LMFDB - Embedded newform 220.2.l.d.23.12

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			23.12
Character	$\chi$	$=$	220.23
Dual form			220.2.l.d.67.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.18156 + 0.777125i) 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} +(-0.491167 + 2.78545i) q^{8} +1.68476i q^{9} +(1.88583 - 2.53843i) q^{10} +1.00000i q^{11} +(-2.13162 - 0.846848i) 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} +(-1.30927 + 1.99064i) q^{18} -2.29700 q^{19} +(4.20090 - 1.53378i) q^{20} -3.77517 q^{21} +(-0.777125 + 1.18156i) 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} +(-2.43073 + 6.11845i) q^{28} -0.133535i q^{29} +(0.529223 + 3.58780i) q^{30} -1.32953i q^{31} +(-5.50439 + 1.30451i) 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} +(-2.71404 - 1.78506i) q^{38} +4.20699 q^{39} +(6.15553 + 1.45237i) q^{40} +7.76381 q^{41} +(-4.46057 - 2.93378i) 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} +(-0.133387 - 4.58542i) q^{48} +3.83595i q^{49} +(-5.42589 - 4.53428i) q^{50} +5.60684i q^{51} +(2.70877 - 6.81830i) 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} +(0.103774 - 0.157780i) q^{58} -6.54413 q^{59} +(-2.16287 + 4.65047i) q^{60} -7.15370 q^{61} +(1.03321 - 1.57092i) 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} +(9.08706 + 3.61010i) q^{68} +6.81958i q^{69} +(10.2982 - 1.51904i) q^{70} +12.5023i q^{71} +(-4.69282 - 0.827498i) 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} +(4.97079 + 3.26936i) q^{78} -2.50310 q^{79} +(6.14444 + 6.49968i) q^{80} +1.10731 q^{81} +(9.17338 + 6.03345i) 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} +(-2.78545 - 0.491167i) q^{88} +14.4239i q^{89} +(4.27665 + 3.17717i) q^{90} -12.0754i q^{91} +(11.0525 + 4.39094i) 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} +(-2.98102 + 4.53240i) 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} + 2 q^{8} - 6 q^{10} + 8 q^{12} + 6 q^{13} + 20 q^{14} - 8 q^{15} + 8 q^{16} - 14 q^{17} - 6 q^{18} - 4 q^{19} + 8 q^{20} - 16 q^{21} - 2 q^{22}+ \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 + 2 * q^8 - 6 * q^10 + 8 * q^12 + 6 * q^13 + 20 * q^14 - 8 * q^15 + 8 * q^16 - 14 * q^17 - 6 * 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 + 8 * q^28 - 24 * q^30 - 38 * q^32 + 4 * q^33 + 52 * q^34 + 10 * q^35 - 4 * q^36 + 20 * q^37 - 48 * q^38 - 32 * q^39 + 46 * q^40 + 12 * q^41 + 32 * q^42 - 2 * q^43 - 10 * q^45 + 4 * q^46 + 44 * q^47 + 44 * q^48 - 18 * q^50 - 52 * q^52 - 28 * q^53 + 40 * q^54 + 2 * q^55 + 4 * q^56 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 32 * q^60 - 12 * q^61 + 20 * q^62 + 10 * q^63 - 28 * q^64 - 30 * q^65 - 16 * q^67 + 68 * q^68 - 40 * q^70 - 38 * q^72 + 22 * q^73 + 20 * q^74 + 56 * q^75 + 4 * q^76 - 2 * q^77 - 40 * q^78 + 20 * q^79 + 12 * q^80 + 12 * q^81 + 12 * q^82 - 2 * q^83 - 120 * q^84 - 14 * q^85 - 20 * q^86 + 48 * q^87 + 14 * q^88 - 10 * q^90 + 4 * q^92 - 20 * q^93 + 20 * q^94 - 92 * q^95 + 40 * q^96 + 16 * q^97 - 82 * 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 $

$2$	1.18156	+	0.777125i	0.835487	+	0.549511i
$2$	1.18156	+	0.777125i	0.835487	+	0.549511i
$3$	−0.810938	+	0.810938i	−0.468195	+	0.468195i	−0.901329	−	0.433134i	$-0.857408\pi$
$3$	−0.810938	+	0.810938i	−0.468195	+	0.468195i	0.433134	+	0.901329i	$0.357408\pi$
$4$	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	0.993511	−	0.113740i	$-0.0362830\pi$
$7$	2.32765	+	2.32765i	0.879771	+	0.879771i	−0.113740	+	0.993511i	$0.536283\pi$
$8$	−0.491167	+	2.78545i	−0.173654	+	0.984807i
$9$			1.68476i			0.561586i
$10$	1.88583	−	2.53843i	0.596351	−	0.802723i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	−2.13162	−	0.846848i	−0.615346	−	0.244464i
$13$	−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	$0.0479938\pi$
$18$	−1.30927	+	1.99064i	−0.308598	+	0.469198i
$19$	−2.29700			−0.526968			−0.263484	−	0.964664i	$-0.584872\pi$
$19$	−2.29700			−0.526968			−0.263484	+	0.964664i	$0.584872\pi$
$20$	4.20090	−	1.53378i	0.939349	−	0.342963i
$21$	−3.77517			−0.823809
$22$	−0.777125	+	1.18156i	−0.165684	+	0.251909i
$23$	4.20475	−	4.20475i	0.876750	−	0.876750i	−0.116447	−	0.993197i	$-0.537150\pi$
$23$	4.20475	−	4.20475i	0.876750	−	0.876750i	0.993197	+	0.116447i	$0.0371504\pi$
$24$	−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
$28$	−2.43073	+	6.11845i	−0.459365	+	1.15628i
$29$		−	0.133535i		−	0.0247969i	−0.999923	−	0.0123984i	$-0.996053\pi$
$29$		−	0.133535i		−	0.0247969i	0.999923	−	0.0123984i	$-0.00394665\pi$
$30$	0.529223	+	3.58780i	0.0966224	+	0.655040i
$31$		−	1.32953i		−	0.238791i	−0.992847	−	0.119395i	$-0.961904\pi$
$31$		−	1.32953i		−	0.238791i	0.992847	−	0.119395i	$-0.0380956\pi$
$32$	−5.50439	+	1.30451i	−0.973047	+	0.230607i
$33$	−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	$-0.0680114\pi$
$38$	−2.71404	−	1.78506i	−0.440275	−	0.289574i
$39$	4.20699			0.673657
$40$	6.15553	+	1.45237i	0.973275	+	0.229641i
$41$	7.76381			1.21250			0.606252	−	0.795273i	$-0.292672\pi$
$41$	7.76381			1.21250			0.606252	+	0.795273i	$0.292672\pi$
$42$	−4.46057	−	2.93378i	−0.688282	−	0.452692i
$43$	−5.00150	+	5.00150i	−0.762722	+	0.762722i	−0.976814	−	0.214092i	$-0.931321\pi$
$43$	−5.00150	+	5.00150i	−0.762722	+	0.762722i	0.214092	+	0.976814i	$0.431321\pi$
$44$	−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	0.0950453	−	0.995473i	$-0.469700\pi$
$47$	−6.17302	−	6.17302i	−0.900428	−	0.900428i	−0.995473	+	0.0950453i	$0.969700\pi$
$48$	−0.133387	−	4.58542i	−0.0192528	−	0.661848i
$49$			3.83595i			0.547993i
$50$	−5.42589	−	4.53428i	−0.767337	−	0.641244i
$51$			5.60684i			0.785115i
$52$	2.70877	−	6.81830i	0.375638	−	0.945528i
$53$	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
$58$	0.103774	−	0.157780i	0.0136261	−	0.0207175i
$59$	−6.54413			−0.851973			−0.425987	−	0.904729i	$-0.640073\pi$
$59$	−6.54413			−0.851973			−0.425987	+	0.904729i	$0.640073\pi$
$60$	−2.16287	+	4.65047i	−0.279225	+	0.600372i
$61$	−7.15370			−0.915937			−0.457969	−	0.888968i	$-0.651423\pi$
$61$	−7.15370			−0.915937			−0.457969	+	0.888968i	$0.651423\pi$
$62$	1.03321	−	1.57092i	0.131218	−	0.199507i
$63$	−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	0.435383	−	0.900245i	$-0.356613\pi$
$67$	−3.80506	−	3.80506i	−0.464862	−	0.464862i	−0.900245	+	0.435383i	$0.856613\pi$
$68$	9.08706	+	3.61010i	1.10197	+	0.437788i
$69$			6.81958i			0.820981i
$70$	10.2982	−	1.51904i	1.23087	−	0.181560i
$71$			12.5023i			1.48375i	0.670539	+	0.741875i	$0.266063\pi$
$71$			12.5023i			1.48375i	−0.670539	+	0.741875i	$0.733937\pi$
$72$	−4.69282	−	0.827498i	−0.553054	−	0.0975216i
$73$	−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
$78$	4.97079	+	3.26936i	0.562832	+	0.370182i
$79$	−2.50310			−0.281621			−0.140810	−	0.990037i	$-0.544971\pi$
$79$	−2.50310			−0.281621			−0.140810	+	0.990037i	$0.544971\pi$
$80$	6.14444	+	6.49968i	0.686969	+	0.726687i
$81$	1.10731			0.123034
$82$	9.17338	+	6.03345i	1.01303	+	0.666283i
$83$	6.44397	−	6.44397i	0.707318	−	0.707318i	−0.258652	−	0.965970i	$-0.583278\pi$
$83$	6.44397	−	6.44397i	0.707318	−	0.707318i	0.965970	+	0.258652i	$0.0832784\pi$
$84$	−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
$88$	−2.78545	−	0.491167i	−0.296930	−	0.0523586i
$89$			14.4239i			1.52893i	0.644663	+	0.764466i	$0.276997\pi$
$89$			14.4239i			1.52893i	−0.644663	+	0.764466i	$0.723003\pi$
$90$	4.27665	+	3.17717i	0.450799	+	0.334903i
$91$		−	12.0754i		−	1.26585i
$92$	11.0525	+	4.39094i	1.15231	+	0.457788i
$93$	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	$0.479101\pi$
$98$	−2.98102	+	4.53240i	−0.301128	+	0.457841i
$99$	−1.68476			−0.169325
$100$	−2.88730	−	9.57411i	−0.288730	−	0.957411i
$101$	10.1986			1.01480			0.507398	−	0.861712i	$-0.330607\pi$
$101$	10.1986			1.01480			0.507398	+	0.861712i	$0.330607\pi$
$102$	−4.35722	+	6.62480i	−0.431429	+	0.655953i
$103$	−1.48098	+	1.48098i	−0.145925	+	0.145925i	−0.776295	−	0.630370i	$-0.782903\pi$
$103$	−1.48098	+	1.48098i	−0.145925	+	0.145925i	0.630370	+	0.776295i	$0.282903\pi$
$104$	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	0.703493	−	0.710702i	$-0.251623\pi$
$107$	−0.0745711	−	0.0745711i	−0.00720906	−	0.00720906i	−0.710702	+	0.703493i	$0.751623\pi$
$108$	3.96728	−	9.98613i	0.381752	−	0.960916i
$109$			7.33400i			0.702470i	0.936287	+	0.351235i	$0.114238\pi$
$109$			7.33400i			0.702470i	−0.936287	+	0.351235i	$0.885762\pi$
$110$	2.53843	+	1.88583i	0.242030	+	0.179807i
$111$			11.7330i			1.11365i
$112$	−13.1616	+	0.382865i	−1.24366	+	0.0361774i
$113$	−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
$118$	−7.73226	−	5.08561i	−0.711813	−	0.468168i
$119$	16.0935			1.47528
$120$	−6.16954	+	3.81397i	−0.563200	+	0.348166i
$121$	−1.00000			−0.0909091
$122$	−8.45250	−	5.55932i	−0.765254	−	0.503317i
$123$	−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	$0.0827713\pi$
$127$	13.7881	+	13.7881i	1.22349	+	1.22349i	0.257113	+	0.966381i	$0.417229\pi$
$128$	−6.75596	−	9.07508i	−0.597148	−	0.802131i
$129$		−	8.11182i		−	0.714206i
$130$	−11.4761	+	1.69280i	−1.00652	+	0.148468i
$131$		−	3.24328i		−	0.283366i	−0.989912	−	0.141683i	$-0.954749\pi$
$131$		−	3.24328i		−	0.283366i	0.989912	−	0.141683i	$-0.0452514\pi$
$132$	0.846848	−	2.13162i	0.0737087	−	0.185534i
$133$	−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	$0.208454\pi$
$138$	−5.29967	+	8.05772i	−0.451138	+	0.685918i
$139$	17.1989			1.45879			0.729395	−	0.684093i	$-0.239802\pi$
$139$	17.1989			1.45879			0.729395	+	0.684093i	$0.239802\pi$
$140$	13.3483	+	6.20813i	1.12814	+	0.524682i
$141$	10.0119			0.843152
$142$	−9.71585	+	14.7722i	−0.815336	+	1.23965i
$143$	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
$148$	19.0159	+	7.55460i	1.56309	+	0.620984i
$149$			10.8861i			0.891821i	0.895078	+	0.445910i	$0.147120\pi$
$149$			10.8861i			0.891821i	−0.895078	+	0.445910i	$0.852880\pi$
$150$	8.07708	−	0.723045i	0.659491	−	0.0590364i
$151$		−	2.79477i		−	0.227435i	−0.993513	−	0.113717i	$-0.963724\pi$
$151$		−	2.79477i		−	0.227435i	0.993513	−	0.113717i	$-0.0362759\pi$
$152$	1.12821	−	6.39819i	0.0915099	−	0.518962i
$153$	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	$0.393522\pi$
$158$	−2.95756	−	1.94522i	−0.235291	−	0.154754i
$159$	−6.38585			−0.506431
$160$	2.20893	+	12.4547i	0.174631	+	0.984634i
$161$	19.5744			1.54268
$162$	1.30835	+	0.860517i	0.102794	+	0.0676086i
$163$	3.44943	−	3.44943i	0.270180	−	0.270180i	−0.558993	−	0.829173i	$-0.688812\pi$
$163$	3.44943	−	3.44943i	0.270180	−	0.270180i	0.829173	+	0.558993i	$0.188812\pi$
$164$	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	$0.00417773\pi$
$167$	13.0913	+	13.0913i	1.01304	+	1.01304i	0.0131243	+	0.999914i	$0.495822\pi$
$168$	1.85424	−	10.5156i	0.143058	−	0.811293i
$169$			0.456653i			0.0351272i
$170$	−2.25606	−	15.2947i	−0.173032	−	1.17305i
$171$		−	3.86989i		−	0.295938i
$172$	−13.1469	−	5.22298i	−1.00244	−	0.398249i
$173$	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
$178$	−11.2092	+	17.0427i	−0.840165	+	1.27740i
$179$	−21.7615			−1.62653			−0.813267	−	0.581891i	$-0.802313\pi$
$179$	−21.7615			−1.62653			−0.813267	+	0.581891i	$0.802313\pi$
$180$	2.58405	+	7.07750i	0.192604	+	0.527525i
$181$	0.340494			0.0253087			0.0126544	−	0.999920i	$-0.495972\pi$
$181$	0.340494			0.0253087			0.0126544	+	0.999920i	$0.495972\pi$
$182$	9.38411	−	14.2678i	0.695597	−	1.05760i
$183$	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
$188$	6.44638	−	16.2263i	0.470150	−	1.18343i
$189$		−	17.6858i		−	1.28645i
$190$	−4.33175	+	5.83078i	−0.314258	+	0.423009i
$191$		−	18.7025i		−	1.35327i	−0.736320	−	0.676634i	$-0.763438\pi$
$191$		−	18.7025i		−	1.35327i	0.736320	−	0.676634i	$-0.236562\pi$
$192$	8.31516	−	3.87731i	0.600095	−	0.279821i
$193$	−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	$0.0748467\pi$
$198$	−1.99064	−	1.30927i	−0.141469	−	0.0930457i
$199$	−17.3630			−1.23083			−0.615415	−	0.788203i	$-0.711012\pi$
$199$	−17.3630			−1.23083			−0.615415	+	0.788203i	$0.711012\pi$
$200$	4.02877	−	13.5561i	0.284877	−	0.958564i
$201$	6.17134			0.435293
$202$	12.0502	+	7.92557i	0.847848	+	0.557641i
$203$	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
$208$	14.6671	−	0.426659i	1.01698	−	0.0295835i
$209$		−	2.29700i		−	0.158887i
$210$	−7.11932	+	9.58302i	−0.491280	+	0.661291i
$211$		−	4.77702i		−	0.328863i	−0.986388	−	0.164432i	$-0.947421\pi$
$211$		−	4.77702i		−	0.328863i	0.986388	−	0.164432i	$-0.0525790\pi$
$212$	−4.11168	+	10.3496i	−0.282391	+	0.710813i
$213$	−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
$218$	−5.69944	+	8.66554i	−0.386015	+	0.586905i
$219$	2.35959			0.159446
$220$	1.53378	+	4.20090i	0.103407	+	0.283224i
$221$	−17.9343			−1.20639
$222$	−9.11805	+	13.8633i	−0.611963	+	0.930441i
$223$	−13.3807	+	13.3807i	−0.896036	+	0.896036i	−0.995083	−	0.0990464i	$-0.968421\pi$
$223$	−13.3807	+	13.3807i	−0.896036	+	0.896036i	0.0990464	+	0.995083i	$0.468421\pi$
$224$	−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	0.234827	−	0.972037i	$-0.424548\pi$
$227$	−11.1072	−	11.1072i	−0.737210	−	0.737210i	−0.972037	+	0.234827i	$0.924548\pi$
$228$	4.89633	+	1.94521i	0.324268	+	0.128825i
$229$			0.0910816i			0.00601884i	0.999995	+	0.00300942i	$0.000957930\pi$
$229$			0.0910816i			0.00601884i	−0.999995	+	0.00300942i	$0.999042\pi$
$230$	−2.74404	−	18.6029i	−0.180937	−	1.22664i
$231$		−	3.77517i		−	0.248388i
$232$	0.371956	+	0.0655881i	0.0244201	+	0.00430607i
$233$	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
$238$	19.0153	+	12.5066i	1.23258	+	0.810684i
$239$	−15.5711			−1.00721			−0.503606	−	0.863933i	$-0.667994\pi$
$239$	−15.5711			−1.00721			−0.503606	+	0.863933i	$0.667994\pi$
$240$	−10.2536	−	0.288085i	−0.661867	−	0.0185958i
$241$	−15.7734			−1.01605			−0.508027	−	0.861341i	$-0.669625\pi$
$241$	−15.7734			−1.01605			−0.508027	+	0.861341i	$0.669625\pi$
$242$	−1.18156	−	0.777125i	−0.0759533	−	0.0499555i
$243$	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
$248$	3.70335	+	0.653022i	0.235163	+	0.0414669i
$249$			10.4513i			0.662326i
$250$	−10.8156	+	11.5335i	−0.684041	+	0.729444i
$251$			16.9874i			1.07223i	0.844144	+	0.536117i	$0.180109\pi$
$251$			16.9874i			1.07223i	−0.844144	+	0.536117i	$0.819891\pi$
$252$	−10.3081	−	4.09519i	−0.649350	−	0.257973i
$253$	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	$-0.0136159\pi$
$258$	6.30390	−	9.58457i	0.392464	−	0.596709i
$259$	33.6777			2.09263
$260$	−14.8752	−	6.91824i	−0.922520	−	0.429051i
$261$	0.224975			0.0139256
$262$	2.52043	−	3.83212i	0.155713	−	0.236749i
$263$	18.1862	−	18.1862i	1.12141	−	1.12141i	0.129882	−	0.991530i	$-0.458540\pi$
$263$	18.1862	−	18.1862i	1.12141	−	1.12141i	0.991530	−	0.129882i	$-0.0414597\pi$
$264$	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
$268$	3.97356	−	10.0019i	0.242724	−	0.610966i
$269$		−	8.30765i		−	0.506526i	−0.967397	−	0.253263i	$-0.918496\pi$
$269$		−	8.30765i		−	0.506526i	0.967397	−	0.253263i	$-0.0815038\pi$
$270$	−16.8080	+	2.47928i	−1.02290	+	0.150884i
$271$		−	8.06316i		−	0.489802i	−0.969548	−	0.244901i	$-0.921245\pi$
$271$		−	8.06316i		−	0.489802i	0.969548	−	0.244901i	$-0.0787554\pi$
$272$	0.568628	+	19.5475i	0.0344781	+	1.18524i
$273$	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	$0.995486\pi$
$278$	20.3214	+	13.3657i	1.21880	+	0.801620i
$279$	2.23994			0.134102
$280$	10.9473	+	17.7086i	0.654228	+	1.05829i
$281$	13.1802			0.786267			0.393133	−	0.919481i	$-0.371391\pi$
$281$	13.1802			0.786267			0.393133	+	0.919481i	$0.371391\pi$
$282$	11.8296	+	7.78048i	0.704442	+	0.463321i
$283$	−5.50850	+	5.50850i	−0.327446	+	0.327446i	−0.851615	−	0.524169i	$-0.824376\pi$
$283$	−5.50850	+	5.50850i	−0.327446	+	0.327446i	0.524169	+	0.851615i	$0.324376\pi$
$284$	−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
$288$	−2.19778	−	9.27356i	−0.129506	−	0.546450i
$289$		−	6.90184i		−	0.405991i
$290$	−0.338971	−	0.251825i	−0.0199050	−	0.0147877i
$291$		−	14.8912i		−	0.872936i
$292$	1.51928	−	3.82420i	0.0889089	−	0.223795i
$293$	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
$298$	−8.45983	+	12.8625i	−0.490065	+	0.745105i
$299$	−21.8134			−1.26150
$300$	10.1054	+	5.42259i	0.583437	+	0.313073i
$301$	−23.2835			−1.34204
$302$	2.17188	−	3.30218i	0.124978	−	0.190019i
$303$	−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	0.528618	−	0.848860i	$-0.322710\pi$
$307$	−5.61109	−	5.61109i	−0.320242	−	0.320242i	−0.848860	+	0.528618i	$0.822710\pi$
$308$	−6.11845	−	2.43073i	−0.348631	−	0.138504i
$309$		−	2.40196i		−	0.136643i
$310$	−3.37493	−	2.50727i	−0.191683	−	0.142403i
$311$		−	5.50196i		−	0.311987i	−0.987758	−	0.155994i	$-0.950142\pi$
$311$		−	5.50196i		−	0.311987i	0.987758	−	0.155994i	$-0.0498579\pi$
$312$	−2.06633	+	11.7184i	−0.116983	+	0.663422i
$313$	−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	$0.376667\pi$
$318$	−7.54524	−	4.96261i	−0.423116	−	0.278289i
$319$	0.133535			0.00747654
$320$	−7.06892	+	16.4326i	−0.395165	+	0.918610i
$321$	0.120945			0.00675049
$322$	23.1283	+	15.2118i	1.28889	+	0.847718i
$323$	−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
$328$	−3.81333	+	21.6257i	−0.210556	+	1.19408i
$329$		−	28.7373i		−	1.58434i
$330$	−3.58780	+	0.529223i	−0.197502	+	0.0291328i
$331$			7.54531i			0.414728i	0.978264	+	0.207364i	$0.0664884\pi$
$331$			7.54531i			0.414728i	−0.978264	+	0.207364i	$0.933512\pi$
$332$	16.9386	+	6.72933i	0.929624	+	0.369320i
$333$	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	$0.990237\pi$
$338$	−0.354877	+	0.539561i	−0.0193027	+	0.0293483i
$339$	20.4241			1.10929
$340$	9.22025	−	19.8248i	0.500038	−	1.07515i
$341$	1.32953			0.0719981
$342$	3.00739	−	4.57250i	0.162621	−	0.247252i
$343$	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	0.783012	−	0.622007i	$-0.213682\pi$
$347$	2.99920	+	2.99920i	0.161005	+	0.161005i	−0.622007	+	0.783012i	$0.713682\pi$
$348$	−0.113084	+	0.284647i	−0.00606195	+	0.0152587i
$349$		−	15.5193i		−	0.830727i	−0.909655	−	0.415364i	$-0.863654\pi$
$349$		−	15.5193i		−	0.830727i	0.909655	−	0.415364i	$-0.136346\pi$
$350$	−2.07537	−	23.1838i	−0.110933	−	1.23923i
$351$			19.7087i			1.05197i
$352$	−1.30451	−	5.50439i	−0.0695305	−	0.293385i
$353$	−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
$358$	−25.7125	−	16.9114i	−1.35895	−	0.893797i
$359$	14.7346			0.777662			0.388831	−	0.921309i	$-0.372879\pi$
$359$	14.7346			0.777662			0.388831	+	0.921309i	$0.372879\pi$
$360$	−2.44690	+	10.3706i	−0.128963	+	0.546578i
$361$	−13.7238			−0.722305
$362$	0.402313	+	0.264607i	0.0211451	+	0.0139074i
$363$	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	0.808706	−	0.588213i	$-0.200168\pi$
$367$	4.22405	+	4.22405i	0.220494	+	0.220494i	−0.588213	+	0.808706i	$0.700168\pi$
$368$	0.691620	+	23.7756i	0.0360532	+	1.23939i
$369$			13.0802i			0.680926i
$370$	−4.72111	−	32.0062i	−0.245439	−	1.66392i
$371$			18.3295i			0.951618i
$372$	−1.12591	+	2.83406i	−0.0583758	+	0.146939i
$373$	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
$378$	13.7440	−	20.8967i	0.706917	−	1.07481i
$379$	−30.3260			−1.55774			−0.778871	−	0.627184i	$-0.784207\pi$
$379$	−30.3260			−1.55774			−0.778871	+	0.627184i	$0.784207\pi$
$380$	−9.64946	+	3.52309i	−0.495007	+	0.180731i
$381$	−22.3626			−1.14567
$382$	14.5342	−	22.0981i	0.743635	−	1.13064i
$383$	−0.188339	+	0.188339i	−0.00962368	+	0.00962368i	−0.711902	−	0.702279i	$-0.752166\pi$
$383$	−0.188339	+	0.188339i	−0.00962368	+	0.00962368i	0.702279	+	0.711902i	$0.252166\pi$
$384$	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
$388$	−24.1343	−	9.58803i	−1.22523	−	0.486759i
$389$			2.57939i			0.130780i	0.997860	+	0.0653900i	$0.0208291\pi$
$389$			2.57939i			0.130780i	−0.997860	+	0.0653900i	$0.979171\pi$
$390$	7.93366	−	10.6792i	0.401736	−	0.540760i
$391$		−	29.0717i		−	1.47022i
$392$	−10.6849	−	1.88409i	−0.539668	−	0.0951611i
$393$	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	$0.226069\pi$
$398$	−20.5154	−	13.4932i	−1.02834	−	0.676354i
$399$	8.67156			0.434121
$400$	15.2950	−	12.8865i	0.764752	−	0.644325i
$401$	5.11905			0.255633			0.127817	−	0.991798i	$-0.459203\pi$
$401$	5.11905			0.255633			0.127817	+	0.991798i	$0.459203\pi$
$402$	7.29179	+	4.79590i	0.363681	+	0.239198i
$403$	−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
$408$	−15.6176	−	2.75390i	−0.773186	−	0.136338i
$409$			23.3497i			1.15457i	0.816542	+	0.577285i	$0.195888\pi$
$409$			23.3497i			1.15457i	−0.816542	+	0.577285i	$0.804112\pi$
$410$	14.6412	−	19.7079i	0.723078	−	0.973305i
$411$			3.49412i			0.172352i
$412$	−3.89288	−	1.54656i	−0.191788	−	0.0761934i
$413$	−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
$418$	1.78506	−	2.71404i	0.0873100	−	0.132748i
$419$	11.0115			0.537948			0.268974	−	0.963147i	$-0.413315\pi$
$419$	11.0115			0.537948			0.268974	+	0.963147i	$0.413315\pi$
$420$	−15.8591	+	5.79027i	−0.773844	+	0.282536i
$421$	26.1518			1.27456			0.637281	−	0.770631i	$-0.280059\pi$
$421$	26.1518			1.27456			0.637281	+	0.770631i	$0.280059\pi$
$422$	3.71234	−	5.64432i	0.180714	−	0.274761i
$423$	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
$428$	0.0778733	−	0.196017i	0.00376415	−	0.00947482i
$429$			4.20699i			0.203115i
$430$	3.26401	+	22.1280i	0.157405	+	1.06711i
$431$			8.71172i			0.419629i	0.977741	+	0.209814i	$0.0672860\pi$
$431$			8.71172i			0.419629i	−0.977741	+	0.209814i	$0.932714\pi$
$432$	21.4816	−	0.624888i	1.03353	−	0.0300649i
$433$	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
$438$	2.78799	+	1.83370i	0.133215	+	0.0876174i
$439$	2.63364			0.125697			0.0628484	−	0.998023i	$-0.479982\pi$
$439$	2.63364			0.125697			0.0628484	+	0.998023i	$0.479982\pi$
$440$	−1.45237	+	6.15553i	−0.0692393	+	0.293454i
$441$	−6.46266			−0.307746
$442$	−21.1904	−	13.9372i	−1.00792	−	0.662925i
$443$	−16.1479	+	16.1479i	−0.767209	+	0.767209i	−0.977614	−	0.210405i	$-0.932522\pi$
$443$	−16.1479	+	16.1479i	−0.767209	+	0.767209i	0.210405	+	0.977614i	$0.432522\pi$
$444$	−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
$448$	−11.1291	−	23.8672i	−0.525802	−	1.12762i
$449$		−	7.50030i		−	0.353961i	−0.984214	−	0.176981i	$-0.943367\pi$
$449$		−	7.50030i		−	0.353961i	0.984214	−	0.176981i	$-0.0566330\pi$
$450$	7.63917	−	9.14132i	0.360114	−	0.430926i
$451$			7.76381i			0.365584i
$452$	13.1506	−	33.1016i	0.618550	−	1.55697i
$453$	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	$0.0495554\pi$
$458$	−0.0707818	+	0.107618i	−0.00330742	+	0.00502866i
$459$	−26.2667			−1.22602
$460$	11.2145	−	24.1129i	0.522881	−	1.12427i
$461$	17.4216			0.811404			0.405702	−	0.914005i	$-0.367027\pi$
$461$	17.4216			0.811404			0.405702	+	0.914005i	$0.367027\pi$
$462$	2.93378	−	4.46057i	0.136492	−	0.207525i
$463$	5.98643	−	5.98643i	0.278213	−	0.278213i	−0.554182	−	0.832395i	$-0.686969\pi$
$463$	5.98643	−	5.98643i	0.278213	−	0.278213i	0.832395	+	0.554182i	$0.186969\pi$
$464$	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	0.368370	−	0.929679i	$-0.379916\pi$
$467$	−12.1300	−	12.1300i	−0.561309	−	0.561309i	−0.929679	+	0.368370i	$0.879916\pi$
$468$	11.4872	+	4.56362i	0.530996	+	0.210953i
$469$		−	17.7137i		−	0.817945i
$470$	−27.3111	+	4.02855i	−1.25977	+	0.185823i
$471$		−	12.5237i		−	0.577063i
$472$	3.21426	−	18.2284i	0.147948	−	0.839029i
$473$	−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
$478$	−18.3982	−	12.1007i	−0.841513	−	0.553474i
$479$	−31.6336			−1.44537			−0.722687	−	0.691175i	$-0.757093\pi$
$479$	−31.6336			−1.44537			−0.722687	+	0.691175i	$0.757093\pi$
$480$	−11.8913	−	8.30872i	−0.542762	−	0.379239i
$481$	−37.5298			−1.71121
$482$	−18.6372	−	12.2579i	−0.848900	−	0.558332i
$483$	−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	0.553745	−	0.832686i	$-0.313198\pi$
$487$	−6.15570	−	6.15570i	−0.278941	−	0.278941i	−0.832686	+	0.553745i	$0.813198\pi$
$488$	3.51366	−	19.9263i	0.159056	−	0.902021i
$489$			5.59454i			0.252994i
$490$	9.73732	+	7.23395i	0.439887	+	0.326797i
$491$		−	7.77056i		−	0.350680i	−0.984508	−	0.175340i	$-0.943897\pi$
$491$		−	7.77056i		−	0.350680i	0.984508	−	0.175340i	$-0.0561025\pi$
$492$	−16.5495	−	6.57477i	−0.746109	−	0.296414i
$493$	−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
$498$	−8.12199	+	12.3488i	−0.363955	+	0.553365i
$499$	36.5174			1.63474			0.817371	−	0.576111i	$-0.195431\pi$
$499$	36.5174			1.63474			0.817371	+	0.576111i	$0.195431\pi$
$500$	−21.7423	+	5.22240i	−0.972344	+	0.233553i
$501$	−21.2325			−0.948599
$502$	−13.2013	+	20.0715i	−0.589203	+	0.895837i
$503$	22.2472	−	22.2472i	0.991952	−	0.991952i	−0.00801619	−	0.999968i	$-0.502552\pi$
$503$	22.2472	−	22.2472i	0.991952	−	0.991952i	0.999968	+	0.00801619i	$0.00255166\pi$
$504$	−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
$508$	−14.3987	+	36.2432i	−0.638837	+	1.60803i
$509$		−	24.6278i		−	1.09161i	−0.837913	−	0.545804i	$-0.816224\pi$
$509$		−	24.6278i		−	1.09161i	0.837913	−	0.545804i	$-0.183776\pi$
$510$	14.2326	+	10.5735i	0.630230	+	0.468204i
$511$		−	6.77278i		−	0.299610i
$512$	11.3140	−	19.5957i	0.500015	−	0.866017i
$513$	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
$518$	39.7921	+	26.1718i	1.74836	+	1.14992i
$519$	−13.6763			−0.600324
$520$	−12.1995	−	19.7342i	−0.534985	−	0.865401i
$521$	−19.3636			−0.848335			−0.424167	−	0.905584i	$-0.639433\pi$
$521$	−19.3636			−0.848335			−0.424167	+	0.905584i	$0.639433\pi$
$522$	0.265821	+	0.174834i	0.0116346	+	0.00765226i
$523$	10.3463	−	10.3463i	0.452413	−	0.452413i	−0.443742	−	0.896155i	$-0.646349\pi$
$523$	10.3463	−	10.3463i	0.452413	−	0.452413i	0.896155	+	0.443742i	$0.146349\pi$
$524$	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
$528$	4.58542	−	0.133387i	0.199555	−	0.00580494i
$529$		−	12.3598i		−	0.537382i
$530$	17.4198	−	2.56952i	0.756666	−	0.111613i
$531$		−	11.0253i		−	0.478457i
$532$	5.58338	−	14.0541i	0.242070	−	0.609321i
$533$	−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
$538$	6.45608	−	9.81596i	0.278341	−	0.423196i
$539$	−3.83595			−0.165226
$540$	−21.7863	−	10.1325i	−0.937534	−	0.436034i
$541$	42.7032			1.83596			0.917978	−	0.396632i	$-0.129821\pi$
$541$	42.7032			1.83596			0.917978	+	0.396632i	$0.129821\pi$
$542$	6.26608	−	9.52708i	0.269151	−	0.409223i
$543$	−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	$0.120803\pi$
$547$	30.3884	+	30.3884i	1.29931	+	1.29931i	0.370468	+	0.928845i	$0.379197\pi$
$548$	5.66294	+	2.24977i	0.241909	+	0.0961053i
$549$		−	12.0523i		−	0.514378i
$550$	4.53428	−	5.42589i	0.193342	−	0.231361i
$551$			0.306731i			0.0130672i
$552$	−18.9956	−	3.34955i	−0.808507	−	0.142566i
$553$	−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	$0.252640\pi$
$558$	2.64662	+	1.74071i	0.112040	+	0.0736903i
$559$	25.9468			1.09743
$560$	−0.826896	+	29.4312i	−0.0349427	+	1.24369i
$561$	−5.60684			−0.236721
$562$	15.5732	+	10.2427i	0.656916	+	0.432062i
$563$	−2.95662	+	2.95662i	−0.124607	+	0.124607i	−0.766660	−	0.642053i	$-0.778083\pi$
$563$	−2.95662	+	2.95662i	−0.124607	+	0.124607i	0.642053	+	0.766660i	$0.278083\pi$
$564$	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
$568$	−34.8246	−	6.14071i	−1.46121	−	0.257659i
$569$			12.9492i			0.542860i	0.962458	+	0.271430i	$0.0874965\pi$
$569$			12.9492i			0.542860i	−0.962458	+	0.271430i	$0.912504\pi$
$570$	−1.21562	−	8.24118i	−0.0509169	−	0.345185i
$571$			39.9223i			1.67069i	0.549722	+	0.835347i	$0.314733\pi$
$571$			39.9223i			1.67069i	−0.549722	+	0.835347i	$0.685267\pi$
$572$	6.81830	+	2.70877i	0.285087	+	0.113259i
$573$	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	$0.227615\pi$
$578$	5.36359	−	8.15492i	0.223096	−	0.339200i
$579$	14.6229			0.607708
$580$	−0.204814	−	0.560968i	−0.00850442	−	0.0232929i
$581$	29.9987			1.24456
$582$	11.5723	−	17.5948i	0.479688	−	0.729327i
$583$	−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	$-0.936972\pi$
$587$	−28.5208	−	28.5208i	−1.17718	−	1.17718i	−0.196717	−	0.980460i	$-0.563028\pi$
$588$	3.24847	−	8.17680i	0.133965	−	0.337206i
$589$			3.05393i			0.125835i
$590$	−12.3411	+	16.6119i	−0.508076	+	0.683899i
$591$			16.8342i			0.692466i
$592$	1.18993	+	40.9058i	0.0489057	+	1.68122i
$593$	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
$598$	−25.7738	−	16.9517i	−1.05397	−	0.693208i
$599$	34.2029			1.39749			0.698746	−	0.715369i	$-0.253742\pi$
$599$	34.2029			1.39749			0.698746	+	0.715369i	$0.253742\pi$
$600$	7.72611	+	14.2603i	0.315417	+	0.582173i
$601$	−5.38036			−0.219469			−0.109735	−	0.993961i	$-0.535000\pi$
$601$	−5.38036			−0.219469			−0.109735	+	0.993961i	$0.535000\pi$
$602$	−27.5108	−	18.0942i	−1.12126	−	0.737466i
$603$	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	0.577610	−	0.816313i	$-0.303985\pi$
$607$	−5.88099	−	5.88099i	−0.238702	−	0.238702i	−0.816313	+	0.577610i	$0.803985\pi$
$608$	12.6436	−	2.99646i	0.512765	−	0.121522i
$609$			0.504118i			0.0204279i
$610$	−13.4907	+	18.1592i	−0.546221	+	0.735244i
$611$			32.0244i			1.29557i
$612$	−6.08214	+	15.3095i	−0.245856	+	0.618850i
$613$	−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	$0.271142\pi$
$618$	1.86662	−	2.83805i	0.0750866	−	0.114163i
$619$	45.2718			1.81963			0.909813	−	0.415019i	$-0.136225\pi$
$619$	45.2718			1.81963			0.909813	+	0.415019i	$0.136225\pi$
$620$	−2.03921	−	5.58522i	−0.0818965	−	0.224308i
$621$	−31.9481			−1.28203
$622$	4.27571	−	6.50087i	0.171440	−	0.260661i
$623$	−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
$628$	−20.2973	−	8.06369i	−0.809951	−	0.321776i
$629$		−	50.0177i		−	1.99434i
$630$	2.55922	+	17.3499i	0.101962	+	0.691237i
$631$		−	20.1928i		−	0.803862i	−0.915670	−	0.401931i	$-0.868339\pi$
$631$		−	20.1928i		−	0.803862i	0.915670	−	0.401931i	$-0.131661\pi$
$632$	1.22944	−	6.97227i	0.0489045	−	0.277342i
$633$	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
$638$	0.157780	+	0.103774i	0.00624655	+	0.00410844i
$639$	−21.0634			−0.833254
$640$	−21.1225	+	13.9226i	−0.834941	+	0.550340i
$641$	10.3412			0.408453			0.204227	−	0.978924i	$-0.434532\pi$
$641$	10.3412			0.408453			0.204227	+	0.978924i	$0.434532\pi$
$642$	0.142903	+	0.0939894i	0.00563995	+	0.00370947i
$643$	−17.8956	+	17.8956i	−0.705734	+	0.705734i	−0.965635	−	0.259901i	$-0.916310\pi$
$643$	−17.8956	+	17.8956i	−0.705734	+	0.705734i	0.259901	+	0.965635i	$0.416310\pi$
$644$	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	$-0.993286\pi$
$647$	−25.9670	−	25.9670i	−1.02087	−	1.02087i	−0.0210925	−	0.999778i	$-0.506714\pi$
$648$	−0.543873	+	3.08436i	−0.0213654	+	0.121165i
$649$		−	6.54413i		−	0.256880i
$650$	2.31276	+	25.8357i	0.0907141	+	1.01336i
$651$			5.01920i			0.196718i
$652$	9.06713	+	3.60218i	0.355096	+	0.141072i
$653$	−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
$658$	22.3325	−	33.9548i	0.870612	−	1.32370i
$659$	8.90498			0.346889			0.173444	−	0.984844i	$-0.444510\pi$
$659$	8.90498			0.346889			0.173444	+	0.984844i	$0.444510\pi$
$660$	−4.65047	−	2.16287i	−0.181019	−	0.0841894i
$661$	−8.91820			−0.346878			−0.173439	−	0.984845i	$-0.555488\pi$
$661$	−8.91820			−0.346878			−0.173439	+	0.984845i	$0.555488\pi$
$662$	−5.86365	+	8.91522i	−0.227897	+	0.346500i
$663$	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
$668$	−13.6711	+	34.4117i	−0.528949	+	1.33143i
$669$		−	21.7018i		−	0.839040i
$670$	−16.8346	+	2.48321i	−0.650377	+	0.0959346i
$671$		−	7.15370i		−	0.276165i
$672$	20.7800	−	4.92474i	0.801605	−	0.189976i
$673$	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	$0.923103\pi$
$678$	24.1323	+	15.8721i	0.926795	+	0.609565i
$679$	−42.7425			−1.64031
$680$	26.3006	−	16.2589i	1.00858	−	0.623499i
$681$	18.0145			0.690316
$682$	1.57092	+	1.03321i	0.0601535	+	0.0395637i
$683$	−9.42261	+	9.42261i	−0.360546	+	0.360546i	−0.864014	−	0.503468i	$-0.832057\pi$
$683$	−9.42261	+	9.42261i	−0.360546	+	0.360546i	0.503468	+	0.864014i	$0.332057\pi$
$684$	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
$688$	−0.822674	−	28.2808i	−0.0313642	−	1.07820i
$689$		−	20.4261i		−	0.778171i
$690$	17.3110	+	12.8606i	0.659020	+	0.489593i
$691$			13.4886i			0.513132i	0.966527	+	0.256566i	$0.0825910\pi$
$691$			13.4886i			0.513132i	−0.966527	+	0.256566i	$0.917409\pi$
$692$	−8.80581	+	22.1653i	−0.334747	+	0.842599i
$693$	−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
$698$	12.0604	−	18.3369i	0.456493	−	0.694062i
$699$	−7.83842			−0.296476
$700$	15.5646	−	29.0059i	0.588286	−	1.09632i
$701$	−4.50941			−0.170318			−0.0851591	−	0.996367i	$-0.527140\pi$
$701$	−4.50941			−0.170318			−0.0851591	+	0.996367i	$0.527140\pi$
$702$	−15.3161	+	23.2870i	−0.578071	+	0.878910i
$703$	−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
$708$	13.9496	+	5.54189i	0.524259	+	0.208277i
$709$			31.4520i			1.18121i	0.806963	+	0.590603i	$0.201110\pi$
$709$			31.4520i			1.18121i	−0.806963	+	0.590603i	$0.798890\pi$
$710$	31.7363	+	23.5772i	1.19104	+	0.884836i
$711$		−	4.21712i		−	0.158154i
$712$	−40.1772	−	7.08455i	−1.50570	−	0.265505i
$713$	−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
$718$	17.4098	+	11.4506i	0.649726	+	0.427333i
$719$	37.1300			1.38471			0.692357	−	0.721555i	$-0.256572\pi$
$719$	37.1300			1.38471			0.692357	+	0.721555i	$0.256572\pi$
$720$	−10.9504	+	10.3519i	−0.408097	+	0.385792i
$721$	−6.89440			−0.256761
$722$	−16.2154	−	10.6651i	−0.603476	−	0.396914i
$723$	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	0.821249	−	0.570570i	$-0.193278\pi$
$727$	6.75902	+	6.75902i	0.250678	+	0.250678i	−0.570570	+	0.821249i	$0.693278\pi$
$728$	33.6355	+	5.93105i	1.24662	+	0.219819i
$729$			20.3503i			0.753715i
$730$	−6.43664	+	0.949444i	−0.238231	+	0.0351405i
$731$			34.5805i			1.27901i
$732$	15.2490	+	6.05810i	0.563619	+	0.223914i
$733$	−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
$738$	−10.1649	+	15.4549i	−0.374176	+	0.568904i
$739$	30.5046			1.12213			0.561065	−	0.827772i	$-0.310392\pi$
$739$	30.5046			1.12213			0.561065	+	0.827772i	$0.310392\pi$
$740$	19.2946	−	41.4860i	0.709283	−	1.52506i
$741$	−9.66345			−0.354996
$742$	−14.2443	+	21.6573i	−0.522924	+	0.795064i
$743$	3.47745	−	3.47745i	0.127575	−	0.127575i	−0.640436	−	0.768011i	$-0.721246\pi$
$743$	3.47745	−	3.47745i	0.127575	−	0.127575i	0.768011	+	0.640436i	$0.221246\pi$
$744$	−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
$748$	−3.61010	+	9.08706i	−0.131998	+	0.332256i
$749$		−	0.347151i		−	0.0126846i
$750$	−0.582160	−	18.1238i	−0.0212575	−	0.661787i
$751$		−	13.3195i		−	0.486036i	−0.970022	−	0.243018i	$-0.921863\pi$
$751$		−	13.3195i		−	0.486036i	0.970022	−	0.243018i	$-0.0781374\pi$
$752$	34.9051	−	1.01537i	1.27286	−	0.0370268i
$753$	−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	$0.155786\pi$
$758$	−35.8319	−	23.5671i	−1.30147	−	0.855996i
$759$	−6.81958			−0.247535
$760$	−14.1393	−	3.33610i	−0.512885	−	0.121013i
$761$	−35.8822			−1.30073			−0.650365	−	0.759622i	$-0.725384\pi$
$761$	−35.8822			−1.30073			−0.650365	+	0.759622i	$0.725384\pi$
$762$	−26.4226	−	17.3785i	−0.957191	−	0.629557i
$763$	−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
$768$	13.7073	+	12.1988i	0.494620	+	0.440187i
$769$		−	15.5077i		−	0.559221i	−0.960114	−	0.279610i	$-0.909795\pi$
$769$		−	15.5077i		−	0.559221i	0.960114	−	0.279610i	$-0.0902053\pi$
$770$	1.51904	+	10.2982i	0.0547424	+	0.371120i
$771$			27.0887i			0.975576i
$772$	9.41531	−	23.6995i	0.338864	−	0.852964i
$773$	−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
$778$	−2.00451	+	3.04769i	−0.0718650	+	0.109265i
$779$	−17.8335			−0.638950
$780$	17.6731	−	6.45259i	0.632799	−	0.231040i
$781$	−12.5023			−0.447367
$782$	22.5924	−	34.3499i	0.807901	−	1.22835i
$783$	−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	0.183367	−	0.983045i	$-0.441300\pi$
$787$	−22.4338	−	22.4338i	−0.799677	−	0.799677i	−0.983045	+	0.183367i	$0.941300\pi$
$788$	27.2833	+	10.8391i	0.971927	+	0.386126i
$789$			29.4958i			1.05008i
$790$	−4.72042	+	6.35396i	−0.167945	+	0.226064i
$791$		−	58.6239i		−	2.08443i
$792$	0.827498	−	4.69282i	0.0294039	−	0.166752i
$793$	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	$0.159809\pi$
$798$	10.2459	+	6.73889i	0.362702	+	0.238554i
$799$	−42.6804			−1.50992
$800$	28.0864	−	3.33996i	0.993003	−	0.118085i
$801$	−24.3008			−0.858628
$802$	6.04845	+	3.97815i	0.213578	+	0.140473i
$803$	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
$808$	−5.00920	+	28.4076i	−0.176223	+	0.999378i
$809$		−	23.4629i		−	0.824913i	−0.910977	−	0.412456i	$-0.864671\pi$
$809$		−	23.4629i		−	0.824913i	0.910977	−	0.412456i	$-0.135329\pi$
$810$	2.08819	−	2.81083i	0.0733717	−	0.0987625i
$811$		−	7.95869i		−	0.279467i	−0.990189	−	0.139734i	$-0.955375\pi$
$811$		−	7.95869i		−	0.279467i	0.990189	−	0.139734i	$-0.0446246\pi$
$812$	0.817028	+	0.324588i	0.0286721	+	0.0113908i
$813$	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
$818$	−18.1457	+	27.5891i	−0.634449	+	0.964629i
$819$	20.3442			0.710883
$820$	32.6150	−	11.9080i	1.13896	−	0.415844i
$821$	32.4930			1.13401			0.567007	−	0.823713i	$-0.308101\pi$
$821$	32.4930			1.13401			0.567007	+	0.823713i	$0.308101\pi$
$822$	−2.71537	+	4.12850i	−0.0947093	+	0.143998i
$823$	−26.1886	+	26.1886i	−0.912878	+	0.912878i	−0.996498	−	0.0836197i	$-0.973352\pi$
$823$	−26.1886	+	26.1886i	−0.912878	+	0.912878i	0.0836197	+	0.996498i	$0.473352\pi$
$824$	−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	0.386089	−	0.922461i	$-0.373826\pi$
$827$	−15.4248	−	15.4248i	−0.536372	−	0.536372i	−0.922461	+	0.386089i	$0.873826\pi$
$828$	−7.39768	+	18.6209i	−0.257087	+	0.647120i
$829$			49.5561i			1.72116i	0.509319	+	0.860578i	$0.329897\pi$
$829$			49.5561i			1.72116i	−0.509319	+	0.860578i	$0.670103\pi$
$830$	−4.20537	−	28.5098i	−0.145971	−	0.989591i
$831$		−	27.3734i		−	0.949574i
$832$	12.4021	+	26.5972i	0.429966	+	0.922093i
$833$	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
$838$	13.0107	+	8.55733i	0.449448	+	0.295608i
$839$	30.8225			1.06411			0.532056	−	0.846709i	$-0.321420\pi$
$839$	30.8225			1.06411			0.532056	+	0.846709i	$0.321420\pi$
$840$	−23.2382	−	5.48296i	−0.801793	−	0.189180i
$841$	28.9822			0.999385
$842$	30.8999	+	20.3233i	1.06488	+	0.700386i
$843$	−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
$848$	−22.2634	+	0.647632i	−0.764530	+	0.0222398i
$849$		−	8.93410i		−	0.306617i
$850$	−34.4324	+	3.08233i	−1.18102	+	0.105723i
$851$		−	60.8363i		−	2.08544i
$852$	10.5875	−	26.6502i	0.362723	−	0.913020i
$853$	−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	$0.933996\pi$
$858$	−3.26936	+	4.97079i	−0.111614	+	0.169700i
$859$	−40.0717			−1.36723			−0.683614	−	0.729843i	$-0.739593\pi$
$859$	−40.0717			−1.36723			−0.683614	+	0.729843i	$0.739593\pi$
$860$	−13.3396	+	28.6820i	−0.454876	+	0.978048i
$861$	−29.3097			−0.998871
$862$	−6.77010	+	10.2934i	−0.230590	+	0.350594i
$863$	8.12174	−	8.12174i	0.276467	−	0.276467i	−0.555230	−	0.831697i	$-0.687370\pi$
$863$	8.12174	−	8.12174i	0.276467	−	0.276467i	0.831697	+	0.555230i	$0.187370\pi$
$864$	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
$868$	8.13466	+	3.23173i	0.276108	+	0.109692i
$869$		−	2.50310i		−	0.0849119i
$870$	0.479098	−	0.0706699i	0.0162430	−	0.00239593i
$871$			19.7399i			0.668862i
$872$	−20.4285	−	3.60222i	−0.691797	−	0.121987i
$873$	−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	$0.219857\pi$
$878$	3.11179	+	2.04667i	0.105018	+	0.0690717i
$879$	−14.8421			−0.500610
$880$	−6.49968	+	6.14444i	−0.219104	+	0.207129i
$881$	35.5301			1.19704			0.598520	−	0.801108i	$-0.295756\pi$
$881$	35.5301			1.19704			0.598520	+	0.801108i	$0.295756\pi$
$882$	−7.63600	−	5.02230i	−0.257117	−	0.169110i
$883$	4.68070	−	4.68070i	0.157518	−	0.157518i	−0.623948	−	0.781466i	$-0.714472\pi$
$883$	4.68070	−	4.68070i	0.157518	−	0.157518i	0.781466	+	0.623948i	$0.214472\pi$
$884$	−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	0.694088	−	0.719890i	$-0.255808\pi$
$887$	−0.768436	−	0.768436i	−0.0258015	−	0.0258015i	−0.719890	+	0.694088i	$0.755808\pi$
$888$	−32.6819	−	5.76289i	−1.09673	−	0.193390i
$889$			64.1878i			2.15279i
$890$	36.6142	+	27.2011i	1.22731	+	0.911781i
$891$			1.10731i			0.0370962i
$892$	−35.1723	−	13.9732i	−1.17766	−	0.467858i
$893$	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
$898$	5.82868	−	8.86203i	0.194505	−	0.295730i
$899$	−0.177539			−0.00592127
$900$	16.1301	−	4.86440i	0.537669	−	0.162147i
$901$	27.2227			0.906921
$902$	−6.03345	+	9.17338i	−0.200892	+	0.305440i
$903$	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	0.835405	−	0.549635i	$-0.185233\pi$
$907$	8.60637	+	8.60637i	0.285770	+	0.285770i	−0.549635	+	0.835405i	$0.685233\pi$
$908$	11.5990	−	29.1962i	0.384928	−	0.968910i
$909$			17.1821i			0.569895i
$910$	−30.6527	−	22.7722i	−1.01613	−	0.754890i
$911$		−	51.6465i		−	1.71113i	−0.517698	−	0.855563i	$-0.673211\pi$
$911$		−	51.6465i		−	1.71113i	0.517698	−	0.855563i	$-0.326789\pi$
$912$	0.306391	+	10.5327i	0.0101456	+	0.348773i
$913$	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
$918$	−31.0356	−	20.4125i	−1.02433	−	0.673714i
$919$	−46.1566			−1.52257			−0.761283	−	0.648420i	$-0.775430\pi$
$919$	−46.1566			−1.52257			−0.761283	+	0.648420i	$0.775430\pi$
$920$	31.9893	−	19.7756i	1.05466	−	0.651982i
$921$	9.10050			0.299872
$922$	20.5846	+	13.5388i	0.677917	+	0.445875i
$923$	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
$928$	0.174198	+	0.735030i	0.00571833	+	0.0241285i
$929$			20.3837i			0.668768i	0.942437	+	0.334384i	$0.108528\pi$
$929$			20.3837i			0.668768i	−0.942437	+	0.334384i	$0.891472\pi$
$930$	4.77010	−	0.703618i	0.156418	−	0.0230725i
$931$		−	8.81119i		−	0.288775i
$932$	−5.04695	+	12.7038i	−0.165318	+	0.416127i
$933$	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	$0.972417\pi$
$938$	13.7658	−	20.9298i	0.449469	−	0.683382i
$939$	3.95936			0.129209
$940$	−35.4003	−	16.4642i	−1.15463	−	0.537002i
$941$	−6.14439			−0.200301			−0.100151	−	0.994972i	$-0.531932\pi$
$941$	−6.14439			−0.200301			−0.100151	+	0.994972i	$0.531932\pi$
$942$	9.73251	−	14.7975i	0.317102	−	0.482129i
$943$	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	$0.139936\pi$
$947$	40.9443	+	40.9443i	1.33051	+	1.33051i	0.425597	+	0.904913i	$0.360064\pi$
$948$	5.33566	+	2.11975i	0.173294	+	0.0688462i
$949$			7.54748i			0.245002i
$950$	12.4633	+	10.4152i	0.404362	+	0.337915i
$951$		−	15.8253i		−	0.513171i
$952$	−7.90457	+	44.8276i	−0.256189	+	1.45287i
$953$	−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
$958$	−37.3769	−	24.5832i	−1.20759	−	0.794249i
$959$	10.0292			0.323861
$960$	−7.59337	−	19.0583i	−0.245075	−	0.615103i
$961$	29.2323			0.942979
$962$	−44.3436	−	29.1654i	−1.42970	−	0.940330i
$963$	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	0.878853	−	0.477093i	$-0.158310\pi$
$967$	12.4934	+	12.4934i	0.401759	+	0.401759i	−0.477093	+	0.878853i	$0.658310\pi$
$968$	0.491167	−	2.78545i	0.0157867	−	0.0895279i
$969$		−	12.8789i		−	0.413730i
$970$	5.99187	+	40.6212i	0.192387	+	1.30427i
$971$			44.5413i			1.42940i	0.699433	+	0.714698i	$0.253436\pi$
$971$			44.5413i			1.42940i	−0.699433	+	0.714698i	$0.746564\pi$
$972$	27.5980	+	10.9641i	0.885208	+	0.351674i
$973$	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	$0.428063\pi$
$978$	−4.34766	+	6.61027i	−0.139023	+	0.211373i
$979$	−14.4239			−0.460991
$980$	5.88351	+	16.1144i	0.187942	+	0.514757i
$981$	−12.3560			−0.394498
$982$	6.03870	−	9.18135i	0.192703	−	0.292989i
$983$	35.6516	−	35.6516i	1.13711	−	1.13711i	0.148143	−	0.988966i	$-0.452670\pi$
$983$	35.6516	−	35.6516i	1.13711	−	1.13711i	0.988966	−	0.148143i	$-0.0473295\pi$
$984$	−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
$988$	−6.22204	+	15.6616i	−0.197949	+	0.498263i
$989$			42.0601i			1.33743i
$990$	−3.17717	+	4.27665i	−0.100977	+	0.135921i
$991$		−	10.1191i		−	0.321445i	−0.987000	−	0.160723i	$-0.948618\pi$
$991$		−	10.1191i		−	0.321445i	0.987000	−	0.160723i	$-0.0513824\pi$
$992$	1.73438	+	7.31825i	0.0550668	+	0.232355i
$993$	−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	$0.0511064\pi$
$998$	43.1474	+	28.3786i	1.36581	+	0.898308i
$999$	−54.9665			−1.73906

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.18156 + 0.777125i) 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} +(-0.491167 + 2.78545i) q^{8} +1.68476i q^{9} +(1.88583 - 2.53843i) q^{10} +1.00000i q^{11} +(-2.13162 - 0.846848i) 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} +(-1.30927 + 1.99064i) q^{18} -2.29700 q^{19} +(4.20090 - 1.53378i) q^{20} -3.77517 q^{21} +(-0.777125 + 1.18156i) 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} +(-2.43073 + 6.11845i) q^{28} -0.133535i q^{29} +(0.529223 + 3.58780i) q^{30} -1.32953i q^{31} +(-5.50439 + 1.30451i) 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} +(-2.71404 - 1.78506i) q^{38} +4.20699 q^{39} +(6.15553 + 1.45237i) q^{40} +7.76381 q^{41} +(-4.46057 - 2.93378i) 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} +(-0.133387 - 4.58542i) q^{48} +3.83595i q^{49} +(-5.42589 - 4.53428i) q^{50} +5.60684i q^{51} +(2.70877 - 6.81830i) 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} +(0.103774 - 0.157780i) q^{58} -6.54413 q^{59} +(-2.16287 + 4.65047i) q^{60} -7.15370 q^{61} +(1.03321 - 1.57092i) 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} +(9.08706 + 3.61010i) q^{68} +6.81958i q^{69} +(10.2982 - 1.51904i) q^{70} +12.5023i q^{71} +(-4.69282 - 0.827498i) 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} +(4.97079 + 3.26936i) q^{78} -2.50310 q^{79} +(6.14444 + 6.49968i) q^{80} +1.10731 q^{81} +(9.17338 + 6.03345i) 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} +(-2.78545 - 0.491167i) q^{88} +14.4239i q^{89} +(4.27665 + 3.17717i) q^{90} -12.0754i q^{91} +(11.0525 + 4.39094i) 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} +(-2.98102 + 4.53240i) q^{98} -1.68476 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} + 4 q^{3} - 4 q^{4} + 2 q^{5} - 12 q^{6} + 2 q^{7} + 2 q^{8} - 6 q^{10} + 8 q^{12} + 6 q^{13} + 20 q^{14} - 8 q^{15} + 8 q^{16} - 14 q^{17} - 6 q^{18} - 4 q^{19} + 8 q^{20} - 16 q^{21} - 2 q^{22}+ \cdots + 20 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 + 4 * q^3 - 4 * q^4 + 2 * q^5 - 12 * q^6 + 2 * q^7 + 2 * q^8 - 6 * q^10 + 8 * q^12 + 6 * q^13 + 20 * q^14 - 8 * q^15 + 8 * q^16 - 14 * q^17 - 6 * 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 + 8 * q^28 - 24 * q^30 - 38 * q^32 + 4 * q^33 + 52 * q^34 + 10 * q^35 - 4 * q^36 + 20 * q^37 - 48 * q^38 - 32 * q^39 + 46 * q^40 + 12 * q^41 + 32 * q^42 - 2 * q^43 - 10 * q^45 + 4 * q^46 + 44 * q^47 + 44 * q^48 - 18 * q^50 - 52 * q^52 - 28 * q^53 + 40 * q^54 + 2 * q^55 + 4 * q^56 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 32 * q^60 - 12 * q^61 + 20 * q^62 + 10 * q^63 - 28 * q^64 - 30 * q^65 - 16 * q^67 + 68 * q^68 - 40 * q^70 - 38 * q^72 + 22 * q^73 + 20 * q^74 + 56 * q^75 + 4 * q^76 - 2 * q^77 - 40 * q^78 + 20 * q^79 + 12 * q^80 + 12 * q^81 + 12 * q^82 - 2 * q^83 - 120 * q^84 - 14 * q^85 - 20 * q^86 + 48 * q^87 + 14 * q^88 - 10 * q^90 + 4 * q^92 - 20 * q^93 + 20 * q^94 - 92 * q^95 + 40 * q^96 + 16 * q^97 - 82 * q^98 + 20 * q^99

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