LMFDB - Embedded newform 693.2.k.c.67.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [693,2,Mod(67,693)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("693.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(693, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.k (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.11
Character	$\chi$	$=$	693.67
Dual form			693.2.k.c.331.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.793665 + 1.37467i) q^{2} +(-0.410682 + 1.68266i) q^{3} +(-0.259808 - 0.450001i) q^{4} -0.790103 q^{5} +(-1.98715 - 1.90002i) q^{6} +(2.64443 - 0.0834765i) q^{7} -2.34986 q^{8} +(-2.66268 - 1.38208i) q^{9} +(0.627077 - 1.08613i) q^{10} -1.00000 q^{11} +(0.863897 - 0.252361i) q^{12} +(-1.66112 + 2.87714i) q^{13} +(-1.98404 + 3.70147i) q^{14} +(0.324481 - 1.32947i) q^{15} +(2.38462 - 4.13028i) q^{16} +(-0.660631 + 1.14425i) q^{17} +(4.01317 - 2.56340i) q^{18} +(-3.91517 - 6.78127i) q^{19} +(0.205275 + 0.355547i) q^{20} +(-0.945560 + 4.48396i) q^{21} +(0.793665 - 1.37467i) q^{22} -6.74532 q^{23} +(0.965045 - 3.95401i) q^{24} -4.37574 q^{25} +(-2.63674 - 4.56697i) q^{26} +(3.41908 - 3.91279i) q^{27} +(-0.724611 - 1.16831i) q^{28} +(-1.26247 - 2.18666i) q^{29} +(1.57006 + 1.50121i) q^{30} +(1.26243 + 2.18660i) q^{31} +(1.43532 + 2.48604i) q^{32} +(0.410682 - 1.68266i) q^{33} +(-1.04864 - 1.81630i) q^{34} +(-2.08938 + 0.0659550i) q^{35} +(0.0698503 + 1.55728i) q^{36} +(0.180045 + 0.311847i) q^{37} +12.4293 q^{38} +(-4.15905 - 3.97668i) q^{39} +1.85663 q^{40} +(-2.75931 + 4.77927i) q^{41} +(-5.41350 - 4.85860i) q^{42} +(4.95776 + 8.58709i) q^{43} +(0.259808 + 0.450001i) q^{44} +(2.10379 + 1.09198i) q^{45} +(5.35353 - 9.27258i) q^{46} +(1.64222 - 2.84440i) q^{47} +(5.97052 + 5.70873i) q^{48} +(6.98606 - 0.441496i) q^{49} +(3.47287 - 6.01519i) q^{50} +(-1.65407 - 1.58154i) q^{51} +1.72629 q^{52} +(-2.91904 + 5.05592i) q^{53} +(2.66518 + 7.80554i) q^{54} +0.790103 q^{55} +(-6.21404 + 0.196158i) q^{56} +(13.0184 - 3.80294i) q^{57} +4.00791 q^{58} +(-2.02016 - 3.49902i) q^{59} +(-0.682568 + 0.199391i) q^{60} +(4.55883 - 7.89613i) q^{61} -4.00779 q^{62} +(-7.15665 - 3.43254i) q^{63} +4.98182 q^{64} +(1.31245 - 2.27324i) q^{65} +(1.98715 + 1.90002i) q^{66} +(0.469982 + 0.814033i) q^{67} +0.686550 q^{68} +(2.77019 - 11.3501i) q^{69} +(1.56760 - 2.92454i) q^{70} +0.366846 q^{71} +(6.25692 + 3.24768i) q^{72} +(-4.39778 + 7.61718i) q^{73} -0.571581 q^{74} +(1.79704 - 7.36287i) q^{75} +(-2.03439 + 3.52366i) q^{76} +(-2.64443 + 0.0834765i) q^{77} +(8.76751 - 2.56116i) q^{78} +(-6.58161 + 11.3997i) q^{79} +(-1.88409 + 3.26334i) q^{80} +(5.17973 + 7.36006i) q^{81} +(-4.37994 - 7.58628i) q^{82} +(2.77954 + 4.81431i) q^{83} +(2.26345 - 0.739468i) q^{84} +(0.521966 - 0.904072i) q^{85} -15.7392 q^{86} +(4.19788 - 1.22628i) q^{87} +2.34986 q^{88} +(-1.06657 - 1.84735i) q^{89} +(-3.17082 + 2.02535i) q^{90} +(-4.15254 + 7.74707i) q^{91} +(1.75249 + 3.03540i) q^{92} +(-4.19775 + 1.22625i) q^{93} +(2.60674 + 4.51500i) q^{94} +(3.09338 + 5.35790i) q^{95} +(-4.77262 + 1.39417i) q^{96} +(-8.32551 - 14.4202i) q^{97} +(-4.93768 + 9.95392i) q^{98} +(2.66268 + 1.38208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 40 q^{4} + 8 q^{5} + 6 q^{6} - q^{7} + 2 q^{9} + 12 q^{10} - 80 q^{11} - 10 q^{12} + 21 q^{13} - 8 q^{14} - 5 q^{15} - 40 q^{16} - 3 q^{17} + 32 q^{18} + 18 q^{19} - 12 q^{20} + 18 q^{21} - 8 q^{23}+ \cdots - 2 q^{99}+O(q^{100}) $ 80 * q - 40 * q^4 + 8 * q^5 + 6 * q^6 - q^7 + 2 * q^9 + 12 * q^10 - 80 * q^11 - 10 * q^12 + 21 * q^13 - 8 * q^14 - 5 * q^15 - 40 * q^16 - 3 * q^17 + 32 * q^18 + 18 * q^19 - 12 * q^20 + 18 * q^21 - 8 * q^23 - 14 * q^24 + 80 * q^25 - 12 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 + 20 * q^30 + 32 * q^31 + 35 * q^32 + 28 * q^34 - 18 * q^35 - 16 * q^36 - 7 * q^37 + 46 * q^38 - 48 * q^39 - 102 * q^40 - 2 * q^41 - 14 * q^42 + 9 * q^43 + 40 * q^44 - 5 * q^45 - 6 * q^46 - 26 * q^47 - 28 * q^48 - 19 * q^49 + 2 * q^50 + 22 * q^51 - 88 * q^52 + 4 * q^53 + 19 * q^54 - 8 * q^55 + 18 * q^56 + 16 * q^57 + 32 * q^58 - 24 * q^59 - 10 * q^60 + 69 * q^61 + 12 * q^62 + 20 * q^63 + 44 * q^64 - 7 * q^65 - 6 * q^66 + 7 * q^67 + 34 * q^68 + 15 * q^69 - 22 * q^70 + 34 * q^71 - 70 * q^72 + 26 * q^73 + 8 * q^74 - 64 * q^75 + 52 * q^76 + q^77 - 60 * q^78 - 5 * q^79 - 47 * q^80 + 46 * q^81 + 60 * q^82 + 4 * q^83 + 29 * q^84 + 13 * q^85 - 38 * q^87 - 38 * q^89 - 43 * q^90 + 13 * q^91 - 21 * q^92 + 35 * q^93 + 56 * q^94 - 20 * q^95 + 15 * q^96 + 49 * q^97 - 84 * q^98 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.793665	+	1.37467i	−0.561206	+	0.972037i	0.436186	+	0.899857i	$0.356329\pi$
$2$	−0.793665	+	1.37467i	−0.561206	+	0.972037i	−0.997392	+	0.0721805i	$0.977004\pi$
$3$	−0.410682	+	1.68266i	−0.237108	+	0.971483i
$3$	−0.410682	+	1.68266i	−0.237108	+	0.971483i
$4$	−0.259808	−	0.450001i	−0.129904	−	0.225001i
$5$	−0.790103			−0.353345			−0.176672	−	0.984270i	$-0.556533\pi$
$5$	−0.790103			−0.353345			−0.176672	+	0.984270i	$0.556533\pi$
$6$	−1.98715	−	1.90002i	−0.811252	−	0.775680i
$7$	2.64443	−	0.0834765i	0.999502	−	0.0315511i
$7$	2.64443	−	0.0834765i	0.999502	−	0.0315511i
$8$	−2.34986			−0.830800
$9$	−2.66268	−	1.38208i	−0.887560	−	0.460692i
$10$	0.627077	−	1.08613i	0.198299	−	0.343464i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	0.863897	−	0.252361i	0.249386	−	0.0728504i
$13$	−1.66112	+	2.87714i	−0.460711	+	0.797975i	−0.998997	−	0.0447877i	$-0.985739\pi$
$13$	−1.66112	+	2.87714i	−0.460711	+	0.797975i	0.538286	+	0.842762i	$0.319072\pi$
$14$	−1.98404	+	3.70147i	−0.530258	+	0.989260i
$15$	0.324481	−	1.32947i	0.0837807	−	0.343269i
$16$	2.38462	−	4.13028i	0.596154	−	1.03257i
$17$	−0.660631	+	1.14425i	−0.160227	+	0.277520i	−0.934950	−	0.354780i	$-0.884556\pi$
$17$	−0.660631	+	1.14425i	−0.160227	+	0.277520i	0.774723	+	0.632300i	$0.217889\pi$
$18$	4.01317	−	2.56340i	0.945914	−	0.604198i
$19$	−3.91517	−	6.78127i	−0.898201	−	1.55573i	−0.829793	−	0.558072i	$-0.811541\pi$
$19$	−3.91517	−	6.78127i	−0.898201	−	1.55573i	−0.0684079	−	0.997657i	$-0.521792\pi$
$20$	0.205275	+	0.355547i	0.0459010	+	0.0795028i
$21$	−0.945560	+	4.48396i	−0.206338	+	0.978481i
$22$	0.793665	−	1.37467i	0.169210	−	0.293080i
$23$	−6.74532			−1.40650			−0.703249	−	0.710944i	$-0.748268\pi$
$23$	−6.74532			−1.40650			−0.703249	+	0.710944i	$0.748268\pi$
$24$	0.965045	−	3.95401i	0.196989	−	0.807108i
$25$	−4.37574			−0.875147
$26$	−2.63674	−	4.56697i	−0.517107	−	0.895656i
$27$	3.41908	−	3.91279i	0.658002	−	0.753016i
$28$	−0.724611	−	1.16831i	−0.136939	−	0.220790i
$29$	−1.26247	−	2.18666i	−0.234435	−	0.406053i	0.724674	−	0.689092i	$-0.241991\pi$
$29$	−1.26247	−	2.18666i	−0.234435	−	0.406053i	−0.959108	+	0.283040i	$0.908657\pi$
$30$	1.57006	+	1.50121i	0.286652	+	0.274082i
$31$	1.26243	+	2.18660i	0.226739	+	0.392724i	0.956840	−	0.290616i	$-0.0938601\pi$
$31$	1.26243	+	2.18660i	0.226739	+	0.392724i	−0.730100	+	0.683340i	$0.760527\pi$
$32$	1.43532	+	2.48604i	0.253730	+	0.439474i
$33$	0.410682	−	1.68266i	0.0714906	−	0.292913i
$34$	−1.04864	−	1.81630i	−0.179840	−	0.311492i
$35$	−2.08938	+	0.0659550i	−0.353169	+	0.0111484i
$36$	0.0698503	+	1.55728i	0.0116417	+	0.259547i
$37$	0.180045	+	0.311847i	0.0295992	+	0.0512673i	0.880446	−	0.474147i	$-0.157244\pi$
$37$	0.180045	+	0.311847i	0.0295992	+	0.0512673i	−0.850846	+	0.525415i	$0.823910\pi$
$38$	12.4293			2.01630
$39$	−4.15905	−	3.97668i	−0.665981	−	0.636779i
$40$	1.85663			0.293559
$41$	−2.75931	+	4.77927i	−0.430933	+	0.746397i	−0.996954	−	0.0779935i	$-0.975149\pi$
$41$	−2.75931	+	4.77927i	−0.430933	+	0.746397i	0.566021	+	0.824391i	$0.308482\pi$
$42$	−5.41350	−	4.85860i	−0.835321	−	0.749698i
$43$	4.95776	+	8.58709i	0.756051	+	1.30952i	0.944850	+	0.327503i	$0.106207\pi$
$43$	4.95776	+	8.58709i	0.756051	+	1.30952i	−0.188799	+	0.982016i	$0.560459\pi$
$44$	0.259808	+	0.450001i	0.0391676	+	0.0678402i
$45$	2.10379	+	1.09198i	0.313615	+	0.162783i
$46$	5.35353	−	9.27258i	0.789335	−	1.36717i
$47$	1.64222	−	2.84440i	0.239542	−	0.414898i	−0.721041	−	0.692892i	$-0.756336\pi$
$47$	1.64222	−	2.84440i	0.239542	−	0.414898i	0.960583	+	0.277994i	$0.0896695\pi$
$48$	5.97052	+	5.70873i	0.861771	+	0.823984i
$49$	6.98606	−	0.441496i	0.998009	−	0.0630709i
$50$	3.47287	−	6.01519i	0.491138	−	0.850676i
$51$	−1.65407	−	1.58154i	−0.231616	−	0.221460i
$52$	1.72629			0.239393
$53$	−2.91904	+	5.05592i	−0.400960	+	0.694484i	−0.993842	−	0.110806i	$-0.964657\pi$
$53$	−2.91904	+	5.05592i	−0.400960	+	0.694484i	0.592882	+	0.805290i	$0.297990\pi$
$54$	2.66518	+	7.80554i	0.362685	+	1.06220i
$55$	0.790103			0.106537
$56$	−6.21404	+	0.196158i	−0.830386	+	0.0262127i
$57$	13.0184	−	3.80294i	1.72434	−	0.503712i
$58$	4.00791			0.526264
$59$	−2.02016	−	3.49902i	−0.263002	−	0.455533i	0.704036	−	0.710164i	$-0.251379\pi$
$59$	−2.02016	−	3.49902i	−0.263002	−	0.455533i	−0.967038	+	0.254631i	$0.918046\pi$
$60$	−0.682568	+	0.199391i	−0.0881191	+	0.0257413i
$61$	4.55883	−	7.89613i	0.583699	−	1.01100i	−0.411338	−	0.911483i	$-0.634938\pi$
$61$	4.55883	−	7.89613i	0.583699	−	1.01100i	0.995036	−	0.0995127i	$-0.0317284\pi$
$62$	−4.00779			−0.508990
$63$	−7.15665	−	3.43254i	−0.901653	−	0.432459i
$64$	4.98182			0.622728
$65$	1.31245	−	2.27324i	0.162790	−	0.281960i
$66$	1.98715	+	1.90002i	0.244602	+	0.233876i
$67$	0.469982	+	0.814033i	0.0574174	+	0.0994499i	0.893305	−	0.449450i	$-0.148380\pi$
$67$	0.469982	+	0.814033i	0.0574174	+	0.0994499i	−0.835888	+	0.548900i	$0.815047\pi$
$68$	0.686550			0.0832564
$69$	2.77019	−	11.3501i	0.333491	−	1.36639i
$70$	1.56760	−	2.92454i	0.187364	−	0.349550i
$71$	0.366846			0.0435366			0.0217683	−	0.999763i	$-0.493070\pi$
$71$	0.366846			0.0435366			0.0217683	+	0.999763i	$0.493070\pi$
$72$	6.25692	+	3.24768i	0.737385	+	0.382743i
$73$	−4.39778	+	7.61718i	−0.514721	+	0.891523i	0.485133	+	0.874440i	$0.338771\pi$
$73$	−4.39778	+	7.61718i	−0.514721	+	0.891523i	−0.999854	+	0.0170828i	$0.994562\pi$
$74$	−0.571581			−0.0664449
$75$	1.79704	−	7.36287i	0.207504	−	0.850191i
$76$	−2.03439	+	3.52366i	−0.233360	+	0.404191i
$77$	−2.64443	+	0.0834765i	−0.301361	+	0.00951302i
$78$	8.76751	−	2.56116i	0.992725	−	0.289994i
$79$	−6.58161	+	11.3997i	−0.740489	+	1.28257i	0.211783	+	0.977317i	$0.432073\pi$
$79$	−6.58161	+	11.3997i	−0.740489	+	1.28257i	−0.952273	+	0.305249i	$0.901260\pi$
$80$	−1.88409	+	3.26334i	−0.210648	+	0.364853i
$81$	5.17973	+	7.36006i	0.575525	+	0.817784i
$82$	−4.37994	−	7.58628i	−0.483684	−	0.837765i
$83$	2.77954	+	4.81431i	0.305094	+	0.528439i	0.977282	−	0.211942i	$-0.0679787\pi$
$83$	2.77954	+	4.81431i	0.305094	+	0.528439i	−0.672188	+	0.740380i	$0.734645\pi$
$84$	2.26345	−	0.739468i	0.246963	−	0.0806825i
$85$	0.521966	−	0.904072i	0.0566152	−	0.0980604i
$86$	−15.7392			−1.69720
$87$	4.19788	−	1.22628i	0.450060	−	0.131471i
$88$	2.34986			0.250496
$89$	−1.06657	−	1.84735i	−0.113056	−	0.195818i	0.803945	−	0.594703i	$-0.202731\pi$
$89$	−1.06657	−	1.84735i	−0.113056	−	0.195818i	−0.917001	+	0.398885i	$0.869397\pi$
$90$	−3.17082	+	2.02535i	−0.334234	+	0.213490i
$91$	−4.15254	+	7.74707i	−0.435305	+	0.812113i
$92$	1.75249	+	3.03540i	0.182710	+	0.316463i
$93$	−4.19775	+	1.22625i	−0.435287	+	0.127156i
$94$	2.60674	+	4.51500i	0.268864	+	0.465687i
$95$	3.09338	+	5.35790i	0.317375	+	0.549709i
$96$	−4.77262	+	1.39417i	−0.487103	+	0.142292i
$97$	−8.32551	−	14.4202i	−0.845328	−	1.46415i	−0.885336	−	0.464951i	$-0.846072\pi$
$97$	−8.32551	−	14.4202i	−0.845328	−	1.46415i	0.0400087	−	0.999199i	$-0.487261\pi$
$98$	−4.93768	+	9.95392i	−0.498781	+	1.00550i
$99$	2.66268	+	1.38208i	0.267609	+	0.138904i
$100$	1.13685	+	1.96909i	0.113685	+	0.196909i
$101$	2.90238			0.288798			0.144399	−	0.989520i	$-0.453875\pi$
$101$	2.90238			0.288798			0.144399	+	0.989520i	$0.453875\pi$
$102$	3.48686	−	1.01858i	0.345251	−	0.100855i
$103$	−5.00129			−0.492792			−0.246396	−	0.969169i	$-0.579246\pi$
$103$	−5.00129			−0.492792			−0.246396	+	0.969169i	$0.579246\pi$
$104$	3.90339	−	6.76086i	0.382759	−	0.662957i
$105$	0.747090	−	3.54279i	0.0729085	−	0.345741i
$106$	−4.63347	−	8.02541i	−0.450043	−	0.779497i
$107$	3.28074	+	5.68241i	0.317161	+	0.549339i	0.979895	−	0.199516i	$-0.0639370\pi$
$107$	3.28074	+	5.68241i	0.317161	+	0.549339i	−0.662733	+	0.748856i	$0.730604\pi$
$108$	−2.64906	−	0.522015i	−0.254906	−	0.0502309i
$109$	1.10183	−	1.90842i	0.105536	−	0.182794i	−0.808421	−	0.588605i	$-0.799677\pi$
$109$	1.10183	−	1.90842i	0.105536	−	0.182794i	0.913957	+	0.405811i	$0.133011\pi$
$110$	−0.627077	+	1.08613i	−0.0597895	+	0.103558i
$111$	−0.598673	+	0.174884i	−0.0568235	+	0.0165992i
$112$	5.96118	−	11.1213i	0.563278	−	1.05086i
$113$	−1.13576	+	1.96720i	−0.106844	+	0.185059i	−0.914490	−	0.404609i	$-0.867408\pi$
$113$	−1.13576	+	1.96720i	−0.106844	+	0.185059i	0.807646	+	0.589667i	$0.200741\pi$
$114$	−5.10450	+	20.9143i	−0.478081	+	1.95880i
$115$	5.32950			0.496979
$116$	−0.656000	+	1.13623i	−0.0609081	+	0.105496i
$117$	8.39945	−	5.36511i	0.776529	−	0.496005i
$118$	6.41332			0.590394
$119$	−1.65148	+	3.08103i	−0.151391	+	0.282438i
$120$	−0.762485	+	3.12407i	−0.0696050	+	0.285188i
$121$	1.00000			0.0909091
$122$	7.23637	+	12.5338i	0.655150	+	1.13475i
$123$	−6.90868	−	6.60575i	−0.622935	−	0.595620i
$124$	0.655981	−	1.13619i	0.0589088	−	0.102033i
$125$	7.40780			0.662574
$126$	10.3986	−	7.11374i	0.926380	−	0.633742i
$127$	−15.6542			−1.38909			−0.694543	−	0.719451i	$-0.744393\pi$
$127$	−15.6542			−1.38909			−0.694543	+	0.719451i	$0.744393\pi$
$128$	−6.82453	+	11.8204i	−0.603209	+	1.04479i
$129$	−16.4852	+	4.81565i	−1.45144	+	0.423994i
$130$	2.08330	+	3.60838i	0.182717	+	0.316476i
$131$	−10.5066			−0.917970			−0.458985	−	0.888444i	$-0.651787\pi$
$131$	−10.5066			−0.917970			−0.458985	+	0.888444i	$0.651787\pi$
$132$	−0.863897	+	0.252361i	−0.0751926	+	0.0219652i
$133$	−10.9195	−	17.6058i	−0.946838	−	1.52662i
$134$	−1.49203			−0.128892
$135$	−2.70142	+	3.09150i	−0.232502	+	0.266074i
$136$	1.55239	−	2.68881i	0.133116	−	0.230564i
$137$	7.24763			0.619207			0.309604	−	0.950866i	$-0.399804\pi$
$137$	7.24763			0.619207			0.309604	+	0.950866i	$0.399804\pi$
$138$	13.4040	+	12.8162i	1.14102	+	1.09099i
$139$	−2.09074	+	3.62126i	−0.177334	+	0.307151i	−0.940966	−	0.338500i	$-0.890081\pi$
$139$	−2.09074	+	3.62126i	−0.177334	+	0.307151i	0.763633	+	0.645651i	$0.223414\pi$
$140$	0.572517	+	0.923086i	0.0483865	+	0.0780150i
$141$	4.11173	+	3.93143i	0.346270	+	0.331086i
$142$	−0.291153	+	0.504291i	−0.0244330	+	0.0423192i
$143$	1.66112	−	2.87714i	0.138910	−	0.240598i
$144$	−12.0578	+	7.70188i	−1.00482	+	0.641823i
$145$	0.997480	+	1.72769i	0.0828362	+	0.143477i
$146$	−6.98073	−	12.0910i	−0.577729	−	1.00066i
$147$	−2.12617	+	11.9365i	−0.175363	+	0.984504i
$148$	0.0935542	−	0.162041i	0.00769011	−	0.0133197i
$149$	−19.9689			−1.63591			−0.817957	−	0.575279i	$-0.804894\pi$
$149$	−19.9689			−1.63591			−0.817957	+	0.575279i	$0.804894\pi$
$150$	8.69526	+	8.31399i	0.709965	+	0.678834i
$151$	−18.0980			−1.47279			−0.736396	−	0.676551i	$-0.763474\pi$
$151$	−18.0980			−1.47279			−0.736396	+	0.676551i	$0.763474\pi$
$152$	9.20008	+	15.9350i	0.746225	+	1.29250i
$153$	3.34048	−	2.13372i	0.270062	−	0.172501i
$154$	1.98404	−	3.70147i	0.159879	−	0.298273i
$155$	−0.997451	−	1.72764i	−0.0801172	−	0.138767i
$156$	−0.708956	+	2.90475i	−0.0567619	+	0.232566i
$157$	−0.265503	−	0.459865i	−0.0211894	−	0.0367012i	0.855236	−	0.518238i	$-0.173412\pi$
$157$	−0.265503	−	0.459865i	−0.0211894	−	0.0367012i	−0.876426	+	0.481537i	$0.840079\pi$
$158$	−10.4472	−	18.0951i	−0.831134	−	1.43957i
$159$	−7.30859	−	6.98812i	−0.579609	−	0.554194i
$160$	−1.13405	−	1.96423i	−0.0896543	−	0.155286i
$161$	−17.8376	+	0.563076i	−1.40580	+	0.0443766i
$162$	−14.2286	+	1.27899i	−1.11790	+	0.100487i
$163$	6.15155	+	10.6548i	0.481827	+	0.834548i	0.999782	−	0.0208593i	$-0.00664021\pi$
$163$	6.15155	+	10.6548i	0.481827	+	0.834548i	−0.517956	+	0.855407i	$0.673307\pi$
$164$	2.86757			0.223920
$165$	−0.324481	+	1.32947i	−0.0252608	+	0.103499i
$166$	−8.82410			−0.684883
$167$	−2.41592	+	4.18449i	−0.186949	+	0.323806i	−0.944232	−	0.329282i	$-0.893193\pi$
$167$	−2.41592	+	4.18449i	−0.186949	+	0.323806i	0.757282	+	0.653088i	$0.226527\pi$
$168$	2.22193	−	10.5367i	0.171426	−	0.812922i
$169$	0.981381	+	1.69980i	0.0754909	+	0.130754i
$170$	0.828533	+	1.43506i	0.0635456	+	0.110064i
$171$	1.05260	+	23.4674i	0.0804947	+	1.79460i
$172$	2.57613	−	4.46200i	0.196428	−	0.340224i
$173$	−2.82594	+	4.89467i	−0.214852	+	0.372135i	−0.953227	−	0.302256i	$-0.902260\pi$
$173$	−2.82594	+	4.89467i	−0.214852	+	0.372135i	0.738375	+	0.674391i	$0.235594\pi$
$174$	−1.64598	+	6.74394i	−0.124781	+	0.511257i
$175$	−11.5713	+	0.365271i	−0.874712	+	0.0276119i
$176$	−2.38462	+	4.13028i	−0.179747	+	0.311331i
$177$	6.71729	−	1.96225i	0.504903	−	0.147492i
$178$	3.38598			0.253790
$179$	3.93925	−	6.82299i	0.294434	−	0.509974i	−0.680419	−	0.732823i	$-0.738202\pi$
$179$	3.93925	−	6.82299i	0.294434	−	0.509974i	0.974853	+	0.222849i	$0.0715357\pi$
$180$	−0.0551889	−	1.23042i	−0.00411354	−	0.0917097i
$181$	5.43763			0.404176			0.202088	−	0.979367i	$-0.435227\pi$
$181$	5.43763			0.404176			0.202088	+	0.979367i	$0.435227\pi$
$182$	−7.35392	−	11.8569i	−0.545109	−	0.878895i
$183$	11.4143	+	10.9138i	0.843766	+	0.806768i
$184$	15.8505			1.16852
$185$	−0.142254	−	0.246391i	−0.0104587	−	0.0181150i
$186$	1.64593	−	6.74375i	0.120685	−	0.494476i
$187$	0.660631	−	1.14425i	0.0483101	−	0.0836756i
$188$	−1.70664			−0.124470
$189$	8.71490	−	10.6325i	0.633916	−	0.773402i
$190$	−9.82044			−0.712450
$191$	−9.31512	+	16.1343i	−0.674018	+	1.16743i	0.302737	+	0.953074i	$0.402100\pi$
$191$	−9.31512	+	16.1343i	−0.674018	+	1.16743i	−0.976755	+	0.214359i	$0.931234\pi$
$192$	−2.04595	+	8.38271i	−0.147654	+	0.604970i
$193$	3.80111	+	6.58371i	0.273610	+	0.473906i	0.969783	−	0.243967i	$-0.0784490\pi$
$193$	3.80111	+	6.58371i	0.273610	+	0.473906i	−0.696174	+	0.717873i	$0.745116\pi$
$194$	26.4307			1.89761
$195$	3.28608	+	3.14199i	0.235321	+	0.225003i
$196$	−2.01371	−	3.02903i	−0.143837	−	0.216360i
$197$	15.8647			1.13031			0.565156	−	0.824984i	$-0.308816\pi$
$197$	15.8647			1.13031			0.565156	+	0.824984i	$0.308816\pi$
$198$	−4.01317	+	2.56340i	−0.285204	+	0.182173i
$199$	8.04885	−	13.9410i	0.570568	−	0.988252i	−0.425940	−	0.904751i	$-0.640057\pi$
$199$	8.04885	−	13.9410i	0.570568	−	0.988252i	0.996508	−	0.0835007i	$-0.0266101\pi$
$200$	10.2824			0.727072
$201$	−1.56275	+	0.456510i	−0.110228	+	0.0321998i
$202$	−2.30352	+	3.98981i	−0.162075	+	0.280722i
$203$	−3.52105	−	5.67709i	−0.247129	−	0.398454i
$204$	−0.281954	+	1.15523i	−0.0197407	+	0.0808822i
$205$	2.18014	−	3.77612i	0.152268	−	0.263736i
$206$	3.96935	−	6.87512i	0.276558	−	0.479012i
$207$	17.9606	+	9.32256i	1.24835	+	0.647962i
$208$	7.92225	+	13.7217i	0.549309	+	0.951432i
$209$	3.91517	+	6.78127i	0.270818	+	0.469070i
$210$	4.27722	+	3.83879i	0.295157	+	0.264902i
$211$	−9.46439	+	16.3928i	−0.651555	+	1.12853i	0.331190	+	0.943564i	$0.392550\pi$
$211$	−9.46439	+	16.3928i	−0.651555	+	1.12853i	−0.982746	+	0.184963i	$0.940784\pi$
$212$	3.03356			0.208346
$213$	−0.150657	+	0.617276i	−0.0103229	+	0.0422951i
$214$	−10.4152			−0.711971
$215$	−3.91714	−	6.78469i	−0.267147	−	0.462712i
$216$	−8.03435	+	9.19449i	−0.546668	+	0.625606i
$217$	3.52095	+	5.67693i	0.239018	+	0.385375i
$218$	1.74897	+	3.02930i	0.118455	+	0.205170i
$219$	−11.0110	−	10.5282i	−0.744056	−	0.711430i
$220$	−0.205275	−	0.355547i	−0.0138397	−	0.0239710i
$221$	−2.19477	−	3.80145i	−0.147636	−	0.255713i
$222$	0.234738	−	0.961775i	0.0157546	−	0.0645501i
$223$	−5.03207	−	8.71580i	−0.336972	−	0.583653i	0.646889	−	0.762584i	$-0.276070\pi$
$223$	−5.03207	−	8.71580i	−0.336972	−	0.583653i	−0.983862	+	0.178931i	$0.942736\pi$
$224$	4.00312	+	6.45435i	0.267470	+	0.431250i
$225$	11.6512	+	6.04760i	0.776746	+	0.403174i
$226$	−1.80283	−	3.12260i	−0.119923	−	0.207712i
$227$	17.8650			1.18574			0.592871	−	0.805297i	$-0.297994\pi$
$227$	17.8650			1.18574			0.592871	+	0.805297i	$0.297994\pi$
$228$	−5.09363	−	4.87028i	−0.337334	−	0.322542i
$229$	−29.1375			−1.92546			−0.962730	−	0.270464i	$-0.912823\pi$
$229$	−29.1375			−1.92546			−0.962730	+	0.270464i	$0.912823\pi$
$230$	−4.22984	+	7.32630i	−0.278907	+	0.483082i
$231$	0.945560	−	4.48396i	0.0622133	−	0.295023i
$232$	2.96662	+	5.13834i	0.194768	+	0.337348i
$233$	−3.36912	−	5.83548i	−0.220718	−	0.382295i	0.734308	−	0.678816i	$-0.237507\pi$
$233$	−3.36912	−	5.83548i	−0.220718	−	0.382295i	−0.955026	+	0.296521i	$0.904173\pi$
$234$	0.708896	+	15.8046i	0.0463420	+	1.03318i
$235$	−1.29752	+	2.24737i	−0.0846408	+	0.146602i
$236$	−1.04971	+	1.81815i	−0.0683302	+	0.118351i
$237$	−16.4788	−	15.7563i	−1.07042	−	1.02348i
$238$	−2.92468	−	4.71554i	−0.189579	−	0.305663i
$239$	−13.4790	+	23.3463i	−0.871885	+	1.51015i	−0.0118403	+	0.999930i	$0.503769\pi$
$239$	−13.4790	+	23.3463i	−0.871885	+	1.51015i	−0.860045	+	0.510219i	$0.829564\pi$
$240$	−4.71733	−	4.51048i	−0.304502	−	0.291150i
$241$	−17.3863			−1.11995			−0.559975	−	0.828509i	$-0.689189\pi$
$241$	−17.3863			−1.11995			−0.559975	+	0.828509i	$0.689189\pi$
$242$	−0.793665	+	1.37467i	−0.0510187	+	0.0883670i
$243$	−14.5117	+	5.69307i	−0.930925	+	0.365211i
$244$	−4.73769			−0.303300
$245$	−5.51971	+	0.348827i	−0.352641	+	0.0222858i
$246$	14.5639	−	4.25440i	0.928560	−	0.271250i
$247$	26.0142			1.65524
$248$	−2.96653	−	5.13819i	−0.188375	−	0.326275i
$249$	−9.24234	+	2.69987i	−0.585710	+	0.171097i
$250$	−5.87931	+	10.1833i	−0.371840	+	0.644046i
$251$	27.5838			1.74107			0.870537	−	0.492103i	$-0.163772\pi$
$251$	27.5838			1.74107			0.870537	+	0.492103i	$0.163772\pi$
$252$	0.314711	+	4.11231i	0.0198249	+	0.259051i
$253$	6.74532			0.424075
$254$	12.4242	−	21.5193i	0.779563	−	1.35024i
$255$	1.30688	+	1.24958i	0.0818402	+	0.0782516i
$256$	−5.85096	−	10.1342i	−0.365685	−	0.633385i
$257$	−30.3024			−1.89021			−0.945105	−	0.326768i	$-0.894040\pi$
$257$	−30.3024			−1.89021			−0.945105	+	0.326768i	$0.894040\pi$
$258$	6.46381	−	26.4837i	0.402419	−	1.64880i
$259$	0.502148	+	0.809628i	0.0312020	+	0.0503078i
$260$	−1.36395			−0.0845883
$261$	0.339419	+	7.56720i	0.0210095	+	0.468398i
$262$	8.33875	−	14.4431i	0.515170	−	0.892301i
$263$	26.7067			1.64680			0.823402	−	0.567459i	$-0.192074\pi$
$263$	26.7067			1.64680			0.823402	+	0.567459i	$0.192074\pi$
$264$	−0.965045	+	3.95401i	−0.0593944	+	0.243352i
$265$	2.30634	−	3.99470i	0.141677	−	0.245392i
$266$	32.8685	−	1.03756i	2.01530	−	0.0636166i
$267$	3.54647	−	1.03599i	0.217041	−	0.0634018i
$268$	0.244211	−	0.422985i	0.0149175	−	0.0258379i
$269$	11.5266	−	19.9647i	0.702789	−	1.21727i	−0.264694	−	0.964332i	$-0.585271\pi$
$269$	11.5266	−	19.9647i	0.702789	−	1.21727i	0.967484	−	0.252934i	$-0.0813956\pi$
$270$	−2.10577	−	6.16718i	−0.128153	−	0.375323i
$271$	0.784917	+	1.35952i	0.0476803	+	0.0825847i	0.888881	−	0.458139i	$-0.151484\pi$
$271$	0.784917	+	1.35952i	0.0476803	+	0.0825847i	−0.841200	+	0.540724i	$0.818150\pi$
$272$	3.15070	+	5.45718i	0.191039	+	0.330890i
$273$	−11.3303	−	10.1689i	−0.685741	−	0.615449i
$274$	−5.75219	+	9.96309i	−0.347503	+	0.601892i
$275$	4.37574			0.263867
$276$	−5.82727	+	1.70226i	−0.350760	+	0.102464i
$277$	−27.6818			−1.66324			−0.831618	−	0.555348i	$-0.812585\pi$
$277$	−27.6818			−1.66324			−0.831618	+	0.555348i	$0.812585\pi$
$278$	−3.31869	−	5.74813i	−0.199042	−	0.344750i
$279$	−0.339409	−	7.56698i	−0.0203199	−	0.453024i
$280$	4.90973	−	0.154985i	0.293413	−	0.00926211i
$281$	−8.79187	−	15.2280i	−0.524479	−	0.908424i	−0.999594	−	0.0285002i	$-0.990927\pi$
$281$	−8.79187	−	15.2280i	−0.524479	−	0.908424i	0.475115	−	0.879924i	$-0.342406\pi$
$282$	−8.66775	+	2.53202i	−0.516157	+	0.150779i
$283$	14.7476	+	25.5437i	0.876657	+	1.51841i	0.854987	+	0.518649i	$0.173565\pi$
$283$	14.7476	+	25.5437i	0.876657	+	1.51841i	0.0216692	+	0.999765i	$0.493102\pi$
$284$	−0.0953096	−	0.165081i	−0.00565558	−	0.00979576i
$285$	−10.2859	+	3.00472i	−0.609285	+	0.177984i
$286$	2.63674	+	4.56697i	0.155914	+	0.270051i
$287$	−6.89787	+	12.8688i	−0.407168	+	0.759622i
$288$	−0.385889	−	8.60324i	−0.0227387	−	0.506951i
$289$	7.62713	+	13.2106i	0.448655	+	0.777093i
$290$	−3.16666			−0.185953
$291$	27.6834	−	8.08687i	1.62283	−	0.474061i
$292$	4.57032			0.267458
$293$	14.3299	−	24.8202i	0.837163	−	1.45001i	−0.0550934	−	0.998481i	$-0.517546\pi$
$293$	14.3299	−	24.8202i	0.837163	−	1.45001i	0.892257	−	0.451528i	$-0.149121\pi$
$294$	−14.7212	−	12.3963i	−0.858559	−	0.722969i
$295$	1.59613	+	2.76458i	0.0929305	+	0.160960i
$296$	−0.423079	−	0.732795i	−0.0245910	−	0.0425928i
$297$	−3.41908	+	3.91279i	−0.198395	+	0.227043i
$298$	15.8486	−	27.4506i	0.918085	−	1.59017i
$299$	11.2048	−	19.4072i	0.647989	−	1.12235i
$300$	−3.78019	+	1.10427i	−0.218249	+	0.0637548i
$301$	13.8273	+	22.2941i	0.796992	+	1.28501i
$302$	14.3637	−	24.8787i	0.826539	−	1.43161i
$303$	−1.19196	+	4.88372i	−0.0684762	+	0.280562i
$304$	−37.3447			−2.14186
$305$	−3.60195	+	6.23876i	−0.206247	+	0.357230i
$306$	0.281930	+	6.28552i	0.0161169	+	0.359319i
$307$	−15.9976			−0.913030			−0.456515	−	0.889716i	$-0.650903\pi$
$307$	−15.9976			−0.913030			−0.456515	+	0.889716i	$0.650903\pi$
$308$	0.724611	+	1.16831i	0.0412885	+	0.0665707i
$309$	2.05394	−	8.41547i	0.116845	−	0.478739i
$310$	3.16657			0.179849
$311$	−2.23457	−	3.87039i	−0.126711	−	0.219470i	0.795689	−	0.605705i	$-0.207109\pi$
$311$	−2.23457	−	3.87039i	−0.126711	−	0.219470i	−0.922400	+	0.386235i	$0.873775\pi$
$312$	9.77317	+	9.34464i	0.553297	+	0.529036i
$313$	9.15801	−	15.8621i	0.517641	−	0.896581i	−0.482149	−	0.876089i	$-0.660144\pi$
$313$	9.15801	−	15.8621i	0.517641	−	0.896581i	0.999790	−	0.0204914i	$-0.00652306\pi$
$314$	0.842882			0.0475666
$315$	5.65449	+	2.71206i	0.318595	+	0.152807i
$316$	6.83983			0.384771
$317$	11.7033	−	20.2707i	0.657323	−	1.13852i	−0.323983	−	0.946063i	$-0.605022\pi$
$317$	11.7033	−	20.2707i	0.657323	−	1.13852i	0.981306	−	0.192454i	$-0.0616447\pi$
$318$	15.4069	−	4.50066i	0.863977	−	0.252384i
$319$	1.26247	+	2.18666i	0.0706847	+	0.122429i
$320$	−3.93615			−0.220038
$321$	−10.9089	+	3.18670i	−0.608876	+	0.177864i
$322$	13.3830	−	24.9676i	0.745806	−	1.39139i
$323$	10.3459			0.575662
$324$	1.96630	−	4.24309i	0.109239	−	0.235727i
$325$	7.26861	−	12.5896i	0.403190	−	0.698346i
$326$	−19.5291			−1.08162
$327$	2.75872	+	2.63776i	0.152558	+	0.145868i
$328$	6.48399	−	11.2306i	0.358019	−	0.620107i
$329$	4.10529	−	7.65891i	0.226332	−	0.422250i
$330$	−1.57006	−	1.50121i	−0.0864287	−	0.0826390i
$331$	14.2891	−	24.7494i	0.785397	−	1.36035i	−0.143364	−	0.989670i	$-0.545792\pi$
$331$	14.2891	−	24.7494i	0.785397	−	1.36035i	0.928761	−	0.370678i	$-0.120875\pi$
$332$	1.44430	−	2.50159i	0.0792660	−	0.137293i
$333$	−0.0484056	−	1.07918i	−0.00265261	−	0.0591389i
$334$	−3.83486	−	6.64217i	−0.209834	−	0.363443i
$335$	−0.371334	−	0.643170i	−0.0202882	−	0.0351401i
$336$	16.2652	+	14.5980i	0.887340	+	0.796384i
$337$	−14.3049	+	24.7769i	−0.779239	+	1.34968i	0.153142	+	0.988204i	$0.451061\pi$
$337$	−14.3049	+	24.7769i	−0.779239	+	1.34968i	−0.932381	+	0.361477i	$0.882273\pi$
$338$	−3.11555			−0.169464
$339$	−2.84369	−	2.71900i	−0.154448	−	0.147676i
$340$	−0.542445			−0.0294182
$341$	−1.26243	−	2.18660i	−0.0683645	−	0.118411i
$342$	−33.0953	−	17.1783i	−1.78959	−	0.928895i
$343$	18.4373	−	1.75068i	0.995522	−	0.0945278i
$344$	−11.6500	−	20.1784i	−0.628127	−	1.08795i
$345$	−2.18873	+	8.96773i	−0.117837	+	0.482806i
$346$	−4.48570	−	7.76946i	−0.241153	−	0.417689i
$347$	−7.81932	−	13.5435i	−0.419763	−	0.727051i	0.576152	−	0.817342i	$-0.304554\pi$
$347$	−7.81932	−	13.5435i	−0.419763	−	0.727051i	−0.995915	+	0.0902912i	$0.971220\pi$
$348$	−1.64247	−	1.57045i	−0.0880457	−	0.0841850i
$349$	7.92010	+	13.7180i	0.423953	+	0.734309i	0.996322	−	0.0856878i	$-0.0273088\pi$
$349$	7.92010	+	13.7180i	0.423953	+	0.734309i	−0.572369	+	0.819996i	$0.693975\pi$
$350$	8.68165	−	16.1967i	0.464054	−	0.865748i
$351$	5.57814	+	16.3368i	0.297739	+	0.871992i
$352$	−1.43532	−	2.48604i	−0.0765026	−	0.132506i
$353$	5.99820			0.319252			0.159626	−	0.987178i	$-0.448971\pi$
$353$	5.99820			0.319252			0.159626	+	0.987178i	$0.448971\pi$
$354$	−2.63384	+	10.7914i	−0.139987	+	0.573558i
$355$	−0.289846			−0.0153834
$356$	−0.554205	+	0.959912i	−0.0293728	+	0.0508752i
$357$	−4.50609	−	4.04420i	−0.238488	−	0.214042i
$358$	6.25289	+	10.8303i	0.330476	+	0.572401i
$359$	12.7482	+	22.0805i	0.672824	+	1.16537i	0.977100	+	0.212782i	$0.0682523\pi$
$359$	12.7482	+	22.0805i	0.672824	+	1.16537i	−0.304276	+	0.952584i	$0.598414\pi$
$360$	−4.94361	−	2.56600i	−0.260551	−	0.135240i
$361$	−21.1570	+	36.6451i	−1.11353	+	1.92869i
$362$	−4.31565	+	7.47493i	−0.226826	+	0.392874i
$363$	−0.410682	+	1.68266i	−0.0215552	+	0.0883167i
$364$	4.56506	−	0.144104i	0.239274	−	0.00755312i
$365$	3.47470	−	6.01836i	0.181874	−	0.315015i
$366$	−24.0619	+	7.02895i	−1.25774	+	0.367409i
$367$	19.2455			1.00461			0.502304	−	0.864691i	$-0.332486\pi$
$367$	19.2455			1.00461			0.502304	+	0.864691i	$0.332486\pi$
$368$	−16.0850	+	27.8601i	−0.838489	+	1.45231i
$369$	13.9525	−	8.91209i	0.726338	−	0.463945i
$370$	0.451608			0.0234780
$371$	−7.29715	+	13.6137i	−0.378849	+	0.706789i
$372$	1.64242	+	1.57041i	0.0851557	+	0.0814218i
$373$	−3.03837			−0.157321			−0.0786605	−	0.996901i	$-0.525064\pi$
$373$	−3.03837			−0.157321			−0.0786605	+	0.996901i	$0.525064\pi$
$374$	1.04864	+	1.81630i	0.0542238	+	0.0939185i
$375$	−3.04225	+	12.4648i	−0.157101	+	0.643679i
$376$	−3.85897	+	6.68393i	−0.199011	+	0.344698i
$377$	8.38843			0.432026
$378$	7.69947	+	20.4188i	0.396018	+	1.05023i
$379$	19.2789			0.990292			0.495146	−	0.868810i	$-0.335114\pi$
$379$	19.2789			0.990292			0.495146	+	0.868810i	$0.335114\pi$
$380$	1.60737	−	2.78405i	0.0824566	−	0.142819i
$381$	6.42890	−	26.3407i	0.329363	−	1.34947i
$382$	−14.7862	−	25.6104i	−0.756526	−	1.31034i
$383$	24.0907			1.23098			0.615488	−	0.788146i	$-0.288959\pi$
$383$	24.0907			1.23098			0.615488	+	0.788146i	$0.288959\pi$
$384$	−17.0870	−	16.3378i	−0.871969	−	0.833735i
$385$	2.08938	−	0.0659550i	0.106484	−	0.00336138i
$386$	−12.0672			−0.614206
$387$	−1.33291	−	29.7167i	−0.0677556	−	1.51058i
$388$	−4.32608	+	7.49298i	−0.219623	+	0.380399i
$389$	3.85879			0.195648			0.0978242	−	0.995204i	$-0.468812\pi$
$389$	3.85879			0.195648			0.0978242	+	0.995204i	$0.468812\pi$
$390$	−6.92724	+	2.02358i	−0.350774	+	0.102468i
$391$	4.45617	−	7.71831i	0.225358	−	0.390332i
$392$	−16.4162	+	1.03745i	−0.829146	+	0.0523993i
$393$	4.31489	−	17.6791i	0.217658	−	0.891792i
$394$	−12.5913	+	21.8087i	−0.634338	+	1.09871i
$395$	5.20015	−	9.00693i	0.261648	−	0.453188i
$396$	−0.0698503	−	1.55728i	−0.00351011	−	0.0782565i
$397$	9.35652	+	16.2060i	0.469590	+	0.813354i	0.999396	−	0.0347652i	$-0.0110683\pi$
$397$	9.35652	+	16.2060i	0.469590	+	0.813354i	−0.529805	+	0.848119i	$0.677735\pi$
$398$	12.7762	+	22.1290i	0.640412	+	1.10923i
$399$	34.1090	−	11.1434i	1.70758	−	0.557866i
$400$	−10.4345	+	18.0730i	−0.521723	+	0.903650i
$401$	−7.49490			−0.374278			−0.187139	−	0.982333i	$-0.559921\pi$
$401$	−7.49490			−0.374278			−0.187139	+	0.982333i	$0.559921\pi$
$402$	0.612752	−	2.51058i	0.0305613	−	0.125216i
$403$	−8.38819			−0.417845
$404$	−0.754063	−	1.30608i	−0.0375161	−	0.0649797i
$405$	−4.09252	−	5.81520i	−0.203359	−	0.288960i
$406$	10.5987	−	0.334566i	0.526002	−	0.0166042i
$407$	−0.180045	−	0.311847i	−0.00892448	−	0.0154577i
$408$	3.88682	+	3.71639i	0.192426	+	0.183989i
$409$	−13.3932	−	23.1976i	−0.662249	−	1.14705i	−0.980023	−	0.198882i	$-0.936269\pi$
$409$	−13.3932	−	23.1976i	−0.662249	−	1.14705i	0.317775	−	0.948166i	$-0.397064\pi$
$410$	3.46061	+	5.99395i	0.170907	+	0.296020i
$411$	−2.97648	+	12.1953i	−0.146819	+	0.601549i
$412$	1.29938	+	2.25059i	0.0640158	+	0.110879i
$413$	−5.63426	−	9.08428i	−0.277244	−	0.447008i
$414$	−27.0702	+	17.2909i	−1.33043	+	0.849803i
$415$	−2.19612	−	3.80380i	−0.107803	−	0.186721i
$416$	−9.53691			−0.467585
$417$	−5.23472	−	5.00518i	−0.256345	−	0.245105i
$418$	−12.4293			−0.607938
$419$	8.08807	−	14.0090i	0.395128	−	0.684382i	−0.597989	−	0.801504i	$-0.704034\pi$
$419$	8.08807	−	14.0090i	0.395128	−	0.684382i	0.993118	+	0.117122i	$0.0373669\pi$
$420$	−1.78836	+	0.584256i	−0.0872631	+	0.0285088i
$421$	4.54073	+	7.86477i	0.221302	+	0.383306i	0.955203	−	0.295950i	$-0.0956362\pi$
$421$	4.54073	+	7.86477i	0.221302	+	0.383306i	−0.733902	+	0.679255i	$0.762303\pi$
$422$	−15.0231	−	26.0208i	−0.731313	−	1.26667i
$423$	−8.30387	+	5.30406i	−0.403748	+	0.257892i
$424$	6.85932	−	11.8807i	0.333118	−	0.576977i
$425$	2.89075	−	5.00692i	0.140222	−	0.242871i
$426$	−0.728978	−	0.697014i	−0.0353191	−	0.0337704i
$427$	11.3964	−	21.2614i	0.551510	−	1.02891i
$428$	1.70473	−	2.95268i	0.0824012	−	0.142723i
$429$	4.15905	+	3.97668i	0.200801	+	0.191996i
$430$	12.4356			0.599698
$431$	−17.7477	+	30.7400i	−0.854878	+	1.48069i	0.0218793	+	0.999761i	$0.493035\pi$
$431$	−17.7477	+	30.7400i	−0.854878	+	1.48069i	−0.876758	+	0.480932i	$0.840298\pi$
$432$	−8.00770	−	23.4522i	−0.385271	−	1.12835i
$433$	−6.00309			−0.288490			−0.144245	−	0.989542i	$-0.546075\pi$
$433$	−6.00309			−0.288490			−0.144245	+	0.989542i	$0.546075\pi$
$434$	−10.5983	+	0.334556i	−0.508737	+	0.0160592i
$435$	−3.31675	+	0.968888i	−0.159026	+	0.0464546i
$436$	−1.14506			−0.0548383
$437$	26.4091	+	45.7418i	1.26332	+	2.18813i
$438$	23.2118	−	6.78063i	1.10910	−	0.323991i
$439$	−12.6474	+	21.9060i	−0.603628	+	1.04551i	0.388639	+	0.921390i	$0.372945\pi$
$439$	−12.6474	+	21.9060i	−0.603628	+	1.04551i	−0.992267	+	0.124124i	$0.960388\pi$
$440$	−1.85663			−0.0885113
$441$	−19.2118	−	8.47971i	−0.914849	−	0.403796i
$442$	6.96765			0.331417
$443$	−1.08997	+	1.88789i	−0.0517862	+	0.0896964i	−0.890756	−	0.454481i	$-0.849825\pi$
$443$	−1.08997	+	1.88789i	−0.0517862	+	0.0896964i	0.838970	+	0.544177i	$0.183158\pi$
$444$	0.234238	+	0.223967i	0.0111164	+	0.0106290i
$445$	0.842697	+	1.45959i	0.0399477	+	0.0691914i
$446$	15.9751			0.756444
$447$	8.20087	−	33.6008i	0.387888	−	1.58926i
$448$	13.1741	−	0.415865i	0.622418	−	0.0196478i
$449$	−29.6454			−1.39905			−0.699526	−	0.714608i	$-0.746605\pi$
$449$	−29.6454			−1.39905			−0.699526	+	0.714608i	$0.746605\pi$
$450$	−17.5606	+	11.2167i	−0.827814	+	0.528762i
$451$	2.75931	−	4.77927i	0.129931	−	0.225047i
$452$	1.18032			0.0555177
$453$	7.43252	−	30.4527i	0.349210	−	1.43079i
$454$	−14.1788	+	24.5585i	−0.665446	+	1.15259i
$455$	3.28094	−	6.12098i	0.153813	−	0.286956i
$456$	−30.5915	+	8.93637i	−1.43258	+	0.418484i
$457$	13.1951	−	22.8545i	0.617239	−	1.06909i	−0.372748	−	0.927933i	$-0.621584\pi$
$457$	13.1951	−	22.8545i	0.617239	−	1.06909i	0.989987	−	0.141157i	$-0.0450822\pi$
$458$	23.1254	−	40.0544i	1.08058	−	1.87162i
$459$	2.21844	+	6.49718i	0.103548	+	0.303262i
$460$	−1.38465	−	2.39828i	−0.0645596	−	0.111821i
$461$	6.95152	+	12.0404i	0.323764	+	0.560776i	0.981262	−	0.192681i	$-0.0617182\pi$
$461$	6.95152	+	12.0404i	0.323764	+	0.560776i	−0.657497	+	0.753457i	$0.728385\pi$
$462$	5.41350	+	4.85860i	0.251859	+	0.226042i
$463$	−5.24629	+	9.08684i	−0.243816	+	0.422301i	−0.961798	−	0.273760i	$-0.911733\pi$
$463$	−5.24629	+	9.08684i	−0.243816	+	0.422301i	0.717982	+	0.696061i	$0.245066\pi$
$464$	−12.0420			−0.559036
$465$	3.31666	−	0.968860i	0.153806	−	0.0449298i
$466$	10.6958			0.495473
$467$	−1.03642	−	1.79514i	−0.0479599	−	0.0830690i	0.841049	−	0.540959i	$-0.181939\pi$
$467$	−1.03642	−	1.79514i	−0.0479599	−	0.0830690i	−0.889009	+	0.457890i	$0.848605\pi$
$468$	−4.59655	−	2.38586i	−0.212476	−	0.110287i
$469$	1.31079	+	2.11342i	0.0605266	+	0.0975888i
$470$	−2.05959	−	3.56732i	−0.0950019	−	0.164548i
$471$	0.882833	−	0.257893i	0.0406788	−	0.0118831i
$472$	4.74708	+	8.22219i	0.218502	+	0.378457i
$473$	−4.95776	−	8.58709i	−0.227958	−	0.394835i
$474$	34.7383	−	10.1477i	1.59558	−	0.466101i
$475$	17.1317	+	29.6730i	0.786058	+	1.36149i
$476$	1.81554	−	0.0573107i	0.0832149	−	0.00262683i
$477$	14.7601	−	9.42796i	0.675820	−	0.431677i
$478$	−21.3956	−	37.0583i	−0.978614	−	1.69501i
$479$	−9.44550			−0.431576			−0.215788	−	0.976440i	$-0.569232\pi$
$479$	−9.44550			−0.431576			−0.215788	+	0.976440i	$0.569232\pi$
$480$	3.77086	−	1.10154i	0.172115	−	0.0502782i
$481$	−1.19630			−0.0545466
$482$	13.7989	−	23.9004i	0.628523	−	1.08863i
$483$	6.37811	−	30.2458i	0.290214	−	1.37623i
$484$	−0.259808	−	0.450001i	−0.0118095	−	0.0204546i
$485$	6.57801	+	11.3935i	0.298692	+	0.517350i
$486$	3.69133	−	24.4671i	0.167442	−	1.10985i
$487$	0.333781	−	0.578125i	0.0151250	−	0.0261973i	−0.858364	−	0.513041i	$-0.828519\pi$
$487$	0.333781	−	0.578125i	0.0151250	−	0.0261973i	0.873489	+	0.486844i	$0.161852\pi$
$488$	−10.7126	+	18.5548i	−0.484937	+	0.839935i
$489$	−20.4547	+	5.97522i	−0.924994	+	0.270209i
$490$	3.90128	−	7.86462i	0.176242	−	0.355287i
$491$	−12.4317	+	21.5323i	−0.561034	+	0.971739i	0.436373	+	0.899766i	$0.356263\pi$
$491$	−12.4317	+	21.5323i	−0.561034	+	0.971739i	−0.997407	+	0.0719731i	$0.977070\pi$
$492$	−1.17766	+	4.82514i	−0.0530931	+	0.217534i
$493$	3.33610			0.150251
$494$	−20.6466	+	35.7609i	−0.928932	+	1.60896i
$495$	−2.10379	−	1.09198i	−0.0945584	−	0.0490810i
$496$	12.0417			0.540687
$497$	0.970099	−	0.0306230i	0.0435149	−	0.00137363i
$498$	3.62390	−	14.8479i	0.162391	−	0.665352i
$499$	1.59692			0.0714879			0.0357440	−	0.999361i	$-0.488620\pi$
$499$	1.59692			0.0714879			0.0357440	+	0.999361i	$0.488620\pi$
$500$	−1.92461	−	3.33352i	−0.0860711	−	0.149080i
$501$	−6.04889	−	5.78366i	−0.270245	−	0.258395i
$502$	−21.8923	+	37.9186i	−0.977101	+	1.69239i
$503$	15.8438			0.706440			0.353220	−	0.935540i	$-0.385087\pi$
$503$	15.8438			0.706440			0.353220	+	0.935540i	$0.385087\pi$
$504$	16.8171	+	8.06598i	0.749094	+	0.359287i
$505$	−2.29318			−0.102045
$506$	−5.35353	+	9.27258i	−0.237993	+	0.412217i
$507$	−3.26322	+	0.953251i	−0.144925	+	0.0423354i
$508$	4.06709	+	7.04441i	0.180448	+	0.312545i
$509$	37.9247			1.68098			0.840491	−	0.541826i	$-0.182267\pi$
$509$	37.9247			1.68098			0.840491	+	0.541826i	$0.182267\pi$
$510$	−2.75498	+	0.804784i	−0.121993	+	0.0356364i
$511$	−10.9938	+	20.5102i	−0.486336	+	0.907319i
$512$	−8.72332			−0.385520
$513$	−39.9199	−	7.86647i	−1.76251	−	0.347313i
$514$	24.0499	−	41.6557i	1.06080	−	1.83735i
$515$	3.95154			0.174126
$516$	6.45004	+	6.16722i	0.283947	+	0.271497i
$517$	−1.64222	+	2.84440i	−0.0722245	+	0.125097i
$518$	−1.51151	+	0.0477135i	−0.0664118	+	0.00209641i
$519$	−7.07550	−	6.76525i	−0.310580	−	0.296961i
$520$	−3.08408	+	5.34178i	−0.135246	+	0.234253i
$521$	5.85356	−	10.1387i	0.256449	−	0.444183i	−0.708839	−	0.705370i	$-0.750781\pi$
$521$	5.85356	−	10.1387i	0.256449	−	0.444183i	0.965288	+	0.261187i	$0.0841141\pi$
$522$	−10.6718	−	5.53924i	−0.467091	−	0.242446i
$523$	−11.7377	−	20.3304i	−0.513256	−	0.888985i	−0.999882	−	0.0153748i	$-0.995106\pi$
$523$	−11.7377	−	20.3304i	−0.513256	−	0.888985i	0.486626	−	0.873610i	$-0.338227\pi$
$524$	2.72971	+	4.72800i	0.119248	+	0.206544i
$525$	4.13752	−	19.6206i	0.180576	−	0.856315i
$526$	−21.1961	+	36.7128i	−0.924196	+	1.60075i
$527$	−3.33601			−0.145319
$528$	−5.97052	−	5.70873i	−0.259834	−	0.248440i
$529$	22.4994			0.978235
$530$	3.66092	+	6.34090i	0.159020	+	0.275431i
$531$	0.543126	+	12.1088i	0.0235697	+	0.525476i
$532$	−5.08566	+	9.48791i	−0.220491	+	0.411353i
$533$	−9.16709	−	15.8779i	−0.397071	−	0.687747i
$534$	−1.39056	+	5.69745i	−0.0601756	+	0.246553i
$535$	−2.59212	−	4.48969i	−0.112067	−	0.194106i
$536$	−1.10439	−	1.91286i	−0.0477024	−	0.0826230i
$537$	9.86297	+	9.43050i	0.425619	+	0.406956i
$538$	18.2965	+	31.6905i	0.788819	+	1.36627i
$539$	−6.98606	+	0.441496i	−0.300911	+	0.0190166i
$540$	2.09303	+	0.412446i	0.0900698	+	0.0177488i
$541$	12.8829	+	22.3139i	0.553880	+	0.959349i	0.997990	+	0.0633762i	$0.0201868\pi$
$541$	12.8829	+	22.3139i	0.553880	+	0.959349i	−0.444109	+	0.895973i	$0.646480\pi$
$542$	−2.49184			−0.107034
$543$	−2.23314	+	9.14967i	−0.0958331	+	0.392650i
$544$	−3.79286			−0.162617
$545$	−0.870558	+	1.50785i	−0.0372906	+	0.0645892i
$546$	22.9713	−	7.50470i	0.983081	−	0.321172i
$547$	12.1408	+	21.0286i	0.519105	+	0.899116i	0.999753	+	0.0222027i	$0.00706793\pi$
$547$	12.1408	+	21.0286i	0.519105	+	0.899116i	−0.480649	+	0.876913i	$0.659599\pi$
$548$	−1.88300	−	3.26144i	−0.0804376	−	0.139322i
$549$	−23.0518	+	14.7242i	−0.983825	+	0.628414i
$550$	−3.47287	+	6.01519i	−0.148084	+	0.256488i
$551$	−9.88555	+	17.1223i	−0.421139	+	0.729433i
$552$	−6.50954	+	26.6711i	−0.277064	+	1.13520i
$553$	−16.4530	+	30.6951i	−0.699654	+	1.30529i
$554$	21.9701	−	38.0533i	0.933418	−	1.61673i
$555$	0.473013	−	0.138176i	0.0200783	−	0.00586526i
$556$	2.17276			0.0921456
$557$	11.5413	−	19.9900i	0.489019	−	0.847005i	−0.510902	−	0.859639i	$-0.670688\pi$
$557$	11.5413	−	19.9900i	0.489019	−	0.847005i	0.999920	+	0.0126342i	$0.00402169\pi$
$558$	10.6715	+	5.53908i	0.451759	+	0.234488i
$559$	−32.9417			−1.39328
$560$	−4.70995	+	8.78697i	−0.199032	+	0.371317i
$561$	1.65407	+	1.58154i	0.0698347	+	0.0667726i
$562$	27.9112			1.17736
$563$	16.0185	+	27.7449i	0.675100	+	1.16931i	0.976440	+	0.215791i	$0.0692330\pi$
$563$	16.0185	+	27.7449i	0.675100	+	1.16931i	−0.301339	+	0.953517i	$0.597434\pi$
$564$	0.700889	−	2.87170i	0.0295128	−	0.120920i
$565$	0.897370	−	1.55429i	0.0377526	−	0.0653895i
$566$	−46.8188			−1.96794
$567$	14.3118	+	19.0308i	0.601041	+	0.799218i
$568$	−0.862035			−0.0361702
$569$	14.0946	−	24.4125i	0.590875	−	1.02343i	−0.403239	−	0.915095i	$-0.632116\pi$
$569$	14.0946	−	24.4125i	0.590875	−	1.02343i	0.994115	−	0.108332i	$-0.0345509\pi$
$570$	4.03308	−	16.5245i	0.168927	−	0.692133i
$571$	−16.2805	−	28.1986i	−0.681317	−	1.18008i	−0.974579	−	0.224044i	$-0.928074\pi$
$571$	−16.2805	−	28.1986i	−0.681317	−	1.18008i	0.293262	−	0.956032i	$-0.405259\pi$
$572$	−1.72629			−0.0721797
$573$	−23.3229	−	22.3002i	−0.974328	−	0.931605i
$574$	−12.2157	−	19.6958i	−0.509875	−	0.822087i
$575$	29.5158			1.23089
$576$	−13.2650	−	6.88526i	−0.552708	−	0.286886i
$577$	−14.8559	+	25.7312i	−0.618459	+	1.07120i	0.371308	+	0.928510i	$0.378909\pi$
$577$	−14.8559	+	25.7312i	−0.618459	+	1.07120i	−0.989767	+	0.142693i	$0.954424\pi$
$578$	−24.2136			−1.00715
$579$	−12.6392	+	3.69215i	−0.525267	+	0.153441i
$580$	0.518308	−	0.897735i	0.0215215	−	0.0372764i
$581$	7.75219	+	12.4991i	0.321615	+	0.518549i
$582$	−10.8546	+	44.4738i	−0.449938	+	1.84350i
$583$	2.91904	−	5.05592i	0.120894	−	0.209395i
$584$	10.3342	−	17.8993i	0.427630	−	0.740677i
$585$	−6.63643	+	4.23899i	−0.274383	+	0.175261i
$586$	22.7463	+	39.3978i	0.939642	+	1.62751i
$587$	−21.2036	−	36.7258i	−0.875168	−	1.51583i	−0.856584	−	0.516008i	$-0.827418\pi$
$587$	−21.2036	−	36.7258i	−0.875168	−	1.51583i	−0.0185836	−	0.999827i	$-0.505916\pi$
$588$	5.92382	−	2.14442i	0.244294	−	0.0884343i
$589$	9.88526	−	17.1218i	0.407315	−	0.705490i
$590$	−5.06718			−0.208613
$591$	−6.51535	+	26.6949i	−0.268006	+	1.09808i
$592$	1.71735			0.0705826
$593$	11.7618	+	20.3721i	0.483000	+	0.836581i	0.999809	−	0.0195197i	$-0.00621369\pi$
$593$	11.7618	+	20.3721i	0.483000	+	0.836581i	−0.516809	+	0.856101i	$0.672880\pi$
$594$	−2.66518	−	7.80554i	−0.109354	−	0.320265i
$595$	1.30484	−	2.43433i	0.0534931	−	0.0997979i
$596$	5.18808	+	8.98602i	0.212512	+	0.368082i
$597$	20.1524	+	19.2688i	0.824785	+	0.788619i
$598$	17.7857	+	30.8057i	0.727310	+	1.25974i
$599$	12.3643	+	21.4155i	0.505190	+	0.875014i	0.999982	+	0.00600284i	$0.00191077\pi$
$599$	12.3643	+	21.4155i	0.505190	+	0.875014i	−0.494792	+	0.869011i	$0.664756\pi$
$600$	−4.22278	+	17.3017i	−0.172394	+	0.706339i
$601$	1.00611	+	1.74264i	0.0410402	+	0.0710838i	0.885816	−	0.464037i	$-0.153599\pi$
$601$	1.00611	+	1.74264i	0.0410402	+	0.0710838i	−0.844776	+	0.535121i	$0.820266\pi$
$602$	−41.6213	+	1.31385i	−1.69636	+	0.0535486i
$603$	−0.126356	−	2.81706i	−0.00514562	−	0.114720i
$604$	4.70200	+	8.14411i	0.191322	+	0.331379i
$605$	−0.790103			−0.0321223
$606$	−5.76748	−	5.51458i	−0.234288	−	0.224015i
$607$	−5.14125			−0.208677			−0.104338	−	0.994542i	$-0.533273\pi$
$607$	−5.14125			−0.208677			−0.104338	+	0.994542i	$0.533273\pi$
$608$	11.2390	−	19.4665i	0.455802	−	0.789471i
$609$	10.9986	−	3.59324i	0.445687	−	0.145606i
$610$	−5.71748	−	9.90297i	−0.231494	−	0.400959i
$611$	5.45582	+	9.44976i	0.220719	+	0.382296i
$612$	−1.82806	−	0.948864i	−0.0738950	−	0.0383556i
$613$	22.1783	−	38.4139i	0.895772	−	1.55152i	0.0629268	−	0.998018i	$-0.479957\pi$
$613$	22.1783	−	38.4139i	0.895772	−	1.55152i	0.832846	−	0.553505i	$-0.186710\pi$
$614$	12.6967	−	21.9914i	0.512398	−	0.887499i
$615$	5.45857	+	5.21922i	0.220111	+	0.210459i
$616$	6.21404	−	0.196158i	0.250371	−	0.00790342i
$617$	−15.5093	+	26.8629i	−0.624381	+	1.08146i	0.364279	+	0.931290i	$0.381316\pi$
$617$	−15.5093	+	26.8629i	−0.624381	+	1.08146i	−0.988660	+	0.150170i	$0.952018\pi$
$618$	9.93834	+	9.50256i	0.399778	+	0.382249i
$619$	−23.4863			−0.943994			−0.471997	−	0.881600i	$-0.656467\pi$
$619$	−23.4863			−0.943994			−0.471997	+	0.881600i	$0.656467\pi$
$620$	−0.518292	+	0.897709i	−0.0208151	+	0.0360529i
$621$	−23.0628	+	26.3930i	−0.925478	+	1.05912i
$622$	7.09401			0.284444
$623$	−2.97467	−	4.79615i	−0.119178	−	0.192154i
$624$	−26.3425	+	7.69517i	−1.05455	+	0.308053i
$625$	16.0258			0.641030
$626$	14.5368	+	25.1784i	0.581006	+	1.00633i
$627$	−13.0184	+	3.80294i	−0.519907	+	0.151875i
$628$	−0.137960	+	0.238953i	−0.00550520	+	0.00953528i
$629$	−0.475772			−0.0189703
$630$	−8.21596	+	5.62058i	−0.327332	+	0.223929i
$631$	−5.23347			−0.208341			−0.104171	−	0.994559i	$-0.533219\pi$
$631$	−5.23347			−0.208341			−0.104171	+	0.994559i	$0.533219\pi$
$632$	15.4659	−	26.7876i	0.615199	−	1.06556i
$633$	−23.6966	−	22.6576i	−0.941856	−	0.900557i
$634$	18.5770	+	32.1763i	0.737787	+	1.27789i
$635$	12.3684			0.490826
$636$	−1.24583	+	5.10445i	−0.0494004	+	0.202404i
$637$	−10.3344	+	20.8333i	−0.409465	+	0.825443i
$638$	−4.00791			−0.158675
$639$	−0.976793	−	0.507009i	−0.0386413	−	0.0200570i
$640$	5.39208	−	9.33936i	0.213141	−	0.369171i
$641$	−48.9720			−1.93428			−0.967140	−	0.254245i	$-0.918173\pi$
$641$	−48.9720			−1.93428			−0.967140	+	0.254245i	$0.918173\pi$
$642$	4.27736	−	17.5253i	0.168814	−	0.691668i
$643$	−0.428303	+	0.741842i	−0.0168906	+	0.0292554i	−0.874347	−	0.485301i	$-0.838710\pi$
$643$	−0.428303	+	0.741842i	−0.0168906	+	0.0292554i	0.857457	+	0.514556i	$0.172043\pi$
$644$	4.88773	+	7.88064i	0.192604	+	0.310541i
$645$	13.0250	−	3.80486i	0.512859	−	0.149816i
$646$	−8.21119	+	14.2222i	−0.323065	+	0.559565i
$647$	−15.6423	+	27.0933i	−0.614964	+	1.06515i	0.375427	+	0.926852i	$0.377496\pi$
$647$	−15.6423	+	27.0933i	−0.614964	+	1.06515i	−0.990391	+	0.138296i	$0.955837\pi$
$648$	−12.1716	−	17.2951i	−0.478146	−	0.679415i
$649$	2.02016	+	3.49902i	0.0792982	+	0.137348i
$650$	11.5377	+	19.9839i	0.452545	+	0.783831i
$651$	−10.9983	+	3.59314i	−0.431058	+	0.140826i
$652$	3.19645	−	5.53641i	0.125183	−	0.216823i
$653$	−26.3069			−1.02947			−0.514734	−	0.857350i	$-0.672109\pi$
$653$	−26.3069			−1.02947			−0.514734	+	0.857350i	$0.672109\pi$
$654$	−5.81554	+	1.69883i	−0.227406	+	0.0664296i
$655$	8.30133			0.324360
$656$	13.1598	+	22.7935i	0.513804	+	0.889935i
$657$	22.2374	−	14.2040i	0.867564	−	0.554152i
$658$	7.27024	+	11.7220i	0.283424	+	0.456972i
$659$	0.619223	+	1.07253i	0.0241215	+	0.0417797i	0.877834	−	0.478965i	$-0.158988\pi$
$659$	0.619223	+	1.07253i	0.0241215	+	0.0417797i	−0.853713	+	0.520744i	$0.825654\pi$
$660$	0.682568	−	0.199391i	0.0265689	−	0.00776130i
$661$	7.61225	+	13.1848i	0.296082	+	0.512829i	0.975236	−	0.221167i	$-0.0709865\pi$
$661$	7.61225	+	13.1848i	0.296082	+	0.512829i	−0.679154	+	0.733996i	$0.737653\pi$
$662$	22.6814	+	39.2854i	0.881539	+	1.52687i
$663$	7.29790	−	2.13186i	0.283427	−	0.0827945i
$664$	−6.53152	−	11.3129i	−0.253472	−	0.439027i
$665$	8.62751	+	13.9104i	0.334560	+	0.539422i
$666$	1.52194	+	0.789968i	0.0589738	+	0.0306107i
$667$	8.51576	+	14.7497i	0.329732	+	0.571112i
$668$	2.51070			0.0971420
$669$	16.7323	−	4.88783i	0.646908	−	0.188974i
$670$	1.17886			0.0455433
$671$	−4.55883	+	7.89613i	−0.175992	+	0.304827i
$672$	−12.5045	+	4.08520i	−0.482371	+	0.157590i
$673$	−13.6540	−	23.6494i	−0.526322	−	0.911617i	−0.999530	−	0.0306661i	$-0.990237\pi$
$673$	−13.6540	−	23.6494i	−0.526322	−	0.911617i	0.473207	−	0.880951i	$-0.343096\pi$
$674$	−22.7066	−	39.3290i	−0.874627	−	1.51490i
$675$	−14.9610	+	17.1213i	−0.575849	+	0.659000i
$676$	0.509942	−	0.883246i	0.0196132	−	0.0339710i
$677$	−19.5508	+	33.8630i	−0.751400	+	1.30146i	0.195744	+	0.980655i	$0.437288\pi$
$677$	−19.5508	+	33.8630i	−0.751400	+	1.30146i	−0.947144	+	0.320808i	$0.896046\pi$
$678$	5.99465	−	1.75115i	0.230223	−	0.0672527i
$679$	−23.2200	−	37.4383i	−0.891102	−	1.43675i
$680$	−1.22655	+	2.12444i	−0.0470359	+	0.0814686i
$681$	−7.33685	+	30.0607i	−0.281149	+	1.15193i
$682$	4.00779			0.153466
$683$	5.15555	−	8.92968i	0.197272	−	0.341685i	−0.750371	−	0.661017i	$-0.770125\pi$
$683$	5.15555	−	8.92968i	0.197272	−	0.341685i	0.947643	+	0.319332i	$0.103459\pi$
$684$	10.2869	−	6.57070i	0.393329	−	0.251237i
$685$	−5.72638			−0.218794
$686$	−12.2265	+	26.7347i	−0.466808	+	1.02073i
$687$	11.9663	−	49.0285i	0.456541	−	1.87055i
$688$	47.2894			1.80289
$689$	−9.69772	−	16.7969i	−0.369454	−	0.639913i
$690$	−10.5905	−	10.1262i	−0.403175	−	0.385496i
$691$	1.69422	−	2.93447i	0.0644511	−	0.111633i	−0.831999	−	0.554777i	$-0.812804\pi$
$691$	1.69422	−	2.93447i	0.0644511	−	0.111633i	0.896450	+	0.443144i	$0.146137\pi$
$692$	2.93681			0.111641
$693$	7.15665	+	3.43254i	0.271859	+	0.130391i
$694$	24.8237			0.942294
$695$	1.65190	−	2.86117i	0.0626600	−	0.108530i
$696$	−9.86441	+	2.88159i	−0.373909	+	0.109226i
$697$	−3.64578	−	6.31467i	−0.138094	−	0.239185i
$698$	−25.1436			−0.951700
$699$	11.2028	−	3.27254i	0.423727	−	0.123779i
$700$	3.17071	+	5.11222i	0.119841	+	0.193224i
$701$	26.6802			1.00770			0.503848	−	0.863792i	$-0.331917\pi$
$701$	26.6802			1.00770			0.503848	+	0.863792i	$0.331917\pi$
$702$	−26.8848	−	5.29782i	−1.01470	−	0.199953i
$703$	1.40981	−	2.44186i	0.0531720	−	0.0920966i
$704$	−4.98182			−0.187760
$705$	−3.24869	−	3.10624i	−0.122353	−	0.116988i
$706$	−4.76056	+	8.24553i	−0.179166	+	0.310325i
$707$	7.67516	−	0.242281i	0.288654	−	0.00911190i
$708$	−2.62823	−	2.51298i	−0.0987748	−	0.0944436i
$709$	−5.07029	+	8.78200i	−0.190419	+	0.329815i	−0.945389	−	0.325944i	$-0.894318\pi$
$709$	−5.07029	+	8.78200i	−0.190419	+	0.329815i	0.754970	+	0.655759i	$0.227651\pi$
$710$	0.230041	−	0.398442i	0.00863327	−	0.0149533i
$711$	33.2800	−	21.2574i	1.24810	−	0.797216i
$712$	2.50628	+	4.34100i	0.0939267	+	0.162686i
$713$	−8.51551	−	14.7493i	−0.318909	−	0.552366i
$714$	9.13576	−	2.98464i	0.341897	−	0.111697i
$715$	−1.31245	+	2.27324i	−0.0490830	+	0.0850142i
$716$	−4.09380			−0.152993
$717$	−33.7483	−	32.2685i	−1.26035	−	1.20509i
$718$	−40.4712			−1.51037
$719$	−8.03810	−	13.9224i	−0.299771	−	0.519218i	0.676313	−	0.736615i	$-0.263577\pi$
$719$	−8.03810	−	13.9224i	−0.299771	−	0.519218i	−0.976083	+	0.217397i	$0.930244\pi$
$720$	9.52693	−	6.08528i	0.355048	−	0.226785i
$721$	−13.2256	+	0.417490i	−0.492547	+	0.0155482i
$722$	−33.5832	−	58.1678i	−1.24984	−	2.16478i
$723$	7.14025	−	29.2552i	0.265549	−	1.08801i
$724$	−1.41274	−	2.44694i	−0.0525041	−	0.0909398i
$725$	5.52423	+	9.56825i	0.205165	+	0.355356i
$726$	−1.98715	−	1.90002i	−0.0737502	−	0.0705163i
$727$	−6.82644	−	11.8237i	−0.253178	−	0.438518i	0.711221	−	0.702969i	$-0.248143\pi$
$727$	−6.82644	−	11.8237i	−0.253178	−	0.438518i	−0.964399	+	0.264451i	$0.914809\pi$
$728$	9.75788	−	18.2045i	0.361651	−	0.674704i
$729$	−3.61980	−	26.7563i	−0.134067	−	0.990972i
$730$	5.51549	+	9.55312i	0.204138	+	0.353577i
$731$	−13.1010			−0.484558
$732$	1.94569	−	7.97192i	0.0719146	−	0.294651i
$733$	1.93274			0.0713874			0.0356937	−	0.999363i	$-0.488636\pi$
$733$	1.93274			0.0713874			0.0356937	+	0.999363i	$0.488636\pi$
$734$	−15.2745	+	26.4562i	−0.563792	+	0.976516i
$735$	1.67989	−	9.43105i	0.0619637	−	0.347869i
$736$	−9.68167	−	16.7691i	−0.356871	−	0.618119i
$737$	−0.469982	−	0.814033i	−0.0173120	−	0.0299853i
$738$	1.17756	+	26.2533i	0.0433466	+	0.966396i
$739$	−6.88244	+	11.9207i	−0.253175	+	0.438511i	−0.964398	−	0.264455i	$-0.914808\pi$
$739$	−6.88244	+	11.9207i	−0.253175	+	0.438511i	0.711223	+	0.702966i	$0.248141\pi$
$740$	−0.0739175	+	0.128029i	−0.00271726	+	0.00470643i
$741$	−10.6836	+	43.7730i	−0.392471	+	1.60804i
$742$	−12.9228	−	20.8359i	−0.474413	−	0.764909i
$743$	1.83262	−	3.17419i	0.0672322	−	0.116450i	−0.830450	−	0.557093i	$-0.811916\pi$
$743$	1.83262	−	3.17419i	0.0672322	−	0.116450i	0.897682	+	0.440644i	$0.145250\pi$
$744$	9.86412	−	2.88150i	0.361636	−	0.105641i
$745$	15.7775			0.578042
$746$	2.41145	−	4.17675i	0.0882895	−	0.152922i
$747$	−0.747288	−	16.6605i	−0.0273418	−	0.609575i
$748$	−0.686550			−0.0251027
$749$	9.15005	+	14.7529i	0.334336	+	0.539059i
$750$	−14.7204	−	14.0750i	−0.537514	−	0.513945i
$751$	−15.6812			−0.572216			−0.286108	−	0.958197i	$-0.592362\pi$
$751$	−15.6812			−0.572216			−0.286108	+	0.958197i	$0.592362\pi$
$752$	−7.83210	−	13.5656i	−0.285607	−	0.494687i
$753$	−11.3282	+	46.4141i	−0.412822	+	1.69142i
$754$	−6.65761	+	11.5313i	−0.242456	+	0.419946i
$755$	14.2993			0.520403
$756$	−7.04885	−	1.15930i	−0.256364	−	0.0421633i
$757$	−25.0896			−0.911897			−0.455949	−	0.890006i	$-0.650700\pi$
$757$	−25.0896			−0.911897			−0.455949	+	0.890006i	$0.650700\pi$
$758$	−15.3010	+	26.5021i	−0.555758	+	0.962601i
$759$	−2.77019	+	11.3501i	−0.100551	+	0.411982i
$760$	−7.26901	−	12.5903i	−0.263675	−	0.456698i
$761$	31.1966			1.13087			0.565437	−	0.824791i	$-0.308707\pi$
$761$	31.1966			1.13087			0.565437	+	0.824791i	$0.308707\pi$
$762$	31.1073	+	29.7433i	1.12690	+	1.07749i
$763$	2.75440	−	5.13868i	0.0997162	−	0.186033i
$764$	9.68058			0.350231
$765$	−2.63933	+	1.68586i	−0.0954251	+	0.0609523i
$766$	−19.1199	+	33.1167i	−0.690831	+	1.19656i
$767$	13.4229			0.484672
$768$	19.4552	−	5.68325i	0.702030	−	0.205076i
$769$	26.9105	−	46.6104i	0.970419	−	1.68081i	0.276128	−	0.961121i	$-0.410949\pi$
$769$	26.9105	−	46.6104i	0.970419	−	1.68081i	0.694291	−	0.719694i	$-0.255718\pi$
$770$	−1.56760	+	2.92454i	−0.0564923	+	0.105393i
$771$	12.4446	−	50.9885i	0.448183	−	1.83631i
$772$	1.97512	−	3.42101i	0.0710861	−	0.123125i
$773$	25.8592	−	44.7894i	0.930089	−	1.61096i	0.146925	−	0.989148i	$-0.453062\pi$
$773$	25.8592	−	44.7894i	0.930089	−	1.61096i	0.783165	−	0.621814i	$-0.213604\pi$
$774$	41.9085	+	21.7528i	1.50637	+	0.781888i
$775$	−5.52407	−	9.56797i	−0.198430	−	0.343692i
$776$	19.5638	+	33.8854i	0.702298	+	1.21642i
$777$	−1.56855	+	0.512444i	−0.0562715	+	0.0183838i
$778$	−3.06259	+	5.30456i	−0.109799	+	0.190178i
$779$	43.2127			1.54826
$780$	0.560148	−	2.29505i	0.0200565	−	0.0821761i
$781$	−0.366846			−0.0131268
$782$	7.07341	+	12.2515i	0.252945	+	0.438113i
$783$	−12.8724	−	2.53659i	−0.460023	−	0.0906504i
$784$	14.8356	−	29.9072i	0.529842	−	1.06811i
$785$	0.209775	+	0.363340i	0.00748718	+	0.0129682i
$786$	20.8783	+	19.9628i	0.744704	+	0.712050i
$787$	8.36175	+	14.4830i	0.298064	+	0.516262i	0.975693	−	0.219142i	$-0.0703257\pi$
$787$	8.36175	+	14.4830i	0.298064	+	0.516262i	−0.677629	+	0.735404i	$0.736992\pi$
$788$	−4.12178	−	7.13913i	−0.146832	−	0.254321i
$789$	−10.9680	+	44.9382i	−0.390470	+	1.59984i
$790$	8.25436	+	14.2970i	0.293677	+	0.508663i
$791$	−2.83924	+	5.29694i	−0.100952	+	0.188338i
$792$	−6.25692	−	3.24768i	−0.222330	−	0.115401i
$793$	15.1455	+	26.2328i	0.537833	+	0.931554i
$794$	−29.7038			−1.05415
$795$	5.77454	+	5.52133i	0.204802	+	0.195822i
$796$	−8.36463			−0.296476
$797$	13.4421	−	23.2824i	0.476144	−	0.824705i	−0.523483	−	0.852036i	$-0.675368\pi$
$797$	13.4421	−	23.2824i	0.476144	−	0.824705i	0.999626	+	0.0273314i	$0.00870094\pi$
$798$	−11.7527	+	55.7326i	−0.416040	+	1.97291i
$799$	2.16980	+	3.75820i	0.0767619	+	0.132955i
$800$	−6.28056	−	10.8783i	−0.222051	−	0.384604i
$801$	0.286749	+	6.39297i	0.0101318	+	0.225884i
$802$	5.94844	−	10.3030i	0.210047	−	0.363812i
$803$	4.39778	−	7.61718i	0.155194	−	0.268804i
$804$	0.611446	+	0.584635i	0.0215641	+	0.0206185i
$805$	14.0935	−	0.444888i	0.496731	−	0.0156802i
$806$	6.65741	−	11.5310i	0.234497	−	0.406161i
$807$	28.8599	+	27.5945i	1.01592	+	0.971371i
$808$	−6.82018			−0.239933
$809$	24.6448	−	42.6861i	0.866466	−	1.50076i	0.000882379	−	1.00000i	$-0.499719\pi$
$809$	24.6448	−	42.6861i	0.866466	−	1.50076i	0.865584	−	0.500764i	$-0.166948\pi$
$810$	11.2421	−	1.01053i	0.395006	−	0.0355065i
$811$	17.2070			0.604219			0.302109	−	0.953273i	$-0.402309\pi$
$811$	17.2070			0.604219			0.302109	+	0.953273i	$0.402309\pi$
$812$	−1.63990	+	3.05943i	−0.0575492	+	0.107365i
$813$	−2.60995	+	0.762418i	−0.0915350	+	0.0267392i
$814$	0.571581			0.0200339
$815$	−4.86036	−	8.41839i	−0.170251	−	0.294883i
$816$	−10.4765	+	3.06039i	−0.366751	+	0.107135i
$817$	38.8209	−	67.2398i	1.35817	−	2.35242i
$818$	42.5187			1.48663
$819$	21.7639	−	14.8888i	0.760493	−	0.520258i
$820$	−2.26568			−0.0791209
$821$	−8.10909	+	14.0454i	−0.283009	+	0.490186i	−0.972124	−	0.234466i	$-0.924666\pi$
$821$	−8.10909	+	14.0454i	−0.283009	+	0.490186i	0.689115	+	0.724652i	$0.257999\pi$
$822$	−14.4022	−	13.7706i	−0.502333	−	0.480306i
$823$	21.4354	+	37.1272i	0.747191	+	1.29417i	0.949164	+	0.314782i	$0.101931\pi$
$823$	21.4354	+	37.1272i	0.747191	+	1.29417i	−0.201973	+	0.979391i	$0.564735\pi$
$824$	11.7523			0.409412
$825$	−1.79704	+	7.36287i	−0.0625648	+	0.256342i
$826$	16.9596	−	0.535361i	0.590100	−	0.0186276i
$827$	−37.5467			−1.30563			−0.652813	−	0.757519i	$-0.726411\pi$
$827$	−37.5467			−1.30563			−0.652813	+	0.757519i	$0.726411\pi$
$828$	−0.471163	−	10.5044i	−0.0163740	−	0.365053i
$829$	−5.52756	+	9.57401i	−0.191980	+	0.332519i	−0.945906	−	0.324440i	$-0.894824\pi$
$829$	−5.52756	+	9.57401i	−0.191980	+	0.332519i	0.753926	+	0.656959i	$0.228158\pi$
$830$	6.97195			0.242000
$831$	11.3684	−	46.5790i	0.394366	−	1.61581i
$832$	−8.27539	+	14.3334i	−0.286898	+	0.496921i
$833$	−4.11003	+	8.28544i	−0.142404	+	0.287074i
$834$	11.0351	−	3.22356i	0.382113	−	0.111623i
$835$	1.90882	−	3.30618i	0.0660576	−	0.114415i
$836$	2.03439	−	3.52366i	0.0703607	−	0.121868i
$837$	12.8720	+	2.53652i	0.444923	+	0.0876749i
$838$	12.8384	+	22.2368i	0.443497	+	0.768159i
$839$	26.9818	+	46.7339i	0.931515	+	1.61343i	0.780733	+	0.624865i	$0.214846\pi$
$839$	26.9818	+	46.7339i	0.931515	+	1.61343i	0.150782	+	0.988567i	$0.451821\pi$
$840$	−1.75555	+	8.32505i	−0.0605724	+	0.287242i
$841$	11.3123	−	19.5936i	0.390081	−	0.675640i
$842$	−14.4153			−0.496783
$843$	29.2341	−	8.53986i	1.00688	−	0.294128i
$844$	9.83571			0.338559
$845$	−0.775392	−	1.34302i	−0.0266743	−	0.0462013i
$846$	−0.700829	−	15.6247i	−0.0240950	−	0.537189i
$847$	2.64443	−	0.0834765i	0.0908638	−	0.00286828i
$848$	13.9216	+	24.1128i	0.478068	+	0.828039i
$849$	−49.0379	+	14.3249i	−1.68298	+	0.491630i
$850$	4.58857	+	7.94764i	0.157387	+	0.272602i
$851$	−1.21446	−	2.10351i	−0.0416312	−	0.0721073i
$852$	0.316917	−	0.0925776i	0.0108574	−	0.00317166i
$853$	18.5707	+	32.1653i	0.635848	+	1.10132i	0.986335	+	0.164753i	$0.0526826\pi$
$853$	18.5707	+	32.1653i	0.635848	+	1.10132i	−0.350487	+	0.936567i	$0.613984\pi$
$854$	20.1824	+	32.5406i	0.690627	+	1.11352i
$855$	−0.831666	−	18.5417i	−0.0284424	−	0.634112i
$856$	−7.70927	−	13.3529i	−0.263498	−	0.456391i
$857$	−0.755127			−0.0257947			−0.0128973	−	0.999917i	$-0.504105\pi$
$857$	−0.755127			−0.0257947			−0.0128973	+	0.999917i	$0.504105\pi$
$858$	−8.76751	+	2.56116i	−0.299318	+	0.0874366i
$859$	−44.1242			−1.50550			−0.752749	−	0.658307i	$-0.771273\pi$
$859$	−44.1242			−1.50550			−0.752749	+	0.658307i	$0.771273\pi$
$860$	−2.03541	+	3.52544i	−0.0694070	+	0.120216i
$861$	−18.8210	−	16.8918i	−0.641417	−	0.575669i
$862$	−28.1715	−	48.7945i	−0.959526	−	1.66195i
$863$	5.91444	+	10.2441i	0.201330	+	0.348714i	0.948957	−	0.315405i	$-0.102140\pi$
$863$	5.91444	+	10.2441i	0.201330	+	0.348714i	−0.747627	+	0.664119i	$0.768807\pi$
$864$	14.6348	+	2.88388i	0.497886	+	0.0981116i
$865$	2.23278	−	3.86729i	0.0759169	−	0.131492i
$866$	4.76445	−	8.25226i	0.161902	−	0.280423i
$867$	−25.3612	+	7.40851i	−0.861313	+	0.251606i
$868$	1.63985	−	3.05934i	0.0556602	−	0.103841i
$869$	6.58161	−	11.3997i	0.223266	−	0.386708i
$870$	1.30049	−	5.32841i	0.0440908	−	0.180650i
$871$	−3.12278			−0.105811
$872$	−2.58914	+	4.48452i	−0.0876793	+	0.151865i
$873$	2.23834	+	49.9029i	0.0757563	+	1.68896i
$874$	−83.8398			−2.83592
$875$	19.5894	−	0.618377i	0.662244	−	0.0209050i
$876$	−1.87695	+	7.69029i	−0.0634163	+	0.259831i
$877$	12.5049			0.422262			0.211131	−	0.977458i	$-0.432285\pi$
$877$	12.5049			0.422262			0.211131	+	0.977458i	$0.432285\pi$
$878$	−20.0756	−	34.7720i	−0.677519	−	1.17350i
$879$	35.8788	+	34.3056i	1.21016	+	1.15710i
$880$	1.88409	−	3.26334i	0.0635127	−	0.110007i
$881$	−25.2425			−0.850443			−0.425221	−	0.905089i	$-0.639804\pi$
$881$	−25.2425			−0.850443			−0.425221	+	0.905089i	$0.639804\pi$
$882$	26.9045	−	19.6798i	0.905923	−	0.662655i
$883$	−30.5827			−1.02919			−0.514594	−	0.857434i	$-0.672057\pi$
$883$	−30.5827			−1.02919			−0.514594	+	0.857434i	$0.672057\pi$
$884$	−1.14044	+	1.97530i	−0.0383571	+	0.0664365i
$885$	−5.30736	+	1.55038i	−0.178405	+	0.0521155i
$886$	−1.73015	−	2.99670i	−0.0581255	−	0.100676i
$887$	−2.54605			−0.0854881			−0.0427441	−	0.999086i	$-0.513610\pi$
$887$	−2.54605			−0.0854881			−0.0427441	+	0.999086i	$0.513610\pi$
$888$	1.40679	−	0.410952i	0.0472089	−	0.0137906i
$889$	−41.3965	+	1.30676i	−1.38839	+	0.0438272i
$890$	−2.67528			−0.0896754
$891$	−5.17973	−	7.36006i	−0.173527	−	0.246571i
$892$	−2.61475	+	4.52888i	−0.0875482	+	0.151638i
$893$	−25.7182			−0.860626
$894$	39.6812	+	37.9413i	1.32714	+	1.26895i
$895$	−3.11242	+	5.39086i	−0.104037	+	0.180197i
$896$	−17.0603	+	31.8280i	−0.569944	+	1.06330i
$897$	28.0541	+	26.8240i	0.936701	+	0.895628i
$898$	23.5285	−	40.7525i	0.785156	−	1.35993i
$899$	3.18756	−	5.52102i	0.106311	−	0.184136i
$900$	−0.305646	−	6.81427i	−0.0101882	−	0.227142i
$901$	−3.85681	−	6.68019i	−0.128489	−	0.222549i
$902$	4.37994	+	7.58628i	0.145836	+	0.252596i
$903$	−43.1921	+	14.1108i	−1.43734	+	0.469578i
$904$	2.66888	−	4.62264i	0.0887657	−	0.153747i
$905$	−4.29629			−0.142813
$906$	35.9634	+	34.3865i	1.19480	+	1.14241i
$907$	11.1489			0.370193			0.185097	−	0.982720i	$-0.440740\pi$
$907$	11.1489			0.370193			0.185097	+	0.982720i	$0.440740\pi$
$908$	−4.64148	−	8.03928i	−0.154033	−	0.266793i
$909$	−7.72812	−	4.01132i	−0.256325	−	0.133047i
$910$	5.81036	+	9.36821i	0.192611	+	0.310553i
$911$	8.26555	+	14.3164i	0.273850	+	0.474322i	0.969844	−	0.243725i	$-0.0783695\pi$
$911$	8.26555	+	14.3164i	0.273850	+	0.474322i	−0.695994	+	0.718047i	$0.745036\pi$
$912$	15.3368	−	62.8383i	0.507852	−	2.08078i
$913$	−2.77954	−	4.81431i	−0.0919894	−	0.159330i
$914$	20.9449	+	36.2777i	0.692796	+	1.19996i
$915$	−9.01844	−	8.62300i	−0.298140	−	0.285067i
$916$	7.57017	+	13.1119i	0.250125	+	0.433230i
$917$	−27.7841	+	0.877057i	−0.917513	+	0.0289630i
$918$	−10.6922	−	2.10696i	−0.352894	−	0.0695400i
$919$	−5.39014	−	9.33599i	−0.177804	−	0.307966i	0.763324	−	0.646016i	$-0.223566\pi$
$919$	−5.39014	−	9.33599i	−0.177804	−	0.307966i	−0.941128	+	0.338050i	$0.890233\pi$
$920$	−12.5236			−0.412890
$921$	6.56992	−	26.9185i	0.216486	−	0.886993i
$922$	−22.0687			−0.726794
$923$	−0.609374	+	1.05547i	−0.0200578	+	0.0347411i
$924$	−2.26345	+	0.739468i	−0.0744621	+	0.0243267i
$925$	−0.787828	−	1.36456i	−0.0259036	−	0.0448664i
$926$	−8.32759	−	14.4238i	−0.273662	−	0.473996i
$927$	13.3168	+	6.91217i	0.437383	+	0.227025i
$928$	3.62408	−	6.27710i	0.118966	−	0.206056i
$929$	10.7333	−	18.5906i	0.352149	−	0.609939i	−0.634477	−	0.772942i	$-0.718785\pi$
$929$	10.7333	−	18.5906i	0.352149	−	0.609939i	0.986626	+	0.163002i	$0.0521179\pi$
$930$	−1.30045	+	5.32826i	−0.0426436	+	0.174720i
$931$	−30.3455	−	45.6458i	−0.994534	−	1.49598i
$932$	−1.75065	+	3.03221i	−0.0573444	+	0.0993235i
$933$	7.43025	−	2.17052i	0.243255	−	0.0710596i
$934$	3.29029			0.107662
$935$	−0.521966	+	0.904072i	−0.0170701	+	0.0295663i
$936$	−19.7375	+	12.6072i	−0.645140	+	0.412080i
$937$	0.227644			0.00743682			0.00371841	−	0.999993i	$-0.498816\pi$
$937$	0.227644			0.00743682			0.00371841	+	0.999993i	$0.498816\pi$
$938$	−3.94558	+	0.124550i	−0.128828	+	0.00406669i
$939$	22.9295	+	21.9241i	0.748277	+	0.715466i
$940$	1.34843			0.0439808
$941$	−0.619039	−	1.07221i	−0.0201801	−	0.0349529i	0.855759	−	0.517375i	$-0.173091\pi$
$941$	−0.619039	−	1.07221i	−0.0201801	−	0.0349529i	−0.875939	+	0.482422i	$0.839757\pi$
$942$	−0.346157	+	1.41828i	−0.0112784	+	0.0462101i
$943$	18.6125	−	32.2377i	0.606106	−	1.04981i
$944$	−19.2692			−0.627159
$945$	−6.88567	+	8.40079i	−0.223991	+	0.273278i
$946$	15.7392			0.511726
$947$	20.5194	−	35.5407i	0.666792	−	1.15492i	−0.312004	−	0.950081i	$-0.601000\pi$
$947$	20.5194	−	35.5407i	0.666792	−	1.15492i	0.978796	−	0.204837i	$-0.0656665\pi$
$948$	−2.80900	+	11.5091i	−0.0912321	+	0.373798i
$949$	−14.6105	−	25.3060i	−0.474275	−	0.821469i
$950$	−54.3874			−1.76456
$951$	29.3024	+	28.0175i	0.950194	+	0.908530i
$952$	3.88074	−	7.23998i	0.125775	−	0.234649i
$953$	15.1554			0.490931			0.245466	−	0.969405i	$-0.421059\pi$
$953$	15.1554			0.490931			0.245466	+	0.969405i	$0.421059\pi$
$954$	1.24572	+	27.7729i	0.0403318	+	0.899181i
$955$	7.35990	−	12.7477i	0.238161	−	0.412507i
$956$	14.0078			0.453046
$957$	−4.19788	+	1.22628i	−0.135698	+	0.0396400i
$958$	7.49656	−	12.9844i	0.242203	−	0.419508i
$959$	19.1659	−	0.605007i	0.618899	−	0.0195367i
$960$	1.61651	−	6.62320i	0.0521726	−	0.213763i
$961$	12.3125	−	21.3259i	0.397178	−	0.687933i
$962$	0.949462	−	1.64452i	0.0306119	−	0.0530214i
$963$	−0.882038	−	19.6647i	−0.0284233	−	0.633685i
$964$	4.51711	+	7.82386i	0.145486	+	0.251990i
$965$	−3.00327	−	5.20181i	−0.0966786	−	0.167452i
$966$	36.5158	+	32.7728i	1.17488	+	1.05445i
$967$	16.4547	−	28.5003i	0.529147	−	0.916509i	−0.470276	−	0.882520i	$-0.655845\pi$
$967$	16.4547	−	28.5003i	0.529147	−	0.916509i	0.999422	−	0.0339892i	$-0.0108212\pi$
$968$	−2.34986			−0.0755273
$969$	−4.24889	+	17.4086i	−0.136494	+	0.559246i
$970$	−20.8830			−0.670511
$971$	−8.00433	−	13.8639i	−0.256871	−	0.444914i	0.708531	−	0.705680i	$-0.249358\pi$
$971$	−8.00433	−	13.8639i	−0.256871	−	0.444914i	−0.965402	+	0.260766i	$0.916025\pi$
$972$	6.33215	+	5.05117i	0.203104	+	0.162016i
$973$	−5.22652	+	9.75071i	−0.167555	+	0.312593i
$974$	0.529820	+	0.917675i	0.0169765	+	0.0294042i
$975$	18.1989	+	17.4009i	0.582832	+	0.557275i
$976$	−21.7421	−	37.6585i	−0.695949	−	1.20542i
$977$	−18.4672	−	31.9861i	−0.590817	−	1.02333i	−0.994123	−	0.108260i	$-0.965472\pi$
$977$	−18.4672	−	31.9861i	−0.590817	−	1.02333i	0.403306	−	0.915065i	$-0.367861\pi$
$978$	8.02025	−	32.8608i	0.256459	−	1.05077i
$979$	1.06657	+	1.84735i	0.0340876	+	0.0590414i
$980$	1.59104	+	2.39325i	0.0508239	+	0.0764495i
$981$	−5.57140	+	3.55871i	−0.177881	+	0.113621i
$982$	−19.7332	−	34.1789i	−0.629711	−	1.09069i
$983$	−54.2260			−1.72954			−0.864771	−	0.502167i	$-0.832536\pi$
$983$	−54.2260			−1.72954			−0.864771	+	0.502167i	$0.832536\pi$
$984$	16.2344	+	15.5226i	0.517534	+	0.494841i
$985$	−12.5347			−0.399390
$986$	−2.64775	+	4.58604i	−0.0843215	+	0.146049i
$987$	11.2014	+	10.0532i	0.356543	+	0.319996i
$988$	−6.75870	−	11.7064i	−0.215023	−	0.372431i
$989$	−33.4417	−	57.9227i	−1.06338	−	1.84184i
$990$	3.17082	−	2.02535i	0.100775	−	0.0643697i
$991$	14.9797	−	25.9456i	0.475845	−	0.824188i	−0.523772	−	0.851859i	$-0.675476\pi$
$991$	14.9797	−	25.9456i	0.475845	−	0.824188i	0.999617	+	0.0276703i	$0.00880887\pi$
$992$	−3.62398	+	6.27691i	−0.115061	+	0.199292i
$993$	35.7765	+	34.2077i	1.13533	+	1.08555i
$994$	−0.727837	+	1.35787i	−0.0230856	+	0.0430690i
$995$	−6.35942	+	11.0148i	−0.201607	+	0.349194i
$996$	3.61618	+	3.45762i	0.114583	+	0.109559i
$997$	20.1738			0.638912			0.319456	−	0.947601i	$-0.396500\pi$
$997$	20.1738			0.638912			0.319456	+	0.947601i	$0.396500\pi$
$998$	−1.26742	+	2.19523i	−0.0401195	+	0.0694889i
$999$	1.83578	+	0.361751i	0.0580814	+	0.0114453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.k.c.67.11	✓	80
7.2	even	3		693.2.l.c.562.30	yes	80
9.7	even	3		693.2.l.c.529.30	yes	80
63.16	even	3	inner	693.2.k.c.331.11	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.k.c.67.11	✓	80	1.1	even	1	trivial
693.2.k.c.331.11	yes	80	63.16	even	3	inner
693.2.l.c.529.30	yes	80	9.7	even	3
693.2.l.c.562.30	yes	80	7.2	even	3

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.793665 + 1.37467i) q^{2} +(-0.410682 + 1.68266i) q^{3} +(-0.259808 - 0.450001i) q^{4} -0.790103 q^{5} +(-1.98715 - 1.90002i) q^{6} +(2.64443 - 0.0834765i) q^{7} -2.34986 q^{8} +(-2.66268 - 1.38208i) q^{9} +(0.627077 - 1.08613i) q^{10} -1.00000 q^{11} +(0.863897 - 0.252361i) q^{12} +(-1.66112 + 2.87714i) q^{13} +(-1.98404 + 3.70147i) q^{14} +(0.324481 - 1.32947i) q^{15} +(2.38462 - 4.13028i) q^{16} +(-0.660631 + 1.14425i) q^{17} +(4.01317 - 2.56340i) q^{18} +(-3.91517 - 6.78127i) q^{19} +(0.205275 + 0.355547i) q^{20} +(-0.945560 + 4.48396i) q^{21} +(0.793665 - 1.37467i) q^{22} -6.74532 q^{23} +(0.965045 - 3.95401i) q^{24} -4.37574 q^{25} +(-2.63674 - 4.56697i) q^{26} +(3.41908 - 3.91279i) q^{27} +(-0.724611 - 1.16831i) q^{28} +(-1.26247 - 2.18666i) q^{29} +(1.57006 + 1.50121i) q^{30} +(1.26243 + 2.18660i) q^{31} +(1.43532 + 2.48604i) q^{32} +(0.410682 - 1.68266i) q^{33} +(-1.04864 - 1.81630i) q^{34} +(-2.08938 + 0.0659550i) q^{35} +(0.0698503 + 1.55728i) q^{36} +(0.180045 + 0.311847i) q^{37} +12.4293 q^{38} +(-4.15905 - 3.97668i) q^{39} +1.85663 q^{40} +(-2.75931 + 4.77927i) q^{41} +(-5.41350 - 4.85860i) q^{42} +(4.95776 + 8.58709i) q^{43} +(0.259808 + 0.450001i) q^{44} +(2.10379 + 1.09198i) q^{45} +(5.35353 - 9.27258i) q^{46} +(1.64222 - 2.84440i) q^{47} +(5.97052 + 5.70873i) q^{48} +(6.98606 - 0.441496i) q^{49} +(3.47287 - 6.01519i) q^{50} +(-1.65407 - 1.58154i) q^{51} +1.72629 q^{52} +(-2.91904 + 5.05592i) q^{53} +(2.66518 + 7.80554i) q^{54} +0.790103 q^{55} +(-6.21404 + 0.196158i) q^{56} +(13.0184 - 3.80294i) q^{57} +4.00791 q^{58} +(-2.02016 - 3.49902i) q^{59} +(-0.682568 + 0.199391i) q^{60} +(4.55883 - 7.89613i) q^{61} -4.00779 q^{62} +(-7.15665 - 3.43254i) q^{63} +4.98182 q^{64} +(1.31245 - 2.27324i) q^{65} +(1.98715 + 1.90002i) q^{66} +(0.469982 + 0.814033i) q^{67} +0.686550 q^{68} +(2.77019 - 11.3501i) q^{69} +(1.56760 - 2.92454i) q^{70} +0.366846 q^{71} +(6.25692 + 3.24768i) q^{72} +(-4.39778 + 7.61718i) q^{73} -0.571581 q^{74} +(1.79704 - 7.36287i) q^{75} +(-2.03439 + 3.52366i) q^{76} +(-2.64443 + 0.0834765i) q^{77} +(8.76751 - 2.56116i) q^{78} +(-6.58161 + 11.3997i) q^{79} +(-1.88409 + 3.26334i) q^{80} +(5.17973 + 7.36006i) q^{81} +(-4.37994 - 7.58628i) q^{82} +(2.77954 + 4.81431i) q^{83} +(2.26345 - 0.739468i) q^{84} +(0.521966 - 0.904072i) q^{85} -15.7392 q^{86} +(4.19788 - 1.22628i) q^{87} +2.34986 q^{88} +(-1.06657 - 1.84735i) q^{89} +(-3.17082 + 2.02535i) q^{90} +(-4.15254 + 7.74707i) q^{91} +(1.75249 + 3.03540i) q^{92} +(-4.19775 + 1.22625i) q^{93} +(2.60674 + 4.51500i) q^{94} +(3.09338 + 5.35790i) q^{95} +(-4.77262 + 1.39417i) q^{96} +(-8.32551 - 14.4202i) q^{97} +(-4.93768 + 9.95392i) q^{98} +(2.66268 + 1.38208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 40 q^{4} + 8 q^{5} + 6 q^{6} - q^{7} + 2 q^{9} + 12 q^{10} - 80 q^{11} - 10 q^{12} + 21 q^{13} - 8 q^{14} - 5 q^{15} - 40 q^{16} - 3 q^{17} + 32 q^{18} + 18 q^{19} - 12 q^{20} + 18 q^{21} - 8 q^{23}+ \cdots - 2 q^{99}+O(q^{100}) \) 80 * q - 40 * q^4 + 8 * q^5 + 6 * q^6 - q^7 + 2 * q^9 + 12 * q^10 - 80 * q^11 - 10 * q^12 + 21 * q^13 - 8 * q^14 - 5 * q^15 - 40 * q^16 - 3 * q^17 + 32 * q^18 + 18 * q^19 - 12 * q^20 + 18 * q^21 - 8 * q^23 - 14 * q^24 + 80 * q^25 - 12 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 + 20 * q^30 + 32 * q^31 + 35 * q^32 + 28 * q^34 - 18 * q^35 - 16 * q^36 - 7 * q^37 + 46 * q^38 - 48 * q^39 - 102 * q^40 - 2 * q^41 - 14 * q^42 + 9 * q^43 + 40 * q^44 - 5 * q^45 - 6 * q^46 - 26 * q^47 - 28 * q^48 - 19 * q^49 + 2 * q^50 + 22 * q^51 - 88 * q^52 + 4 * q^53 + 19 * q^54 - 8 * q^55 + 18 * q^56 + 16 * q^57 + 32 * q^58 - 24 * q^59 - 10 * q^60 + 69 * q^61 + 12 * q^62 + 20 * q^63 + 44 * q^64 - 7 * q^65 - 6 * q^66 + 7 * q^67 + 34 * q^68 + 15 * q^69 - 22 * q^70 + 34 * q^71 - 70 * q^72 + 26 * q^73 + 8 * q^74 - 64 * q^75 + 52 * q^76 + q^77 - 60 * q^78 - 5 * q^79 - 47 * q^80 + 46 * q^81 + 60 * q^82 + 4 * q^83 + 29 * q^84 + 13 * q^85 - 38 * q^87 - 38 * q^89 - 43 * q^90 + 13 * q^91 - 21 * q^92 + 35 * q^93 + 56 * q^94 - 20 * q^95 + 15 * q^96 + 49 * q^97 - 84 * q^98 - 2 * q^99

Introduction

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