	25.8844i	0.651605	+	1.12861i
$527$	−17.3992	−	10.0454i	−0.757920	−	0.437585i
$528$	−4.15896	+	4.82416i	−0.180996	+	0.209944i
$529$	18.3953			0.799795
$530$	−8.35306			−0.362834
$531$	22.8265	−	18.1375i	0.990587	−	0.787100i
$532$	−11.0313	+	1.46271i	−0.478268	+	0.0634167i
$533$	−5.24622	+	9.87736i	−0.227239	+	0.427836i
$534$	−1.09496	−	3.13814i	−0.0473837	−	0.135801i
$535$	45.7361	−	26.4057i	1.97734	−	1.14162i
$536$	9.27410	−	5.35441i	0.400580	−	0.231275i
$537$	−17.4106	+	20.1953i	−0.751325	+	0.871493i
$538$			12.8056i			0.552087i
$539$	6.70856	+	24.8522i	0.288958	+	1.07046i
$540$	20.6903	+	0.829229i	0.890368	+	0.0356844i
$541$	−11.5793	−	20.0559i	−0.497831	−	0.862269i	0.502166	−	0.864771i	$-0.332537\pi$
$541$	−11.5793	−	20.0559i	−0.497831	−	0.862269i	−0.999997	+	0.00250239i	$0.999203\pi$
$542$	31.5846			1.35667
$543$	−13.6392	−	39.0896i	−0.585314	−	1.67749i
$544$		−	2.34449i		−	0.100519i
$545$	33.7364			1.44511
$546$	14.1350	+	8.55582i	0.604922	+	0.366155i
$547$	22.8911			0.978751			0.489375	−	0.872073i	$-0.337225\pi$
$547$	22.8911			0.978751			0.489375	+	0.872073i	$0.337225\pi$
$548$		−	12.5570i		−	0.536407i
$549$	−0.821267	+	0.122299i	−0.0350508	+	0.00521959i
$550$	−40.0120			−1.70612
$551$	8.23716	+	14.2672i	0.350915	+	0.607802i
$552$	3.50925	−	1.22445i	0.149364	−	0.0521161i
$553$	7.64749	+	3.15939i	0.325204	+	0.134351i
$554$		−	16.2877i		−	0.691999i
$555$	−36.0389	−	31.0696i	−1.52977	−	1.31883i
$556$	13.3742	−	7.72159i	0.567192	−	0.327468i
$557$	−4.14652	+	2.39399i	−0.175694	+	0.101437i	−0.585268	−	0.810840i	$-0.699011\pi$
$557$	−4.14652	+	2.39399i	−0.175694	+	0.101437i	0.409574	+	0.912277i	$0.365677\pi$
$558$	3.78657	+	25.4278i	0.160298	+	1.07644i
$559$	−10.3593	−	16.5619i	−0.438151	−	0.700492i
$560$	−9.74460	−	4.02576i	−0.411785	−	0.170119i
$561$	−9.75063	+	11.3102i	−0.411672	+	0.477516i
$562$	−13.4422			−0.567027
$563$	−5.95034			−0.250777			−0.125388	−	0.992108i	$-0.540018\pi$
$563$	−5.95034			−0.250777			−0.125388	+	0.992108i	$0.540018\pi$
$564$	15.2570	+	13.1533i	0.642437	+	0.553853i
$565$	−40.5542	−	23.4140i	−1.70613	−	0.985034i
$566$	−6.47874	−	11.2215i	−0.272322	−	0.471675i
$567$	−9.87195	−	21.6690i	−0.414583	−	0.910012i
$568$	−1.87136	−	3.24128i	−0.0785204	−	0.136001i
$569$			6.07137i			0.254525i	0.991869	+	0.127263i	$0.0406191\pi$
$569$			6.07137i			0.254525i	−0.991869	+	0.127263i	$0.959381\pi$
$570$	−27.4100	+	9.56394i	−1.14808	+	0.400590i
$571$	−14.4318	+	24.9966i	−0.603951	+	1.04607i	0.388265	+	0.921548i	$0.373075\pi$
$571$	−14.4318	+	24.9966i	−0.603951	+	1.04607i	−0.992216	+	0.124527i	$0.960259\pi$
$572$	−11.2411	+	7.03122i	−0.470015	+	0.293990i
$573$	−25.9787	−	4.93927i	−1.08528	−	0.206341i
$574$	−8.13571	+	1.07877i	−0.339578	+	0.0450268i
$575$	20.2201	+	11.6741i	0.843237	+	0.486843i
$576$	−2.34880	+	1.86631i	−0.0978668	+	0.0777630i
$577$	19.0046	+	10.9723i	0.791170	+	0.456782i	0.840374	−	0.542007i	$-0.182335\pi$
$577$	19.0046	+	10.9723i	0.791170	+	0.456782i	−0.0492043	+	0.998789i	$0.515669\pi$
$578$			11.5034i			0.478478i
$579$	−21.9220	−	18.8992i	−0.911047	−	0.785425i
$580$			15.6091i			0.648132i
$581$	27.3576	−	21.0326i	1.13498	−	0.872577i
$582$	−3.14790	−	2.71384i	−0.130484	−	0.112492i
$583$	−7.70818			−0.319240
$584$	0.273908	−	0.474423i	0.0113344	−	0.0196318i
$585$	40.6313	+	14.3918i	1.67990	+	0.595030i
$586$	22.4489	−	12.9609i	0.927354	−	0.535408i
$587$	−14.7245	+	25.5036i	−0.607746	+	1.05265i	0.383865	+	0.923389i	$0.374593\pi$
$587$	−14.7245	+	25.5036i	−0.607746	+	1.05265i	−0.991611	+	0.129258i	$0.958740\pi$
$588$	0.917779	+	12.0896i	0.0378486	+	0.498565i
$589$	−18.0212	−	31.2136i	−0.742550	−	1.28613i
$590$	−33.5395	+	19.3641i	−1.38080	+	0.797205i
$591$	3.57518	+	0.679741i	0.147063	+	0.0279608i
$592$	6.89376			0.283332
$593$	14.9324	+	25.8636i	0.613199	+	1.06209i	0.990698	+	0.136082i	$0.0434509\pi$
$593$	14.9324	+	25.8636i	0.613199	+	1.06209i	−0.377499	+	0.926010i	$0.623216\pi$
$594$	19.0929	+	0.765210i	0.783392	+	0.0313969i
$595$	−22.8461	−	9.43834i	−0.936598	−	0.386934i
$596$	3.50132	+	2.02149i	0.143420	+	0.0828033i
$597$	8.64196	+	24.7676i	0.353692	+	1.01367i
$598$	7.73216	−	0.273473i	0.316192	−	0.0111832i
$599$	10.6949	+	6.17470i	0.436981	+	0.252291i	0.702316	−	0.711865i	$-0.252149\pi$
$599$	10.6949	+	6.17470i	0.436981	+	0.252291i	−0.265335	+	0.964156i	$0.585483\pi$
$600$	−18.5140	−	3.52003i	−0.755833	−	0.143705i
$601$	37.8812	+	21.8707i	1.54521	+	0.892126i	0.998497	+	0.0548042i	$0.0174535\pi$
$601$	37.8812	+	21.8707i	1.54521	+	0.892126i	0.546710	+	0.837322i	$0.315880\pi$
$602$	5.47335	−	13.2486i	0.223077	−	0.539972i
$603$	−29.8848	−	11.7901i	−1.21700	−	0.480128i
$604$	−4.77604	+	8.27235i	−0.194334	+	0.336597i
$605$	−10.0549			−0.408789
$606$	8.52194	−	9.88495i	0.346180	−	0.401549i
$607$	27.0879	+	15.6392i	1.09947	+	0.634776i	0.936080	−	0.351786i	$-0.114426\pi$
$607$	27.0879	+	15.6392i	1.09947	+	0.634776i	0.163385	+	0.986562i	$0.447759\pi$
$608$	2.10297	−	3.64245i	0.0852867	−	0.147721i
$609$	16.0232	−	8.08974i	0.649293	−	0.327813i
$610$	1.10296			0.0446575
$611$	22.2372	+	35.5515i	0.899619	+	1.43826i
$612$	−5.50674	+	4.37554i	−0.222597	+	0.176871i
$613$	−0.732877	−	1.26938i	−0.0296006	−	0.0512698i	0.850846	−	0.525416i	$-0.176090\pi$
$613$	−0.732877	−	1.26938i	−0.0296006	−	0.0512698i	−0.880446	+	0.474146i	$0.842757\pi$
$614$	20.1696			0.813977
$615$	−20.2152	+	7.05351i	−0.815154	+	0.284425i
$616$	−8.99228	−	3.71496i	−0.362309	−	0.149680i
$617$	8.81211	−	5.08767i	0.354762	−	0.204822i	−0.312019	−	0.950076i	$-0.601005\pi$
$617$	8.81211	−	5.08767i	0.354762	−	0.204822i	0.666781	+	0.745254i	$0.267672\pi$
$618$	−11.8210	−	10.1910i	−0.475509	−	0.409942i
$619$	−21.4340	−	12.3749i	−0.861507	−	0.497391i	0.00300980	−	0.999995i	$-0.499042\pi$
$619$	−21.4340	−	12.3749i	−0.861507	−	0.497391i	−0.864517	+	0.502604i	$0.832375\pi$
$620$		−	34.1494i		−	1.37147i
$621$	−9.42535	−	5.95733i	−0.378226	−	0.239059i
$622$	−20.8342	−	12.0287i	−0.835377	−	0.482305i
$623$	4.02499	−	3.09442i	0.161258	−	0.123975i
$624$	−5.81997	+	2.26450i	−0.232985	+	0.0906525i
$625$	−19.4920	−	33.7612i	−0.779680	−	1.35045i
$626$	3.95875	+	6.85676i	0.158224	+	0.274051i
$627$	−25.2939	+	8.82557i	−1.01014	+	0.352459i
$628$	−17.0665	−	9.85334i	−0.681027	−	0.393191i
$629$	16.1623			0.644434
$630$	8.73075	+	30.4015i	0.347841	+	1.21122i
$631$	−1.30186	−	2.25489i	−0.0518264	−	0.0897659i	0.838948	−	0.544211i	$-0.183171\pi$
$631$	−1.30186	−	2.25489i	−0.0518264	−	0.0897659i	−0.890775	+	0.454445i	$0.849838\pi$
$632$	−2.70844	+	1.56372i	−0.107736	+	0.0622013i
$633$	−5.16021	+	27.1408i	−0.205100	+	1.07875i
$634$	13.8155	+	23.9291i	0.548682	+	0.950346i
$635$	−5.79239			−0.229864
$636$	−3.56667	−	0.678122i	−0.141427	−	0.0268893i
$637$	−5.62087	+	24.6050i	−0.222707	+	0.974885i
$638$			14.4040i			0.570260i
$639$	−4.12061	+	10.4447i	−0.163009	+	0.413186i
$640$	3.45115	−	1.99252i	0.136419	−	0.0787613i
$641$		−	7.19114i		−	0.284033i	−0.989864	−	0.142017i	$-0.954641\pi$
$641$		−	7.19114i		−	0.284033i	0.989864	−	0.142017i	$-0.0453586\pi$
$642$	21.6725	−	7.56199i	0.855344	−	0.298448i
$643$	−5.48347	+	3.16588i	−0.216247	+	0.124850i	−0.604211	−	0.796824i	$-0.706512\pi$
$643$	−5.48347	+	3.16588i	−0.216247	+	0.124850i	0.387964	+	0.921674i	$0.373178\pi$
$644$	3.46036	+	4.50098i	0.136357	+	0.177363i
$645$	6.98500	−	36.7385i	0.275034	−	1.44658i
$646$	4.93038	−	8.53968i	0.193983	−	0.335989i
$647$	4.25106	+	7.36305i	0.167126	+	0.289471i	0.937408	−	0.348232i	$-0.113218\pi$
$647$	4.25106	+	7.36305i	0.167126	+	0.289471i	−0.770282	+	0.637703i	$0.779885\pi$
$648$	8.76720	+	2.03376i	0.344408	+	0.0798936i
$649$	−30.9501	+	17.8691i	−1.21490	+	0.701423i
$650$	−34.6467	−	18.4021i	−1.35895	−	0.721790i
$651$	−35.0554	+	17.6987i	−1.37393	+	0.693665i
$652$	−0.179871	+	0.311545i	−0.00704428	+	0.0122010i
$653$		−	27.5804i		−	1.07930i	−0.841889	−	0.539651i	$-0.818556\pi$
$653$		−	27.5804i		−	1.07930i	0.841889	−	0.539651i	$-0.181444\pi$
$654$	14.4050	+	2.73880i	0.563282	+	0.107096i
$655$	35.1852	−	60.9426i	1.37480	−	2.38122i
$656$	1.55096	−	2.68634i	0.0605549	−	0.104884i
$657$	−1.62553	+	0.242065i	−0.0634178	+	0.00944385i
$658$	−11.7490	+	28.4393i	−0.458025	+	1.10868i
$659$	21.6640	−	12.5077i	0.843908	−	0.487230i	−0.0146829	−	0.999892i	$-0.504674\pi$
$659$	21.6640	−	12.5077i	0.843908	−	0.487230i	0.858591	+	0.512662i	$0.171341\pi$
$660$	−24.9357	−	4.74097i	−0.970621	−	0.184542i
$661$	−13.0123	+	7.51267i	−0.506121	+	0.292209i	−0.731238	−	0.682123i	$-0.761057\pi$
$661$	−13.0123	+	7.51267i	−0.506121	+	0.292209i	0.225117	+	0.974332i	$0.427724\pi$
$662$	11.5403	+	6.66281i	0.448527	+	0.258957i
$663$	−13.6448	+	5.30909i	−0.529922	+	0.206188i
$664$			13.0428i			0.506159i
$665$	−27.0282	−	35.1562i	−1.04811	−	1.36330i
$666$	−12.8659	−	16.1921i	−0.498544	−	0.627431i
$667$	4.20257	−	7.27907i	0.162724	−	0.281847i
$668$	1.89219	−	3.27738i	0.0732112	−	0.126805i
$669$	31.3446	+	5.95947i	1.21185	+	0.230407i
$670$	36.9577	+	21.3375i	1.42780	+	0.824341i
$671$	1.01781			0.0392920
$672$	−3.83402	−	2.51004i	−0.147900	−	0.0968271i
$673$	−2.09904	+	3.63565i	−0.0809121	+	0.140144i	−0.903642	−	0.428289i	$-0.859117\pi$
$673$	−2.09904	+	3.63565i	−0.0809121	+	0.140144i	0.822730	+	0.568433i	$0.192450\pi$
$674$		−	6.30526i		−	0.242869i
$675$	26.2851	+	50.0554i	1.01171	+	1.92663i
$676$	−12.9675	+	0.918426i	−0.498751	+	0.0353241i
$677$	18.0619	+	31.2842i	0.694177	+	1.20235i	0.970457	+	0.241272i	$0.0775646\pi$
$677$	18.0619	+	31.2842i	0.694177	+	1.20235i	−0.276281	+	0.961077i	$0.589102\pi$
$678$	−15.4154	−	13.2898i	−0.592025	−	0.510392i
$679$	2.42411	−	5.86772i	0.0930289	−	0.225182i
$680$	8.09117	−	4.67144i	0.310282	−	0.179142i
$681$	−16.0078	+	5.58545i	−0.613419	+	0.214035i
$682$		−	31.5130i		−	1.20669i
$683$		−	10.1587i		−	0.388711i	−0.980931	−	0.194355i	$-0.937738\pi$
$683$		−	10.1587i		−	0.388711i	0.980931	−	0.194355i	$-0.0622615\pi$
$684$	−12.4802	+	1.85849i	−0.477192	+	0.0710610i
$685$	43.3359	−	25.0200i	1.65578	−	0.955966i
$686$	−17.0907	+	7.13499i	−0.652526	+	0.272415i
$687$	−4.85858	+	5.63567i	−0.185366	+	0.215014i
$688$	2.70900	+	4.69212i	0.103279	+	0.178885i
$689$	−6.67456	−	3.54510i	−0.254280	−	0.135058i
$690$	11.2180	+	9.67120i	0.427063	+	0.368176i
$691$			7.39733i			0.281408i	0.990052	+	0.140704i	$0.0449365\pi$
$691$			7.39733i			0.281408i	−0.990052	+	0.140704i	$0.955063\pi$
$692$	−10.7432	+	18.6077i	−0.408394	+	0.707360i
$693$	8.05670	+	28.0544i	0.306049	+	1.06570i
$694$	14.8278			0.562857
$695$	53.2967	+	30.7709i	2.02166	+	1.16721i
$696$	−1.26718	+	6.66491i	−0.0480324	+	0.252633i
$697$	3.63621	−	6.29810i	0.137731	−	0.238557i
$698$	1.48396	−	2.57029i	0.0561685	−	0.0972868i
$699$	11.3457	−	13.1604i	0.429136	−	0.497772i
$700$	−3.78397	−	28.5375i	−0.143021	−	1.07862i
$701$			16.0990i			0.608049i	0.952664	+	0.304025i	$0.0983306\pi$
$701$			16.0990i			0.608049i	−0.952664	+	0.304025i	$0.901669\pi$
$702$	16.1807	+	9.44370i	0.610703	+	0.356430i
$703$	25.1102	+	14.4974i	0.947048	+	0.546779i
$704$	3.18471	−	1.83869i	0.120028	−	0.0692983i
$705$	−14.9939	+	78.8625i	−0.564704	+	2.97013i
$706$	−7.45381	+	4.30346i	−0.280528	+	0.161963i
$707$	18.4257	+	7.61214i	0.692968	+	0.286284i
$708$	−15.8930	+	5.54541i	−0.597296	+	0.208409i
$709$	23.8720	−	41.3476i	0.896534	−	1.55284i	0.0646386	−	0.997909i	$-0.479411\pi$
$709$	23.8720	−	41.3476i	0.896534	−	1.55284i	0.831895	−	0.554933i	$-0.187256\pi$
$710$	7.45744	−	12.9167i	0.279873	−	0.484753i
$711$	8.72765	+	3.44320i	0.327313	+	0.129130i
$712$			1.91893i			0.0719149i
$713$	−9.19435	+	15.9251i	−0.344331	+	0.596399i
$714$	−8.98880	−	5.88477i	−0.336397	−	0.220232i
$715$	−46.6640	−	24.7849i	−1.74513	−	0.926904i
$716$	13.3321	−	7.69731i	0.498245	−	0.287662i
$717$	6.75776	+	19.3676i	0.252373	+	0.723295i
$718$	−3.98329	−	6.89926i	−0.148655	−	0.257478i
$719$	−5.29444	+	9.17024i	−0.197449	+	0.341992i	−0.947701	−	0.319160i	$-0.896599\pi$
$719$	−5.29444	+	9.17024i	−0.197449	+	0.341992i	0.750251	+	0.661153i	$0.229932\pi$
$720$	−11.1210	−	4.38740i	−0.414454	−	0.163509i
$721$	9.10301	−	22.0344i	0.339014	−	0.820604i
$722$	−1.13456	+	0.655036i	−0.0422238	+	0.0243779i
$723$	0.539448	+	1.54605i	0.0200623	+	0.0574981i
$724$			23.9027i			0.888339i
$725$	−36.9085	+	21.3092i	−1.37075	+	0.791402i
$726$	−4.29332	−	0.816278i	−0.159340	−	0.0302949i
$727$		−	6.29062i		−	0.233306i	−0.993173	−	0.116653i	$-0.962783\pi$
$727$		−	6.29062i		−	0.233306i	0.993173	−	0.116653i	$-0.0372166\pi$
$728$	−6.07791	−	7.35248i	−0.225262	−	0.272501i
$729$	−11.5854	−	24.3881i	−0.429090	−	0.903262i
$730$	2.18307			0.0807992
$731$	6.35120	+	11.0006i	0.234908	+	0.406872i
$732$	0.470951	+	0.0895408i	0.0174068	+	0.00330952i
$733$	−24.4353	+	14.1077i	−0.902538	+	0.521080i	−0.878023	−	0.478619i	$-0.841138\pi$
$733$	−24.4353	+	14.1077i	−0.902538	+	0.521080i	−0.0245151	+	0.999699i	$0.507804\pi$
$734$	11.3921	+	19.7318i	0.420492	+	0.728313i
$735$	−39.8942	+	27.2561i	−1.47152	+	1.00536i
$736$	−2.14586			−0.0790974
$737$	34.1044	+	19.6902i	1.25625	+	0.725298i
$738$	−9.20427	+	1.37065i	−0.338814	+	0.0504544i
$739$	−12.9234	−	22.3840i	−0.475396	−	0.823410i	0.524207	−	0.851591i	$-0.324362\pi$
$739$	−12.9234	−	22.3840i	−0.475396	−	0.823410i	−0.999603	+	0.0281813i	$0.991028\pi$
$740$	13.7360	+	23.7914i	0.504944	+	0.874589i
$741$	−25.9611	−	3.99089i	−0.953706	−	0.146609i
$742$	−0.728969	−	5.49765i	−0.0267613	−	0.201825i
$743$	6.50706	+	3.75685i	0.238721	+	0.137826i	0.614589	−	0.788848i	$-0.289322\pi$
$743$	6.50706	+	3.75685i	0.238721	+	0.137826i	−0.375868	+	0.926673i	$0.622655\pi$
$744$	2.77233	−	14.5814i	0.101639	−	0.534581i
$745$			16.1114i			0.590277i
$746$	18.1228	+	10.4632i	0.663524	+	0.383086i
$747$	30.6350	−	24.3420i	1.12088	−	0.890626i
$748$	7.46650	−	4.31079i	0.273002	−	0.157618i
$749$	21.3706	+	27.7972i	0.780863	+	1.01569i
$750$	−13.3719	−	38.3236i	−0.488273	−	1.39938i
$751$	−1.42590			−0.0520318			−0.0260159	−	0.999662i	$-0.508282\pi$
$751$	−1.42590			−0.0520318			−0.0260159	+	0.999662i	$0.508282\pi$
$752$	−5.81511	−	10.0721i	−0.212055	−	0.367290i
$753$	−20.8521	−	17.9769i	−0.759894	−	0.655114i
$754$	−6.62461	+	12.4725i	−0.241254	+	0.454222i
$755$	−38.0655			−1.38534
$756$	1.25987	+	13.6899i	0.0458209	+	0.497896i
$757$	−11.4225	+	19.7843i	−0.415157	+	0.719074i	−0.995445	−	0.0953379i	$-0.969607\pi$
$757$	−11.4225	+	19.7843i	−0.415157	+	0.719074i	0.580288	+	0.814412i	$0.302940\pi$
$758$	−0.131421	−	0.0758760i	−0.00477343	−	0.00275594i
$759$	10.3520	+	8.92454i	0.375752	+	0.323940i
$760$	16.7609			0.607980
$761$	−12.9583	+	22.4444i	−0.469737	+	0.813608i	−0.999401	−	0.0345990i	$-0.988985\pi$
$761$	−12.9583	+	22.4444i	−0.469737	+	0.813608i	0.529664	+	0.848207i	$0.322318\pi$
$762$	−2.47329	−	0.470240i	−0.0895977	−	0.0170350i
$763$	2.94416	+	22.2039i	0.106586	+	0.803836i
$764$	13.2220	+	7.63375i	0.478357	+	0.276179i
$765$	−26.0730	−	10.2862i	−0.942670	−	0.371899i
$766$	9.82943	+	5.67502i	0.355152	+	0.205047i
$767$	−35.0182	+	1.23853i	−1.26443	+	0.0447208i
$768$	1.63536	−	0.570612i	0.0590110	−	0.0205902i
$769$	−34.4344	−	19.8807i	−1.24174	−	0.716918i	−0.272290	−	0.962215i	$-0.587781\pi$
$769$	−34.4344	−	19.8807i	−1.24174	−	0.716918i	−0.969448	+	0.245298i	$0.921114\pi$
$770$	−5.09646	−	38.4358i	−0.183663	−	1.38513i
$771$	−33.0296	+	11.5247i	−1.18953	+	0.415054i
$772$	8.35541	+	14.4720i	0.300718	+	0.520859i
$773$	−33.6086			−1.20882			−0.604409	−	0.796674i	$-0.706591\pi$
$773$	−33.6086			−1.20882			−0.604409	+	0.796674i	$0.706591\pi$
$774$	5.96503	−	15.1199i	0.214409	−	0.543472i
$775$	80.7482	−	46.6200i	2.90056	−	1.67464i
$776$	1.19980	+	2.07811i	0.0430702	+	0.0745998i
$777$	17.3036	−	26.4308i	0.620765	−	0.948199i
$778$	10.6702	−	18.4814i	0.382546	−	0.662590i
$779$	11.2986	−	6.52325i	0.404814	−	0.233720i
$780$	−19.4115	−	15.5735i	−0.695045	−	0.557621i
$781$	6.88169	−	11.9194i	0.246246	−	0.426511i
$782$	−5.03093			−0.179906
$783$	18.0195	−	9.46243i	0.643965	−	0.338160i
$784$	1.79918	−	6.76483i	0.0642566	−	0.241601i
$785$		−	78.5320i		−	2.80293i
$786$	19.9712	−	23.1654i	0.712347	−	0.826281i
$787$		−	8.78106i		−	0.313011i	−0.987677	−	0.156505i	$-0.949977\pi$
$787$		−	8.78106i		−	0.313011i	0.987677	−	0.156505i	$-0.0500229\pi$
$788$	−1.81961	−	1.05055i	−0.0648210	−	0.0374244i
$789$	−33.8029	+	39.2094i	−1.20341	+	1.39589i
$790$	−10.7932	−	6.23148i	−0.384006	−	0.221706i
$791$	11.8710	−	28.7345i	0.422084	−	1.02168i
$792$	−10.2624	−	4.04868i	−0.364658	−	0.143864i
$793$	0.881324	+	0.468103i	0.0312967	+	0.0166228i
$794$	8.17044	−	14.1516i	0.289958	−	0.502222i
$795$	−4.76636	−	13.6603i	−0.169045	−	0.484480i
$796$		−	15.1451i		−	0.536803i
$797$	−20.1467	−	34.8951i	−0.713633	−	1.23605i	−0.963484	−	0.267764i	$-0.913715\pi$
$797$	−20.1467	−	34.8951i	−0.713633	−	1.23605i	0.249852	−	0.968284i	$-0.419618\pi$
$798$	−8.68667	−	17.2055i	−0.307505	−	0.609069i
$799$	−13.6334	−	23.6138i	−0.482316	−	0.835396i
$800$	9.42285	+	5.44029i	0.333148	+	0.192343i
$801$	4.50719	−	3.58132i	0.159254	−	0.126540i
$802$	27.9807			0.988031
$803$	2.01453			0.0710913
$804$	14.0483	+	12.1112i	0.495445	+	0.427129i
$805$	−8.63871	+	20.9105i	−0.304474	+	0.736999i
$806$	14.4933	−	27.2873i	0.510503	−	0.961153i
$807$	−20.9417	+	7.30701i	−0.737183	+	0.257219i
$808$	−6.52563	+	3.76758i	−0.229571	+	0.132543i
$809$	34.1196	−	19.6990i	1.19958	−	0.692578i	0.239119	−	0.970990i	$-0.423141\pi$
$809$	34.1196	−	19.6990i	1.19958	−	0.692578i	0.960462	+	0.278412i	$0.0898080\pi$
$810$	10.4500	+	34.3092i	0.367177	+	1.20550i
$811$		−	37.3886i		−	1.31289i	−0.754374	−	0.656445i	$-0.772059\pi$
$811$		−	37.3886i		−	1.31289i	0.754374	−	0.656445i	$-0.227941\pi$
$812$	−10.2733	+	1.36220i	−0.360521	+	0.0478038i
$813$	18.0225	+	51.6522i	0.632078	+	1.81152i
$814$	12.6755	+	21.9546i	0.444276	+	0.769509i
$815$	−1.43358			−0.0502163
$816$	3.83408	−	1.33779i	0.134220	−	0.0468321i
$817$			22.7877i			0.797242i
$818$	−29.9985			−1.04887
$819$	−5.92625	+	27.9978i	−0.207080	+	0.978324i
$820$	12.3613			0.431675
$821$			16.6446i			0.580900i	0.956890	+	0.290450i	$0.0938051\pi$
$821$			16.6446i			0.580900i	−0.956890	+	0.290450i	$0.906195\pi$
$822$	20.5352	−	7.16515i	0.716246	−	0.249913i
$823$	16.5335			0.576322			0.288161	−	0.957582i	$-0.406956\pi$
$823$	16.5335			0.576322			0.288161	+	0.957582i	$0.406956\pi$
$824$	4.50547	+	7.80371i	0.156956	+	0.271855i
$825$	−22.8314	−	65.4341i	−0.794886	−	2.27812i
$826$	−15.6716	−	20.3845i	−0.545285	−	0.709266i
$827$		−	14.7699i		−	0.513598i	−0.966465	−	0.256799i	$-0.917332\pi$
$827$		−	14.7699i		−	0.513598i	0.966465	−	0.256799i	$-0.0826679\pi$
$828$	4.00484	+	5.04020i	0.139178	+	0.175159i
$829$	−11.9041	+	6.87283i	−0.413446	+	0.238703i	−0.692269	−	0.721639i	$-0.743389\pi$
$829$	−11.9041	+	6.87283i	−0.413446	+	0.238703i	0.278823	+	0.960342i	$0.410056\pi$
$830$	−45.0127	+	25.9881i	−1.56241	+	0.902060i
$831$	26.6363	−	9.29396i	0.924002	−	0.322404i
$832$	3.60330	−	0.127442i	0.124922	−	0.00441827i
$833$	4.21816	−	15.8601i	0.146151	−	0.549518i
$834$	20.2590	+	17.4656i	0.701513	+	0.604783i
$835$	15.0809			0.521898
$836$	15.4669			0.534932
$837$	−39.4229	+	20.7018i	−1.36266	+	0.715560i
$838$	−20.9944	−	12.1211i	−0.725238	−	0.418717i
$839$	−8.42008	−	14.5840i	−0.290693	−	0.503496i	0.683280	−	0.730156i	$-0.260553\pi$
$839$	−8.42008	−	14.5840i	−0.290693	−	0.503496i	−0.973974	+	0.226660i	$0.927219\pi$
$840$	1.02318	−	18.2331i	0.0353030	−	0.629101i
$841$	−6.82888	−	11.8280i	−0.235479	−	0.407861i
$842$		−	6.28451i		−	0.216579i
$843$	−7.67031	−	21.9829i	−0.264179	−	0.757131i
$844$	7.97522	−	13.8135i	0.274518	−	0.475480i
$845$	−29.0077	−	42.9229i	−0.997895	−	1.47659i
$846$	−12.8045	+	32.4561i	−0.440227	+	1.11587i
$847$	−0.877485	−	6.61771i	−0.0301507	−	0.227387i
$848$	1.81528	+	1.04805i	0.0623369	+	0.0359902i
$849$	14.6544	−	16.9982i	0.502936	−	0.583377i
$850$	22.0918	+	12.7547i	0.757741	+	0.437482i
$851$		−	14.7930i		−	0.507098i
$852$	4.23285	−	4.90986i	0.145015	−	0.168209i
$853$		−	1.83840i		−	0.0629455i	−0.999505	−	0.0314728i	$-0.989980\pi$
$853$		−	1.83840i		−	0.0629455i	0.999505	−	0.0314728i	$-0.0100197\pi$
$854$	0.0962548	+	0.725923i	0.00329377	+	0.0248406i
$855$	−31.2810	−	39.3680i	−1.06979	−	1.34636i
$856$	−13.2524			−0.452958
$857$	13.7264	−	23.7748i	0.468884	−	0.812132i	−0.530483	−	0.847696i	$-0.677989\pi$
$857$	13.7264	−	23.7748i	0.468884	−	0.812132i	0.999367	+	0.0355640i	$0.0113228\pi$
$858$	−17.9129	−	14.3712i	−0.611536	−	0.490624i
$859$	4.55171	−	2.62793i	0.155302	−	0.0896638i	−0.420335	−	0.907369i	$-0.638087\pi$
$859$	4.55171	−	2.62793i	0.155302	−	0.0896638i	0.575637	+	0.817705i	$0.304754\pi$
$860$	−10.7955	+	18.6983i	−0.368122	+	0.637607i
$861$	−6.40650	−	12.6893i	−0.218333	−	0.432449i
$862$	−7.26788	−	12.5883i	−0.247545	−	0.428760i
$863$	−36.9075	+	21.3086i	−1.25635	+	0.725352i	−0.972362	−	0.233477i	$-0.924990\pi$
$863$	−36.9075	+	21.3086i	−1.25635	+	0.725352i	−0.283984	+	0.958829i	$0.591656\pi$
$864$	−4.39235	−	2.77620i	−0.149431	−	0.0944482i
$865$	−85.6241			−2.91131
$866$	−8.33288	−	14.4330i	−0.283163	−	0.490452i
$867$	−18.8122	+	6.56397i	−0.638895	+	0.222924i
$868$	22.4758	−	2.98021i	0.762877	−	0.101155i
$869$	−9.95996	−	5.75039i	−0.337869	−	0.195068i
$870$	−25.5265	+	8.90673i	−0.865428	+	0.301966i
$871$	20.4754	+	32.7350i	0.693784	+	1.10918i
$872$	−7.33155	−	4.23287i	−0.248278	−	0.143343i
$873$	2.64188	−	6.69649i	0.0894140	−	0.226642i
$874$	−7.81618	−	4.51267i	−0.264386	−	0.152643i
$875$	49.1540	−	37.7897i	1.66171	−	1.27753i
$876$	0.932148	+	0.177227i	0.0314944	+	0.00598795i
$877$	−24.1723	+	41.8676i	−0.816240	+	1.41377i	0.0921943	+	0.995741i	$0.470612\pi$
$877$	−24.1723	+	41.8676i	−0.816240	+	1.41377i	−0.908434	+	0.418028i	$0.862721\pi$
$878$	2.49431			0.0841788
$879$	34.0053	+	29.3164i	1.14697	+	0.988816i
$880$	12.6912	+	7.32727i	0.427820	+	0.247002i
$881$	18.3105	−	31.7147i	0.616896	−	1.06849i	−0.373153	−	0.927770i	$-0.621723\pi$
$881$	18.3105	−	31.7147i	0.616896	−	1.06849i	0.990049	−	0.140725i	$-0.0449432\pi$
$882$	−19.2471	+	8.39935i	−0.648084	+	0.282821i
$883$	−13.8342			−0.465558			−0.232779	−	0.972530i	$-0.574782\pi$
$883$	−13.8342			−0.465558			−0.232779	+	0.972530i	$0.574782\pi$
$884$	8.44788	−	0.298787i	0.284133	−	0.0100493i
$885$	−50.8052	−	43.7998i	−1.70780	−	1.47231i
$886$	−0.144245	−	0.249840i	−0.00484601	−	0.00839354i
$887$	−35.3010			−1.18529			−0.592646	−	0.805463i	$-0.701917\pi$
$887$	−35.3010			−1.18529			−0.592646	+	0.805463i	$0.701917\pi$
$888$	3.93366	+	11.2738i	0.132005	+	0.378323i
$889$	−0.505500	−	3.81232i	−0.0169539	−	0.127861i
$890$	−6.62251	+	3.82351i	−0.221987	+	0.128164i
$891$	9.64326	+	31.6604i	0.323061	+	1.06066i
$892$	−15.9530	−	9.21049i	−0.534147	−	0.308390i
$893$		−	48.9160i		−	1.63691i
$894$	−1.30796	+	6.87940i	−0.0437449	+	0.230082i
$895$	53.1291	+	30.6741i	1.77591	+	1.02532i
$896$	1.61258	+	2.09752i	0.0538724	+	0.0700732i
$897$	4.85929	+	12.4888i	0.162247	+	0.416990i
$898$	2.23455	+	3.87035i	0.0745677	+	0.129155i
$899$	−16.7828	−	29.0687i	−0.559738	−	0.969495i
$900$	−4.80782	−	32.2857i	−0.160261	−	1.07619i
$901$	4.25590	+	2.45714i	0.141784	+	0.0818593i
$902$	11.4070			0.379810
$903$	24.7894	+	1.39109i	0.824938	+	0.0462927i
$904$	5.87547	+	10.1766i	0.195415	+	0.338469i
$905$	−82.4919	+	47.6267i	−2.74212	+	1.58317i
$906$	−16.2535	−	3.09025i	−0.539988	−	0.102667i
$907$	2.94787	+	5.10587i	0.0978825	+	0.169538i	0.910808	−	0.412830i	$-0.135460\pi$
$907$	2.94787	+	5.10587i	0.0978825	+	0.169538i	−0.812925	+	0.582368i	$0.802126\pi$
$908$	9.78852			0.324843
$909$	21.0282	+	8.29596i	0.697460	+	0.275160i
$910$	13.2641	−	35.6258i	0.439702	−	1.18098i
$911$		−	31.6741i		−	1.04941i	−0.851284	−	0.524705i	$-0.824176\pi$
$911$		−	31.6741i		−	1.04941i	0.851284	−	0.524705i	$-0.175824\pi$
$912$	7.15670	+	1.36069i	0.236982	+	0.0450568i
$913$	−41.5376	+	23.9817i	−1.37469	+	0.793679i
$914$			32.2831i			1.06783i
$915$	0.629361	+	1.80373i	0.0208060	+	0.0596296i
$916$	3.72044	−	2.14800i	0.122927	−	0.0709718i
$917$	43.1805	+	17.8390i	1.42595	+	0.589097i
$918$	−10.2978	−	6.50876i	−0.339878	−	0.214821i
$919$	0.762637	−	1.32093i	0.0251571	−	0.0435733i	−0.853173	−	0.521628i	$-0.825325\pi$
$919$	0.762637	−	1.32093i	0.0251571	−	0.0435733i	0.878330	+	0.478055i	$0.158658\pi$
$920$	−4.27567	−	7.40567i	−0.140965	−	0.244158i
$921$	11.5090	+	32.9845i	0.379234	+	1.08688i
$922$	−33.5166	+	19.3508i	−1.10381	+	0.637285i
$923$	11.4408	−	7.15613i	0.376579	−	0.235547i
$924$	0.944185	−	16.8254i	0.0310614	−	0.553516i
$925$	−37.5040	+	64.9589i	−1.23313	+	2.13584i
$926$		−	3.56780i		−	0.117245i
$927$	9.92076	−	25.1466i	0.325841	−	0.825924i
$928$	1.95846	−	3.39215i	0.0642895	−	0.111353i
$929$	−2.29866	+	3.98140i	−0.0754166	+	0.130625i	−0.901267	−	0.433263i	$-0.857362\pi$
$929$	−2.29866	+	3.98140i	−0.0754166	+	0.130625i	0.825851	+	0.563889i	$0.190695\pi$
$930$	55.8466	−	19.4861i	1.83128	−	0.638973i
$931$	20.7797	−	20.8569i	0.681026	−	0.683558i
$932$	−8.68795	+	5.01599i	−0.284583	+	0.164304i
$933$	7.78291	−	40.9352i	0.254801	−	1.34016i
$934$	−31.6897	+	18.2961i	−1.03692	+	0.598666i
$935$	29.7543	+	17.1787i	0.973071	+	0.561803i
$936$	−7.02422	−	8.22559i	−0.229594	−	0.268862i
$937$		−	39.4304i		−	1.28814i	−0.764969	−	0.644068i	$-0.777246\pi$
$937$		−	39.4304i		−	1.28814i	0.764969	−	0.644068i	$-0.222754\pi$
$938$	−10.8182	+	26.1862i	−0.353228	+	0.855009i
$939$	−8.95436	+	10.3865i	−0.292214	+	0.338952i
$940$	23.1735	−	40.1376i	0.755835	−	1.30914i
$941$	13.7435	−	23.8044i	0.448024	−	0.776001i	−0.550233	−	0.835011i	$-0.685461\pi$
$941$	13.7435	−	23.8044i	0.448024	−	0.776001i	0.998257	+	0.0590103i	$0.0187945\pi$
$942$	6.37542	−	33.5323i	0.207722	−	1.09254i
$943$	−5.76451	−	3.32814i	−0.187718	−	0.108379i
$944$	9.71836			0.316306
$945$	−44.7355	+	31.6254i	−1.45525	+	1.02877i
$946$	−9.96202	+	17.2547i	−0.323893	+	0.560999i
$947$			25.0049i			0.812549i	0.913751	+	0.406275i	$0.133172\pi$
$947$			25.0049i			0.812549i	−0.913751	+	0.406275i	$0.866828\pi$
$948$	−4.10271	−	3.53699i	−0.133250	−	0.114876i
$949$	1.74440	+	0.926512i	0.0566255	+	0.0300759i
$950$	22.8815	+	39.6320i	0.742374	+	1.28583i
$951$	−31.2494	+	36.2475i	−1.01333	+	1.17541i
$952$	3.78067	+	4.91761i	0.122532	+	0.159381i
$953$	0.606011	−	0.349881i	0.0196306	−	0.0113337i	−0.490153	−	0.871637i	$-0.663059\pi$
$953$	0.606011	−	0.349881i	0.0196306	−	0.0113337i	0.509783	+	0.860303i	$0.329726\pi$
$954$	−0.926209	−	6.21973i	−0.0299871	−	0.201371i
$955$			60.8416i			1.96879i
$956$		−	11.8430i		−	0.383030i
$957$	−23.5557	+	8.21910i	−0.761449	+	0.265686i
$958$	−1.79988	+	1.03916i	−0.0581516	+	0.0335738i
$959$	20.2491	+	26.3385i	0.653877	+	0.850514i
$960$	5.22776	+	4.50691i	0.168725	+	0.145460i
$961$	21.2173	+	36.7494i	0.684428	+	1.18546i
$962$	0.878557	+	24.8403i	0.0283258	+	0.800883i
$963$	24.7331	+	31.1273i	0.797015	+	1.00306i
$964$		−	0.945386i		−	0.0304488i
$965$	−33.2967	+	57.6716i	−1.07186	+	1.85651i
$966$	−5.38620	+	8.22725i	−0.173298	+	0.264707i
$967$	−0.670100			−0.0215490			−0.0107745	−	0.999942i	$-0.503430\pi$
$967$	−0.670100			−0.0215490			−0.0107745	+	0.999942i	$0.503430\pi$
$968$	2.18511	+	1.26158i	0.0702322	+	0.0405486i
$969$	16.7788	+	3.19011i	0.539012	+	0.102481i
$970$	−4.78125	+	8.28136i	−0.153517	+	0.265898i
$971$	−8.39787	+	14.5455i	−0.269500	+	0.466788i	−0.968733	−	0.248106i	$-0.920192\pi$
$971$	−8.39787	+	14.5455i	−0.269500	+	0.466788i	0.699232	+	0.714894i	$0.253525\pi$
$972$	1.67674	+	15.4980i	0.0537816	+	0.497099i
$973$	−15.6010	+	37.7631i	−0.500144	+	1.21063i
$974$		−	21.7401i		−	0.696598i
$975$	10.3243	−	67.1602i	0.330641	−	2.15085i
$976$	−0.239694	−	0.138387i	−0.00767241	−	0.00442967i
$977$	−25.8552	+	14.9275i	−0.827182	+	0.477574i	−0.852887	−	0.522096i	$-0.825150\pi$
$977$	−25.8552	+	14.9275i	−0.827182	+	0.477574i	0.0257050	+	0.999670i	$0.491817\pi$
$978$	−0.612125	−	0.116382i	−0.0195736	−	0.00372148i
$979$	−6.11123	+	3.52832i	−0.195316	+	0.112766i
$980$	26.9314	−	7.26982i	0.860291	−	0.232226i
$981$	3.74077	+	25.1202i	0.119434	+	0.802027i
$982$	0.827022	−	1.43244i	0.0263913	−	0.0457111i
$983$	−18.1058	+	31.3601i	−0.577484	+	1.00023i	0.418283	+	0.908317i	$0.362632\pi$
$983$	−18.1058	+	31.3601i	−0.577484	+	1.00023i	−0.995767	+	0.0919149i	$0.970701\pi$
$984$	5.27814	+	1.00352i	0.168261	+	0.0319910i
$985$		−	8.37300i		−	0.266786i
$986$	4.59158	−	7.95285i	0.146226	−	0.253270i
$987$	−53.2126	−	2.98611i	−1.69378	−	0.0950489i
$988$	13.3928	+	7.11342i	0.426083	+	0.226308i
$989$	10.0686	−	5.81312i	0.320163	−	0.184846i
$990$	−6.47543	−	43.4841i	−0.205803	−	1.38202i
$991$	−3.14263	−	5.44319i	−0.0998288	−	0.172909i	0.811785	−	0.583957i	$-0.198496\pi$
$991$	−3.14263	−	5.44319i	−0.0998288	−	0.172909i	−0.911614	+	0.411048i	$0.865163\pi$
$992$	−4.28470	+	7.42132i	−0.136039	+	0.235627i
$993$	−4.31104	+	22.6745i	−0.136807	+	0.719552i
$994$	9.15203	+	3.78095i	0.290285	+	0.119924i
$995$	52.2679	−	30.1769i	1.65700	−	0.956672i
$996$	−21.3297	+	7.44239i	−0.675857	+	0.235821i
$997$		−	23.6323i		−	0.748442i	−0.927340	−	0.374221i	$-0.877910\pi$
$997$		−	23.6323i		−	0.748442i	0.927340	−	0.374221i	$-0.122090\pi$
$998$	34.9140	−	20.1576i	1.10518	−	0.638078i
$999$	19.1385	−	30.2798i	0.605514	−	0.958010i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bb.a.269.17	yes	76
3.2	odd	2	inner	546.2.bb.a.269.34	yes	76
7.5	odd	6		546.2.u.a.425.11	yes	76
13.3	even	3		546.2.u.a.185.28	yes	76
21.5	even	6		546.2.u.a.425.28	yes	76
39.29	odd	6		546.2.u.a.185.11	✓	76
91.68	odd	6	inner	546.2.bb.a.341.15	yes	76
273.68	even	6	inner	546.2.bb.a.341.36	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.11	✓	76	39.29	odd	6
546.2.u.a.185.28	yes	76	13.3	even	3
546.2.u.a.425.11	yes	76	7.5	odd	6
546.2.u.a.425.28	yes	76	21.5	even	6
546.2.bb.a.269.17	yes	76	1.1	even	1	trivial
546.2.bb.a.269.34	yes	76	3.2	odd	2	inner
546.2.bb.a.341.15	yes	76	91.68	odd	6	inner
546.2.bb.a.341.36	yes	76	273.68	even	6	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.63536 - 0.570612i) q^{3} -1.00000 q^{4} +(-1.99252 - 3.45115i) q^{5} +(-0.570612 - 1.63536i) q^{6} +(2.09752 - 1.61258i) q^{7} +1.00000i q^{8} +(2.34880 - 1.86631i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.63536 - 0.570612i) q^{3} -1.00000 q^{4} +(-1.99252 - 3.45115i) q^{5} +(-0.570612 - 1.63536i) q^{6} +(2.09752 - 1.61258i) q^{7} +1.00000i q^{8} +(2.34880 - 1.86631i) q^{9} +(-3.45115 + 1.99252i) q^{10} +(-3.18471 + 1.83869i) q^{11} +(-1.63536 + 0.570612i) q^{12} +(-3.60330 + 0.127442i) q^{13} +(-1.61258 - 2.09752i) q^{14} +(-5.22776 - 4.50691i) q^{15} +1.00000 q^{16} +2.34449 q^{17} +(-1.86631 - 2.34880i) q^{18} +(3.64245 + 2.10297i) q^{19} +(1.99252 + 3.45115i) q^{20} +(2.51004 - 3.83402i) q^{21} +(1.83869 + 3.18471i) q^{22} -2.14586i q^{23} +(0.570612 + 1.63536i) q^{24} +(-5.44029 + 9.42285i) q^{25} +(0.127442 + 3.60330i) q^{26} +(2.77620 - 4.39235i) q^{27} +(-2.09752 + 1.61258i) q^{28} +(3.39215 + 1.95846i) q^{29} +(-4.50691 + 5.22776i) q^{30} +(-7.42132 - 4.28470i) q^{31} -1.00000i q^{32} +(-4.15896 + 4.82416i) q^{33} -2.34449i q^{34} +(-9.74460 - 4.02576i) q^{35} +(-2.34880 + 1.86631i) q^{36} +6.89376 q^{37} +(2.10297 - 3.64245i) q^{38} +(-5.81997 + 2.26450i) q^{39} +(3.45115 - 1.99252i) q^{40} +(1.55096 - 2.68634i) q^{41} +(-3.83402 - 2.51004i) q^{42} +(2.70900 + 4.69212i) q^{43} +(3.18471 - 1.83869i) q^{44} +(-11.1210 - 4.38740i) q^{45} -2.14586 q^{46} +(-5.81511 - 10.0721i) q^{47} +(1.63536 - 0.570612i) q^{48} +(1.79918 - 6.76483i) q^{49} +(9.42285 + 5.44029i) q^{50} +(3.83408 - 1.33779i) q^{51} +(3.60330 - 0.127442i) q^{52} +(1.81528 + 1.04805i) q^{53} +(-4.39235 - 2.77620i) q^{54} +(12.6912 + 7.32727i) q^{55} +(1.61258 + 2.09752i) q^{56} +(7.15670 + 1.36069i) q^{57} +(1.95846 - 3.39215i) q^{58} +9.71836 q^{59} +(5.22776 + 4.50691i) q^{60} +(-0.239694 - 0.138387i) q^{61} +(-4.28470 + 7.42132i) q^{62} +(1.91709 - 7.70226i) q^{63} -1.00000 q^{64} +(7.61947 + 12.1816i) q^{65} +(4.82416 + 4.15896i) q^{66} +(-5.35441 - 9.27410i) q^{67} -2.34449 q^{68} +(-1.22445 - 3.50925i) q^{69} +(-4.02576 + 9.74460i) q^{70} +(-3.24128 + 1.87136i) q^{71} +(1.86631 + 2.34880i) q^{72} +(-0.474423 - 0.273908i) q^{73} -6.89376i q^{74} +(-3.52003 + 18.5140i) q^{75} +(-3.64245 - 2.10297i) q^{76} +(-3.71496 + 8.99228i) q^{77} +(2.26450 + 5.81997i) q^{78} +(1.56372 + 2.70844i) q^{79} +(-1.99252 - 3.45115i) q^{80} +(2.03376 - 8.76720i) q^{81} +(-2.68634 - 1.55096i) q^{82} +13.0428 q^{83} +(-2.51004 + 3.83402i) q^{84} +(-4.67144 - 8.09117i) q^{85} +(4.69212 - 2.70900i) q^{86} +(6.66491 + 1.26718i) q^{87} +(-1.83869 - 3.18471i) q^{88} +1.91893 q^{89} +(-4.38740 + 11.1210i) q^{90} +(-7.35248 + 6.07791i) q^{91} +2.14586i q^{92} +(-14.5814 - 2.77233i) q^{93} +(-10.0721 + 5.81511i) q^{94} -16.7609i q^{95} +(-0.570612 - 1.63536i) q^{96} +(2.07811 - 1.19980i) q^{97} +(-6.76483 - 1.79918i) q^{98} +(-4.04868 + 10.2624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

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