LMFDB - Embedded newform 1110.2.ba.a.619.1

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			619.1
Character	$\chi$	$=$	1110.619
Dual form			1110.2.ba.a.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.83366 - 1.27972i) q^{5} -1.00000i q^{6} +(2.57051 - 1.48408i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.83366 - 1.27972i) 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} +(2.22786 + 0.191439i) 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} +(-0.191439 + 2.22786i) q^{20} +(-1.48408 + 2.57051i) q^{21} +(3.13191 - 5.42463i) q^{22} +2.48256 q^{23} +(-0.866025 + 0.500000i) q^{24} +(1.72463 + 4.69315i) q^{25} +3.01207 q^{26} +1.00000i q^{27} +(-2.57051 - 1.48408i) q^{28} +7.54443i q^{29} +(-1.27972 + 1.83366i) q^{30} +7.23491i q^{31} +(-0.500000 - 0.866025i) q^{32} +(5.42463 - 3.13191i) q^{33} +(-0.790063 - 1.36843i) q^{34} +(-6.61265 - 0.568222i) q^{35} -1.00000 q^{36} +(4.55074 - 4.03618i) q^{37} +1.41613i q^{38} +(2.60853 + 1.50604i) q^{39} +(-1.83366 - 1.27972i) 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} +(-4.92670 - 0.852997i) q^{50} -1.58013i q^{51} +(-1.50604 + 2.60853i) q^{52} +(0.224349 + 0.129528i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(11.4857 + 8.01594i) 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} +(-0.576628 + 6.71047i) q^{65} +6.26383i q^{66} +(-12.1887 + 7.03717i) q^{67} +1.58013 q^{68} +(-2.14996 + 1.24128i) q^{69} +(3.79842 - 5.44261i) 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} +(0.191439 - 2.22786i) 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} +(-3.15494 - 0.271102i) 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} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	$ 36 q - 18 q^{2} - 18 q^{4} + 2 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} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 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} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * 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 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * 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 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

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
$5$	−1.83366	−	1.27972i	−0.820039	−	0.572308i
$5$	−1.83366	−	1.27972i	−0.820039	−	0.572308i
$6$		−	1.00000i		−	0.408248i
$7$	2.57051	−	1.48408i	0.971560	−	0.560930i	0.0718486	−	0.997416i	$-0.477110\pi$
$7$	2.57051	−	1.48408i	0.971560	−	0.560930i	0.899711	+	0.436485i	$0.143777\pi$
$8$	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	$-0.303830\pi$
$13$	−1.50604	−	2.60853i	−0.417699	−	0.723476i	−0.995708	+	0.0925545i	$0.970497\pi$
$14$			2.96816i			0.793275i
$15$	2.22786	+	0.191439i	0.575230	+	0.0494293i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.790063	+	1.36843i	−0.191619	+	0.331893i	−0.945787	−	0.324788i	$-0.894707\pi$
$17$	−0.790063	+	1.36843i	−0.191619	+	0.331893i	0.754168	+	0.656681i	$0.228040\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	1.22640	−	0.708065i	0.281356	−	0.162441i	−0.352681	−	0.935744i	$-0.614730\pi$
$19$	1.22640	−	0.708065i	0.281356	−	0.162441i	0.634037	+	0.773302i	$0.281397\pi$
$20$	−0.191439	+	2.22786i	−0.0428070	+	0.498164i
$21$	−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	$-0.416665\pi$
$23$	2.48256			0.517650			0.258825	+	0.965924i	$0.416665\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	1.72463	+	4.69315i	0.344927	+	0.938630i
$26$	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	$0.247032\pi$
$29$			7.54443i			1.40097i	−0.713669	+	0.700483i	$0.752968\pi$
$30$	−1.27972	+	1.83366i	−0.233644	+	0.334779i
$31$			7.23491i			1.29943i	0.760179	+	0.649714i	$0.225111\pi$
$31$			7.23491i			1.29943i	−0.760179	+	0.649714i	$0.774889\pi$
$32$	−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
$35$	−6.61265	−	0.568222i	−1.11774	−	0.0960471i
$36$	−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
$40$	−1.83366	−	1.27972i	−0.289927	−	0.202341i
$41$	2.98646	+	5.17270i	0.466407	+	0.807841i	0.999264	−	0.0383648i	$-0.0122149\pi$
$41$	2.98646	+	5.17270i	0.466407	+	0.807841i	−0.532857	+	0.846205i	$0.678882\pi$
$42$	−1.48408	−	2.57051i	−0.228999	−	0.396638i
$43$	0.168736			0.0257321			0.0128660	−	0.999917i	$-0.495905\pi$
$43$	0.168736			0.0257321			0.0128660	+	0.999917i	$0.495905\pi$
$44$	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
$50$	−4.92670	−	0.852997i	−0.696741	−	0.120632i
$51$		−	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	$-0.327670\pi$
$53$	0.224349	+	0.129528i	0.0308167	+	0.0177920i	−0.484513	+	0.874784i	$0.661003\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	11.4857	+	8.01594i	1.54874	+	1.08087i
$56$	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	0.244877	−	0.969554i	$-0.421252\pi$
$59$	−3.62814	−	2.09471i	−0.472343	−	0.272707i	−0.717220	+	0.696847i	$0.754586\pi$
$60$	−0.948138	−	2.02510i	−0.122404	−	0.261439i
$61$	−8.53298	+	4.92652i	−1.09254	+	0.630776i	−0.934251	−	0.356617i	$-0.883930\pi$
$61$	−8.53298	+	4.92652i	−1.09254	+	0.630776i	−0.158286	+	0.987393i	$0.550597\pi$
$62$	−6.26562	−	3.61746i	−0.795734	−	0.459417i
$63$		−	2.96816i		−	0.373954i
$64$	1.00000			0.125000
$65$	−0.576628	+	6.71047i	−0.0715219	+	0.832331i
$66$			6.26383i			0.771024i
$67$	−12.1887	+	7.03717i	−1.48909	+	0.859727i	−0.999922	−	0.0124627i	$-0.996033\pi$
$67$	−12.1887	+	7.03717i	−1.48909	+	0.859727i	−0.489168	+	0.872190i	$0.662700\pi$
$68$	1.58013			0.191619
$69$	−2.14996	+	1.24128i	−0.258825	+	0.149433i
$70$	3.79842	−	5.44261i	0.453998	−	0.650517i
$71$	−3.03888	−	5.26349i	−0.360648	−	0.624661i	0.627419	−	0.778681i	$-0.284111\pi$
$71$	−3.03888	−	5.26349i	−0.360648	−	0.624661i	−0.988068	+	0.154021i	$0.950778\pi$
$72$	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	−0.616296	−	0.787515i	$-0.711368\pi$
$79$	−2.15482	+	1.24409i	−0.242436	+	0.139971i	0.373860	+	0.927485i	$0.378034\pi$
$80$	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	$-0.177233\pi$
$83$	7.43197	+	4.29085i	0.815765	+	0.470982i	−0.0331890	+	0.999449i	$0.510566\pi$
$84$	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	−0.186104	−	0.982530i	$-0.559586\pi$
$89$	−10.6609	−	6.15507i	−1.13005	−	0.652436i	−0.943948	+	0.330094i	$0.892920\pi$
$90$	0.191439	−	2.22786i	0.0201794	−	0.234837i
$91$	−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
$95$	−3.15494	−	0.271102i	−0.323690	−	0.0278145i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−2.84049			−0.288408			−0.144204	−	0.989548i	$-0.546062\pi$
$97$	−2.84049			−0.288408			−0.144204	+	0.989548i	$0.546062\pi$
$98$	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	$-0.377487\pi$
$103$	7.62088			0.750908			0.375454	+	0.926841i	$0.377487\pi$
$104$	−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	$-0.955137\pi$
$107$	−14.1039	+	8.14287i	−1.36347	+	0.787201i	−0.373388	+	0.927675i	$0.621804\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	17.7175	+	10.2292i	1.69703	+	0.979779i	0.948555	+	0.316614i	$0.102546\pi$
$109$	17.7175	+	10.2292i	1.69703	+	0.979779i	0.748473	+	0.663166i	$0.230787\pi$
$110$	−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	$-0.673248\pi$
$113$	5.12360	−	8.87433i	0.481988	−	0.834827i	0.999786	+	0.0206756i	$0.00658172\pi$
$114$	−0.708065	−	1.22640i	−0.0663164	−	0.114863i
$115$	−4.55218	−	3.17698i	−0.424493	−	0.296255i
$116$	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
$120$	2.22786	+	0.191439i	0.203375	+	0.0174759i
$121$	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	$-0.579699\pi$
$127$	−13.6437	−	7.87719i	−1.21068	−	0.698988i	−0.962908	+	0.269830i	$0.913033\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−0.146130	+	0.0843682i	−0.0128660	+	0.00742820i
$130$	−5.52312	−	3.85461i	−0.484410	−	0.338072i
$131$	−2.88557	−	1.66599i	−0.252114	−	0.145558i	0.368618	−	0.929581i	$-0.379831\pi$
$131$	−2.88557	−	1.66599i	−0.252114	−	0.145558i	−0.620732	+	0.784023i	$0.713164\pi$
$132$	−5.42463	−	3.13191i	−0.472154	−	0.272598i
$133$	2.10165	−	3.64017i	0.182236	−	0.315643i
$134$		−	14.0743i		−	1.21584i
$135$	1.27972	−	1.83366i	0.110141	−	0.157817i
$136$	−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	−0.586784	−	0.809743i	$-0.699606\pi$
$139$	4.80867	−	8.32886i	0.407866	−	0.706445i	0.994650	+	0.103298i	$0.0329397\pi$
$140$	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
$145$	9.65476	−	13.8339i	0.801784	−	1.14885i
$146$	−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	$0.673249\pi$
$150$	4.69315	−	1.72463i	0.383194	−	0.140816i
$151$	1.29954	+	2.25088i	0.105755	+	0.183174i	0.914047	−	0.405609i	$-0.132941\pi$
$151$	1.29954	+	2.25088i	0.105755	+	0.183174i	−0.808291	+	0.588783i	$0.799607\pi$
$152$	1.22640	−	0.708065i	0.0994745	−	0.0574316i
$153$	0.790063	+	1.36843i	0.0638728	+	0.110631i
$154$		−	18.5921i		−	1.49819i
$155$	9.25866	−	13.2664i	0.743673	−	1.06558i
$156$		−	3.01207i		−	0.241159i
$157$	−13.0579	−	7.53899i	−1.04214	−	0.601677i	−0.121698	−	0.992567i	$-0.538834\pi$
$157$	−13.0579	−	7.53899i	−1.04214	−	0.601677i	−0.920437	+	0.390890i	$0.872167\pi$
$158$		−	2.48817i		−	0.197949i
$159$	−0.259056			−0.0205445
$160$	−0.191439	+	2.22786i	−0.0151346	+	0.176128i
$161$	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	$-0.736228\pi$
$163$	3.83470	−	6.64189i	0.300357	−	0.520233i	0.976217	+	0.216797i	$0.0695609\pi$
$164$	2.98646	−	5.17270i	0.233203	−	0.403920i
$165$	−13.9549	−	1.19914i	−1.08639	−	0.0933529i
$166$	−7.43197	+	4.29085i	−0.576833	+	0.333035i
$167$	4.05425	+	7.02216i	0.313727	+	0.543391i	0.979166	−	0.203061i	$-0.0650890\pi$
$167$	4.05425	+	7.02216i	0.313727	+	0.543391i	−0.665439	+	0.746452i	$0.731756\pi$
$168$	−1.48408	+	2.57051i	−0.114499	+	0.198319i
$169$	1.96371	−	3.40125i	0.151055	−	0.261634i
$170$	−0.302498	+	3.52030i	−0.0232005	+	0.269995i
$171$		−	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	$-0.183215\pi$
$173$	10.3502	+	5.97567i	0.786908	+	0.454322i	−0.0519646	+	0.998649i	$0.516548\pi$
$174$	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	$0.153090\pi$
$179$			12.3788i			0.925237i	−0.886557	+	0.462619i	$0.846910\pi$
$180$	1.83366	+	1.27972i	0.136673	+	0.0953847i
$181$	8.22148	+	14.2400i	0.611098	+	1.05845i	0.991056	+	0.133449i	$0.0426053\pi$
$181$	8.22148	+	14.2400i	0.611098	+	1.05845i	−0.379958	+	0.925004i	$0.624061\pi$
$182$	7.74255	−	4.47016i	0.573916	−	0.331351i
$183$	4.92652	−	8.53298i	0.364179	−	0.630776i
$184$	2.48256			0.183017
$185$	−13.5097	+	1.57733i	−0.993253	+	0.115968i
$186$	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
$190$	1.81225	−	2.59670i	0.131474	−	0.188385i
$191$			21.9231i			1.58630i	0.609025	+	0.793151i	$0.291561\pi$
$191$			21.9231i			1.58630i	−0.609025	+	0.793151i	$0.708439\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−16.1168			−1.16011			−0.580055	−	0.814577i	$-0.696969\pi$
$193$	−16.1168			−1.16011			−0.580055	+	0.814577i	$0.696969\pi$
$194$	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	$-0.267869\pi$
$197$	4.96458	+	2.86630i	0.353712	+	0.204216i	−0.312607	+	0.949883i	$0.601202\pi$
$198$	−3.13191	−	5.42463i	−0.222575	−	0.385512i
$199$			26.3301i			1.86649i	0.359242	+	0.933244i	$0.383035\pi$
$199$			26.3301i			1.86649i	−0.359242	+	0.933244i	$0.616965\pi$
$200$	1.72463	+	4.69315i	0.121950	+	0.331856i
$201$	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
$205$	1.14345	−	13.3068i	0.0798620	−	0.929389i
$206$	−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
$210$	−0.568222	+	6.61265i	−0.0392111	+	0.456316i
$211$	−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
$215$	−0.309405	−	0.215935i	−0.0211013	−	0.0147267i
$216$			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
$220$	1.19914	−	13.9549i	0.0808460	−	0.940840i
$221$	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
$225$	4.92670	+	0.852997i	0.328447	+	0.0568665i
$226$	5.12360	+	8.87433i	0.340817	+	0.590312i
$227$	−6.45977	−	11.1887i	−0.428750	−	0.742617i	0.568012	−	0.823020i	$-0.307713\pi$
$227$	−6.45977	−	11.1887i	−0.428750	−	0.742617i	−0.996762	+	0.0804031i	$0.974379\pi$
$228$	1.41613			0.0937855
$229$	−8.72881	−	15.1187i	−0.576816	−	0.999075i	−0.995842	−	0.0911002i	$-0.970962\pi$
$229$	−8.72881	−	15.1187i	−0.576816	−	0.999075i	0.419026	−	0.907974i	$-0.362372\pi$
$230$	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
$235$	4.25451	−	6.09613i	0.277534	−	0.397668i
$236$			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	−0.0478771	−	0.998853i	$-0.515246\pi$
$239$	−14.4833	−	8.36195i	−0.936848	−	0.540889i	−0.888971	+	0.457964i	$0.848579\pi$
$240$	−1.27972	+	1.83366i	−0.0826056	+	0.118362i
$241$	15.6125	−	9.01387i	1.00569	−	0.580634i	0.0957620	−	0.995404i	$-0.469471\pi$
$241$	15.6125	−	9.01387i	1.00569	−	0.580634i	0.909926	+	0.414770i	$0.136138\pi$
$242$	−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
$250$	7.94231	+	7.86891i	0.502316	+	0.497673i
$251$			11.1889i			0.706234i	0.935579	+	0.353117i	$0.114878\pi$
$251$			11.1889i			0.706234i	−0.935579	+	0.353117i	$0.885122\pi$
$252$	−2.57051	+	1.48408i	−0.161927	+	0.0934884i
$253$	−15.5503			−0.977640
$254$	13.6437	−	7.87719i	0.856082	−	0.494259i
$255$	−2.02212	+	2.89742i	−0.126630	+	0.181443i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.59009	−	13.1464i	0.473457	−	0.820052i	−0.526081	−	0.850434i	$-0.676339\pi$
$257$	7.59009	−	13.1464i	0.473457	−	0.820052i	0.999538	+	0.0303827i	$0.00967261\pi$
$258$		−	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	$-0.485403\pi$
$263$	15.1450	−	8.74396i	0.933879	−	0.539176i	0.888036	+	0.459773i	$0.152069\pi$
$264$	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	−0.839599	−	0.543207i	$-0.817210\pi$
$271$	0.833496	−	1.44366i	0.0506313	−	0.0876959i	0.890230	+	0.455511i	$0.150543\pi$
$272$	−0.790063	−	1.36843i	−0.0479046	−	0.0829733i
$273$	8.94033			0.541093
$274$	−16.0570	−	9.27049i	−0.970036	−	0.560051i
$275$	−10.8028	−	29.3971i	−0.651434	−	1.77271i
$276$	2.14996	+	1.24128i	0.129412	+	0.0747163i
$277$	−0.338790	−	0.586802i	−0.0203559	−	0.0352575i	0.855668	−	0.517525i	$-0.173147\pi$
$277$	−0.338790	−	0.586802i	−0.0203559	−	0.0352575i	−0.876024	+	0.482268i	$0.839813\pi$
$278$	4.80867	+	8.32886i	0.288405	+	0.499532i
$279$	6.26562	+	3.61746i	0.375113	+	0.216571i
$280$	−6.61265	−	0.568222i	−0.395181	−	0.0339578i
$281$	−6.56367	−	3.78954i	−0.391556	−	0.226065i	0.291278	−	0.956638i	$-0.405919\pi$
$281$	−6.56367	−	3.78954i	−0.391556	−	0.226065i	−0.682834	+	0.730574i	$0.739253\pi$
$282$	3.32457			0.197975
$283$	−4.41293	−	7.64343i	−0.262322	−	0.454354i	0.704537	−	0.709667i	$-0.251155\pi$
$283$	−4.41293	−	7.64343i	−0.262322	−	0.454354i	−0.966858	+	0.255313i	$0.917821\pi$
$284$	−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	$-0.630240\pi$
$293$	3.38540	−	1.95456i	0.197777	−	0.114187i	0.595618	+	0.803268i	$0.296907\pi$
$294$	−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
$300$	−0.852997	+	4.92670i	−0.0492478	+	0.284443i
$301$	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
$305$	21.9512	+	1.88626i	1.25692	+	0.108007i
$306$	−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	0.192976	−	0.981204i	$-0.438186\pi$
$311$	−9.88071	−	5.70463i	−0.560284	−	0.323480i	−0.753259	+	0.657724i	$0.771520\pi$
$312$	2.60853	+	1.50604i	0.147679	+	0.0852625i
$313$	16.6242	−	28.7939i	0.939653	−	1.62753i	0.173534	−	0.984828i	$-0.444481\pi$
$313$	16.6242	−	28.7939i	0.939653	−	1.62753i	0.766119	−	0.642699i	$-0.222185\pi$
$314$	13.0579	−	7.53899i	0.736901	−	0.425450i
$315$	−3.79842	+	5.44261i	−0.214017	+	0.306656i
$316$	2.15482	+	1.24409i	0.121218	+	0.0699854i
$317$	−14.8439	−	8.57012i	−0.833716	−	0.481346i	0.0214076	−	0.999771i	$-0.493185\pi$
$317$	−14.8439	−	8.57012i	−0.833716	−	0.481346i	−0.855123	+	0.518425i	$0.826519\pi$
$318$	0.129528	−	0.224349i	0.00726356	−	0.0125809i
$319$		−	47.2570i		−	2.64588i
$320$	−1.83366	−	1.27972i	−0.102505	−	0.0715385i
$321$	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
$330$	8.01594	−	11.4857i	0.441263	−	0.632269i
$331$	−11.0933	−	6.40472i	−0.609743	−	0.352035i	0.163122	−	0.986606i	$-0.447844\pi$
$331$	−11.0933	−	6.40472i	−0.609743	−	0.352035i	−0.772865	+	0.634571i	$0.781177\pi$
$332$		−	8.58170i		−	0.470982i
$333$	−1.22007	−	5.95915i	−0.0668594	−	0.326559i
$334$	−8.10849			−0.443677
$335$	31.3556	+	2.69438i	1.71314	+	0.147209i
$336$	−1.48408	−	2.57051i	−0.0809633	−	0.140233i
$337$	19.3464	−	11.1697i	1.05387	−	0.608450i	0.130137	−	0.991496i	$-0.458458\pi$
$337$	19.3464	−	11.1697i	1.05387	−	0.608450i	0.923729	+	0.383046i	$0.125125\pi$
$338$	1.96371	+	3.40125i	0.106812	+	0.185003i
$339$			10.2472i			0.556551i
$340$	−2.89742	−	2.02212i	−0.157135	−	0.109665i
$341$		−	45.3182i		−	2.45412i
$342$	1.22640	+	0.708065i	0.0663164	+	0.0382878i
$343$			15.4048i			0.831779i
$344$	0.168736			0.00909766
$345$	5.53079	+	0.475259i	0.297768	+	0.0255871i
$346$	−10.3502	+	5.97567i	−0.556428	+	0.321254i
$347$	−20.7908			−1.11611			−0.558055	−	0.829804i	$-0.688452\pi$
$347$	−20.7908			−1.11611			−0.558055	+	0.829804i	$0.688452\pi$
$348$	−3.77222	+	6.53367i	−0.202212	+	0.350241i
$349$	−16.7072	+	28.9376i	−0.894313	+	1.54900i	−0.0596613	+	0.998219i	$0.519002\pi$
$349$	−16.7072	+	28.9376i	−0.894313	+	1.54900i	−0.834652	+	0.550778i	$0.814331\pi$
$350$	−13.9300	+	5.11900i	−0.744592	+	0.273622i
$351$	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	$-0.753604\pi$
$353$	4.65698	−	8.06613i	0.247866	−	0.429317i	0.962934	+	0.269739i	$0.0869374\pi$
$354$	−2.09471	+	3.62814i	−0.111332	+	0.192833i
$355$	−1.16352	+	13.5404i	−0.0617531	+	0.718648i
$356$			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
$365$	8.67145	−	12.4250i	0.453885	−	0.650354i
$366$	4.92652	+	8.53298i	0.257513	+	0.446026i
$367$	−16.4851	+	9.51770i	−0.860518	+	0.496820i	−0.864186	−	0.503173i	$-0.832166\pi$
$367$	−16.4851	+	9.51770i	−0.860518	+	0.496820i	0.00366800	+	0.999993i	$0.498832\pi$
$368$	−1.24128	+	2.14996i	−0.0647062	+	0.112074i
$369$	5.97292			0.310938
$370$	5.38884	−	12.4884i	0.280153	−	0.649241i
$371$	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	$-0.749993\pi$
$373$	−8.65720	+	4.99823i	−0.448253	+	0.258799i	0.258839	+	0.965920i	$0.416660\pi$
$374$	4.94882	+	8.57161i	0.255897	+	0.443227i
$375$	2.94379	+	10.7858i	0.152017	+	0.556978i
$376$			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	0.175722	+	0.984440i	$0.443774\pi$
$379$	−14.8869	+	25.7849i	−0.764689	+	1.32448i	−0.940411	+	0.340041i	$0.889559\pi$
$380$	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	$-0.220953\pi$
$383$	−3.32148	−	5.75297i	−0.169720	−	0.293963i	−0.938321	+	0.345765i	$0.887620\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	41.4205	+	3.55925i	2.11098	+	0.181396i
$386$	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	0.130448	−	0.991455i	$-0.458358\pi$
$389$	20.7940	−	12.0054i	1.05430	−	0.608699i	0.923849	+	0.382756i	$0.125025\pi$
$390$	6.71047	+	0.576628i	0.339798	+	0.0291987i
$391$	−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
$395$	5.54330	+	0.476333i	0.278914	+	0.0239669i
$396$	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
$400$	−4.92670	−	0.852997i	−0.246335	−	0.0426499i
$401$		−	15.0009i		−	0.749111i	−0.927204	−	0.374556i	$-0.877795\pi$
$401$		−	15.0009i		−	0.749111i	0.927204	−	0.374556i	$-0.122205\pi$
$402$	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
$405$	−0.191439	+	2.22786i	−0.00951268	+	0.110703i
$406$	−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	0.599724	−	0.800207i	$-0.295277\pi$
$409$	4.17795	+	2.41214i	0.206586	+	0.119273i	−0.393138	+	0.919480i	$0.628610\pi$
$410$	10.9523	+	7.64367i	0.540897	+	0.377494i
$411$	−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	0.240201	+	0.970723i	$0.422787\pi$
$419$	−14.7497	+	25.5472i	−0.720570	+	1.24806i	−0.960771	+	0.277341i	$0.910547\pi$
$420$	−5.44261	−	3.79842i	−0.265572	−	0.185344i
$421$			9.61863i			0.468783i	0.972142	+	0.234392i	$0.0753098\pi$
$421$			9.61863i			0.468783i	−0.972142	+	0.234392i	$0.924690\pi$
$422$	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
$425$	−7.78481	−	1.34784i	−0.377619	−	0.0653800i
$426$	−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	−0.904571	−	0.426323i	$-0.859809\pi$
$431$	−20.5042	+	11.8381i	−0.987650	+	0.570220i	−0.0830792	+	0.996543i	$0.526475\pi$
$432$	−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
$435$	−1.44430	+	16.8079i	−0.0692488	+	0.805878i
$436$		−	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	−0.473603	−	0.880739i	$-0.657047\pi$
$439$	1.09660	−	0.633123i	0.0523379	−	0.0302173i	0.525941	+	0.850521i	$0.323713\pi$
$440$	11.4857	+	8.01594i	0.547561	+	0.382145i
$441$	−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	−0.371038	−	0.928618i	$-0.620998\pi$
$449$	5.24759	−	3.02970i	0.247649	−	0.142980i	0.618687	+	0.785637i	$0.287665\pi$
$450$	−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	$-0.146861\pi$
$457$	1.32927	+	2.30237i	0.0621808	+	0.107700i	−0.833259	+	0.552883i	$0.813528\pi$
$458$	17.4576			0.815741
$459$	−1.36843	−	0.790063i	−0.0638728	−	0.0368770i
$460$	−0.475259	+	5.53079i	−0.0221590	+	0.257874i
$461$	−4.86751	−	2.81026i	−0.226703	−	0.130887i	0.382347	−	0.924019i	$-0.375116\pi$
$461$	−4.86751	−	2.81026i	−0.226703	−	0.130887i	−0.609050	+	0.793132i	$0.708449\pi$
$462$	9.29603	+	16.1012i	0.432491	+	0.749096i
$463$	−11.8584	−	20.5393i	−0.551106	−	0.954543i	−0.998195	−	0.0600541i	$-0.980873\pi$
$463$	−11.8584	−	20.5393i	−0.551106	−	0.954543i	0.447089	−	0.894489i	$-0.352461\pi$
$464$	−6.53367	−	3.77222i	−0.303318	−	0.175121i
$465$	−1.38504	+	16.1184i	−0.0642299	+	0.747471i
$466$	7.79970	+	4.50316i	0.361314	+	0.208605i
$467$	−10.9683			−0.507550			−0.253775	−	0.967263i	$-0.581672\pi$
$467$	−10.9683			−0.507550			−0.253775	+	0.967263i	$0.581672\pi$
$468$	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	0.316762	−	0.948505i	$-0.397404\pi$
$479$	−7.57886	−	4.37566i	−0.346287	−	0.199929i	−0.663049	+	0.748576i	$0.730738\pi$
$480$	−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
$485$	5.20850	+	3.63503i	0.236506	+	0.165058i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	−29.7243			−1.34694			−0.673469	−	0.739216i	$-0.735196\pi$
$487$	−29.7243			−1.34694			−0.673469	+	0.739216i	$0.735196\pi$
$488$	−8.53298	+	4.92652i	−0.386270	+	0.223013i
$489$			7.66940i			0.346822i
$490$	0.346505	−	4.03243i	0.0156535	−	0.182167i
$491$	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	0.329782	−	0.944057i	$-0.393025\pi$
$499$	29.3135	−	16.9241i	1.31225	−	0.757628i	0.982468	+	0.186429i	$0.0596913\pi$
$500$	−10.7858	+	2.94379i	−0.482357	+	0.131650i
$501$	−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	$-0.974833\pi$
$503$	−9.64473	+	16.7052i	−0.430037	+	0.744846i	0.566839	+	0.823829i	$0.308166\pi$
$504$		−	2.96816i		−	0.132213i
$505$	−17.2718	−	12.0541i	−0.768586	−	0.536399i
$506$	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	−0.409798	−	0.912176i	$-0.634401\pi$
$509$	13.1997	−	22.8626i	0.585069	−	1.01337i	0.994867	−	0.101192i	$-0.0322657\pi$
$510$	−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
$515$	−13.9741	−	9.75260i	−0.615774	−	0.429751i
$516$	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
$520$	−0.576628	+	6.71047i	−0.0252868	+	0.294274i
$521$	14.5158	+	25.1422i	0.635950	+	1.10150i	0.986313	+	0.164884i	$0.0527249\pi$
$521$	14.5158	+	25.1422i	0.635950	+	1.10150i	−0.350363	+	0.936614i	$0.613942\pi$
$522$	−6.53367	+	3.77222i	−0.285971	+	0.165105i
$523$	9.58818	+	16.6072i	0.419262	+	0.726183i	0.995865	−	0.0908411i	$-0.0289555\pi$
$523$	9.58818	+	16.6072i	0.419262	+	0.726183i	−0.576603	+	0.817024i	$0.695622\pi$
$524$			3.33197i			0.145558i
$525$	−14.6233	−	2.53184i	−0.638212	−	0.110498i
$526$			17.4879i			0.762509i
$527$	−9.90047	−	5.71604i	−0.431271	−	0.248995i
$528$			6.26383i			0.272598i
$529$	−16.8369			−0.732039
$530$	0.577139	+	0.0495933i	0.0250693	+	0.00215420i
$531$	−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
$535$	36.2823	+	3.11773i	1.56862	+	0.134791i
$536$	−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
$540$	−2.22786	−	0.191439i	−0.0958717	−	0.00823822i
$541$			23.7744i			1.02214i	0.859539	+	0.511070i	$0.170751\pi$
$541$			23.7744i			1.02214i	−0.859539	+	0.511070i	$0.829249\pi$
$542$	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	$-0.535366\pi$
$547$	−5.18635			−0.221752			−0.110876	+	0.993834i	$0.535366\pi$
$548$	16.0570	−	9.27049i	0.685919	−	0.396016i
$549$			9.85304i			0.420518i
$550$	30.8600	+	5.34303i	1.31588	+	0.227827i
$551$	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
$555$	10.9111	−	8.12086i	0.463150	−	0.344711i
$556$	−9.61734			−0.407866
$557$	19.7296	−	34.1727i	0.835972	−	1.44795i	−0.0572653	−	0.998359i	$-0.518238\pi$
$557$	19.7296	−	34.1727i	0.835972	−	1.44795i	0.893237	−	0.449586i	$-0.148429\pi$
$558$	−6.26562	+	3.61746i	−0.265245	+	0.153139i
$559$	−0.254123	−	0.440154i	−0.0107483	−	0.0186165i
$560$	3.79842	−	5.44261i	0.160513	−	0.229992i
$561$			9.89764i			0.417879i
$562$	6.56367	−	3.78954i	0.276872	−	0.159852i
$563$	−1.04534			−0.0440558			−0.0220279	−	0.999757i	$-0.507012\pi$
$563$	−1.04534			−0.0440558			−0.0220279	+	0.999757i	$0.507012\pi$
$564$	−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	$0.0585362\pi$
$569$			8.72389i			0.365725i	−0.983139	+	0.182862i	$0.941464\pi$
$570$	−0.271102	+	3.15494i	−0.0113552	+	0.132146i
$571$	−7.10327	+	12.3032i	−0.297263	+	0.514874i	−0.975509	−	0.219961i	$-0.929407\pi$
$571$	−7.10327	+	12.3032i	−0.297263	+	0.514874i	0.678246	+	0.734835i	$0.262740\pi$
$572$	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
$575$	4.28151	+	11.6510i	0.178551	+	0.485881i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−17.7802	+	30.7962i	−0.740199	+	1.28206i	0.212205	+	0.977225i	$0.431935\pi$
$577$	−17.7802	+	30.7962i	−0.740199	+	1.28206i	−0.952404	+	0.304837i	$0.901398\pi$
$578$	−14.5032			−0.603254
$579$	13.9575	−	8.05838i	0.580055	−	0.334895i
$580$	−16.8079	−	1.44430i	−0.697911	−	0.0599712i
$581$	25.4719			1.05675
$582$			2.84049i			0.117742i
$583$	−1.40528	−	0.811340i	−0.0582008	−	0.0336023i
$584$			6.77606i			0.280395i
$585$	5.52312	+	3.85461i	0.228353	+	0.159368i
$586$			3.90912i			0.161484i
$587$	−7.07285	−	12.2505i	−0.291928	−	0.505634i	0.682338	−	0.731037i	$-0.260963\pi$
$587$	−7.07285	−	12.2505i	−0.291928	−	0.505634i	−0.974266	+	0.225403i	$0.927630\pi$
$588$	1.56751	−	0.905002i	0.0646430	−	0.0373216i
$589$	5.12279	+	8.87293i	0.211081	+	0.365603i
$590$	−9.33341	−	0.802017i	−0.384251	−	0.0330185i
$591$	−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
$595$	6.00199	−	8.60002i	0.246057	−	0.352566i
$596$	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	0.896758	−	0.442521i	$-0.145916\pi$
$599$	1.59438	+	2.76154i	0.0651445	+	0.112834i	−0.831614	+	0.555355i	$0.812583\pi$
$600$	−3.84015	−	3.20207i	−0.156773	−	0.130724i
$601$	−13.6020	+	23.5594i	−0.554837	+	0.961006i	0.443079	+	0.896483i	$0.353886\pi$
$601$	−13.6020	+	23.5594i	−0.554837	+	0.961006i	−0.997916	+	0.0645235i	$0.979447\pi$
$602$			0.500837i			0.0204126i
$603$			14.0743i			0.573151i
$604$	1.29954	−	2.25088i	0.0528777	−	0.0915868i
$605$	−51.7744	−	36.1336i	−2.10493	−	1.46904i
$606$		−	9.41930i		−	0.382633i
$607$	4.70400	−	8.14756i	0.190929	−	0.330699i	−0.754629	−	0.656152i	$-0.772183\pi$
$607$	4.70400	−	8.14756i	0.190929	−	0.330699i	0.945558	+	0.325452i	$0.105517\pi$
$608$	−1.22640	−	0.708065i	−0.0497373	−	0.0287158i
$609$	−19.3930	−	11.1966i	−0.785844	−	0.453707i
$610$	−12.6091	+	18.0671i	−0.510529	+	0.731517i
$611$	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	$-0.105952\pi$
$613$	28.0938	+	16.2200i	1.13470	+	0.655118i	0.189586	+	0.981864i	$0.439286\pi$
$614$	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	$-0.374528\pi$
$617$	−5.55242	−	3.20569i	−0.223532	−	0.129056i	−0.607585	+	0.794255i	$0.707861\pi$
$618$		−	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	$0.259495\pi$
$620$	−16.1184	−	1.38504i	−0.647329	−	0.0556247i
$621$			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
$625$	−19.0513	+	16.1879i	−0.762051	+	0.647517i
$626$	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	−0.268129	−	0.963383i	$-0.586405\pi$
$631$	−31.0607	−	17.9329i	−1.23651	−	0.713898i	−0.968379	+	0.249485i	$0.919739\pi$
$632$	−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	−0.229126	−	0.973397i	$-0.573587\pi$
$641$	18.4422	−	31.9428i	0.728424	−	1.26167i	0.957549	−	0.288270i	$-0.0930800\pi$
$642$	8.14287	+	14.1039i	0.321374	+	0.556635i
$643$	15.4850			0.610669			0.305335	−	0.952245i	$-0.401232\pi$
$643$	15.4850			0.610669			0.305335	+	0.952245i	$0.401232\pi$
$644$	−6.38144	−	3.68432i	−0.251464	−	0.145183i
$645$	0.375921	+	0.0323027i	0.0148019	+	0.00127192i
$646$	−1.93787	−	1.11883i	−0.0762447	−	0.0440199i
$647$	−22.4223	−	38.8366i	−0.881512	−	1.52682i	−0.849660	−	0.527331i	$-0.823193\pi$
$647$	−22.4223	−	38.8366i	−0.881512	−	1.52682i	−0.0318523	−	0.999493i	$-0.510141\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	22.7260	+	13.1209i	0.892074	+	0.515039i
$650$	5.19472	+	14.1361i	0.203754	+	0.554464i
$651$	−18.5974	−	10.7372i	−0.728889	−	0.420824i
$652$	−7.66940			−0.300357
$653$	−19.8488	−	34.3792i	−0.776745	−	1.34536i	−0.933808	−	0.357774i	$-0.883536\pi$
$653$	−19.8488	−	34.3792i	−0.776745	−	1.34536i	0.157063	−	0.987589i	$-0.449797\pi$
$654$	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	0.972277	+	0.233830i	$0.0751260\pi$
$659$	17.6781	+	30.6194i	0.688642	+	1.19276i	−0.283636	+	0.958932i	$0.591541\pi$
$660$	5.93897	+	12.6849i	0.231174	+	0.493758i
$661$	−25.7382	+	14.8599i	−1.00110	+	0.577984i	−0.908573	−	0.417726i	$-0.862827\pi$
$661$	−25.7382	+	14.8599i	−1.00110	+	0.577984i	−0.0925251	+	0.995710i	$0.529494\pi$
$662$	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
$670$	−18.0112	+	25.8076i	−0.695834	+	0.997034i
$671$	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	$-0.873948\pi$
$673$	−27.2357	+	15.7245i	−1.04986	+	0.606136i	−0.127249	+	0.991871i	$0.540615\pi$
$674$			22.3393i			0.860478i
$675$	−4.69315	+	1.72463i	−0.180639	+	0.0663812i
$676$	−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	−0.412814	−	0.910815i	$-0.635454\pi$
$683$	15.2201	−	26.3620i	0.582382	−	1.00872i	0.995196	−	0.0979004i	$-0.0312127\pi$
$684$	−1.22640	+	0.708065i	−0.0468927	+	0.0270735i
$685$	23.7273	−	33.9979i	0.906572	−	1.29899i
$686$	−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
$690$	−3.17698	+	4.55218i	−0.120946	+	0.173298i
$691$	−5.21565	+	9.03378i	−0.198413	+	0.343661i	−0.948014	−	0.318229i	$-0.896912\pi$
$691$	−5.21565	+	9.03378i	−0.198413	+	0.343661i	0.749601	+	0.661890i	$0.230245\pi$
$692$		−	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
$700$	2.53184	−	14.6233i	0.0956945	−	0.552707i
$701$	−36.0512	−	20.8142i	−1.36163	−	0.786140i	−0.371793	−	0.928316i	$-0.621257\pi$
$701$	−36.0512	−	20.8142i	−1.36163	−	0.786140i	−0.989841	+	0.142176i	$0.954590\pi$
$702$			3.01207i			0.113683i
$703$	2.72316	−	8.17221i	0.102706	−	0.308221i
$704$	−6.26383			−0.236077
$705$	−0.636451	+	7.40666i	−0.0239701	+	0.278951i
$706$	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	$-0.750214\pi$
$709$		−	37.6310i		−	1.41326i	0.707583	−	0.706630i	$-0.249786\pi$
$710$	−11.1445	−	7.77782i	−0.418247	−	0.291896i
$711$			2.48817i			0.0933138i
$712$	−10.6609	−	6.15507i	−0.399534	−	0.230671i
$713$			17.9611i			0.672648i
$714$	4.69008			0.175522
$715$	3.61190	−	42.0332i	0.135077	−	1.57195i
$716$	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	−0.924700	−	0.380696i	$-0.875685\pi$
$719$	−3.55712	+	6.16111i	−0.132658	+	0.229770i	0.792042	+	0.610466i	$0.209018\pi$
$720$	0.191439	−	2.22786i	0.00713451	−	0.0830274i
$721$	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
$725$	−35.4071	+	13.0114i	−1.31499	+	0.483230i
$726$		−	28.2355i		−	1.04792i
$727$	12.2381	+	21.1969i	0.453884	+	0.786151i	0.998623	−	0.0524549i	$-0.0167046\pi$
$727$	12.2381	+	21.1969i	0.453884	+	0.786151i	−0.544739	+	0.838606i	$0.683371\pi$
$728$	−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	$-0.879992\pi$
$733$	−29.1268	+	16.8164i	−1.07582	+	0.621127i	−0.146057	+	0.989276i	$0.546658\pi$
$734$		−	19.0354i		−	0.702610i
$735$	2.31630	−	3.31893i	0.0854379	−	0.122421i
$736$	−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	$0.555496\pi$
$740$	8.12086	+	10.9111i	0.298529	+	0.401099i
$741$	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	$-0.606151\pi$
$743$	8.92177	−	5.15098i	0.327308	−	0.188971i	0.654645	+	0.755936i	$0.272818\pi$
$744$	−3.61746	−	6.26562i	−0.132622	−	0.229709i
$745$	23.1795	+	16.1771i	0.849233	+	0.592683i
$746$		−	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
$755$	0.497566	−	5.79040i	0.0181083	−	0.210734i
$756$	1.48408	−	2.57051i	0.0539756	−	0.0934884i
$757$	5.74529	−	9.95114i	0.208816	−	0.361680i	−0.742526	−	0.669818i	$-0.766372\pi$
$757$	5.74529	−	9.95114i	0.208816	−	0.361680i	0.951342	+	0.308137i	$0.0997056\pi$
$758$	−14.8869	−	25.7849i	−0.540717	−	0.936549i
$759$	13.4670	−	7.77516i	0.488820	−	0.282220i
$760$	−3.15494	−	0.271102i	−0.114442	−	0.00983392i
$761$	−8.92596	+	15.4602i	−0.323566	+	0.560433i	−0.981221	−	0.192887i	$-0.938215\pi$
$761$	−8.92596	+	15.4602i	−0.323566	+	0.560433i	0.657655	+	0.753319i	$0.271548\pi$
$762$	−7.87719	+	13.6437i	−0.285361	+	0.494259i
$763$	60.7239			2.19835
$764$	18.9860	−	10.9616i	0.686889	−	0.396575i
$765$	0.302498	−	3.52030i	0.0109368	−	0.127277i
$766$	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	$0.0852178\pi$
$769$			14.6714i			0.529066i	−0.964377	+	0.264533i	$0.914782\pi$
$770$	−23.7926	+	34.0916i	−0.857427	+	1.22858i
$771$			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	$-0.762648\pi$
$773$	−14.3016	+	8.25702i	−0.514392	+	0.296984i	0.220245	+	0.975445i	$0.429314\pi$
$774$	0.0843682	+	0.146130i	0.00303255	+	0.00525253i
$775$	−33.9545	+	12.4776i	−1.21968	+	0.448208i
$776$	−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
$780$	−3.85461	+	5.52312i	−0.138017	+	0.197760i
$781$	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
$790$	−3.18417	+	4.56247i	−0.113288	+	0.162325i
$791$		−	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
$795$	0.475021	+	0.331519i	0.0168472	+	0.0117578i
$796$	22.8025	−	13.1650i	0.808213	−	0.466622i
$797$	−22.9530	+	39.7558i	−0.813039	+	1.40822i	0.0976891	+	0.995217i	$0.468855\pi$
$797$	−22.9530	+	39.7558i	−0.813039	+	1.40822i	−0.910728	+	0.413007i	$0.864478\pi$
$798$	−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
$805$	−16.4163	−	1.41065i	−0.578599	−	0.0497187i
$806$			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	−0.915378	−	0.402596i	$-0.868108\pi$
$809$	−29.1372	+	16.8223i	−1.02441	+	0.591442i	−0.109030	+	0.994038i	$0.534775\pi$
$810$	−1.83366	−	1.27972i	−0.0644283	−	0.0449648i
$811$	−20.1485	−	34.8982i	−0.707508	−	1.22544i	−0.965779	−	0.259368i	$-0.916486\pi$
$811$	−20.1485	−	34.8982i	−0.707508	−	1.22544i	0.258270	−	0.966073i	$-0.416847\pi$
$812$	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	−0.958475	−	0.285177i	$-0.907948\pi$
$821$	−20.8081	−	36.0407i	−0.726208	−	1.25783i	0.232267	−	0.972652i	$-0.425386\pi$
$822$	18.5410			0.646691
$823$	−20.7861	−	12.0008i	−0.724557	−	0.418323i	0.0918706	−	0.995771i	$-0.470715\pi$
$823$	−20.7861	−	12.0008i	−0.724557	−	0.418323i	−0.816428	+	0.577448i	$0.804049\pi$
$824$	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	0.886110	+	0.463476i	$0.153398\pi$
$827$	24.2840	+	42.0611i	0.844437	+	1.46261i	−0.0416731	+	0.999131i	$0.513269\pi$
$828$	−2.48256			−0.0862749
$829$	24.1340	+	13.9338i	0.838209	+	0.483940i	0.856655	−	0.515890i	$-0.172539\pi$
$829$	24.1340	+	13.9338i	0.838209	+	0.483940i	−0.0184462	+	0.999830i	$0.505872\pi$
$830$	19.1188	+	1.64287i	0.663624	+	0.0570249i
$831$	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
$835$	1.55228	−	18.0646i	0.0537189	−	0.625150i
$836$	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	−0.654056	−	0.756446i	$-0.726934\pi$
$839$	9.50280	−	16.4593i	0.328073	−	0.568239i	0.982129	+	0.188206i	$0.0602674\pi$
$840$	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	$-0.905714\pi$
$853$	−6.58416	+	11.4041i	−0.225437	+	0.390469i	0.731013	+	0.682363i	$0.239048\pi$
$854$	−14.6227	−	25.3273i	−0.500379	−	0.866682i
$855$	−1.81225	+	2.59670i	−0.0619776	+	0.0888054i
$856$	−14.1039	+	8.14287i	−0.482060	+	0.278318i
$857$	19.7749			0.675498			0.337749	−	0.941236i	$-0.390335\pi$
$857$	19.7749			0.675498			0.337749	+	0.941236i	$0.390335\pi$
$858$	16.3394	−	9.43355i	0.557817	−	0.322056i
$859$			35.7398i			1.21943i	0.792622	+	0.609714i	$0.208716\pi$
$859$			35.7398i			1.21943i	−0.792622	+	0.609714i	$0.791284\pi$
$860$	−0.0323027	+	0.375921i	−0.00110151	+	0.0128188i
$861$	−17.7286			−0.604190
$862$		−	23.6762i		−	0.806413i
$863$	−20.1510	−	11.6342i	−0.685947	−	0.396031i	0.116145	−	0.993232i	$-0.462946\pi$
$863$	−20.1510	−	11.6342i	−0.685947	−	0.396031i	−0.802092	+	0.597201i	$0.796280\pi$
$864$	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
$870$	−13.8339	−	9.65476i	−0.469014	−	0.327327i
$871$	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
$875$	−8.73765	−	32.0141i	−0.295386	−	1.08227i
$876$	−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	0.973770	+	0.227535i	$0.0730666\pi$
$881$	20.3003	+	35.1612i	0.683936	+	1.18461i	−0.289834	+	0.957077i	$0.593600\pi$
$882$	1.81000			0.0609460
$883$	−0.657211	−	1.13832i	−0.0221169	−	0.0383076i	0.854755	−	0.519032i	$-0.173707\pi$
$883$	−0.657211	−	1.13832i	−0.0221169	−	0.0383076i	−0.876872	+	0.480724i	$0.840374\pi$
$884$	−2.37973	−	4.12181i	−0.0800389	−	0.138631i
$885$	−7.68197	−	5.36127i	−0.258226	−	0.180217i
$886$	−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
$890$	−27.4252	−	2.35664i	−0.919296	−	0.0789948i
$891$	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
$895$	15.8414	−	22.6986i	0.529521	−	0.758730i
$896$			2.96816i			0.0991594i
$897$	6.47583	+	3.73882i	0.216222	+	0.124836i
$898$			6.05939i			0.202205i
$899$	−54.5833			−1.82045
$900$	−1.72463	−	4.69315i	−0.0574878	−	0.156438i
$901$	−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
$905$	3.14782	−	36.6326i	0.104637	−	1.21771i
$906$	2.25088	−	1.29954i	0.0747803	−	0.0431744i
$907$	12.1081	+	20.9718i	0.402041	+	0.696356i	0.993972	−	0.109633i	$-0.0349675\pi$
$907$	12.1081	+	20.9718i	0.402041	+	0.696356i	−0.591931	+	0.805989i	$0.701634\pi$
$908$	−6.45977	+	11.1887i	−0.214375	+	0.371308i
$909$	4.70965	−	8.15736i	0.156209	−	0.270562i
$910$	−19.9178	−	1.71153i	−0.660268	−	0.0567366i
$911$		−	2.47896i		−	0.0821316i	−0.999156	−	0.0410658i	$-0.986925\pi$
$911$		−	2.47896i		−	0.0821316i	0.999156	−	0.0410658i	$-0.0130753\pi$
$912$	−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	$-0.695914\pi$
$919$		−	49.5042i		−	1.63299i	0.577351	−	0.816496i	$-0.304086\pi$
$920$	−4.55218	−	3.17698i	−0.150081	−	0.104742i
$921$	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
$925$	26.7908	+	14.3963i	0.880875	+	0.473349i
$926$	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	0.752192	−	0.658944i	$-0.228996\pi$
$929$	−5.93027	−	10.2715i	−0.194566	−	0.336998i	−0.946758	+	0.321946i	$0.895663\pi$
$930$	−13.2664	−	9.25866i	−0.435022	−	0.303603i
$931$		−	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	$-0.127262\pi$
$937$	31.9762	+	18.4614i	1.04462	+	0.603109i	0.123478	+	0.992347i	$0.460595\pi$
$938$	−20.8875	−	36.1782i	−0.682000	−	1.18126i
$939$			33.2483i			1.08502i
$940$	−7.40666	−	0.636451i	−0.241579	−	0.0207588i
$941$	15.6361	−	27.0826i	0.509723	−	0.882867i	−0.490213	−	0.871603i	$-0.663081\pi$
$941$	15.6361	−	27.0826i	0.509723	−	0.882867i	0.999937	−	0.0112642i	$-0.00358558\pi$
$942$	−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
$945$	0.568222	−	6.61265i	0.0184843	−	0.215110i
$946$	0.528468	−	0.915333i	0.0171820	−	0.0297600i
$947$	5.70640	−	9.88378i	0.185433	−	0.321180i	−0.758289	−	0.651918i	$-0.773965\pi$
$947$	5.70640	−	9.88378i	0.185433	−	0.321180i	0.943722	+	0.330739i	$0.107298\pi$
$948$	−2.48817			−0.0808121
$949$	17.6756	−	10.2050i	0.573773	−	0.331268i
$950$	−6.64611	+	2.44231i	−0.215628	+	0.0792388i
$951$	17.1402			0.555810
$952$			4.69008i			0.152006i
$953$	13.8302	+	7.98489i	0.448005	+	0.258656i	0.706987	−	0.707226i	$-0.250054\pi$
$953$	13.8302	+	7.98489i	0.448005	+	0.258656i	−0.258982	+	0.965882i	$0.583387\pi$
$954$			0.259056i			0.00838724i
$955$	28.0555	−	40.1996i	0.907854	−	1.30083i
$956$			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
$960$	2.22786	+	0.191439i	0.0719038	+	0.00617866i
$961$	−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
$965$	29.5527	+	20.6249i	0.951335	+	0.663940i
$966$	−3.68432	−	6.38144i	−0.118541	−	0.205319i
$967$	−25.5697	−	44.2879i	−0.822265	−	1.42420i	−0.903992	−	0.427550i	$-0.859377\pi$
$967$	−25.5697	−	44.2879i	−0.822265	−	1.42420i	0.0817272	−	0.996655i	$-0.473956\pi$
$968$	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	−0.403150	−	0.915134i	$-0.632085\pi$
$971$	18.4146	−	31.8951i	0.590954	−	1.02356i	0.994104	−	0.108429i	$-0.0345819\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	28.5459i		−	0.915138i
$974$	14.8622	−	25.7420i	0.476214	−	0.824827i
$975$	−2.56929	+	14.8396i	−0.0822831	+	0.475247i
$976$		−	9.85304i		−	0.315388i
$977$	−10.5788	+	18.3230i	−0.338446	+	0.586205i	−0.984141	−	0.177390i	$-0.943234\pi$
$977$	−10.5788	+	18.3230i	−0.338446	+	0.586205i	0.645695	+	0.763595i	$0.276568\pi$
$978$	−6.64189	−	3.83470i	−0.212384	−	0.122620i
$979$	66.7780	+	38.5543i	2.13423	+	1.23220i
$980$	3.31893	+	2.31630i	0.106019	+	0.0739914i
$981$	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	$-0.207869\pi$
$983$	20.8546	+	12.0404i	0.665159	+	0.384030i	−0.129081	+	0.991634i	$0.541203\pi$
$984$	−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
$990$	−1.19914	+	13.9549i	−0.0381112	+	0.443516i
$991$		−	26.8078i		−	0.851576i	−0.904823	−	0.425788i	$-0.859997\pi$
$991$		−	26.8078i		−	0.851576i	0.904823	−	0.425788i	$-0.140003\pi$
$992$	6.26562	−	3.61746i	0.198934	−	0.114854i
$993$	12.8094			0.406495
$994$	15.6229	−	9.01988i	0.495528	−	0.286093i
$995$	33.6951	−	48.2804i	1.06821	−	1.53059i
$996$	4.29085	+	7.43197i	0.135961	+	0.235491i
$997$	−3.27932	+	5.67994i	−0.103857	+	0.179886i	−0.913271	−	0.407353i	$-0.866452\pi$
$997$	−3.27932	+	5.67994i	−0.103857	+	0.179886i	0.809414	+	0.587239i	$0.199785\pi$
$998$			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.a.619.1	yes	36
5.4	even	2		1110.2.ba.b.619.18	yes	36
37.11	even	6		1110.2.ba.b.529.18	yes	36
185.159	even	6	inner	1110.2.ba.a.529.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.1	✓	36	185.159	even	6	inner
1110.2.ba.a.619.1	yes	36	1.1	even	1	trivial
1110.2.ba.b.529.18	yes	36	37.11	even	6
1110.2.ba.b.619.18	yes	36	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.83366 - 1.27972i) q^{5} -1.00000i q^{6} +(2.57051 - 1.48408i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.83366 - 1.27972i) 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} +(2.22786 + 0.191439i) 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} +(-0.191439 + 2.22786i) q^{20} +(-1.48408 + 2.57051i) q^{21} +(3.13191 - 5.42463i) q^{22} +2.48256 q^{23} +(-0.866025 + 0.500000i) q^{24} +(1.72463 + 4.69315i) q^{25} +3.01207 q^{26} +1.00000i q^{27} +(-2.57051 - 1.48408i) q^{28} +7.54443i q^{29} +(-1.27972 + 1.83366i) q^{30} +7.23491i q^{31} +(-0.500000 - 0.866025i) q^{32} +(5.42463 - 3.13191i) q^{33} +(-0.790063 - 1.36843i) q^{34} +(-6.61265 - 0.568222i) q^{35} -1.00000 q^{36} +(4.55074 - 4.03618i) q^{37} +1.41613i q^{38} +(2.60853 + 1.50604i) q^{39} +(-1.83366 - 1.27972i) 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} +(-4.92670 - 0.852997i) q^{50} -1.58013i q^{51} +(-1.50604 + 2.60853i) q^{52} +(0.224349 + 0.129528i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(11.4857 + 8.01594i) 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} +(-0.576628 + 6.71047i) q^{65} +6.26383i q^{66} +(-12.1887 + 7.03717i) q^{67} +1.58013 q^{68} +(-2.14996 + 1.24128i) q^{69} +(3.79842 - 5.44261i) 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} +(0.191439 - 2.22786i) 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} +(-3.15494 - 0.271102i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * 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 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * 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 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * q^95 + 52 * q^97 + 10 * q^98 + 2 * q^99

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