LMFDB - Embedded newform 1110.2.ba.b.529.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(529,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1110.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.18
Character	$\chi$	$=$	1110.529
Dual form			1110.2.ba.b.619.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.191439 - 2.22786i) q^{5} +1.00000i q^{6} +(-2.57051 - 1.48408i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.191439 - 2.22786i) q^{5} +1.00000i q^{6} +(-2.57051 - 1.48408i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(2.02510 - 0.948138i) q^{10} -6.26383 q^{11} +(-0.866025 + 0.500000i) q^{12} +(1.50604 - 2.60853i) q^{13} -2.96816i q^{14} +(1.27972 - 1.83366i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.790063 + 1.36843i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.22640 + 0.708065i) q^{19} +(1.83366 + 1.27972i) q^{20} +(-1.48408 - 2.57051i) q^{21} +(-3.13191 - 5.42463i) q^{22} -2.48256 q^{23} +(-0.866025 - 0.500000i) q^{24} +(-4.92670 - 0.852997i) q^{25} +3.01207 q^{26} +1.00000i q^{27} +(2.57051 - 1.48408i) q^{28} -7.54443i q^{29} +(2.22786 + 0.191439i) q^{30} -7.23491i q^{31} +(0.500000 - 0.866025i) q^{32} +(-5.42463 - 3.13191i) q^{33} +(-0.790063 + 1.36843i) q^{34} +(-3.79842 + 5.44261i) q^{35} -1.00000 q^{36} +(-4.55074 - 4.03618i) q^{37} +1.41613i q^{38} +(2.60853 - 1.50604i) q^{39} +(-0.191439 + 2.22786i) q^{40} +(2.98646 - 5.17270i) q^{41} +(1.48408 - 2.57051i) q^{42} -0.168736 q^{43} +(3.13191 - 5.42463i) q^{44} +(2.02510 - 0.948138i) q^{45} +(-1.24128 - 2.14996i) q^{46} +3.32457i q^{47} -1.00000i q^{48} +(0.905002 + 1.56751i) q^{49} +(-1.72463 - 4.69315i) q^{50} +1.58013i q^{51} +(1.50604 + 2.60853i) q^{52} +(-0.224349 + 0.129528i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-1.19914 + 13.9549i) q^{55} +(2.57051 + 1.48408i) q^{56} +(0.708065 + 1.22640i) q^{57} +(6.53367 - 3.77222i) q^{58} +(-3.62814 + 2.09471i) q^{59} +(0.948138 + 2.02510i) q^{60} +(-8.53298 - 4.92652i) q^{61} +(6.26562 - 3.61746i) q^{62} -2.96816i q^{63} +1.00000 q^{64} +(-5.52312 - 3.85461i) q^{65} -6.26383i q^{66} +(12.1887 + 7.03717i) q^{67} -1.58013 q^{68} +(-2.14996 - 1.24128i) q^{69} +(-6.61265 - 0.568222i) q^{70} +(-3.03888 + 5.26349i) q^{71} +(-0.500000 - 0.866025i) q^{72} +6.77606i q^{73} +(1.22007 - 5.95915i) q^{74} +(-3.84015 - 3.20207i) q^{75} +(-1.22640 + 0.708065i) q^{76} +(16.1012 + 9.29603i) q^{77} +(2.60853 + 1.50604i) q^{78} +(-2.15482 - 1.24409i) q^{79} +(-2.02510 + 0.948138i) q^{80} +(-0.500000 + 0.866025i) q^{81} +5.97292 q^{82} +(-7.43197 + 4.29085i) q^{83} +2.96816 q^{84} +(3.19992 - 1.49818i) q^{85} +(-0.0843682 - 0.146130i) q^{86} +(3.77222 - 6.53367i) q^{87} +6.26383 q^{88} +(-10.6609 + 6.15507i) q^{89} +(1.83366 + 1.27972i) q^{90} +(-7.74255 + 4.47016i) q^{91} +(1.24128 - 2.14996i) q^{92} +(3.61746 - 6.26562i) q^{93} +(-2.87916 + 1.66228i) q^{94} +(1.81225 - 2.59670i) q^{95} +(0.866025 - 0.500000i) q^{96} +2.84049 q^{97} +(-0.905002 + 1.56751i) q^{98} +(-3.13191 - 5.42463i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9	$ 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} + 14 q^{13} + 2 q^{15} - 18 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{20} + 2 q^{22} + 20 q^{23} - 2 q^{25} + 28 q^{26} - 2 q^{30} + 18 q^{32} + 6 q^{33} - 20 q^{35} - 36 q^{36} - 20 q^{37} + 6 q^{39} - 4 q^{40} + 10 q^{41} - 2 q^{44} + 2 q^{45} + 10 q^{46} + 10 q^{49} - 4 q^{50} + 14 q^{52} + 12 q^{53} + 40 q^{55} - 8 q^{57} - 30 q^{58} + 18 q^{59} - 4 q^{60} - 6 q^{61} + 12 q^{62} + 36 q^{64} - 32 q^{65} - 36 q^{67} + 12 q^{69} - 40 q^{70} - 24 q^{71} - 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} + 24 q^{77} + 6 q^{78} - 2 q^{80} - 18 q^{81} + 20 q^{82} - 36 q^{83} + 26 q^{85} + 10 q^{87} - 4 q^{88} - 2 q^{90} - 36 q^{91} - 10 q^{92} - 12 q^{93} + 12 q^{94} + 18 q^{95} - 52 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 + 14 * q^13 + 2 * q^15 - 18 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^20 + 2 * q^22 + 20 * q^23 - 2 * q^25 + 28 * q^26 - 2 * q^30 + 18 * q^32 + 6 * q^33 - 20 * q^35 - 36 * q^36 - 20 * q^37 + 6 * q^39 - 4 * q^40 + 10 * q^41 - 2 * q^44 + 2 * q^45 + 10 * q^46 + 10 * q^49 - 4 * q^50 + 14 * q^52 + 12 * q^53 + 40 * q^55 - 8 * q^57 - 30 * q^58 + 18 * q^59 - 4 * q^60 - 6 * q^61 + 12 * q^62 + 36 * q^64 - 32 * q^65 - 36 * q^67 + 12 * q^69 - 40 * q^70 - 24 * q^71 - 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 + 24 * q^77 + 6 * q^78 - 2 * q^80 - 18 * q^81 + 20 * q^82 - 36 * q^83 + 26 * q^85 + 10 * q^87 - 4 * q^88 - 2 * q^90 - 36 * q^91 - 10 * q^92 - 12 * q^93 + 12 * q^94 + 18 * q^95 - 52 * q^97 - 10 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.191439	−	2.22786i	0.0856141	−	0.996328i
$5$	0.191439	−	2.22786i	0.0856141	−	0.996328i
$6$			1.00000i			0.408248i
$7$	−2.57051	−	1.48408i	−0.971560	−	0.560930i	−0.0718486	−	0.997416i	$-0.522890\pi$
$7$	−2.57051	−	1.48408i	−0.971560	−	0.560930i	−0.899711	+	0.436485i	$0.856223\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	2.02510	−	0.948138i	0.640393	−	0.299828i
$11$	−6.26383			−1.88861			−0.944307	−	0.329065i	$-0.893267\pi$
$11$	−6.26383			−1.88861			−0.944307	+	0.329065i	$0.893267\pi$
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$	1.50604	−	2.60853i	0.417699	−	0.723476i	−0.578008	−	0.816031i	$-0.696170\pi$
$13$	1.50604	−	2.60853i	0.417699	−	0.723476i	0.995708	+	0.0925545i	$0.0295032\pi$
$14$		−	2.96816i		−	0.793275i
$15$	1.27972	−	1.83366i	0.330422	−	0.473450i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.790063	+	1.36843i	0.191619	+	0.331893i	0.945787	−	0.324788i	$-0.105293\pi$
$17$	0.790063	+	1.36843i	0.191619	+	0.331893i	−0.754168	+	0.656681i	$0.771960\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	1.22640	+	0.708065i	0.281356	+	0.162441i	0.634037	−	0.773302i	$-0.281397\pi$
$19$	1.22640	+	0.708065i	0.281356	+	0.162441i	−0.352681	+	0.935744i	$0.614730\pi$
$20$	1.83366	+	1.27972i	0.410019	+	0.286154i
$21$	−1.48408	−	2.57051i	−0.323853	−	0.560930i
$22$	−3.13191	−	5.42463i	−0.667726	−	1.15654i
$23$	−2.48256			−0.517650			−0.258825	−	0.965924i	$-0.583335\pi$
$23$	−2.48256			−0.517650			−0.258825	+	0.965924i	$0.583335\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	−4.92670	−	0.852997i	−0.985340	−	0.170599i
$26$	3.01207			0.590716
$27$			1.00000i			0.192450i
$28$	2.57051	−	1.48408i	0.485780	−	0.280465i
$29$		−	7.54443i		−	1.40097i	−0.713669	−	0.700483i	$-0.752968\pi$
$29$		−	7.54443i		−	1.40097i	0.713669	−	0.700483i	$-0.247032\pi$
$30$	2.22786	+	0.191439i	0.406749	+	0.0349518i
$31$		−	7.23491i		−	1.29943i	−0.760179	−	0.649714i	$-0.774889\pi$
$31$		−	7.23491i		−	1.29943i	0.760179	−	0.649714i	$-0.225111\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−5.42463	−	3.13191i	−0.944307	−	0.545196i
$34$	−0.790063	+	1.36843i	−0.135495	+	0.234684i
$35$	−3.79842	+	5.44261i	−0.642050	+	0.919969i
$36$	−1.00000			−0.166667
$37$	−4.55074	−	4.03618i	−0.748137	−	0.663545i
$37$	−4.55074	−	4.03618i	−0.748137	−	0.663545i
$38$			1.41613i			0.229727i
$39$	2.60853	−	1.50604i	0.417699	−	0.241159i
$40$	−0.191439	+	2.22786i	−0.0302692	+	0.352255i
$41$	2.98646	−	5.17270i	0.466407	−	0.807841i	−0.532857	−	0.846205i	$-0.678882\pi$
$41$	2.98646	−	5.17270i	0.466407	−	0.807841i	0.999264	+	0.0383648i	$0.0122149\pi$
$42$	1.48408	−	2.57051i	0.228999	−	0.396638i
$43$	−0.168736			−0.0257321			−0.0128660	−	0.999917i	$-0.504095\pi$
$43$	−0.168736			−0.0257321			−0.0128660	+	0.999917i	$0.504095\pi$
$44$	3.13191	−	5.42463i	0.472154	−	0.817794i
$45$	2.02510	−	0.948138i	0.301884	−	0.141340i
$46$	−1.24128	−	2.14996i	−0.183017	−	0.316994i
$47$			3.32457i			0.484938i	0.970159	+	0.242469i	$0.0779572\pi$
$47$			3.32457i			0.484938i	−0.970159	+	0.242469i	$0.922043\pi$
$48$		−	1.00000i		−	0.144338i
$49$	0.905002	+	1.56751i	0.129286	+	0.223930i
$50$	−1.72463	−	4.69315i	−0.243900	−	0.663711i
$51$			1.58013i			0.221262i
$52$	1.50604	+	2.60853i	0.208850	+	0.361738i
$53$	−0.224349	+	0.129528i	−0.0308167	+	0.0177920i	−0.515329	−	0.856992i	$-0.672330\pi$
$53$	−0.224349	+	0.129528i	−0.0308167	+	0.0177920i	0.484513	+	0.874784i	$0.338997\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	−1.19914	+	13.9549i	−0.161692	+	1.88168i
$56$	2.57051	+	1.48408i	0.343498	+	0.198319i
$57$	0.708065	+	1.22640i	0.0937855	+	0.162441i
$58$	6.53367	−	3.77222i	0.857913	−	0.495316i
$59$	−3.62814	+	2.09471i	−0.472343	+	0.272707i	−0.717220	−	0.696847i	$-0.754586\pi$
$59$	−3.62814	+	2.09471i	−0.472343	+	0.272707i	0.244877	+	0.969554i	$0.421252\pi$
$60$	0.948138	+	2.02510i	0.122404	+	0.261439i
$61$	−8.53298	−	4.92652i	−1.09254	−	0.630776i	−0.158286	−	0.987393i	$-0.550597\pi$
$61$	−8.53298	−	4.92652i	−1.09254	−	0.630776i	−0.934251	+	0.356617i	$0.883930\pi$
$62$	6.26562	−	3.61746i	0.795734	−	0.459417i
$63$		−	2.96816i		−	0.373954i
$64$	1.00000			0.125000
$65$	−5.52312	−	3.85461i	−0.685059	−	0.478105i
$66$		−	6.26383i		−	0.771024i
$67$	12.1887	+	7.03717i	1.48909	+	0.859727i	0.999922	−	0.0124627i	$-0.00396711\pi$
$67$	12.1887	+	7.03717i	1.48909	+	0.859727i	0.489168	+	0.872190i	$0.337300\pi$
$68$	−1.58013			−0.191619
$69$	−2.14996	−	1.24128i	−0.258825	−	0.149433i
$70$	−6.61265	−	0.568222i	−0.790363	−	0.0679156i
$71$	−3.03888	+	5.26349i	−0.360648	+	0.624661i	−0.988068	−	0.154021i	$-0.950778\pi$
$71$	−3.03888	+	5.26349i	−0.360648	+	0.624661i	0.627419	+	0.778681i	$0.284111\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$			6.77606i			0.793077i	0.918018	+	0.396539i	$0.129789\pi$
$73$			6.77606i			0.793077i	−0.918018	+	0.396539i	$0.870211\pi$
$74$	1.22007	−	5.95915i	0.141830	−	0.692737i
$75$	−3.84015	−	3.20207i	−0.443422	−	0.369743i
$76$	−1.22640	+	0.708065i	−0.140678	+	0.0812206i
$77$	16.1012	+	9.29603i	1.83490	+	1.05938i
$78$	2.60853	+	1.50604i	0.295358	+	0.170525i
$79$	−2.15482	−	1.24409i	−0.242436	−	0.139971i	0.373860	−	0.927485i	$-0.378034\pi$
$79$	−2.15482	−	1.24409i	−0.242436	−	0.139971i	−0.616296	+	0.787515i	$0.711368\pi$
$80$	−2.02510	+	0.948138i	−0.226413	+	0.106005i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.97292			0.659599
$83$	−7.43197	+	4.29085i	−0.815765	+	0.470982i	−0.848954	−	0.528467i	$-0.822767\pi$
$83$	−7.43197	+	4.29085i	−0.815765	+	0.470982i	0.0331890	+	0.999449i	$0.489434\pi$
$84$	2.96816			0.323853
$85$	3.19992	−	1.49818i	0.347080	−	0.162500i
$86$	−0.0843682	−	0.146130i	−0.00909766	−	0.0157576i
$87$	3.77222	−	6.53367i	0.404424	−	0.700483i
$88$	6.26383			0.667726
$89$	−10.6609	+	6.15507i	−1.13005	+	0.652436i	−0.943948	−	0.330094i	$-0.892920\pi$
$89$	−10.6609	+	6.15507i	−1.13005	+	0.652436i	−0.186104	+	0.982530i	$0.559586\pi$
$90$	1.83366	+	1.27972i	0.193285	+	0.134894i
$91$	−7.74255	+	4.47016i	−0.811640	+	0.468600i
$92$	1.24128	−	2.14996i	0.129412	−	0.224149i
$93$	3.61746	−	6.26562i	0.375113	−	0.649714i
$94$	−2.87916	+	1.66228i	−0.296963	+	0.171451i
$95$	1.81225	−	2.59670i	0.185933	−	0.266416i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	2.84049			0.288408			0.144204	−	0.989548i	$-0.453938\pi$
$97$	2.84049			0.288408			0.144204	+	0.989548i	$0.453938\pi$
$98$	−0.905002	+	1.56751i	−0.0914190	+	0.158342i
$99$	−3.13191	−	5.42463i	−0.314769	−	0.545196i
$100$	3.20207	−	3.84015i	0.320207	−	0.384015i
$101$	9.41930			0.937256			0.468628	−	0.883396i	$-0.344749\pi$
$101$	9.41930			0.937256			0.468628	+	0.883396i	$0.344749\pi$
$102$	−1.36843	+	0.790063i	−0.135495	+	0.0782279i
$103$	−7.62088			−0.750908			−0.375454	−	0.926841i	$-0.622513\pi$
$103$	−7.62088			−0.750908			−0.375454	+	0.926841i	$0.622513\pi$
$104$	−1.50604	+	2.60853i	−0.147679	+	0.255788i
$105$	−6.01083	+	2.81423i	−0.586597	+	0.274641i
$106$	−0.224349	−	0.129528i	−0.0217907	−	0.0125809i
$107$	14.1039	+	8.14287i	1.36347	+	0.787201i	0.990084	−	0.140474i	$-0.0448625\pi$
$107$	14.1039	+	8.14287i	1.36347	+	0.787201i	0.373388	+	0.927675i	$0.378196\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	17.7175	−	10.2292i	1.69703	−	0.979779i	0.748473	−	0.663166i	$-0.230787\pi$
$109$	17.7175	−	10.2292i	1.69703	−	0.979779i	0.948555	−	0.316614i	$-0.102546\pi$
$110$	−12.6849	+	5.93897i	−1.20946	+	0.566259i
$111$	−1.92296	−	5.77081i	−0.182519	−	0.547741i
$112$			2.96816i			0.280465i
$113$	−5.12360	−	8.87433i	−0.481988	−	0.834827i	0.517799	−	0.855502i	$-0.326752\pi$
$113$	−5.12360	−	8.87433i	−0.481988	−	0.834827i	−0.999786	+	0.0206756i	$0.993418\pi$
$114$	−0.708065	+	1.22640i	−0.0663164	+	0.114863i
$115$	−0.475259	+	5.53079i	−0.0443181	+	0.515749i
$116$	6.53367	+	3.77222i	0.606636	+	0.350241i
$117$	3.01207			0.278466
$118$	−3.62814	−	2.09471i	−0.333997	−	0.192833i
$119$		−	4.69008i		−	0.429939i
$120$	−1.27972	+	1.83366i	−0.116822	+	0.167390i
$121$	28.2355			2.56687
$122$		−	9.85304i		−	0.892052i
$123$	5.17270	−	2.98646i	0.466407	−	0.269280i
$124$	6.26562	+	3.61746i	0.562669	+	0.324857i
$125$	−2.84352	+	10.8127i	−0.254332	+	0.967117i
$126$	2.57051	−	1.48408i	0.228999	−	0.132213i
$127$	13.6437	−	7.87719i	1.21068	−	0.698988i	0.247775	−	0.968818i	$-0.420301\pi$
$127$	13.6437	−	7.87719i	1.21068	−	0.698988i	0.962908	+	0.269830i	$0.0869674\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−0.146130	−	0.0843682i	−0.0128660	−	0.00742820i
$130$	0.576628	−	6.71047i	0.0505736	−	0.588547i
$131$	−2.88557	+	1.66599i	−0.252114	+	0.145558i	−0.620732	−	0.784023i	$-0.713164\pi$
$131$	−2.88557	+	1.66599i	−0.252114	+	0.145558i	0.368618	+	0.929581i	$0.379831\pi$
$132$	5.42463	−	3.13191i	0.472154	−	0.272598i
$133$	−2.10165	−	3.64017i	−0.182236	−	0.315643i
$134$			14.0743i			1.21584i
$135$	2.22786	+	0.191439i	0.191743	+	0.0164764i
$136$	−0.790063	−	1.36843i	−0.0677474	−	0.117342i
$137$			18.5410i			1.58406i	0.610481	+	0.792031i	$0.290976\pi$
$137$			18.5410i			1.58406i	−0.610481	+	0.792031i	$0.709024\pi$
$138$		−	2.48256i		−	0.211330i
$139$	4.80867	+	8.32886i	0.407866	+	0.706445i	0.994650	−	0.103298i	$-0.0329397\pi$
$139$	4.80867	+	8.32886i	0.407866	+	0.706445i	−0.586784	+	0.809743i	$0.699606\pi$
$140$	−2.81423	−	6.01083i	−0.237846	−	0.508008i
$141$	−1.66228	+	2.87916i	−0.139989	+	0.242469i
$142$	−6.07775			−0.510034
$143$	−9.43355	+	16.3394i	−0.788873	+	1.36637i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−16.8079	−	1.44430i	−1.39582	−	0.119942i
$146$	−5.86824	+	3.38803i	−0.485659	+	0.280395i
$147$			1.81000i			0.149287i
$148$	5.77081	−	1.92296i	0.474357	−	0.158066i
$149$	−12.6411			−1.03560			−0.517800	−	0.855501i	$-0.673249\pi$
$149$	−12.6411			−1.03560			−0.517800	+	0.855501i	$0.673249\pi$
$150$	0.852997	−	4.92670i	0.0696470	−	0.402264i
$151$	1.29954	−	2.25088i	0.105755	−	0.183174i	−0.808291	−	0.588783i	$-0.799607\pi$
$151$	1.29954	−	2.25088i	0.105755	−	0.183174i	0.914047	+	0.405609i	$0.132941\pi$
$152$	−1.22640	−	0.708065i	−0.0994745	−	0.0574316i
$153$	−0.790063	+	1.36843i	−0.0638728	+	0.110631i
$154$			18.5921i			1.49819i
$155$	−16.1184	−	1.38504i	−1.29466	−	0.111249i
$156$			3.01207i			0.241159i
$157$	13.0579	−	7.53899i	1.04214	−	0.601677i	0.121698	−	0.992567i	$-0.461166\pi$
$157$	13.0579	−	7.53899i	1.04214	−	0.601677i	0.920437	+	0.390890i	$0.127833\pi$
$158$		−	2.48817i		−	0.197949i
$159$	−0.259056			−0.0205445
$160$	−1.83366	−	1.27972i	−0.144964	−	0.101171i
$161$	6.38144	+	3.68432i	0.502928	+	0.290365i
$162$	−1.00000			−0.0785674
$163$	−3.83470	−	6.64189i	−0.300357	−	0.520233i	0.675860	−	0.737030i	$-0.263772\pi$
$163$	−3.83470	−	6.64189i	−0.300357	−	0.520233i	−0.976217	+	0.216797i	$0.930439\pi$
$164$	2.98646	+	5.17270i	0.233203	+	0.403920i
$165$	−8.01594	+	11.4857i	−0.624040	+	0.894164i
$166$	−7.43197	−	4.29085i	−0.576833	−	0.333035i
$167$	−4.05425	+	7.02216i	−0.313727	+	0.543391i	−0.979166	−	0.203061i	$-0.934911\pi$
$167$	−4.05425	+	7.02216i	−0.313727	+	0.543391i	0.665439	+	0.746452i	$0.268244\pi$
$168$	1.48408	+	2.57051i	0.114499	+	0.198319i
$169$	1.96371	+	3.40125i	0.151055	+	0.261634i
$170$	2.89742	+	2.02212i	0.222222	+	0.155090i
$171$			1.41613i			0.108294i
$172$	0.0843682	−	0.146130i	0.00643301	−	0.0111423i
$173$	−10.3502	+	5.97567i	−0.786908	+	0.454322i	−0.838873	−	0.544327i	$-0.816785\pi$
$173$	−10.3502	+	5.97567i	−0.786908	+	0.454322i	0.0519646	+	0.998649i	$0.483452\pi$
$174$	7.54443			0.571942
$175$	11.3982	+	9.50427i	0.861623	+	0.718455i
$176$	3.13191	+	5.42463i	0.236077	+	0.408897i
$177$	−4.18941			−0.314895
$178$	−10.6609	−	6.15507i	−0.799068	−	0.461342i
$179$		−	12.3788i		−	0.925237i	−0.886557	−	0.462619i	$-0.846910\pi$
$179$		−	12.3788i		−	0.925237i	0.886557	−	0.462619i	$-0.153090\pi$
$180$	−0.191439	+	2.22786i	−0.0142690	+	0.166055i
$181$	8.22148	−	14.2400i	0.611098	−	1.05845i	−0.379958	−	0.925004i	$-0.624061\pi$
$181$	8.22148	−	14.2400i	0.611098	−	1.05845i	0.991056	−	0.133449i	$-0.0426053\pi$
$182$	−7.74255	−	4.47016i	−0.573916	−	0.331351i
$183$	−4.92652	−	8.53298i	−0.364179	−	0.630776i
$184$	2.48256			0.183017
$185$	−9.86324	+	9.36571i	−0.725159	+	0.688581i
$186$	7.23491			0.530489
$187$	−4.94882	−	8.57161i	−0.361894	−	0.626818i
$188$	−2.87916	−	1.66228i	−0.209984	−	0.121234i
$189$	1.48408	−	2.57051i	0.107951	−	0.186977i
$190$	3.15494	+	0.271102i	0.228883	+	0.0196678i
$191$		−	21.9231i		−	1.58630i	−0.609025	−	0.793151i	$-0.708439\pi$
$191$		−	21.9231i		−	1.58630i	0.609025	−	0.793151i	$-0.291561\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	16.1168			1.16011			0.580055	−	0.814577i	$-0.303031\pi$
$193$	16.1168			1.16011			0.580055	+	0.814577i	$0.303031\pi$
$194$	1.42025	+	2.45994i	0.101968	+	0.176613i
$195$	−2.85586	−	6.09975i	−0.204512	−	0.436812i
$196$	−1.81000			−0.129286
$197$	−4.96458	+	2.86630i	−0.353712	+	0.204216i	−0.666319	−	0.745667i	$-0.732131\pi$
$197$	−4.96458	+	2.86630i	−0.353712	+	0.204216i	0.312607	+	0.949883i	$0.398798\pi$
$198$	3.13191	−	5.42463i	0.222575	−	0.385512i
$199$		−	26.3301i		−	1.86649i	−0.359242	−	0.933244i	$-0.616965\pi$
$199$		−	26.3301i		−	1.86649i	0.359242	−	0.933244i	$-0.383035\pi$
$200$	4.92670	+	0.852997i	0.348370	+	0.0603160i
$201$	7.03717	+	12.1887i	0.496363	+	0.859727i
$202$	4.70965	+	8.15736i	0.331370	+	0.573950i
$203$	−11.1966	+	19.3930i	−0.785844	+	1.36112i
$204$	−1.36843	−	0.790063i	−0.0958093	−	0.0553155i
$205$	−10.9523	−	7.64367i	−0.764943	−	0.533857i
$206$	−3.81044	−	6.59988i	−0.265486	−	0.459835i
$207$	−1.24128	−	2.14996i	−0.0862749	−	0.149433i
$208$	−3.01207			−0.208850
$209$	−7.68198	−	4.43520i	−0.531374	−	0.306789i
$210$	−5.44261	−	3.79842i	−0.375576	−	0.262116i
$211$	−18.7965			−1.29400			−0.647002	−	0.762488i	$-0.723978\pi$
$211$	−18.7965			−1.29400			−0.647002	+	0.762488i	$0.723978\pi$
$212$		−	0.259056i		−	0.0177920i
$213$	−5.26349	+	3.03888i	−0.360648	+	0.208220i
$214$			16.2857i			1.11327i
$215$	−0.0323027	+	0.375921i	−0.00220303	+	0.0256376i
$216$		−	1.00000i		−	0.0680414i
$217$	−10.7372	+	18.5974i	−0.728889	+	1.26247i
$218$	17.7175	+	10.2292i	1.19998	+	0.692809i
$219$	−3.38803	+	5.86824i	−0.228942	+	0.396539i
$220$	−11.4857	−	8.01594i	−0.774369	−	0.540435i
$221$	4.75946			0.320156
$222$	4.03618	−	4.55074i	0.270891	−	0.305425i
$223$			25.7573i			1.72483i	0.506199	+	0.862417i	$0.331050\pi$
$223$			25.7573i			1.72483i	−0.506199	+	0.862417i	$0.668950\pi$
$224$	−2.57051	+	1.48408i	−0.171749	+	0.0991594i
$225$	−1.72463	−	4.69315i	−0.114976	−	0.312877i
$226$	5.12360	−	8.87433i	0.340817	−	0.590312i
$227$	6.45977	−	11.1887i	0.428750	−	0.742617i	−0.568012	−	0.823020i	$-0.692287\pi$
$227$	6.45977	−	11.1887i	0.428750	−	0.742617i	0.996762	+	0.0804031i	$0.0256207\pi$
$228$	−1.41613			−0.0937855
$229$	−8.72881	+	15.1187i	−0.576816	+	0.999075i	0.419026	+	0.907974i	$0.362372\pi$
$229$	−8.72881	+	15.1187i	−0.576816	+	0.999075i	−0.995842	+	0.0911002i	$0.970962\pi$
$230$	−5.02743	+	2.35381i	−0.331499	+	0.155206i
$231$	9.29603	+	16.1012i	0.611634	+	1.05938i
$232$			7.54443i			0.495316i
$233$		−	9.00632i		−	0.590024i	−0.955494	−	0.295012i	$-0.904676\pi$
$233$		−	9.00632i		−	0.590024i	0.955494	−	0.295012i	$-0.0953236\pi$
$234$	1.50604	+	2.60853i	0.0984527	+	0.170525i
$235$	7.40666	+	0.636451i	0.483157	+	0.0415175i
$236$		−	4.18941i		−	0.272707i
$237$	−1.24409	−	2.15482i	−0.0808121	−	0.139971i
$238$	4.06173	−	2.34504i	0.263283	−	0.152006i
$239$	−14.4833	+	8.36195i	−0.936848	+	0.540889i	−0.888971	−	0.457964i	$-0.848579\pi$
$239$	−14.4833	+	8.36195i	−0.936848	+	0.540889i	−0.0478771	+	0.998853i	$0.515246\pi$
$240$	−2.22786	−	0.191439i	−0.143808	−	0.0123573i
$241$	15.6125	+	9.01387i	1.00569	+	0.580634i	0.909926	−	0.414770i	$-0.136138\pi$
$241$	15.6125	+	9.01387i	1.00569	+	0.580634i	0.0957620	+	0.995404i	$0.469471\pi$
$242$	14.1178	+	24.4527i	0.907524	+	1.57188i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	8.53298	−	4.92652i	0.546268	−	0.315388i
$245$	3.66544	−	1.71613i	0.234176	−	0.109640i
$246$	5.17270	+	2.98646i	0.329800	+	0.190410i
$247$	3.69402	−	2.13274i	0.235045	−	0.135703i
$248$			7.23491i			0.459417i
$249$	−8.58170			−0.543843
$250$	−10.7858	+	2.94379i	−0.682156	+	0.186181i
$251$		−	11.1889i		−	0.706234i	−0.935579	−	0.353117i	$-0.885122\pi$
$251$		−	11.1889i		−	0.706234i	0.935579	−	0.353117i	$-0.114878\pi$
$252$	2.57051	+	1.48408i	0.161927	+	0.0934884i
$253$	15.5503			0.977640
$254$	13.6437	+	7.87719i	0.856082	+	0.494259i
$255$	3.52030	+	0.302498i	0.220450	+	0.0189431i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.59009	−	13.1464i	−0.473457	−	0.820052i	0.526081	−	0.850434i	$-0.323661\pi$
$257$	−7.59009	−	13.1464i	−0.473457	−	0.820052i	−0.999538	+	0.0303827i	$0.990327\pi$
$258$		−	0.168736i		−	0.0105051i
$259$	5.70767	+	17.1287i	0.354657	+	1.06433i
$260$	6.09975	−	2.85586i	0.378290	−	0.177113i
$261$	6.53367	−	3.77222i	0.404424	−	0.233494i
$262$	−2.88557	−	1.66599i	−0.178271	−	0.102925i
$263$	−15.1450	−	8.74396i	−0.933879	−	0.539176i	−0.0458430	−	0.998949i	$-0.514597\pi$
$263$	−15.1450	−	8.74396i	−0.933879	−	0.539176i	−0.888036	+	0.459773i	$0.847931\pi$
$264$	5.42463	+	3.13191i	0.333863	+	0.192756i
$265$	0.245621	+	0.524614i	0.0150884	+	0.0322268i
$266$	2.10165	−	3.64017i	0.128861	−	0.223193i
$267$	−12.3101			−0.753368
$268$	−12.1887	+	7.03717i	−0.744545	+	0.429863i
$269$	20.3177			1.23879			0.619395	−	0.785079i	$-0.287378\pi$
$269$	20.3177			1.23879			0.619395	+	0.785079i	$0.287378\pi$
$270$	0.948138	+	2.02510i	0.0577018	+	0.123244i
$271$	0.833496	+	1.44366i	0.0506313	+	0.0876959i	0.890230	−	0.455511i	$-0.150543\pi$
$271$	0.833496	+	1.44366i	0.0506313	+	0.0876959i	−0.839599	+	0.543207i	$0.817210\pi$
$272$	0.790063	−	1.36843i	0.0479046	−	0.0829733i
$273$	−8.94033			−0.541093
$274$	−16.0570	+	9.27049i	−0.970036	+	0.560051i
$275$	30.8600	+	5.34303i	1.86093	+	0.322197i
$276$	2.14996	−	1.24128i	0.129412	−	0.0747163i
$277$	0.338790	−	0.586802i	0.0203559	−	0.0352575i	−0.855668	−	0.517525i	$-0.826853\pi$
$277$	0.338790	−	0.586802i	0.0203559	−	0.0352575i	0.876024	+	0.482268i	$0.160187\pi$
$278$	−4.80867	+	8.32886i	−0.288405	+	0.499532i
$279$	6.26562	−	3.61746i	0.375113	−	0.216571i
$280$	3.79842	−	5.44261i	0.226999	−	0.325258i
$281$	−6.56367	+	3.78954i	−0.391556	+	0.226065i	−0.682834	−	0.730574i	$-0.739253\pi$
$281$	−6.56367	+	3.78954i	−0.391556	+	0.226065i	0.291278	+	0.956638i	$0.405919\pi$
$282$	−3.32457			−0.197975
$283$	4.41293	−	7.64343i	0.262322	−	0.454354i	−0.704537	−	0.709667i	$-0.748845\pi$
$283$	4.41293	−	7.64343i	0.262322	−	0.454354i	0.966858	+	0.255313i	$0.0821785\pi$
$284$	−3.03888	−	5.26349i	−0.180324	−	0.312330i
$285$	2.86781	−	1.34269i	0.169874	−	0.0795339i
$286$	−18.8671			−1.11563
$287$	−15.3534	+	8.86431i	−0.906285	+	0.523244i
$288$	1.00000			0.0589256
$289$	7.25160	−	12.5601i	0.426565	−	0.738832i
$290$	−7.15316	−	15.2782i	−0.420048	−	0.897169i
$291$	2.45994	+	1.42025i	0.144204	+	0.0832563i
$292$	−5.86824	−	3.38803i	−0.343413	−	0.198269i
$293$	−3.38540	−	1.95456i	−0.197777	−	0.114187i	0.397841	−	0.917454i	$-0.369760\pi$
$293$	−3.38540	−	1.95456i	−0.197777	−	0.114187i	−0.595618	+	0.803268i	$0.703093\pi$
$294$	−1.56751	+	0.905002i	−0.0914190	+	0.0527808i
$295$	3.97214	+	8.48398i	0.231267	+	0.493957i
$296$	4.55074	+	4.03618i	0.264506	+	0.234598i
$297$		−	6.26383i		−	0.363464i
$298$	−6.32056	−	10.9475i	−0.366140	−	0.634173i
$299$	−3.73882	+	6.47583i	−0.216222	+	0.374507i
$300$	4.69315	−	1.72463i	0.270959	−	0.0995718i
$301$	0.433738	+	0.250419i	0.0250002	+	0.0144339i
$302$	2.59909			0.149561
$303$	8.15736	+	4.70965i	0.468628	+	0.270562i
$304$		−	1.41613i		−	0.0812206i
$305$	−12.6091	+	18.0671i	−0.721997	+	1.03452i
$306$	−1.58013			−0.0903298
$307$		−	3.33162i		−	0.190146i	−0.995470	−	0.0950728i	$-0.969692\pi$
$307$		−	3.33162i		−	0.190146i	0.995470	−	0.0950728i	$-0.0303084\pi$
$308$	−16.1012	+	9.29603i	−0.917451	+	0.529691i
$309$	−6.59988	−	3.81044i	−0.375454	−	0.216768i
$310$	−6.85969	−	14.6514i	−0.389604	−	0.832145i
$311$	−9.88071	+	5.70463i	−0.560284	+	0.323480i	−0.753259	−	0.657724i	$-0.771520\pi$
$311$	−9.88071	+	5.70463i	−0.560284	+	0.323480i	0.192976	+	0.981204i	$0.438186\pi$
$312$	−2.60853	+	1.50604i	−0.147679	+	0.0852625i
$313$	−16.6242	−	28.7939i	−0.939653	−	1.62753i	−0.766119	−	0.642699i	$-0.777815\pi$
$313$	−16.6242	−	28.7939i	−0.939653	−	1.62753i	−0.173534	−	0.984828i	$-0.555519\pi$
$314$	13.0579	+	7.53899i	0.736901	+	0.425450i
$315$	−6.61265	−	0.568222i	−0.372581	−	0.0320157i
$316$	2.15482	−	1.24409i	0.121218	−	0.0699854i
$317$	14.8439	−	8.57012i	0.833716	−	0.481346i	−0.0214076	−	0.999771i	$-0.506815\pi$
$317$	14.8439	−	8.57012i	0.833716	−	0.481346i	0.855123	+	0.518425i	$0.173481\pi$
$318$	−0.129528	−	0.224349i	−0.00726356	−	0.0125809i
$319$			47.2570i			2.64588i
$320$	0.191439	−	2.22786i	0.0107018	−	0.124541i
$321$	8.14287	+	14.1039i	0.454491	+	0.787201i
$322$			7.36865i			0.410639i
$323$			2.23766i			0.124507i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−9.64486	+	11.5668i	−0.535001	+	0.641611i
$326$	3.83470	−	6.64189i	0.212384	−	0.367860i
$327$	20.4584			1.13135
$328$	−2.98646	+	5.17270i	−0.164900	+	0.285615i
$329$	4.93393	−	8.54582i	0.272016	−	0.471146i
$330$	−13.9549	−	1.19914i	−0.768193	−	0.0660105i
$331$	−11.0933	+	6.40472i	−0.609743	+	0.352035i	−0.772865	−	0.634571i	$-0.781177\pi$
$331$	−11.0933	+	6.40472i	−0.609743	+	0.352035i	0.163122	+	0.986606i	$0.447844\pi$
$332$		−	8.58170i		−	0.470982i
$333$	1.22007	−	5.95915i	0.0668594	−	0.326559i
$334$	−8.10849			−0.443677
$335$	18.0112	−	25.8076i	0.984057	−	1.41002i
$336$	−1.48408	+	2.57051i	−0.0809633	+	0.140233i
$337$	−19.3464	−	11.1697i	−1.05387	−	0.608450i	−0.130137	−	0.991496i	$-0.541542\pi$
$337$	−19.3464	−	11.1697i	−1.05387	−	0.608450i	−0.923729	+	0.383046i	$0.874875\pi$
$338$	−1.96371	+	3.40125i	−0.106812	+	0.185003i
$339$		−	10.2472i		−	0.556551i
$340$	−0.302498	+	3.52030i	−0.0164052	+	0.190915i
$341$			45.3182i			2.45412i
$342$	−1.22640	+	0.708065i	−0.0663164	+	0.0382878i
$343$			15.4048i			0.831779i
$344$	0.168736			0.00909766
$345$	−3.17698	+	4.55218i	−0.171043	+	0.245081i
$346$	−10.3502	−	5.97567i	−0.556428	−	0.321254i
$347$	20.7908			1.11611			0.558055	−	0.829804i	$-0.311548\pi$
$347$	20.7908			1.11611			0.558055	+	0.829804i	$0.311548\pi$
$348$	3.77222	+	6.53367i	0.202212	+	0.350241i
$349$	−16.7072	−	28.9376i	−0.894313	−	1.54900i	−0.834652	−	0.550778i	$-0.814331\pi$
$349$	−16.7072	−	28.9376i	−0.894313	−	1.54900i	−0.0596613	−	0.998219i	$-0.519002\pi$
$350$	−2.53184	+	14.6233i	−0.135332	+	0.781646i
$351$	2.60853	+	1.50604i	0.139233	+	0.0803863i
$352$	−3.13191	+	5.42463i	−0.166932	+	0.289134i
$353$	−4.65698	−	8.06613i	−0.247866	−	0.429317i	0.715067	−	0.699056i	$-0.246396\pi$
$353$	−4.65698	−	8.06613i	−0.247866	−	0.429317i	−0.962934	+	0.269739i	$0.913063\pi$
$354$	−2.09471	−	3.62814i	−0.111332	−	0.192833i
$355$	11.1445	+	7.77782i	0.591491	+	0.412804i
$356$		−	12.3101i		−	0.652436i
$357$	2.34504	−	4.06173i	0.124113	−	0.214969i
$358$	10.7204	−	6.18942i	0.566590	−	0.327121i
$359$	−8.84677			−0.466915			−0.233457	−	0.972367i	$-0.575004\pi$
$359$	−8.84677			−0.466915			−0.233457	+	0.972367i	$0.575004\pi$
$360$	−2.02510	+	0.948138i	−0.106732	+	0.0499713i
$361$	−8.49729	−	14.7177i	−0.447226	−	0.774618i
$362$	16.4430			0.864223
$363$	24.4527	+	14.1178i	1.28343	+	0.740990i
$364$		−	8.94033i		−	0.468600i
$365$	15.0961	+	1.29720i	0.790165	+	0.0678986i
$366$	4.92652	−	8.53298i	0.257513	−	0.446026i
$367$	16.4851	+	9.51770i	0.860518	+	0.496820i	0.864186	−	0.503173i	$-0.167834\pi$
$367$	16.4851	+	9.51770i	0.860518	+	0.496820i	−0.00366800	+	0.999993i	$0.501168\pi$
$368$	1.24128	+	2.14996i	0.0647062	+	0.112074i
$369$	5.97292			0.310938
$370$	−13.0426	−	3.85896i	−0.678051	−	0.200618i
$371$	0.768920			0.0399203
$372$	3.61746	+	6.26562i	0.187556	+	0.324857i
$373$	8.65720	+	4.99823i	0.448253	+	0.258799i	0.707092	−	0.707122i	$-0.250007\pi$
$373$	8.65720	+	4.99823i	0.448253	+	0.258799i	−0.258839	+	0.965920i	$0.583340\pi$
$374$	4.94882	−	8.57161i	0.255897	−	0.443227i
$375$	−7.86891	+	7.94231i	−0.406349	+	0.410139i
$376$		−	3.32457i		−	0.171451i
$377$	−19.6799	−	11.3622i	−1.01357	−	0.585182i
$378$	2.96816			0.152666
$379$	−14.8869	−	25.7849i	−0.764689	−	1.32448i	−0.940411	−	0.340041i	$-0.889559\pi$
$379$	−14.8869	−	25.7849i	−0.764689	−	1.32448i	0.175722	−	0.984440i	$-0.443774\pi$
$380$	1.34269	+	2.86781i	0.0688784	+	0.147115i
$381$	15.7544			0.807122
$382$	18.9860	−	10.9616i	0.971408	−	0.560842i
$383$	3.32148	−	5.75297i	0.169720	−	0.293963i	−0.768602	−	0.639728i	$-0.779047\pi$
$383$	3.32148	−	5.75297i	0.169720	−	0.293963i	0.938321	+	0.345765i	$0.112380\pi$
$384$			1.00000i			0.0510310i
$385$	23.7926	−	34.0916i	1.21259	−	1.73747i
$386$	8.05838	+	13.9575i	0.410161	+	0.710419i
$387$	−0.0843682	−	0.146130i	−0.00428868	−	0.00742820i
$388$	−1.42025	+	2.45994i	−0.0721021	+	0.124884i
$389$	20.7940	+	12.0054i	1.05430	+	0.608699i	0.923849	−	0.382756i	$-0.125025\pi$
$389$	20.7940	+	12.0054i	1.05430	+	0.608699i	0.130448	+	0.991455i	$0.458358\pi$
$390$	3.85461	−	5.52312i	0.195186	−	0.279674i
$391$	−1.96138	−	3.39721i	−0.0991912	−	0.171804i
$392$	−0.905002	−	1.56751i	−0.0457095	−	0.0791711i
$393$	−3.33197			−0.168076
$394$	−4.96458	−	2.86630i	−0.250112	−	0.144402i
$395$	−3.18417	+	4.56247i	−0.160213	+	0.229563i
$396$	6.26383			0.314769
$397$		−	18.5483i		−	0.930913i	−0.885071	−	0.465456i	$-0.845890\pi$
$397$		−	18.5483i		−	0.930913i	0.885071	−	0.465456i	$-0.154110\pi$
$398$	22.8025	−	13.1650i	1.14299	−	0.659904i
$399$		−	4.20331i		−	0.210429i
$400$	1.72463	+	4.69315i	0.0862317	+	0.234657i
$401$			15.0009i			0.749111i	0.927204	+	0.374556i	$0.122205\pi$
$401$			15.0009i			0.749111i	−0.927204	+	0.374556i	$0.877795\pi$
$402$	−7.03717	+	12.1887i	−0.350982	+	0.607919i
$403$	−18.8725	−	10.8960i	−0.940106	−	0.542770i
$404$	−4.70965	+	8.15736i	−0.234314	+	0.405844i
$405$	1.83366	+	1.27972i	0.0911154	+	0.0635898i
$406$	−22.3931			−1.11135
$407$	28.5050	+	25.2820i	1.41294	+	1.25318i
$408$		−	1.58013i		−	0.0782279i
$409$	4.17795	−	2.41214i	0.206586	−	0.119273i	−0.393138	−	0.919480i	$-0.628610\pi$
$409$	4.17795	−	2.41214i	0.206586	−	0.119273i	0.599724	+	0.800207i	$0.295277\pi$
$410$	1.14345	−	13.3068i	0.0564710	−	0.657177i
$411$	−9.27049	+	16.0570i	−0.457279	+	0.792031i
$412$	3.81044	−	6.59988i	0.187727	−	0.325153i
$413$	12.4349			0.611880
$414$	1.24128	−	2.14996i	0.0610056	−	0.105665i
$415$	8.13664	+	17.3788i	0.399412	+	0.853092i
$416$	−1.50604	−	2.60853i	−0.0738395	−	0.127894i
$417$			9.61734i			0.470963i
$418$		−	8.87039i		−	0.433865i
$419$	−14.7497	−	25.5472i	−0.720570	−	1.24806i	−0.960771	−	0.277341i	$-0.910547\pi$
$419$	−14.7497	−	25.5472i	−0.720570	−	1.24806i	0.240201	−	0.970723i	$-0.422787\pi$
$420$	0.568222	−	6.61265i	0.0277264	−	0.322664i
$421$		−	9.61863i		−	0.468783i	−0.972142	−	0.234392i	$-0.924690\pi$
$421$		−	9.61863i		−	0.468783i	0.972142	−	0.234392i	$-0.0753098\pi$
$422$	−9.39825	−	16.2782i	−0.457500	−	0.792413i
$423$	−2.87916	+	1.66228i	−0.139989	+	0.0808230i
$424$	0.224349	−	0.129528i	0.0108953	−	0.00629043i
$425$	−2.72514	−	7.41577i	−0.132189	−	0.359718i
$426$	−5.26349	−	3.03888i	−0.255017	−	0.147234i
$427$	14.6227	+	25.3273i	0.707643	+	1.22567i
$428$	−14.1039	+	8.14287i	−0.681736	+	0.393601i
$429$	−16.3394	+	9.43355i	−0.788873	+	0.455456i
$430$	−0.341708	+	0.159985i	−0.0164786	+	0.00771518i
$431$	−20.5042	−	11.8381i	−0.987650	−	0.570220i	−0.0830792	−	0.996543i	$-0.526475\pi$
$431$	−20.5042	−	11.8381i	−0.987650	−	0.570220i	−0.904571	+	0.426323i	$0.859809\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$		−	4.67045i		−	0.224448i	−0.993683	−	0.112224i	$-0.964203\pi$
$433$		−	4.67045i		−	0.224448i	0.993683	−	0.112224i	$-0.0357973\pi$
$434$	−21.4744			−1.03080
$435$	−13.8339	−	9.65476i	−0.663286	−	0.462910i
$436$			20.4584i			0.979779i
$437$	−3.04462	−	1.75781i	−0.145644	−	0.0840876i
$438$	−6.77606			−0.323772
$439$	1.09660	+	0.633123i	0.0523379	+	0.0302173i	0.525941	−	0.850521i	$-0.323713\pi$
$439$	1.09660	+	0.633123i	0.0523379	+	0.0302173i	−0.473603	+	0.880739i	$0.657047\pi$
$440$	1.19914	−	13.9549i	0.0571668	−	0.665274i
$441$	−0.905002	+	1.56751i	−0.0430953	+	0.0746433i
$442$	2.37973	+	4.12181i	0.113192	+	0.196055i
$443$			3.37801i			0.160494i	0.996775	+	0.0802470i	$0.0255709\pi$
$443$			3.37801i			0.160494i	−0.996775	+	0.0802470i	$0.974429\pi$
$444$	5.95915	+	1.22007i	0.282809	+	0.0579020i
$445$	11.6717	+	24.9293i	0.553292	+	1.18176i
$446$	−22.3064	+	12.8786i	−1.05624	+	0.609821i
$447$	−10.9475	−	6.32056i	−0.517800	−	0.298952i
$448$	−2.57051	−	1.48408i	−0.121445	−	0.0701163i
$449$	5.24759	+	3.02970i	0.247649	+	0.142980i	0.618687	−	0.785637i	$-0.287665\pi$
$449$	5.24759	+	3.02970i	0.247649	+	0.142980i	−0.371038	+	0.928618i	$0.620998\pi$
$450$	3.20207	−	3.84015i	0.150947	−	0.181026i
$451$	−18.7067	+	32.4009i	−0.880863	+	1.52570i
$452$	10.2472			0.481988
$453$	2.25088	−	1.29954i	0.105755	−	0.0610579i
$454$	12.9195			0.606344
$455$	8.47666	+	18.1051i	0.397392	+	0.848779i
$456$	−0.708065	−	1.22640i	−0.0331582	−	0.0574316i
$457$	−1.32927	+	2.30237i	−0.0621808	+	0.107700i	−0.895440	−	0.445182i	$-0.853139\pi$
$457$	−1.32927	+	2.30237i	−0.0621808	+	0.107700i	0.833259	+	0.552883i	$0.186472\pi$
$458$	−17.4576			−0.815741
$459$	−1.36843	+	0.790063i	−0.0638728	+	0.0368770i
$460$	−4.55218	−	3.17698i	−0.212246	−	0.148128i
$461$	−4.86751	+	2.81026i	−0.226703	+	0.130887i	−0.609050	−	0.793132i	$-0.708449\pi$
$461$	−4.86751	+	2.81026i	−0.226703	+	0.130887i	0.382347	+	0.924019i	$0.375116\pi$
$462$	−9.29603	+	16.1012i	−0.432491	+	0.749096i
$463$	11.8584	−	20.5393i	0.551106	−	0.954543i	−0.447089	−	0.894489i	$-0.647539\pi$
$463$	11.8584	−	20.5393i	0.551106	−	0.954543i	0.998195	−	0.0600541i	$-0.0191273\pi$
$464$	−6.53367	+	3.77222i	−0.303318	+	0.175121i
$465$	−13.2664	−	9.25866i	−0.615214	−	0.429360i
$466$	7.79970	−	4.50316i	0.361314	−	0.208605i
$467$	10.9683			0.507550			0.253775	−	0.967263i	$-0.418328\pi$
$467$	10.9683			0.507550			0.253775	+	0.967263i	$0.418328\pi$
$468$	−1.50604	+	2.60853i	−0.0696165	+	0.120579i
$469$	−20.8875	−	36.1782i	−0.964494	−	1.67055i
$470$	3.15215	+	6.73258i	0.145398	+	0.310551i
$471$	15.0780			0.694757
$472$	3.62814	−	2.09471i	0.166999	−	0.0964167i
$473$	1.05694			0.0485979
$474$	1.24409	−	2.15482i	0.0571428	−	0.0989743i
$475$	−5.43815	−	4.53454i	−0.249520	−	0.208059i
$476$	4.06173	+	2.34504i	0.186169	+	0.107485i
$477$	−0.224349	−	0.129528i	−0.0102722	−	0.00593067i
$478$	−14.4833	−	8.36195i	−0.662452	−	0.382467i
$479$	−7.57886	+	4.37566i	−0.346287	+	0.199929i	−0.663049	−	0.748576i	$-0.730738\pi$
$479$	−7.57886	+	4.37566i	−0.346287	+	0.199929i	0.316762	+	0.948505i	$0.397404\pi$
$480$	−0.948138	−	2.02510i	−0.0432764	−	0.0924328i
$481$	−17.3821	+	5.79210i	−0.792555	+	0.264097i
$482$			18.0277i			0.821141i
$483$	3.68432	+	6.38144i	0.167643	+	0.290365i
$484$	−14.1178	+	24.4527i	−0.641716	+	1.11149i
$485$	0.543781	−	6.32821i	0.0246918	−	0.287349i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	29.7243			1.34694			0.673469	−	0.739216i	$-0.264804\pi$
$487$	29.7243			1.34694			0.673469	+	0.739216i	$0.264804\pi$
$488$	8.53298	+	4.92652i	0.386270	+	0.223013i
$489$		−	7.66940i		−	0.346822i
$490$	3.31893	+	2.31630i	0.149934	+	0.104640i
$491$	4.90317			0.221277			0.110639	−	0.993861i	$-0.464710\pi$
$491$	4.90317			0.221277			0.110639	+	0.993861i	$0.464710\pi$
$492$			5.97292i			0.269280i
$493$	10.3240	−	5.96058i	0.464971	−	0.268451i
$494$	3.69402	+	2.13274i	0.166202	+	0.0959566i
$495$	−12.6849	+	5.93897i	−0.570143	+	0.266937i
$496$	−6.26562	+	3.61746i	−0.281334	+	0.162429i
$497$	15.6229	−	9.01988i	0.700783	−	0.404597i
$498$	−4.29085	−	7.43197i	−0.192278	−	0.333035i
$499$	29.3135	+	16.9241i	1.31225	+	0.757628i	0.982468	−	0.186429i	$-0.0596913\pi$
$499$	29.3135	+	16.9241i	1.31225	+	0.757628i	0.329782	+	0.944057i	$0.393025\pi$
$500$	−7.94231	−	7.86891i	−0.355191	−	0.351908i
$501$	−7.02216	+	4.05425i	−0.313727	+	0.181130i
$502$	9.68983	−	5.59443i	0.432478	−	0.249692i
$503$	9.64473	+	16.7052i	0.430037	+	0.744846i	0.996876	−	0.0789825i	$-0.0251671\pi$
$503$	9.64473	+	16.7052i	0.430037	+	0.744846i	−0.566839	+	0.823829i	$0.691834\pi$
$504$			2.96816i			0.132213i
$505$	1.80322	−	20.9849i	0.0802423	−	0.933814i
$506$	7.77516	+	13.4670i	0.345648	+	0.598680i
$507$			3.92742i			0.174423i
$508$			15.7544i			0.698988i
$509$	13.1997	+	22.8626i	0.585069	+	1.01337i	0.994867	+	0.101192i	$0.0322657\pi$
$509$	13.1997	+	22.8626i	0.585069	+	1.01337i	−0.409798	+	0.912176i	$0.634401\pi$
$510$	1.49818	+	3.19992i	0.0663405	+	0.141695i
$511$	10.0562	−	17.4179i	0.444861	−	0.770522i
$512$	−1.00000			−0.0441942
$513$	−0.708065	+	1.22640i	−0.0312618	+	0.0541471i
$514$	7.59009	−	13.1464i	0.334785	−	0.579864i
$515$	−1.45893	+	16.9782i	−0.0642883	+	0.748151i
$516$	0.146130	−	0.0843682i	0.00643301	−	0.00371410i
$517$		−	20.8245i		−	0.915861i
$518$	−11.9801	+	13.5073i	−0.526374	+	0.593478i
$519$	−11.9513			−0.524606
$520$	5.52312	+	3.85461i	0.242205	+	0.169036i
$521$	14.5158	−	25.1422i	0.635950	−	1.10150i	−0.350363	−	0.936614i	$-0.613942\pi$
$521$	14.5158	−	25.1422i	0.635950	−	1.10150i	0.986313	−	0.164884i	$-0.0527249\pi$
$522$	6.53367	+	3.77222i	0.285971	+	0.165105i
$523$	−9.58818	+	16.6072i	−0.419262	+	0.726183i	−0.995865	−	0.0908411i	$-0.971044\pi$
$523$	−9.58818	+	16.6072i	−0.419262	+	0.726183i	0.576603	+	0.817024i	$0.304378\pi$
$524$		−	3.33197i		−	0.145558i
$525$	5.11900	+	13.9300i	0.223411	+	0.607957i
$526$		−	17.4879i		−	0.762509i
$527$	9.90047	−	5.71604i	0.431271	−	0.248995i
$528$			6.26383i			0.272598i
$529$	−16.8369			−0.732039
$530$	−0.331519	+	0.475021i	−0.0144003	+	0.0206336i
$531$	−3.62814	−	2.09471i	−0.157448	−	0.0909025i
$532$	4.20331			0.182236
$533$	−8.99544	−	15.5806i	−0.389636	−	0.674869i
$534$	−6.15507	−	10.6609i	−0.266356	−	0.461342i
$535$	20.8412	−	29.8626i	0.901044	−	1.29107i
$536$	−12.1887	−	7.03717i	−0.526473	−	0.303959i
$537$	6.18942	−	10.7204i	0.267093	−	0.462619i
$538$	10.1588	+	17.5956i	0.437978	+	0.758601i
$539$	−5.66877	−	9.81860i	−0.244171	−	0.422917i
$540$	−1.27972	+	1.83366i	−0.0550704	+	0.0789083i
$541$		−	23.7744i		−	1.02214i	−0.859539	−	0.511070i	$-0.829249\pi$
$541$		−	23.7744i		−	1.02214i	0.859539	−	0.511070i	$-0.170751\pi$
$542$	−0.833496	+	1.44366i	−0.0358017	+	0.0620104i
$543$	14.2400	−	8.22148i	0.611098	−	0.352818i
$544$	1.58013			0.0677474
$545$	−19.3974	−	41.4303i	−0.830892	−	1.77468i
$546$	−4.47016	−	7.74255i	−0.191305	−	0.331351i
$547$	5.18635			0.221752			0.110876	−	0.993834i	$-0.464634\pi$
$547$	5.18635			0.221752			0.110876	+	0.993834i	$0.464634\pi$
$548$	−16.0570	−	9.27049i	−0.685919	−	0.396016i
$549$		−	9.85304i		−	0.420518i
$550$	10.8028	+	29.3971i	0.460633	+	1.25350i
$551$	5.34195	−	9.25252i	0.227575	−	0.394171i
$552$	2.14996	+	1.24128i	0.0915084	+	0.0528324i
$553$	3.69266	+	6.39587i	0.157028	+	0.271980i
$554$	0.677580			0.0287876
$555$	−13.2247	+	3.17933i	−0.561356	+	0.134955i
$556$	−9.61734			−0.407866
$557$	−19.7296	−	34.1727i	−0.835972	−	1.44795i	−0.893237	−	0.449586i	$-0.851571\pi$
$557$	−19.7296	−	34.1727i	−0.835972	−	1.44795i	0.0572653	−	0.998359i	$-0.481762\pi$
$558$	6.26562	+	3.61746i	0.265245	+	0.153139i
$559$	−0.254123	+	0.440154i	−0.0107483	+	0.0186165i
$560$	6.61265	+	0.568222i	0.279435	+	0.0240118i
$561$		−	9.89764i		−	0.417879i
$562$	−6.56367	−	3.78954i	−0.276872	−	0.159852i
$563$	1.04534			0.0440558			0.0220279	−	0.999757i	$-0.492988\pi$
$563$	1.04534			0.0440558			0.0220279	+	0.999757i	$0.492988\pi$
$564$	−1.66228	−	2.87916i	−0.0699947	−	0.121234i
$565$	−20.7516	+	9.71576i	−0.873027	+	0.408745i
$566$	8.82587			0.370979
$567$	2.57051	−	1.48408i	0.107951	−	0.0623256i
$568$	3.03888	−	5.26349i	0.127508	−	0.220851i
$569$		−	8.72389i		−	0.365725i	−0.983139	−	0.182862i	$-0.941464\pi$
$569$		−	8.72389i		−	0.365725i	0.983139	−	0.182862i	$-0.0585362\pi$
$570$	2.59670	+	1.81225i	0.108764	+	0.0759068i
$571$	−7.10327	−	12.3032i	−0.297263	−	0.514874i	0.678246	−	0.734835i	$-0.262740\pi$
$571$	−7.10327	−	12.3032i	−0.297263	−	0.514874i	−0.975509	+	0.219961i	$0.929407\pi$
$572$	−9.43355	−	16.3394i	−0.394436	−	0.683184i
$573$	10.9616	−	18.9860i	0.457926	−	0.793151i
$574$	−15.3534	−	8.86431i	−0.640840	−	0.369989i
$575$	12.2308	+	2.11762i	0.510061	+	0.0883107i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	17.7802	+	30.7962i	0.740199	+	1.28206i	0.952404	+	0.304837i	$0.0986021\pi$
$577$	17.7802	+	30.7962i	0.740199	+	1.28206i	−0.212205	+	0.977225i	$0.568065\pi$
$578$	14.5032			0.603254
$579$	13.9575	+	8.05838i	0.580055	+	0.334895i
$580$	9.65476	−	13.8339i	0.400892	−	0.574423i
$581$	25.4719			1.05675
$582$			2.84049i			0.117742i
$583$	1.40528	−	0.811340i	0.0582008	−	0.0336023i
$584$		−	6.77606i		−	0.280395i
$585$	0.576628	−	6.71047i	0.0238406	−	0.277444i
$586$		−	3.90912i		−	0.161484i
$587$	7.07285	−	12.2505i	0.291928	−	0.505634i	−0.682338	−	0.731037i	$-0.739037\pi$
$587$	7.07285	−	12.2505i	0.291928	−	0.505634i	0.974266	+	0.225403i	$0.0723699\pi$
$588$	−1.56751	−	0.905002i	−0.0646430	−	0.0373216i
$589$	5.12279	−	8.87293i	0.211081	−	0.365603i
$590$	−5.36127	+	7.68197i	−0.220720	+	0.316262i
$591$	−5.73260			−0.235808
$592$	−1.22007	+	5.95915i	−0.0501446	+	0.244919i
$593$		−	16.5862i		−	0.681113i	−0.940224	−	0.340556i	$-0.889385\pi$
$593$		−	16.5862i		−	0.681113i	0.940224	−	0.340556i	$-0.110615\pi$
$594$	5.42463	−	3.13191i	0.222575	−	0.128504i
$595$	−10.4488	−	0.897863i	−0.428360	−	0.0368088i
$596$	6.32056	−	10.9475i	0.258900	−	0.448428i
$597$	13.1650	−	22.8025i	0.538809	−	0.933244i
$598$	−7.47765			−0.305784
$599$	1.59438	−	2.76154i	0.0651445	−	0.112834i	−0.831614	−	0.555355i	$-0.812583\pi$
$599$	1.59438	−	2.76154i	0.0651445	−	0.112834i	0.896758	+	0.442521i	$0.145916\pi$
$600$	3.84015	+	3.20207i	0.156773	+	0.130724i
$601$	−13.6020	−	23.5594i	−0.554837	−	0.961006i	−0.997916	−	0.0645235i	$-0.979447\pi$
$601$	−13.6020	−	23.5594i	−0.554837	−	0.961006i	0.443079	−	0.896483i	$-0.353886\pi$
$602$			0.500837i			0.0204126i
$603$			14.0743i			0.573151i
$604$	1.29954	+	2.25088i	0.0528777	+	0.0915868i
$605$	5.40538	−	62.9047i	0.219760	−	2.55744i
$606$			9.41930i			0.382633i
$607$	−4.70400	−	8.14756i	−0.190929	−	0.330699i	0.754629	−	0.656152i	$-0.227817\pi$
$607$	−4.70400	−	8.14756i	−0.190929	−	0.330699i	−0.945558	+	0.325452i	$0.894483\pi$
$608$	1.22640	−	0.708065i	0.0497373	−	0.0287158i
$609$	−19.3930	+	11.1966i	−0.785844	+	0.453707i
$610$	−21.9512	−	1.88626i	−0.888777	−	0.0763723i
$611$	8.67223	+	5.00692i	0.350841	+	0.202558i
$612$	−0.790063	−	1.36843i	−0.0319364	−	0.0553155i
$613$	−28.0938	+	16.2200i	−1.13470	+	0.655118i	−0.945112	−	0.326746i	$-0.894048\pi$
$613$	−28.0938	+	16.2200i	−1.13470	+	0.655118i	−0.189586	+	0.981864i	$0.560714\pi$
$614$	2.88527	−	1.66581i	0.116440	−	0.0672266i
$615$	−5.66316	−	12.0958i	−0.228360	−	0.487749i
$616$	−16.1012	−	9.29603i	−0.648736	−	0.374548i
$617$	5.55242	−	3.20569i	0.223532	−	0.129056i	−0.384053	−	0.923311i	$-0.625472\pi$
$617$	5.55242	−	3.20569i	0.223532	−	0.129056i	0.607585	+	0.794255i	$0.292139\pi$
$618$		−	7.62088i		−	0.306557i
$619$	34.1202			1.37141			0.685703	−	0.727882i	$-0.259495\pi$
$619$	34.1202			1.37141			0.685703	+	0.727882i	$0.259495\pi$
$620$	9.25866	−	13.2664i	0.371837	−	0.532791i
$621$		−	2.48256i		−	0.0996217i
$622$	−9.88071	−	5.70463i	−0.396181	−	0.228735i
$623$	36.5385			1.46389
$624$	−2.60853	−	1.50604i	−0.104425	−	0.0602897i
$625$	23.5448	+	8.40493i	0.941792	+	0.336197i
$626$	16.6242	−	28.7939i	0.664435	−	1.15084i
$627$	−4.43520	−	7.68198i	−0.177125	−	0.306789i
$628$			15.0780i			0.601677i
$629$	1.92787	−	9.41621i	0.0768690	−	0.375449i
$630$	−2.81423	−	6.01083i	−0.112122	−	0.239477i
$631$	−31.0607	+	17.9329i	−1.23651	+	0.713898i	−0.968379	−	0.249485i	$-0.919739\pi$
$631$	−31.0607	+	17.9329i	−1.23651	+	0.713898i	−0.268129	+	0.963383i	$0.586405\pi$
$632$	2.15482	+	1.24409i	0.0857142	+	0.0494871i
$633$	−16.2782	−	9.39825i	−0.647002	−	0.373547i
$634$	14.8439	+	8.57012i	0.589526	+	0.340363i
$635$	−14.9373	−	31.9042i	−0.592770	−	1.26608i
$636$	0.129528	−	0.224349i	0.00513611	−	0.00889601i
$637$	5.45186			0.216011
$638$	−40.9258	+	23.6285i	−1.62027	+	0.935461i
$639$	−6.07775			−0.240432
$640$	2.02510	−	0.948138i	0.0800491	−	0.0374784i
$641$	18.4422	+	31.9428i	0.728424	+	1.26167i	0.957549	+	0.288270i	$0.0930800\pi$
$641$	18.4422	+	31.9428i	0.728424	+	1.26167i	−0.229126	+	0.973397i	$0.573587\pi$
$642$	−8.14287	+	14.1039i	−0.321374	+	0.556635i
$643$	−15.4850			−0.610669			−0.305335	−	0.952245i	$-0.598768\pi$
$643$	−15.4850			−0.610669			−0.305335	+	0.952245i	$0.598768\pi$
$644$	−6.38144	+	3.68432i	−0.251464	+	0.145183i
$645$	−0.215935	+	0.309405i	−0.00850244	+	0.0121828i
$646$	−1.93787	+	1.11883i	−0.0762447	+	0.0440199i
$647$	22.4223	−	38.8366i	0.881512	−	1.52682i	0.0318523	−	0.999493i	$-0.489859\pi$
$647$	22.4223	−	38.8366i	0.881512	−	1.52682i	0.849660	−	0.527331i	$-0.176807\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	22.7260	−	13.1209i	0.892074	−	0.515039i
$650$	−14.8396	−	2.56929i	−0.582056	−	0.100776i
$651$	−18.5974	+	10.7372i	−0.728889	+	0.420824i
$652$	7.66940			0.300357
$653$	19.8488	−	34.3792i	0.776745	−	1.34536i	−0.157063	−	0.987589i	$-0.550203\pi$
$653$	19.8488	−	34.3792i	0.776745	−	1.34536i	0.933808	−	0.357774i	$-0.116464\pi$
$654$	10.2292	+	17.7175i	0.399993	+	0.692809i
$655$	3.15917	+	6.74758i	0.123439	+	0.263650i
$656$	−5.97292			−0.233203
$657$	−5.86824	+	3.38803i	−0.228942	+	0.132180i
$658$	9.86786			0.384689
$659$	17.6781	−	30.6194i	0.688642	−	1.19276i	−0.283636	−	0.958932i	$-0.591541\pi$
$659$	17.6781	−	30.6194i	0.688642	−	1.19276i	0.972277	−	0.233830i	$-0.0751260\pi$
$660$	−5.93897	−	12.6849i	−0.231174	−	0.493758i
$661$	−25.7382	−	14.8599i	−1.00110	−	0.577984i	−0.0925251	−	0.995710i	$-0.529494\pi$
$661$	−25.7382	−	14.8599i	−1.00110	−	0.577984i	−0.908573	+	0.417726i	$0.862827\pi$
$662$	−11.0933	−	6.40472i	−0.431154	−	0.248927i
$663$	4.12181	+	2.37973i	0.160078	+	0.0924210i
$664$	7.43197	−	4.29085i	0.288416	−	0.166517i
$665$	−8.51212	+	3.98531i	−0.330086	+	0.154544i
$666$	5.77081	−	1.92296i	0.223614	−	0.0745133i
$667$			18.7295i			0.725209i
$668$	−4.05425	−	7.02216i	−0.156864	−	0.271696i
$669$	−12.8786	+	22.3064i	−0.497916	+	0.862417i
$670$	31.3556	+	2.69438i	1.21137	+	0.104093i
$671$	53.4491	+	30.8589i	2.06338	+	1.19129i
$672$	−2.96816			−0.114499
$673$	27.2357	+	15.7245i	1.04986	+	0.606136i	0.922610	−	0.385735i	$-0.126052\pi$
$673$	27.2357	+	15.7245i	1.04986	+	0.606136i	0.127249	+	0.991871i	$0.459385\pi$
$674$		−	22.3393i		−	0.860478i
$675$	0.852997	−	4.92670i	0.0328319	−	0.189629i
$676$	−3.92742			−0.151055
$677$			47.8139i			1.83764i	0.394678	+	0.918820i	$0.370856\pi$
$677$			47.8139i			1.83764i	−0.394678	+	0.918820i	$0.629144\pi$
$678$	8.87433	−	5.12360i	0.340817	−	0.196771i
$679$	−7.30150	−	4.21552i	−0.280206	−	0.161777i
$680$	−3.19992	+	1.49818i	−0.122711	+	0.0574525i
$681$	11.1887	−	6.45977i	0.428750	−	0.247539i
$682$	−39.2467	+	22.6591i	−1.50283	+	0.867662i
$683$	−15.2201	−	26.3620i	−0.582382	−	1.00872i	−0.995196	−	0.0979004i	$-0.968787\pi$
$683$	−15.2201	−	26.3620i	−0.582382	−	1.00872i	0.412814	−	0.910815i	$-0.364546\pi$
$684$	−1.22640	−	0.708065i	−0.0468927	−	0.0270735i
$685$	41.3067	+	3.54946i	1.57825	+	0.135618i
$686$	−13.3409	+	7.70238i	−0.509359	+	0.294078i
$687$	−15.1187	+	8.72881i	−0.576816	+	0.333025i
$688$	0.0843682	+	0.146130i	0.00321651	+	0.00557115i
$689$			0.780294i			0.0297269i
$690$	−5.53079	−	0.475259i	−0.210554	−	0.0180928i
$691$	−5.21565	−	9.03378i	−0.198413	−	0.343661i	0.749601	−	0.661890i	$-0.230245\pi$
$691$	−5.21565	−	9.03378i	−0.198413	−	0.343661i	−0.948014	+	0.318229i	$0.896912\pi$
$692$		−	11.9513i		−	0.454322i
$693$			18.5921i			0.706254i
$694$	10.3954	+	18.0054i	0.394604	+	0.683475i
$695$	19.4761	−	9.11857i	0.738770	−	0.345887i
$696$	−3.77222	+	6.53367i	−0.142985	+	0.247658i
$697$	9.43798			0.357489
$698$	16.7072	−	28.9376i	0.632375	−	1.09531i
$699$	4.50316	−	7.79970i	0.170325	−	0.295012i
$700$	−13.9300	+	5.11900i	−0.526506	+	0.193480i
$701$	−36.0512	+	20.8142i	−1.36163	+	0.786140i	−0.989841	−	0.142176i	$-0.954590\pi$
$701$	−36.0512	+	20.8142i	−1.36163	+	0.786140i	−0.371793	+	0.928316i	$0.621257\pi$
$702$			3.01207i			0.113683i
$703$	−2.72316	−	8.17221i	−0.102706	−	0.308221i
$704$	−6.26383			−0.236077
$705$	6.09613	+	4.25451i	0.229594	+	0.160234i
$706$	4.65698	−	8.06613i	0.175268	−	0.303573i
$707$	−24.2124	−	13.9790i	−0.910600	−	0.525735i
$708$	2.09471	−	3.62814i	0.0787239	−	0.136354i
$709$			37.6310i			1.41326i	0.707583	+	0.706630i	$0.249786\pi$
$709$			37.6310i			1.41326i	−0.707583	+	0.706630i	$0.750214\pi$
$710$	−1.16352	+	13.5404i	−0.0436661	+	0.508161i
$711$		−	2.48817i		−	0.0933138i
$712$	10.6609	−	6.15507i	0.399534	−	0.230671i
$713$			17.9611i			0.672648i
$714$	4.69008			0.175522
$715$	34.5959	+	24.1446i	1.29381	+	0.902957i
$716$	10.7204	+	6.18942i	0.400640	+	0.231309i
$717$	−16.7239			−0.624565
$718$	−4.42339	−	7.66153i	−0.165079	−	0.285926i
$719$	−3.55712	−	6.16111i	−0.132658	−	0.229770i	0.792042	−	0.610466i	$-0.209018\pi$
$719$	−3.55712	−	6.16111i	−0.132658	−	0.229770i	−0.924700	+	0.380696i	$0.875685\pi$
$720$	−1.83366	−	1.27972i	−0.0683366	−	0.0476923i
$721$	19.5895	+	11.3100i	0.729552	+	0.421207i
$722$	8.49729	−	14.7177i	0.316236	−	0.547737i
$723$	9.01387	+	15.6125i	0.335229	+	0.580634i
$724$	8.22148	+	14.2400i	0.305549	+	0.529227i
$725$	−6.43538	+	37.1692i	−0.239004	+	1.38043i
$726$			28.2355i			1.04792i
$727$	−12.2381	+	21.1969i	−0.453884	+	0.786151i	−0.998623	−	0.0524549i	$-0.983295\pi$
$727$	−12.2381	+	21.1969i	−0.453884	+	0.786151i	0.544739	+	0.838606i	$0.316629\pi$
$728$	7.74255	−	4.47016i	0.286958	−	0.165675i
$729$	−1.00000			−0.0370370
$730$	6.42464	+	13.7222i	0.237786	+	0.507881i
$731$	−0.133312	−	0.230904i	−0.00493074	−	0.00854029i
$732$	9.85304			0.364179
$733$	29.1268	+	16.8164i	1.07582	+	0.621127i	0.929767	−	0.368149i	$-0.120008\pi$
$733$	29.1268	+	16.8164i	1.07582	+	0.621127i	0.146057	+	0.989276i	$0.453342\pi$
$734$			19.0354i			0.702610i
$735$	4.03243	+	0.346505i	0.148738	+	0.0127810i
$736$	−1.24128	+	2.14996i	−0.0457542	+	0.0792486i
$737$	−76.3481	−	44.0796i	−2.81232	−	1.62369i
$738$	2.98646	+	5.17270i	0.109933	+	0.190410i
$739$	−9.43102			−0.346926			−0.173463	−	0.984840i	$-0.555496\pi$
$739$	−9.43102			−0.346926			−0.173463	+	0.984840i	$0.555496\pi$
$740$	−3.17933	−	13.2247i	−0.116874	−	0.486149i
$741$	4.26549			0.156697
$742$	0.384460	+	0.665904i	0.0141140	+	0.0244461i
$743$	−8.92177	−	5.15098i	−0.327308	−	0.188971i	0.327337	−	0.944908i	$-0.393849\pi$
$743$	−8.92177	−	5.15098i	−0.327308	−	0.188971i	−0.654645	+	0.755936i	$0.727182\pi$
$744$	−3.61746	+	6.26562i	−0.132622	+	0.229709i
$745$	−2.42000	+	28.1626i	−0.0886620	+	1.03180i
$746$			9.99647i			0.365997i
$747$	−7.43197	−	4.29085i	−0.271922	−	0.156994i
$748$	9.89764			0.361894
$749$	−24.1694	−	41.8626i	−0.883131	−	1.52963i
$750$	−10.8127	−	2.84352i	−0.394824	−	0.103831i
$751$	−22.2258			−0.811031			−0.405516	−	0.914088i	$-0.632908\pi$
$751$	−22.2258			−0.811031			−0.405516	+	0.914088i	$0.632908\pi$
$752$	2.87916	−	1.66228i	0.104992	−	0.0606172i
$753$	5.59443	−	9.68983i	0.203872	−	0.353117i
$754$		−	22.7244i		−	0.827573i
$755$	−4.76585	−	3.32610i	−0.173447	−	0.121049i
$756$	1.48408	+	2.57051i	0.0539756	+	0.0934884i
$757$	−5.74529	−	9.95114i	−0.208816	−	0.361680i	0.742526	−	0.669818i	$-0.233628\pi$
$757$	−5.74529	−	9.95114i	−0.208816	−	0.361680i	−0.951342	+	0.308137i	$0.900294\pi$
$758$	14.8869	−	25.7849i	0.540717	−	0.936549i
$759$	13.4670	+	7.77516i	0.488820	+	0.282220i
$760$	−1.81225	+	2.59670i	−0.0657372	+	0.0941923i
$761$	−8.92596	−	15.4602i	−0.323566	−	0.560433i	0.657655	−	0.753319i	$-0.271548\pi$
$761$	−8.92596	−	15.4602i	−0.323566	−	0.560433i	−0.981221	+	0.192887i	$0.938215\pi$
$762$	7.87719	+	13.6437i	0.285361	+	0.494259i
$763$	−60.7239			−2.19835
$764$	18.9860	+	10.9616i	0.686889	+	0.396575i
$765$	2.89742	+	2.02212i	0.104756	+	0.0731099i
$766$	6.64296			0.240020
$767$			12.6188i			0.455639i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$		−	14.6714i		−	0.529066i	−0.964377	−	0.264533i	$-0.914782\pi$
$769$		−	14.6714i		−	0.529066i	0.964377	−	0.264533i	$-0.0852178\pi$
$770$	41.4205	+	3.55925i	1.49269	+	0.128266i
$771$		−	15.1802i		−	0.546701i
$772$	−8.05838	+	13.9575i	−0.290027	+	0.502342i
$773$	14.3016	+	8.25702i	0.514392	+	0.296984i	0.734637	−	0.678460i	$-0.237352\pi$
$773$	14.3016	+	8.25702i	0.514392	+	0.296984i	−0.220245	+	0.975445i	$0.570686\pi$
$774$	0.0843682	−	0.146130i	0.00303255	−	0.00525253i
$775$	−6.17136	+	35.6442i	−0.221682	+	1.28038i
$776$	−2.84049			−0.101968
$777$	−3.62137	+	17.6877i	−0.129916	+	0.634544i
$778$			24.0108i			0.860830i
$779$	7.32522	−	4.22922i	0.262453	−	0.151527i
$780$	6.71047	+	0.576628i	0.240273	+	0.0206466i
$781$	19.0350	−	32.9696i	0.681125	−	1.17974i
$782$	1.96138	−	3.39721i	0.0701388	−	0.121484i
$783$	7.54443			0.269616
$784$	0.905002	−	1.56751i	0.0323215	−	0.0559825i
$785$	−14.2960	−	30.5345i	−0.510247	−	1.08982i
$786$	−1.66599	−	2.88557i	−0.0594238	−	0.102925i
$787$			10.9227i			0.389353i	0.980868	+	0.194676i	$0.0623657\pi$
$787$			10.9227i			0.389353i	−0.980868	+	0.194676i	$0.937634\pi$
$788$		−	5.73260i		−	0.204216i
$789$	−8.74396	−	15.1450i	−0.311293	−	0.539176i
$790$	−5.54330	−	0.476333i	−0.197222	−	0.0169472i
$791$			30.4154i			1.08145i
$792$	3.13191	+	5.42463i	0.111288	+	0.192756i
$793$	−25.7020	+	14.8390i	−0.912704	+	0.526950i
$794$	16.0633	−	9.27415i	0.570065	−	0.329127i
$795$	−0.0495933	+	0.577139i	−0.00175889	+	0.0204690i
$796$	22.8025	+	13.1650i	0.808213	+	0.466622i
$797$	22.9530	+	39.7558i	0.813039	+	1.40822i	0.910728	+	0.413007i	$0.135522\pi$
$797$	22.9530	+	39.7558i	0.813039	+	1.40822i	−0.0976891	+	0.995217i	$0.531145\pi$
$798$	3.64017	−	2.10165i	0.128861	−	0.0743977i
$799$	−4.54944	+	2.62662i	−0.160947	+	0.0929231i
$800$	−3.20207	+	3.84015i	−0.113210	+	0.135770i
$801$	−10.6609	−	6.15507i	−0.376684	−	0.217479i
$802$	−12.9912	+	7.50047i	−0.458735	+	0.264851i
$803$		−	42.4440i		−	1.49782i
$804$	−14.0743			−0.496363
$805$	9.42980	−	13.5116i	0.332357	−	0.476222i
$806$		−	21.7921i		−	0.767593i
$807$	17.5956	+	10.1588i	0.619395	+	0.357608i
$808$	−9.41930			−0.331370
$809$	−29.1372	−	16.8223i	−1.02441	−	0.591442i	−0.109030	−	0.994038i	$-0.534775\pi$
$809$	−29.1372	−	16.8223i	−1.02441	−	0.591442i	−0.915378	+	0.402596i	$0.868108\pi$
$810$	−0.191439	+	2.22786i	−0.00672648	+	0.0782789i
$811$	−20.1485	+	34.8982i	−0.707508	+	1.22544i	0.258270	+	0.966073i	$0.416847\pi$
$811$	−20.1485	+	34.8982i	−0.707508	+	1.22544i	−0.965779	+	0.259368i	$0.916486\pi$
$812$	−11.1966	−	19.3930i	−0.392922	−	0.680561i
$813$			1.66699i			0.0584640i
$814$	−7.64231	+	37.3271i	−0.267863	+	1.30831i
$815$	−15.5313	+	7.27165i	−0.544038	+	0.254715i
$816$	1.36843	−	0.790063i	0.0479046	−	0.0276578i
$817$	−0.206939	−	0.119476i	−0.00723988	−	0.00417995i
$818$	4.17795	+	2.41214i	0.146078	+	0.0843384i
$819$	−7.74255	−	4.47016i	−0.270547	−	0.156200i
$820$	12.0958	−	5.66316i	0.422403	−	0.197766i
$821$	−20.8081	+	36.0407i	−0.726208	+	1.25783i	0.232267	+	0.972652i	$0.425386\pi$
$821$	−20.8081	+	36.0407i	−0.726208	+	1.25783i	−0.958475	+	0.285177i	$0.907948\pi$
$822$	−18.5410			−0.646691
$823$	20.7861	−	12.0008i	0.724557	−	0.418323i	−0.0918706	−	0.995771i	$-0.529285\pi$
$823$	20.7861	−	12.0008i	0.724557	−	0.418323i	0.816428	+	0.577448i	$0.195951\pi$
$824$	7.62088			0.265486
$825$	24.0540	+	20.0572i	0.837454	+	0.698302i
$826$	6.21743	+	10.7689i	0.216332	+	0.374698i
$827$	−24.2840	+	42.0611i	−0.844437	+	1.46261i	0.0416731	+	0.999131i	$0.486731\pi$
$827$	−24.2840	+	42.0611i	−0.844437	+	1.46261i	−0.886110	+	0.463476i	$0.846602\pi$
$828$	2.48256			0.0862749
$829$	24.1340	−	13.9338i	0.838209	−	0.483940i	−0.0184462	−	0.999830i	$-0.505872\pi$
$829$	24.1340	−	13.9338i	0.838209	−	0.483940i	0.856655	+	0.515890i	$0.172539\pi$
$830$	−10.9822	+	15.7359i	−0.381197	+	0.546202i
$831$	0.586802	−	0.338790i	0.0203559	−	0.0117525i
$832$	1.50604	−	2.60853i	0.0522124	−	0.0904345i
$833$	−1.43002	+	2.47686i	−0.0495472	+	0.0858182i
$834$	−8.32886	+	4.80867i	−0.288405	+	0.166511i
$835$	14.8682	+	10.3766i	0.514537	+	0.359097i
$836$	7.68198	−	4.43520i	0.265687	−	0.153394i
$837$	7.23491			0.250075
$838$	14.7497	−	25.5472i	0.509520	−	0.882515i
$839$	9.50280	+	16.4593i	0.328073	+	0.568239i	0.982129	−	0.188206i	$-0.0602674\pi$
$839$	9.50280	+	16.4593i	0.328073	+	0.568239i	−0.654056	+	0.756446i	$0.726934\pi$
$840$	6.01083	−	2.81423i	0.207393	−	0.0971002i
$841$	−27.9184			−0.962704
$842$	8.32998	−	4.80932i	0.287070	−	0.165740i
$843$	−7.57907			−0.261037
$844$	9.39825	−	16.2782i	0.323501	−	0.560320i
$845$	7.95342	−	3.72374i	0.273606	−	0.128100i
$846$	−2.87916	−	1.66228i	−0.0989875	−	0.0571505i
$847$	−72.5796	−	41.9038i	−2.49386	−	1.43983i
$848$	0.224349	+	0.129528i	0.00770417	+	0.00444800i
$849$	7.64343	−	4.41293i	0.262322	−	0.151451i
$850$	5.05967	−	6.06793i	0.173545	−	0.208128i
$851$	11.2975	+	10.0201i	0.387273	+	0.343484i
$852$		−	6.07775i		−	0.208220i
$853$	6.58416	+	11.4041i	0.225437	+	0.390469i	0.956451	−	0.291894i	$-0.0942855\pi$
$853$	6.58416	+	11.4041i	0.225437	+	0.390469i	−0.731013	+	0.682363i	$0.760952\pi$
$854$	−14.6227	+	25.3273i	−0.500379	+	0.866682i
$855$	3.15494	+	0.271102i	0.107897	+	0.00927151i
$856$	−14.1039	−	8.14287i	−0.482060	−	0.278318i
$857$	−19.7749			−0.675498			−0.337749	−	0.941236i	$-0.609665\pi$
$857$	−19.7749			−0.675498			−0.337749	+	0.941236i	$0.609665\pi$
$858$	−16.3394	−	9.43355i	−0.557817	−	0.322056i
$859$		−	35.7398i		−	1.21943i	−0.792622	−	0.609714i	$-0.791284\pi$
$859$		−	35.7398i		−	1.21943i	0.792622	−	0.609714i	$-0.208716\pi$
$860$	−0.309405	−	0.215935i	−0.0105506	−	0.00736333i
$861$	−17.7286			−0.604190
$862$		−	23.6762i		−	0.806413i
$863$	20.1510	−	11.6342i	0.685947	−	0.396031i	−0.116145	−	0.993232i	$-0.537054\pi$
$863$	20.1510	−	11.6342i	0.685947	−	0.396031i	0.802092	+	0.597201i	$0.203720\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	11.3315	+	24.2027i	0.385283	+	0.822916i
$866$	4.04473	−	2.33522i	0.137445	−	0.0793542i
$867$	12.5601	−	7.25160i	0.426565	−	0.246277i
$868$	−10.7372	−	18.5974i	−0.364444	−	0.631236i
$869$	13.4974	+	7.79275i	0.457869	+	0.264351i
$870$	1.44430	−	16.8079i	0.0489663	−	0.569842i
$871$	36.7133	−	21.1965i	1.24398	−	0.718215i
$872$	−17.7175	+	10.2292i	−0.599990	+	0.346404i
$873$	1.42025	+	2.45994i	0.0480680	+	0.0832563i
$874$		−	3.51563i		−	0.118918i
$875$	23.3562	−	23.5741i	0.789584	−	0.796950i
$876$	−3.38803	−	5.86824i	−0.114471	−	0.198269i
$877$		−	3.77956i		−	0.127627i	−0.997962	−	0.0638133i	$-0.979674\pi$
$877$		−	3.77956i		−	0.127627i	0.997962	−	0.0638133i	$-0.0203262\pi$
$878$			1.26625i			0.0427337i
$879$	−1.95456	−	3.38540i	−0.0659257	−	0.114187i
$880$	12.6849	−	5.93897i	0.427607	−	0.200203i
$881$	20.3003	−	35.1612i	0.683936	−	1.18461i	−0.289834	−	0.957077i	$-0.593600\pi$
$881$	20.3003	−	35.1612i	0.683936	−	1.18461i	0.973770	−	0.227535i	$-0.0730666\pi$
$882$	−1.81000			−0.0609460
$883$	0.657211	−	1.13832i	0.0221169	−	0.0383076i	−0.854755	−	0.519032i	$-0.826293\pi$
$883$	0.657211	−	1.13832i	0.0221169	−	0.0383076i	0.876872	+	0.480724i	$0.159626\pi$
$884$	−2.37973	+	4.12181i	−0.0800389	+	0.138631i
$885$	−0.802017	+	9.33341i	−0.0269595	+	0.313739i
$886$	−2.92544	+	1.68900i	−0.0982821	+	0.0567432i
$887$			49.3593i			1.65732i	0.559750	+	0.828661i	$0.310897\pi$
$887$			49.3593i			1.65732i	−0.559750	+	0.828661i	$0.689103\pi$
$888$	1.92296	+	5.77081i	0.0645304	+	0.193656i
$889$	−46.7616			−1.56833
$890$	−15.7535	+	22.5726i	−0.528060	+	0.756637i
$891$	3.13191	−	5.42463i	0.104923	−	0.181732i
$892$	−22.3064	−	12.8786i	−0.746875	−	0.431208i
$893$	−2.35401	+	4.07726i	−0.0787739	+	0.136440i
$894$		−	12.6411i		−	0.422782i
$895$	−27.5783	−	2.36979i	−0.921840	−	0.0792134i
$896$		−	2.96816i		−	0.0991594i
$897$	−6.47583	+	3.73882i	−0.216222	+	0.124836i
$898$			6.05939i			0.202205i
$899$	−54.5833			−1.82045
$900$	4.92670	+	0.852997i	0.164223	+	0.0284332i
$901$	−0.354500	−	0.204670i	−0.0118101	−	0.00681856i
$902$	−37.4134			−1.24573
$903$	0.250419	+	0.433738i	0.00833341	+	0.0144339i
$904$	5.12360	+	8.87433i	0.170408	+	0.295156i
$905$	−30.1509	−	21.0424i	−1.00225	−	0.699473i
$906$	2.25088	+	1.29954i	0.0747803	+	0.0431744i
$907$	−12.1081	+	20.9718i	−0.402041	+	0.696356i	−0.993972	−	0.109633i	$-0.965033\pi$
$907$	−12.1081	+	20.9718i	−0.402041	+	0.696356i	0.591931	+	0.805989i	$0.298366\pi$
$908$	6.45977	+	11.1887i	0.214375	+	0.371308i
$909$	4.70965	+	8.15736i	0.156209	+	0.270562i
$910$	−11.4411	+	16.3935i	−0.379269	+	0.543441i
$911$			2.47896i			0.0821316i	0.999156	+	0.0410658i	$0.0130753\pi$
$911$			2.47896i			0.0821316i	−0.999156	+	0.0410658i	$0.986925\pi$
$912$	0.708065	−	1.22640i	0.0234464	−	0.0406103i
$913$	46.5526	−	26.8771i	1.54067	−	0.889504i
$914$	−2.65855			−0.0879370
$915$	−19.9534	+	9.34204i	−0.659639	+	0.308838i
$916$	−8.72881	−	15.1187i	−0.288408	−	0.499537i
$917$	9.88985			0.326592
$918$	−1.36843	−	0.790063i	−0.0451649	−	0.0260760i
$919$			49.5042i			1.63299i	0.577351	+	0.816496i	$0.304086\pi$
$919$			49.5042i			1.63299i	−0.577351	+	0.816496i	$0.695914\pi$
$920$	0.475259	−	5.53079i	0.0156688	−	0.182345i
$921$	1.66581	−	2.88527i	0.0548903	−	0.0950728i
$922$	−4.86751	−	2.81026i	−0.160303	−	0.0925509i
$923$	9.15331	+	15.8540i	0.301285	+	0.521841i
$924$	−18.5921			−0.611634
$925$	18.9773	+	23.7668i	0.623969	+	0.781449i
$926$	23.7168			0.779381
$927$	−3.81044	−	6.59988i	−0.125151	−	0.216768i
$928$	−6.53367	−	3.77222i	−0.214478	−	0.123829i
$929$	−5.93027	+	10.2715i	−0.194566	+	0.336998i	−0.946758	−	0.321946i	$-0.895663\pi$
$929$	−5.93027	+	10.2715i	−0.194566	+	0.336998i	0.752192	+	0.658944i	$0.228996\pi$
$930$	1.38504	−	16.1184i	0.0454174	−	0.528542i
$931$			2.56320i			0.0840055i
$932$	7.79970	+	4.50316i	0.255488	+	0.147506i
$933$	−11.4093			−0.373523
$934$	5.48413	+	9.49879i	0.179446	+	0.310810i
$935$	−20.0437	+	9.38433i	−0.655500	+	0.306900i
$936$	−3.01207			−0.0984527
$937$	−31.9762	+	18.4614i	−1.04462	+	0.603109i	−0.921137	−	0.389238i	$-0.872738\pi$
$937$	−31.9762	+	18.4614i	−1.04462	+	0.603109i	−0.123478	+	0.992347i	$0.539405\pi$
$938$	20.8875	−	36.1782i	0.682000	−	1.18126i
$939$		−	33.2483i		−	1.08502i
$940$	−4.25451	+	6.09613i	−0.138767	+	0.198834i
$941$	15.6361	+	27.0826i	0.509723	+	0.882867i	0.999937	+	0.0112642i	$0.00358558\pi$
$941$	15.6361	+	27.0826i	0.509723	+	0.882867i	−0.490213	+	0.871603i	$0.663081\pi$
$942$	7.53899	+	13.0579i	0.245634	+	0.425450i
$943$	−7.41407	+	12.8415i	−0.241435	+	0.418178i
$944$	3.62814	+	2.09471i	0.118086	+	0.0681769i
$945$	−5.44261	−	3.79842i	−0.177048	−	0.123563i
$946$	0.528468	+	0.915333i	0.0171820	+	0.0297600i
$947$	−5.70640	−	9.88378i	−0.185433	−	0.321180i	0.758289	−	0.651918i	$-0.226035\pi$
$947$	−5.70640	−	9.88378i	−0.185433	−	0.321180i	−0.943722	+	0.330739i	$0.892702\pi$
$948$	2.48817			0.0808121
$949$	17.6756	+	10.2050i	0.573773	+	0.331268i
$950$	1.20796	−	6.97685i	0.0391912	−	0.226359i
$951$	17.1402			0.555810
$952$			4.69008i			0.152006i
$953$	−13.8302	+	7.98489i	−0.448005	+	0.258656i	−0.706987	−	0.707226i	$-0.749946\pi$
$953$	−13.8302	+	7.98489i	−0.448005	+	0.258656i	0.258982	+	0.965882i	$0.416613\pi$
$954$		−	0.259056i		−	0.00838724i
$955$	−48.8416	−	4.19694i	−1.58048	−	0.135810i
$956$		−	16.7239i		−	0.540889i
$957$	−23.6285	+	40.9258i	−0.763801	+	1.32294i
$958$	−7.57886	−	4.37566i	−0.244862	−	0.141371i
$959$	27.5163	−	47.6597i	0.888549	−	1.53901i
$960$	1.27972	−	1.83366i	0.0413028	−	0.0591812i
$961$	−21.3439			−0.688514
$962$	−13.7072	−	12.1573i	−0.441936	−	0.391966i
$963$			16.2857i			0.524801i
$964$	−15.6125	+	9.01387i	−0.502844	+	0.290317i
$965$	3.08537	−	35.9058i	0.0993217	−	1.15585i
$966$	−3.68432	+	6.38144i	−0.118541	+	0.205319i
$967$	25.5697	−	44.2879i	0.822265	−	1.42420i	−0.0817272	−	0.996655i	$-0.526044\pi$
$967$	25.5697	−	44.2879i	0.822265	−	1.42420i	0.903992	−	0.427550i	$-0.140623\pi$
$968$	−28.2355			−0.907524
$969$	−1.11883	+	1.93787i	−0.0359421	+	0.0622535i
$970$	5.75228	−	2.69318i	0.184695	−	0.0864727i
$971$	18.4146	+	31.8951i	0.590954	+	1.02356i	0.994104	+	0.108429i	$0.0345819\pi$
$971$	18.4146	+	31.8951i	0.590954	+	1.02356i	−0.403150	+	0.915134i	$0.632085\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	28.5459i		−	0.915138i
$974$	14.8622	+	25.7420i	0.476214	+	0.824827i
$975$	−14.1361	+	5.19472i	−0.452718	+	0.166364i
$976$			9.85304i			0.315388i
$977$	10.5788	+	18.3230i	0.338446	+	0.586205i	0.984141	−	0.177390i	$-0.0567655\pi$
$977$	10.5788	+	18.3230i	0.338446	+	0.586205i	−0.645695	+	0.763595i	$0.723432\pi$
$978$	6.64189	−	3.83470i	0.212384	−	0.122620i
$979$	66.7780	−	38.5543i	2.13423	−	1.23220i
$980$	−0.346505	+	4.03243i	−0.0110687	+	0.128811i
$981$	17.7175	+	10.2292i	0.565676	+	0.326593i
$982$	2.45159	+	4.24627i	0.0782333	+	0.135504i
$983$	−20.8546	+	12.0404i	−0.665159	+	0.384030i	−0.794240	−	0.607605i	$-0.792131\pi$
$983$	−20.8546	+	12.0404i	−0.665159	+	0.384030i	0.129081	+	0.991634i	$0.458797\pi$
$984$	−5.17270	+	2.98646i	−0.164900	+	0.0952049i
$985$	5.43530	+	11.6091i	0.173183	+	0.369897i
$986$	10.3240	+	5.96058i	0.328784	+	0.189823i
$987$	8.54582	−	4.93393i	0.272016	−	0.157049i
$988$			4.26549i			0.135703i
$989$	0.418898			0.0133202
$990$	−11.4857	−	8.01594i	−0.365041	−	0.254763i
$991$			26.8078i			0.851576i	0.904823	+	0.425788i	$0.140003\pi$
$991$			26.8078i			0.851576i	−0.904823	+	0.425788i	$0.859997\pi$
$992$	−6.26562	−	3.61746i	−0.198934	−	0.114854i
$993$	−12.8094			−0.406495
$994$	15.6229	+	9.01988i	0.495528	+	0.286093i
$995$	−58.6597	−	5.04060i	−1.85964	−	0.159798i
$996$	4.29085	−	7.43197i	0.135961	−	0.235491i
$997$	3.27932	+	5.67994i	0.103857	+	0.179886i	0.913271	−	0.407353i	$-0.133548\pi$
$997$	3.27932	+	5.67994i	0.103857	+	0.179886i	−0.809414	+	0.587239i	$0.800215\pi$
$998$			33.8483i			1.07145i
$999$	4.03618	−	4.55074i	0.127699	−	0.143979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.ba.b.529.18	yes	36
5.4	even	2		1110.2.ba.a.529.1	✓	36
37.27	even	6		1110.2.ba.a.619.1	yes	36
185.64	even	6	inner	1110.2.ba.b.619.18	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.1	✓	36	5.4	even	2
1110.2.ba.a.619.1	yes	36	37.27	even	6
1110.2.ba.b.529.18	yes	36	1.1	even	1	trivial
1110.2.ba.b.619.18	yes	36	185.64	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.191439 - 2.22786i) q^{5} +1.00000i q^{6} +(-2.57051 - 1.48408i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.191439 - 2.22786i) q^{5} +1.00000i q^{6} +(-2.57051 - 1.48408i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(2.02510 - 0.948138i) q^{10} -6.26383 q^{11} +(-0.866025 + 0.500000i) q^{12} +(1.50604 - 2.60853i) q^{13} -2.96816i q^{14} +(1.27972 - 1.83366i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.790063 + 1.36843i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.22640 + 0.708065i) q^{19} +(1.83366 + 1.27972i) q^{20} +(-1.48408 - 2.57051i) q^{21} +(-3.13191 - 5.42463i) q^{22} -2.48256 q^{23} +(-0.866025 - 0.500000i) q^{24} +(-4.92670 - 0.852997i) q^{25} +3.01207 q^{26} +1.00000i q^{27} +(2.57051 - 1.48408i) q^{28} -7.54443i q^{29} +(2.22786 + 0.191439i) q^{30} -7.23491i q^{31} +(0.500000 - 0.866025i) q^{32} +(-5.42463 - 3.13191i) q^{33} +(-0.790063 + 1.36843i) q^{34} +(-3.79842 + 5.44261i) q^{35} -1.00000 q^{36} +(-4.55074 - 4.03618i) q^{37} +1.41613i q^{38} +(2.60853 - 1.50604i) q^{39} +(-0.191439 + 2.22786i) q^{40} +(2.98646 - 5.17270i) q^{41} +(1.48408 - 2.57051i) q^{42} -0.168736 q^{43} +(3.13191 - 5.42463i) q^{44} +(2.02510 - 0.948138i) q^{45} +(-1.24128 - 2.14996i) q^{46} +3.32457i q^{47} -1.00000i q^{48} +(0.905002 + 1.56751i) q^{49} +(-1.72463 - 4.69315i) q^{50} +1.58013i q^{51} +(1.50604 + 2.60853i) q^{52} +(-0.224349 + 0.129528i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-1.19914 + 13.9549i) q^{55} +(2.57051 + 1.48408i) q^{56} +(0.708065 + 1.22640i) q^{57} +(6.53367 - 3.77222i) q^{58} +(-3.62814 + 2.09471i) q^{59} +(0.948138 + 2.02510i) q^{60} +(-8.53298 - 4.92652i) q^{61} +(6.26562 - 3.61746i) q^{62} -2.96816i q^{63} +1.00000 q^{64} +(-5.52312 - 3.85461i) q^{65} -6.26383i q^{66} +(12.1887 + 7.03717i) q^{67} -1.58013 q^{68} +(-2.14996 - 1.24128i) q^{69} +(-6.61265 - 0.568222i) q^{70} +(-3.03888 + 5.26349i) q^{71} +(-0.500000 - 0.866025i) q^{72} +6.77606i q^{73} +(1.22007 - 5.95915i) q^{74} +(-3.84015 - 3.20207i) q^{75} +(-1.22640 + 0.708065i) q^{76} +(16.1012 + 9.29603i) q^{77} +(2.60853 + 1.50604i) q^{78} +(-2.15482 - 1.24409i) q^{79} +(-2.02510 + 0.948138i) q^{80} +(-0.500000 + 0.866025i) q^{81} +5.97292 q^{82} +(-7.43197 + 4.29085i) q^{83} +2.96816 q^{84} +(3.19992 - 1.49818i) q^{85} +(-0.0843682 - 0.146130i) q^{86} +(3.77222 - 6.53367i) q^{87} +6.26383 q^{88} +(-10.6609 + 6.15507i) q^{89} +(1.83366 + 1.27972i) q^{90} +(-7.74255 + 4.47016i) q^{91} +(1.24128 - 2.14996i) q^{92} +(3.61746 - 6.26562i) q^{93} +(-2.87916 + 1.66228i) q^{94} +(1.81225 - 2.59670i) q^{95} +(0.866025 - 0.500000i) q^{96} +2.84049 q^{97} +(-0.905002 + 1.56751i) q^{98} +(-3.13191 - 5.42463i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} + 14 q^{13} + 2 q^{15} - 18 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{20} + 2 q^{22} + 20 q^{23} - 2 q^{25} + 28 q^{26} - 2 q^{30} + 18 q^{32} + 6 q^{33} - 20 q^{35} - 36 q^{36} - 20 q^{37} + 6 q^{39} - 4 q^{40} + 10 q^{41} - 2 q^{44} + 2 q^{45} + 10 q^{46} + 10 q^{49} - 4 q^{50} + 14 q^{52} + 12 q^{53} + 40 q^{55} - 8 q^{57} - 30 q^{58} + 18 q^{59} - 4 q^{60} - 6 q^{61} + 12 q^{62} + 36 q^{64} - 32 q^{65} - 36 q^{67} + 12 q^{69} - 40 q^{70} - 24 q^{71} - 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} + 24 q^{77} + 6 q^{78} - 2 q^{80} - 18 q^{81} + 20 q^{82} - 36 q^{83} + 26 q^{85} + 10 q^{87} - 4 q^{88} - 2 q^{90} - 36 q^{91} - 10 q^{92} - 12 q^{93} + 12 q^{94} + 18 q^{95} - 52 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 + 14 * q^13 + 2 * q^15 - 18 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^20 + 2 * q^22 + 20 * q^23 - 2 * q^25 + 28 * q^26 - 2 * q^30 + 18 * q^32 + 6 * q^33 - 20 * q^35 - 36 * q^36 - 20 * q^37 + 6 * q^39 - 4 * q^40 + 10 * q^41 - 2 * q^44 + 2 * q^45 + 10 * q^46 + 10 * q^49 - 4 * q^50 + 14 * q^52 + 12 * q^53 + 40 * q^55 - 8 * q^57 - 30 * q^58 + 18 * q^59 - 4 * q^60 - 6 * q^61 + 12 * q^62 + 36 * q^64 - 32 * q^65 - 36 * q^67 + 12 * q^69 - 40 * q^70 - 24 * q^71 - 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 + 24 * q^77 + 6 * q^78 - 2 * q^80 - 18 * q^81 + 20 * q^82 - 36 * q^83 + 26 * q^85 + 10 * q^87 - 4 * q^88 - 2 * q^90 - 36 * q^91 - 10 * q^92 - 12 * q^93 + 12 * q^94 + 18 * q^95 - 52 * q^97 - 10 * q^98 + 2 * q^99

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