LMFDB - Embedded newform 220.2.l.c.23.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(23,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$220 = 2^{2} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	220.l (of order $4$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [28,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.6
Character	$\chi$	$=$	220.23
Dual form			220.2.l.c.67.6

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.777125 - 1.18156i) q^{2} +(0.810938 - 0.810938i) q^{3} +(-0.792153 + 1.83644i) q^{4} +(0.127766 - 2.23241i) q^{5} +(-1.58837 - 0.327969i) q^{6} +(-2.32765 - 2.32765i) q^{7} +(2.78545 - 0.491167i) q^{8} +1.68476i q^{9} +(-2.73701 + 1.58390i) q^{10} -1.00000i q^{11} +(0.846848 + 2.13162i) q^{12} +(-2.59390 - 2.59390i) q^{13} +(-0.941377 + 4.55914i) q^{14} +(-1.70674 - 1.91396i) q^{15} +(-2.74499 - 2.90947i) q^{16} +(3.45701 - 3.45701i) q^{17} +(1.99064 - 1.30927i) q^{18} +2.29700 q^{19} +(3.99847 + 2.00305i) q^{20} -3.77517 q^{21} +(-1.18156 + 0.777125i) q^{22} +(-4.20475 + 4.20475i) q^{23} +(1.86052 - 2.65714i) q^{24} +(-4.96735 - 0.570454i) q^{25} +(-1.04906 + 5.08063i) q^{26} +(3.79905 + 3.79905i) q^{27} +(6.11845 - 2.43073i) q^{28} -0.133535i q^{29} +(-0.935102 + 3.50400i) q^{30} +1.32953i q^{31} +(-1.30451 + 5.50439i) q^{32} +(-0.810938 - 0.810938i) q^{33} +(-6.77118 - 1.39812i) q^{34} +(-5.49369 + 4.89890i) q^{35} +(-3.09395 - 1.33459i) q^{36} +(7.23425 - 7.23425i) q^{37} +(-1.78506 - 2.71404i) q^{38} -4.20699 q^{39} +(-0.740602 - 6.28104i) q^{40} +7.76381 q^{41} +(2.93378 + 4.46057i) q^{42} +(5.00150 - 5.00150i) q^{43} +(1.83644 + 0.792153i) q^{44} +(3.76108 + 0.215255i) q^{45} +(8.23576 + 1.70053i) q^{46} +(6.17302 + 6.17302i) q^{47} +(-4.58542 - 0.133387i) q^{48} +3.83595i q^{49} +(3.18623 + 6.31252i) q^{50} -5.60684i q^{51} +(6.81830 - 2.70877i) q^{52} +(3.93732 + 3.93732i) q^{53} +(1.53645 - 7.44113i) q^{54} +(-2.23241 - 0.127766i) q^{55} +(-7.62684 - 5.34031i) q^{56} +(1.86272 - 1.86272i) q^{57} +(-0.157780 + 0.103774i) q^{58} +6.54413 q^{59} +(4.86686 - 1.61817i) q^{60} -7.15370 q^{61} +(1.57092 - 1.03321i) q^{62} +(3.92154 - 3.92154i) q^{63} +(7.51751 - 2.73625i) q^{64} +(-6.12208 + 5.45925i) q^{65} +(-0.327969 + 1.58837i) q^{66} +(3.80506 + 3.80506i) q^{67} +(3.61010 + 9.08706i) q^{68} +6.81958i q^{69} +(10.0576 + 2.68405i) q^{70} -12.5023i q^{71} +(0.827498 + 4.69282i) q^{72} +(-1.45485 - 1.45485i) q^{73} +(-14.1696 - 2.92576i) q^{74} +(-4.49082 + 3.56561i) q^{75} +(-1.81957 + 4.21829i) q^{76} +(-2.32765 + 2.32765i) q^{77} +(3.26936 + 4.97079i) q^{78} +2.50310 q^{79} +(-6.84587 + 5.75622i) q^{80} +1.10731 q^{81} +(-6.03345 - 9.17338i) q^{82} +(-6.44397 + 6.44397i) q^{83} +(2.99051 - 6.93285i) q^{84} +(-7.27579 - 8.15917i) q^{85} +(-9.79635 - 2.02277i) q^{86} +(-0.108289 - 0.108289i) q^{87} +(-0.491167 - 2.78545i) q^{88} +14.4239i q^{89} +(-2.66850 - 4.61121i) q^{90} +12.0754i q^{91} +(-4.39094 - 11.0525i) q^{92} +(1.07817 + 1.07817i) q^{93} +(2.49656 - 12.0910i) q^{94} +(0.293479 - 5.12786i) q^{95} +(3.40584 + 5.52159i) q^{96} +(-9.18145 + 9.18145i) q^{97} +(4.53240 - 2.98102i) q^{98} +1.68476 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 12 q^{6} - 2 q^{7} - 14 q^{8} + 6 q^{10} - 8 q^{12} + 6 q^{13} - 20 q^{14} + 8 q^{15} + 8 q^{16} - 14 q^{17} + 34 q^{18} + 4 q^{19} + 8 q^{20} - 16 q^{21}+ \cdots - 20 q^{99}+O(q^{100})$ 28 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 12 * q^6 - 2 * q^7 - 14 * q^8 + 6 * q^10 - 8 * q^12 + 6 * q^13 - 20 * q^14 + 8 * q^15 + 8 * q^16 - 14 * q^17 + 34 * q^18 + 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 - 8 * q^23 + 28 * q^24 - 4 * q^25 + 4 * q^26 + 44 * q^27 - 28 * q^28 - 2 * q^32 + 4 * q^33 - 52 * q^34 - 10 * q^35 - 4 * q^36 + 20 * q^37 + 16 * q^38 + 32 * q^39 - 6 * q^40 + 12 * q^41 - 32 * q^42 + 2 * q^43 - 10 * q^45 + 4 * q^46 - 44 * q^47 - 36 * q^48 + 22 * q^50 + 24 * q^52 - 28 * q^53 - 40 * q^54 - 2 * q^55 + 4 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^59 - 48 * q^60 - 12 * q^61 - 24 * q^62 - 10 * q^63 + 28 * q^64 - 30 * q^65 + 16 * q^67 - 32 * q^68 + 72 * q^70 + 18 * q^72 + 22 * q^73 - 20 * q^74 - 56 * q^75 + 4 * q^76 - 2 * q^77 + 104 * q^78 - 20 * q^79 - 44 * q^80 + 12 * q^81 - 92 * q^82 + 2 * q^83 + 120 * q^84 - 14 * q^85 - 20 * q^86 - 48 * q^87 + 2 * q^88 + 70 * q^90 + 52 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^95 + 40 * q^96 + 16 * q^97 + 18 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$ .

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.777125	−	1.18156i	−0.549511	−	0.835487i
$2$	−0.777125	−	1.18156i	−0.549511	−	0.835487i
$3$	0.810938	−	0.810938i	0.468195	−	0.468195i	−0.433134	−	0.901329i	$-0.642592\pi$
$3$	0.810938	−	0.810938i	0.468195	−	0.468195i	0.901329	+	0.433134i	$0.142592\pi$
$4$	−0.792153	+	1.83644i	−0.396076	+	0.918218i
$5$	0.127766	−	2.23241i	0.0571387	−	0.998366i
$5$	0.127766	−	2.23241i	0.0571387	−	0.998366i
$6$	−1.58837	−	0.327969i	−0.648449	−	0.133893i
$7$	−2.32765	−	2.32765i	−0.879771	−	0.879771i	0.113740	−	0.993511i	$-0.463717\pi$
$7$	−2.32765	−	2.32765i	−0.879771	−	0.879771i	−0.993511	+	0.113740i	$0.963717\pi$
$8$	2.78545	−	0.491167i	0.984807	−	0.173654i
$9$			1.68476i			0.561586i
$10$	−2.73701	+	1.58390i	−0.865520	+	0.500874i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	0.846848	+	2.13162i	0.244464	+	0.615346i
$13$	−2.59390	−	2.59390i	−0.719419	−	0.719419i	0.249067	−	0.968486i	$-0.419876\pi$
$13$	−2.59390	−	2.59390i	−0.719419	−	0.719419i	−0.968486	+	0.249067i	$0.919876\pi$
$14$	−0.941377	+	4.55914i	−0.251594	+	1.21848i
$15$	−1.70674	−	1.91396i	−0.440678	−	0.494182i
$16$	−2.74499	−	2.90947i	−0.686247	−	0.727368i
$17$	3.45701	−	3.45701i	0.838448	−	0.838448i	−0.150206	−	0.988655i	$-0.547994\pi$
$17$	3.45701	−	3.45701i	0.838448	−	0.838448i	0.988655	+	0.150206i	$0.0479938\pi$
$18$	1.99064	−	1.30927i	0.469198	−	0.308598i
$19$	2.29700			0.526968			0.263484	−	0.964664i	$-0.415128\pi$
$19$	2.29700			0.526968			0.263484	+	0.964664i	$0.415128\pi$
$20$	3.99847	+	2.00305i	0.894086	+	0.447895i
$21$	−3.77517			−0.823809
$22$	−1.18156	+	0.777125i	−0.251909	+	0.165684i
$23$	−4.20475	+	4.20475i	−0.876750	+	0.876750i	−0.993197	−	0.116447i	$-0.962850\pi$
$23$	−4.20475	+	4.20475i	−0.876750	+	0.876750i	0.116447	+	0.993197i	$0.462850\pi$
$24$	1.86052	−	2.65714i	0.379778	−	0.542386i
$25$	−4.96735	−	0.570454i	−0.993470	−	0.114091i
$26$	−1.04906	+	5.08063i	−0.205737	+	0.996393i
$27$	3.79905	+	3.79905i	0.731127	+	0.731127i
$28$	6.11845	−	2.43073i	1.15628	−	0.459365i
$29$		−	0.133535i		−	0.0247969i	−0.999923	−	0.0123984i	$-0.996053\pi$
$29$		−	0.133535i		−	0.0247969i	0.999923	−	0.0123984i	$-0.00394665\pi$
$30$	−0.935102	+	3.50400i	−0.170726	+	0.639739i
$31$			1.32953i			0.238791i	0.992847	+	0.119395i	$0.0380956\pi$
$31$			1.32953i			0.238791i	−0.992847	+	0.119395i	$0.961904\pi$
$32$	−1.30451	+	5.50439i	−0.230607	+	0.973047i
$33$	−0.810938	−	0.810938i	−0.141166	−	0.141166i
$34$	−6.77118	−	1.39812i	−1.16125	−	0.239776i
$35$	−5.49369	+	4.89890i	−0.928602	+	0.828065i
$36$	−3.09395	−	1.33459i	−0.515659	−	0.222431i
$37$	7.23425	−	7.23425i	1.18930	−	1.18930i	0.212042	−	0.977260i	$-0.431989\pi$
$37$	7.23425	−	7.23425i	1.18930	−	1.18930i	0.977260	−	0.212042i	$-0.0680114\pi$
$38$	−1.78506	−	2.71404i	−0.289574	−	0.440275i
$39$	−4.20699			−0.673657
$40$	−0.740602	−	6.28104i	−0.117099	−	0.993120i
$41$	7.76381			1.21250			0.606252	−	0.795273i	$-0.292672\pi$
$41$	7.76381			1.21250			0.606252	+	0.795273i	$0.292672\pi$
$42$	2.93378	+	4.46057i	0.452692	+	0.688282i
$43$	5.00150	−	5.00150i	0.762722	−	0.762722i	−0.214092	−	0.976814i	$-0.568679\pi$
$43$	5.00150	−	5.00150i	0.762722	−	0.762722i	0.976814	+	0.214092i	$0.0686791\pi$
$44$	1.83644	+	0.792153i	0.276853	+	0.119422i
$45$	3.76108	+	0.215255i	0.560669	+	0.0320883i
$46$	8.23576	+	1.70053i	1.21430	+	0.250730i
$47$	6.17302	+	6.17302i	0.900428	+	0.900428i	0.995473	−	0.0950453i	$-0.0302996\pi$
$47$	6.17302	+	6.17302i	0.900428	+	0.900428i	−0.0950453	+	0.995473i	$0.530300\pi$
$48$	−4.58542	−	0.133387i	−0.661848	−	0.0192528i
$49$			3.83595i			0.547993i
$50$	3.18623	+	6.31252i	0.450601	+	0.892725i
$51$		−	5.60684i		−	0.785115i
$52$	6.81830	−	2.70877i	0.945528	−	0.375638i
$53$	3.93732	+	3.93732i	0.540833	+	0.540833i	0.923773	−	0.382940i	$-0.125088\pi$
$53$	3.93732	+	3.93732i	0.540833	+	0.540833i	−0.382940	+	0.923773i	$0.625088\pi$
$54$	1.53645	−	7.44113i	0.209085	−	1.01261i
$55$	−2.23241	−	0.127766i	−0.301019	−	0.0172280i
$56$	−7.62684	−	5.34031i	−1.01918	−	0.713629i
$57$	1.86272	−	1.86272i	0.246724	−	0.246724i
$58$	−0.157780	+	0.103774i	−0.0207175	+	0.0136261i
$59$	6.54413			0.851973			0.425987	−	0.904729i	$-0.359927\pi$
$59$	6.54413			0.851973			0.425987	+	0.904729i	$0.359927\pi$
$60$	4.86686	−	1.61817i	0.628309	−	0.208905i
$61$	−7.15370			−0.915937			−0.457969	−	0.888968i	$-0.651423\pi$
$61$	−7.15370			−0.915937			−0.457969	+	0.888968i	$0.651423\pi$
$62$	1.57092	−	1.03321i	0.199507	−	0.131218i
$63$	3.92154	−	3.92154i	0.494067	−	0.494067i
$64$	7.51751	−	2.73625i	0.939689	−	0.342031i
$65$	−6.12208	+	5.45925i	−0.759350	+	0.677137i
$66$	−0.327969	+	1.58837i	−0.0403702	+	0.195515i
$67$	3.80506	+	3.80506i	0.464862	+	0.464862i	0.900245	−	0.435383i	$-0.143387\pi$
$67$	3.80506	+	3.80506i	0.464862	+	0.464862i	−0.435383	+	0.900245i	$0.643387\pi$
$68$	3.61010	+	9.08706i	0.437788	+	1.10197i
$69$			6.81958i			0.820981i
$70$	10.0576	+	2.68405i	1.20211	+	0.320805i
$71$		−	12.5023i		−	1.48375i	−0.670539	−	0.741875i	$-0.733937\pi$
$71$		−	12.5023i		−	1.48375i	0.670539	−	0.741875i	$-0.266063\pi$
$72$	0.827498	+	4.69282i	0.0975216	+	0.553054i
$73$	−1.45485	−	1.45485i	−0.170277	−	0.170277i	0.616824	−	0.787101i	$-0.288419\pi$
$73$	−1.45485	−	1.45485i	−0.170277	−	0.170277i	−0.787101	+	0.616824i	$0.788419\pi$
$74$	−14.1696	−	2.92576i	−1.64718	−	0.340112i
$75$	−4.49082	+	3.56561i	−0.518555	+	0.411721i
$76$	−1.81957	+	4.21829i	−0.208719	+	0.483871i
$77$	−2.32765	+	2.32765i	−0.265261	+	0.265261i
$78$	3.26936	+	4.97079i	0.370182	+	0.562832i
$79$	2.50310			0.281621			0.140810	−	0.990037i	$-0.455029\pi$
$79$	2.50310			0.281621			0.140810	+	0.990037i	$0.455029\pi$
$80$	−6.84587	+	5.75622i	−0.765391	+	0.643565i
$81$	1.10731			0.123034
$82$	−6.03345	−	9.17338i	−0.666283	−	1.01303i
$83$	−6.44397	+	6.44397i	−0.707318	+	0.707318i	−0.965970	−	0.258652i	$-0.916722\pi$
$83$	−6.44397	+	6.44397i	−0.707318	+	0.707318i	0.258652	+	0.965970i	$0.416722\pi$
$84$	2.99051	−	6.93285i	0.326291	−	0.756436i
$85$	−7.27579	−	8.15917i	−0.789170	−	0.884986i
$86$	−9.79635	−	2.02277i	−1.05637	−	0.218120i
$87$	−0.108289	−	0.108289i	−0.0116098	−	0.0116098i
$88$	−0.491167	−	2.78545i	−0.0523586	−	0.296930i
$89$			14.4239i			1.52893i	0.644663	+	0.764466i	$0.276997\pi$
$89$			14.4239i			1.52893i	−0.644663	+	0.764466i	$0.723003\pi$
$90$	−2.66850	−	4.61121i	−0.281284	−	0.486064i
$91$			12.0754i			1.26585i
$92$	−4.39094	−	11.0525i	−0.457788	−	1.15231i
$93$	1.07817	+	1.07817i	0.111801	+	0.111801i
$94$	2.49656	−	12.0910i	0.257501	−	1.24709i
$95$	0.293479	−	5.12786i	0.0301103	−	0.526107i
$96$	3.40584	+	5.52159i	0.347607	+	0.563545i
$97$	−9.18145	+	9.18145i	−0.932235	+	0.932235i	−0.997845	−	0.0656101i	$-0.979101\pi$
$97$	−9.18145	+	9.18145i	−0.932235	+	0.932235i	0.0656101	+	0.997845i	$0.479101\pi$
$98$	4.53240	−	2.98102i	0.457841	−	0.301128i
$99$	1.68476			0.169325
$100$	4.98250	−	8.67033i	0.498250	−	0.867033i
$101$	10.1986			1.01480			0.507398	−	0.861712i	$-0.330607\pi$
$101$	10.1986			1.01480			0.507398	+	0.861712i	$0.330607\pi$
$102$	−6.62480	+	4.35722i	−0.655953	+	0.431429i
$103$	1.48098	−	1.48098i	0.145925	−	0.145925i	−0.630370	−	0.776295i	$-0.717097\pi$
$103$	1.48098	−	1.48098i	0.145925	−	0.145925i	0.776295	+	0.630370i	$0.217097\pi$
$104$	−8.49923	−	5.95116i	−0.833418	−	0.583559i
$105$	−0.482338	+	8.42774i	−0.0470714	+	0.822463i
$106$	1.59238	−	7.71196i	0.154665	−	0.749052i
$107$	0.0745711	+	0.0745711i	0.00720906	+	0.00720906i	0.710702	−	0.703493i	$-0.248377\pi$
$107$	0.0745711	+	0.0745711i	0.00720906	+	0.00720906i	−0.703493	+	0.710702i	$0.748377\pi$
$108$	−9.98613	+	3.96728i	−0.960916	+	0.381752i
$109$			7.33400i			0.702470i	0.936287	+	0.351235i	$0.114238\pi$
$109$			7.33400i			0.702470i	−0.936287	+	0.351235i	$0.885762\pi$
$110$	1.58390	+	2.73701i	0.151019	+	0.260964i
$111$		−	11.7330i		−	1.11365i
$112$	−0.382865	+	13.1616i	−0.0361774	+	1.24366i
$113$	−12.5929	−	12.5929i	−1.18464	−	1.18464i	−0.978528	−	0.206114i	$-0.933918\pi$
$113$	−12.5929	−	12.5929i	−1.18464	−	1.18464i	−0.206114	−	0.978528i	$-0.566082\pi$
$114$	−3.64848	−	0.753344i	−0.341712	−	0.0705572i
$115$	8.84951	+	9.92396i	0.825221	+	0.925414i
$116$	0.245229	+	0.105780i	0.0227689	+	0.00982146i
$117$	4.37010	−	4.37010i	0.404016	−	0.404016i
$118$	−5.08561	−	7.73226i	−0.468168	−	0.711813i
$119$	−16.0935			−1.47528
$120$	−5.69412	−	4.49295i	−0.519800	−	0.410149i
$121$	−1.00000			−0.0909091
$122$	5.55932	+	8.45250i	0.503317	+	0.765254i
$123$	6.29597	−	6.29597i	0.567688	−	0.567688i
$124$	−2.44160	−	1.05319i	−0.219262	−	0.0945794i
$125$	−1.90815	+	11.0163i	−0.170670	+	0.985328i
$126$	−7.68105	−	1.58599i	−0.684282	−	0.141292i
$127$	−13.7881	−	13.7881i	−1.22349	−	1.22349i	−0.966381	−	0.257113i	$-0.917229\pi$
$127$	−13.7881	−	13.7881i	−1.22349	−	1.22349i	−0.257113	−	0.966381i	$-0.582771\pi$
$128$	−9.07508	−	6.75596i	−0.802131	−	0.597148i
$129$		−	8.11182i		−	0.714206i
$130$	11.2080	+	2.99106i	0.983010	+	0.262333i
$131$			3.24328i			0.283366i	0.989912	+	0.141683i	$0.0452514\pi$
$131$			3.24328i			0.283366i	−0.989912	+	0.141683i	$0.954749\pi$
$132$	2.13162	−	0.846848i	0.185534	−	0.0737087i
$133$	−5.34662	−	5.34662i	−0.463611	−	0.463611i
$134$	1.53889	−	7.45291i	0.132940	−	0.643833i
$135$	8.96644	−	7.99566i	0.771709	−	0.688157i
$136$	7.93137	−	11.3273i	0.680110	−	0.971309i
$137$	2.15437	−	2.15437i	0.184060	−	0.184060i	−0.609062	−	0.793122i	$-0.708454\pi$
$137$	2.15437	−	2.15437i	0.184060	−	0.184060i	0.793122	+	0.609062i	$0.208454\pi$
$138$	8.05772	−	5.29967i	0.685918	−	0.451138i
$139$	−17.1989			−1.45879			−0.729395	−	0.684093i	$-0.760198\pi$
$139$	−17.1989			−1.45879			−0.729395	+	0.684093i	$0.760198\pi$
$140$	−4.64467	−	13.9695i	−0.392546	−	1.18064i
$141$	10.0119			0.843152
$142$	−14.7722	+	9.71585i	−1.23965	+	0.815336i
$143$	−2.59390	+	2.59390i	−0.216913	+	0.216913i
$144$	4.90176	−	4.62464i	0.408480	−	0.385387i
$145$	−0.298106	−	0.0170613i	−0.0247564	−	0.00141686i
$146$	−0.588388	+	2.84959i	−0.0486953	+	0.235834i
$147$	3.11072	+	3.11072i	0.256568	+	0.256568i
$148$	7.55460	+	19.0159i	0.620984	+	1.56309i
$149$			10.8861i			0.891821i	0.895078	+	0.445910i	$0.147120\pi$
$149$			10.8861i			0.891821i	−0.895078	+	0.445910i	$0.852880\pi$
$150$	7.70290	+	2.53523i	0.628939	+	0.207000i
$151$			2.79477i			0.227435i	0.993513	+	0.113717i	$0.0362759\pi$
$151$			2.79477i			0.227435i	−0.993513	+	0.113717i	$0.963724\pi$
$152$	6.39819	−	1.12821i	0.518962	−	0.0915099i
$153$	5.82423	+	5.82423i	0.470861	+	0.470861i
$154$	4.55914	+	0.941377i	0.367386	+	0.0758583i
$155$	2.96806	+	0.169869i	0.238401	+	0.0136442i
$156$	3.33258	−	7.72586i	0.266820	−	0.618564i
$157$	−7.72176	+	7.72176i	−0.616263	+	0.616263i	−0.944571	−	0.328308i	$-0.893522\pi$
$157$	−7.72176	+	7.72176i	−0.616263	+	0.616263i	0.328308	+	0.944571i	$0.393522\pi$
$158$	−1.94522	−	2.95756i	−0.154754	−	0.235291i
$159$	6.38585			0.506431
$160$	12.1214	+	3.61548i	0.958281	+	0.285829i
$161$	19.5744			1.54268
$162$	−0.860517	−	1.30835i	−0.0676086	−	0.102794i
$163$	−3.44943	+	3.44943i	−0.270180	+	0.270180i	−0.829173	−	0.558993i	$-0.811188\pi$
$163$	−3.44943	+	3.44943i	−0.270180	+	0.270180i	0.558993	+	0.829173i	$0.311188\pi$
$164$	−6.15012	+	14.2577i	−0.480244	+	1.11334i
$165$	−1.91396	+	1.70674i	−0.149002	+	0.132869i
$166$	12.6217	+	2.60615i	0.979634	+	0.202276i
$167$	−13.0913	−	13.0913i	−1.01304	−	1.01304i	−0.999914	−	0.0131243i	$-0.995822\pi$
$167$	−13.0913	−	13.0913i	−1.01304	−	1.01304i	−0.0131243	−	0.999914i	$-0.504178\pi$
$168$	−10.5156	+	1.85424i	−0.811293	+	0.143058i
$169$			0.456653i			0.0351272i
$170$	−3.98632	+	14.9375i	−0.305737	+	1.14565i
$171$			3.86989i			0.295938i
$172$	5.22298	+	13.1469i	0.398249	+	1.00244i
$173$	8.43240	+	8.43240i	0.641104	+	0.641104i	0.950827	−	0.309723i	$-0.100236\pi$
$173$	8.43240	+	8.43240i	0.641104	+	0.641104i	−0.309723	+	0.950827i	$0.600236\pi$
$174$	−0.0437954	+	0.212103i	−0.00332012	+	0.0160795i
$175$	10.2345	+	12.8901i	0.773653	+	0.974400i
$176$	−2.90947	+	2.74499i	−0.219310	+	0.206911i
$177$	5.30689	−	5.30689i	0.398890	−	0.398890i
$178$	17.0427	−	11.2092i	1.27740	−	0.840165i
$179$	21.7615			1.62653			0.813267	−	0.581891i	$-0.197687\pi$
$179$	21.7615			1.62653			0.813267	+	0.581891i	$0.197687\pi$
$180$	−3.37465	+	6.73647i	−0.251532	+	0.502107i
$181$	0.340494			0.0253087			0.0126544	−	0.999920i	$-0.495972\pi$
$181$	0.340494			0.0253087			0.0126544	+	0.999920i	$0.495972\pi$
$182$	14.2678	−	9.38411i	1.05760	−	0.695597i
$183$	−5.80121	+	5.80121i	−0.428838	+	0.428838i
$184$	−9.64690	+	13.7774i	−0.711179	+	1.01568i
$185$	−15.2255	−	17.0741i	−1.11940	−	1.25531i
$186$	0.436045	−	2.11179i	0.0319723	−	0.154844i
$187$	−3.45701	−	3.45701i	−0.252802	−	0.252802i
$188$	−16.2263	+	6.44638i	−1.18343	+	0.470150i
$189$		−	17.6858i		−	1.28645i
$190$	−6.28692	+	3.63823i	−0.456101	+	0.263945i
$191$			18.7025i			1.35327i	0.736320	+	0.676634i	$0.236562\pi$
$191$			18.7025i			1.35327i	−0.736320	+	0.676634i	$0.763438\pi$
$192$	3.87731	−	8.31516i	0.279821	−	0.600095i
$193$	−9.01606	−	9.01606i	−0.648990	−	0.648990i	0.303759	−	0.952749i	$-0.401758\pi$
$193$	−9.01606	−	9.01606i	−0.648990	−	0.648990i	−0.952749	+	0.303759i	$0.901758\pi$
$194$	17.9835	+	3.71327i	1.29114	+	0.266597i
$195$	−0.537510	+	9.39174i	−0.0384919	+	0.672556i
$196$	−7.04448	−	3.03866i	−0.503177	−	0.217047i
$197$	10.3795	−	10.3795i	0.739505	−	0.739505i	−0.232977	−	0.972482i	$-0.574847\pi$
$197$	10.3795	−	10.3795i	0.739505	−	0.739505i	0.972482	+	0.232977i	$0.0748467\pi$
$198$	−1.30927	−	1.99064i	−0.0930457	−	0.141469i
$199$	17.3630			1.23083			0.615415	−	0.788203i	$-0.288988\pi$
$199$	17.3630			1.23083			0.615415	+	0.788203i	$0.288988\pi$
$200$	−14.1165	+	0.850827i	−0.998189	+	0.0601625i
$201$	6.17134			0.435293
$202$	−7.92557	−	12.0502i	−0.557641	−	0.847848i
$203$	−0.310824	+	0.310824i	−0.0218156	+	0.0218156i
$204$	10.2966	+	4.44147i	0.720906	+	0.310965i
$205$	0.991951	−	17.3320i	0.0692809	−	1.21052i
$206$	−2.90076	−	0.598953i	−0.202106	−	0.0417311i
$207$	−7.08399	−	7.08399i	−0.492371	−	0.492371i
$208$	−0.426659	+	14.6671i	−0.0295835	+	1.01698i
$209$		−	2.29700i		−	0.158887i
$210$	10.3327	−	5.97950i	0.713023	−	0.412625i
$211$			4.77702i			0.328863i	0.986388	+	0.164432i	$0.0525790\pi$
$211$			4.77702i			0.328863i	−0.986388	+	0.164432i	$0.947421\pi$
$212$	−10.3496	+	4.11168i	−0.710813	+	0.282391i
$213$	−10.1386	−	10.1386i	−0.694684	−	0.694684i
$214$	0.0301589	−	0.146061i	0.00206162	−	0.00998452i
$215$	−10.5264	−	11.8045i	−0.717895	−	0.805057i
$216$	12.4480	+	8.71611i	0.846982	+	0.593056i
$217$	3.09469	−	3.09469i	0.210081	−	0.210081i
$218$	8.66554	−	5.69944i	0.586905	−	0.386015i
$219$	−2.35959			−0.159446
$220$	2.00305	−	3.99847i	0.135045	−	0.269577i
$221$	−17.9343			−1.20639
$222$	−13.8633	+	9.11805i	−0.930441	+	0.611963i
$223$	13.3807	−	13.3807i	0.896036	−	0.896036i	−0.0990464	−	0.995083i	$-0.531579\pi$
$223$	13.3807	−	13.3807i	0.896036	−	0.896036i	0.995083	+	0.0990464i	$0.0315792\pi$
$224$	15.8488	−	9.77586i	1.05894	−	0.653177i
$225$	0.961077	−	8.36879i	0.0640718	−	0.557919i
$226$	−5.09297	+	24.6655i	−0.338779	+	1.64073i
$227$	11.1072	+	11.1072i	0.737210	+	0.737210i	0.972037	−	0.234827i	$-0.0754525\pi$
$227$	11.1072	+	11.1072i	0.737210	+	0.737210i	−0.234827	+	0.972037i	$0.575452\pi$
$228$	1.94521	+	4.89633i	0.128825	+	0.324268i
$229$			0.0910816i			0.00601884i	0.999995	+	0.00300942i	$0.000957930\pi$
$229$			0.0910816i			0.00601884i	−0.999995	+	0.00300942i	$0.999042\pi$
$230$	4.84854	−	18.1684i	0.319703	−	1.19799i
$231$			3.77517i			0.248388i
$232$	−0.0655881	−	0.371956i	−0.00430607	−	0.0244201i
$233$	4.83294	+	4.83294i	0.316616	+	0.316616i	0.847466	−	0.530850i	$-0.178127\pi$
$233$	4.83294	+	4.83294i	0.316616	+	0.316616i	−0.530850	+	0.847466i	$0.678127\pi$
$234$	−8.55964	−	1.76741i	−0.559561	−	0.115539i
$235$	14.5694	−	12.9920i	0.950406	−	0.847507i
$236$	−5.18395	+	12.0179i	−0.337446	+	0.782297i
$237$	2.02986	−	2.02986i	0.131854	−	0.131854i
$238$	12.5066	+	19.0153i	0.810684	+	1.23258i
$239$	15.5711			1.00721			0.503606	−	0.863933i	$-0.332006\pi$
$239$	15.5711			1.00721			0.503606	+	0.863933i	$0.332006\pi$
$240$	−0.883637	+	10.2195i	−0.0570385	+	0.659667i
$241$	−15.7734			−1.01605			−0.508027	−	0.861341i	$-0.669625\pi$
$241$	−15.7734			−1.01605			−0.508027	+	0.861341i	$0.669625\pi$
$242$	0.777125	+	1.18156i	0.0499555	+	0.0759533i
$243$	−10.4992	+	10.4992i	−0.673523	+	0.673523i
$244$	5.66682	−	13.1373i	0.362781	−	0.841030i
$245$	8.56344	+	0.490105i	0.547098	+	0.0313116i
$246$	−12.3318	−	2.54629i	−0.786247	−	0.162345i
$247$	−5.95819	−	5.95819i	−0.379111	−	0.379111i
$248$	0.653022	+	3.70335i	0.0414669	+	0.235163i
$249$			10.4513i			0.662326i
$250$	14.4993	−	6.30646i	0.917014	−	0.398856i
$251$		−	16.9874i		−	1.07223i	−0.844144	−	0.536117i	$-0.819891\pi$
$251$		−	16.9874i		−	1.07223i	0.844144	−	0.536117i	$-0.180109\pi$
$252$	4.09519	+	10.3081i	0.257973	+	0.649350i
$253$	4.20475	+	4.20475i	0.264350	+	0.264350i
$254$	−5.57633	+	27.0065i	−0.349890	+	1.69454i
$255$	−12.5168	−	0.716364i	−0.783832	−	0.0448605i
$256$	−0.930077	+	15.9729i	−0.0581298	+	0.998309i
$257$	16.7021	−	16.7021i	1.04185	−	1.04185i	0.0427626	−	0.999085i	$-0.486384\pi$
$257$	16.7021	−	16.7021i	1.04185	−	1.04185i	0.999085	−	0.0427626i	$-0.0136159\pi$
$258$	−9.58457	+	6.30390i	−0.596709	+	0.392464i
$259$	−33.6777			−2.09263
$260$	−5.17594	−	15.5674i	−0.320998	−	0.965447i
$261$	0.224975			0.0139256
$262$	3.83212	−	2.52043i	0.236749	−	0.155713i
$263$	−18.1862	+	18.1862i	−1.12141	+	1.12141i	−0.129882	+	0.991530i	$0.541460\pi$
$263$	−18.1862	+	18.1862i	−1.12141	+	1.12141i	−0.991530	+	0.129882i	$0.958540\pi$
$264$	−2.65714	−	1.86052i	−0.163535	−	0.114507i
$265$	9.29280	−	8.28668i	0.570852	−	0.509047i
$266$	−2.16234	+	10.4723i	−0.132582	+	0.642100i
$267$	11.6969	+	11.6969i	0.715839	+	0.715839i
$268$	−10.0019	+	3.97356i	−0.610966	+	0.242724i
$269$		−	8.30765i		−	0.506526i	−0.967397	−	0.253263i	$-0.918496\pi$
$269$		−	8.30765i		−	0.506526i	0.967397	−	0.253263i	$-0.0815038\pi$
$270$	−16.4154	−	4.38073i	−0.999008	−	0.266603i
$271$			8.06316i			0.489802i	0.969548	+	0.244901i	$0.0787554\pi$
$271$			8.06316i			0.489802i	−0.969548	+	0.244901i	$0.921245\pi$
$272$	−19.5475	−	0.568628i	−1.18524	−	0.0344781i
$273$	9.79241	+	9.79241i	0.592664	+	0.592664i
$274$	−4.21972	−	0.871294i	−0.254923	−	0.0526368i
$275$	−0.570454	+	4.96735i	−0.0343996	+	0.299543i
$276$	−12.5237	−	5.40215i	−0.753839	−	0.325171i
$277$	−16.8776	+	16.8776i	−1.01408	+	1.01408i	−0.0141792	+	0.999899i	$0.504514\pi$
$277$	−16.8776	+	16.8776i	−1.01408	+	1.01408i	−0.999899	+	0.0141792i	$0.995486\pi$
$278$	13.3657	+	20.3214i	0.801620	+	1.21880i
$279$	−2.23994			−0.134102
$280$	−12.8962	+	16.3440i	−0.770698	+	0.976739i
$281$	13.1802			0.786267			0.393133	−	0.919481i	$-0.371391\pi$
$281$	13.1802			0.786267			0.393133	+	0.919481i	$0.371391\pi$
$282$	−7.78048	−	11.8296i	−0.463321	−	0.704442i
$283$	5.50850	−	5.50850i	0.327446	−	0.327446i	−0.524169	−	0.851615i	$-0.675624\pi$
$283$	5.50850	−	5.50850i	0.327446	−	0.327446i	0.851615	+	0.524169i	$0.175624\pi$
$284$	22.9597	+	9.90373i	1.36240	+	0.587678i
$285$	−3.92038	−	4.39637i	−0.232223	−	0.260418i
$286$	5.08063	+	1.04906i	0.300424	+	0.0620320i
$287$	−18.0715	−	18.0715i	−1.06673	−	1.06673i
$288$	−9.27356	−	2.19778i	−0.546450	−	0.129506i
$289$		−	6.90184i		−	0.405991i
$290$	0.211507	+	0.365488i	0.0124201	+	0.0214622i
$291$			14.8912i			0.872936i
$292$	3.82420	−	1.51928i	0.223795	−	0.0889089i
$293$	9.15116	+	9.15116i	0.534617	+	0.534617i	0.921943	−	0.387326i	$-0.126601\pi$
$293$	9.15116	+	9.15116i	0.534617	+	0.534617i	−0.387326	+	0.921943i	$0.626601\pi$
$294$	1.25807	−	6.09291i	0.0733723	−	0.355346i
$295$	0.836118	−	14.6092i	0.0486807	−	0.850582i
$296$	16.5974	−	23.7039i	0.964707	−	1.37776i
$297$	3.79905	−	3.79905i	0.220443	−	0.220443i
$298$	12.8625	−	8.45983i	0.745105	−	0.490065i
$299$	21.8134			1.26150
$300$	−2.99060	−	11.0716i	−0.172663	−	0.639219i
$301$	−23.2835			−1.34204
$302$	3.30218	−	2.17188i	0.190019	−	0.124978i
$303$	8.27041	−	8.27041i	0.475122	−	0.475122i
$304$	−6.30524	−	6.68306i	−0.361630	−	0.383300i
$305$	−0.914000	+	15.9700i	−0.0523355	+	0.914441i
$306$	2.35550	−	11.4078i	0.134655	−	0.652141i
$307$	5.61109	+	5.61109i	0.320242	+	0.320242i	0.848860	−	0.528618i	$-0.177290\pi$
$307$	5.61109	+	5.61109i	0.320242	+	0.320242i	−0.528618	+	0.848860i	$0.677290\pi$
$308$	−2.43073	−	6.11845i	−0.138504	−	0.348631i
$309$		−	2.40196i		−	0.136643i
$310$	−2.10585	−	3.63895i	−0.119604	−	0.206678i
$311$			5.50196i			0.311987i	0.987758	+	0.155994i	$0.0498579\pi$
$311$			5.50196i			0.311987i	−0.987758	+	0.155994i	$0.950142\pi$
$312$	−11.7184	+	2.06633i	−0.663422	+	0.116983i
$313$	−2.44122	−	2.44122i	−0.137986	−	0.137986i	0.634740	−	0.772726i	$-0.281107\pi$
$313$	−2.44122	−	2.44122i	−0.137986	−	0.137986i	−0.772726	+	0.634740i	$0.781107\pi$
$314$	15.1245	+	3.12292i	0.853523	+	0.176237i
$315$	−8.25346	−	9.25554i	−0.465030	−	0.521491i
$316$	−1.98284	+	4.59678i	−0.111543	+	0.258589i
$317$	−9.75741	+	9.75741i	−0.548031	+	0.548031i	−0.925871	−	0.377840i	$-0.876667\pi$
$317$	−9.75741	+	9.75741i	−0.548031	+	0.548031i	0.377840	+	0.925871i	$0.376667\pi$
$318$	−4.96261	−	7.54524i	−0.278289	−	0.423116i
$319$	−0.133535			−0.00747654
$320$	−5.14795	−	17.1318i	−0.287779	−	0.957697i
$321$	0.120945			0.00675049
$322$	−15.2118	−	23.1283i	−0.847718	−	1.28889i
$323$	7.94075	−	7.94075i	0.441835	−	0.441835i
$324$	−0.877157	+	2.03350i	−0.0487310	+	0.112972i
$325$	11.4051	+	14.3645i	0.632642	+	0.796800i
$326$	6.75633	+	1.39506i	0.374199	+	0.0772651i
$327$	5.94742	+	5.94742i	0.328893	+	0.328893i
$328$	21.6257	−	3.81333i	1.19408	−	0.210556i
$329$		−	28.7373i		−	1.58434i
$330$	3.50400	+	0.935102i	0.192889	+	0.0514757i
$331$		−	7.54531i		−	0.414728i	−0.978264	−	0.207364i	$-0.933512\pi$
$331$		−	7.54531i		−	0.414728i	0.978264	−	0.207364i	$-0.0664884\pi$
$332$	−6.72933	−	16.9386i	−0.369320	−	0.929624i
$333$	12.1880	+	12.1880i	0.667896	+	0.667896i
$334$	−5.29455	+	25.6418i	−0.289705	+	1.40306i
$335$	8.98064	−	8.00832i	0.490665	−	0.437541i
$336$	10.3628	+	10.9838i	0.565337	+	0.599213i
$337$	−18.9119	+	18.9119i	−1.03020	+	1.03020i	−0.0306672	+	0.999530i	$0.509763\pi$
$337$	−18.9119	+	18.9119i	−1.03020	+	1.03020i	−0.999530	+	0.0306672i	$0.990237\pi$
$338$	0.539561	−	0.354877i	0.0293483	−	0.0193027i
$339$	−20.4241			−1.10929
$340$	20.7473	−	6.89821i	1.12518	−	0.374108i
$341$	1.32953			0.0719981
$342$	4.57250	−	3.00739i	0.247252	−	0.162621i
$343$	−7.36481	+	7.36481i	−0.397662	+	0.397662i
$344$	11.4749	−	16.3880i	0.618684	−	0.883583i
$345$	15.2241	+	0.871310i	0.819639	+	0.0469098i
$346$	3.41033	−	16.5164i	0.183340	−	0.887927i
$347$	−2.99920	−	2.99920i	−0.161005	−	0.161005i	0.622007	−	0.783012i	$-0.286318\pi$
$347$	−2.99920	−	2.99920i	−0.161005	−	0.161005i	−0.783012	+	0.622007i	$0.786318\pi$
$348$	0.284647	−	0.113084i	0.0152587	−	0.00606195i
$349$		−	15.5193i		−	0.830727i	−0.909655	−	0.415364i	$-0.863654\pi$
$349$		−	15.5193i		−	0.830727i	0.909655	−	0.415364i	$-0.136346\pi$
$350$	7.27693	−	22.1098i	0.388968	−	1.18182i
$351$		−	19.7087i		−	1.05197i
$352$	5.50439	+	1.30451i	0.293385	+	0.0695305i
$353$	−11.8752	−	11.8752i	−0.632053	−	0.632053i	0.316530	−	0.948583i	$-0.397482\pi$
$353$	−11.8752	−	11.8752i	−0.632053	−	0.632053i	−0.948583	+	0.316530i	$0.897482\pi$
$354$	−10.3945	−	2.14627i	−0.552461	−	0.114073i
$355$	−27.9103	−	1.59737i	−1.48133	−	0.0847795i
$356$	−26.4886	−	11.4259i	−1.40389	−	0.605574i
$357$	−13.0508	+	13.0508i	−0.690721	+	0.690721i
$358$	−16.9114	−	25.7125i	−0.893797	−	1.35895i
$359$	−14.7346			−0.777662			−0.388831	−	0.921309i	$-0.627121\pi$
$359$	−14.7346			−0.777662			−0.388831	+	0.921309i	$0.627121\pi$
$360$	10.5820	−	1.24774i	0.557723	−	0.0657615i
$361$	−13.7238			−0.722305
$362$	−0.264607	−	0.402313i	−0.0139074	−	0.0211451i
$363$	−0.810938	+	0.810938i	−0.0425632	+	0.0425632i
$364$	−22.1757	−	9.56557i	−1.16232	−	0.501372i
$365$	−3.43371	+	3.06195i	−0.179729	+	0.160270i
$366$	11.3627	+	2.34619i	0.593939	+	0.122637i
$367$	−4.22405	−	4.22405i	−0.220494	−	0.220494i	0.588213	−	0.808706i	$-0.299832\pi$
$367$	−4.22405	−	4.22405i	−0.220494	−	0.220494i	−0.808706	+	0.588213i	$0.799832\pi$
$368$	23.7756	+	0.691620i	1.23939	+	0.0360532i
$369$			13.0802i			0.680926i
$370$	−8.34189	+	31.2586i	−0.433674	+	1.62506i
$371$		−	18.3295i		−	0.951618i
$372$	−2.83406	+	1.12591i	−0.146939	+	0.0583758i
$373$	14.7500	+	14.7500i	0.763727	+	0.763727i	0.976994	−	0.213267i	$-0.0684104\pi$
$373$	14.7500	+	14.7500i	0.763727	+	0.763727i	−0.213267	+	0.976994i	$0.568410\pi$
$374$	−1.39812	+	6.77118i	−0.0722953	+	0.350130i
$375$	7.38615	+	10.4809i	0.381419	+	0.541233i
$376$	20.2267	+	14.1627i	1.04311	+	0.730385i
$377$	−0.346377	+	0.346377i	−0.0178393	+	0.0178393i
$378$	−20.8967	+	13.7440i	−1.07481	+	0.706917i
$379$	30.3260			1.55774			0.778871	−	0.627184i	$-0.215793\pi$
$379$	30.3260			1.55774			0.778871	+	0.627184i	$0.215793\pi$
$380$	9.18450	+	4.60100i	0.471155	+	0.236026i
$381$	−22.3626			−1.14567
$382$	22.0981	−	14.5342i	1.13064	−	0.743635i
$383$	0.188339	−	0.188339i	0.00962368	−	0.00962368i	−0.702279	−	0.711902i	$-0.747834\pi$
$383$	0.188339	−	0.188339i	0.00962368	−	0.00962368i	0.711902	+	0.702279i	$0.247834\pi$
$384$	−12.8380	+	1.88066i	−0.655136	+	0.0959721i
$385$	4.89890	+	5.49369i	0.249671	+	0.279984i
$386$	−3.64638	+	17.6596i	−0.185596	+	0.898849i
$387$	8.42633	+	8.42633i	0.428334	+	0.428334i
$388$	−9.58803	−	24.1343i	−0.486759	−	1.22523i
$389$			2.57939i			0.130780i	0.997860	+	0.0653900i	$0.0208291\pi$
$389$			2.57939i			0.130780i	−0.997860	+	0.0653900i	$0.979171\pi$
$390$	11.5146	−	6.66346i	0.583064	−	0.337417i
$391$			29.0717i			1.47022i
$392$	1.88409	+	10.6849i	0.0951611	+	0.539668i
$393$	2.63010	+	2.63010i	0.132671	+	0.132671i
$394$	−20.3300	−	4.19778i	−1.02421	−	0.211481i
$395$	0.319811	−	5.58796i	0.0160915	−	0.281161i
$396$	−1.33459	+	3.09395i	−0.0670655	+	0.155477i
$397$	2.11644	−	2.11644i	0.106221	−	0.106221i	−0.651999	−	0.758220i	$-0.726069\pi$
$397$	2.11644	−	2.11644i	0.106221	−	0.106221i	0.758220	+	0.651999i	$0.226069\pi$
$398$	−13.4932	−	20.5154i	−0.676354	−	1.02834i
$399$	−8.67156			−0.434121
$400$	11.9756	+	16.0183i	0.598780	+	0.800913i
$401$	5.11905			0.255633			0.127817	−	0.991798i	$-0.459203\pi$
$401$	5.11905			0.255633			0.127817	+	0.991798i	$0.459203\pi$
$402$	−4.79590	−	7.29179i	−0.239198	−	0.363681i
$403$	3.44867	−	3.44867i	0.171791	−	0.171791i
$404$	−8.07882	+	18.7290i	−0.401936	+	0.931803i
$405$	0.141476	−	2.47197i	0.00703002	−	0.122833i
$406$	0.608806	+	0.125707i	0.0302145	+	0.00623874i
$407$	−7.23425	−	7.23425i	−0.358588	−	0.358588i
$408$	−2.75390	−	15.6176i	−0.136338	−	0.773186i
$409$			23.3497i			1.15457i	0.816542	+	0.577285i	$0.195888\pi$
$409$			23.3497i			1.15457i	−0.816542	+	0.577285i	$0.804112\pi$
$410$	−21.2497	+	12.2971i	−1.04945	+	0.607312i
$411$		−	3.49412i		−	0.172352i
$412$	1.54656	+	3.89288i	0.0761934	+	0.191788i
$413$	−15.2325	−	15.2325i	−0.749541	−	0.749541i
$414$	−2.86499	+	13.8753i	−0.140806	+	0.681933i
$415$	13.5623	+	15.2089i	0.665747	+	0.746578i
$416$	17.6616	−	10.8941i	0.865931	−	0.534126i
$417$	−13.9472	+	13.9472i	−0.682998	+	0.682998i
$418$	−2.71404	+	1.78506i	−0.132748	+	0.0873100i
$419$	−11.0115			−0.537948			−0.268974	−	0.963147i	$-0.586685\pi$
$419$	−11.0115			−0.537948			−0.268974	+	0.963147i	$0.586685\pi$
$420$	−15.0949	−	7.56184i	−0.736556	−	0.368980i
$421$	26.1518			1.27456			0.637281	−	0.770631i	$-0.280059\pi$
$421$	26.1518			1.27456			0.637281	+	0.770631i	$0.280059\pi$
$422$	5.64432	−	3.71234i	0.274761	−	0.180714i
$423$	−10.4001	+	10.4001i	−0.505668	+	0.505668i
$424$	12.9011	+	9.03335i	0.626534	+	0.438698i
$425$	−19.1443	+	15.2001i	−0.928633	+	0.737314i
$426$	−4.10036	+	19.8583i	−0.198663	+	0.962136i
$427$	16.6513	+	16.6513i	0.805815	+	0.805815i
$428$	−0.196017	+	0.0778733i	−0.00947482	+	0.00376415i
$429$			4.20699i			0.203115i
$430$	−5.76729	+	21.6111i	−0.278124	+	1.04218i
$431$		−	8.71172i		−	0.419629i	−0.977741	−	0.209814i	$-0.932714\pi$
$431$		−	8.71172i		−	0.419629i	0.977741	−	0.209814i	$-0.0672860\pi$
$432$	0.624888	−	21.4816i	0.0300649	−	1.03353i
$433$	18.5625	+	18.5625i	0.892057	+	0.892057i	0.994717	−	0.102659i	$-0.0327351\pi$
$433$	18.5625	+	18.5625i	0.892057	+	0.892057i	−0.102659	+	0.994717i	$0.532735\pi$
$434$	−6.06151	−	1.25159i	−0.290962	−	0.0600782i
$435$	−0.255581	+	0.227910i	−0.0122542	+	0.0109274i
$436$	−13.4684	−	5.80965i	−0.645020	−	0.278232i
$437$	−9.65830	+	9.65830i	−0.462019	+	0.462019i
$438$	1.83370	+	2.78799i	0.0876174	+	0.133215i
$439$	−2.63364			−0.125697			−0.0628484	−	0.998023i	$-0.520018\pi$
$439$	−2.63364			−0.125697			−0.0628484	+	0.998023i	$0.520018\pi$
$440$	−6.28104	+	0.740602i	−0.299437	+	0.0353068i
$441$	−6.46266			−0.307746
$442$	13.9372	+	21.1904i	0.662925	+	1.00792i
$443$	16.1479	−	16.1479i	0.767209	−	0.767209i	−0.210405	−	0.977614i	$-0.567478\pi$
$443$	16.1479	−	16.1479i	0.767209	−	0.767209i	0.977614	+	0.210405i	$0.0674784\pi$
$444$	21.5470	+	9.29437i	1.02257	+	0.441091i
$445$	32.2002	+	1.84289i	1.52644	+	0.0873613i
$446$	−26.2085	−	5.41157i	−1.24101	−	0.256245i
$447$	8.82792	+	8.82792i	0.417546	+	0.417546i
$448$	−23.8672	−	11.1291i	−1.12762	−	0.525802i
$449$		−	7.50030i		−	0.353961i	−0.984214	−	0.176981i	$-0.943367\pi$
$449$		−	7.50030i		−	0.353961i	0.984214	−	0.176981i	$-0.0566330\pi$
$450$	−10.6351	+	5.36803i	−0.501342	+	0.253051i
$451$		−	7.76381i		−	0.365584i
$452$	33.1016	−	13.1506i	1.55697	−	0.618550i
$453$	2.26638	+	2.26638i	0.106484	+	0.106484i
$454$	4.49209	−	21.7554i	0.210824	−	1.02103i
$455$	26.9573	+	1.54283i	1.26378	+	0.0723289i
$456$	4.27362	−	6.10344i	0.200131	−	0.285820i
$457$	17.8043	−	17.8043i	0.832851	−	0.832851i	−0.155055	−	0.987906i	$-0.549555\pi$
$457$	17.8043	−	17.8043i	0.832851	−	0.832851i	0.987906	+	0.155055i	$0.0495554\pi$
$458$	0.107618	−	0.0707818i	0.00502866	−	0.00330742i
$459$	26.2667			1.22602
$460$	−25.2349	+	8.39027i	−1.17658	+	0.391198i
$461$	17.4216			0.811404			0.405702	−	0.914005i	$-0.367027\pi$
$461$	17.4216			0.811404			0.405702	+	0.914005i	$0.367027\pi$
$462$	4.46057	−	2.93378i	0.207525	−	0.136492i
$463$	−5.98643	+	5.98643i	−0.278213	+	0.278213i	−0.832395	−	0.554182i	$-0.813031\pi$
$463$	−5.98643	+	5.98643i	−0.278213	+	0.278213i	0.554182	+	0.832395i	$0.313031\pi$
$464$	−0.388517	+	0.366553i	−0.0180365	+	0.0170168i
$465$	2.54467	−	2.26916i	0.118006	−	0.105230i
$466$	1.95459	−	9.46618i	0.0905447	−	0.438512i
$467$	12.1300	+	12.1300i	0.561309	+	0.561309i	0.929679	−	0.368370i	$-0.120084\pi$
$467$	12.1300	+	12.1300i	0.561309	+	0.561309i	−0.368370	+	0.929679i	$0.620084\pi$
$468$	4.56362	+	11.4872i	0.210953	+	0.530996i
$469$		−	17.7137i		−	0.817945i
$470$	−26.6731	−	7.11818i	−1.23034	−	0.328337i
$471$			12.5237i			0.577063i
$472$	18.2284	−	3.21426i	0.839029	−	0.147948i
$473$	−5.00150	−	5.00150i	−0.229969	−	0.229969i
$474$	−3.97585	−	0.820939i	−0.182617	−	0.0377070i
$475$	−11.4100	−	1.31033i	−0.523527	−	0.0601221i
$476$	12.7485	−	29.5546i	0.584325	−	1.35463i
$477$	−6.63344	+	6.63344i	−0.303724	+	0.303724i
$478$	−12.1007	−	18.3982i	−0.553474	−	0.841513i
$479$	31.6336			1.44537			0.722687	−	0.691175i	$-0.242907\pi$
$479$	31.6336			1.44537			0.722687	+	0.691175i	$0.242907\pi$
$480$	12.7616	−	6.89777i	0.582486	−	0.314839i
$481$	−37.5298			−1.71121
$482$	12.2579	+	18.6372i	0.558332	+	0.848900i
$483$	15.8736	−	15.8736i	0.722275	−	0.722275i
$484$	0.792153	−	1.83644i	0.0360069	−	0.0834743i
$485$	19.3237	+	21.6699i	0.877445	+	0.983979i
$486$	20.5646	+	4.24620i	0.932828	+	0.192612i
$487$	6.15570	+	6.15570i	0.278941	+	0.278941i	0.832686	−	0.553745i	$-0.186802\pi$
$487$	6.15570	+	6.15570i	0.278941	+	0.278941i	−0.553745	+	0.832686i	$0.686802\pi$
$488$	−19.9263	+	3.51366i	−0.902021	+	0.159056i
$489$			5.59454i			0.252994i
$490$	−6.07578	−	10.4991i	−0.274476	−	0.474299i
$491$			7.77056i			0.350680i	0.984508	+	0.175340i	$0.0561025\pi$
$491$			7.77056i			0.350680i	−0.984508	+	0.175340i	$0.943897\pi$
$492$	6.57477	+	16.5495i	0.296414	+	0.746109i
$493$	−0.461633	−	0.461633i	−0.0207909	−	0.0207909i
$494$	−2.40968	+	11.6702i	−0.108417	+	0.525067i
$495$	0.215255	−	3.76108i	0.00967499	−	0.169048i
$496$	3.86824	−	3.64955i	0.173689	−	0.163869i
$497$	−29.1010	+	29.1010i	−1.30536	+	1.30536i
$498$	12.3488	−	8.12199i	0.553365	−	0.363955i
$499$	−36.5174			−1.63474			−0.817371	−	0.576111i	$-0.804569\pi$
$499$	−36.5174			−1.63474			−0.817371	+	0.576111i	$0.804569\pi$
$500$	−18.7192	−	12.2308i	−0.837147	−	0.546977i
$501$	−21.2325			−0.948599
$502$	−20.0715	+	13.2013i	−0.895837	+	0.589203i
$503$	−22.2472	+	22.2472i	−0.991952	+	0.991952i	−0.999968	−	0.00801619i	$-0.997448\pi$
$503$	−22.2472	+	22.2472i	−0.991952	+	0.991952i	0.00801619	+	0.999968i	$0.497448\pi$
$504$	8.99713	−	12.8494i	0.400764	−	0.572358i
$505$	1.30303	−	22.7674i	0.0579841	−	1.01314i
$506$	1.70053	−	8.23576i	0.0755979	−	0.366124i
$507$	0.370317	+	0.370317i	0.0164464	+	0.0164464i
$508$	36.2432	−	14.3987i	1.60803	−	0.638837i
$509$		−	24.6278i		−	1.09161i	−0.837913	−	0.545804i	$-0.816224\pi$
$509$		−	24.6278i		−	1.09161i	0.837913	−	0.545804i	$-0.183776\pi$
$510$	8.88069	+	15.3460i	0.393244	+	0.679533i
$511$			6.77278i			0.299610i
$512$	19.5957	−	11.3140i	0.866017	−	0.500015i
$513$	8.72641	+	8.72641i	0.385281	+	0.385281i
$514$	−32.7141	−	6.75485i	−1.44296	−	0.297944i
$515$	−3.11694	−	3.49537i	−0.137349	−	0.154024i
$516$	14.8968	+	6.42580i	0.655796	+	0.282880i
$517$	6.17302	−	6.17302i	0.271489	−	0.271489i
$518$	26.1718	+	39.7921i	1.14992	+	1.74836i
$519$	13.6763			0.600324
$520$	−14.3714	+	18.2135i	−0.630226	+	0.798713i
$521$	−19.3636			−0.848335			−0.424167	−	0.905584i	$-0.639433\pi$
$521$	−19.3636			−0.848335			−0.424167	+	0.905584i	$0.639433\pi$
$522$	−0.174834	−	0.265821i	−0.00765226	−	0.0116346i
$523$	−10.3463	+	10.3463i	−0.452413	+	0.452413i	−0.896155	−	0.443742i	$-0.853651\pi$
$523$	−10.3463	+	10.3463i	−0.452413	+	0.452413i	0.443742	+	0.896155i	$0.353651\pi$
$524$	−5.95607	−	2.56917i	−0.260192	−	0.112235i
$525$	18.7526	+	2.15356i	0.818430	+	0.0939890i
$526$	35.6210	+	7.35508i	1.55315	+	0.320697i
$527$	4.59620	+	4.59620i	0.200214	+	0.200214i
$528$	−0.133387	+	4.58542i	−0.00580494	+	0.199555i
$529$		−	12.3598i		−	0.537382i
$530$	−17.0129	−	4.54017i	−0.738991	−	0.197213i
$531$			11.0253i			0.478457i
$532$	14.0541	−	5.58338i	0.609321	−	0.242070i
$533$	−20.1386	−	20.1386i	−0.872298	−	0.872298i
$534$	4.73060	−	22.9105i	0.204713	−	0.991435i
$535$	0.176001	−	0.156946i	0.00760920	−	0.00678536i
$536$	12.4678	+	8.72991i	0.538525	+	0.377075i
$537$	17.6473	−	17.6473i	0.761535	−	0.761535i
$538$	−9.81596	+	6.45608i	−0.423196	+	0.278341i
$539$	3.83595			0.165226
$540$	7.58073	+	22.8001i	0.326223	+	0.981159i
$541$	42.7032			1.83596			0.917978	−	0.396632i	$-0.129821\pi$
$541$	42.7032			1.83596			0.917978	+	0.396632i	$0.129821\pi$
$542$	9.52708	−	6.26608i	0.409223	−	0.269151i
$543$	0.276120	−	0.276120i	0.0118494	−	0.0118494i
$544$	14.5190	+	23.5384i	0.622498	+	1.00920i
$545$	16.3725	+	0.937037i	0.701323	+	0.0401382i
$546$	3.96036	−	19.1802i	0.169488	−	0.820838i
$547$	−30.3884	−	30.3884i	−1.29931	−	1.29931i	−0.928845	−	0.370468i	$-0.879197\pi$
$547$	−30.3884	−	30.3884i	−1.29931	−	1.29931i	−0.370468	−	0.928845i	$-0.620803\pi$
$548$	2.24977	+	5.66294i	0.0961053	+	0.241909i
$549$		−	12.0523i		−	0.514378i
$550$	6.31252	−	3.18623i	0.269167	−	0.135861i
$551$		−	0.306731i		−	0.0130672i
$552$	3.34955	+	18.9956i	0.142566	+	0.808507i
$553$	−5.82636	−	5.82636i	−0.247762	−	0.247762i
$554$	33.0579	+	6.82585i	1.40450	+	0.290002i
$555$	−26.1930	−	1.49909i	−1.11183	−	0.0636326i
$556$	13.6241	−	31.5846i	0.577792	−	1.33949i
$557$	−0.276867	+	0.276867i	−0.0117312	+	0.0117312i	−0.712948	−	0.701217i	$-0.752640\pi$
$557$	−0.276867	+	0.276867i	−0.0117312	+	0.0117312i	0.701217	+	0.712948i	$0.252640\pi$
$558$	1.74071	+	2.64662i	0.0736903	+	0.112040i
$559$	−25.9468			−1.09743
$560$	29.3333	+	2.53632i	1.23956	+	0.107179i
$561$	−5.60684			−0.236721
$562$	−10.2427	−	15.5732i	−0.432062	−	0.656916i
$563$	2.95662	−	2.95662i	0.124607	−	0.124607i	−0.642053	−	0.766660i	$-0.721917\pi$
$563$	2.95662	−	2.95662i	0.124607	−	0.124607i	0.766660	+	0.642053i	$0.221917\pi$
$564$	−7.93093	+	18.3862i	−0.333952	+	0.774197i
$565$	−29.7216	+	26.5037i	−1.25040	+	1.11502i
$566$	−10.7894	−	2.22781i	−0.453512	−	0.0936418i
$567$	−2.57743	−	2.57743i	−0.108242	−	0.108242i
$568$	−6.14071	−	34.8246i	−0.257659	−	1.46121i
$569$			12.9492i			0.542860i	0.962458	+	0.271430i	$0.0874965\pi$
$569$			12.9492i			0.542860i	−0.962458	+	0.271430i	$0.912504\pi$
$570$	−2.14793	+	8.04868i	−0.0899669	+	0.337122i
$571$		−	39.9223i		−	1.67069i	−0.549722	−	0.835347i	$-0.685267\pi$
$571$		−	39.9223i		−	1.67069i	0.549722	−	0.835347i	$-0.314733\pi$
$572$	−2.70877	−	6.81830i	−0.113259	−	0.285087i
$573$	15.1666	+	15.1666i	0.633593	+	0.633593i
$574$	−7.30867	+	35.3963i	−0.305058	+	1.47741i
$575$	23.2851	−	18.4878i	0.971054	−	0.770996i
$576$	4.60992	+	12.6652i	0.192080	+	0.527716i
$577$	2.38695	−	2.38695i	0.0993698	−	0.0993698i	−0.655674	−	0.755044i	$-0.727615\pi$
$577$	2.38695	−	2.38695i	0.0993698	−	0.0993698i	0.755044	+	0.655674i	$0.227615\pi$
$578$	−8.15492	+	5.36359i	−0.339200	+	0.223096i
$579$	−14.6229			−0.607708
$580$	0.267478	−	0.533938i	0.0111064	−	0.0221706i
$581$	29.9987			1.24456
$582$	17.5948	−	11.5723i	0.729327	−	0.479688i
$583$	3.93732	−	3.93732i	0.163067	−	0.163067i
$584$	−4.76700	−	3.33785i	−0.197260	−	0.138121i
$585$	−9.19753	−	10.3142i	−0.380271	−	0.426441i
$586$	3.70102	−	17.9242i	0.152888	−	0.740443i
$587$	28.5208	+	28.5208i	1.17718	+	1.17718i	0.980460	+	0.196717i	$0.0630282\pi$
$587$	28.5208	+	28.5208i	1.17718	+	1.17718i	0.196717	+	0.980460i	$0.436972\pi$
$588$	−8.17680	+	3.24847i	−0.337206	+	0.133965i
$589$			3.05393i			0.125835i
$590$	−17.9114	+	10.3653i	−0.737400	+	0.426731i
$591$		−	16.8342i		−	0.692466i
$592$	−40.9058	−	1.18993i	−1.68122	−	0.0489057i
$593$	9.99834	+	9.99834i	0.410583	+	0.410583i	0.881942	−	0.471359i	$-0.156236\pi$
$593$	9.99834	+	9.99834i	0.410583	+	0.410583i	−0.471359	+	0.881942i	$0.656236\pi$
$594$	−7.44113	−	1.53645i	−0.305313	−	0.0630415i
$595$	−2.05620	+	35.9273i	−0.0842959	+	1.47287i
$596$	−19.9915	−	8.62342i	−0.818886	−	0.353229i
$597$	14.0803	−	14.0803i	0.576269	−	0.576269i
$598$	−16.9517	−	25.7738i	−0.693208	−	1.05397i
$599$	−34.2029			−1.39749			−0.698746	−	0.715369i	$-0.746258\pi$
$599$	−34.2029			−1.39749			−0.698746	+	0.715369i	$0.746258\pi$
$600$	−10.7577	+	12.1376i	−0.439179	+	0.495515i
$601$	−5.38036			−0.219469			−0.109735	−	0.993961i	$-0.535000\pi$
$601$	−5.38036			−0.219469			−0.109735	+	0.993961i	$0.535000\pi$
$602$	18.0942	+	27.5108i	0.737466	+	1.12126i
$603$	−6.41062	+	6.41062i	−0.261060	+	0.261060i
$604$	−5.13241	−	2.21388i	−0.208835	−	0.0900816i
$605$	−0.127766	+	2.23241i	−0.00519443	+	0.0907606i
$606$	−16.1991	−	3.34481i	−0.658043	−	0.135874i
$607$	5.88099	+	5.88099i	0.238702	+	0.238702i	0.816313	−	0.577610i	$-0.196015\pi$
$607$	5.88099	+	5.88099i	0.238702	+	0.238702i	−0.577610	+	0.816313i	$0.696015\pi$
$608$	−2.99646	+	12.6436i	−0.121522	+	0.512765i
$609$			0.504118i			0.0204279i
$610$	19.5798	−	11.3308i	0.792762	−	0.458769i
$611$		−	32.0244i		−	1.29557i
$612$	−15.3095	+	6.08214i	−0.618850	+	0.245856i
$613$	−22.2048	−	22.2048i	−0.896844	−	0.896844i	0.0983117	−	0.995156i	$-0.468656\pi$
$613$	−22.2048	−	22.2048i	−0.896844	−	0.896844i	−0.995156	+	0.0983117i	$0.968656\pi$
$614$	2.26930	−	10.9903i	0.0915816	−	0.443534i
$615$	−13.2508	−	14.8596i	−0.534324	−	0.599198i
$616$	−5.34031	+	7.62684i	−0.215167	+	0.307294i
$617$	−2.33151	+	2.33151i	−0.0938630	+	0.0938630i	−0.752479	−	0.658616i	$-0.771142\pi$
$617$	−2.33151	+	2.33151i	−0.0938630	+	0.0938630i	0.658616	+	0.752479i	$0.271142\pi$
$618$	−2.83805	+	1.86662i	−0.114163	+	0.0750866i
$619$	−45.2718			−1.81963			−0.909813	−	0.415019i	$-0.863775\pi$
$619$	−45.2718			−1.81963			−0.909813	+	0.415019i	$0.863775\pi$
$620$	−2.66311	+	5.31610i	−0.106953	+	0.213500i
$621$	−31.9481			−1.28203
$622$	6.50087	−	4.27571i	0.260661	−	0.171440i
$623$	33.5739	−	33.5739i	1.34511	−	1.34511i
$624$	11.5481	+	12.2401i	0.462295	+	0.489997i
$625$	24.3492	+	5.66729i	0.973967	+	0.226692i
$626$	−0.987308	+	4.78158i	−0.0394608	+	0.191110i
$627$	−1.86272	−	1.86272i	−0.0743900	−	0.0743900i
$628$	−8.06369	−	20.2973i	−0.321776	−	0.809951i
$629$		−	50.0177i		−	1.99434i
$630$	−4.52197	+	16.9446i	−0.180160	+	0.675091i
$631$			20.1928i			0.803862i	0.915670	+	0.401931i	$0.131661\pi$
$631$			20.1928i			0.803862i	−0.915670	+	0.401931i	$0.868339\pi$
$632$	6.97227	−	1.22944i	0.277342	−	0.0489045i
$633$	3.87386	+	3.87386i	0.153972	+	0.153972i
$634$	19.1117	+	3.94620i	0.759021	+	0.156724i
$635$	−32.5424	+	29.0191i	−1.29140	+	1.15159i
$636$	−5.05857	+	11.7272i	−0.200585	+	0.465014i
$637$	9.95009	−	9.95009i	0.394237	−	0.394237i
$638$	0.103774	+	0.157780i	0.00410844	+	0.00624655i
$639$	21.0634			0.833254
$640$	−16.2416	+	19.3962i	−0.642005	+	0.766700i
$641$	10.3412			0.408453			0.204227	−	0.978924i	$-0.434532\pi$
$641$	10.3412			0.408453			0.204227	+	0.978924i	$0.434532\pi$
$642$	−0.0939894	−	0.142903i	−0.00370947	−	0.00563995i
$643$	17.8956	−	17.8956i	0.705734	−	0.705734i	−0.259901	−	0.965635i	$-0.583690\pi$
$643$	17.8956	−	17.8956i	0.705734	−	0.705734i	0.965635	+	0.259901i	$0.0836900\pi$
$644$	−15.5059	+	35.9471i	−0.611018	+	1.41651i
$645$	−18.1089	−	1.03641i	−0.713039	−	0.0408088i
$646$	−15.5534	−	3.21149i	−0.611941	−	0.126354i
$647$	25.9670	+	25.9670i	1.02087	+	1.02087i	0.999778	+	0.0210925i	$0.00671445\pi$
$647$	25.9670	+	25.9670i	1.02087	+	1.02087i	0.0210925	+	0.999778i	$0.493286\pi$
$648$	3.08436	−	0.543873i	0.121165	−	0.0213654i
$649$		−	6.54413i		−	0.256880i
$650$	8.10929	−	24.6388i	0.318073	−	0.966415i
$651$		−	5.01920i		−	0.196718i
$652$	−3.60218	−	9.06713i	−0.141072	−	0.355096i
$653$	−18.9456	−	18.9456i	−0.741398	−	0.741398i	0.231449	−	0.972847i	$-0.425653\pi$
$653$	−18.9456	−	18.9456i	−0.741398	−	0.741398i	−0.972847	+	0.231449i	$0.925653\pi$
$654$	2.40532	−	11.6491i	0.0940556	−	0.455516i
$655$	7.24034	+	0.414381i	0.282904	+	0.0161912i
$656$	−21.3116	−	22.5886i	−0.832077	−	0.881937i
$657$	2.45107	−	2.45107i	0.0956255	−	0.0956255i
$658$	−33.9548	+	22.3325i	−1.32370	+	0.870612i
$659$	−8.90498			−0.346889			−0.173444	−	0.984844i	$-0.555490\pi$
$659$	−8.90498			−0.346889			−0.173444	+	0.984844i	$0.555490\pi$
$660$	−1.61817	−	4.86686i	−0.0629871	−	0.189442i
$661$	−8.91820			−0.346878			−0.173439	−	0.984845i	$-0.555488\pi$
$661$	−8.91820			−0.346878			−0.173439	+	0.984845i	$0.555488\pi$
$662$	−8.91522	+	5.86365i	−0.346500	+	0.227897i
$663$	−14.5436	+	14.5436i	−0.564827	+	0.564827i
$664$	−14.7843	+	21.1145i	−0.573743	+	0.819400i
$665$	−12.6190	+	11.2528i	−0.489344	+	0.436363i
$666$	4.92920	−	23.8723i	0.191002	−	0.925035i
$667$	0.561482	+	0.561482i	0.0217407	+	0.0217407i
$668$	34.4117	−	13.6711i	1.33143	−	0.528949i
$669$		−	21.7018i		−	0.839040i
$670$	−16.4414	−	4.38766i	−0.635185	−	0.169510i
$671$			7.15370i			0.276165i
$672$	4.92474	−	20.7800i	0.189976	−	0.801605i
$673$	13.4501	+	13.4501i	0.518463	+	0.518463i	0.917106	−	0.398643i	$-0.130519\pi$
$673$	13.4501	+	13.4501i	0.518463	+	0.518463i	−0.398643	+	0.917106i	$0.630519\pi$
$674$	37.0424	+	7.64857i	1.42682	+	0.294612i
$675$	−16.7040	−	21.0384i	−0.642938	−	0.809768i
$676$	−0.838614	−	0.361739i	−0.0322544	−	0.0139130i
$677$	−31.4884	+	31.4884i	−1.21020	+	1.21020i	−0.239236	+	0.970961i	$0.576897\pi$
$677$	−31.4884	+	31.4884i	−1.21020	+	1.21020i	−0.970961	+	0.239236i	$0.923103\pi$
$678$	15.8721	+	24.1323i	0.609565	+	0.926795i
$679$	42.7425			1.64031
$680$	−24.2739	−	19.1534i	−0.930862	−	0.734498i
$681$	18.0145			0.690316
$682$	−1.03321	−	1.57092i	−0.0395637	−	0.0601535i
$683$	9.42261	−	9.42261i	0.360546	−	0.360546i	−0.503468	−	0.864014i	$-0.667943\pi$
$683$	9.42261	−	9.42261i	0.360546	−	0.360546i	0.864014	+	0.503468i	$0.167943\pi$
$684$	−7.10681	−	3.06554i	−0.271735	−	0.117214i
$685$	−4.53419	−	5.08470i	−0.173242	−	0.194276i
$686$	14.4253	+	2.97856i	0.550761	+	0.113722i
$687$	0.0738615	+	0.0738615i	0.00281799	+	0.00281799i
$688$	−28.2808	−	0.822674i	−1.07820	−	0.0313642i
$689$		−	20.4261i		−	0.778171i
$690$	−10.8015	−	18.6653i	−0.411208	−	0.710575i
$691$		−	13.4886i		−	0.513132i	−0.966527	−	0.256566i	$-0.917409\pi$
$691$		−	13.4886i		−	0.513132i	0.966527	−	0.256566i	$-0.0825910\pi$
$692$	−22.1653	+	8.80581i	−0.842599	+	0.334747i
$693$	−3.92154	−	3.92154i	−0.148967	−	0.148967i
$694$	−1.21297	+	5.87448i	−0.0460437	+	0.222992i
$695$	−2.19743	+	38.3950i	−0.0833533	+	1.45641i
$696$	−0.354822	−	0.248446i	−0.0134495	−	0.00941731i
$697$	26.8396	−	26.8396i	1.01662	−	1.01662i
$698$	−18.3369	+	12.0604i	−0.694062	+	0.456493i
$699$	7.83842			0.296476
$700$	−31.7791	+	8.58400i	−1.20114	+	0.324445i
$701$	−4.50941			−0.170318			−0.0851591	−	0.996367i	$-0.527140\pi$
$701$	−4.50941			−0.170318			−0.0851591	+	0.996367i	$0.527140\pi$
$702$	−23.2870	+	15.3161i	−0.878910	+	0.578071i
$703$	16.6171	−	16.6171i	0.626724	−	0.626724i
$704$	−2.73625	−	7.51751i	−0.103126	−	0.283327i
$705$	1.27918	−	22.3507i	0.0481766	−	0.841774i
$706$	−4.80270	+	23.2597i	−0.180752	+	0.875391i
$707$	−23.7387	−	23.7387i	−0.892788	−	0.892788i
$708$	5.54189	+	13.9496i	0.208277	+	0.524259i
$709$			31.4520i			1.18121i	0.806963	+	0.590603i	$0.201110\pi$
$709$			31.4520i			1.18121i	−0.806963	+	0.590603i	$0.798890\pi$
$710$	19.8024	+	34.2190i	0.743172	+	1.28422i
$711$			4.21712i			0.158154i
$712$	7.08455	+	40.1772i	0.265505	+	1.50570i
$713$	−5.59034	−	5.59034i	−0.209360	−	0.209360i
$714$	25.5624	+	5.27815i	0.956647	+	0.197530i
$715$	5.45925	+	6.12208i	0.204164	+	0.228953i
$716$	−17.2385	+	39.9637i	−0.644231	+	1.49351i
$717$	12.6272	−	12.6272i	0.471572	−	0.471572i
$718$	11.4506	+	17.4098i	0.427333	+	0.649726i
$719$	−37.1300			−1.38471			−0.692357	−	0.721555i	$-0.743428\pi$
$719$	−37.1300			−1.38471			−0.692357	+	0.721555i	$0.743428\pi$
$720$	−9.69785	−	11.5336i	−0.361417	−	0.429833i
$721$	−6.89440			−0.256761
$722$	10.6651	+	16.2154i	0.396914	+	0.603476i
$723$	−12.7912	+	12.7912i	−0.475712	+	0.475712i
$724$	−0.269723	+	0.625295i	−0.0100242	+	0.0232389i
$725$	−0.0761757	+	0.663317i	−0.00282909	+	0.0246350i
$726$	1.58837	+	0.327969i	0.0589499	+	0.0121721i
$727$	−6.75902	−	6.75902i	−0.250678	−	0.250678i	0.570570	−	0.821249i	$-0.306722\pi$
$727$	−6.75902	−	6.75902i	−0.250678	−	0.250678i	−0.821249	+	0.570570i	$0.806722\pi$
$728$	5.93105	+	33.6355i	0.219819	+	1.24662i
$729$			20.3503i			0.753715i
$730$	6.28629	+	1.67761i	0.232666	+	0.0620910i
$731$		−	34.5805i		−	1.27901i
$732$	−6.05810	−	15.2490i	−0.223914	−	0.563619i
$733$	−2.90537	−	2.90537i	−0.107312	−	0.107312i	0.651412	−	0.758724i	$-0.274177\pi$
$733$	−2.90537	−	2.90537i	−0.107312	−	0.107312i	−0.758724	+	0.651412i	$0.774177\pi$
$734$	−1.70834	+	8.27357i	−0.0630559	+	0.305383i
$735$	7.34186	−	6.54698i	0.270809	−	0.241489i
$736$	−17.6594	−	28.6297i	−0.650935	−	1.05530i
$737$	3.80506	−	3.80506i	0.140161	−	0.140161i
$738$	15.4549	−	10.1649i	0.568904	−	0.374176i
$739$	−30.5046			−1.12213			−0.561065	−	0.827772i	$-0.689608\pi$
$739$	−30.5046			−1.12213			−0.561065	+	0.827772i	$0.689608\pi$
$740$	43.4165	−	14.4354i	1.59602	−	0.530656i
$741$	−9.66345			−0.354996
$742$	−21.6573	+	14.2443i	−0.795064	+	0.522924i
$743$	−3.47745	+	3.47745i	−0.127575	+	0.127575i	−0.768011	−	0.640436i	$-0.778754\pi$
$743$	−3.47745	+	3.47745i	−0.127575	+	0.127575i	0.640436	+	0.768011i	$0.278754\pi$
$744$	3.53275	+	2.47362i	0.129517	+	0.0906875i
$745$	24.3022	+	1.39087i	0.890364	+	0.0509575i
$746$	5.96537	−	28.8906i	0.218408	−	1.05776i
$747$	−10.8565	−	10.8565i	−0.397220	−	0.397220i
$748$	9.08706	−	3.61010i	0.332256	−	0.131998i
$749$		−	0.347151i		−	0.0126846i
$750$	6.64385	−	16.8722i	0.242599	−	0.616084i
$751$			13.3195i			0.486036i	0.970022	+	0.243018i	$0.0781374\pi$
$751$			13.3195i			0.486036i	−0.970022	+	0.243018i	$0.921863\pi$
$752$	1.01537	−	34.9051i	0.0370268	−	1.27286i
$753$	−13.7757	−	13.7757i	−0.502014	−	0.502014i
$754$	0.678443	+	0.140086i	0.0247074	+	0.00510163i
$755$	6.23908	+	0.357076i	0.227063	+	0.0129953i
$756$	32.4787	+	14.0098i	1.18124	+	0.509532i
$757$	11.3493	−	11.3493i	0.412496	−	0.412496i	−0.470111	−	0.882607i	$-0.655786\pi$
$757$	11.3493	−	11.3493i	0.412496	−	0.412496i	0.882607	+	0.470111i	$0.155786\pi$
$758$	−23.5671	−	35.8319i	−0.855996	−	1.30147i
$759$	6.81958			0.247535
$760$	−1.70116	−	14.4276i	−0.0617076	−	0.523342i
$761$	−35.8822			−1.30073			−0.650365	−	0.759622i	$-0.725384\pi$
$761$	−35.8822			−1.30073			−0.650365	+	0.759622i	$0.725384\pi$
$762$	17.3785	+	26.4226i	0.629557	+	0.957191i
$763$	17.0710	−	17.0710i	0.618013	−	0.618013i
$764$	−34.3460	−	14.8153i	−1.24259	−	0.535997i
$765$	13.7462	−	12.2580i	0.496996	−	0.443187i
$766$	−0.368896	−	0.0761703i	−0.0133288	−	0.00275214i
$767$	−16.9748	−	16.9748i	−0.612926	−	0.612926i
$768$	12.1988	+	13.7073i	0.440187	+	0.494620i
$769$		−	15.5077i		−	0.559221i	−0.960114	−	0.279610i	$-0.909795\pi$
$769$		−	15.5077i		−	0.559221i	0.960114	−	0.279610i	$-0.0902053\pi$
$770$	2.68405	−	10.0576i	0.0967263	−	0.362451i
$771$		−	27.0887i		−	0.975576i
$772$	23.6995	−	9.41531i	0.852964	−	0.338864i
$773$	−0.694601	−	0.694601i	−0.0249831	−	0.0249831i	0.694505	−	0.719488i	$-0.255623\pi$
$773$	−0.694601	−	0.694601i	−0.0249831	−	0.0249831i	−0.719488	+	0.694505i	$0.755623\pi$
$774$	3.40787	−	16.5045i	0.122493	−	0.593242i
$775$	0.758436	−	6.60425i	0.0272438	−	0.237232i
$776$	−21.0649	+	30.0841i	−0.756185	+	1.07996i
$777$	−27.3105	+	27.3105i	−0.979758	+	0.979758i
$778$	3.04769	−	2.00451i	0.109265	−	0.0718650i
$779$	17.8335			0.638950
$780$	−16.8215	−	8.42679i	−0.602307	−	0.301728i
$781$	−12.5023			−0.447367
$782$	34.3499	−	22.5924i	1.22835	−	0.807901i
$783$	0.507307	−	0.507307i	0.0181297	−	0.0181297i
$784$	11.1606	−	10.5297i	0.398593	−	0.376059i
$785$	16.2516	+	18.2247i	0.580044	+	0.650469i
$786$	1.06369	−	5.15152i	0.0379407	−	0.183749i
$787$	22.4338	+	22.4338i	0.799677	+	0.799677i	0.983045	−	0.183367i	$-0.0586997\pi$
$787$	22.4338	+	22.4338i	0.799677	+	0.799677i	−0.183367	+	0.983045i	$0.558700\pi$
$788$	10.8391	+	27.2833i	0.386126	+	0.971927i
$789$			29.4958i			1.05008i
$790$	−6.85102	+	3.96467i	−0.243749	+	0.141057i
$791$			58.6239i			2.08443i
$792$	4.69282	−	0.827498i	0.166752	−	0.0294039i
$793$	18.5560	+	18.5560i	0.658943	+	0.658943i
$794$	−4.14544	−	0.855956i	−0.147116	−	0.0303767i
$795$	0.815895	−	14.2559i	0.0289368	−	0.505603i
$796$	−13.7541	+	31.8860i	−0.487503	+	1.13017i
$797$	11.1617	−	11.1617i	0.395367	−	0.395367i	−0.481229	−	0.876595i	$-0.659809\pi$
$797$	11.1617	−	11.1617i	0.395367	−	0.395367i	0.876595	+	0.481229i	$0.159809\pi$
$798$	6.73889	+	10.2459i	0.238554	+	0.362702i
$799$	42.6804			1.50992
$800$	9.61995	−	26.5981i	0.340117	−	0.940383i
$801$	−24.3008			−0.858628
$802$	−3.97815	−	6.04845i	−0.140473	−	0.213578i
$803$	−1.45485	+	1.45485i	−0.0513406	+	0.0513406i
$804$	−4.88864	+	11.3333i	−0.172409	+	0.399694i
$805$	2.50094	−	43.6982i	0.0881467	−	1.54016i
$806$	−6.75485	−	1.39475i	−0.237930	−	0.0491280i
$807$	−6.73699	−	6.73699i	−0.237153	−	0.237153i
$808$	28.4076	−	5.00920i	0.999378	−	0.176223i
$809$		−	23.4629i		−	0.824913i	−0.910977	−	0.412456i	$-0.864671\pi$
$809$		−	23.4629i		−	0.824913i	0.910977	−	0.412456i	$-0.135329\pi$
$810$	−3.03072	+	1.75387i	−0.106489	+	0.0616247i
$811$			7.95869i			0.279467i	0.990189	+	0.139734i	$0.0446246\pi$
$811$			7.95869i			0.279467i	−0.990189	+	0.139734i	$0.955375\pi$
$812$	−0.324588	−	0.817028i	−0.0113908	−	0.0286721i
$813$	6.53872	+	6.53872i	0.229323	+	0.229323i
$814$	−2.92576	+	14.1696i	−0.102548	+	0.496644i
$815$	7.25983	+	8.14127i	0.254301	+	0.285176i
$816$	−16.3130	+	15.3907i	−0.571068	+	0.538783i
$817$	11.4885	−	11.4885i	0.401930	−	0.401930i
$818$	27.5891	−	18.1457i	0.964629	−	0.634449i
$819$	−20.3442			−0.710883
$820$	31.0434	+	15.5513i	1.08408	+	0.543074i
$821$	32.4930			1.13401			0.567007	−	0.823713i	$-0.308101\pi$
$821$	32.4930			1.13401			0.567007	+	0.823713i	$0.308101\pi$
$822$	−4.12850	+	2.71537i	−0.143998	+	0.0947093i
$823$	26.1886	−	26.1886i	0.912878	−	0.912878i	−0.0836197	−	0.996498i	$-0.526648\pi$
$823$	26.1886	−	26.1886i	0.912878	−	0.912878i	0.996498	+	0.0836197i	$0.0266481\pi$
$824$	3.39779	−	4.85260i	0.118367	−	0.169048i
$825$	3.56561	+	4.49082i	0.124139	+	0.156350i
$826$	−6.16049	+	29.8356i	−0.214351	+	1.03811i
$827$	15.4248	+	15.4248i	0.536372	+	0.536372i	0.922461	−	0.386089i	$-0.126174\pi$
$827$	15.4248	+	15.4248i	0.536372	+	0.536372i	−0.386089	+	0.922461i	$0.626174\pi$
$828$	18.6209	−	7.39768i	0.647120	−	0.257087i
$829$			49.5561i			1.72116i	0.509319	+	0.860578i	$0.329897\pi$
$829$			49.5561i			1.72116i	−0.509319	+	0.860578i	$0.670103\pi$
$830$	7.43062	−	27.8439i	0.257921	−	0.966475i
$831$			27.3734i			0.949574i
$832$	−26.5972	−	12.4021i	−0.922093	−	0.429966i
$833$	13.2609	+	13.2609i	0.459464	+	0.459464i
$834$	27.3182	+	5.64069i	0.945951	+	0.195321i
$835$	−30.8979	+	27.5527i	−1.06927	+	0.953499i
$836$	4.21829	+	1.81957i	0.145893	+	0.0629313i
$837$	−5.05095	+	5.05095i	−0.174586	+	0.174586i
$838$	8.55733	+	13.0107i	0.295608	+	0.449448i
$839$	−30.8225			−1.06411			−0.532056	−	0.846709i	$-0.678580\pi$
$839$	−30.8225			−1.06411			−0.532056	+	0.846709i	$0.678580\pi$
$840$	2.79590	+	23.7120i	0.0964676	+	0.818141i
$841$	28.9822			0.999385
$842$	−20.3233	−	30.8999i	−0.700386	−	1.06488i
$843$	10.6884	−	10.6884i	0.368126	−	0.368126i
$844$	−8.77268	−	3.78413i	−0.301968	−	0.130255i
$845$	1.01944	+	0.0583448i	0.0350698	+	0.00200712i
$846$	20.3704	+	4.20611i	0.700349	+	0.144609i
$847$	2.32765	+	2.32765i	0.0799792	+	0.0799792i
$848$	0.647632	−	22.2634i	0.0222398	−	0.764530i
$849$		−	8.93410i		−	0.306617i
$850$	32.8373	+	10.8076i	1.12631	+	0.370698i
$851$			60.8363i			2.08544i
$852$	26.6502	−	10.5875i	0.913020	−	0.362723i
$853$	−6.00707	−	6.00707i	−0.205678	−	0.205678i	0.596750	−	0.802428i	$-0.296459\pi$
$853$	−6.00707	−	6.00707i	−0.205678	−	0.205678i	−0.802428	+	0.596750i	$0.796459\pi$
$854$	6.73433	−	32.6147i	0.230444	−	1.11605i
$855$	8.63920	+	0.494441i	0.295455	+	0.0169095i
$856$	0.244341	+	0.171087i	0.00835141	+	0.00584765i
$857$	−34.6744	+	34.6744i	−1.18445	+	1.18445i	−0.205876	+	0.978578i	$0.566004\pi$
$857$	−34.6744	+	34.6744i	−1.18445	+	1.18445i	−0.978578	+	0.205876i	$0.933996\pi$
$858$	4.97079	−	3.26936i	0.169700	−	0.111614i
$859$	40.0717			1.36723			0.683614	−	0.729843i	$-0.260407\pi$
$859$	40.0717			1.36723			0.683614	+	0.729843i	$0.260407\pi$
$860$	30.0166	−	9.98014i	1.02356	−	0.340320i
$861$	−29.3097			−0.998871
$862$	−10.2934	+	6.77010i	−0.350594	+	0.230590i
$863$	−8.12174	+	8.12174i	−0.276467	+	0.276467i	−0.831697	−	0.555230i	$-0.812630\pi$
$863$	−8.12174	+	8.12174i	−0.276467	+	0.276467i	0.555230	+	0.831697i	$0.312630\pi$
$864$	−25.8673	+	15.9555i	−0.880024	+	0.542818i
$865$	19.9020	−	17.7472i	0.676688	−	0.603425i
$866$	7.50726	−	36.3581i	0.255107	−	1.23550i
$867$	−5.59696	−	5.59696i	−0.190083	−	0.190083i
$868$	3.23173	+	8.13466i	0.109692	+	0.276108i
$869$		−	2.50310i		−	0.0849119i
$870$	0.467907	+	0.124869i	0.0158635	+	0.00423346i
$871$		−	19.7399i		−	0.668862i
$872$	3.60222	+	20.4285i	0.121987	+	0.691797i
$873$	−15.4685	−	15.4685i	−0.523531	−	0.523531i
$874$	18.9175	+	3.90612i	0.639895	+	0.132127i
$875$	30.0837	−	21.2006i	1.01701	−	0.716713i
$876$	1.86915	−	4.33323i	0.0631529	−	0.146406i
$877$	3.96001	−	3.96001i	0.133720	−	0.133720i	−0.637079	−	0.770799i	$-0.719857\pi$
$877$	3.96001	−	3.96001i	0.133720	−	0.133720i	0.770799	+	0.637079i	$0.219857\pi$
$878$	2.04667	+	3.11179i	0.0690717	+	0.105018i
$879$	14.8421			0.500610
$880$	5.75622	+	6.84587i	0.194042	+	0.230774i
$881$	35.5301			1.19704			0.598520	−	0.801108i	$-0.295756\pi$
$881$	35.5301			1.19704			0.598520	+	0.801108i	$0.295756\pi$
$882$	5.02230	+	7.63600i	0.169110	+	0.257117i
$883$	−4.68070	+	4.68070i	−0.157518	+	0.157518i	−0.781466	−	0.623948i	$-0.785528\pi$
$883$	−4.68070	+	4.68070i	−0.157518	+	0.157518i	0.623948	+	0.781466i	$0.285528\pi$
$884$	14.2067	−	32.9352i	0.477823	−	1.10773i
$885$	−11.1691	−	12.5252i	−0.375446	−	0.421030i
$886$	−31.6286	−	6.53071i	−1.06258	−	0.219404i
$887$	0.768436	+	0.768436i	0.0258015	+	0.0258015i	0.719890	−	0.694088i	$-0.244192\pi$
$887$	0.768436	+	0.768436i	0.0258015	+	0.0258015i	−0.694088	+	0.719890i	$0.744192\pi$
$888$	−5.76289	−	32.6819i	−0.193390	−	1.09673i
$889$			64.1878i			2.15279i
$890$	−22.8461	−	39.4785i	−0.765803	−	1.32332i
$891$		−	1.10731i		−	0.0370962i
$892$	13.9732	+	35.1723i	0.467858	+	1.17766i
$893$	14.1794	+	14.1794i	0.474496	+	0.474496i
$894$	3.57029	−	17.2911i	0.119408	−	0.578301i
$895$	2.78039	−	48.5808i	0.0929380	−	1.62388i
$896$	5.39811	+	36.8492i	0.180338	+	1.23104i
$897$	17.6893	−	17.6893i	0.590629	−	0.590629i
$898$	−8.86203	+	5.82868i	−0.295730	+	0.194505i
$899$	0.177539			0.00592127
$900$	14.6074	+	8.39432i	0.486914	+	0.279811i
$901$	27.2227			0.906921
$902$	−9.17338	+	6.03345i	−0.305440	+	0.200892i
$903$	−18.8815	+	18.8815i	−0.628337	+	0.628337i
$904$	−41.2622	−	28.8918i	−1.37236	−	0.960926i
$905$	0.0435036	−	0.760124i	0.00144611	−	0.0252674i
$906$	0.916597	−	4.43912i	0.0304519	−	0.147480i
$907$	−8.60637	−	8.60637i	−0.285770	−	0.285770i	0.549635	−	0.835405i	$-0.314767\pi$
$907$	−8.60637	−	8.60637i	−0.285770	−	0.285770i	−0.835405	+	0.549635i	$0.814767\pi$
$908$	−29.1962	+	11.5990i	−0.968910	+	0.384928i
$909$			17.1821i			0.569895i
$910$	−19.1263	−	33.0506i	−0.634030	−	1.09562i
$911$			51.6465i			1.71113i	0.517698	+	0.855563i	$0.326789\pi$
$911$			51.6465i			1.71113i	−0.517698	+	0.855563i	$0.673211\pi$
$912$	−10.5327	−	0.306391i	−0.348773	−	0.0101456i
$913$	6.44397	+	6.44397i	0.213264	+	0.213264i
$914$	−34.8730	−	7.20063i	−1.15350	−	0.238176i
$915$	12.2095	+	13.6919i	0.403634	+	0.452640i
$916$	−0.167265	−	0.0721505i	−0.00552661	−	0.00238392i
$917$	7.54923	−	7.54923i	0.249298	−	0.249298i
$918$	−20.4125	−	31.0356i	−0.673714	−	1.02433i
$919$	46.1566			1.52257			0.761283	−	0.648420i	$-0.224570\pi$
$919$	46.1566			1.52257			0.761283	+	0.648420i	$0.224570\pi$
$920$	29.5242	+	23.2962i	0.973385	+	0.768051i
$921$	9.10050			0.299872
$922$	−13.5388	−	20.5846i	−0.445875	−	0.677917i
$923$	−32.4297	+	32.4297i	−1.06744	+	1.06744i
$924$	−6.93285	−	2.99051i	−0.228074	−	0.0983805i
$925$	−40.0618	+	31.8082i	−1.31723	+	1.04585i
$926$	11.7255	+	2.42110i	0.385324	+	0.0795623i
$927$	2.49509	+	2.49509i	0.0819495	+	0.0819495i
$928$	0.735030	+	0.174198i	0.0241285	+	0.00571833i
$929$			20.3837i			0.668768i	0.942437	+	0.334384i	$0.108528\pi$
$929$			20.3837i			0.668768i	−0.942437	+	0.334384i	$0.891472\pi$
$930$	−4.65867	−	1.24325i	−0.152764	−	0.0407677i
$931$			8.81119i			0.288775i
$932$	−12.7038	+	5.04695i	−0.416127	+	0.165318i
$933$	4.46175	+	4.46175i	0.146071	+	0.146071i
$934$	4.90575	−	23.7588i	0.160521	−	0.777412i
$935$	−8.15917	+	7.27579i	−0.266833	+	0.237944i
$936$	10.0263	−	14.3192i	0.327719	−	0.468036i
$937$	−33.1448	+	33.1448i	−1.08279	+	1.08279i	−0.0865463	+	0.996248i	$0.527583\pi$
$937$	−33.1448	+	33.1448i	−1.08279	+	1.08279i	−0.996248	+	0.0865463i	$0.972417\pi$
$938$	−20.9298	+	13.7658i	−0.683382	+	0.449469i
$939$	−3.95936			−0.129209
$940$	12.3178	+	37.0475i	0.401763	+	1.20836i
$941$	−6.14439			−0.200301			−0.100151	−	0.994972i	$-0.531932\pi$
$941$	−6.14439			−0.200301			−0.100151	+	0.994972i	$0.531932\pi$
$942$	14.7975	−	9.73251i	0.482129	−	0.317102i
$943$	−32.6449	+	32.6449i	−1.06306	+	1.06306i
$944$	−17.9636	−	19.0400i	−0.584664	−	0.619699i
$945$	−39.4819	−	2.25964i	−1.28435	−	0.0735060i
$946$	−2.02277	+	9.79635i	−0.0657658	+	0.318507i
$947$	−40.9443	−	40.9443i	−1.33051	−	1.33051i	−0.904913	−	0.425597i	$-0.860064\pi$
$947$	−40.9443	−	40.9443i	−1.33051	−	1.33051i	−0.425597	−	0.904913i	$-0.639936\pi$
$948$	2.11975	+	5.33566i	0.0688462	+	0.173294i
$949$			7.54748i			0.245002i
$950$	7.31877	+	14.4999i	0.237452	+	0.470438i
$951$			15.8253i			0.513171i
$952$	−44.8276	+	7.90457i	−1.45287	+	0.256189i
$953$	−7.56504	−	7.56504i	−0.245056	−	0.245056i	0.573882	−	0.818938i	$-0.305437\pi$
$953$	−7.56504	−	7.56504i	−0.245056	−	0.245056i	−0.818938	+	0.573882i	$0.805437\pi$
$954$	12.9928	+	2.68277i	0.420658	+	0.0868580i
$955$	41.7518	+	2.38955i	1.35106	+	0.0773239i
$956$	−12.3347	+	28.5954i	−0.398933	+	0.924840i
$957$	−0.108289	+	0.108289i	−0.00350048	+	0.00350048i
$958$	−24.5832	−	37.3769i	−0.794249	−	1.20759i
$959$	−10.0292			−0.323861
$960$	−18.0675	−	9.71816i	−0.583126	−	0.313652i
$961$	29.2323			0.942979
$962$	29.1654	+	44.3436i	0.940330	+	1.42970i
$963$	−0.125634	+	0.125634i	−0.00404851	+	0.00404851i
$964$	12.4949	−	28.9668i	0.402435	−	0.932959i
$965$	−21.2795	+	18.9756i	−0.685012	+	0.610847i
$966$	−31.0914	−	6.41979i	−1.00035	−	0.206553i
$967$	−12.4934	−	12.4934i	−0.401759	−	0.401759i	0.477093	−	0.878853i	$-0.341690\pi$
$967$	−12.4934	−	12.4934i	−0.401759	−	0.401759i	−0.878853	+	0.477093i	$0.841690\pi$
$968$	−2.78545	+	0.491167i	−0.0895279	+	0.0157867i
$969$		−	12.8789i		−	0.413730i
$970$	10.5872	−	39.6723i	0.339936	−	1.27380i
$971$		−	44.5413i		−	1.42940i	−0.699433	−	0.714698i	$-0.746564\pi$
$971$		−	44.5413i		−	1.42940i	0.699433	−	0.714698i	$-0.253436\pi$
$972$	−10.9641	−	27.5980i	−0.351674	−	0.885208i
$973$	40.0330	+	40.0330i	1.28340	+	1.28340i
$974$	2.48956	−	12.0571i	0.0797706	−	0.386333i
$975$	20.8976	+	2.39989i	0.669258	+	0.0768580i
$976$	19.6368	+	20.8135i	0.628559	+	0.666224i
$977$	−23.4582	+	23.4582i	−0.750494	+	0.750494i	−0.974571	−	0.224077i	$-0.928063\pi$
$977$	−23.4582	+	23.4582i	−0.750494	+	0.750494i	0.224077	+	0.974571i	$0.428063\pi$
$978$	6.61027	−	4.34766i	0.211373	−	0.139023i
$979$	14.4239			0.460991
$980$	−7.68360	+	15.3380i	−0.245444	+	0.489953i
$981$	−12.3560			−0.394498
$982$	9.18135	−	6.03870i	0.292989	−	0.192703i
$983$	−35.6516	+	35.6516i	−1.13711	+	1.13711i	−0.148143	+	0.988966i	$0.547330\pi$
$983$	−35.6516	+	35.6516i	−1.13711	+	1.13711i	−0.988966	+	0.148143i	$0.952670\pi$
$984$	14.4448	−	20.6295i	0.460482	−	0.657645i
$985$	−21.8451	−	24.4974i	−0.696043	−	0.780552i
$986$	−0.186699	+	0.904192i	−0.00594570	+	0.0287953i
$987$	−23.3042	−	23.3042i	−0.741780	−	0.741780i
$988$	15.6616	−	6.22204i	0.498263	−	0.197949i
$989$			42.0601i			1.33743i
$990$	−4.61121	+	2.66850i	−0.146554	+	0.0848104i
$991$			10.1191i			0.321445i	0.987000	+	0.160723i	$0.0513824\pi$
$991$			10.1191i			0.321445i	−0.987000	+	0.160723i	$0.948618\pi$
$992$	−7.31825	−	1.73438i	−0.232355	−	0.0550668i
$993$	−6.11878	−	6.11878i	−0.194174	−	0.194174i
$994$	56.9997	+	11.7694i	1.80792	+	0.373302i
$995$	2.21840	−	38.7614i	0.0703281	−	1.22882i
$996$	−19.1932	−	8.27905i	−0.608159	−	0.262332i
$997$	26.1214	−	26.1214i	0.827272	−	0.827272i	−0.159867	−	0.987139i	$-0.551106\pi$
$997$	26.1214	−	26.1214i	0.827272	−	0.827272i	0.987139	+	0.159867i	$0.0511064\pi$
$998$	28.3786	+	43.1474i	0.898308	+	1.36581i
$999$	54.9665			1.73906

Display

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instead) (See

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.l.c.23.6	✓	28
4.3	odd	2		220.2.l.d.23.12	yes	28
5.2	odd	4		220.2.l.d.67.12	yes	28
20.7	even	4	inner	220.2.l.c.67.6	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.c.23.6	✓	28	1.1	even	1	trivial
220.2.l.c.67.6	yes	28	20.7	even	4	inner
220.2.l.d.23.12	yes	28	4.3	odd	2
220.2.l.d.67.12	yes	28	5.2	odd	4

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	220.2.l.c.23.6

Level	$220$
Weight	$2$
Character	220.23
Analytic conductor	$1.757$
Analytic rank	$0$
Dimension	$28$
Inner twists	$2$