LMFDB - Embedded newform 558.2.g.a.211.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(211,558)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("558.211"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-16] 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:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.7
Character	$\chi$	$=$	558.211
Dual form			558.2.g.a.439.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.551268 - 1.64198i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.55594 - 2.69497i) q^{5} +(-1.14636 + 1.29840i) q^{6} +(-2.29219 + 3.97020i) q^{7} +1.00000 q^{8} +(-2.39221 + 1.81034i) q^{9} +(-1.55594 + 2.69497i) q^{10} +1.33410 q^{11} +(1.69763 + 0.343579i) q^{12} +(0.620478 + 1.07470i) q^{13} +4.58439 q^{14} +(-3.56735 + 4.04048i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.0749387 - 0.129798i) q^{17} +(2.76391 + 1.16654i) q^{18} +(1.97095 + 3.41379i) q^{19} +3.11188 q^{20} +(7.78261 + 1.57510i) q^{21} +(-0.667052 - 1.15537i) q^{22} +(-1.63368 + 2.82961i) q^{23} +(-0.551268 - 1.64198i) q^{24} +(-2.34191 + 4.05631i) q^{25} +(0.620478 - 1.07470i) q^{26} +(4.29130 + 2.92997i) q^{27} +(-2.29219 - 3.97020i) q^{28} +(-2.07708 - 3.59761i) q^{29} +(5.28283 + 1.06918i) q^{30} +(-2.36375 - 5.04110i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.735450 - 2.19058i) q^{33} +(-0.0749387 + 0.129798i) q^{34} +14.2661 q^{35} +(-0.371701 - 2.97688i) q^{36} +(-1.03856 - 1.79883i) q^{37} +(1.97095 - 3.41379i) q^{38} +(1.42259 - 1.61126i) q^{39} +(-1.55594 - 2.69497i) q^{40} +(2.12854 + 3.68673i) q^{41} +(-2.52723 - 7.52748i) q^{42} +(-2.91648 + 5.05149i) q^{43} +(-0.667052 + 1.15537i) q^{44} +(8.60096 + 3.63014i) q^{45} +3.26736 q^{46} +(3.12000 + 5.40400i) q^{47} +(-1.14636 + 1.29840i) q^{48} +(-7.00831 - 12.1388i) q^{49} +4.68383 q^{50} +(-0.171814 + 0.194601i) q^{51} -1.24096 q^{52} +(-5.25836 + 9.10775i) q^{53} +(0.391783 - 5.18136i) q^{54} +(-2.07579 - 3.59537i) q^{55} +(-2.29219 + 3.97020i) q^{56} +(4.51885 - 5.11818i) q^{57} +(-2.07708 + 3.59761i) q^{58} -7.46343 q^{59} +(-1.71548 - 5.10966i) q^{60} +(7.11213 + 12.3186i) q^{61} +(-3.18384 + 4.56762i) q^{62} +(-1.70402 - 13.6472i) q^{63} +1.00000 q^{64} +(1.93086 - 3.34434i) q^{65} +(-1.52937 + 1.73221i) q^{66} +(5.08029 + 8.79932i) q^{67} +0.149877 q^{68} +(5.54677 + 1.12259i) q^{69} +(-7.13305 - 12.3548i) q^{70} +(-2.53810 + 4.39612i) q^{71} +(-2.39221 + 1.81034i) q^{72} +(-3.53384 + 6.12079i) q^{73} +(-1.03856 + 1.79883i) q^{74} +(7.95141 + 1.60926i) q^{75} -3.94190 q^{76} +(-3.05803 + 5.29666i) q^{77} +(-2.10669 - 0.426366i) q^{78} +(-1.07150 + 1.85590i) q^{79} +(-1.55594 + 2.69497i) q^{80} +(2.44531 - 8.66144i) q^{81} +(2.12854 - 3.68673i) q^{82} +16.6710 q^{83} +(-5.25538 + 5.95239i) q^{84} +(-0.233201 + 0.403915i) q^{85} +5.83296 q^{86} +(-4.76218 + 5.39377i) q^{87} +1.33410 q^{88} -9.78493 q^{89} +(-1.15669 - 9.26372i) q^{90} -5.68903 q^{91} +(-1.63368 - 2.82961i) q^{92} +(-6.97433 + 6.66023i) q^{93} +(3.12000 - 5.40400i) q^{94} +(6.13337 - 10.6233i) q^{95} +(1.69763 + 0.343579i) q^{96} +(5.24560 + 9.08564i) q^{97} +(-7.00831 + 12.1388i) q^{98} +(-3.19146 + 2.41519i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} + 4 q^{3} - 16 q^{4} - q^{5} - 2 q^{6} + q^{7} + 32 q^{8} + 12 q^{9} - q^{10} + 4 q^{11} - 2 q^{12} - 10 q^{13} - 2 q^{14} - 13 q^{15} - 16 q^{16} - 4 q^{17} - 6 q^{18} + 4 q^{19} + 2 q^{20}+ \cdots + 19 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 + 4 * q^3 - 16 * q^4 - q^5 - 2 * q^6 + q^7 + 32 * q^8 + 12 * q^9 - q^10 + 4 * q^11 - 2 * q^12 - 10 * q^13 - 2 * q^14 - 13 * q^15 - 16 * q^16 - 4 * q^17 - 6 * q^18 + 4 * q^19 + 2 * q^20 + 10 * q^21 - 2 * q^22 - q^23 + 4 * q^24 - 19 * q^25 - 10 * q^26 + 7 * q^27 + q^28 - 3 * q^29 + 14 * q^30 - q^31 - 16 * q^32 - 7 * q^33 - 4 * q^34 - 6 * q^36 - 19 * q^37 + 4 * q^38 + 19 * q^39 - q^40 + 10 * q^41 - 11 * q^42 - 13 * q^43 - 2 * q^44 + 14 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 - 13 * q^49 + 38 * q^50 + 20 * q^51 + 20 * q^52 - 7 * q^53 - 17 * q^54 - 11 * q^55 + q^56 - 5 * q^57 - 3 * q^58 + 12 * q^59 - q^60 + 7 * q^61 + 11 * q^62 - 42 * q^63 + 32 * q^64 - 8 * q^65 + 5 * q^66 - 8 * q^67 + 8 * q^68 + 43 * q^69 + 7 * q^71 + 12 * q^72 + 7 * q^73 - 19 * q^74 - 41 * q^75 - 8 * q^76 - q^77 - 11 * q^78 - 34 * q^79 - q^80 + 10 * q^82 - 28 * q^83 + q^84 + 13 * q^85 + 26 * q^86 - 54 * q^87 + 4 * q^88 + 2 * q^89 - 19 * q^90 + 24 * q^91 - q^92 - 15 * q^93 - 6 * q^94 + 21 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + 19 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.551268	−	1.64198i	−0.318275	−	0.947999i
$3$	−0.551268	−	1.64198i	−0.318275	−	0.947999i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.55594	−	2.69497i	−0.695839	−	1.20523i	−0.969897	−	0.243515i	$-0.921700\pi$
$5$	−1.55594	−	2.69497i	−0.695839	−	1.20523i	0.274059	−	0.961713i	$-0.411634\pi$
$6$	−1.14636	+	1.29840i	−0.468001	+	0.530071i
$7$	−2.29219	+	3.97020i	−0.866368	+	1.50059i	−0.000686007		1.00000i	$0.500218\pi$
$7$	−2.29219	+	3.97020i	−0.866368	+	1.50059i	−0.865682	+	0.500594i	$0.833115\pi$
$8$	1.00000			0.353553
$9$	−2.39221	+	1.81034i	−0.797402	+	0.603448i
$10$	−1.55594	+	2.69497i	−0.492032	+	0.852225i
$11$	1.33410			0.402248			0.201124	−	0.979566i	$-0.435541\pi$
$11$	1.33410			0.402248			0.201124	+	0.979566i	$0.435541\pi$
$12$	1.69763	+	0.343579i	0.490064	+	0.0991826i
$13$	0.620478	+	1.07470i	0.172090	+	0.298068i	0.939150	−	0.343507i	$-0.111615\pi$
$13$	0.620478	+	1.07470i	0.172090	+	0.298068i	−0.767061	+	0.641575i	$0.778281\pi$
$14$	4.58439			1.22523
$15$	−3.56735	+	4.04048i	−0.921086	+	1.04325i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.0749387	−	0.129798i	−0.0181753	−	0.0314805i	0.856795	−	0.515658i	$-0.172452\pi$
$17$	−0.0749387	−	0.129798i	−0.0181753	−	0.0314805i	−0.874970	+	0.484177i	$0.839119\pi$
$18$	2.76391	+	1.16654i	0.651459	+	0.274956i
$19$	1.97095	+	3.41379i	0.452167	+	0.783177i	0.998520	−	0.0543782i	$-0.0173177\pi$
$19$	1.97095	+	3.41379i	0.452167	+	0.783177i	−0.546353	+	0.837555i	$0.683984\pi$
$20$	3.11188			0.695839
$21$	7.78261	+	1.57510i	1.69830	+	0.343715i
$22$	−0.667052	−	1.15537i	−0.142216	−	0.246325i
$23$	−1.63368	+	2.82961i	−0.340646	+	0.590015i	−0.984553	−	0.175088i	$-0.943979\pi$
$23$	−1.63368	+	2.82961i	−0.340646	+	0.590015i	0.643907	+	0.765104i	$0.277312\pi$
$24$	−0.551268	−	1.64198i	−0.112527	−	0.335168i
$25$	−2.34191	+	4.05631i	−0.468383	+	0.811263i
$26$	0.620478	−	1.07470i	0.121686	−	0.210766i
$27$	4.29130	+	2.92997i	0.825861	+	0.563874i
$28$	−2.29219	−	3.97020i	−0.433184	−	0.750297i
$29$	−2.07708	−	3.59761i	−0.385704	−	0.668059i	0.606163	−	0.795341i	$-0.292708\pi$
$29$	−2.07708	−	3.59761i	−0.385704	−	0.668059i	−0.991867	+	0.127282i	$0.959375\pi$
$30$	5.28283	+	1.06918i	0.964509	+	0.195204i
$31$	−2.36375	−	5.04110i	−0.424542	−	0.905408i
$31$	−2.36375	−	5.04110i	−0.424542	−	0.905408i
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.735450	−	2.19058i	−0.128025	−	0.381330i
$34$	−0.0749387	+	0.129798i	−0.0128519	+	0.0222601i
$35$	14.2661			2.41141
$36$	−0.371701	−	2.97688i	−0.0619501	−	0.496147i
$37$	−1.03856	−	1.79883i	−0.170737	−	0.295726i	0.767940	−	0.640521i	$-0.221282\pi$
$37$	−1.03856	−	1.79883i	−0.170737	−	0.295726i	−0.938678	+	0.344795i	$0.887948\pi$
$38$	1.97095	−	3.41379i	0.319731	−	0.553790i
$39$	1.42259	−	1.61126i	0.227796	−	0.258008i
$40$	−1.55594	−	2.69497i	−0.246016	−	0.426112i
$41$	2.12854	+	3.68673i	0.332422	+	0.575771i	0.982986	−	0.183680i	$-0.0588010\pi$
$41$	2.12854	+	3.68673i	0.332422	+	0.575771i	−0.650564	+	0.759451i	$0.725468\pi$
$42$	−2.52723	−	7.52748i	−0.389960	−	1.16152i
$43$	−2.91648	+	5.05149i	−0.444759	+	0.770345i	−0.998035	−	0.0626529i	$-0.980044\pi$
$43$	−2.91648	+	5.05149i	−0.444759	+	0.770345i	0.553277	+	0.832998i	$0.313377\pi$
$44$	−0.667052	+	1.15537i	−0.100562	+	0.174178i
$45$	8.60096	+	3.63014i	1.28216	+	0.541149i
$46$	3.26736			0.481746
$47$	3.12000	+	5.40400i	0.455099	+	0.788255i	0.998694	−	0.0510930i	$-0.0162705\pi$
$47$	3.12000	+	5.40400i	0.455099	+	0.788255i	−0.543595	+	0.839348i	$0.682937\pi$
$48$	−1.14636	+	1.29840i	−0.165463	+	0.187408i
$49$	−7.00831	−	12.1388i	−1.00119	−	1.73411i
$50$	4.68383			0.662393
$51$	−0.171814	+	0.194601i	−0.0240588	+	0.0272496i
$52$	−1.24096			−0.172090
$53$	−5.25836	+	9.10775i	−0.722291	+	1.25105i	0.237788	+	0.971317i	$0.423578\pi$
$53$	−5.25836	+	9.10775i	−0.722291	+	1.25105i	−0.960079	+	0.279728i	$0.909756\pi$
$54$	0.391783	−	5.18136i	0.0533149	−	0.705094i
$55$	−2.07579	−	3.59537i	−0.279900	−	0.484800i
$56$	−2.29219	+	3.97020i	−0.306307	+	0.530540i
$57$	4.51885	−	5.11818i	0.598537	−	0.677919i
$58$	−2.07708	+	3.59761i	−0.272734	+	0.472389i
$59$	−7.46343			−0.971656			−0.485828	−	0.874054i	$-0.661482\pi$
$59$	−7.46343			−0.971656			−0.485828	+	0.874054i	$0.661482\pi$
$60$	−1.71548	−	5.10966i	−0.221468	−	0.659654i
$61$	7.11213	+	12.3186i	0.910615	+	1.57723i	0.813197	+	0.581988i	$0.197725\pi$
$61$	7.11213	+	12.3186i	0.910615	+	1.57723i	0.0974178	+	0.995244i	$0.468942\pi$
$62$	−3.18384	+	4.56762i	−0.404348	+	0.580088i
$63$	−1.70402	−	13.6472i	−0.214686	−	1.71939i
$64$	1.00000			0.125000
$65$	1.93086	−	3.34434i	0.239493	−	0.414815i
$66$	−1.52937	+	1.73221i	−0.188252	+	0.213220i
$67$	5.08029	+	8.79932i	0.620656	+	1.07501i	0.989364	+	0.145462i	$0.0464669\pi$
$67$	5.08029	+	8.79932i	0.620656	+	1.07501i	−0.368708	+	0.929545i	$0.620200\pi$
$68$	0.149877			0.0181753
$69$	5.54677	+	1.12259i	0.667753	+	0.135144i
$70$	−7.13305	−	12.3548i	−0.852562	−	1.47668i
$71$	−2.53810	+	4.39612i	−0.301217	+	0.521724i	−0.976412	−	0.215916i	$-0.930726\pi$
$71$	−2.53810	+	4.39612i	−0.301217	+	0.521724i	0.675195	+	0.737640i	$0.264060\pi$
$72$	−2.39221	+	1.81034i	−0.281924	+	0.213351i
$73$	−3.53384	+	6.12079i	−0.413605	+	0.716384i	−0.995281	−	0.0970360i	$-0.969064\pi$
$73$	−3.53384	+	6.12079i	−0.413605	+	0.716384i	0.581676	+	0.813421i	$0.302397\pi$
$74$	−1.03856	+	1.79883i	−0.120730	+	0.209110i
$75$	7.95141	+	1.60926i	0.918150	+	0.185822i
$76$	−3.94190			−0.452167
$77$	−3.05803	+	5.29666i	−0.348495	+	0.603611i
$78$	−2.10669	−	0.426366i	−0.238535	−	0.0482765i
$79$	−1.07150	+	1.85590i	−0.120554	+	0.208805i	−0.919986	−	0.391951i	$-0.871800\pi$
$79$	−1.07150	+	1.85590i	−0.120554	+	0.208805i	0.799432	+	0.600756i	$0.205134\pi$
$80$	−1.55594	+	2.69497i	−0.173960	+	0.301307i
$81$	2.44531	−	8.66144i	0.271701	−	0.962382i
$82$	2.12854	−	3.68673i	0.235058	−	0.407132i
$83$	16.6710			1.82988			0.914942	−	0.403584i	$-0.132236\pi$
$83$	16.6710			1.82988			0.914942	+	0.403584i	$0.132236\pi$
$84$	−5.25538	+	5.95239i	−0.573409	+	0.649458i
$85$	−0.233201	+	0.403915i	−0.0252942	+	0.0438108i
$86$	5.83296			0.628984
$87$	−4.76218	+	5.39377i	−0.510559	+	0.578273i
$88$	1.33410			0.142216
$89$	−9.78493			−1.03720			−0.518600	−	0.855017i	$-0.673547\pi$
$89$	−9.78493			−1.03720			−0.518600	+	0.855017i	$0.673547\pi$
$90$	−1.15669	−	9.26372i	−0.121926	−	0.976482i
$91$	−5.68903			−0.596372
$92$	−1.63368	−	2.82961i	−0.170323	−	0.295008i
$93$	−6.97433	+	6.66023i	−0.723204	+	0.690634i
$94$	3.12000	−	5.40400i	0.321804	−	0.557380i
$95$	6.13337	−	10.6233i	0.629271	−	1.08993i
$96$	1.69763	+	0.343579i	0.173264	+	0.0350663i
$97$	5.24560	+	9.08564i	0.532610	+	0.922507i	0.999275	+	0.0380731i	$0.0121220\pi$
$97$	5.24560	+	9.08564i	0.532610	+	0.922507i	−0.466665	+	0.884434i	$0.654545\pi$
$98$	−7.00831	+	12.1388i	−0.707947	+	1.22620i
$99$	−3.19146	+	2.41519i	−0.320753	+	0.242736i
$100$	−2.34191	−	4.05631i	−0.234191	−	0.405631i
$101$	−8.67516	−	15.0258i	−0.863210	−	1.49512i	−0.868813	−	0.495140i	$-0.835117\pi$
$101$	−8.67516	−	15.0258i	−0.863210	−	1.49512i	0.00560271	−	0.999984i	$-0.498217\pi$
$102$	0.254437	+	0.0514947i	0.0251930	+	0.00509873i
$103$	−9.73922	−	16.8688i	−0.959633	−	1.66213i	−0.723390	−	0.690440i	$-0.757417\pi$
$103$	−9.73922	−	16.8688i	−0.959633	−	1.66213i	−0.236244	−	0.971694i	$-0.575916\pi$
$104$	0.620478	+	1.07470i	0.0608429	+	0.105383i
$105$	−7.86444	−	23.4247i	−0.767491	−	2.28601i
$106$	10.5167			1.02147
$107$	3.59396	+	6.22492i	0.347441	+	0.601786i	0.985794	−	0.167958i	$-0.0537173\pi$
$107$	3.59396	+	6.22492i	0.347441	+	0.601786i	−0.638353	+	0.769744i	$0.720384\pi$
$108$	−4.68308	+	2.25139i	−0.450630	+	0.216640i
$109$	−18.7502			−1.79594			−0.897972	−	0.440053i	$-0.854960\pi$
$109$	−18.7502			−1.79594			−0.897972	+	0.440053i	$0.854960\pi$
$110$	−2.07579	+	3.59537i	−0.197919	+	0.342806i
$111$	−2.38112	+	2.69693i	−0.226006	+	0.255981i
$112$	4.58439			0.433184
$113$	0.0474322	+	0.0821550i	0.00446205	+	0.00772849i	0.868248	−	0.496131i	$-0.165246\pi$
$113$	0.0474322	+	0.0821550i	0.00446205	+	0.00772849i	−0.863786	+	0.503859i	$0.831913\pi$
$114$	−6.69190	−	1.35435i	−0.626754	−	0.126847i
$115$	10.1676			0.948137
$116$	4.15416			0.385704
$117$	−3.42989	−	1.44763i	−0.317093	−	0.133833i
$118$	3.73172	+	6.46352i	0.343532	+	0.595016i
$119$	0.687096			0.0629860
$120$	−3.56735	+	4.04048i	−0.325653	+	0.368844i
$121$	−9.22016			−0.838197
$122$	7.11213	−	12.3186i	0.643902	−	1.11527i
$123$	4.88016	−	5.52740i	0.440029	−	0.498389i
$124$	5.54760	+	0.473480i	0.498189	+	0.0425197i
$125$	−0.983892			−0.0880020
$126$	−10.9668	+	8.29932i	−0.977001	+	0.739362i
$127$	7.33116	+	12.6979i	0.650535	+	1.12676i	0.982993	+	0.183642i	$0.0587887\pi$
$127$	7.33116	+	12.6979i	0.650535	+	1.12676i	−0.332458	+	0.943118i	$0.607878\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	9.90221	+	2.00408i	0.871841	+	0.176449i
$130$	−3.86171			−0.338695
$131$	13.0426			1.13954			0.569770	−	0.821804i	$-0.307032\pi$
$131$	13.0426			1.13954			0.569770	+	0.821804i	$0.307032\pi$
$132$	2.26482	+	0.458370i	0.197127	+	0.0398960i
$133$	−18.0712			−1.56697
$134$	5.08029	−	8.79932i	0.438870	−	0.760145i
$135$	1.21918	−	16.1238i	0.104931	−	1.38772i
$136$	−0.0749387	−	0.129798i	−0.00642594	−	0.0111301i
$137$	−12.6594			−1.08157			−0.540783	−	0.841162i	$-0.681872\pi$
$137$	−12.6594			−1.08157			−0.540783	+	0.841162i	$0.681872\pi$
$138$	−1.80119	−	5.36494i	−0.153327	−	0.456694i
$139$	−5.83185	+	10.1011i	−0.494651	+	0.856760i	−0.999981	−	0.00616566i	$-0.998037\pi$
$139$	−5.83185	+	10.1011i	−0.494651	+	0.856760i	0.505330	+	0.862926i	$0.331371\pi$
$140$	−7.13305	+	12.3548i	−0.602852	+	1.04417i
$141$	7.15331	−	8.10204i	0.602418	−	0.682315i
$142$	5.07621			0.425986
$143$	0.827783	+	1.43376i	0.0692227	+	0.119897i
$144$	2.76391	+	1.16654i	0.230326	+	0.0972117i
$145$	−6.46363	+	11.1953i	−0.536776	+	0.929723i
$146$	7.06768			0.584925
$147$	−16.0682	+	18.1992i	−1.32528	+	1.50105i
$148$	2.07711			0.170737
$149$	−12.3389			−1.01084			−0.505421	−	0.862873i	$-0.668663\pi$
$149$	−12.3389			−1.01084			−0.505421	+	0.862873i	$0.668663\pi$
$150$	−2.58204	−	7.69076i	−0.210823	−	0.627948i
$151$	−6.11145	−	10.5853i	−0.497342	−	0.861422i	0.502653	−	0.864488i	$-0.332357\pi$
$151$	−6.11145	−	10.5853i	−0.497342	−	0.861422i	−0.999995	+	0.00306606i	$0.999024\pi$
$152$	1.97095	+	3.41379i	0.159865	+	0.276895i
$153$	0.414247	+	0.174838i	0.0334899	+	0.0141348i
$154$	6.11606			0.492846
$155$	−9.90775	+	14.2139i	−0.795810	+	1.14169i
$156$	0.684100	+	2.03763i	0.0547718	+	0.163141i
$157$	3.03194	−	5.25148i	0.241975	−	0.419113i	−0.719302	−	0.694698i	$-0.755538\pi$
$157$	3.03194	−	5.25148i	0.241975	−	0.419113i	0.961277	+	0.275584i	$0.0888714\pi$
$158$	2.14301			0.170489
$159$	17.8535	+	3.61332i	1.41588	+	0.286555i
$160$	3.11188			0.246016
$161$	−7.48942	−	12.9721i	−0.590249	−	1.02234i
$162$	−8.72368	+	2.21302i	−0.685397	+	0.173871i
$163$	−5.64799			−0.442385			−0.221192	−	0.975230i	$-0.570995\pi$
$163$	−5.64799			−0.442385			−0.221192	+	0.975230i	$0.570995\pi$
$164$	−4.25707			−0.332422
$165$	−4.75922	+	5.39043i	−0.370505	+	0.419644i
$166$	−8.33552	−	14.4375i	−0.646962	−	1.12057i
$167$	−2.82903			−0.218917			−0.109459	−	0.993991i	$-0.534912\pi$
$167$	−2.82903			−0.218917			−0.109459	+	0.993991i	$0.534912\pi$
$168$	7.78261	+	1.57510i	0.600441	+	0.121521i
$169$	5.73001	−	9.92467i	0.440770	−	0.763436i
$170$	0.466401			0.0357713
$171$	−10.8951	−	4.59839i	−0.833166	−	0.351647i
$172$	−2.91648	−	5.05149i	−0.222379	−	0.385172i
$173$	−4.46276			−0.339298			−0.169649	−	0.985505i	$-0.554263\pi$
$173$	−4.46276			−0.339298			−0.169649	+	0.985505i	$0.554263\pi$
$174$	7.05223	+	1.42728i	0.534629	+	0.108202i
$175$	−10.7362	−	18.5957i	−0.811584	−	1.40570i
$176$	−0.667052	−	1.15537i	−0.0502810	−	0.0870892i
$177$	4.11435	+	12.2548i	0.309254	+	0.921129i
$178$	4.89246	+	8.47400i	0.366706	+	0.635153i
$179$	−10.2557	−	17.7634i	−0.766546	−	1.32770i	−0.939425	−	0.342754i	$-0.888640\pi$
$179$	−10.2557	−	17.7634i	−0.766546	−	1.32770i	0.172879	−	0.984943i	$-0.444693\pi$
$180$	−7.44427	+	5.63358i	−0.554863	+	0.419902i
$181$	−6.84106	+	11.8491i	−0.508492	+	0.880734i	0.491459	+	0.870900i	$0.336464\pi$
$181$	−6.84106	+	11.8491i	−0.508492	+	0.880734i	−0.999952	+	0.00983384i	$0.996870\pi$
$182$	2.84451	+	4.92684i	0.210849	+	0.365202i
$183$	16.3062	−	18.4688i	1.20539	−	1.36525i
$184$	−1.63368	+	2.82961i	−0.120436	+	0.208602i
$185$	−3.23187	+	5.59776i	−0.237611	+	0.411555i
$186$	9.25510	+	2.70983i	0.678617	+	0.198694i
$187$	−0.0999761	−	0.173164i	−0.00731097	−	0.0126630i
$188$	−6.24000			−0.455099
$189$	−21.4691	+	10.3212i	−1.56165	+	0.750759i
$190$	−12.2667			−0.889923
$191$	21.5616			1.56014			0.780071	−	0.625691i	$-0.215183\pi$
$191$	21.5616			1.56014			0.780071	+	0.625691i	$0.215183\pi$
$192$	−0.551268	−	1.64198i	−0.0397843	−	0.118500i
$193$	8.63437			0.621515			0.310758	−	0.950489i	$-0.399417\pi$
$193$	8.63437			0.621515			0.310758	+	0.950489i	$0.399417\pi$
$194$	5.24560	−	9.08564i	0.376612	−	0.652311i
$195$	−6.55577	−	1.32680i	−0.469468	−	0.0950143i
$196$	14.0166			1.00119
$197$	4.09993	−	7.10129i	0.292108	−	0.505946i	−0.682200	−	0.731166i	$-0.738977\pi$
$197$	4.09993	−	7.10129i	0.292108	−	0.505946i	0.974308	+	0.225220i	$0.0723099\pi$
$198$	3.68734	+	1.55629i	0.262048	+	0.110600i
$199$	−12.5910	+	21.8082i	−0.892549	+	1.54594i	−0.0557403	+	0.998445i	$0.517752\pi$
$199$	−12.5910	+	21.8082i	−0.892549	+	1.54594i	−0.836809	+	0.547495i	$0.815581\pi$
$200$	−2.34191	+	4.05631i	−0.165598	+	0.286825i
$201$	11.6477	−	13.1925i	0.821566	−	0.930529i
$202$	−8.67516	+	15.0258i	−0.610382	+	1.05721i
$203$	19.0443			1.33665
$204$	−0.0826226	−	0.246096i	−0.00578474	−	0.0172302i
$205$	6.62376	−	11.4727i	0.462624	−	0.801288i
$206$	−9.73922	+	16.8688i	−0.678563	+	1.17531i
$207$	−1.21448	−	9.72654i	−0.0844121	−	0.676042i
$208$	0.620478	−	1.07470i	0.0430224	−	0.0745170i
$209$	2.62946	+	4.55435i	0.181883	+	0.315031i
$210$	−16.3541	+	18.5231i	−1.12854	+	1.27822i
$211$	23.6580			1.62868			0.814342	−	0.580386i	$-0.197098\pi$
$211$	23.6580			1.62868			0.814342	+	0.580386i	$0.197098\pi$
$212$	−5.25836	−	9.10775i	−0.361146	−	0.625523i
$213$	8.61753	+	1.74408i	0.590463	+	0.119502i
$214$	3.59396	−	6.22492i	0.245678	−	0.425527i
$215$	18.1515			1.23792
$216$	4.29130	+	2.92997i	0.291986	+	0.199360i
$217$	25.4323	+	2.17062i	1.72646	+	0.147351i
$218$	9.37510	+	16.2382i	0.634962	+	1.09979i
$219$	11.9983	+	2.42830i	0.810771	+	0.164090i
$220$	4.15158			0.279900
$221$	0.0929957	−	0.161073i	0.00625557	−	0.0108350i
$222$	3.52617	+	0.713651i	0.236661	+	0.0478971i
$223$	2.53277	−	4.38688i	0.169607	−	0.293767i	−0.768675	−	0.639640i	$-0.779084\pi$
$223$	2.53277	−	4.38688i	0.169607	−	0.293767i	0.938282	+	0.345872i	$0.112417\pi$
$224$	−2.29219	−	3.97020i	−0.153154	−	0.265270i
$225$	−1.74098	−	13.9432i	−0.116065	−	0.929547i
$226$	0.0474322	−	0.0821550i	0.00315514	−	0.00546487i
$227$	6.58421			0.437010			0.218505	−	0.975836i	$-0.429882\pi$
$227$	6.58421			0.437010			0.218505	+	0.975836i	$0.429882\pi$
$228$	2.17305	+	6.47253i	0.143913	+	0.428654i
$229$	14.3825			0.950420			0.475210	−	0.879872i	$-0.342372\pi$
$229$	14.3825			0.950420			0.475210	+	0.879872i	$0.342372\pi$
$230$	−5.08382	−	8.80543i	−0.335217	−	0.580613i
$231$	10.3828	+	2.10135i	0.683139	+	0.138258i
$232$	−2.07708	−	3.59761i	−0.136367	−	0.236195i
$233$	−8.92149			−0.584466			−0.292233	−	0.956347i	$-0.594398\pi$
$233$	−8.92149			−0.584466			−0.292233	+	0.956347i	$0.594398\pi$
$234$	0.461264	+	3.69418i	0.0301538	+	0.241496i
$235$	9.70909	−	16.8166i	0.633351	−	1.09700i
$236$	3.73172	−	6.46352i	0.242914	−	0.420740i
$237$	3.63804	+	0.736292i	0.236316	+	0.0478273i
$238$	−0.343548	−	0.595043i	−0.0222689	−	0.0385709i
$239$	−12.3222	−	21.3427i	−0.797057	−	1.38054i	−0.921525	−	0.388320i	$-0.873056\pi$
$239$	−12.3222	−	21.3427i	−0.797057	−	1.38054i	0.124467	−	0.992224i	$-0.460278\pi$
$240$	5.28283	+	1.06918i	0.341006	+	0.0690151i
$241$	2.18737	−	3.78864i	0.140901	−	0.244048i	−0.786935	−	0.617036i	$-0.788333\pi$
$241$	2.18737	−	3.78864i	0.140901	−	0.244048i	0.927836	+	0.372988i	$0.121667\pi$
$242$	4.61008	+	7.98490i	0.296347	+	0.513289i
$243$	−15.5699	+	0.759622i	−0.998812	+	0.0487298i
$244$	−14.2243			−0.910615
$245$	−21.8091	+	37.7744i	−1.39333	+	2.41332i
$246$	−7.22695	−	1.46264i	−0.460773	−	0.0932545i
$247$	−2.44587	+	4.23636i	−0.155627	+	0.269553i
$248$	−2.36375	−	5.04110i	−0.150098	−	0.320110i
$249$	−9.19022	−	27.3735i	−0.582406	−	1.73473i
$250$	0.491946	+	0.852076i	0.0311134	+	0.0538900i
$251$	1.93269	+	3.34751i	0.121990	+	0.211293i	0.920552	−	0.390619i	$-0.127739\pi$
$251$	1.93269	+	3.34751i	0.121990	+	0.211293i	−0.798562	+	0.601912i	$0.794406\pi$
$252$	12.6708	+	5.34787i	0.798187	+	0.336884i
$253$	−2.17950	+	3.77500i	−0.137024	+	0.237332i
$254$	7.33116	−	12.6979i	0.459998	−	0.796740i
$255$	0.791777	+	0.160245i	0.0495830	+	0.0100350i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.06614	−	5.31071i	−0.191261	−	0.331273i	0.754408	−	0.656406i	$-0.227924\pi$
$257$	−3.06614	−	5.31071i	−0.191261	−	0.331273i	−0.945668	+	0.325133i	$0.894591\pi$
$258$	−3.21552	−	9.57761i	−0.200190	−	0.596276i
$259$	9.52229			0.591686
$260$	1.93086	+	3.34434i	0.119747	+	0.207407i
$261$	11.4817	+	4.84599i	0.710700	+	0.299959i
$262$	−6.52132	−	11.2953i	−0.402888	−	0.697823i
$263$	−5.88220	−	10.1883i	−0.362712	−	0.628236i	0.625694	−	0.780068i	$-0.284816\pi$
$263$	−5.88220	−	10.1883i	−0.362712	−	0.628236i	−0.988406	+	0.151833i	$0.951482\pi$
$264$	−0.735450	−	2.19058i	−0.0452638	−	0.134821i
$265$	32.7268			2.01039
$266$	9.03561	+	15.6501i	0.554009	+	0.959571i
$267$	5.39412	+	16.0667i	0.330115	+	0.983264i
$268$	−10.1606			−0.620656
$269$	0.468648	−	0.811722i	0.0285740	−	0.0494915i	−0.851385	−	0.524542i	$-0.824237\pi$
$269$	0.468648	−	0.811722i	0.0285740	−	0.0494915i	0.879959	+	0.475050i	$0.157570\pi$
$270$	−14.5732	+	7.00606i	−0.886897	+	0.426375i
$271$	3.51279			0.213387			0.106693	−	0.994292i	$-0.465974\pi$
$271$	3.51279			0.213387			0.106693	+	0.994292i	$0.465974\pi$
$272$	−0.0749387	+	0.129798i	−0.00454383	+	0.00787014i
$273$	3.13618	+	9.34128i	0.189810	+	0.565360i
$274$	6.32971	+	10.9634i	0.382392	+	0.662322i
$275$	−3.12436	+	5.41155i	−0.188406	+	0.326329i
$276$	−3.74558	+	4.24235i	−0.225457	+	0.255359i
$277$	−2.32215	−	4.02208i	−0.139524	−	0.241663i	0.787792	−	0.615941i	$-0.211224\pi$
$277$	−2.32215	−	4.02208i	−0.139524	−	0.241663i	−0.927317	+	0.374278i	$0.877891\pi$
$278$	11.6637			0.699542
$279$	14.7807	+	7.78015i	0.884898	+	0.465785i
$280$	14.2661			0.852562
$281$	−4.54740	−	7.87634i	−0.271275	−	0.469863i	0.697913	−	0.716182i	$-0.254112\pi$
$281$	−4.54740	−	7.87634i	−0.271275	−	0.469863i	−0.969189	+	0.246319i	$0.920779\pi$
$282$	−10.5932	−	2.14393i	−0.630818	−	0.127669i
$283$	−10.3405	+	17.9104i	−0.614682	+	1.06466i	0.375759	+	0.926718i	$0.377382\pi$
$283$	−10.3405	+	17.9104i	−0.614682	+	1.06466i	−0.990440	+	0.137942i	$0.955951\pi$
$284$	−2.53810	−	4.39612i	−0.150609	−	0.260862i
$285$	−20.8244	−	4.21459i	−1.23353	−	0.249651i
$286$	0.827783	−	1.43376i	0.0489479	−	0.0847802i
$287$	−19.5161			−1.15200
$288$	−0.371701	−	2.97688i	−0.0219027	−	0.175415i
$289$	8.48877	−	14.7030i	0.499339	−	0.864881i
$290$	12.9273			0.759115
$291$	12.0267	−	13.6218i	0.705019	−	0.798524i
$292$	−3.53384	−	6.12079i	−0.206802	−	0.358192i
$293$	32.9908			1.92735			0.963673	−	0.267086i	$-0.0860607\pi$
$293$	32.9908			1.92735			0.963673	+	0.267086i	$0.0860607\pi$
$294$	23.7951	+	4.81581i	1.38776	+	0.280864i
$295$	11.6127	+	20.1137i	0.676116	+	1.17107i
$296$	−1.03856	−	1.79883i	−0.0603648	−	0.104555i
$297$	5.72504	+	3.90889i	0.332201	+	0.226817i
$298$	6.16945	+	10.6858i	0.357386	+	0.619011i
$299$	−4.05465			−0.234486
$300$	−5.36937	+	6.08150i	−0.310001	+	0.351115i
$301$	−13.3703	−	23.1580i	−0.770650	−	1.33480i
$302$	−6.11145	+	10.5853i	−0.351674	+	0.609118i
$303$	−19.8898	+	22.5277i	−1.14264	+	1.29418i
$304$	1.97095	−	3.41379i	0.113042	−	0.195794i
$305$	22.1321	−	38.3340i	1.26728	−	2.19500i
$306$	−0.0557095	−	0.446168i	−0.00318470	−	0.0255057i
$307$	3.21069	+	5.56107i	0.183244	+	0.317387i	0.942983	−	0.332840i	$-0.108007\pi$
$307$	3.21069	+	5.56107i	0.183244	+	0.317387i	−0.759740	+	0.650227i	$0.774674\pi$
$308$	−3.05803	−	5.29666i	−0.174247	−	0.301805i
$309$	−22.3294	+	25.2909i	−1.27027	+	1.43875i
$310$	17.2635	+	1.47341i	0.980500	+	0.0836843i
$311$	−12.2441	+	21.2074i	−0.694299	+	1.20256i	0.276117	+	0.961124i	$0.410952\pi$
$311$	−12.2441	+	21.2074i	−0.694299	+	1.20256i	−0.970416	+	0.241438i	$0.922381\pi$
$312$	1.42259	−	1.61126i	0.0805382	−	0.0912198i
$313$	−2.51364	+	4.35375i	−0.142079	+	0.246088i	−0.928279	−	0.371884i	$-0.878712\pi$
$313$	−2.51364	+	4.35375i	−0.142079	+	0.246088i	0.786200	+	0.617972i	$0.212045\pi$
$314$	−6.06388			−0.342205
$315$	−34.1274	+	25.8265i	−1.92286	+	1.45516i
$316$	−1.07150	−	1.85590i	−0.0602769	−	0.104403i
$317$	−12.3015	+	21.3069i	−0.690924	+	1.19671i	0.280612	+	0.959821i	$0.409463\pi$
$317$	−12.3015	+	21.3069i	−0.690924	+	1.19671i	−0.971536	+	0.236893i	$0.923871\pi$
$318$	−5.79753	−	17.2683i	−0.325109	−	0.968356i
$319$	−2.77104	−	4.79959i	−0.155149	−	0.268725i
$320$	−1.55594	−	2.69497i	−0.0869798	−	0.150653i
$321$	8.23997	−	9.33281i	0.459910	−	0.520907i
$322$	−7.48942	+	12.9721i	−0.417369	+	0.722904i
$323$	0.295401	−	0.511650i	0.0164366	−	0.0284689i
$324$	6.27837	+	6.44842i	0.348798	+	0.358245i
$325$	−5.81243			−0.322415
$326$	2.82400	+	4.89130i	0.156407	+	0.270904i
$327$	10.3364	+	30.7875i	0.571604	+	1.70255i
$328$	2.12854	+	3.68673i	0.117529	+	0.203566i
$329$	−28.6066			−1.57713
$330$	7.04786	+	1.42639i	0.387972	+	0.0785204i
$331$	29.5951			1.62669			0.813347	−	0.581778i	$-0.197643\pi$
$331$	29.5951			1.62669			0.813347	+	0.581778i	$0.197643\pi$
$332$	−8.33552	+	14.4375i	−0.457471	+	0.792363i
$333$	5.74094	+	2.42303i	0.314602	+	0.132781i
$334$	1.41452	+	2.45002i	0.0773989	+	0.134059i
$335$	15.8093	−	27.3825i	0.863753	−	1.49606i
$336$	−2.52723	−	7.52748i	−0.137872	−	0.410658i
$337$	−3.92175	+	6.79268i	−0.213632	+	0.370021i	−0.952848	−	0.303447i	$-0.901863\pi$
$337$	−3.92175	+	6.79268i	−0.213632	+	0.370021i	0.739217	+	0.673468i	$0.235196\pi$
$338$	−11.4600			−0.623343
$339$	0.108749	−	0.123172i	0.00590644	−	0.00668980i
$340$	−0.233201	−	0.403915i	−0.0126471	−	0.0219054i
$341$	−3.15349	−	6.72535i	−0.170771	−	0.364198i
$342$	1.46521	+	11.7346i	0.0792293	+	0.634534i
$343$	32.1670			1.73685
$344$	−2.91648	+	5.05149i	−0.157246	+	0.272358i
$345$	−5.60510	−	16.6951i	−0.301768	−	0.898833i
$346$	2.23138	+	3.86487i	0.119960	+	0.207776i
$347$	−21.5902			−1.15902			−0.579511	−	0.814965i	$-0.696756\pi$
$347$	−21.5902			−1.15902			−0.579511	+	0.814965i	$0.696756\pi$
$348$	−2.29006	−	6.82105i	−0.122760	−	0.365647i
$349$	5.68590	+	9.84826i	0.304359	+	0.527165i	0.977118	−	0.212696i	$-0.0682244\pi$
$349$	5.68590	+	9.84826i	0.304359	+	0.527165i	−0.672759	+	0.739861i	$0.734891\pi$
$350$	−10.7362	+	18.5957i	−0.573876	+	0.993983i
$351$	−0.486186	+	6.42985i	−0.0259507	+	0.343200i
$352$	−0.667052	+	1.15537i	−0.0355540	+	0.0615814i
$353$	−17.9443	+	31.0805i	−0.955079	+	1.65425i	−0.220893	+	0.975298i	$0.570897\pi$
$353$	−17.9443	+	31.0805i	−0.955079	+	1.65425i	−0.734186	+	0.678948i	$0.762436\pi$
$354$	8.55581	−	9.69055i	0.454736	−	0.515047i
$355$	15.7966			0.838395
$356$	4.89246	−	8.47400i	0.259300	−	0.449121i
$357$	−0.378774	−	1.12820i	−0.0200469	−	0.0597106i
$358$	−10.2557	+	17.7634i	−0.542030	+	0.938824i
$359$	−7.70252	+	13.3412i	−0.406524	+	0.704119i	−0.994497	−	0.104760i	$-0.966592\pi$
$359$	−7.70252	+	13.3412i	−0.406524	+	0.704119i	0.587974	+	0.808880i	$0.299926\pi$
$360$	8.60096	+	3.63014i	0.453310	+	0.191325i
$361$	1.73070	−	2.99766i	0.0910895	−	0.157772i
$362$	13.6821			0.719117
$363$	5.08278	+	15.1393i	0.266777	+	0.794609i
$364$	2.84451	−	4.92684i	0.149093	−	0.258237i
$365$	21.9938			1.15121
$366$	−24.1476	−	4.88715i	−1.26221	−	0.255456i
$367$	−24.1363			−1.25990			−0.629952	−	0.776634i	$-0.716926\pi$
$367$	−24.1363			−1.25990			−0.629952	+	0.776634i	$0.716926\pi$
$368$	3.26736			0.170323
$369$	−11.7662	−	4.96605i	−0.612522	−	0.258522i
$370$	6.46373			0.336033
$371$	−24.1064	−	41.7535i	−1.25154	−	2.16773i
$372$	−2.28077	−	9.37006i	−0.118252	−	0.485815i
$373$	1.91057	−	3.30921i	0.0989258	−	0.171344i	−0.812315	−	0.583220i	$-0.801793\pi$
$373$	1.91057	−	3.30921i	0.0989258	−	0.171344i	0.911240	+	0.411875i	$0.135126\pi$
$374$	−0.0999761	+	0.173164i	−0.00516964	+	0.00895408i
$375$	0.542388	+	1.61553i	0.0280088	+	0.0834258i
$376$	3.12000	+	5.40400i	0.160902	+	0.278690i
$377$	2.57757	−	4.46448i	0.132751	−	0.229932i
$378$	19.6730	+	13.4321i	1.01187	+	0.690875i
$379$	8.90867	+	15.4303i	0.457608	+	0.792600i	0.998834	−	0.0482772i	$-0.0153731\pi$
$379$	8.90867	+	15.4303i	0.457608	+	0.792600i	−0.541226	+	0.840877i	$0.682040\pi$
$380$	6.13337	+	10.6233i	0.314635	+	0.544965i
$381$	16.8083	−	19.0376i	0.861118	−	0.975326i
$382$	−10.7808	−	18.6729i	−0.551594	−	0.955388i
$383$	4.42885	+	7.67099i	0.226304	+	0.391969i	0.956710	−	0.291044i	$-0.0940025\pi$
$383$	4.42885	+	7.67099i	0.226304	+	0.391969i	−0.730406	+	0.683013i	$0.760669\pi$
$384$	−1.14636	+	1.29840i	−0.0585001	+	0.0662588i
$385$	19.0325			0.969984
$386$	−4.31718	−	7.47758i	−0.219739	−	0.380599i
$387$	−2.16811	−	17.3640i	−0.110211	−	0.882663i
$388$	−10.4912			−0.532610
$389$	16.4029	−	28.4106i	0.831659	−	1.44048i	−0.0650625	−	0.997881i	$-0.520725\pi$
$389$	16.4029	−	28.4106i	0.831659	−	1.44048i	0.896722	−	0.442595i	$-0.145942\pi$
$390$	2.12884	+	6.34086i	0.107798	+	0.321082i
$391$	0.489703			0.0247653
$392$	−7.00831	−	12.1388i	−0.353973	−	0.613100i
$393$	−7.18999	−	21.4158i	−0.362687	−	1.08028i
$394$	−8.19987			−0.413103
$395$	6.66880			0.335544
$396$	−0.495888	−	3.97148i	−0.0249193	−	0.199574i
$397$	−6.83989	−	11.8470i	−0.343284	−	0.594586i	0.641756	−	0.766909i	$-0.278206\pi$
$397$	−6.83989	−	11.8470i	−0.343284	−	0.594586i	−0.985041	+	0.172323i	$0.944873\pi$
$398$	25.1819			1.26226
$399$	9.96209	+	29.6726i	0.498728	+	1.48549i
$400$	4.68383			0.234191
$401$	7.20073	−	12.4720i	0.359587	−	0.622823i	−0.628305	−	0.777967i	$-0.716251\pi$
$401$	7.20073	−	12.4720i	0.359587	−	0.622823i	0.987892	+	0.155144i	$0.0495842\pi$
$402$	−17.2489	−	3.49096i	−0.860298	−	0.174113i
$403$	3.95101	−	5.66822i	0.196814	−	0.282354i
$404$	17.3503			0.863210
$405$	−27.1471	+	6.88666i	−1.34895	+	0.342201i
$406$	−9.52214	−	16.4928i	−0.472576	−	0.818526i
$407$	−1.38554	−	2.39983i	−0.0686788	−	0.118955i
$408$	−0.171814	+	0.194601i	−0.00850606	+	0.00963420i
$409$	26.6692			1.31871			0.659354	−	0.751833i	$-0.270830\pi$
$409$	26.6692			1.31871			0.659354	+	0.751833i	$0.270830\pi$
$410$	−13.2475			−0.654249
$411$	6.97873	+	20.7865i	0.344235	+	1.02532i
$412$	19.4784			0.959633
$413$	17.1076	−	29.6313i	0.841812	−	1.45806i
$414$	−7.81619	+	5.91504i	−0.384145	+	0.290708i
$415$	−25.9392	−	44.9280i	−1.27330	−	2.20543i
$416$	−1.24096			−0.0608429
$417$	19.8007	+	4.00740i	0.969643	+	0.196243i
$418$	2.62946	−	4.55435i	0.128611	−	0.222761i
$419$	−4.60283	+	7.97234i	−0.224863	+	0.389474i	−0.956278	−	0.292458i	$-0.905527\pi$
$419$	−4.60283	+	7.97234i	−0.224863	+	0.389474i	0.731415	+	0.681932i	$0.238860\pi$
$420$	24.2186	+	4.90152i	1.18175	+	0.239170i
$421$	7.76674			0.378528			0.189264	−	0.981926i	$-0.439390\pi$
$421$	7.76674			0.378528			0.189264	+	0.981926i	$0.439390\pi$
$422$	−11.8290	−	20.4884i	−0.575827	−	0.997361i
$423$	−17.2468	−	7.27921i	−0.838568	−	0.353928i
$424$	−5.25836	+	9.10775i	−0.255369	+	0.442311i
$425$	0.702000			0.0340520
$426$	−2.79835	−	8.33504i	−0.135581	−	0.403834i
$427$	−65.2096			−3.15571
$428$	−7.18792			−0.347441
$429$	1.89788	−	2.14959i	0.0916306	−	0.103783i
$430$	−9.07574	−	15.7196i	−0.437671	−	0.758069i
$431$	−5.51395	−	9.55044i	−0.265597	−	0.460028i	0.702123	−	0.712056i	$-0.252236\pi$
$431$	−5.51395	−	9.55044i	−0.265597	−	0.460028i	−0.967720	+	0.252028i	$0.918903\pi$
$432$	0.391783	−	5.18136i	0.0188497	−	0.249288i
$433$	6.89412			0.331310			0.165655	−	0.986184i	$-0.447026\pi$
$433$	6.89412			0.331310			0.165655	+	0.986184i	$0.447026\pi$
$434$	−10.8364	−	23.1104i	−0.520162	−	1.10933i
$435$	21.9457	+	4.44153i	1.05222	+	0.212955i
$436$	9.37510	−	16.2382i	0.448986	−	0.777666i
$437$	−12.8796			−0.616115
$438$	−3.89619	−	11.6050i	−0.186167	−	0.554508i
$439$	9.79493			0.467486			0.233743	−	0.972298i	$-0.424903\pi$
$439$	9.79493			0.467486			0.233743	+	0.972298i	$0.424903\pi$
$440$	−2.07579	−	3.59537i	−0.0989594	−	0.171403i
$441$	38.7407	+	16.3510i	1.84479	+	0.778617i
$442$	−0.185991			−0.00884671
$443$	9.40792			0.446984			0.223492	−	0.974706i	$-0.428254\pi$
$443$	9.40792			0.446984			0.223492	+	0.974706i	$0.428254\pi$
$444$	−1.14505	−	3.41058i	−0.0543414	−	0.161859i
$445$	15.2248	+	26.3701i	0.721724	+	1.25006i
$446$	−5.06553			−0.239860
$447$	6.80204	+	20.2602i	0.321725	+	0.958276i
$448$	−2.29219	+	3.97020i	−0.108296	+	0.187574i
$449$	1.70834			0.0806214			0.0403107	−	0.999187i	$-0.487165\pi$
$449$	1.70834			0.0806214			0.0403107	+	0.999187i	$0.487165\pi$
$450$	−11.2047	+	8.47934i	−0.528194	+	0.399720i
$451$	2.83969	+	4.91849i	0.133716	+	0.231603i
$452$	−0.0948645			−0.00446205
$453$	−14.0119	+	15.8702i	−0.658335	+	0.745649i
$454$	−3.29211	−	5.70210i	−0.154506	−	0.267613i
$455$	8.85180	+	15.3318i	0.414979	+	0.718765i
$456$	4.51885	−	5.11818i	0.211615	−	0.239681i
$457$	−14.1345	−	24.4816i	−0.661182	−	1.14520i	−0.980305	−	0.197487i	$-0.936722\pi$
$457$	−14.1345	−	24.4816i	−0.661182	−	1.14520i	0.319124	−	0.947713i	$-0.396612\pi$
$458$	−7.19123	−	12.4556i	−0.336024	−	0.582011i
$459$	0.0587194	−	0.776569i	0.00274079	−	0.0362471i
$460$	−5.08382	+	8.80543i	−0.237034	+	0.410555i
$461$	−5.37864	−	9.31608i	−0.250508	−	0.433893i	0.713158	−	0.701004i	$-0.247264\pi$
$461$	−5.37864	−	9.31608i	−0.250508	−	0.433893i	−0.963666	+	0.267111i	$0.913931\pi$
$462$	−3.37159	−	10.0425i	−0.156860	−	0.467217i
$463$	−13.2241	+	22.9049i	−0.614577	+	1.06448i	0.375881	+	0.926668i	$0.377340\pi$
$463$	−13.2241	+	22.9049i	−0.614577	+	1.06448i	−0.990458	+	0.137811i	$0.955993\pi$
$464$	−2.07708	+	3.59761i	−0.0964260	+	0.167015i
$465$	28.8008	+	8.43268i	1.33560	+	0.391056i
$466$	4.46075	+	7.72624i	0.206640	+	0.357911i
$467$	5.38886			0.249367			0.124683	−	0.992197i	$-0.460208\pi$
$467$	5.38886			0.249367			0.124683	+	0.992197i	$0.460208\pi$
$468$	2.96863	−	2.24656i	0.137225	−	0.103847i
$469$	−46.5800			−2.15087
$470$	−19.4182			−0.895694
$471$	−10.2942	−	2.08342i	−0.474334	−	0.0959989i
$472$	−7.46343			−0.343532
$473$	−3.89089	+	6.73922i	−0.178903	+	0.309869i
$474$	−1.18137	−	3.51878i	−0.0542623	−	0.161623i
$475$	−18.4632			−0.847149
$476$	−0.343548	+	0.595043i	−0.0157465	+	0.0272737i
$477$	−3.90907	−	31.3071i	−0.178984	−	1.43345i
$478$	−12.3222	+	21.3427i	−0.563605	+	0.976192i
$479$	7.47596	−	12.9487i	0.341585	−	0.591643i	−0.643142	−	0.765747i	$-0.722370\pi$
$479$	7.47596	−	12.9487i	0.341585	−	0.591643i	0.984727	+	0.174104i	$0.0557029\pi$
$480$	−1.71548	−	5.10966i	−0.0783007	−	0.233223i
$481$	1.28880	−	2.23227i	0.0587643	−	0.101783i
$482$	−4.37475			−0.199264
$483$	−17.1712	+	19.4486i	−0.781316	+	0.884940i
$484$	4.61008	−	7.98490i	0.209549	−	0.362950i
$485$	16.3237	−	28.2735i	0.741221	−	1.28383i
$486$	8.44282	+	13.1042i	0.382974	+	0.594416i
$487$	13.2397	−	22.9319i	0.599949	−	1.03914i	−0.392879	−	0.919590i	$-0.628521\pi$
$487$	13.2397	−	22.9319i	0.599949	−	1.03914i	0.992828	−	0.119552i	$-0.0381459\pi$
$488$	7.11213	+	12.3186i	0.321951	+	0.557636i
$489$	3.11356	+	9.27390i	0.140800	+	0.419380i
$490$	43.6181			1.97047
$491$	−8.88757	−	15.3937i	−0.401090	−	0.694709i	0.592767	−	0.805374i	$-0.298035\pi$
$491$	−8.88757	−	15.3937i	−0.401090	−	0.694709i	−0.993858	+	0.110665i	$0.964702\pi$
$492$	2.34679	+	6.99004i	0.105801	+	0.315135i
$493$	−0.311307	+	0.539200i	−0.0140206	+	0.0242844i
$494$	4.89173			0.220089
$495$	11.4746	+	4.84299i	0.515744	+	0.217676i
$496$	−3.18384	+	4.56762i	−0.142959	+	0.205092i
$497$	−11.6357	−	20.1535i	−0.521930	−	0.904010i
$498$	−19.1111	+	21.6457i	−0.856388	+	0.969969i
$499$	−1.43327			−0.0641621			−0.0320811	−	0.999485i	$-0.510213\pi$
$499$	−1.43327			−0.0641621			−0.0320811	+	0.999485i	$0.510213\pi$
$500$	0.491946	−	0.852076i	0.0220005	−	0.0381060i
$501$	1.55956	+	4.64522i	0.0696758	+	0.207533i
$502$	1.93269	−	3.34751i	0.0862600	−	0.149407i
$503$	20.0308	+	34.6944i	0.893130	+	1.54695i	0.836102	+	0.548574i	$0.184829\pi$
$503$	20.0308	+	34.6944i	0.893130	+	1.54695i	0.0570283	+	0.998373i	$0.481837\pi$
$504$	−1.70402	−	13.6472i	−0.0759031	−	0.607894i
$505$	−26.9961	+	46.7586i	−1.20131	+	2.08073i
$506$	4.35900			0.193781
$507$	−19.4549	−	3.93742i	−0.864023	−	0.174867i
$508$	−14.6623			−0.650535
$509$	−8.75980	−	15.1724i	−0.388271	−	0.672505i	0.603946	−	0.797025i	$-0.293594\pi$
$509$	−8.75980	−	15.1724i	−0.388271	−	0.672505i	−0.992217	+	0.124520i	$0.960261\pi$
$510$	−0.257112	−	0.765822i	−0.0113851	−	0.0339112i
$511$	−16.2005	−	28.0601i	−0.716668	−	1.24131i
$512$	1.00000			0.0441942
$513$	−1.54437	+	20.4244i	−0.0681856	+	0.901760i
$514$	−3.06614	+	5.31071i	−0.135242	+	0.234246i
$515$	−30.3073	+	52.4938i	−1.33550	+	2.31315i
$516$	−6.68669	+	7.57353i	−0.294365	+	0.333406i
$517$	4.16241	+	7.20951i	0.183063	+	0.317074i
$518$	−4.76114	−	8.24654i	−0.209193	−	0.362332i
$519$	2.46018	+	7.32777i	0.107990	+	0.321654i
$520$	1.93086	−	3.34434i	0.0846737	−	0.146659i
$521$	−4.04021	−	6.99786i	−0.177005	−	0.306582i	0.763848	−	0.645396i	$-0.223308\pi$
$521$	−4.04021	−	6.99786i	−0.177005	−	0.306582i	−0.940853	+	0.338814i	$0.889974\pi$
$522$	−1.54410	−	12.3665i	−0.0675836	−	0.541265i
$523$	−24.3174			−1.06332			−0.531662	−	0.846956i	$-0.678432\pi$
$523$	−24.3174			−1.06332			−0.531662	+	0.846956i	$0.678432\pi$
$524$	−6.52132	+	11.2953i	−0.284885	+	0.493436i
$525$	−24.6153	+	27.8799i	−1.07430	+	1.21678i
$526$	−5.88220	+	10.1883i	−0.256476	+	0.444230i
$527$	−0.477186	+	0.684583i	−0.0207866	+	0.0298209i
$528$	−1.52937	+	1.73221i	−0.0665573	+	0.0753846i
$529$	6.16219	+	10.6732i	0.267921	+	0.464053i
$530$	−16.3634	−	28.3423i	−0.710781	−	1.23111i
$531$	17.8541	−	13.5114i	0.774801	−	0.586344i
$532$	9.03561	−	15.6501i	0.391743	−	0.678519i
$533$	−2.64142	+	4.57508i	−0.114413	+	0.198169i
$534$	11.2171	−	12.7048i	0.485411	−	0.549790i
$535$	11.1840	−	19.3712i	0.483526	−	0.837491i
$536$	5.08029	+	8.79932i	0.219435	+	0.380073i
$537$	−23.5135	+	26.6320i	−1.01468	+	1.14926i
$538$	−0.937296			−0.0404097
$539$	−9.34983	−	16.1944i	−0.402726	−	0.697541i
$540$	13.3540	+	9.11774i	0.574666	+	0.392365i
$541$	−10.9176	−	18.9098i	−0.469384	−	0.812998i	0.530003	−	0.847996i	$-0.322191\pi$
$541$	−10.9176	−	18.9098i	−0.469384	−	0.812998i	−0.999387	+	0.0349982i	$0.988857\pi$
$542$	−1.75640	−	3.04217i	−0.0754437	−	0.130672i
$543$	23.2272	+	4.70089i	0.996775	+	0.201734i
$544$	0.149877			0.00642594
$545$	29.1742	+	50.5313i	1.24969	+	2.16452i
$546$	6.52170	−	7.38665i	0.279103	−	0.316120i
$547$	−10.4229			−0.445652			−0.222826	−	0.974858i	$-0.571528\pi$
$547$	−10.4229			−0.445652			−0.222826	+	0.974858i	$0.571528\pi$
$548$	6.32971	−	10.9634i	0.270392	−	0.468332i
$549$	−39.3145	−	16.5932i	−1.67790	−	0.708179i
$550$	6.24872			0.266446
$551$	8.18765	−	14.1814i	0.348806	−	0.604149i
$552$	5.54677	+	1.12259i	0.236086	+	0.0477808i
$553$	−4.91220	−	8.50817i	−0.208888	−	0.361804i
$554$	−2.32215	+	4.02208i	−0.0986586	+	0.170882i
$555$	10.9730	+	2.22080i	0.465779	+	0.0942677i
$556$	−5.83185	−	10.1011i	−0.247325	−	0.428380i
$557$	2.94050			0.124593			0.0622966	−	0.998058i	$-0.480158\pi$
$557$	2.94050			0.124593			0.0622966	+	0.998058i	$0.480158\pi$
$558$	−0.652550	−	16.6905i	−0.0276247	−	0.706567i
$559$	−7.23845			−0.306154
$560$	−7.13305	−	12.3548i	−0.301426	−	0.522086i
$561$	−0.229218	+	0.259618i	−0.00967759	+	0.0109611i
$562$	−4.54740	+	7.87634i	−0.191821	+	0.332243i
$563$	5.44557	+	9.43200i	0.229503	+	0.397512i	0.957661	−	0.287898i	$-0.0929565\pi$
$563$	5.44557	+	9.43200i	0.229503	+	0.397512i	−0.728158	+	0.685410i	$0.759623\pi$
$564$	3.43992	+	10.2460i	0.144847	+	0.431433i
$565$	0.147604	−	0.255657i	0.00620973	−	0.0107556i
$566$	20.6811			0.869291
$567$	28.7825	+	29.5621i	1.20875	+	1.24149i
$568$	−2.53810	+	4.39612i	−0.106496	+	0.184457i
$569$	−20.0804			−0.841815			−0.420907	−	0.907104i	$-0.638288\pi$
$569$	−20.0804			−0.841815			−0.420907	+	0.907104i	$0.638288\pi$
$570$	6.76227	+	20.1418i	0.283240	+	0.843646i
$571$	−4.49816	−	7.79104i	−0.188242	−	0.326045i	0.756422	−	0.654084i	$-0.226946\pi$
$571$	−4.49816	−	7.79104i	−0.188242	−	0.326045i	−0.944664	+	0.328039i	$0.893612\pi$
$572$	−1.65557			−0.0692227
$573$	−11.8862	−	35.4038i	−0.496554	−	1.47901i
$574$	9.75804	+	16.9014i	0.407293	+	0.705452i
$575$	−7.65187	−	13.2534i	−0.319105	−	0.552706i
$576$	−2.39221	+	1.81034i	−0.0996753	+	0.0754310i
$577$	15.7593	+	27.2959i	0.656069	+	1.13634i	0.981625	+	0.190822i	$0.0611153\pi$
$577$	15.7593	+	27.2959i	0.656069	+	1.13634i	−0.325556	+	0.945523i	$0.605551\pi$
$578$	−16.9775			−0.706172
$579$	−4.75985	−	14.1775i	−0.197813	−	0.589196i
$580$	−6.46363	−	11.1953i	−0.268388	−	0.464861i
$581$	−38.2133	+	66.1873i	−1.58535	+	2.74591i
$582$	−17.8102	−	3.60455i	−0.738256	−	0.149413i
$583$	−7.01520	+	12.1507i	−0.290540	+	0.503230i
$584$	−3.53384	+	6.12079i	−0.146231	+	0.253280i
$585$	1.43540	+	11.4959i	0.0593465	+	0.475296i
$586$	−16.4954	−	28.5709i	−0.681420	−	1.18025i
$587$	−13.6051	−	23.5647i	−0.561541	−	0.972618i	−0.997362	−	0.0725849i	$-0.976875\pi$
$587$	−13.6051	−	23.5647i	−0.561541	−	0.972618i	0.435821	−	0.900033i	$-0.356458\pi$
$588$	−7.72692	−	23.0150i	−0.318653	−	0.949124i
$589$	12.5504	−	18.0051i	0.517130	−	0.741888i
$590$	11.6127	−	20.1137i	0.478086	−	0.828070i
$591$	−13.9204	−	2.81730i	−0.572607	−	0.115888i
$592$	−1.03856	+	1.79883i	−0.0426844	+	0.0739315i
$593$	21.2264			0.871663			0.435831	−	0.900028i	$-0.356454\pi$
$593$	21.2264			0.871663			0.435831	+	0.900028i	$0.356454\pi$
$594$	0.522680	−	6.91248i	0.0214458	−	0.283622i
$595$	−1.06908	−	1.85170i	−0.0438281	−	0.0759125i
$596$	6.16945	−	10.6858i	0.252710	−	0.437707i
$597$	42.7496	+	8.65197i	1.74963	+	0.354101i
$598$	2.02732	+	3.51143i	0.0829035	+	0.143593i
$599$	−6.55307	−	11.3502i	−0.267751	−	0.463758i	0.700530	−	0.713623i	$-0.252947\pi$
$599$	−6.55307	−	11.3502i	−0.267751	−	0.463758i	−0.968281	+	0.249865i	$0.919614\pi$
$600$	7.95141	+	1.60926i	0.324615	+	0.0656979i
$601$	−0.717544	+	1.24282i	−0.0292692	+	0.0506958i	−0.880289	−	0.474438i	$-0.842651\pi$
$601$	−0.717544	+	1.24282i	−0.0292692	+	0.0506958i	0.851020	+	0.525134i	$0.175985\pi$
$602$	−13.3703	+	23.1580i	−0.544932	+	0.943849i
$603$	−28.0829	−	11.8527i	−1.14362	−	0.482680i
$604$	12.2229			0.497342
$605$	14.3460	+	24.8481i	0.583250	+	1.01022i
$606$	29.4544	+	5.96120i	1.19651	+	0.242157i
$607$	−11.9384	−	20.6780i	−0.484566	−	0.839292i	0.515277	−	0.857024i	$-0.327689\pi$
$607$	−11.9384	−	20.6780i	−0.484566	−	0.839292i	−0.999843	+	0.0177314i	$0.994356\pi$
$608$	−3.94190			−0.159865
$609$	−10.4985	−	31.2704i	−0.425421	−	1.26714i
$610$	−44.2643			−1.79221
$611$	−3.87179	+	6.70613i	−0.156636	+	0.271301i
$612$	−0.358538	+	0.271330i	−0.0144930	+	0.0109678i
$613$	−1.45406	−	2.51851i	−0.0587290	−	0.101722i	0.835166	−	0.549998i	$-0.185371\pi$
$613$	−1.45406	−	2.51851i	−0.0587290	−	0.101722i	−0.893895	+	0.448276i	$0.852038\pi$
$614$	3.21069	−	5.56107i	0.129573	−	0.224427i
$615$	−22.4894	−	4.55157i	−0.906861	−	0.183537i
$616$	−3.05803	+	5.29666i	−0.123211	+	0.213409i
$617$	−5.80574			−0.233730			−0.116865	−	0.993148i	$-0.537284\pi$
$617$	−5.80574			−0.233730			−0.116865	+	0.993148i	$0.537284\pi$
$618$	33.0672	+	6.69237i	1.33016	+	0.269207i
$619$	10.3101	+	17.8576i	0.414397	+	0.717756i	0.995365	−	0.0961703i	$-0.0306593\pi$
$619$	10.3101	+	17.8576i	0.414397	+	0.717756i	−0.580968	+	0.813926i	$0.697326\pi$
$620$	−7.35573	−	15.6873i	−0.295413	−	0.630018i
$621$	−15.3013	+	7.35608i	−0.614020	+	0.295190i
$622$	24.4882			0.981888
$623$	22.4290	−	38.8481i	0.898597	−	1.55642i
$624$	−2.10669	−	0.426366i	−0.0843350	−	0.0170683i
$625$	13.2404	+	22.9331i	0.529618	+	0.917325i
$626$	5.02727			0.200930
$627$	6.02863	−	6.82819i	0.240760	−	0.272692i
$628$	3.03194	+	5.25148i	0.120988	+	0.209557i
$629$	−0.155656	+	0.269604i	−0.00620641	+	0.0107498i
$630$	39.4302	+	16.6420i	1.57094	+	0.663032i
$631$	3.33343	−	5.77367i	0.132702	−	0.229846i	−0.792015	−	0.610501i	$-0.790968\pi$
$631$	3.33343	−	5.77367i	0.132702	−	0.229846i	0.924717	+	0.380655i	$0.124301\pi$
$632$	−1.07150	+	1.85590i	−0.0426222	+	0.0738238i
$633$	−13.0419	−	38.8460i	−0.518369	−	1.54399i
$634$	24.6031			0.977113
$635$	22.8137	−	39.5145i	0.905335	−	1.56809i
$636$	−12.0560	+	13.6549i	−0.478051	+	0.541454i
$637$	8.69702	−	15.0637i	0.344588	−	0.596844i
$638$	−2.77104	+	4.79959i	−0.109707	+	0.190017i
$639$	−1.88683	−	15.1113i	−0.0746418	−	0.597793i
$640$	−1.55594	+	2.69497i	−0.0615040	+	0.106528i
$641$	−14.1363			−0.558348			−0.279174	−	0.960240i	$-0.590061\pi$
$641$	−14.1363			−0.558348			−0.279174	+	0.960240i	$0.590061\pi$
$642$	−12.2024	−	2.46961i	−0.481592	−	0.0974679i
$643$	4.04321	−	7.00304i	0.159448	−	0.276173i	−0.775221	−	0.631690i	$-0.782362\pi$
$643$	4.04321	−	7.00304i	0.159448	−	0.276173i	0.934670	+	0.355517i	$0.115695\pi$
$644$	14.9788			0.590249
$645$	−10.0063	−	29.8044i	−0.393999	−	1.17355i
$646$	−0.590802			−0.0232448
$647$	−28.6420			−1.12603			−0.563016	−	0.826446i	$-0.690359\pi$
$647$	−28.6420			−1.12603			−0.563016	+	0.826446i	$0.690359\pi$
$648$	2.44531	−	8.66144i	0.0960608	−	0.340253i
$649$	−9.95700			−0.390847
$650$	2.90621	+	5.03371i	0.113991	+	0.197438i
$651$	−10.4559	−	42.9560i	−0.409800	−	1.68358i
$652$	2.82400	−	4.89130i	0.110596	−	0.191558i
$653$	−10.8274	+	18.7535i	−0.423707	+	0.733882i	−0.996299	−	0.0859586i	$-0.972605\pi$
$653$	−10.8274	+	18.7535i	−0.423707	+	0.733882i	0.572592	+	0.819841i	$0.305938\pi$
$654$	21.4946	−	24.3453i	0.840504	−	0.951977i
$655$	−20.2936	−	35.1495i	−0.792936	−	1.37341i
$656$	2.12854	−	3.68673i	0.0831054	−	0.143943i
$657$	−2.62706	−	21.0397i	−0.102491	−	0.820836i
$658$	14.3033	+	24.7741i	0.557601	+	0.965793i
$659$	6.43258	+	11.1416i	0.250578	+	0.434014i	0.963685	−	0.267041i	$-0.0860461\pi$
$659$	6.43258	+	11.1416i	0.250578	+	0.434014i	−0.713107	+	0.701055i	$0.752713\pi$
$660$	−2.28863	−	6.81682i	−0.0890850	−	0.265344i
$661$	23.0465	+	39.9177i	0.896404	+	1.55262i	0.832057	+	0.554690i	$0.187163\pi$
$661$	23.0465	+	39.9177i	0.896404	+	1.55262i	0.0643470	+	0.997928i	$0.479504\pi$
$662$	−14.7976	−	25.6301i	−0.575123	−	0.996143i
$663$	−0.315745	−	0.0639026i	−0.0122625	−	0.00248177i
$664$	16.6710			0.646962
$665$	28.1178	+	48.7014i	1.09036	+	1.88856i
$666$	−0.772063	−	6.18332i	−0.0299168	−	0.239599i
$667$	13.5731			0.525554
$668$	1.41452	−	2.45002i	0.0547293	−	0.0947939i
$669$	−8.59941	−	1.74041i	−0.332472	−	0.0672881i
$670$	−31.6185			−1.22153
$671$	9.48833	+	16.4343i	0.366293	+	0.634438i
$672$	−5.25538	+	5.95239i	−0.202731	+	0.229618i
$673$	26.1599			1.00839			0.504195	−	0.863590i	$-0.331789\pi$
$673$	26.1599			1.00839			0.504195	+	0.863590i	$0.331789\pi$
$674$	7.84351			0.302121
$675$	−21.9347	+	10.5451i	−0.844269	+	0.405881i
$676$	5.73001	+	9.92467i	0.220385	+	0.381718i
$677$	−4.76289			−0.183053			−0.0915264	−	0.995803i	$-0.529175\pi$
$677$	−4.76289			−0.183053			−0.0915264	+	0.995803i	$0.529175\pi$
$678$	−0.161045	−	0.0325934i	−0.00618489	−	0.00125174i
$679$	−48.0957			−1.84574
$680$	−0.233201	+	0.403915i	−0.00894283	+	0.0154894i
$681$	−3.62967	−	10.8112i	−0.139089	−	0.414284i
$682$	−4.24758	+	6.09368i	−0.162648	+	0.233339i
$683$	8.17127			0.312665			0.156332	−	0.987704i	$-0.450033\pi$
$683$	8.17127			0.312665			0.156332	+	0.987704i	$0.450033\pi$
$684$	9.42985	−	7.13620i	0.360559	−	0.272859i
$685$	19.6973	+	34.1168i	0.752596	+	1.30353i
$686$	−16.0835	−	27.8574i	−0.614070	−	1.06360i
$687$	−7.92859	−	23.6157i	−0.302495	−	0.900997i
$688$	5.83296			0.222379
$689$	−13.0508			−0.497196
$690$	−11.6558	+	13.2017i	−0.443729	+	0.502580i
$691$	29.9051			1.13764			0.568821	−	0.822461i	$-0.307400\pi$
$691$	29.9051			1.13764			0.568821	+	0.822461i	$0.307400\pi$
$692$	2.23138	−	3.86487i	0.0848244	−	0.146920i
$693$	−2.27334	−	18.2068i	−0.0863571	−	0.691619i
$694$	10.7951	+	18.6976i	0.409776	+	0.709753i
$695$	36.2961			1.37679
$696$	−4.76218	+	5.39377i	−0.180510	+	0.204450i
$697$	0.319020	−	0.552558i	0.0120837	−	0.0209296i
$698$	5.68590	−	9.84826i	0.215214	−	0.372762i
$699$	4.91813	+	14.6489i	0.186021	+	0.554073i
$700$	21.4725			0.811584
$701$	23.4373	+	40.5945i	0.885214	+	1.53323i	0.845469	+	0.534025i	$0.179321\pi$
$701$	23.4373	+	40.5945i	0.885214	+	1.53323i	0.0397448	+	0.999210i	$0.487345\pi$
$702$	5.81150	−	2.79387i	0.219341	−	0.105448i
$703$	4.09389	−	7.09082i	0.154404	−	0.267435i
$704$	1.33410			0.0502810
$705$	−32.9649	−	6.67167i	−1.24153	−	0.251270i
$706$	35.8886			1.35069
$707$	79.5406			2.99143
$708$	−12.6702	−	2.56428i	−0.476174	−	0.0963714i
$709$	−3.89645	−	6.74886i	−0.146334	−	0.253459i	0.783536	−	0.621347i	$-0.213414\pi$
$709$	−3.89645	−	6.74886i	−0.146334	−	0.253459i	−0.929870	+	0.367888i	$0.880081\pi$
$710$	−7.89828	−	13.6802i	−0.296417	−	0.513410i
$711$	−0.796558	−	6.37949i	−0.0298733	−	0.239250i
$712$	−9.78493			−0.366706
$713$	18.1260	+	1.54703i	0.678823	+	0.0579366i
$714$	−0.787662	+	0.892128i	−0.0294775	+	0.0333870i
$715$	2.57597	−	4.46170i	0.0963357	−	0.166858i
$716$	20.5114			0.766546
$717$	−28.2515	+	31.9984i	−1.05507	+	1.19500i
$718$	15.4050			0.574911
$719$	17.0942	+	29.6080i	0.637506	+	1.10419i	0.985978	+	0.166874i	$0.0533673\pi$
$719$	17.0942	+	29.6080i	0.637506	+	1.10419i	−0.348472	+	0.937319i	$0.613299\pi$
$720$	−1.15669	−	9.26372i	−0.0431073	−	0.345238i
$721$	89.2967			3.32558
$722$	−3.46140			−0.128820
$723$	−7.42671	−	1.50307i	−0.276202	−	0.0558998i
$724$	−6.84106	−	11.8491i	−0.254246	−	0.440367i
$725$	19.4574			0.722629
$726$	10.5697	−	11.9715i	0.392277	−	0.444304i
$727$	−17.1460	+	29.6978i	−0.635911	+	1.10143i	0.350410	+	0.936596i	$0.386042\pi$
$727$	−17.1460	+	29.6978i	−0.635911	+	1.10143i	−0.986321	+	0.164834i	$0.947291\pi$
$728$	−5.68903			−0.210849
$729$	9.83050	+	25.1468i	0.364092	+	0.931363i
$730$	−10.9969	−	19.0472i	−0.407014	−	0.704968i
$731$	0.874228			0.0323345
$732$	7.84138	+	23.3560i	0.289826	+	0.863262i
$733$	−22.2772	−	38.5853i	−0.822829	−	1.42518i	−0.903567	−	0.428446i	$-0.859061\pi$
$733$	−22.2772	−	38.5853i	−0.822829	−	1.42518i	0.0807386	−	0.996735i	$-0.474272\pi$
$734$	12.0681	+	20.9026i	0.445444	+	0.771531i
$735$	74.0475	+	14.9863i	2.73128	+	0.552776i
$736$	−1.63368	−	2.82961i	−0.0602182	−	0.104301i
$737$	6.77764	+	11.7392i	0.249657	+	0.432419i
$738$	1.58236	+	12.6728i	0.0582474	+	0.466493i
$739$	6.95587	−	12.0479i	0.255876	−	0.443190i	−0.709257	−	0.704950i	$-0.750970\pi$
$739$	6.95587	−	12.0479i	0.255876	−	0.443190i	0.965133	+	0.261760i	$0.0843029\pi$
$740$	−3.23187	−	5.59776i	−0.118806	−	0.205778i
$741$	8.30436	+	1.68069i	0.305068	+	0.0617418i
$742$	−24.1064	+	41.7535i	−0.884973	+	1.53282i
$743$	−24.5094	+	42.4516i	−0.899164	+	1.55740i	−0.0705989	+	0.997505i	$0.522491\pi$
$743$	−24.5094	+	42.4516i	−0.899164	+	1.55740i	−0.828565	+	0.559893i	$0.810842\pi$
$744$	−6.97433	+	6.66023i	−0.255691	+	0.244176i
$745$	19.1986	+	33.2530i	0.703383	+	1.21829i
$746$	−3.82115			−0.139902
$747$	−39.8806	+	30.1803i	−1.45915	+	1.10424i
$748$	0.199952			0.00731097
$749$	−32.9522			−1.20405
$750$	1.12790	−	1.27749i	0.0411850	−	0.0466473i
$751$	−48.8939			−1.78417			−0.892083	−	0.451872i	$-0.850756\pi$
$751$	−48.8939			−1.78417			−0.892083	+	0.451872i	$0.850756\pi$
$752$	3.12000	−	5.40400i	0.113775	−	0.197064i
$753$	4.43112	−	5.01881i	0.161479	−	0.182896i
$754$	−5.15513			−0.187739
$755$	−19.0181	+	32.9403i	−0.692140	+	1.19882i
$756$	1.79609	−	23.7534i	0.0653230	−	0.863902i
$757$	5.33750	−	9.24482i	0.193995	−	0.336009i	−0.752576	−	0.658506i	$-0.771189\pi$
$757$	5.33750	−	9.24482i	0.193995	−	0.336009i	0.946571	+	0.322497i	$0.104522\pi$
$758$	8.90867	−	15.4303i	0.323577	−	0.560453i
$759$	7.39997	+	1.49766i	0.268602	+	0.0543616i
$760$	6.13337	−	10.6233i	0.222481	−	0.385348i
$761$	11.9965			0.434872			0.217436	−	0.976075i	$-0.430231\pi$
$761$	11.9965			0.434872			0.217436	+	0.976075i	$0.430231\pi$
$762$	−24.8912	−	5.03766i	−0.901714	−	0.182495i
$763$	42.9791	−	74.4420i	1.55595	−	2.69498i
$764$	−10.7808	+	18.6729i	−0.390036	+	0.675562i
$765$	−0.173362	−	1.38842i	−0.00626790	−	0.0501985i
$766$	4.42885	−	7.67099i	0.160021	−	0.277164i
$767$	−4.63090	−	8.02095i	−0.167212	−	0.289620i
$768$	1.69763	+	0.343579i	0.0612580	+	0.0123978i
$769$	−27.6879			−0.998450			−0.499225	−	0.866472i	$-0.666382\pi$
$769$	−27.6879			−0.998450			−0.499225	+	0.866472i	$0.666382\pi$
$770$	−9.51623	−	16.4826i	−0.342941	−	0.593992i
$771$	−7.02983	+	7.96218i	−0.253173	+	0.286751i
$772$	−4.31718	+	7.47758i	−0.155379	+	0.269124i
$773$	25.5025			0.917262			0.458631	−	0.888627i	$-0.348340\pi$
$773$	25.5025			0.917262			0.458631	+	0.888627i	$0.348340\pi$
$774$	−13.9536	+	10.5597i	−0.501553	+	0.379559i
$775$	25.9840	+	2.21770i	0.933372	+	0.0796620i
$776$	5.24560	+	9.08564i	0.188306	+	0.326156i
$777$	−5.24933	−	15.6354i	−0.188319	−	0.560918i
$778$	−32.8058			−1.17614
$779$	−8.39049	+	14.5328i	−0.300620	+	0.520690i
$780$	4.42693	−	5.01406i	0.158510	−	0.179532i
$781$	−3.38610	+	5.86489i	−0.121164	+	0.209862i
$782$	−0.244851	−	0.424095i	−0.00875587	−	0.0151656i
$783$	1.62753	−	21.5242i	0.0581632	−	0.769212i
$784$	−7.00831	+	12.1388i	−0.250297	+	0.433527i
$785$	−18.8701			−0.673503
$786$	−14.9516	+	16.9346i	−0.533306	+	0.604037i
$787$	36.3521			1.29581			0.647906	−	0.761720i	$-0.275645\pi$
$787$	36.3521			1.29581			0.647906	+	0.761720i	$0.275645\pi$
$788$	4.09993	+	7.10129i	0.146054	+	0.252973i
$789$	−13.4863	+	15.2749i	−0.480124	+	0.543802i
$790$	−3.33440	−	5.77535i	−0.118633	−	0.205478i
$791$	−0.434896			−0.0154631
$792$	−3.19146	+	2.41519i	−0.113403	+	0.0858200i
$793$	−8.82585	+	15.2868i	−0.313415	+	0.542851i
$794$	−6.83989	+	11.8470i	−0.242739	+	0.420436i
$795$	−18.0413	−	53.7368i	−0.639857	−	1.90585i
$796$	−12.5910	−	21.8082i	−0.446275	−	0.772970i
$797$	−20.6523	−	35.7708i	−0.731542	−	1.26707i	−0.956224	−	0.292635i	$-0.905468\pi$
$797$	−20.6523	−	35.7708i	−0.731542	−	1.26707i	0.224682	−	0.974432i	$-0.427866\pi$
$798$	20.7162	−	23.4637i	0.733345	−	0.830607i
$799$	0.467618	−	0.809938i	0.0165431	−	0.0286535i
$800$	−2.34191	−	4.05631i	−0.0827992	−	0.143412i
$801$	23.4076	−	17.7141i	0.827066	−	0.625896i
$802$	−14.4015			−0.508533
$803$	−4.71451	+	8.16578i	−0.166372	+	0.288164i
$804$	5.60120	+	16.6835i	0.197539	+	0.588381i
$805$	−23.3062	+	40.3675i	−0.821436	+	1.42277i
$806$	−6.88433	−	0.587568i	−0.242490	−	0.0206962i
$807$	−1.59118	−	0.322035i	−0.0560123	−	0.0113362i
$808$	−8.67516	−	15.0258i	−0.305191	−	0.528606i
$809$	16.3208	+	28.2685i	0.573809	+	0.993867i	0.996170	+	0.0874390i	$0.0278683\pi$
$809$	16.3208	+	28.2685i	0.573809	+	0.993867i	−0.422361	+	0.906428i	$0.638798\pi$
$810$	19.5376	+	20.0667i	0.686480	+	0.705073i
$811$	22.4869	−	38.9485i	0.789623	−	1.36767i	−0.136576	−	0.990630i	$-0.543610\pi$
$811$	22.4869	−	38.9485i	0.789623	−	1.36767i	0.926198	−	0.377037i	$-0.123057\pi$
$812$	−9.52214	+	16.4928i	−0.334162	+	0.578785i
$813$	−1.93649	−	5.76794i	−0.0679157	−	0.202291i
$814$	−1.38554	+	2.39983i	−0.0485632	+	0.0841140i
$815$	8.78795	+	15.2212i	0.307828	+	0.533174i
$816$	0.254437	+	0.0514947i	0.00890706	+	0.00180267i
$817$	−22.9929			−0.804421
$818$	−13.3346	−	23.0962i	−0.466233	−	0.807540i
$819$	13.6093	−	10.2991i	0.475549	−	0.359880i
$820$	6.62376	+	11.4727i	0.231312	+	0.400644i
$821$	15.6852	+	27.1675i	0.547416	+	0.948152i	0.998451	+	0.0556455i	$0.0177217\pi$
$821$	15.6852	+	27.1675i	0.547416	+	0.948152i	−0.451035	+	0.892506i	$0.648945\pi$
$822$	14.5123	−	16.4370i	0.506174	−	0.573307i
$823$	22.1049			0.770529			0.385265	−	0.922806i	$-0.374110\pi$
$823$	22.1049			0.770529			0.385265	+	0.922806i	$0.374110\pi$
$824$	−9.73922	−	16.8688i	−0.339282	−	0.587653i
$825$	10.6080	+	2.14693i	0.369324	+	0.0747464i
$826$	−34.2153			−1.19050
$827$	23.0821	−	39.9794i	0.802643	−	1.39022i	−0.115228	−	0.993339i	$-0.536760\pi$
$827$	23.0821	−	39.9794i	0.802643	−	1.39022i	0.917871	−	0.396879i	$-0.129907\pi$
$828$	9.03067	+	3.81150i	0.313838	+	0.132459i
$829$	−24.0399			−0.834941			−0.417470	−	0.908691i	$-0.637083\pi$
$829$	−24.0399			−0.834941			−0.417470	+	0.908691i	$0.637083\pi$
$830$	−25.9392	+	44.9280i	−0.900362	+	1.55947i
$831$	−5.32405	+	6.03017i	−0.184689	+	0.209184i
$832$	0.620478	+	1.07470i	0.0215112	+	0.0372585i
$833$	−1.05039	+	1.81932i	−0.0363938	+	0.0630359i
$834$	−6.42982	−	19.1516i	−0.222647	−	0.663165i
$835$	4.40181	+	7.62417i	0.152331	+	0.263845i
$836$	−5.25891			−0.181883
$837$	4.62672	−	28.5586i	0.159923	−	0.987130i
$838$	9.20566			0.318004
$839$	14.5576	+	25.2145i	0.502584	+	0.870501i	0.999996	+	0.00298609i	$0.000950505\pi$
$839$	14.5576	+	25.2145i	0.502584	+	0.870501i	−0.497412	+	0.867515i	$0.665716\pi$
$840$	−7.86444	−	23.4247i	−0.271349	−	0.808228i
$841$	5.87148	−	10.1697i	0.202465	−	0.350679i
$842$	−3.88337	−	6.72619i	−0.133830	−	0.231800i
$843$	−10.4260	+	11.8087i	−0.359089	+	0.406714i
$844$	−11.8290	+	20.4884i	−0.407171	+	0.705241i
$845$	−35.6623			−1.22682
$846$	2.31941	+	18.5758i	0.0797431	+	0.638648i
$847$	21.1344	−	36.6059i	0.726187	−	1.25779i
$848$	10.5167			0.361146
$849$	35.1089	+	7.10558i	1.20493	+	0.243863i
$850$	−0.351000	−	0.607950i	−0.0120392	−	0.0208525i
$851$	6.78666			0.232644
$852$	−5.81918	+	6.59096i	−0.199362	+	0.225803i
$853$	17.1589	+	29.7202i	0.587511	+	1.01760i	0.994557	+	0.104192i	$0.0332255\pi$
$853$	17.1589	+	29.7202i	0.587511	+	1.01760i	−0.407046	+	0.913408i	$0.633441\pi$
$854$	32.6048	+	56.4731i	1.11571	+	1.93247i
$855$	4.55956	+	36.5167i	0.155934	+	1.24884i
$856$	3.59396	+	6.22492i	0.122839	+	0.212763i
$857$	21.0304			0.718384			0.359192	−	0.933264i	$-0.383052\pi$
$857$	21.0304			0.718384			0.359192	+	0.933264i	$0.383052\pi$
$858$	−2.81054	−	0.568817i	−0.0959503	−	0.0194191i
$859$	19.8615	+	34.4011i	0.677666	+	1.17375i	0.975682	+	0.219190i	$0.0703416\pi$
$859$	19.8615	+	34.4011i	0.677666	+	1.17375i	−0.298017	+	0.954561i	$0.596325\pi$
$860$	−9.07574	+	15.7196i	−0.309480	+	0.536036i
$861$	10.7586	+	32.0451i	0.366652	+	1.09209i
$862$	−5.51395	+	9.55044i	−0.187806	+	0.325289i
$863$	−4.83556	+	8.37543i	−0.164604	+	0.285103i	−0.936515	−	0.350628i	$-0.885968\pi$
$863$	−4.83556	+	8.37543i	−0.164604	+	0.285103i	0.771910	+	0.635731i	$0.219301\pi$
$864$	−4.68308	+	2.25139i	−0.159322	+	0.0765937i
$865$	6.94380	+	12.0270i	0.236096	+	0.408931i
$866$	−3.44706	−	5.97048i	−0.117136	−	0.202885i
$867$	−28.8216	−	5.83312i	−0.978833	−	0.198103i
$868$	−14.5960	+	20.9397i	−0.495420	+	0.710741i
$869$	−1.42950	+	2.47597i	−0.0484925	+	0.0839914i
$870$	−7.12639	−	21.2263i	−0.241607	−	0.719640i
$871$	−6.30442	+	10.9196i	−0.213617	+	0.369996i
$872$	−18.7502			−0.634962
$873$	−28.9967	−	12.2384i	−0.981389	−	0.414207i
$874$	6.43980	+	11.1541i	0.217830	+	0.377292i
$875$	2.25527	−	3.90625i	0.0762421	−	0.132055i
$876$	−8.10213	+	9.17670i	−0.273746	+	0.310052i
$877$	0.644777	+	1.11679i	0.0217726	+	0.0377112i	0.876706	−	0.481026i	$-0.159736\pi$
$877$	0.644777	+	1.11679i	0.0217726	+	0.0377112i	−0.854934	+	0.518737i	$0.826402\pi$
$878$	−4.89746	−	8.48266i	−0.165281	−	0.286276i
$879$	−18.1868	−	54.1704i	−0.613425	−	1.82712i
$880$	−2.07579	+	3.59537i	−0.0699749	+	0.121200i
$881$	3.34561	−	5.79477i	0.112717	−	0.195231i	−0.804148	−	0.594429i	$-0.797378\pi$
$881$	3.34561	−	5.79477i	0.112717	−	0.195231i	0.916865	+	0.399198i	$0.130711\pi$
$882$	−5.20999	−	41.7259i	−0.175429	−	1.40498i
$883$	−31.4442			−1.05818			−0.529090	−	0.848566i	$-0.677467\pi$
$883$	−31.4442			−1.05818			−0.529090	+	0.848566i	$0.677467\pi$
$884$	0.0929957	+	0.161073i	0.00312778	+	0.00541748i
$885$	26.6247	−	30.1559i	0.894979	−	1.01368i
$886$	−4.70396	−	8.14750i	−0.158033	−	0.273721i
$887$	10.2290			0.343455			0.171728	−	0.985144i	$-0.445065\pi$
$887$	10.2290			0.343455			0.171728	+	0.985144i	$0.445065\pi$
$888$	−2.38112	+	2.69693i	−0.0799053	+	0.0905030i
$889$	−67.2178			−2.25441
$890$	15.2248	−	26.3701i	0.510336	−	0.883928i
$891$	3.26230	−	11.5553i	0.109291	−	0.387116i
$892$	2.53277	+	4.38688i	0.0848033	+	0.146884i
$893$	−12.2987	+	21.3021i	−0.411562	+	0.712846i
$894$	14.1449	−	16.0209i	0.473075	−	0.535818i
$895$	−31.9145	+	55.2776i	−1.06679	+	1.84773i
$896$	4.58439			0.153154
$897$	2.23520	+	6.65766i	0.0746311	+	0.222293i
$898$	−0.854168	−	1.47946i	−0.0285040	−	0.0493703i
$899$	−13.2262	+	18.9746i	−0.441118	+	0.632839i
$900$	12.9457	+	5.46387i	0.431522	+	0.182129i
$901$	1.57622			0.0525114
$902$	2.83969	−	4.91849i	0.0945514	−	0.163768i
$903$	−30.6544	+	34.7200i	−1.02011	+	1.15541i
$904$	0.0474322	+	0.0821550i	0.00157757	+	0.00273244i
$905$	42.5772			1.41531
$906$	20.7500	+	4.19952i	0.689371	+	0.139520i
$907$	0.617394	+	1.06936i	0.0205002	+	0.0355075i	0.876094	−	0.482141i	$-0.160141\pi$
$907$	0.617394	+	1.06936i	0.0205002	+	0.0355075i	−0.855593	+	0.517649i	$0.826807\pi$
$908$	−3.29211	+	5.70210i	−0.109252	+	0.189231i
$909$	47.9547	+	20.2398i	1.59056	+	0.671313i
$910$	8.85180	−	15.3318i	0.293434	−	0.508243i
$911$	−19.5291	+	33.8254i	−0.647029	+	1.12069i	0.336800	+	0.941576i	$0.390655\pi$
$911$	−19.5291	+	33.8254i	−0.647029	+	1.12069i	−0.983829	+	0.179111i	$0.942678\pi$
$912$	−6.69190	−	1.35435i	−0.221591	−	0.0448471i
$913$	22.2409			0.736067
$914$	−14.1345	+	24.4816i	−0.467526	+	0.809779i
$915$	−75.1444	−	15.2083i	−2.48420	−	0.502769i
$916$	−7.19123	+	12.4556i	−0.237605	+	0.411544i
$917$	−29.8963	+	51.7818i	−0.987262	+	1.70999i
$918$	−0.701888	+	0.337432i	−0.0231658	+	0.0111369i
$919$	−16.7981	+	29.0952i	−0.554118	+	0.959761i	0.443853	+	0.896099i	$0.353611\pi$
$919$	−16.7981	+	29.0952i	−0.554118	+	0.959761i	−0.997972	+	0.0636615i	$0.979722\pi$
$920$	10.1676			0.335217
$921$	7.36123	−	8.33753i	0.242561	−	0.274731i
$922$	−5.37864	+	9.31608i	−0.177136	+	0.306809i
$923$	−6.29935			−0.207346
$924$	−7.01123	+	7.94111i	−0.230652	+	0.261243i
$925$	9.72883			0.319882
$926$	26.4483			0.869144
$927$	53.8366	+	22.7224i	1.76823	+	0.746300i
$928$	4.15416			0.136367
$929$	−11.3421	−	19.6450i	−0.372121	−	0.644532i	0.617771	−	0.786358i	$-0.288036\pi$
$929$	−11.3421	−	19.6450i	−0.372121	−	0.644532i	−0.989892	+	0.141826i	$0.954703\pi$
$930$	−7.09749	−	29.1586i	−0.232736	−	0.956147i
$931$	27.6261	−	47.8498i	0.905409	−	1.56821i
$932$	4.46075	−	7.72624i	0.146117	−	0.253081i
$933$	41.5720	+	8.41362i	1.36100	+	0.275450i
$934$	−2.69443	−	4.66689i	−0.0881645	−	0.152705i
$935$	−0.311114	+	0.538865i	−0.0101745	+	0.0176228i
$936$	−3.42989	−	1.44763i	−0.112109	−	0.0473171i
$937$	−6.51559	−	11.2853i	−0.212855	−	0.368676i	0.739752	−	0.672880i	$-0.234943\pi$
$937$	−6.51559	−	11.2853i	−0.212855	−	0.368676i	−0.952607	+	0.304204i	$0.901610\pi$
$938$	23.2900	+	40.3395i	0.760446	+	1.31713i
$939$	8.53446	+	1.72726i	0.278511	+	0.0563671i
$940$	9.70909	+	16.8166i	0.316676	+	0.548498i
$941$	−4.50872	−	7.80933i	−0.146980	−	0.254577i	0.783130	−	0.621858i	$-0.213622\pi$
$941$	−4.50872	−	7.80933i	−0.146980	−	0.254577i	−0.930110	+	0.367281i	$0.880289\pi$
$942$	3.34283	+	9.95678i	0.108915	+	0.324410i
$943$	−13.9094			−0.452952
$944$	3.73172	+	6.46352i	0.121457	+	0.210370i
$945$	61.2201	+	41.7993i	1.99149	+	1.35973i
$946$	7.78178			0.253007
$947$	−18.6517	+	32.3058i	−0.606100	+	1.04980i	0.385776	+	0.922592i	$0.373934\pi$
$947$	−18.6517	+	32.3058i	−0.606100	+	1.04980i	−0.991877	+	0.127204i	$0.959400\pi$
$948$	−2.45667	+	2.78249i	−0.0797889	+	0.0903711i
$949$	−8.77069			−0.284709
$950$	9.23160	+	15.9896i	0.299513	+	0.518771i
$951$	41.7670	+	8.45309i	1.35439	+	0.274110i
$952$	0.687096			0.0222689
$953$	29.3112			0.949484			0.474742	−	0.880125i	$-0.342541\pi$
$953$	29.3112			0.949484			0.474742	+	0.880125i	$0.342541\pi$
$954$	−25.1582	+	19.0389i	−0.814526	+	0.616407i
$955$	−33.5486	−	58.1079i	−1.08561	−	1.88033i
$956$	24.6444			0.797057
$957$	−6.35325	+	7.19586i	−0.205371	+	0.232609i
$958$	−14.9519			−0.483074
$959$	29.0178	−	50.2604i	0.937035	−	1.62299i
$960$	−3.56735	+	4.04048i	−0.115136	+	0.130406i
$961$	−19.8253	+	23.8318i	−0.639527	+	0.768768i
$962$	−2.57761			−0.0831053
$963$	−19.8667	−	8.38499i	−0.640197	−	0.270203i
$964$	2.18737	+	3.78864i	0.0704506	+	0.122024i
$965$	−13.4346	−	23.2694i	−0.432474	−	0.749068i
$966$	25.4286	+	5.14641i	0.818150	+	0.165583i
$967$	39.5265			1.27109			0.635543	−	0.772066i	$-0.280776\pi$
$967$	39.5265			1.27109			0.635543	+	0.772066i	$0.280776\pi$
$968$	−9.22016			−0.296347
$969$	−1.00296	−	0.202987i	−0.0322199	−	0.00652088i
$970$	−32.6474			−1.04824
$971$	−13.7924	+	23.8892i	−0.442620	+	0.766640i	−0.997883	−	0.0650346i	$-0.979284\pi$
$971$	−13.7924	+	23.8892i	−0.442620	+	0.766640i	0.555263	+	0.831675i	$0.312618\pi$
$972$	7.12712	−	13.8638i	0.228602	−	0.444681i
$973$	−26.7355	−	46.3072i	−0.857100	−	1.48454i
$974$	−26.4795			−0.848456
$975$	3.20421	+	9.54390i	0.102617	+	0.305649i
$976$	7.11213	−	12.3186i	0.227654	−	0.394308i
$977$	16.5528	−	28.6704i	0.529572	−	0.917246i	−0.469833	−	0.882756i	$-0.655686\pi$
$977$	16.5528	−	28.6704i	0.529572	−	0.917246i	0.999405	−	0.0344909i	$-0.0109810\pi$
$978$	6.47465	−	7.33337i	0.207037	−	0.234495i
$979$	−13.0541			−0.417211
$980$	−21.8091	−	37.7744i	−0.696665	−	1.20666i
$981$	44.8544	−	33.9443i	1.43209	−	1.08376i
$982$	−8.88757	+	15.3937i	−0.283614	+	0.491234i
$983$	31.4255			1.00232			0.501160	−	0.865355i	$-0.332907\pi$
$983$	31.4255			1.00232			0.501160	+	0.865355i	$0.332907\pi$
$984$	4.88016	−	5.52740i	0.155574	−	0.176207i
$985$	−25.5170			−0.813041
$986$	0.622615			0.0198281
$987$	15.7699	+	46.9715i	0.501962	+	1.49512i
$988$	−2.44587	−	4.23636i	−0.0778134	−	0.134777i
$989$	−9.52917	−	16.5050i	−0.303010	−	0.524829i
$990$	−1.54314	−	12.3588i	−0.0490444	−	0.392788i
$991$	−15.2001			−0.482848			−0.241424	−	0.970420i	$-0.577615\pi$
$991$	−15.2001			−0.482848			−0.241424	+	0.970420i	$0.577615\pi$
$992$	5.54760	+	0.473480i	0.176136	+	0.0150330i
$993$	−16.3148	−	48.5946i	−0.517736	−	1.54210i
$994$	−11.6357	+	20.1535i	−0.369061	+	0.639232i
$995$	78.3632			2.48428
$996$	28.3013	+	5.72781i	0.896761	+	0.181493i
$997$	−53.7634			−1.70270			−0.851352	−	0.524595i	$-0.824217\pi$
$997$	−53.7634			−1.70270			−0.851352	+	0.524595i	$0.824217\pi$
$998$	0.716637	+	1.24125i	0.0226847	+	0.0392911i
$999$	0.813777	−	10.7623i	0.0257468	−	0.340503i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.g.a.211.7	✓	32
3.2	odd	2		1674.2.g.b.955.14		32
9.2	odd	6		1674.2.h.b.397.3		32
9.7	even	3		558.2.h.a.25.5	yes	32
31.5	even	3		558.2.h.a.67.5	yes	32
93.5	odd	6		1674.2.h.b.253.3		32
279.160	even	3	inner	558.2.g.a.439.7	yes	32
279.191	odd	6		1674.2.g.b.1369.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.g.a.211.7	✓	32	1.1	even	1	trivial
558.2.g.a.439.7	yes	32	279.160	even	3	inner
558.2.h.a.25.5	yes	32	9.7	even	3
558.2.h.a.67.5	yes	32	31.5	even	3
1674.2.g.b.955.14		32	3.2	odd	2
1674.2.g.b.1369.14		32	279.191	odd	6
1674.2.h.b.253.3		32	93.5	odd	6
1674.2.h.b.397.3		32	9.2	odd	6

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:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.551268 - 1.64198i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.55594 - 2.69497i) q^{5} +(-1.14636 + 1.29840i) q^{6} +(-2.29219 + 3.97020i) q^{7} +1.00000 q^{8} +(-2.39221 + 1.81034i) q^{9} +(-1.55594 + 2.69497i) q^{10} +1.33410 q^{11} +(1.69763 + 0.343579i) q^{12} +(0.620478 + 1.07470i) q^{13} +4.58439 q^{14} +(-3.56735 + 4.04048i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.0749387 - 0.129798i) q^{17} +(2.76391 + 1.16654i) q^{18} +(1.97095 + 3.41379i) q^{19} +3.11188 q^{20} +(7.78261 + 1.57510i) q^{21} +(-0.667052 - 1.15537i) q^{22} +(-1.63368 + 2.82961i) q^{23} +(-0.551268 - 1.64198i) q^{24} +(-2.34191 + 4.05631i) q^{25} +(0.620478 - 1.07470i) q^{26} +(4.29130 + 2.92997i) q^{27} +(-2.29219 - 3.97020i) q^{28} +(-2.07708 - 3.59761i) q^{29} +(5.28283 + 1.06918i) q^{30} +(-2.36375 - 5.04110i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.735450 - 2.19058i) q^{33} +(-0.0749387 + 0.129798i) q^{34} +14.2661 q^{35} +(-0.371701 - 2.97688i) q^{36} +(-1.03856 - 1.79883i) q^{37} +(1.97095 - 3.41379i) q^{38} +(1.42259 - 1.61126i) q^{39} +(-1.55594 - 2.69497i) q^{40} +(2.12854 + 3.68673i) q^{41} +(-2.52723 - 7.52748i) q^{42} +(-2.91648 + 5.05149i) q^{43} +(-0.667052 + 1.15537i) q^{44} +(8.60096 + 3.63014i) q^{45} +3.26736 q^{46} +(3.12000 + 5.40400i) q^{47} +(-1.14636 + 1.29840i) q^{48} +(-7.00831 - 12.1388i) q^{49} +4.68383 q^{50} +(-0.171814 + 0.194601i) q^{51} -1.24096 q^{52} +(-5.25836 + 9.10775i) q^{53} +(0.391783 - 5.18136i) q^{54} +(-2.07579 - 3.59537i) q^{55} +(-2.29219 + 3.97020i) q^{56} +(4.51885 - 5.11818i) q^{57} +(-2.07708 + 3.59761i) q^{58} -7.46343 q^{59} +(-1.71548 - 5.10966i) q^{60} +(7.11213 + 12.3186i) q^{61} +(-3.18384 + 4.56762i) q^{62} +(-1.70402 - 13.6472i) q^{63} +1.00000 q^{64} +(1.93086 - 3.34434i) q^{65} +(-1.52937 + 1.73221i) q^{66} +(5.08029 + 8.79932i) q^{67} +0.149877 q^{68} +(5.54677 + 1.12259i) q^{69} +(-7.13305 - 12.3548i) q^{70} +(-2.53810 + 4.39612i) q^{71} +(-2.39221 + 1.81034i) q^{72} +(-3.53384 + 6.12079i) q^{73} +(-1.03856 + 1.79883i) q^{74} +(7.95141 + 1.60926i) q^{75} -3.94190 q^{76} +(-3.05803 + 5.29666i) q^{77} +(-2.10669 - 0.426366i) q^{78} +(-1.07150 + 1.85590i) q^{79} +(-1.55594 + 2.69497i) q^{80} +(2.44531 - 8.66144i) q^{81} +(2.12854 - 3.68673i) q^{82} +16.6710 q^{83} +(-5.25538 + 5.95239i) q^{84} +(-0.233201 + 0.403915i) q^{85} +5.83296 q^{86} +(-4.76218 + 5.39377i) q^{87} +1.33410 q^{88} -9.78493 q^{89} +(-1.15669 - 9.26372i) q^{90} -5.68903 q^{91} +(-1.63368 - 2.82961i) q^{92} +(-6.97433 + 6.66023i) q^{93} +(3.12000 - 5.40400i) q^{94} +(6.13337 - 10.6233i) q^{95} +(1.69763 + 0.343579i) q^{96} +(5.24560 + 9.08564i) q^{97} +(-7.00831 + 12.1388i) q^{98} +(-3.19146 + 2.41519i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} + 4 q^{3} - 16 q^{4} - q^{5} - 2 q^{6} + q^{7} + 32 q^{8} + 12 q^{9} - q^{10} + 4 q^{11} - 2 q^{12} - 10 q^{13} - 2 q^{14} - 13 q^{15} - 16 q^{16} - 4 q^{17} - 6 q^{18} + 4 q^{19} + 2 q^{20}+ \cdots + 19 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 + 4 * q^3 - 16 * q^4 - q^5 - 2 * q^6 + q^7 + 32 * q^8 + 12 * q^9 - q^10 + 4 * q^11 - 2 * q^12 - 10 * q^13 - 2 * q^14 - 13 * q^15 - 16 * q^16 - 4 * q^17 - 6 * q^18 + 4 * q^19 + 2 * q^20 + 10 * q^21 - 2 * q^22 - q^23 + 4 * q^24 - 19 * q^25 - 10 * q^26 + 7 * q^27 + q^28 - 3 * q^29 + 14 * q^30 - q^31 - 16 * q^32 - 7 * q^33 - 4 * q^34 - 6 * q^36 - 19 * q^37 + 4 * q^38 + 19 * q^39 - q^40 + 10 * q^41 - 11 * q^42 - 13 * q^43 - 2 * q^44 + 14 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 - 13 * q^49 + 38 * q^50 + 20 * q^51 + 20 * q^52 - 7 * q^53 - 17 * q^54 - 11 * q^55 + q^56 - 5 * q^57 - 3 * q^58 + 12 * q^59 - q^60 + 7 * q^61 + 11 * q^62 - 42 * q^63 + 32 * q^64 - 8 * q^65 + 5 * q^66 - 8 * q^67 + 8 * q^68 + 43 * q^69 + 7 * q^71 + 12 * q^72 + 7 * q^73 - 19 * q^74 - 41 * q^75 - 8 * q^76 - q^77 - 11 * q^78 - 34 * q^79 - q^80 + 10 * q^82 - 28 * q^83 + q^84 + 13 * q^85 + 26 * q^86 - 54 * q^87 + 4 * q^88 + 2 * q^89 - 19 * q^90 + 24 * q^91 - q^92 - 15 * q^93 - 6 * q^94 + 21 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + 19 * q^99

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