LMFDB - Embedded newform 143.2.h.c.92.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(14,143)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("143.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			92.3
Character	$\chi$	$=$	143.92
Dual form			143.2.h.c.14.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.743923 - 0.540492i) q^{2} +(-0.330114 + 1.01599i) q^{3} +(-0.356744 - 1.09794i) q^{4} +(-2.64538 + 1.92198i) q^{5} +(0.794711 - 0.577391i) q^{6} +(0.656608 + 2.02083i) q^{7} +(-0.896347 + 2.75867i) q^{8} +(1.50380 + 1.09257i) q^{9} +O(q^{10})$	\(q+(-0.743923 - 0.540492i) q^{2} +(-0.330114 + 1.01599i) q^{3} +(-0.356744 - 1.09794i) q^{4} +(-2.64538 + 1.92198i) q^{5} +(0.794711 - 0.577391i) q^{6} +(0.656608 + 2.02083i) q^{7} +(-0.896347 + 2.75867i) q^{8} +(1.50380 + 1.09257i) q^{9} +3.00678 q^{10} +(-2.93820 + 1.53849i) q^{11} +1.23326 q^{12} +(-0.809017 - 0.587785i) q^{13} +(0.603777 - 1.85823i) q^{14} +(-1.07943 - 3.32214i) q^{15} +(0.289917 - 0.210637i) q^{16} +(-2.27764 + 1.65480i) q^{17} +(-0.528184 - 1.62558i) q^{18} +(0.205036 - 0.631037i) q^{19} +(3.05395 + 2.21883i) q^{20} -2.26989 q^{21} +(3.01734 + 0.443553i) q^{22} +4.97564 q^{23} +(-2.50687 - 1.82135i) q^{24} +(1.75895 - 5.41348i) q^{25} +(0.284153 + 0.874534i) q^{26} +(-4.19921 + 3.05091i) q^{27} +(1.98452 - 1.44184i) q^{28} +(-1.48693 - 4.57630i) q^{29} +(-0.992579 + 3.05484i) q^{30} +(-0.969968 - 0.704723i) q^{31} +5.47175 q^{32} +(-0.593147 - 3.49305i) q^{33} +2.58879 q^{34} +(-5.62098 - 4.08388i) q^{35} +(0.663115 - 2.04086i) q^{36} +(1.42882 + 4.39746i) q^{37} +(-0.493602 + 0.358623i) q^{38} +(0.864249 - 0.627914i) q^{39} +(-2.93094 - 9.02050i) q^{40} +(2.32942 - 7.16922i) q^{41} +(1.68862 + 1.22686i) q^{42} -0.661961 q^{43} +(2.73737 + 2.67714i) q^{44} -6.07803 q^{45} +(-3.70149 - 2.68929i) q^{46} +(-2.37126 + 7.29797i) q^{47} +(0.118299 + 0.364086i) q^{48} +(2.01049 - 1.46071i) q^{49} +(-4.23446 + 3.07652i) q^{50} +(-0.929374 - 2.86032i) q^{51} +(-0.356744 + 1.09794i) q^{52} +(6.50589 + 4.72680i) q^{53} +4.77288 q^{54} +(4.81571 - 9.71708i) q^{55} -6.16336 q^{56} +(0.573440 + 0.416628i) q^{57} +(-1.36729 + 4.20809i) q^{58} +(3.17656 + 9.77644i) q^{59} +(-3.26245 + 2.37031i) q^{60} +(-5.70932 + 4.14806i) q^{61} +(0.340685 + 1.04852i) q^{62} +(-1.22050 + 3.75632i) q^{63} +(-4.65040 - 3.37871i) q^{64} +3.26987 q^{65} +(-1.44671 + 2.91915i) q^{66} +14.7519 q^{67} +(2.62941 + 1.91038i) q^{68} +(-1.64253 + 5.05518i) q^{69} +(1.97427 + 6.07619i) q^{70} +(-11.6958 + 8.49747i) q^{71} +(-4.36198 + 3.16916i) q^{72} +(-0.428847 - 1.31986i) q^{73} +(1.31386 - 4.04364i) q^{74} +(4.91937 + 3.57413i) q^{75} -0.765989 q^{76} +(-5.03828 - 4.92742i) q^{77} -0.982317 q^{78} +(10.8604 + 7.89054i) q^{79} +(-0.362101 + 1.11443i) q^{80} +(0.00974075 + 0.0299789i) q^{81} +(-5.60781 + 4.07431i) q^{82} +(2.85627 - 2.07520i) q^{83} +(0.809770 + 2.49221i) q^{84} +(2.84472 - 8.75516i) q^{85} +(0.492448 + 0.357785i) q^{86} +5.14031 q^{87} +(-1.61055 - 9.48456i) q^{88} +8.08446 q^{89} +(4.52159 + 3.28513i) q^{90} +(0.656608 - 2.02083i) q^{91} +(-1.77503 - 5.46297i) q^{92} +(1.03619 - 0.752835i) q^{93} +(5.70853 - 4.14749i) q^{94} +(0.670443 + 2.06341i) q^{95} +(-1.80630 + 5.55922i) q^{96} +(-5.75645 - 4.18231i) q^{97} -2.28516 q^{98} +(-6.09938 - 0.896617i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) $ 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.743923	−	0.540492i	−0.526033	−	0.382185i	0.292839	−	0.956162i	$-0.405400\pi$
$2$	−0.743923	−	0.540492i	−0.526033	−	0.382185i	−0.818872	+	0.573976i	$0.805400\pi$
$3$	−0.330114	+	1.01599i	−0.190591	+	0.586580i	−1.00000		0.000666344i	$-0.999788\pi$
$3$	−0.330114	+	1.01599i	−0.190591	+	0.586580i	0.809408	+	0.587246i	$0.199788\pi$
$4$	−0.356744	−	1.09794i	−0.178372	−	0.548972i
$5$	−2.64538	+	1.92198i	−1.18305	+	0.859537i	−0.992513	−	0.122143i	$-0.961023\pi$
$5$	−2.64538	+	1.92198i	−1.18305	+	0.859537i	−0.190539	+	0.981680i	$0.561023\pi$
$6$	0.794711	−	0.577391i	0.324439	−	0.235719i
$7$	0.656608	+	2.02083i	0.248174	+	0.763802i	0.995098	+	0.0988926i	$0.0315300\pi$
$7$	0.656608	+	2.02083i	0.248174	+	0.763802i	−0.746924	+	0.664910i	$0.768470\pi$
$8$	−0.896347	+	2.75867i	−0.316906	+	0.975338i
$9$	1.50380	+	1.09257i	0.501266	+	0.364191i
$10$	3.00678			0.950826
$11$	−2.93820	+	1.53849i	−0.885901	+	0.463874i
$11$	−2.93820	+	1.53849i	−0.885901	+	0.463874i
$12$	1.23326			0.356012
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$14$	0.603777	−	1.85823i	0.161366	−	0.496634i
$15$	−1.07943	−	3.32214i	−0.278708	−	0.857774i
$16$	0.289917	−	0.210637i	0.0724792	−	0.0526593i
$17$	−2.27764	+	1.65480i	−0.552408	+	0.401348i	−0.828673	−	0.559734i	$-0.810903\pi$
$17$	−2.27764	+	1.65480i	−0.552408	+	0.401348i	0.276264	+	0.961082i	$0.410903\pi$
$18$	−0.528184	−	1.62558i	−0.124494	−	0.383153i
$19$	0.205036	−	0.631037i	0.0470386	−	0.144770i	−0.924779	−	0.380506i	$-0.875750\pi$
$19$	0.205036	−	0.631037i	0.0470386	−	0.144770i	0.971817	+	0.235736i	$0.0757500\pi$
$20$	3.05395	+	2.21883i	0.682885	+	0.496145i
$21$	−2.26989			−0.495331
$22$	3.01734	+	0.443553i	0.643299	+	0.0945657i
$23$	4.97564			1.03749			0.518746	−	0.854928i	$-0.326399\pi$
$23$	4.97564			1.03749			0.518746	+	0.854928i	$0.326399\pi$
$24$	−2.50687	−	1.82135i	−0.511714	−	0.371782i
$25$	1.75895	−	5.41348i	0.351789	−	1.08270i
$26$	0.284153	+	0.874534i	0.0557270	+	0.171510i
$27$	−4.19921	+	3.05091i	−0.808139	+	0.587147i
$28$	1.98452	−	1.44184i	0.375039	−	0.272482i
$29$	−1.48693	−	4.57630i	−0.276116	−	0.849798i	−0.988922	−	0.148436i	$-0.952576\pi$
$29$	−1.48693	−	4.57630i	−0.276116	−	0.849798i	0.712806	−	0.701361i	$-0.247424\pi$
$30$	−0.992579	+	3.05484i	−0.181219	+	0.557735i
$31$	−0.969968	−	0.704723i	−0.174211	−	0.126572i	0.497263	−	0.867600i	$-0.334339\pi$
$31$	−0.969968	−	0.704723i	−0.174211	−	0.126572i	−0.671474	+	0.741028i	$0.734339\pi$
$32$	5.47175			0.967279
$33$	−0.593147	−	3.49305i	−0.103254	−	0.608062i
$34$	2.58879			0.443974
$35$	−5.62098	−	4.08388i	−0.950119	−	0.690302i
$36$	0.663115	−	2.04086i	0.110519	−	0.340143i
$37$	1.42882	+	4.39746i	0.234897	+	0.722938i	0.997135	+	0.0756416i	$0.0241005\pi$
$37$	1.42882	+	4.39746i	0.234897	+	0.722938i	−0.762238	+	0.647297i	$0.775900\pi$
$38$	−0.493602	+	0.358623i	−0.0800728	+	0.0581763i
$39$	0.864249	−	0.627914i	0.138391	−	0.100547i
$40$	−2.93094	−	9.02050i	−0.463422	−	1.42627i
$41$	2.32942	−	7.16922i	0.363794	−	1.11964i	−0.586938	−	0.809632i	$-0.699667\pi$
$41$	2.32942	−	7.16922i	0.363794	−	1.11964i	0.950733	−	0.310012i	$-0.100333\pi$
$42$	1.68862	+	1.22686i	0.260560	+	0.189308i
$43$	−0.661961			−0.100948			−0.0504741	−	0.998725i	$-0.516073\pi$
$43$	−0.661961			−0.100948			−0.0504741	+	0.998725i	$0.516073\pi$
$44$	2.73737	+	2.67714i	0.412674	+	0.403593i
$45$	−6.07803			−0.906060
$46$	−3.70149	−	2.68929i	−0.545755	−	0.396514i
$47$	−2.37126	+	7.29797i	−0.345883	+	1.06452i	0.615226	+	0.788351i	$0.289065\pi$
$47$	−2.37126	+	7.29797i	−0.345883	+	1.06452i	−0.961109	+	0.276168i	$0.910935\pi$
$48$	0.118299	+	0.364086i	0.0170749	+	0.0525512i
$49$	2.01049	−	1.46071i	0.287214	−	0.208673i
$50$	−4.23446	+	3.07652i	−0.598843	+	0.435085i
$51$	−0.929374	−	2.86032i	−0.130138	−	0.400525i
$52$	−0.356744	+	1.09794i	−0.0494715	+	0.152258i
$53$	6.50589	+	4.72680i	0.893652	+	0.649276i	0.936828	−	0.349791i	$-0.113747\pi$
$53$	6.50589	+	4.72680i	0.893652	+	0.649276i	−0.0431754	+	0.999068i	$0.513747\pi$
$54$	4.77288			0.649507
$55$	4.81571	−	9.71708i	0.649350	−	1.31025i
$56$	−6.16336			−0.823613
$57$	0.573440	+	0.416628i	0.0759539	+	0.0551838i
$58$	−1.36729	+	4.20809i	−0.179534	+	0.552549i
$59$	3.17656	+	9.77644i	0.413552	+	1.27278i	0.913539	+	0.406751i	$0.133338\pi$
$59$	3.17656	+	9.77644i	0.413552	+	1.27278i	−0.499987	+	0.866033i	$0.666662\pi$
$60$	−3.26245	+	2.37031i	−0.421181	+	0.306006i
$61$	−5.70932	+	4.14806i	−0.731004	+	0.531105i	−0.889881	−	0.456193i	$-0.849213\pi$
$61$	−5.70932	+	4.14806i	−0.731004	+	0.531105i	0.158877	+	0.987298i	$0.449213\pi$
$62$	0.340685	+	1.04852i	0.0432670	+	0.133162i
$63$	−1.22050	+	3.75632i	−0.153769	+	0.473251i
$64$	−4.65040	−	3.37871i	−0.581300	−	0.422339i
$65$	3.26987			0.405578
$66$	−1.44671	+	2.91915i	−0.178078	+	0.359323i
$67$	14.7519			1.80223			0.901113	−	0.433585i	$-0.142752\pi$
$67$	14.7519			1.80223			0.901113	+	0.433585i	$0.142752\pi$
$68$	2.62941	+	1.91038i	0.318863	+	0.231668i
$69$	−1.64253	+	5.05518i	−0.197737	+	0.608572i
$70$	1.97427	+	6.07619i	0.235971	+	0.726243i
$71$	−11.6958	+	8.49747i	−1.38803	+	1.00846i	−0.391954	+	0.919985i	$0.628201\pi$
$71$	−11.6958	+	8.49747i	−1.38803	+	1.00846i	−0.996078	+	0.0884799i	$0.971799\pi$
$72$	−4.36198	+	3.16916i	−0.514064	+	0.373489i
$73$	−0.428847	−	1.31986i	−0.0501928	−	0.154477i	0.922819	−	0.385235i	$-0.125880\pi$
$73$	−0.428847	−	1.31986i	−0.0501928	−	0.154477i	−0.973011	+	0.230758i	$0.925880\pi$
$74$	1.31386	−	4.04364i	0.152733	−	0.470064i
$75$	4.91937	+	3.57413i	0.568039	+	0.412705i
$76$	−0.765989			−0.0878650
$77$	−5.03828	−	4.92742i	−0.574166	−	0.561532i
$78$	−0.982317			−0.111226
$79$	10.8604	+	7.89054i	1.22189	+	0.887755i	0.996256	−	0.0864566i	$-0.0275544\pi$
$79$	10.8604	+	7.89054i	1.22189	+	0.887755i	0.225635	+	0.974212i	$0.427554\pi$
$80$	−0.362101	+	1.11443i	−0.0404841	+	0.124597i
$81$	0.00974075	+	0.0299789i	0.00108231	+	0.00333099i
$82$	−5.60781	+	4.07431i	−0.619279	+	0.449933i
$83$	2.85627	−	2.07520i	0.313516	−	0.227783i	−0.419888	−	0.907576i	$-0.637931\pi$
$83$	2.85627	−	2.07520i	0.313516	−	0.227783i	0.733404	+	0.679793i	$0.237931\pi$
$84$	0.809770	+	2.49221i	0.0883531	+	0.271923i
$85$	2.84472	−	8.75516i	0.308554	−	0.949631i
$86$	0.492448	+	0.357785i	0.0531021	+	0.0385809i
$87$	5.14031			0.551099
$88$	−1.61055	−	9.48456i	−0.171685	−	1.01106i
$89$	8.08446			0.856951			0.428476	−	0.903553i	$-0.359051\pi$
$89$	8.08446			0.856951			0.428476	+	0.903553i	$0.359051\pi$
$90$	4.52159	+	3.28513i	0.476617	+	0.346283i
$91$	0.656608	−	2.02083i	0.0688312	−	0.211841i
$92$	−1.77503	−	5.46297i	−0.185059	−	0.569554i
$93$	1.03619	−	0.752835i	0.107448	−	0.0780654i
$94$	5.70853	−	4.14749i	0.588789	−	0.427781i
$95$	0.670443	+	2.06341i	0.0687860	+	0.211702i
$96$	−1.80630	+	5.55922i	−0.184355	+	0.567386i
$97$	−5.75645	−	4.18231i	−0.584479	−	0.424649i	0.255857	−	0.966715i	$-0.417642\pi$
$97$	−5.75645	−	4.18231i	−0.584479	−	0.424649i	−0.840336	+	0.542066i	$0.817642\pi$
$98$	−2.28516			−0.230836
$99$	−6.09938	−	0.896617i	−0.613011	−	0.0901134i
$100$	−6.57119			−0.657119
$101$	−15.8013	−	11.4803i	−1.57229	−	1.14233i	−0.924923	−	0.380155i	$-0.875871\pi$
$101$	−15.8013	−	11.4803i	−1.57229	−	1.14233i	−0.647366	−	0.762180i	$-0.724129\pi$
$102$	−0.854596	+	2.63018i	−0.0846176	+	0.260426i
$103$	4.31665	+	13.2853i	0.425332	+	1.30904i	0.902676	+	0.430321i	$0.141600\pi$
$103$	4.31665	+	13.2853i	0.425332	+	1.30904i	−0.477343	+	0.878717i	$0.658400\pi$
$104$	2.34667	−	1.70495i	0.230110	−	0.167184i
$105$	6.00473	−	4.36269i	0.586002	−	0.425755i
$106$	−2.28508	−	7.03276i	−0.221947	−	0.683082i
$107$	−1.63246	+	5.02420i	−0.157816	+	0.485708i	−0.998435	−	0.0559185i	$-0.982191\pi$
$107$	−1.63246	+	5.02420i	−0.157816	+	0.485708i	0.840619	+	0.541627i	$0.182191\pi$
$108$	4.84777	+	3.52211i	0.466477	+	0.338915i
$109$	−16.8632			−1.61520			−0.807600	−	0.589731i	$-0.799234\pi$
$109$	−16.8632			−1.61520			−0.807600	+	0.589731i	$0.799234\pi$
$110$	−8.83452	+	4.62591i	−0.842338	+	0.441063i
$111$	−4.93943			−0.468830
$112$	0.616024	+	0.447567i	0.0582088	+	0.0422911i
$113$	3.03798	−	9.34996i	0.285790	−	0.879570i	−0.700371	−	0.713779i	$-0.746982\pi$
$113$	3.03798	−	9.34996i	0.285790	−	0.879570i	0.986161	−	0.165791i	$-0.0530178\pi$
$114$	−0.201411	−	0.619879i	−0.0188638	−	0.0580570i
$115$	−13.1625	+	9.56309i	−1.22741	+	0.891763i
$116$	−4.49407	+	3.26513i	−0.417264	+	0.303160i
$117$	−0.574400	−	1.76782i	−0.0531033	−	0.163435i
$118$	2.92097	−	8.98982i	0.268897	−	0.827580i
$119$	−4.83959	−	3.51617i	−0.443644	−	0.322326i
$120$	10.1322			0.924943
$121$	6.26607	−	9.04082i	0.569643	−	0.821892i
$122$	6.48929			0.587513
$123$	6.51485	+	4.73332i	0.587424	+	0.426789i
$124$	−0.427717	+	1.31638i	−0.0384101	+	0.118214i
$125$	0.699299	+	2.15222i	0.0625472	+	0.192500i
$126$	2.93822	−	2.13474i	0.261757	−	0.190178i
$127$	11.1616	−	8.10938i	0.990432	−	0.719591i	0.0304166	−	0.999537i	$-0.490317\pi$
$127$	11.1616	−	8.10938i	0.990432	−	0.719591i	0.960016	+	0.279946i	$0.0903166\pi$
$128$	−1.74836	−	5.38089i	−0.154534	−	0.475608i
$129$	0.218523	−	0.672543i	0.0192398	−	0.0592141i
$130$	−2.43253	−	1.76734i	−0.213347	−	0.155006i
$131$	4.79990			0.419369			0.209685	−	0.977769i	$-0.432756\pi$
$131$	4.79990			0.419369			0.209685	+	0.977769i	$0.432756\pi$
$132$	−3.62357	+	1.89737i	−0.315392	+	0.165145i
$133$	1.40985			0.122249
$134$	−10.9742	−	7.97325i	−0.948030	−	0.688784i
$135$	5.24473	−	16.1416i	0.451395	−	1.38925i
$136$	−2.52350	−	7.76653i	−0.216388	−	0.665974i
$137$	14.8930	−	10.8204i	1.27240	−	0.924450i	0.273102	−	0.961985i	$-0.411950\pi$
$137$	14.8930	−	10.8204i	1.27240	−	0.924450i	0.999295	+	0.0375347i	$0.0119505\pi$
$138$	3.95419	−	2.87289i	0.336603	−	0.244557i
$139$	4.39085	+	13.5137i	0.372427	+	1.14621i	0.945198	+	0.326497i	$0.105868\pi$
$139$	4.39085	+	13.5137i	0.372427	+	1.14621i	−0.572771	+	0.819715i	$0.694132\pi$
$140$	−2.47863	+	7.62843i	−0.209482	+	0.644720i
$141$	−6.63185	−	4.81832i	−0.558503	−	0.405776i
$142$	13.2936			1.11557
$143$	3.28136	+	0.482364i	0.274401	+	0.0403373i
$144$	0.666113			0.0555094
$145$	12.7291	+	9.24821i	1.05709	+	0.768022i
$146$	−0.394342	+	1.21366i	−0.0326360	+	0.100443i
$147$	0.820369	+	2.52483i	0.0676629	+	0.208245i
$148$	4.31845	−	3.13753i	0.354974	−	0.257904i
$149$	18.5138	−	13.4511i	1.51671	−	1.10196i	0.553624	−	0.832767i	$-0.313244\pi$
$149$	18.5138	−	13.4511i	1.51671	−	1.10196i	0.963087	−	0.269189i	$-0.0867556\pi$
$150$	−1.72784	−	5.31775i	−0.141078	−	0.434193i
$151$	−2.88729	+	8.88616i	−0.234964	+	0.723146i	0.762162	+	0.647387i	$0.224138\pi$
$151$	−2.88729	+	8.88616i	−0.234964	+	0.723146i	−0.997126	+	0.0757593i	$0.975862\pi$
$152$	1.55704	+	1.13126i	0.126293	+	0.0917570i
$153$	−5.23310			−0.423071
$154$	1.08486	+	6.38877i	0.0874208	+	0.514822i
$155$	3.92040			0.314894
$156$	−0.997730	−	0.724893i	−0.0798823	−	0.0580379i
$157$	−2.07044	+	6.37216i	−0.165239	+	0.508554i	−0.999054	−	0.0434905i	$-0.986152\pi$
$157$	−2.07044	+	6.37216i	−0.165239	+	0.508554i	0.833815	+	0.552045i	$0.186152\pi$
$158$	−3.81453	−	11.7399i	−0.303468	−	0.933977i
$159$	−6.95005	+	5.04951i	−0.551175	+	0.400452i
$160$	−14.4749	+	10.5166i	−1.14434	+	0.831412i
$161$	3.26704	+	10.0549i	0.257479	+	0.792439i
$162$	0.00895700	−	0.0275668i	0.000703729	−	0.00216585i
$163$	−6.87897	−	4.99786i	−0.538802	−	0.391463i	0.284838	−	0.958576i	$-0.408060\pi$
$163$	−6.87897	−	4.99786i	−0.538802	−	0.391463i	−0.823640	+	0.567113i	$0.808060\pi$
$164$	−8.70241			−0.679544
$165$	8.28269	+	8.10044i	0.644806	+	0.630618i
$166$	−3.24647			−0.251975
$167$	−5.45236	−	3.96137i	−0.421916	−	0.306540i	0.356492	−	0.934298i	$-0.383973\pi$
$167$	−5.45236	−	3.96137i	−0.421916	−	0.306540i	−0.778408	+	0.627758i	$0.783973\pi$
$168$	2.03461	−	6.26188i	0.156973	−	0.483115i
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$	−6.84835	+	4.97562i	−0.525244	+	0.381612i
$171$	0.997788	−	0.724936i	0.0763028	−	0.0554372i
$172$	0.236151	+	0.726797i	0.0180063	+	0.0554177i
$173$	−7.62444	+	23.4656i	−0.579676	+	1.78406i	0.0399993	+	0.999200i	$0.487264\pi$
$173$	−7.62444	+	23.4656i	−0.579676	+	1.78406i	−0.619675	+	0.784859i	$0.712736\pi$
$174$	−3.82400	−	2.77830i	−0.289896	−	0.210622i
$175$	12.0947			0.914271
$176$	−0.527771	+	1.06493i	−0.0397822	+	0.0802721i
$177$	−10.9813			−0.825408
$178$	−6.01422	−	4.36958i	−0.450785	−	0.327514i
$179$	4.52367	−	13.9224i	0.338115	−	1.04061i	−0.627052	−	0.778977i	$-0.715739\pi$
$179$	4.52367	−	13.9224i	0.338115	−	1.04061i	0.965167	−	0.261634i	$-0.0842613\pi$
$180$	2.16830	+	6.67334i	0.161616	+	0.497402i
$181$	−2.63479	+	1.91429i	−0.195842	+	0.142288i	−0.681385	−	0.731925i	$-0.738622\pi$
$181$	−2.63479	+	1.91429i	−0.195842	+	0.142288i	0.485543	+	0.874213i	$0.338622\pi$
$182$	−1.58071	+	1.14845i	−0.117170	+	0.0851289i
$183$	−2.32965	−	7.16992i	−0.172213	−	0.530016i
$184$	−4.45989	+	13.7261i	−0.328788	+	1.01190i
$185$	−12.2316	−	8.88680i	−0.899287	−	0.653370i
$186$	−1.17775			−0.0863565
$187$	4.14626	−	8.36627i	0.303204	−	0.611802i
$188$	8.85870			0.646087
$189$	−8.92260	−	6.48265i	−0.649024	−	0.471543i
$190$	0.616499	−	1.89739i	0.0447255	−	0.137651i
$191$	−0.228112	−	0.702057i	−0.0165056	−	0.0507990i	0.942464	−	0.334306i	$-0.108502\pi$
$191$	−0.228112	−	0.702057i	−0.0165056	−	0.0507990i	−0.958970	+	0.283507i	$0.908502\pi$
$192$	4.96788	−	3.60938i	0.358526	−	0.260484i
$193$	−0.0584681	+	0.0424796i	−0.00420863	+	0.00305775i	−0.589888	−	0.807485i	$-0.700828\pi$
$193$	−0.0584681	+	0.0424796i	−0.00420863	+	0.00305775i	0.585679	+	0.810543i	$0.300828\pi$
$194$	2.02185	+	6.22263i	0.145161	+	0.446759i
$195$	−1.07943	+	3.32214i	−0.0772996	+	0.237904i
$196$	−2.32101	−	1.68631i	−0.165786	−	0.120451i
$197$	−19.8099			−1.41140			−0.705700	−	0.708511i	$-0.749367\pi$
$197$	−19.8099			−1.41140			−0.705700	+	0.708511i	$0.749367\pi$
$198$	4.05286	+	3.96368i	0.288024	+	0.281687i
$199$	2.03673			0.144380			0.0721898	−	0.997391i	$-0.477001\pi$
$199$	2.03673			0.144380			0.0721898	+	0.997391i	$0.477001\pi$
$200$	13.3574	+	9.70471i	0.944510	+	0.686226i
$201$	−4.86979	+	14.9877i	−0.343488	+	1.05715i
$202$	5.54994	+	17.0809i	0.390492	+	1.20181i
$203$	8.27160	−	6.00967i	0.580553	−	0.421796i
$204$	−2.80892	+	2.04080i	−0.196664	+	0.142885i
$205$	7.61691	+	23.4424i	0.531988	+	1.63729i
$206$	3.96933	−	12.2163i	0.276556	−	0.851153i
$207$	7.48236	+	5.43625i	0.520060	+	0.377845i
$208$	−0.358357			−0.0248476
$209$	0.368409	+	2.16956i	0.0254834	+	0.150072i
$210$	−6.82506			−0.470974
$211$	−11.7440	−	8.53254i	−0.808492	−	0.587404i	0.104901	−	0.994483i	$-0.466548\pi$
$211$	−11.7440	−	8.53254i	−0.808492	−	0.587404i	−0.913393	+	0.407079i	$0.866548\pi$
$212$	2.86883	−	8.82936i	0.197032	−	0.606403i
$213$	−4.77238	−	14.6879i	−0.326998	−	1.00640i
$214$	3.92997	−	2.85529i	0.268647	−	0.195183i
$215$	1.75114	−	1.27228i	0.119427	−	0.0867687i
$216$	−4.65250	−	14.3189i	−0.316562	−	0.974279i
$217$	0.787238	−	2.42287i	0.0534412	−	0.164475i
$218$	12.5449	+	9.11441i	0.849649	+	0.617306i
$219$	1.48252			0.100180
$220$	−12.3868	−	1.82087i	−0.835117	−	0.122763i
$221$	2.81531			0.189379
$222$	3.67456	+	2.66972i	0.246620	+	0.179180i
$223$	−7.23756	+	22.2749i	−0.484663	+	1.49164i	0.347806	+	0.937566i	$0.386927\pi$
$223$	−7.23756	+	22.2749i	−0.484663	+	1.49164i	−0.832469	+	0.554072i	$0.813073\pi$
$224$	3.59280	+	11.0575i	0.240054	+	0.738810i
$225$	8.55973	−	6.21901i	0.570648	−	0.414600i
$226$	−7.31360	+	5.31364i	−0.486493	+	0.353458i
$227$	−3.36195	−	10.3470i	−0.223141	−	0.686756i	−0.998475	−	0.0552054i	$-0.982419\pi$
$227$	−3.36195	−	10.3470i	−0.223141	−	0.686756i	0.775334	−	0.631551i	$-0.217581\pi$
$228$	0.252864	−	0.778234i	0.0167463	−	0.0515398i
$229$	1.71173	+	1.24365i	0.113115	+	0.0821826i	0.642904	−	0.765946i	$-0.277729\pi$
$229$	1.71173	+	1.24365i	0.113115	+	0.0821826i	−0.529790	+	0.848129i	$0.677729\pi$
$230$	14.9606			0.986475
$231$	6.66940	−	3.49221i	0.438814	−	0.229771i
$232$	13.9573			0.916343
$233$	7.53703	+	5.47597i	0.493767	+	0.358743i	0.806631	−	0.591055i	$-0.201288\pi$
$233$	7.53703	+	5.47597i	0.493767	+	0.358743i	−0.312864	+	0.949798i	$0.601288\pi$
$234$	−0.528184	+	1.62558i	−0.0345284	+	0.106268i
$235$	−7.75370	−	23.8634i	−0.505796	−	1.55668i
$236$	9.60077	−	6.97537i	0.624957	−	0.454058i
$237$	−11.6018	+	8.42924i	−0.753621	+	0.547538i
$238$	1.69982	+	5.23151i	0.110183	+	0.339109i
$239$	−2.98569	+	9.18900i	−0.193128	+	0.594387i	0.806865	+	0.590735i	$0.201162\pi$
$239$	−2.98569	+	9.18900i	−0.193128	+	0.594387i	−0.999993	+	0.00365150i	$0.998838\pi$
$240$	−1.01271	−	0.735778i	−0.0653703	−	0.0474943i
$241$	3.90318			0.251426			0.125713	−	0.992067i	$-0.459878\pi$
$241$	3.90318			0.251426			0.125713	+	0.992067i	$0.459878\pi$
$242$	−9.54796	+	3.33891i	−0.613766	+	0.214634i
$243$	−15.6052			−1.00107
$244$	6.59111	+	4.78872i	0.421953	+	0.306567i
$245$	−2.51107	+	7.72827i	−0.160426	+	0.493741i
$246$	−2.28823	−	7.04245i	−0.145892	−	0.449010i
$247$	−0.536792	+	0.390002i	−0.0341553	+	0.0248153i
$248$	2.81353	−	2.04415i	0.178659	−	0.129804i
$249$	1.16548	+	3.58698i	0.0738593	+	0.227316i
$250$	0.643033	−	1.97905i	0.0406689	−	0.125166i
$251$	2.92494	+	2.12509i	0.184621	+	0.134135i	0.676257	−	0.736666i	$-0.263601\pi$
$251$	2.92494	+	2.12509i	0.184621	+	0.134135i	−0.491636	+	0.870801i	$0.663601\pi$
$252$	4.55963			0.287230
$253$	−14.6194	+	7.65499i	−0.919115	+	0.481265i
$254$	−12.6864			−0.796017
$255$	7.95604	+	5.78040i	0.498226	+	0.361983i
$256$	−5.16027	+	15.8817i	−0.322517	+	0.992605i
$257$	1.41708	+	4.36131i	0.0883947	+	0.272051i	0.985476	−	0.169815i	$-0.0543169\pi$
$257$	1.41708	+	4.36131i	0.0883947	+	0.272051i	−0.897081	+	0.441865i	$0.854317\pi$
$258$	−0.526068	+	0.382211i	−0.0327516	+	0.0237954i
$259$	−7.94835	+	5.77482i	−0.493887	+	0.358830i
$260$	−1.16651	−	3.59014i	−0.0723437	−	0.222651i
$261$	2.76390	−	8.50642i	0.171081	−	0.526534i
$262$	−3.57076	−	2.59431i	−0.220602	−	0.160277i
$263$	−12.0031			−0.740143			−0.370071	−	0.929003i	$-0.620667\pi$
$263$	−12.0031			−0.740143			−0.370071	+	0.929003i	$0.620667\pi$
$264$	10.1678	+	1.49469i	0.625788	+	0.0919915i
$265$	−26.2954			−1.61531
$266$	−1.04882	−	0.762011i	−0.0643072	−	0.0467219i
$267$	−2.66879	+	8.21370i	−0.163327	+	0.502670i
$268$	−5.26263	−	16.1967i	−0.321466	−	0.989372i
$269$	24.3756	−	17.7099i	1.48621	−	1.07979i	0.510716	−	0.859749i	$-0.329380\pi$
$269$	24.3756	−	17.7099i	1.48621	−	1.07979i	0.975490	−	0.220043i	$-0.0706197\pi$
$270$	−12.6261	+	9.17339i	−0.768400	+	0.558275i
$271$	−3.62211	−	11.1477i	−0.220028	−	0.677175i	−0.998758	−	0.0498169i	$-0.984136\pi$
$271$	−3.62211	−	11.1477i	−0.220028	−	0.677175i	0.778731	−	0.627358i	$-0.215864\pi$
$272$	−0.311764	+	0.959510i	−0.0189034	+	0.0581788i
$273$	1.83638	+	1.33421i	0.111143	+	0.0807500i
$274$	−16.9276			−1.02263
$275$	3.16047	+	18.6120i	0.190583	+	1.12235i
$276$	6.13626			0.369360
$277$	19.3905	+	14.0880i	1.16506	+	0.846467i	0.990410	−	0.138163i	$-0.0441197\pi$
$277$	19.3905	+	14.0880i	1.16506	+	0.846467i	0.174653	+	0.984630i	$0.444120\pi$
$278$	4.03756	−	12.4263i	0.242157	−	0.745282i
$279$	−0.688675	−	2.11952i	−0.0412299	−	0.126893i
$280$	16.3044	−	11.8459i	0.974376	−	0.707926i
$281$	14.5358	−	10.5609i	0.867132	−	0.630008i	−0.0626837	−	0.998033i	$-0.519966\pi$
$281$	14.5358	−	10.5609i	0.867132	−	0.630008i	0.929816	+	0.368025i	$0.119966\pi$
$282$	2.32932	+	7.16892i	0.138709	+	0.426903i
$283$	3.96516	−	12.2035i	0.235704	−	0.725423i	−0.761323	−	0.648373i	$-0.775450\pi$
$283$	3.96516	−	12.2035i	0.235704	−	0.725423i	0.997027	−	0.0770502i	$-0.0245502\pi$
$284$	13.5021	+	9.80988i	0.801205	+	0.582110i
$285$	−2.31772			−0.137290
$286$	−2.18037	−	2.13239i	−0.128928	−	0.126091i
$287$	16.0173			0.945471
$288$	8.22842	+	5.97830i	0.484864	+	0.352274i
$289$	−2.80402	+	8.62989i	−0.164942	+	0.507641i
$290$	−4.47087	−	13.7599i	−0.262538	−	0.808010i
$291$	6.14945	−	4.46784i	0.360487	−	0.261909i
$292$	−1.29614	+	0.941701i	−0.0758508	+	0.0551089i
$293$	3.75819	+	11.5665i	0.219556	+	0.675723i	0.998799	+	0.0490013i	$0.0156039\pi$
$293$	3.75819	+	11.5665i	0.219556	+	0.675723i	−0.779243	+	0.626722i	$0.784396\pi$
$294$	0.754361	−	2.32169i	0.0439952	−	0.135403i
$295$	−27.1934	−	19.7571i	−1.58326	−	1.15030i
$296$	−13.4119			−0.779549
$297$	7.64433	−	15.4246i	0.443569	−	0.895029i
$298$	−21.0431			−1.21899
$299$	−4.02537	−	2.92461i	−0.232793	−	0.169134i
$300$	2.16924	−	6.67624i	0.125241	−	0.385453i
$301$	−0.434649	−	1.33771i	−0.0250528	−	0.0771044i
$302$	6.95082	−	5.05007i	0.399975	−	0.290599i
$303$	16.8801	−	12.2641i	0.969735	−	0.704554i
$304$	−0.0734763	−	0.226137i	−0.00421415	−	0.0129698i
$305$	7.13083	−	21.9464i	0.408310	−	1.25665i
$306$	3.89302	+	2.82845i	0.222549	+	0.161692i
$307$	18.3989			1.05008			0.525040	−	0.851077i	$-0.324050\pi$
$307$	18.3989			1.05008			0.525040	+	0.851077i	$0.324050\pi$
$308$	−3.61266	+	7.28958i	−0.205850	+	0.415363i
$309$	−14.9227			−0.848920
$310$	−2.91648	−	2.11895i	−0.165645	−	0.120348i
$311$	0.518242	−	1.59499i	0.0293868	−	0.0904433i	−0.935287	−	0.353889i	$-0.884859\pi$
$311$	0.518242	−	1.59499i	0.0293868	−	0.0904433i	0.964674	+	0.263446i	$0.0848590\pi$
$312$	0.957541	+	2.94701i	0.0542101	+	0.166841i
$313$	−20.2648	+	14.7233i	−1.14544	+	0.832209i	−0.987867	−	0.155299i	$-0.950366\pi$
$313$	−20.2648	+	14.7233i	−1.14544	+	0.832209i	−0.157569	+	0.987508i	$0.550366\pi$
$314$	4.98435	−	3.62134i	0.281283	−	0.204364i
$315$	−3.99088	−	12.2827i	−0.224861	−	0.692050i
$316$	4.78900	−	14.7390i	0.269402	−	0.829135i
$317$	7.00922	+	5.09250i	0.393677	+	0.286023i	0.766961	−	0.641694i	$-0.221768\pi$
$317$	7.00922	+	5.09250i	0.393677	+	0.286023i	−0.373284	+	0.927717i	$0.621768\pi$
$318$	7.89952			0.442983
$319$	11.4095	+	11.1585i	0.638810	+	0.624754i
$320$	18.7959			1.05072
$321$	−4.56562	−	3.31712i	−0.254828	−	0.185143i
$322$	3.00417	−	9.24589i	0.167416	−	0.515254i
$323$	0.577242	+	1.77657i	0.0321186	+	0.0988509i
$324$	0.0294403	−	0.0213896i	0.00163557	−	0.00118831i
$325$	−4.60498	+	3.34571i	−0.255438	+	0.185587i
$326$	2.41612	+	7.43605i	0.133816	+	0.411845i
$327$	5.56677	−	17.1328i	0.307843	−	0.947444i
$328$	17.6895	+	12.8522i	0.976742	+	0.709645i
$329$	−16.3050			−0.898921
$330$	−1.78346	−	10.5028i	−0.0981764	−	0.578161i
$331$	−24.5615			−1.35002			−0.675011	−	0.737808i	$-0.735861\pi$
$331$	−24.5615			−1.35002			−0.675011	+	0.737808i	$0.735861\pi$
$332$	−3.29741	−	2.39571i	−0.180969	−	0.131482i
$333$	−2.65589	+	8.17399i	−0.145542	+	0.447932i
$334$	1.91505	+	5.89391i	0.104787	+	0.322500i
$335$	−39.0243	+	28.3528i	−2.13212	+	1.54908i
$336$	−0.658080	+	0.478123i	−0.0359012	+	0.0260838i
$337$	0.321195	+	0.988535i	0.0174966	+	0.0538489i	0.959424	−	0.281969i	$-0.0909874\pi$
$337$	0.321195	+	0.988535i	0.0174966	+	0.0538489i	−0.941927	+	0.335818i	$0.890987\pi$
$338$	0.284153	−	0.874534i	0.0154559	−	0.0475684i
$339$	8.49654	+	6.17310i	0.461469	+	0.335277i
$340$	−10.6275			−0.576358
$341$	3.93418	+	0.578329i	0.213048	+	0.0313183i
$342$	−1.13410			−0.0613251
$343$	16.3051	+	11.8464i	0.880393	+	0.639643i
$344$	0.593347	−	1.82613i	0.0319911	−	0.0984585i
$345$	−5.37085	−	16.5298i	−0.289157	−	0.889934i
$346$	18.3550	−	13.3357i	0.986769	−	0.716930i
$347$	−12.4296	+	9.03063i	−0.667255	+	0.484789i	−0.869105	−	0.494627i	$-0.835305\pi$
$347$	−12.4296	+	9.03063i	−0.667255	+	0.484789i	0.201850	+	0.979416i	$0.435305\pi$
$348$	−1.83377	−	5.64378i	−0.0983007	−	0.302538i
$349$	8.37440	−	25.7737i	0.448271	−	1.37964i	−0.430585	−	0.902550i	$-0.641693\pi$
$349$	8.37440	−	25.7737i	0.448271	−	1.37964i	0.878856	−	0.477087i	$-0.158307\pi$
$350$	−8.99750	−	6.53707i	−0.480937	−	0.349421i
$351$	5.19051			0.277049
$352$	−16.0771	+	8.41826i	−0.856913	+	0.448695i
$353$	−17.7354			−0.943958			−0.471979	−	0.881610i	$-0.656460\pi$
$353$	−17.7354			−0.943958			−0.471979	+	0.881610i	$0.656460\pi$
$354$	8.16928	+	5.93533i	0.434192	+	0.315459i
$355$	14.6078	−	44.9581i	0.775301	−	2.38613i
$356$	−2.88408	−	8.87629i	−0.152856	−	0.470442i
$357$	5.16999	−	3.75622i	0.273625	−	0.198800i
$358$	−10.8902	+	7.91221i	−0.575566	+	0.418173i
$359$	1.40204	+	4.31504i	0.0739968	+	0.227739i	0.981214	−	0.192925i	$-0.0617973\pi$
$359$	1.40204	+	4.31504i	0.0739968	+	0.227739i	−0.907217	+	0.420664i	$0.861797\pi$
$360$	5.44802	−	16.7673i	0.287136	−	0.883714i
$361$	15.0152	+	10.9091i	0.790271	+	0.574166i
$362$	2.99474			0.157400
$363$	7.11683	+	9.35074i	0.373537	+	0.490786i
$364$	−2.45300			−0.128572
$365$	3.67120	+	2.66729i	0.192160	+	0.139612i
$366$	−2.14220	+	6.59303i	−0.111975	+	0.344623i
$367$	0.0813747	+	0.250445i	0.00424772	+	0.0130731i	0.953158	−	0.302473i	$-0.0978123\pi$
$367$	0.0813747	+	0.250445i	0.00424772	+	0.0130731i	−0.948910	+	0.315546i	$0.897812\pi$
$368$	1.44252	−	1.04805i	0.0751966	−	0.0546335i
$369$	11.3359	−	8.23600i	0.590122	−	0.428749i
$370$	4.29615	+	13.2222i	0.223346	+	0.687389i
$371$	−5.28025	+	16.2510i	−0.274137	+	0.843707i
$372$	−1.19623	−	0.869109i	−0.0620214	−	0.0450612i
$373$	−18.1075			−0.937572			−0.468786	−	0.883312i	$-0.655308\pi$
$373$	−18.1075			−0.937572			−0.468786	+	0.883312i	$0.655308\pi$
$374$	−7.60640	+	3.98284i	−0.393318	+	0.205948i
$375$	−2.41747			−0.124838
$376$	−18.0072	−	13.0830i	−0.928653	−	0.674706i
$377$	−1.48693	+	4.57630i	−0.0765808	+	0.235691i
$378$	3.13391	+	9.64518i	0.161191	+	0.496095i
$379$	11.4377	−	8.31000i	0.587517	−	0.426856i	−0.253909	−	0.967228i	$-0.581716\pi$
$379$	11.4377	−	8.31000i	0.587517	−	0.426856i	0.841426	+	0.540372i	$0.181716\pi$
$380$	2.02634	−	1.47222i	0.103949	−	0.0755232i
$381$	4.55442	+	14.0171i	0.233330	+	0.718115i
$382$	−0.209758	+	0.645569i	−0.0107322	+	0.0330302i
$383$	−14.8383	−	10.7806i	−0.758200	−	0.550864i	0.140158	−	0.990129i	$-0.455239\pi$
$383$	−14.8383	−	10.7806i	−0.758200	−	0.550864i	−0.898358	+	0.439265i	$0.855239\pi$
$384$	6.04407			0.308435
$385$	22.7986	+	3.35142i	1.16192	+	0.170804i
$386$	0.0664557			0.00338250
$387$	−0.995457	−	0.723242i	−0.0506019	−	0.0367644i
$388$	−2.53836	+	7.81228i	−0.128866	+	0.396608i
$389$	−1.59919	−	4.92180i	−0.0810822	−	0.249545i	0.902295	−	0.431119i	$-0.141881\pi$
$389$	−1.59919	−	4.92180i	−0.0810822	−	0.249545i	−0.983377	+	0.181573i	$0.941881\pi$
$390$	2.59860	−	1.88800i	0.131585	−	0.0956024i
$391$	−11.3327	+	8.23368i	−0.573119	+	0.416395i
$392$	2.22752	+	6.85560i	0.112507	+	0.346260i
$393$	−1.58451	+	4.87663i	−0.0799281	+	0.245993i
$394$	14.7371	+	10.7071i	0.742443	+	0.539417i
$395$	−43.8954			−2.20862
$396$	1.19148	+	7.01665i	0.0598742	+	0.352600i
$397$	24.6815			1.23873			0.619365	−	0.785103i	$-0.287390\pi$
$397$	24.6815			1.23873			0.619365	+	0.785103i	$0.287390\pi$
$398$	−1.51517	−	1.10083i	−0.0759485	−	0.0551798i
$399$	−0.465410	+	1.43239i	−0.0232997	+	0.0717090i
$400$	−0.630331	−	1.93996i	−0.0315165	−	0.0969979i
$401$	20.3901	−	14.8142i	1.01823	−	0.739788i	0.0523114	−	0.998631i	$-0.483341\pi$
$401$	20.3901	−	14.8142i	1.01823	−	0.739788i	0.965919	+	0.258843i	$0.0833412\pi$
$402$	11.7235	−	8.51759i	0.584713	−	0.424819i
$403$	0.370495	+	1.14027i	0.0184557	+	0.0568007i
$404$	−6.96774	+	21.4445i	−0.346658	+	1.06690i
$405$	−0.0833870	−	0.0605842i	−0.00414354	−	0.00301045i
$406$	−9.40161			−0.466594
$407$	−10.9636	−	10.7224i	−0.543447	−	0.531490i
$408$	8.72372			0.431889
$409$	7.10201	+	5.15991i	0.351172	+	0.255141i	0.749361	−	0.662162i	$-0.230361\pi$
$409$	7.10201	+	5.15991i	0.351172	+	0.255141i	−0.398189	+	0.917304i	$0.630361\pi$
$410$	7.00405	−	21.5562i	0.345905	−	1.06459i
$411$	6.07700	+	18.7031i	0.299756	+	0.922554i
$412$	13.0466	−	9.47889i	0.642758	−	0.466991i
$413$	−17.6708	+	12.8386i	−0.869522	+	0.631745i
$414$	−2.62805	−	8.08830i	−0.129162	−	0.397518i
$415$	−3.56742	+	10.9794i	−0.175118	+	0.538957i
$416$	−4.42674	−	3.21622i	−0.217039	−	0.157688i
$417$	−15.1792			−0.743327
$418$	0.898563	−	1.81311i	0.0439501	−	0.0886821i
$419$	28.0705			1.37133			0.685667	−	0.727915i	$-0.259511\pi$
$419$	28.0705			1.37133			0.685667	+	0.727915i	$0.259511\pi$
$420$	−6.93214	−	5.03650i	−0.338254	−	0.245756i
$421$	−3.82119	+	11.7604i	−0.186233	+	0.573167i	−0.999967	−	0.00807013i	$-0.997431\pi$
$421$	−3.82119	+	11.7604i	−0.186233	+	0.573167i	0.813734	+	0.581237i	$0.197431\pi$
$422$	4.12489	+	12.6951i	0.200796	+	0.617988i
$423$	−11.5395	+	8.38391i	−0.561068	+	0.407640i
$424$	−18.8712	+	13.7107i	−0.916468	+	0.665853i
$425$	4.95199	+	15.2406i	0.240207	+	0.739280i
$426$	−4.38839	+	13.5061i	−0.212618	+	0.654371i
$427$	−12.1313	−	8.81392i	−0.587076	−	0.426536i
$428$	6.09867			0.294790
$429$	−1.57330	+	3.17458i	−0.0759595	+	0.153270i
$430$	−1.99037			−0.0959842
$431$	1.56812	+	1.13931i	0.0755337	+	0.0548784i	0.624911	−	0.780696i	$-0.285135\pi$
$431$	1.56812	+	1.13931i	0.0755337	+	0.0548784i	−0.549378	+	0.835574i	$0.685135\pi$
$432$	−0.574789	+	1.76902i	−0.0276546	+	0.0851120i
$433$	−2.61508	−	8.04838i	−0.125673	−	0.386780i	0.868350	−	0.495951i	$-0.165180\pi$
$433$	−2.61508	−	8.04838i	−0.125673	−	0.386780i	−0.994023	+	0.109171i	$0.965180\pi$
$434$	−1.89518	+	1.37693i	−0.0909718	+	0.0660949i
$435$	−13.5981	+	9.87959i	−0.651979	+	0.473690i
$436$	6.01584	+	18.5148i	0.288106	+	0.886700i
$437$	1.02019	−	3.13981i	0.0488021	−	0.150198i
$438$	−1.10288	−	0.801291i	−0.0526978	−	0.0382872i
$439$	9.66663			0.461363			0.230682	−	0.973029i	$-0.425904\pi$
$439$	9.66663			0.461363			0.230682	+	0.973029i	$0.425904\pi$
$440$	22.4897	+	21.9948i	1.07215	+	1.04856i
$441$	4.61931			0.219967
$442$	−2.09438	−	1.52165i	−0.0996194	−	0.0723777i
$443$	−2.55848	+	7.87418i	−0.121557	+	0.374114i	−0.993258	−	0.115924i	$-0.963017\pi$
$443$	−2.55848	+	7.87418i	−0.121557	+	0.374114i	0.871701	+	0.490038i	$0.163017\pi$
$444$	1.76211	+	5.42322i	0.0836261	+	0.257375i
$445$	−21.3865	+	15.5382i	−1.01382	+	0.736581i
$446$	17.4236	−	12.6590i	0.825031	−	0.599420i
$447$	7.55444	+	23.2502i	0.357313	+	1.09970i
$448$	3.77432	−	11.6162i	0.178320	−	0.548812i
$449$	−29.2861	−	21.2776i	−1.38210	−	1.00415i	−0.996681	−	0.0814075i	$-0.974058\pi$
$449$	−29.2861	−	21.2776i	−1.38210	−	1.00415i	−0.385415	−	0.922744i	$-0.625942\pi$
$450$	−9.72910			−0.458634
$451$	4.18549	+	24.6484i	0.197087	+	1.16065i
$452$	−11.3495			−0.533836
$453$	−8.07508	−	5.86689i	−0.379401	−	0.275651i
$454$	−3.09145	+	9.51450i	−0.145089	+	0.446538i
$455$	2.14702	+	6.60786i	0.100654	+	0.309781i
$456$	−1.66334	+	1.20849i	−0.0778931	+	0.0565926i
$457$	−9.15931	+	6.65463i	−0.428455	+	0.311291i	−0.781031	−	0.624493i	$-0.785306\pi$
$457$	−9.15931	+	6.65463i	−0.428455	+	0.311291i	0.352576	+	0.935783i	$0.385306\pi$
$458$	−0.601217	−	1.85036i	−0.0280930	−	0.0864615i
$459$	4.51564	−	13.8977i	0.210772	−	0.648690i
$460$	15.1954	+	11.0401i	0.708488	+	0.514746i
$461$	27.2502			1.26917			0.634585	−	0.772853i	$-0.281171\pi$
$461$	27.2502			1.26917			0.634585	+	0.772853i	$0.281171\pi$
$462$	−6.84903	−	1.00682i	−0.318646	−	0.0468413i
$463$	9.28695			0.431601			0.215801	−	0.976437i	$-0.430764\pi$
$463$	9.28695			0.431601			0.215801	+	0.976437i	$0.430764\pi$
$464$	−1.39502	−	1.01354i	−0.0647624	−	0.0470526i
$465$	−1.29418	+	3.98307i	−0.0600161	+	0.184711i
$466$	−2.64725	−	8.14740i	−0.122632	−	0.377421i
$467$	−3.79853	+	2.75979i	−0.175775	+	0.127708i	−0.672194	−	0.740375i	$-0.734648\pi$
$467$	−3.79853	+	2.75979i	−0.175775	+	0.127708i	0.496419	+	0.868083i	$0.334648\pi$
$468$	−1.73606	+	1.26132i	−0.0802492	+	0.0583045i
$469$	9.68618	+	29.8110i	0.447266	+	1.37654i
$470$	−7.12984	+	21.9434i	−0.328875	+	1.01217i
$471$	−5.79055	−	4.20708i	−0.266814	−	0.193852i
$472$	−29.8173			−1.37245
$473$	1.94498	−	1.01842i	0.0894301	−	0.0468272i
$474$	13.1868			0.605690
$475$	−3.05546	−	2.21992i	−0.140194	−	0.101857i
$476$	−2.13406	+	6.56797i	−0.0978146	+	0.301042i
$477$	4.61916	+	14.2163i	0.211497	+	0.650921i
$478$	7.18770	−	5.22217i	0.328758	−	0.238856i
$479$	3.59304	−	2.61050i	0.164170	−	0.119277i	−0.502667	−	0.864480i	$-0.667648\pi$
$479$	3.59304	−	2.61050i	0.164170	−	0.119277i	0.666837	+	0.745204i	$0.267648\pi$
$480$	−5.90638	−	18.1780i	−0.269588	−	0.829706i
$481$	1.42882	−	4.39746i	0.0651487	−	0.200507i
$482$	−2.90366	−	2.10964i	−0.132258	−	0.0960913i
$483$	−11.2942			−0.513902
$484$	−12.1617	−	3.65454i	−0.552804	−	0.166115i
$485$	23.2663			1.05647
$486$	11.6091	+	8.43449i	0.526598	+	0.382596i
$487$	6.90692	−	21.2573i	0.312982	−	0.963261i	−0.663595	−	0.748092i	$-0.730970\pi$
$487$	6.90692	−	21.2573i	0.312982	−	0.963261i	0.976577	−	0.215168i	$-0.0690300\pi$
$488$	−6.32562	−	19.4682i	−0.286347	−	0.881286i
$489$	7.34860	−	5.33907i	0.332315	−	0.241441i
$490$	6.04511	−	4.39203i	0.273090	−	0.198412i
$491$	1.37801	+	4.24107i	0.0621885	+	0.191397i	0.977324	−	0.211750i	$-0.0679164\pi$
$491$	1.37801	+	4.24107i	0.0621885	+	0.191397i	−0.915135	+	0.403147i	$0.867916\pi$
$492$	2.87279	−	8.84153i	0.129515	−	0.398607i
$493$	10.9596	+	7.96258i	0.493593	+	0.358617i
$494$	0.610125			0.0274508
$495$	17.8585	−	9.35102i	0.802679	−	0.420297i
$496$	−0.429651			−0.0192919
$497$	−24.8515	−	18.0557i	−1.11474	−	0.809907i
$498$	1.07170	−	3.29837i	0.0480242	−	0.147803i
$499$	−11.1311	−	34.2580i	−0.498296	−	1.53360i	−0.811756	−	0.583997i	$-0.801488\pi$
$499$	−11.1311	−	34.2580i	−0.498296	−	1.53360i	0.313460	−	0.949601i	$-0.398512\pi$
$500$	2.11355	−	1.53558i	0.0945207	−	0.0686733i
$501$	5.82459	−	4.23181i	0.260224	−	0.189064i
$502$	−1.02733	−	3.16181i	−0.0458522	−	0.141119i
$503$	11.7493	−	36.1605i	0.523874	−	1.61232i	−0.242658	−	0.970112i	$-0.578019\pi$
$503$	11.7493	−	36.1605i	0.523874	−	1.61232i	0.766532	−	0.642207i	$-0.221981\pi$
$504$	−9.26845	−	6.73392i	−0.412850	−	0.299953i
$505$	63.8655			2.84198
$506$	15.0132	+	2.20696i	0.667417	+	0.0981112i
$507$	−1.06827			−0.0474436
$508$	−12.8855	−	9.36185i	−0.571701	−	0.415365i
$509$	3.76098	−	11.5751i	0.166702	−	0.513057i	−0.832455	−	0.554092i	$-0.813065\pi$
$509$	3.76098	−	11.5751i	0.166702	−	0.513057i	0.999158	+	0.0410349i	$0.0130655\pi$
$510$	−2.79442	−	8.60034i	−0.123739	−	0.380830i
$511$	2.38562	−	1.73325i	0.105534	−	0.0766747i
$512$	3.26824	−	2.37452i	0.144437	−	0.104940i
$513$	1.06424	+	3.27541i	0.0469875	+	0.144613i
$514$	1.30306	−	4.01040i	0.0574754	−	0.176891i
$515$	−36.9533	−	26.8481i	−1.62836	−	1.18307i
$516$	−0.816372			−0.0359388
$517$	−4.26066	−	25.0911i	−0.187384	−	1.10350i
$518$	9.03420			0.396940
$519$	−21.3238	−	15.4927i	−0.936011	−	0.680052i
$520$	−2.93094	+	9.02050i	−0.128530	+	0.395575i
$521$	−1.39789	−	4.30227i	−0.0612428	−	0.188486i	0.915754	−	0.401739i	$-0.131594\pi$
$521$	−1.39789	−	4.30227i	−0.0612428	−	0.188486i	−0.976997	+	0.213253i	$0.931594\pi$
$522$	−6.65378	+	4.83425i	−0.291228	+	0.211590i
$523$	−0.796159	+	0.578444i	−0.0348136	+	0.0252936i	−0.605056	−	0.796183i	$-0.706849\pi$
$523$	−0.796159	+	0.578444i	−0.0348136	+	0.0252936i	0.570242	+	0.821476i	$0.306849\pi$
$524$	−1.71233	−	5.27002i	−0.0748037	−	0.230222i
$525$	−3.99262	+	12.2880i	−0.174252	+	0.536293i
$526$	8.92938	+	6.48758i	0.389340	+	0.282872i
$527$	3.37541			0.147035
$528$	−0.907729	−	0.887756i	−0.0395038	−	0.0386346i
$529$	1.75695			0.0763892
$530$	19.5618	+	14.2124i	0.849708	+	0.617349i
$531$	−5.90458	+	18.1724i	−0.256237	+	0.788616i
$532$	−0.502955	−	1.54794i	−0.0218058	−	0.0671115i
$533$	−6.09850	+	4.43082i	−0.264155	+	0.191920i
$534$	6.42481	−	4.66790i	0.278029	−	0.202000i
$535$	−5.33795	−	16.4285i	−0.230780	−	0.710266i
$536$	−13.2228	+	40.6955i	−0.571137	+	1.75778i
$537$	12.6517	+	9.19197i	0.545960	+	0.396663i
$538$	−27.7056			−1.19447
$539$	−3.65995	+	7.38500i	−0.157645	+	0.318094i
$540$	−19.5936			−0.843176
$541$	16.7069	+	12.1382i	0.718284	+	0.521864i	0.885835	−	0.464000i	$-0.153586\pi$
$541$	16.7069	+	12.1382i	0.718284	+	0.521864i	−0.167552	+	0.985863i	$0.553586\pi$
$542$	−3.33067	+	10.2508i	−0.143065	+	0.440308i
$543$	−1.07511	−	3.30884i	−0.0461373	−	0.141996i
$544$	−12.4627	+	9.05466i	−0.534333	+	0.388215i
$545$	44.6096	−	32.4108i	1.91086	−	1.38832i
$546$	−0.644997	−	1.98510i	−0.0276033	−	0.0849543i
$547$	−2.79076	+	8.58908i	−0.119324	+	0.367242i	−0.992824	−	0.119582i	$-0.961845\pi$
$547$	−2.79076	+	8.58908i	−0.119324	+	0.367242i	0.873500	+	0.486824i	$0.161845\pi$
$548$	−17.1932	−	12.4916i	−0.734458	−	0.533615i
$549$	−13.1177			−0.559851
$550$	7.70850	−	15.5541i	0.328692	−	0.663230i
$551$	−3.19269			−0.136013
$552$	−12.4733	−	9.06238i	−0.530899	−	0.385720i
$553$	−8.81443	+	27.1280i	−0.374828	+	1.15360i
$554$	−6.81058	−	20.9608i	−0.289354	−	0.890540i
$555$	13.0667	−	9.49351i	0.554650	−	0.402977i
$556$	13.2708	−	9.64182i	0.562809	−	0.408904i
$557$	−6.95106	−	21.3932i	−0.294526	−	0.906458i	−0.983380	−	0.181558i	$-0.941886\pi$
$557$	−6.95106	−	21.3932i	−0.294526	−	0.906458i	0.688854	−	0.724900i	$-0.258114\pi$
$558$	−0.633264	+	1.94899i	−0.0268082	+	0.0825072i
$559$	0.535538	+	0.389091i	0.0226508	+	0.0164568i
$560$	−2.48983			−0.105215
$561$	7.13128	+	6.97436i	0.301083	+	0.294458i
$562$	−16.5216			−0.696920
$563$	22.8089	+	16.5717i	0.961282	+	0.698413i	0.953448	−	0.301557i	$-0.0975063\pi$
$563$	22.8089	+	16.5717i	0.961282	+	0.698413i	0.00783422	+	0.999969i	$0.497506\pi$
$564$	−2.92438	+	9.00031i	−0.123139	+	0.378982i
$565$	9.93382	+	30.5732i	0.417919	+	1.28622i
$566$	−9.54567	+	6.93533i	−0.401234	+	0.291514i
$567$	−0.0541865	+	0.0393688i	−0.00227562	+	0.00165334i
$568$	−12.9583	−	39.8815i	−0.543717	−	1.67339i
$569$	−1.90175	+	5.85299i	−0.0797256	+	0.245370i	−0.982973	−	0.183750i	$-0.941176\pi$
$569$	−1.90175	+	5.85299i	−0.0797256	+	0.245370i	0.903247	+	0.429120i	$0.141176\pi$
$570$	1.72420	+	1.25271i	0.0722190	+	0.0524702i
$571$	21.3203			0.892226			0.446113	−	0.894977i	$-0.352808\pi$
$571$	21.3203			0.892226			0.446113	+	0.894977i	$0.352808\pi$
$572$	−0.640996	−	3.77483i	−0.0268014	−	0.157834i
$573$	0.788582			0.0329435
$574$	−11.9156	−	8.65721i	−0.497349	−	0.361345i
$575$	8.75187	−	26.9355i	0.364978	−	1.12329i
$576$	−3.30177	−	10.1618i	−0.137574	−	0.423409i
$577$	6.47663	−	4.70554i	0.269625	−	0.195894i	−0.444754	−	0.895653i	$-0.646709\pi$
$577$	6.47663	−	4.70554i	0.269625	−	0.195894i	0.714380	+	0.699758i	$0.246709\pi$
$578$	6.75036	−	4.90442i	0.280778	−	0.203997i
$579$	−0.0238575	−	0.0734259i	−0.000991485	−	0.00305148i
$580$	5.61301	−	17.2751i	0.233067	−	0.717308i
$581$	6.06907	+	4.40944i	0.251788	+	0.182934i
$582$	−6.98955			−0.289726
$583$	−26.3878	−	3.87903i	−1.09287	−	0.160653i
$584$	4.02544			0.166574
$585$	4.91723	+	3.57258i	0.203302	+	0.147708i
$586$	3.45580	−	10.6359i	0.142758	−	0.439364i
$587$	3.58316	+	11.0278i	0.147893	+	0.455168i	0.997372	−	0.0724552i	$-0.0230834\pi$
$587$	3.58316	+	11.0278i	0.147893	+	0.455168i	−0.849479	+	0.527623i	$0.823083\pi$
$588$	2.47947	−	1.80144i	0.102252	−	0.0742901i
$589$	−0.643586	+	0.467592i	−0.0265185	+	0.0192668i
$590$	9.55120	+	29.3956i	0.393217	+	1.21020i
$591$	6.53954	−	20.1266i	0.269001	−	0.827899i
$592$	1.34051	+	0.973936i	0.0550945	+	0.0400285i
$593$	−4.74313			−0.194777			−0.0973885	−	0.995246i	$-0.531049\pi$
$593$	−4.74313			−0.194777			−0.0973885	+	0.995246i	$0.531049\pi$
$594$	−14.0237	+	7.34305i	−0.575399	+	0.301289i
$595$	19.5606			0.801905
$596$	−21.3732	−	15.5286i	−0.875482	−	0.636075i
$597$	−0.672351	+	2.06928i	−0.0275175	+	0.0846902i
$598$	1.41384	+	4.35136i	0.0578164	+	0.177940i
$599$	14.7909	−	10.7462i	0.604340	−	0.439078i	−0.243077	−	0.970007i	$-0.578157\pi$
$599$	14.7909	−	10.7462i	0.604340	−	0.439078i	0.847417	+	0.530929i	$0.178157\pi$
$600$	−14.2693	+	10.3673i	−0.582542	+	0.423241i
$601$	−5.57800	−	17.1673i	−0.227532	−	0.700270i	−0.998025	−	0.0628219i	$-0.979990\pi$
$601$	−5.57800	−	17.1673i	−0.227532	−	0.700270i	0.770493	−	0.637448i	$-0.220010\pi$
$602$	−0.399677	+	1.23008i	−0.0162896	+	0.0501343i
$603$	22.1838	+	16.1175i	0.903395	+	0.656355i
$604$	10.7865			0.438898
$605$	0.800147	+	35.9597i	0.0325306	+	1.46197i
$606$	−19.1861			−0.779383
$607$	5.85382	+	4.25305i	0.237599	+	0.172626i	0.700213	−	0.713934i	$-0.253088\pi$
$607$	5.85382	+	4.25305i	0.237599	+	0.172626i	−0.462614	+	0.886560i	$0.653088\pi$
$608$	1.12191	−	3.45288i	0.0454994	−	0.140033i
$609$	3.37517	+	10.3877i	0.136769	+	0.420931i
$610$	−17.1667	+	12.4723i	−0.695058	+	0.504989i
$611$	6.20803	−	4.51040i	0.251150	−	0.182471i
$612$	1.86688	+	5.74565i	0.0754640	+	0.232254i
$613$	11.3928	−	35.0633i	0.460149	−	1.41619i	−0.404833	−	0.914391i	$-0.632670\pi$
$613$	11.3928	−	35.0633i	0.460149	−	1.41619i	0.864982	−	0.501803i	$-0.167330\pi$
$614$	−13.6874	−	9.94445i	−0.552377	−	0.401325i
$615$	−26.3316			−1.06179
$616$	18.1092	−	9.48229i	0.729640	−	0.382052i
$617$	−0.581622			−0.0234152			−0.0117076	−	0.999931i	$-0.503727\pi$
$617$	−0.581622			−0.0234152			−0.0117076	+	0.999931i	$0.503727\pi$
$618$	11.1013	+	8.06557i	0.446560	+	0.324445i
$619$	7.96816	−	24.5235i	0.320267	−	0.985681i	−0.653264	−	0.757130i	$-0.726601\pi$
$619$	7.96816	−	24.5235i	0.320267	−	0.985681i	0.973532	−	0.228552i	$-0.0733990\pi$
$620$	−1.39858	−	4.30439i	−0.0561683	−	0.172868i
$621$	−20.8937	+	15.1802i	−0.838437	+	0.609160i
$622$	−1.24761	+	0.906441i	−0.0500245	+	0.0363450i
$623$	5.30832	+	16.3373i	0.212673	+	0.654541i
$624$	0.118299	−	0.364086i	0.00473574	−	0.0145751i
$625$	17.0385	+	12.3792i	0.681538	+	0.495167i
$626$	23.0333			0.920596
$627$	−2.32586	−	0.341904i	−0.0928860	−	0.0136544i
$628$	7.73490			0.308656
$629$	−10.5313	−	7.65141i	−0.419909	−	0.305082i
$630$	−3.66977	+	11.2944i	−0.146207	+	0.449980i
$631$	−3.33174	−	10.2541i	−0.132635	−	0.408208i	0.862580	−	0.505921i	$-0.168847\pi$
$631$	−3.33174	−	10.2541i	−0.132635	−	0.408208i	−0.995215	+	0.0977133i	$0.968847\pi$
$632$	−31.5021	+	22.8876i	−1.25309	+	0.910420i
$633$	12.5458	−	9.11506i	0.498651	−	0.362291i
$634$	−2.46187	−	7.57685i	−0.0977733	−	0.300915i
$635$	−13.9406	+	42.9048i	−0.553217	+	1.70263i
$636$	8.02346	+	5.82939i	0.318151	+	0.231150i
$637$	−2.48511			−0.0984636
$638$	−2.45674	−	14.4678i	−0.0972634	−	0.572785i
$639$	−26.8722			−1.06305
$640$	14.9671	+	10.8742i	0.591625	+	0.429841i
$641$	1.90581	−	5.86548i	0.0752750	−	0.231673i	−0.906338	−	0.422553i	$-0.861134\pi$
$641$	1.90581	−	5.86548i	0.0752750	−	0.231673i	0.981613	+	0.190880i	$0.0611342\pi$
$642$	1.60360	+	4.93536i	0.0632889	+	0.194783i
$643$	23.6790	−	17.2038i	0.933807	−	0.678451i	−0.0131147	−	0.999914i	$-0.504175\pi$
$643$	23.6790	−	17.2038i	0.933807	−	0.678451i	0.946922	+	0.321463i	$0.104175\pi$
$644$	9.87425	−	7.17406i	0.389100	−	0.282698i
$645$	0.714541	+	2.19913i	0.0281350	+	0.0865907i
$646$	0.530797	−	1.63362i	0.0208839	−	0.0642741i
$647$	−7.07542	−	5.14060i	−0.278164	−	0.202098i	0.439952	−	0.898021i	$-0.354995\pi$
$647$	−7.07542	−	5.14060i	−0.278164	−	0.202098i	−0.718116	+	0.695923i	$0.754995\pi$
$648$	−0.0914331			−0.00359183
$649$	−24.3744	−	23.8380i	−0.956777	−	0.935725i
$650$	5.23408			0.205298
$651$	2.20172	+	1.59965i	0.0862923	+	0.0626950i
$652$	−3.03335	+	9.33568i	−0.118795	+	0.365613i
$653$	12.0376	+	37.0478i	0.471067	+	1.44979i	0.851190	+	0.524858i	$0.175882\pi$
$653$	12.0376	+	37.0478i	0.471067	+	1.44979i	−0.380123	+	0.924936i	$0.624118\pi$
$654$	−13.4014	+	9.73666i	−0.524035	+	0.380733i
$655$	−12.6976	+	9.22533i	−0.496135	+	0.360463i
$656$	−0.834764	−	2.56914i	−0.0325921	−	0.100308i
$657$	0.797140	−	2.45334i	0.0310994	−	0.0957141i
$658$	12.1296	+	8.81269i	0.472862	+	0.343555i
$659$	44.8488			1.74706			0.873531	−	0.486768i	$-0.161824\pi$
$659$	44.8488			1.74706			0.873531	+	0.486768i	$0.161824\pi$
$660$	5.93903	−	11.9837i	0.231177	−	0.466465i
$661$	−39.3976			−1.53239			−0.766195	−	0.642609i	$-0.777852\pi$
$661$	−39.3976			−1.53239			−0.766195	+	0.642609i	$0.777852\pi$
$662$	18.2719	+	13.2753i	0.710156	+	0.515958i
$663$	−0.929374	+	2.86032i	−0.0360939	+	0.111086i
$664$	3.16459	+	9.73960i	0.122810	+	0.377970i
$665$	−3.72959	+	2.70970i	−0.144627	+	0.105078i
$666$	6.39375	−	4.64533i	0.247753	−	0.180003i
$667$	−7.39842	−	22.7700i	−0.286468	−	0.881658i
$668$	−2.40427	+	7.39958i	−0.0930240	+	0.286298i
$669$	−20.2418	−	14.7065i	−0.782592	−	0.568587i
$670$	44.3555			1.71360
$671$	10.3934	−	20.9716i	0.401232	−	0.809600i
$672$	−12.4203			−0.479123
$673$	25.4093	+	18.4609i	0.979455	+	0.711616i	0.957587	−	0.288145i	$-0.0930386\pi$
$673$	25.4093	+	18.4609i	0.979455	+	0.711616i	0.0218681	+	0.999761i	$0.493039\pi$
$674$	0.295351	−	0.908997i	0.0113765	−	0.0350133i
$675$	9.12983	+	28.0987i	0.351407	+	1.08152i
$676$	0.933967	−	0.678567i	0.0359218	−	0.0260987i
$677$	−25.3152	+	18.3926i	−0.972944	+	0.706885i	−0.956121	−	0.292973i	$-0.905355\pi$
$677$	−25.3152	+	18.3926i	−0.972944	+	0.706885i	−0.0168234	+	0.999858i	$0.505355\pi$
$678$	−2.98426	−	9.18462i	−0.114610	−	0.352733i
$679$	4.67200	−	14.3790i	0.179295	−	0.551814i
$680$	21.6028	+	15.6953i	0.828428	+	0.601888i
$681$	11.6223			0.445366
$682$	−2.61414	−	2.55662i	−0.100101	−	0.0978981i
$683$	0.221320			0.00846859			0.00423430	−	0.999991i	$-0.498652\pi$
$683$	0.221320			0.00846859			0.00423430	+	0.999991i	$0.498652\pi$
$684$	−1.15189	−	0.836900i	−0.0440438	−	0.0319997i
$685$	−18.6011	+	57.2483i	−0.710711	+	2.18734i
$686$	−5.72689	−	17.6255i	−0.218654	−	0.672947i
$687$	−1.82860	+	1.32855i	−0.0697653	+	0.0506874i
$688$	−0.191914	+	0.139434i	−0.00731665	+	0.00531585i
$689$	−2.48503	−	7.64813i	−0.0946720	−	0.291370i
$690$	−4.93871	+	15.1998i	−0.188013	+	0.578646i
$691$	7.49000	+	5.44180i	0.284933	+	0.207016i	0.721066	−	0.692866i	$-0.243652\pi$
$691$	7.49000	+	5.44180i	0.284933	+	0.207016i	−0.436133	+	0.899882i	$0.643652\pi$
$692$	28.4839			1.08280
$693$	−2.19299	−	12.9146i	−0.0833049	−	0.490583i
$694$	14.1276			0.536278
$695$	−37.5885	−	27.3096i	−1.42581	−	1.03591i
$696$	−4.60750	+	14.1804i	−0.174647	+	0.537508i
$697$	6.55805	+	20.1836i	0.248404	+	0.764509i
$698$	−20.1604	+	14.6474i	−0.763082	+	0.554412i
$699$	−8.05159	+	5.84982i	−0.304539	+	0.221261i
$700$	−4.31470	−	13.2793i	−0.163080	−	0.501909i
$701$	2.40529	−	7.40272i	0.0908465	−	0.279597i	−0.895302	−	0.445459i	$-0.853041\pi$
$701$	2.40529	−	7.40272i	0.0908465	−	0.279597i	0.986149	+	0.165862i	$0.0530406\pi$
$702$	−3.86134	−	2.80543i	−0.145737	−	0.105884i
$703$	3.06792			0.115709
$704$	18.8619	+	2.77273i	0.710886	+	0.104501i
$705$	26.8045			1.00952
$706$	13.1937	+	9.58582i	0.496553	+	0.360767i
$707$	12.8245	−	39.4698i	0.482316	−	1.48442i
$708$	3.91753	+	12.0569i	0.147230	+	0.453126i
$709$	3.57587	−	2.59802i	0.134295	−	0.0975707i	−0.518610	−	0.855011i	$-0.673550\pi$
$709$	3.57587	−	2.59802i	0.134295	−	0.0975707i	0.652904	+	0.757440i	$0.273550\pi$
$710$	−35.1666	+	25.5500i	−1.31978	+	0.958875i
$711$	7.71086	+	23.7316i	0.289180	+	0.890004i
$712$	−7.24648	+	22.3024i	−0.271573	+	0.835817i
$713$	−4.82621	−	3.50645i	−0.180743	−	0.131317i
$714$	−5.87628			−0.219914
$715$	−9.60755	+	5.03068i	−0.359302	+	0.188137i
$716$	−16.8998			−0.631577
$717$	−8.35028	−	6.06683i	−0.311847	−	0.226570i
$718$	1.28923	−	3.96785i	0.0481137	−	0.148079i
$719$	10.6002	+	32.6239i	0.395319	+	1.21667i	0.928713	+	0.370800i	$0.120916\pi$
$719$	10.6002	+	32.6239i	0.395319	+	1.21667i	−0.533394	+	0.845867i	$0.679084\pi$
$720$	−1.76212	+	1.28026i	−0.0656705	+	0.0477124i
$721$	−24.0130	+	17.4464i	−0.894290	+	0.649740i
$722$	−5.27381	−	16.2311i	−0.196271	−	0.604060i
$723$	−1.28849	+	3.96557i	−0.0479196	+	0.147481i
$724$	3.04173	+	2.20994i	0.113045	+	0.0821319i
$725$	−27.3891			−1.01721
$726$	−0.240376	−	10.8028i	−0.00892118	−	0.400930i
$727$	−20.3993			−0.756567			−0.378284	−	0.925690i	$-0.623486\pi$
$727$	−20.3993			−0.756567			−0.378284	+	0.925690i	$0.623486\pi$
$728$	4.98626	+	3.62273i	0.184803	+	0.134267i
$729$	5.12227	−	15.7647i	0.189714	−	0.583879i
$730$	−1.28945	−	3.96851i	−0.0477246	−	0.146881i
$731$	1.50771	−	1.09541i	0.0557646	−	0.0405154i
$732$	−7.04109	+	5.11565i	−0.260246	+	0.189080i
$733$	−13.7042	−	42.1773i	−0.506178	−	1.55786i	−0.798781	−	0.601621i	$-0.794522\pi$
$733$	−13.7042	−	42.1773i	−0.506178	−	1.55786i	0.292604	−	0.956234i	$-0.405478\pi$
$734$	0.0748272	−	0.230294i	0.00276192	−	0.00850032i
$735$	−7.02288	−	5.10242i	−0.259043	−	0.188206i
$736$	27.2255			1.00354
$737$	−43.3439	+	22.6956i	−1.59659	+	0.836005i
$738$	−12.8845			−0.474285
$739$	19.0857	+	13.8666i	0.702081	+	0.510091i	0.880609	−	0.473843i	$-0.157134\pi$
$739$	19.0857	+	13.8666i	0.702081	+	0.510091i	−0.178529	+	0.983935i	$0.557134\pi$
$740$	−5.39365	+	16.6000i	−0.198275	+	0.610227i
$741$	−0.219034	−	0.674119i	−0.00804643	−	0.0247644i
$742$	12.7116	−	9.23552i	0.466658	−	0.339047i
$743$	0.0930565	−	0.0676095i	0.00341391	−	0.00248035i	−0.586077	−	0.810255i	$-0.699328\pi$
$743$	0.0930565	−	0.0676095i	0.00341391	−	0.00248035i	0.589491	+	0.807775i	$0.299328\pi$
$744$	1.14804	+	3.53331i	0.0420892	+	0.129537i
$745$	−23.1234	+	71.1665i	−0.847176	+	2.60734i
$746$	13.4706	+	9.78697i	0.493194	+	0.358326i
$747$	6.56256			0.240112
$748$	−10.6649	−	1.56775i	−0.389946	−	0.0573225i
$749$	−11.2250			−0.410151
$750$	1.79841	+	1.30662i	0.0656688	+	0.0477112i
$751$	14.4922	−	44.6023i	0.528827	−	1.62756i	−0.227795	−	0.973709i	$-0.573152\pi$
$751$	14.4922	−	44.6023i	0.528827	−	1.62756i	0.756622	−	0.653853i	$-0.226848\pi$
$752$	0.849756	+	2.61528i	0.0309874	+	0.0953695i
$753$	−3.12463	+	2.27017i	−0.113868	+	0.0827298i
$754$	3.57961	−	2.60074i	0.130362	−	0.0947134i
$755$	−9.44107	−	29.0566i	−0.343596	−	1.05748i
$756$	−3.93451	+	12.1092i	−0.143097	+	0.440406i
$757$	27.9644	+	20.3173i	1.01638	+	0.738446i	0.965538	−	0.260261i	$-0.0838085\pi$
$757$	27.9644	+	20.3173i	1.01638	+	0.738446i	0.0508453	+	0.998707i	$0.483808\pi$
$758$	−13.0003			−0.472191
$759$	−2.95129	−	17.3801i	−0.107125	−	0.630859i
$760$	−6.29322			−0.228279
$761$	−8.34434	−	6.06252i	−0.302482	−	0.219766i	0.426182	−	0.904637i	$-0.359858\pi$
$761$	−8.34434	−	6.06252i	−0.302482	−	0.219766i	−0.728664	+	0.684871i	$0.759858\pi$
$762$	4.18797	−	12.8892i	0.151714	−	0.466928i
$763$	−11.0725	−	34.0776i	−0.400851	−	1.23369i
$764$	−0.689442	+	0.500909i	−0.0249431	+	0.0181222i
$765$	13.8436	−	10.0579i	0.500515	−	0.363645i
$766$	5.21169	+	16.0399i	0.188306	+	0.579546i
$767$	3.17656	−	9.77644i	0.114699	−	0.353007i
$768$	−14.4321	−	10.4855i	−0.520773	−	0.378364i
$769$	−4.71751			−0.170118			−0.0850589	−	0.996376i	$-0.527108\pi$
$769$	−4.71751			−0.170118			−0.0850589	+	0.996376i	$0.527108\pi$
$770$	−15.1490	−	14.8157i	−0.545932	−	0.533919i
$771$	−4.89882			−0.176427
$772$	0.0674984	+	0.0490405i	0.00242932	+	0.00176500i
$773$	−11.5492	+	35.5447i	−0.415395	+	1.27845i	0.496503	+	0.868035i	$0.334617\pi$
$773$	−11.5492	+	35.5447i	−0.415395	+	1.27845i	−0.911897	+	0.410418i	$0.865383\pi$
$774$	0.349637	+	1.07607i	0.0125674	+	0.0386786i
$775$	−5.52113	+	4.01133i	−0.198325	+	0.144091i
$776$	16.6974	−	12.1314i	0.599401	−	0.435491i
$777$	−3.24327	−	9.98176i	−0.116352	−	0.358094i
$778$	−1.47052	+	4.52579i	−0.0527206	+	0.162257i
$779$	−4.04643	−	2.93990i	−0.144978	−	0.105333i
$780$	4.03261			0.144391
$781$	21.2912	−	42.9612i	0.761860	−	1.53727i
$782$	12.8809			0.460620
$783$	20.2058	+	14.6804i	0.722096	+	0.524634i
$784$	0.275197	−	0.846969i	0.00982846	−	0.0302489i
$785$	−6.77008	−	20.8362i	−0.241635	−	0.743675i
$786$	3.81453	−	2.77142i	0.136060	−	0.0988533i
$787$	−2.09195	+	1.51989i	−0.0745700	+	0.0541782i	−0.624446	−	0.781068i	$-0.714675\pi$
$787$	−2.09195	+	1.51989i	−0.0745700	+	0.0541782i	0.549876	+	0.835246i	$0.314675\pi$
$788$	7.06708	+	21.7502i	0.251754	+	0.774820i
$789$	3.96239	−	12.1950i	0.141065	−	0.434153i
$790$	32.6548	+	23.7251i	1.16181	+	0.844101i
$791$	20.8894			0.742743
$792$	7.94063	−	16.0225i	0.282158	−	0.569335i
$793$	7.05711			0.250605
$794$	−18.3611	−	13.3401i	−0.651613	−	0.473424i
$795$	8.68047	−	26.7158i	0.307865	−	0.947510i
$796$	−0.726589	−	2.23621i	−0.0257533	−	0.0792604i
$797$	−28.7520	+	20.8896i	−1.01845	+	0.739947i	−0.965964	−	0.258675i	$-0.916714\pi$
$797$	−28.7520	+	20.8896i	−1.01845	+	0.739947i	−0.0524851	+	0.998622i	$0.516714\pi$
$798$	1.12042	−	0.814034i	0.0396625	−	0.0288165i
$799$	−6.67583	−	20.5461i	−0.236174	−	0.726868i
$800$	9.62452	−	29.6212i	0.340278	−	1.04727i
$801$	12.1574	+	8.83287i	0.429561	+	0.312094i
$802$	−23.1756			−0.818359
$803$	3.29063	+	3.21822i	0.116124	+	0.113569i
$804$	18.1929			0.641614
$805$	−27.9680	−	20.3199i	−0.985741	−	0.716183i
$806$	0.340685	−	1.04852i	0.0120001	−	0.0369325i
$807$	9.94629	+	30.6115i	0.350126	+	1.07758i
$808$	45.8339	−	33.3003i	1.61243	−	1.17150i
$809$	−6.80569	+	4.94462i	−0.239275	+	0.173844i	−0.700960	−	0.713200i	$-0.747245\pi$
$809$	−6.80569	+	4.94462i	−0.239275	+	0.173844i	0.461685	+	0.887044i	$0.347245\pi$
$810$	0.0292883	+	0.0901400i	0.00102908	+	0.00316720i
$811$	−14.5898	+	44.9028i	−0.512317	+	1.57675i	0.275793	+	0.961217i	$0.411059\pi$
$811$	−14.5898	+	44.9028i	−0.512317	+	1.57675i	−0.788111	+	0.615534i	$0.788941\pi$
$812$	−9.54913	−	6.93785i	−0.335109	−	0.243471i
$813$	12.5216			0.439153
$814$	2.36074	+	13.9024i	0.0827438	+	0.487279i
$815$	27.8033			0.973907
$816$	−0.871931	−	0.633495i	−0.0305237	−	0.0221768i
$817$	−0.135726	+	0.417722i	−0.00474846	+	0.0146143i
$818$	−2.49446	−	7.67716i	−0.0872167	−	0.268426i
$819$	3.19531	−	2.32153i	0.111653	−	0.0811209i
$820$	23.0212	−	16.7259i	0.803935	−	0.584093i
$821$	15.7548	+	48.4884i	0.549847	+	1.69226i	0.709177	+	0.705031i	$0.249067\pi$
$821$	15.7548	+	48.4884i	0.549847	+	1.69226i	−0.159330	+	0.987225i	$0.550933\pi$
$822$	5.58804	−	17.1982i	0.194905	−	0.599856i
$823$	−37.3293	−	27.1213i	−1.30122	−	0.945390i	−0.301251	−	0.953545i	$-0.597404\pi$
$823$	−37.3293	−	27.1213i	−1.30122	−	0.945390i	−0.999967	+	0.00815507i	$0.997404\pi$
$824$	−40.5190			−1.41154
$825$	−19.9529	−	2.93310i	−0.694670	−	0.102117i
$826$	20.0848			0.698841
$827$	−25.5450	−	18.5595i	−0.888285	−	0.645377i	0.0471450	−	0.998888i	$-0.484988\pi$
$827$	−25.5450	−	18.5595i	−0.888285	−	0.645377i	−0.935430	+	0.353511i	$0.884988\pi$
$828$	3.29942	−	10.1546i	0.114663	−	0.352895i
$829$	−1.69129	−	5.20526i	−0.0587410	−	0.180786i	0.917381	−	0.398011i	$-0.130299\pi$
$829$	−1.69129	−	5.20526i	−0.0587410	−	0.180786i	−0.976122	+	0.217225i	$0.930299\pi$
$830$	8.58816	−	6.23966i	0.298099	−	0.216582i
$831$	−20.7143	+	15.0498i	−0.718571	+	0.522073i
$832$	1.77629	+	5.46687i	0.0615819	+	0.189530i
$833$	−2.16199	+	6.65394i	−0.0749087	+	0.230545i
$834$	11.2921	+	8.20421i	0.391014	+	0.284089i
$835$	22.0373			0.762631
$836$	2.25063	−	1.17847i	0.0778397	−	0.0407583i
$837$	6.22315			0.215103
$838$	−20.8823	−	15.1719i	−0.721367	−	0.524104i
$839$	−11.7389	+	36.1287i	−0.405273	+	1.24730i	0.515395	+	0.856953i	$0.327645\pi$
$839$	−11.7389	+	36.1287i	−0.405273	+	1.24730i	−0.920667	+	0.390348i	$0.872355\pi$
$840$	6.65291	+	20.4756i	0.229547	+	0.706474i
$841$	4.72992	−	3.43649i	0.163101	−	0.118500i
$842$	9.19907	−	6.68352i	0.317021	−	0.230329i
$843$	5.93123	+	18.2544i	0.204282	+	0.628716i
$844$	−5.17864	+	15.9382i	−0.178256	+	0.548616i
$845$	−2.64538	−	1.92198i	−0.0910039	−	0.0661182i
$846$	13.1159			0.450934
$847$	22.3843	+	6.72640i	0.769134	+	0.231122i
$848$	2.88181			0.0989617
$849$	11.0896	+	8.05709i	0.380595	+	0.276519i
$850$	4.55355	−	14.0144i	0.156185	−	0.480689i
$851$	7.10930	+	21.8802i	0.243704	+	0.750043i
$852$	−14.4239	+	10.4796i	−0.494156	+	0.359026i
$853$	38.2326	−	27.7776i	1.30906	−	0.951087i	0.309059	−	0.951043i	$-0.399986\pi$
$853$	38.2326	−	27.7776i	1.30906	−	0.951087i	1.00000		4.39223e-5i	$-1.39809e-5\pi$
$854$	4.26092	+	13.1138i	0.145806	+	0.448744i
$855$	−1.24622	+	3.83546i	−0.0426198	+	0.131170i
$856$	−12.3969	−	9.00686i	−0.423716	−	0.307848i
$857$	−7.29306			−0.249126			−0.124563	−	0.992212i	$-0.539753\pi$
$857$	−7.29306			−0.249126			−0.124563	+	0.992212i	$0.539753\pi$
$858$	2.88625	−	1.51129i	0.0985348	−	0.0515946i
$859$	7.83405			0.267294			0.133647	−	0.991029i	$-0.457331\pi$
$859$	7.83405			0.267294			0.133647	+	0.991029i	$0.457331\pi$
$860$	−2.02160	−	1.46878i	−0.0689360	−	0.0500849i
$861$	−5.28753	+	16.2733i	−0.180199	+	0.554594i
$862$	−0.550775	−	1.69511i	−0.0187595	−	0.0577357i
$863$	−21.2367	+	15.4293i	−0.722904	+	0.525221i	−0.887311	−	0.461172i	$-0.847429\pi$
$863$	−21.2367	+	15.4293i	−0.722904	+	0.525221i	0.164407	+	0.986393i	$0.447429\pi$
$864$	−22.9771	+	16.6938i	−0.781695	+	0.567935i
$865$	−24.9310	−	76.7296i	−0.847678	−	2.60888i
$866$	−2.40467	+	7.40080i	−0.0817139	+	0.251489i
$867$	−7.84220	−	5.69769i	−0.266335	−	0.193504i
$868$	−2.94102			−0.0998247
$869$	−44.0496	−	6.47535i	−1.49428	−	0.219661i
$870$	15.4558			0.524000
$871$	−11.9345	−	8.67092i	−0.404385	−	0.293803i
$872$	15.1153	−	46.5200i	0.511867	−	1.57537i
$873$	−4.08707	−	12.5787i	−0.138326	−	0.425724i
$874$	−2.45598	+	1.78438i	−0.0830748	+	0.0603574i
$875$	−3.89011	+	2.82633i	−0.131510	+	0.0955473i
$876$	−0.528881	−	1.62773i	−0.0178692	−	0.0549958i
$877$	−4.91223	+	15.1183i	−0.165874	+	0.510508i	−0.999100	−	0.0424251i	$-0.986492\pi$
$877$	−4.91223	+	15.1183i	−0.165874	+	0.510508i	0.833225	+	0.552933i	$0.186492\pi$
$878$	−7.19123	−	5.22474i	−0.242692	−	0.176326i
$879$	−12.9921			−0.438211
$880$	−0.650621	−	3.83151i	−0.0219324	−	0.129160i
$881$	42.1115			1.41877			0.709386	−	0.704820i	$-0.248972\pi$
$881$	42.1115			1.41877			0.709386	+	0.704820i	$0.248972\pi$
$882$	−3.43641	−	2.49670i	−0.115710	−	0.0840683i
$883$	−5.86799	+	18.0598i	−0.197474	+	0.607761i	0.802465	+	0.596699i	$0.203521\pi$
$883$	−5.86799	+	18.0598i	−0.197474	+	0.607761i	−0.999939	+	0.0110624i	$0.996479\pi$
$884$	−1.00435	−	3.09106i	−0.0337798	−	0.103964i
$885$	29.0499	−	21.1060i	0.976500	−	0.709469i
$886$	6.15924	−	4.47495i	0.206924	−	0.150339i
$887$	−11.3457	−	34.9185i	−0.380951	−	1.17245i	−0.939375	−	0.342892i	$-0.888594\pi$
$887$	−11.3457	−	34.9185i	−0.380951	−	1.17245i	0.558423	−	0.829556i	$-0.311406\pi$
$888$	4.42744	−	13.6263i	0.148575	−	0.457268i
$889$	23.7165	+	17.2310i	0.795425	+	0.577910i
$890$	24.3082			0.814812
$891$	−0.0747427	−	0.0730981i	−0.00250398	−	0.00244888i
$892$	27.0386			0.905318
$893$	4.11910	+	2.99270i	0.137840	+	0.100147i
$894$	6.94660	−	21.3794i	0.232329	−	0.715036i
$895$	14.7918	+	45.5246i	0.494436	+	1.52172i
$896$	9.72589	−	7.06627i	0.324919	−	0.236068i
$897$	4.30019	−	3.12427i	0.143579	−	0.104316i
$898$	10.2862	+	31.6578i	0.343256	+	1.05643i
$899$	−1.78275	+	5.48674i	−0.0594581	+	0.182993i
$900$	−9.88175	−	7.17951i	−0.329392	−	0.239317i
$901$	−22.6400			−0.754247
$902$	10.2086	−	20.5987i	0.339908	−	0.685863i
$903$	1.50258			0.0500027
$904$	23.0704	+	16.7616i	0.767309	+	0.557483i
$905$	3.29080	−	10.1280i	0.109390	−	0.336667i
$906$	2.83623	+	8.72903i	0.0942276	+	0.290003i
$907$	−15.2820	+	11.1030i	−0.507432	+	0.368671i	−0.811848	−	0.583868i	$-0.801538\pi$
$907$	−15.2820	+	11.1030i	−0.507432	+	0.368671i	0.304417	+	0.952539i	$0.401538\pi$
$908$	−10.1611	+	7.38248i	−0.337208	+	0.244996i
$909$	−11.2189	−	34.5282i	−0.372107	−	1.14523i
$910$	1.97427	−	6.07619i	0.0654465	−	0.201424i
$911$	3.59032	+	2.60852i	0.118953	+	0.0864241i	0.645671	−	0.763616i	$-0.276578\pi$
$911$	3.59032	+	2.60852i	0.118953	+	0.0864241i	−0.526718	+	0.850040i	$0.676578\pi$
$912$	0.254007			0.00841102
$913$	−5.19961	+	10.4917i	−0.172082	+	0.347225i
$914$	10.4106			0.344352
$915$	19.9433	+	14.4896i	0.659305	+	0.479013i
$916$	0.754806	−	2.32305i	0.0249395	−	0.0767558i
$917$	3.15165	+	9.69979i	0.104077	+	0.320315i
$918$	−10.8709	+	7.89816i	−0.358793	+	0.260678i
$919$	−7.30168	+	5.30498i	−0.240860	+	0.174995i	−0.701667	−	0.712506i	$-0.747560\pi$
$919$	−7.30168	+	5.30498i	−0.240860	+	0.174995i	0.460806	+	0.887501i	$0.347560\pi$
$920$	−14.5833	−	44.8827i	−0.480797	−	1.47974i
$921$	−6.07373	+	18.6930i	−0.200136	+	0.615956i
$922$	−20.2721	−	14.7285i	−0.667625	−	0.485058i
$923$	14.4568			0.475850
$924$	−6.21353	−	6.07680i	−0.204410	−	0.199912i
$925$	26.3188			0.865356
$926$	−6.90877	−	5.01952i	−0.227036	−	0.164952i
$927$	−8.02378	+	24.6947i	−0.263536	+	0.811079i
$928$	−8.13612	−	25.0404i	−0.267081	−	0.821991i
$929$	−1.32459	+	0.962371i	−0.0434584	+	0.0315744i	−0.609302	−	0.792938i	$-0.708550\pi$
$929$	−1.32459	+	0.962371i	−0.0434584	+	0.0315744i	0.565844	+	0.824512i	$0.308550\pi$
$930$	3.11559	−	2.26361i	0.102164	−	0.0742266i
$931$	−0.509538	−	1.56820i	−0.0166994	−	0.0513955i
$932$	3.32353	−	10.2288i	0.108866	−	0.335054i
$933$	1.44940	+	1.05305i	0.0474513	+	0.0344754i
$934$	4.31746			0.141271
$935$	5.11139	+	30.1010i	0.167160	+	0.984409i
$936$	5.39170			0.176233
$937$	−45.6874	−	33.1938i	−1.49254	−	1.08440i	−0.973236	−	0.229808i	$-0.926190\pi$
$937$	−45.6874	−	33.1938i	−1.49254	−	1.08440i	−0.519307	−	0.854588i	$-0.673810\pi$
$938$	8.90682	−	27.4124i	0.290818	−	0.895046i
$939$	−8.26893	−	25.4492i	−0.269846	−	0.830502i
$940$	−23.4347	+	17.0263i	−0.764354	+	0.555336i
$941$	14.2375	−	10.3442i	0.464130	−	0.337210i	−0.331019	−	0.943624i	$-0.607393\pi$
$941$	14.2375	−	10.3442i	0.464130	−	0.337210i	0.795149	+	0.606414i	$0.207393\pi$
$942$	2.03383	+	6.25949i	0.0662658	+	0.203945i
$943$	11.5903	−	35.6714i	0.377434	−	1.16162i
$944$	2.98022	+	2.16525i	0.0969978	+	0.0704730i
$945$	36.0632			1.17314
$946$	−1.99736	−	0.293615i	−0.0649399	−	0.00954624i
$947$	12.1548			0.394978			0.197489	−	0.980305i	$-0.436721\pi$
$947$	12.1548			0.394978			0.197489	+	0.980305i	$0.436721\pi$
$948$	13.3937	+	9.73111i	0.435008	+	0.316052i
$949$	−0.428847	+	1.31986i	−0.0139210	+	0.0428443i
$950$	1.07318	+	3.30290i	0.0348185	+	0.107160i
$951$	−7.48774	+	5.44016i	−0.242807	+	0.176409i
$952$	14.0379	−	10.1991i	0.454971	−	0.330556i
$953$	3.69279	+	11.3652i	0.119621	+	0.368156i	0.992883	−	0.119096i	$-0.0379995\pi$
$953$	3.69279	+	11.3652i	0.119621	+	0.368156i	−0.873262	+	0.487252i	$0.837999\pi$
$954$	4.24750	−	13.0725i	0.137518	−	0.423237i
$955$	1.95278	+	1.41878i	0.0631906	+	0.0459107i
$956$	11.1541			0.360751
$957$	−15.1033	+	7.90834i	−0.488220	+	0.255640i
$958$	−4.08390			−0.131945
$959$	31.6451	+	22.9915i	1.02187	+	0.742435i
$960$	−6.20479	+	19.0964i	−0.200259	+	0.616333i
$961$	−9.13532	−	28.1156i	−0.294688	−	0.906956i
$962$	−3.43973	+	2.49911i	−0.110901	+	0.0805744i
$963$	−7.94421	+	5.77181i	−0.255999	+	0.185994i
$964$	−1.39243	−	4.28547i	−0.0448473	−	0.138026i
$965$	0.0730256	−	0.224750i	0.00235078	−	0.00723494i
$966$	8.40198	+	6.10439i	0.270329	+	0.196406i
$967$	−56.8476			−1.82809			−0.914047	−	0.405608i	$-0.867060\pi$
$967$	−56.8476			−1.82809			−0.914047	+	0.405608i	$0.867060\pi$
$968$	19.3241	+	25.3897i	0.621099	+	0.816057i
$969$	−1.99552			−0.0641055
$970$	−17.3084	−	12.5753i	−0.555738	−	0.403767i
$971$	1.38321	−	4.25707i	0.0443892	−	0.136616i	−0.926406	−	0.376527i	$-0.877118\pi$
$971$	1.38321	−	4.25707i	0.0443892	−	0.136616i	0.970795	+	0.239911i	$0.0771182\pi$
$972$	5.56706	+	17.1337i	0.178564	+	0.549562i
$973$	−24.4257	+	17.7463i	−0.783053	+	0.568921i
$974$	−16.6276	+	12.0807i	−0.532783	+	0.387090i
$975$	−1.87903	−	5.78306i	−0.0601771	−	0.185206i
$976$	−0.781493	+	2.40519i	−0.0250150	+	0.0769882i
$977$	13.5035	+	9.81086i	0.432015	+	0.313877i	0.782454	−	0.622708i	$-0.213968\pi$
$977$	13.5035	+	9.81086i	0.432015	+	0.313877i	−0.350439	+	0.936586i	$0.613968\pi$
$978$	−8.35251			−0.267084
$979$	−23.7538	+	12.4379i	−0.759174	+	0.397517i
$980$	9.38102			0.299666
$981$	−25.3588	−	18.4243i	−0.809645	−	0.588242i
$982$	1.26713	−	3.89983i	0.0404358	−	0.124448i
$983$	6.54544	+	20.1448i	0.208767	+	0.642520i	0.999538	+	0.0304066i	$0.00968021\pi$
$983$	6.54544	+	20.1448i	0.208767	+	0.642520i	−0.790770	+	0.612113i	$0.790320\pi$
$984$	−18.8972	+	13.7296i	−0.602422	+	0.437685i
$985$	52.4049	−	38.0744i	1.66976	−	1.21315i
$986$	−3.84935	−	11.8471i	−0.122588	−	0.377288i
$987$	5.38249	−	16.5656i	0.171327	−	0.527289i
$988$	0.619698	+	0.450237i	0.0197152	+	0.0143240i
$989$	−3.29368			−0.104733
$990$	−18.3395	−	2.69593i	−0.582867	−	0.0856822i
$991$	−52.5294			−1.66865			−0.834326	−	0.551272i	$-0.814143\pi$
$991$	−52.5294			−1.66865			−0.834326	+	0.551272i	$0.814143\pi$
$992$	−5.30743	−	3.85607i	−0.168511	−	0.122430i
$993$	8.10809	−	24.9541i	0.257302	−	0.791895i
$994$	8.72866	+	26.8640i	0.276856	+	0.852076i
$995$	−5.38792	+	3.91455i	−0.170808	+	0.124100i
$996$	3.52253	−	2.55927i	0.111616	−	0.0810934i
$997$	−16.5391	−	50.9021i	−0.523798	−	1.61209i	−0.766680	−	0.642029i	$-0.778093\pi$
$997$	−16.5391	−	50.9021i	−0.523798	−	1.61209i	0.242882	−	0.970056i	$-0.421907\pi$
$998$	−10.2355	+	31.5016i	−0.323998	+	0.997165i
$999$	−19.4162	−	14.1067i	−0.614300	−	0.446315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.h.c.92.3	yes	28
11.3	even	5	inner	143.2.h.c.14.3	✓	28
11.5	even	5		1573.2.a.s.1.9		14
11.6	odd	10		1573.2.a.r.1.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.c.14.3	✓	28	11.3	even	5	inner
143.2.h.c.92.3	yes	28	1.1	even	1	trivial
1573.2.a.r.1.6		14	11.6	odd	10
1573.2.a.s.1.9		14	11.5	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.743923 - 0.540492i) q^{2} +(-0.330114 + 1.01599i) q^{3} +(-0.356744 - 1.09794i) q^{4} +(-2.64538 + 1.92198i) q^{5} +(0.794711 - 0.577391i) q^{6} +(0.656608 + 2.02083i) q^{7} +(-0.896347 + 2.75867i) q^{8} +(1.50380 + 1.09257i) q^{9} +O(q^{10})\)	\(q+(-0.743923 - 0.540492i) q^{2} +(-0.330114 + 1.01599i) q^{3} +(-0.356744 - 1.09794i) q^{4} +(-2.64538 + 1.92198i) q^{5} +(0.794711 - 0.577391i) q^{6} +(0.656608 + 2.02083i) q^{7} +(-0.896347 + 2.75867i) q^{8} +(1.50380 + 1.09257i) q^{9} +3.00678 q^{10} +(-2.93820 + 1.53849i) q^{11} +1.23326 q^{12} +(-0.809017 - 0.587785i) q^{13} +(0.603777 - 1.85823i) q^{14} +(-1.07943 - 3.32214i) q^{15} +(0.289917 - 0.210637i) q^{16} +(-2.27764 + 1.65480i) q^{17} +(-0.528184 - 1.62558i) q^{18} +(0.205036 - 0.631037i) q^{19} +(3.05395 + 2.21883i) q^{20} -2.26989 q^{21} +(3.01734 + 0.443553i) q^{22} +4.97564 q^{23} +(-2.50687 - 1.82135i) q^{24} +(1.75895 - 5.41348i) q^{25} +(0.284153 + 0.874534i) q^{26} +(-4.19921 + 3.05091i) q^{27} +(1.98452 - 1.44184i) q^{28} +(-1.48693 - 4.57630i) q^{29} +(-0.992579 + 3.05484i) q^{30} +(-0.969968 - 0.704723i) q^{31} +5.47175 q^{32} +(-0.593147 - 3.49305i) q^{33} +2.58879 q^{34} +(-5.62098 - 4.08388i) q^{35} +(0.663115 - 2.04086i) q^{36} +(1.42882 + 4.39746i) q^{37} +(-0.493602 + 0.358623i) q^{38} +(0.864249 - 0.627914i) q^{39} +(-2.93094 - 9.02050i) q^{40} +(2.32942 - 7.16922i) q^{41} +(1.68862 + 1.22686i) q^{42} -0.661961 q^{43} +(2.73737 + 2.67714i) q^{44} -6.07803 q^{45} +(-3.70149 - 2.68929i) q^{46} +(-2.37126 + 7.29797i) q^{47} +(0.118299 + 0.364086i) q^{48} +(2.01049 - 1.46071i) q^{49} +(-4.23446 + 3.07652i) q^{50} +(-0.929374 - 2.86032i) q^{51} +(-0.356744 + 1.09794i) q^{52} +(6.50589 + 4.72680i) q^{53} +4.77288 q^{54} +(4.81571 - 9.71708i) q^{55} -6.16336 q^{56} +(0.573440 + 0.416628i) q^{57} +(-1.36729 + 4.20809i) q^{58} +(3.17656 + 9.77644i) q^{59} +(-3.26245 + 2.37031i) q^{60} +(-5.70932 + 4.14806i) q^{61} +(0.340685 + 1.04852i) q^{62} +(-1.22050 + 3.75632i) q^{63} +(-4.65040 - 3.37871i) q^{64} +3.26987 q^{65} +(-1.44671 + 2.91915i) q^{66} +14.7519 q^{67} +(2.62941 + 1.91038i) q^{68} +(-1.64253 + 5.05518i) q^{69} +(1.97427 + 6.07619i) q^{70} +(-11.6958 + 8.49747i) q^{71} +(-4.36198 + 3.16916i) q^{72} +(-0.428847 - 1.31986i) q^{73} +(1.31386 - 4.04364i) q^{74} +(4.91937 + 3.57413i) q^{75} -0.765989 q^{76} +(-5.03828 - 4.92742i) q^{77} -0.982317 q^{78} +(10.8604 + 7.89054i) q^{79} +(-0.362101 + 1.11443i) q^{80} +(0.00974075 + 0.0299789i) q^{81} +(-5.60781 + 4.07431i) q^{82} +(2.85627 - 2.07520i) q^{83} +(0.809770 + 2.49221i) q^{84} +(2.84472 - 8.75516i) q^{85} +(0.492448 + 0.357785i) q^{86} +5.14031 q^{87} +(-1.61055 - 9.48456i) q^{88} +8.08446 q^{89} +(4.52159 + 3.28513i) q^{90} +(0.656608 - 2.02083i) q^{91} +(-1.77503 - 5.46297i) q^{92} +(1.03619 - 0.752835i) q^{93} +(5.70853 - 4.14749i) q^{94} +(0.670443 + 2.06341i) q^{95} +(-1.80630 + 5.55922i) q^{96} +(-5.75645 - 4.18231i) q^{97} -2.28516 q^{98} +(-6.09938 - 0.896617i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

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