LMFDB - Embedded newform 170.2.r.b.167.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(23,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([12, 15]))

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

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

chi := DirichletCharacter("170.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$170 = 2 \cdot 5 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	170.r (of order $16$ , degree $8$ , 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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			167.4
Character	$\chi$	$=$	170.167
Dual form			170.2.r.b.113.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.923880 - 0.382683i) q^{2} +(0.530147 + 0.793420i) q^{3} +(0.707107 + 0.707107i) q^{4} +(1.12276 - 1.93376i) q^{5} +(-0.186163 - 0.935903i) q^{6} +(0.736366 + 3.70196i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(0.799590 - 1.93038i) q^{9} +(-1.77731 + 1.35690i) q^{10} +(-2.74651 + 0.546316i) q^{11} +(-0.186163 + 0.935903i) q^{12} +5.74893 q^{13} +(0.736366 - 3.70196i) q^{14} +(2.12951 - 0.134356i) q^{15} +1.00000i q^{16} +(3.33833 + 2.41983i) q^{17} +(-1.47745 + 1.47745i) q^{18} +(0.119335 + 0.288099i) q^{19} +(2.16128 - 0.573463i) q^{20} +(-2.54683 + 2.54683i) q^{21} +(2.74651 + 0.546316i) q^{22} +(-3.97327 - 2.65485i) q^{23} +(0.530147 - 0.793420i) q^{24} +(-2.47883 - 4.34228i) q^{25} +(-5.31132 - 2.20002i) q^{26} +(4.76321 - 0.947462i) q^{27} +(-2.09699 + 3.13837i) q^{28} +(0.463177 - 0.309485i) q^{29} +(-2.01882 - 0.690799i) q^{30} +(-5.00121 - 0.994802i) q^{31} +(0.382683 - 0.923880i) q^{32} +(-1.88951 - 1.88951i) q^{33} +(-2.15819 - 3.51315i) q^{34} +(7.98545 + 2.73245i) q^{35} +(1.93038 - 0.799590i) q^{36} +(-8.56427 + 5.72246i) q^{37} -0.311836i q^{38} +(3.04777 + 4.56132i) q^{39} +(-2.21622 - 0.297276i) q^{40} +(-7.70784 - 5.15021i) q^{41} +(3.32759 - 1.37833i) q^{42} +(-8.32027 + 3.44637i) q^{43} +(-2.32838 - 1.55578i) q^{44} +(-2.83514 - 3.71356i) q^{45} +(2.65485 + 3.97327i) q^{46} -5.61274i q^{47} +(-0.793420 + 0.530147i) q^{48} +(-6.69512 + 2.77321i) q^{49} +(0.628422 + 4.96035i) q^{50} +(-0.150134 + 3.93156i) q^{51} +(4.06511 + 4.06511i) q^{52} +(-2.52221 + 6.08916i) q^{53} +(-4.76321 - 0.947462i) q^{54} +(-2.02723 + 5.92447i) q^{55} +(3.13837 - 2.09699i) q^{56} +(-0.165319 + 0.247417i) q^{57} +(-0.546354 + 0.108677i) q^{58} +(3.14785 + 1.30388i) q^{59} +(1.60079 + 1.41079i) q^{60} +(5.67092 - 8.48713i) q^{61} +(4.23982 + 2.83296i) q^{62} +(7.73498 + 1.53858i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(6.45465 - 11.1170i) q^{65} +(1.02260 + 2.46877i) q^{66} +(1.94198 - 1.94198i) q^{67} +(0.649481 + 4.07163i) q^{68} -4.55993i q^{69} +(-6.33193 - 5.58036i) q^{70} +(0.782371 - 3.93324i) q^{71} -2.08943 q^{72} +(-0.167388 + 0.841518i) q^{73} +(10.1022 - 2.00946i) q^{74} +(2.13111 - 4.26880i) q^{75} +(-0.119335 + 0.288099i) q^{76} +(-4.04488 - 9.76520i) q^{77} +(-1.07024 - 5.38044i) q^{78} +(-0.872680 - 4.38726i) q^{79} +(1.93376 + 1.12276i) q^{80} +(-1.15541 - 1.15541i) q^{81} +(5.15021 + 7.70784i) q^{82} +(-1.36475 - 0.565299i) q^{83} -3.60176 q^{84} +(8.42749 - 3.73864i) q^{85} +9.00580 q^{86} +(0.491103 + 0.203422i) q^{87} +(1.55578 + 2.32838i) q^{88} +(7.49831 + 7.49831i) q^{89} +(1.19821 + 4.51585i) q^{90} +(4.23331 + 21.2823i) q^{91} +(-0.932261 - 4.68679i) q^{92} +(-1.86208 - 4.49545i) q^{93} +(-2.14790 + 5.18549i) q^{94} +(0.691097 + 0.0927014i) q^{95} +(0.935903 - 0.186163i) q^{96} +(-3.04671 + 15.3169i) q^{97} +7.24674 q^{98} +(-1.14149 + 5.73865i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$40 q - 16 q^{10} - 16 q^{18} + 8 q^{25} - 8 q^{26} + 24 q^{27} - 8 q^{28} + 8 q^{29} + 16 q^{30} - 16 q^{31} - 32 q^{33} + 8 q^{34} - 32 q^{35} - 32 q^{39} - 56 q^{41} - 24 q^{42} + 16 q^{43} + 16 q^{44}+ \cdots + 160 q^{99}+O(q^{100})$ 40 * q - 16 * q^10 - 16 * q^18 + 8 * q^25 - 8 * q^26 + 24 * q^27 - 8 * q^28 + 8 * q^29 + 16 * q^30 - 16 * q^31 - 32 * q^33 + 8 * q^34 - 32 * q^35 - 32 * q^39 - 56 * q^41 - 24 * q^42 + 16 * q^43 + 16 * q^44 + 24 * q^45 + 16 * q^49 - 32 * q^51 - 16 * q^52 + 16 * q^53 - 24 * q^54 - 8 * q^55 - 8 * q^56 - 120 * q^57 + 16 * q^58 + 8 * q^60 + 24 * q^61 - 8 * q^62 - 24 * q^63 - 32 * q^65 + 16 * q^67 - 8 * q^70 + 24 * q^71 + 56 * q^72 + 88 * q^73 + 32 * q^74 + 8 * q^75 + 24 * q^77 + 32 * q^78 - 104 * q^79 + 8 * q^80 + 48 * q^81 + 16 * q^82 + 16 * q^83 + 136 * q^85 + 96 * q^86 + 136 * q^87 - 16 * q^89 + 24 * q^90 + 48 * q^91 - 8 * q^92 - 8 * q^93 - 8 * q^94 - 136 * q^95 + 16 * q^97 + 72 * q^98 + 160 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$ .

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.923880	−	0.382683i	−0.653281	−	0.270598i
$2$	−0.923880	−	0.382683i	−0.653281	−	0.270598i
$3$	0.530147	+	0.793420i	0.306080	+	0.458081i	0.952341	−	0.305035i	$-0.0986682\pi$
$3$	0.530147	+	0.793420i	0.306080	+	0.458081i	−0.646261	+	0.763117i	$0.723668\pi$
$4$	0.707107	+	0.707107i	0.353553	+	0.353553i
$5$	1.12276	−	1.93376i	0.502112	−	0.864802i
$5$	1.12276	−	1.93376i	0.502112	−	0.864802i
$6$	−0.186163	−	0.935903i	−0.0760006	−	0.382081i
$7$	0.736366	+	3.70196i	0.278320	+	1.39921i	0.826541	+	0.562876i	$0.190305\pi$
$7$	0.736366	+	3.70196i	0.278320	+	1.39921i	−0.548221	+	0.836333i	$0.684695\pi$
$8$	−0.382683	−	0.923880i	−0.135299	−	0.326641i
$9$	0.799590	−	1.93038i	0.266530	−	0.643460i
$10$	−1.77731	+	1.35690i	−0.562035	+	0.429089i
$11$	−2.74651	+	0.546316i	−0.828105	+	0.164720i	−0.590906	−	0.806741i	$-0.701230\pi$
$11$	−2.74651	+	0.546316i	−0.828105	+	0.164720i	−0.237200	+	0.971461i	$0.576230\pi$
$12$	−0.186163	+	0.935903i	−0.0537405	+	0.270172i
$13$	5.74893			1.59447			0.797233	−	0.603672i	$-0.206296\pi$
$13$	5.74893			1.59447			0.797233	+	0.603672i	$0.206296\pi$
$14$	0.736366	−	3.70196i	0.196802	−	0.989390i
$15$	2.12951	−	0.134356i	0.549837	−	0.0346905i
$16$			1.00000i			0.250000i
$17$	3.33833	+	2.41983i	0.809664	+	0.586894i
$17$	3.33833	+	2.41983i	0.809664	+	0.586894i
$18$	−1.47745	+	1.47745i	−0.348238	+	0.348238i
$19$	0.119335	+	0.288099i	0.0273772	+	0.0660944i	0.936977	−	0.349391i	$-0.113612\pi$
$19$	0.119335	+	0.288099i	0.0273772	+	0.0660944i	−0.909600	+	0.415486i	$0.863612\pi$
$20$	2.16128	−	0.573463i	0.483277	−	0.128230i
$21$	−2.54683	+	2.54683i	−0.555764	+	0.555764i
$22$	2.74651	+	0.546316i	0.585559	+	0.116475i
$23$	−3.97327	−	2.65485i	−0.828484	−	0.553575i	0.0674705	−	0.997721i	$-0.478507\pi$
$23$	−3.97327	−	2.65485i	−0.828484	−	0.553575i	−0.895954	+	0.444146i	$0.853507\pi$
$24$	0.530147	−	0.793420i	0.108216	−	0.161956i
$25$	−2.47883	−	4.34228i	−0.495766	−	0.868456i
$26$	−5.31132	−	2.20002i	−1.04164	−	0.431459i
$27$	4.76321	−	0.947462i	0.916681	−	0.182339i
$28$	−2.09699	+	3.13837i	−0.396294	+	0.593096i
$29$	0.463177	−	0.309485i	0.0860098	−	0.0574699i	−0.511822	−	0.859092i	$-0.671029\pi$
$29$	0.463177	−	0.309485i	0.0860098	−	0.0574699i	0.597832	+	0.801622i	$0.296029\pi$
$30$	−2.01882	−	0.690799i	−0.368585	−	0.126122i
$31$	−5.00121	−	0.994802i	−0.898244	−	0.178672i	−0.275688	−	0.961247i	$-0.588906\pi$
$31$	−5.00121	−	0.994802i	−0.898244	−	0.178672i	−0.622556	+	0.782575i	$0.713906\pi$
$32$	0.382683	−	0.923880i	0.0676495	−	0.163320i
$33$	−1.88951	−	1.88951i	−0.328922	−	0.328922i
$34$	−2.15819	−	3.51315i	−0.370126	−	0.602500i
$35$	7.98545	+	2.73245i	1.34979	+	0.461869i
$36$	1.93038	−	0.799590i	0.321730	−	0.133265i
$37$	−8.56427	+	5.72246i	−1.40796	+	0.940767i	−0.408348	+	0.912826i	$0.633895\pi$
$37$	−8.56427	+	5.72246i	−1.40796	+	0.940767i	−0.999610	+	0.0279411i	$0.991105\pi$
$38$		−	0.311836i		−	0.0505865i
$39$	3.04777	+	4.56132i	0.488035	+	0.730395i
$40$	−2.21622	−	0.297276i	−0.350415	−	0.0470035i
$41$	−7.70784	−	5.15021i	−1.20376	−	0.804328i	−0.218576	−	0.975820i	$-0.570141\pi$
$41$	−7.70784	−	5.15021i	−1.20376	−	0.804328i	−0.985186	+	0.171492i	$0.945141\pi$
$42$	3.32759	−	1.37833i	0.513459	−	0.212682i
$43$	−8.32027	+	3.44637i	−1.26883	+	0.525566i	−0.912608	−	0.408835i	$-0.865935\pi$
$43$	−8.32027	+	3.44637i	−1.26883	+	0.525566i	−0.356221	+	0.934402i	$0.615935\pi$
$44$	−2.32838	−	1.55578i	−0.351017	−	0.234542i
$45$	−2.83514	−	3.71356i	−0.422638	−	0.553585i
$46$	2.65485	+	3.97327i	0.391437	+	0.585827i
$47$		−	5.61274i		−	0.818702i	−0.912377	−	0.409351i	$-0.865755\pi$
$47$		−	5.61274i		−	0.818702i	0.912377	−	0.409351i	$-0.134245\pi$
$48$	−0.793420	+	0.530147i	−0.114520	+	0.0765201i
$49$	−6.69512	+	2.77321i	−0.956445	+	0.396173i
$50$	0.628422	+	4.96035i	0.0888723	+	0.701500i
$51$	−0.150134	+	3.93156i	−0.0210230	+	0.550529i
$52$	4.06511	+	4.06511i	0.563729	+	0.563729i
$53$	−2.52221	+	6.08916i	−0.346453	+	0.836411i	0.650580	+	0.759437i	$0.274526\pi$
$53$	−2.52221	+	6.08916i	−0.346453	+	0.836411i	−0.997033	+	0.0769735i	$0.975474\pi$
$54$	−4.76321	−	0.947462i	−0.648191	−	0.128933i
$55$	−2.02723	+	5.92447i	−0.273351	+	0.798856i
$56$	3.13837	−	2.09699i	0.419382	−	0.280222i
$57$	−0.165319	+	0.247417i	−0.0218970	+	0.0327712i
$58$	−0.546354	+	0.108677i	−0.0717398	+	0.0142699i
$59$	3.14785	+	1.30388i	0.409815	+	0.169751i	0.578060	−	0.815994i	$-0.303810\pi$
$59$	3.14785	+	1.30388i	0.409815	+	0.169751i	−0.168245	+	0.985745i	$0.553810\pi$
$60$	1.60079	+	1.41079i	0.206662	+	0.182132i
$61$	5.67092	−	8.48713i	0.726086	−	1.08667i	−0.266346	−	0.963877i	$-0.585817\pi$
$61$	5.67092	−	8.48713i	0.726086	−	1.08667i	0.992433	−	0.122788i	$-0.0391835\pi$
$62$	4.23982	+	2.83296i	0.538458	+	0.359786i
$63$	7.73498	+	1.53858i	0.974516	+	0.193843i
$64$	−0.707107	+	0.707107i	−0.0883883	+	0.0883883i
$65$	6.45465	−	11.1170i	0.800601	−	1.37890i
$66$	1.02260	+	2.46877i	0.125873	+	0.303884i
$67$	1.94198	−	1.94198i	0.237251	−	0.237251i	−0.578460	−	0.815711i	$-0.696346\pi$
$67$	1.94198	−	1.94198i	0.237251	−	0.237251i	0.815711	+	0.578460i	$0.196346\pi$
$68$	0.649481	+	4.07163i	0.0787611	+	0.493758i
$69$		−	4.55993i		−	0.548952i
$70$	−6.33193	−	5.58036i	−0.756810	−	0.666980i
$71$	0.782371	−	3.93324i	0.0928503	−	0.466790i	−0.906185	−	0.422881i	$-0.861019\pi$
$71$	0.782371	−	3.93324i	0.0928503	−	0.466790i	0.999036	−	0.0439090i	$-0.0139812\pi$
$72$	−2.08943			−0.246242
$73$	−0.167388	+	0.841518i	−0.0195913	+	0.0984922i	−0.989344	−	0.145598i	$-0.953489\pi$
$73$	−0.167388	+	0.841518i	−0.0195913	+	0.0984922i	0.969752	+	0.244090i	$0.0784893\pi$
$74$	10.1022	−	2.00946i	1.17436	−	0.233595i
$75$	2.13111	−	4.26880i	0.246079	−	0.492918i
$76$	−0.119335	+	0.288099i	−0.0136886	+	0.0330472i
$77$	−4.04488	−	9.76520i	−0.460957	−	1.11285i
$78$	−1.07024	−	5.38044i	−0.121180	−	0.609215i
$79$	−0.872680	−	4.38726i	−0.0981841	−	0.493605i	−0.998317	−	0.0579898i	$-0.981531\pi$
$79$	−0.872680	−	4.38726i	−0.0981841	−	0.493605i	0.900133	−	0.435615i	$-0.143469\pi$
$80$	1.93376	+	1.12276i	0.216201	+	0.125528i
$81$	−1.15541	−	1.15541i	−0.128379	−	0.128379i
$82$	5.15021	+	7.70784i	0.568746	+	0.851188i
$83$	−1.36475	−	0.565299i	−0.149801	−	0.0620496i	0.306523	−	0.951863i	$-0.400834\pi$
$83$	−1.36475	−	0.565299i	−0.149801	−	0.0620496i	−0.456324	+	0.889814i	$0.650834\pi$
$84$	−3.60176			−0.392984
$85$	8.42749	−	3.73864i	0.914089	−	0.405513i
$86$	9.00580			0.971120
$87$	0.491103	+	0.203422i	0.0526518	+	0.0218091i
$88$	1.55578	+	2.32838i	0.165846	+	0.248206i
$89$	7.49831	+	7.49831i	0.794819	+	0.794819i	0.982273	−	0.187454i	$-0.0600236\pi$
$89$	7.49831	+	7.49831i	0.794819	+	0.794819i	−0.187454	+	0.982273i	$0.560024\pi$
$90$	1.19821	+	4.51585i	0.126302	+	0.476012i
$91$	4.23331	+	21.2823i	0.443772	+	2.23099i
$92$	−0.932261	−	4.68679i	−0.0971949	−	0.488632i
$93$	−1.86208	−	4.49545i	−0.193088	−	0.466157i
$94$	−2.14790	+	5.18549i	−0.221539	+	0.534843i
$95$	0.691097	+	0.0927014i	0.0709051	+	0.00951097i
$96$	0.935903	−	0.186163i	0.0955202	−	0.0190002i
$97$	−3.04671	+	15.3169i	−0.309347	+	1.55519i	0.443059	+	0.896492i	$0.353893\pi$
$97$	−3.04671	+	15.3169i	−0.309347	+	1.55519i	−0.752406	+	0.658699i	$0.771107\pi$
$98$	7.24674			0.732031
$99$	−1.14149	+	5.73865i	−0.114724	+	0.576756i
$100$	1.31766	−	4.82325i	0.131766	−	0.482325i
$101$			5.19202i			0.516626i	0.966061	+	0.258313i	$0.0831665\pi$
$101$			5.19202i			0.516626i	−0.966061	+	0.258313i	$0.916833\pi$
$102$	1.64325	−	3.57483i	0.162706	−	0.353961i
$103$	10.3087	−	10.3087i	1.01575	−	1.01575i	0.0158769	−	0.999874i	$-0.494946\pi$
$103$	10.3087	−	10.3087i	1.01575	−	1.01575i	0.999874	−	0.0158769i	$-0.00505400\pi$
$104$	−2.20002	−	5.31132i	−0.215730	−	0.520818i
$105$	2.06548	+	7.78442i	0.201570	+	0.759681i
$106$	4.66044	−	4.66044i	0.452662	−	0.452662i
$107$	−14.1573	−	2.81607i	−1.36864	−	0.272240i	−0.544565	−	0.838719i	$-0.683305\pi$
$107$	−14.1573	−	2.81607i	−1.36864	−	0.272240i	−0.824076	+	0.566479i	$0.808305\pi$
$108$	4.03806	+	2.69814i	0.388562	+	0.259629i
$109$	4.51551	−	6.75794i	0.432508	−	0.647293i	−0.549641	−	0.835401i	$-0.685235\pi$
$109$	4.51551	−	6.75794i	0.432508	−	0.647293i	0.982148	+	0.188108i	$0.0602354\pi$
$110$	4.14011	−	4.69771i	0.394744	−	0.447909i
$111$	−9.08064	−	3.76132i	−0.861896	−	0.357009i
$112$	−3.70196	+	0.736366i	−0.349802	+	0.0695800i
$113$	−2.35754	+	3.52830i	−0.221779	+	0.331915i	−0.925628	−	0.378434i	$-0.876463\pi$
$113$	−2.35754	+	3.52830i	−0.221779	+	0.331915i	0.703850	+	0.710349i	$0.251463\pi$
$114$	0.247417	−	0.165319i	0.0231727	−	0.0154835i
$115$	−9.59486	+	4.70258i	−0.894725	+	0.438518i
$116$	0.546354	+	0.108677i	0.0507277	+	0.0100904i
$117$	4.59679	−	11.0976i	0.424973	−	1.02598i
$118$	−2.40926	−	2.40926i	−0.221790	−	0.221790i
$119$	−6.49986	+	14.1402i	−0.595842	+	1.29623i
$120$	−0.939056	−	1.91599i	−0.0857237	−	0.174905i
$121$	−2.91779	+	1.20859i	−0.265254	+	0.109872i
$122$	−8.48713	+	5.67092i	−0.768388	+	0.513421i
$123$		−	8.84592i		−	0.797610i
$124$	−2.83296	−	4.23982i	−0.254407	−	0.380747i
$125$	−11.1800	−	0.0818737i	−0.999973	−	0.00732300i
$126$	−6.55740	−	4.38152i	−0.584180	−	0.390336i
$127$	18.5435	−	7.68099i	1.64547	−	0.681577i	0.648640	−	0.761095i	$-0.275338\pi$
$127$	18.5435	−	7.68099i	1.64547	−	0.681577i	0.996833	+	0.0795178i	$0.0253380\pi$
$128$	0.923880	−	0.382683i	0.0816602	−	0.0338248i
$129$	−7.14538	−	4.77439i	−0.629116	−	0.420362i
$130$	−10.2176	+	7.80071i	−0.896145	+	0.684167i
$131$	9.72499	+	14.5545i	0.849677	+	1.27163i	0.960637	+	0.277806i	$0.0896073\pi$
$131$	9.72499	+	14.5545i	0.849677	+	1.27163i	−0.110960	+	0.993825i	$0.535393\pi$
$132$		−	2.67218i		−	0.232583i
$133$	−0.978657	+	0.653918i	−0.0848603	+	0.0567019i
$134$	−2.53732	+	1.05099i	−0.219191	+	0.0907921i
$135$	3.51577	−	10.2747i	0.302590	−	0.884302i
$136$	0.958103	−	4.01024i	0.0821567	−	0.343875i
$137$	0.812756	+	0.812756i	0.0694385	+	0.0694385i	0.740973	−	0.671535i	$-0.234365\pi$
$137$	0.812756	+	0.812756i	0.0694385	+	0.0694385i	−0.671535	+	0.740973i	$0.734365\pi$
$138$	−1.74501	+	4.21283i	−0.148545	+	0.358620i
$139$	6.48365	+	1.28968i	0.549936	+	0.109389i	0.462234	−	0.886758i	$-0.347048\pi$
$139$	6.48365	+	1.28968i	0.549936	+	0.109389i	0.0877014	+	0.996147i	$0.472048\pi$
$140$	3.71443	+	7.57870i	0.313927	+	0.640517i
$141$	4.45326	−	2.97557i	0.375032	−	0.250588i
$142$	−2.22800	+	3.33444i	−0.186970	+	0.279820i
$143$	−15.7895	+	3.14073i	−1.32039	+	0.262641i
$144$	1.93038	+	0.799590i	0.160865	+	0.0666325i
$145$	−0.0784331	−	1.24315i	−0.00651351	−	0.103238i
$146$	0.476681	−	0.713404i	0.0394504	−	0.0590417i
$147$	−5.74971	−	3.84183i	−0.474228	−	0.316869i
$148$	−10.1022	−	2.00946i	−0.830400	−	0.165177i
$149$	−6.06959	+	6.06959i	−0.497240	+	0.497240i	−0.910578	−	0.413338i	$-0.864363\pi$
$149$	−6.06959	+	6.06959i	−0.497240	+	0.497240i	0.413338	+	0.910578i	$0.364363\pi$
$150$	−3.60249	+	3.12832i	−0.294142	+	0.255426i
$151$	−1.69264	−	4.08639i	−0.137745	−	0.332545i	0.839922	−	0.542708i	$-0.182601\pi$
$151$	−1.69264	−	4.08639i	−0.137745	−	0.332545i	−0.977667	+	0.210162i	$0.932601\pi$
$152$	0.220501	−	0.220501i	0.0178850	−	0.0178850i
$153$	7.34048	−	4.50938i	0.593442	−	0.364562i
$154$			10.5698i			0.851737i
$155$	−7.53885	+	8.55420i	−0.605535	+	0.687090i
$156$	−1.07024	+	5.38044i	−0.0856875	+	0.430780i
$157$	−13.3044			−1.06181			−0.530903	−	0.847432i	$-0.678147\pi$
$157$	−13.3044			−1.06181			−0.530903	+	0.847432i	$0.678147\pi$
$158$	−0.872680	+	4.38726i	−0.0694267	+	0.349031i
$159$	−6.16841	+	1.22697i	−0.489187	+	0.0973053i
$160$	−1.35690	−	1.77731i	−0.107272	−	0.140509i
$161$	6.90238	−	16.6638i	0.543984	−	1.31329i
$162$	0.625305	+	1.50962i	0.0491286	+	0.118607i
$163$	2.97940	+	14.9784i	0.233364	+	1.17320i	0.902710	+	0.430250i	$0.141575\pi$
$163$	2.97940	+	14.9784i	0.233364	+	1.17320i	−0.669345	+	0.742951i	$0.733425\pi$
$164$	−1.80851	−	9.09201i	−0.141221	−	0.709967i
$165$	−5.77532	+	1.53239i	−0.449608	+	0.119297i
$166$	1.04454	+	1.04454i	0.0810717	+	0.0810717i
$167$	0.262363	+	0.392653i	0.0203022	+	0.0303844i	0.841482	−	0.540285i	$-0.181684\pi$
$167$	0.262363	+	0.392653i	0.0203022	+	0.0303844i	−0.821180	+	0.570670i	$0.806684\pi$
$168$	3.32759	+	1.37833i	0.256729	+	0.106341i
$169$	20.0502			1.54232
$170$	−9.21670	+	0.228994i	−0.706889	+	0.0175630i
$171$	0.651559			0.0498260
$172$	−8.32027	−	3.44637i	−0.634415	−	0.262783i
$173$	−4.97303	−	7.44267i	−0.378093	−	0.565856i	0.592806	−	0.805345i	$-0.298020\pi$
$173$	−4.97303	−	7.44267i	−0.378093	−	0.565856i	−0.970899	+	0.239489i	$0.923020\pi$
$174$	−0.375874	−	0.375874i	−0.0284949	−	0.0284949i
$175$	14.2496	−	12.3740i	1.07717	−	0.935389i
$176$	−0.546316	−	2.74651i	−0.0411801	−	0.207026i
$177$	0.634295	+	3.18882i	0.0476765	+	0.239686i
$178$	−4.05806	−	9.79701i	−0.304164	−	0.734317i
$179$	2.79239	−	6.74143i	0.208713	−	0.503878i	−0.784508	−	0.620119i	$-0.787084\pi$
$179$	2.79239	−	6.74143i	0.208713	−	0.503878i	0.993221	+	0.116241i	$0.0370844\pi$
$180$	0.621137	−	4.63063i	0.0462968	−	0.345147i
$181$	−2.13090	+	0.423862i	−0.158389	+	0.0315054i	−0.273648	−	0.961830i	$-0.588230\pi$
$181$	−2.13090	+	0.423862i	−0.158389	+	0.0315054i	0.115259	+	0.993335i	$0.463230\pi$
$182$	4.23331	−	21.2823i	0.313794	−	1.57755i
$183$	9.74028			0.720022
$184$	−0.932261	+	4.68679i	−0.0687272	+	0.345515i
$185$	1.45025	+	22.9862i	0.106625	+	1.68998i
$186$			4.86584i			0.356781i
$187$	−10.4908	−	4.82230i	−0.767160	−	0.352642i
$188$	3.96880	−	3.96880i	0.289455	−	0.289455i
$189$	7.01493	+	16.9355i	0.510261	+	1.23188i
$190$	−0.603015	−	0.350116i	−0.0437473	−	0.0254001i
$191$	9.99830	−	9.99830i	0.723451	−	0.723451i	−0.245855	−	0.969307i	$-0.579069\pi$
$191$	9.99830	−	9.99830i	0.723451	−	0.723451i	0.969307	+	0.245855i	$0.0790688\pi$
$192$	−0.935903	−	0.186163i	−0.0675430	−	0.0134351i
$193$	1.10146	+	0.735974i	0.0792850	+	0.0529766i	0.594581	−	0.804036i	$-0.297318\pi$
$193$	1.10146	+	0.735974i	0.0792850	+	0.0529766i	−0.515296	+	0.857012i	$0.672318\pi$
$194$	8.67631	−	12.9850i	0.622922	−	0.932269i
$195$	12.2424	−	0.772401i	0.876696	−	0.0553128i
$196$	−6.69512	−	2.77321i	−0.478223	−	0.198086i
$197$	1.71612	−	0.341358i	0.122269	−	0.0243208i	−0.133577	−	0.991038i	$-0.542646\pi$
$197$	1.71612	−	0.341358i	0.122269	−	0.0243208i	0.255845	+	0.966718i	$0.417646\pi$
$198$	3.25068	−	4.86499i	0.231016	−	0.345740i
$199$	−2.83249	+	1.89261i	−0.200790	+	0.134164i	−0.651900	−	0.758305i	$-0.726028\pi$
$199$	−2.83249	+	1.89261i	−0.200790	+	0.134164i	0.451111	+	0.892468i	$0.351028\pi$
$200$	−3.06314	+	3.95186i	−0.216596	+	0.279439i
$201$	2.57035	+	0.511274i	0.181298	+	0.0360625i
$202$	1.98690	−	4.79680i	0.139798	−	0.337502i
$203$	1.48677	+	1.48677i	0.104351	+	0.104351i
$204$	−2.88619	+	2.67387i	−0.202074	+	0.187208i
$205$	−18.6133	+	9.12264i	−1.30001	+	0.637153i
$206$	−13.4690	+	5.57905i	−0.938431	+	0.388711i
$207$	−8.30186	+	5.54713i	−0.577019	+	0.385552i
$208$			5.74893i			0.398617i
$209$	−0.485147	−	0.726074i	−0.0335583	−	0.0502236i
$210$	1.07072	−	7.98229i	0.0738865	−	0.550830i
$211$	−0.412646	−	0.275721i	−0.0284077	−	0.0189814i	0.541285	−	0.840839i	$-0.317938\pi$
$211$	−0.412646	−	0.275721i	−0.0284077	−	0.0189814i	−0.569693	+	0.821858i	$0.692938\pi$
$212$	−6.08916	+	2.52221i	−0.418205	+	0.173226i
$213$	3.53549	−	1.46445i	0.242247	−	0.100342i
$214$	12.0020	+	8.01948i	0.820440	+	0.548201i
$215$	−2.67721	+	19.9588i	−0.182584	+	1.36118i
$216$	−2.69814	−	4.03806i	−0.183585	−	0.274755i
$217$		−	19.2468i		−	1.30656i
$218$	−6.75794	+	4.51551i	−0.457706	+	0.305829i
$219$	−0.756417	+	0.313318i	−0.0511140	+	0.0211721i
$220$	−5.62270	+	2.75577i	−0.379082	+	0.185794i
$221$	19.1918	+	13.9114i	1.29098	+	0.935782i
$222$	6.95002	+	6.95002i	0.466455	+	0.466455i
$223$	9.42022	−	22.7424i	0.630824	−	1.52294i	−0.207764	−	0.978179i	$-0.566619\pi$
$223$	9.42022	−	22.7424i	0.630824	−	1.52294i	0.838588	−	0.544766i	$-0.183381\pi$
$224$	3.70196	+	0.736366i	0.247348	+	0.0492005i
$225$	−10.3643	+	1.31304i	−0.690953	+	0.0875362i
$226$	3.52830	−	2.35754i	0.234699	−	0.156821i
$227$	−13.2991	+	19.9035i	−0.882694	+	1.32104i	0.0636798	+	0.997970i	$0.479716\pi$
$227$	−13.2991	+	19.9035i	−0.882694	+	1.32104i	−0.946374	+	0.323074i	$0.895284\pi$
$228$	−0.291848	+	0.0580523i	−0.0193281	+	0.00384460i
$229$	2.19707	+	0.910057i	0.145187	+	0.0601383i	0.454094	−	0.890954i	$-0.349963\pi$
$229$	2.19707	+	0.910057i	0.145187	+	0.0601383i	−0.308907	+	0.951092i	$0.599963\pi$
$230$	10.6641	−	0.672823i	0.703170	−	0.0443646i
$231$	5.60353	−	8.38628i	0.368685	−	0.551776i
$232$	−0.463177	−	0.309485i	−0.0304090	−	0.0203187i
$233$	10.5416	+	2.09685i	0.690602	+	0.137369i	0.527901	−	0.849306i	$-0.322979\pi$
$233$	10.5416	+	2.09685i	0.690602	+	0.137369i	0.162701	+	0.986675i	$0.447979\pi$
$234$	−8.49375	+	8.49375i	−0.555254	+	0.555254i
$235$	−10.8537	−	6.30174i	−0.708015	−	0.411080i
$236$	1.30388	+	3.14785i	0.0848755	+	0.204908i
$237$	3.01829	−	3.01829i	0.196059	−	0.196059i
$238$	11.4163	−	10.5765i	0.740011	−	0.685572i
$239$		−	20.1117i		−	1.30091i	−0.759543	−	0.650457i	$-0.774577\pi$
$239$		−	20.1117i		−	1.30091i	0.759543	−	0.650457i	$-0.225423\pi$
$240$	0.134356	+	2.12951i	0.00867262	+	0.137459i
$241$	−0.884741	+	4.44789i	−0.0569912	+	0.286514i	−0.998762	−	0.0497410i	$-0.984160\pi$
$241$	−0.884741	+	4.44789i	−0.0569912	+	0.286514i	0.941771	+	0.336255i	$0.109160\pi$
$242$	3.15820			0.203016
$243$	3.14658	−	15.8189i	0.201853	−	1.01478i
$244$	10.0112	−	1.99136i	0.640904	−	0.127484i
$245$	−2.15428	+	16.0604i	−0.137632	+	1.02606i
$246$	−3.38519	+	8.17256i	−0.215832	+	0.521064i
$247$	0.686046	+	1.65626i	0.0436520	+	0.105385i
$248$	0.994802	+	5.00121i	0.0631700	+	0.317577i
$249$	−0.274999	−	1.38251i	−0.0174273	−	0.0876132i
$250$	10.2977	+	4.35406i	0.651282	+	0.275375i
$251$	−2.34040	−	2.34040i	−0.147725	−	0.147725i	0.629376	−	0.777101i	$-0.283311\pi$
$251$	−2.34040	−	2.34040i	−0.147725	−	0.147725i	−0.777101	+	0.629376i	$0.783311\pi$
$252$	4.38152	+	6.55740i	0.276010	+	0.413077i
$253$	12.3630	+	5.12094i	0.777257	+	0.321950i
$254$	−20.0714			−1.25939
$255$	7.43412	+	4.70451i	0.465542	+	0.294608i
$256$	−1.00000			−0.0625000
$257$	13.1832	+	5.46064i	0.822343	+	0.340626i	0.753867	−	0.657027i	$-0.228186\pi$
$257$	13.1832	+	5.46064i	0.822343	+	0.340626i	0.0684760	+	0.997653i	$0.478186\pi$
$258$	4.77439	+	7.14538i	0.297241	+	0.444852i
$259$	−27.4908	−	27.4908i	−1.70819	−	1.70819i
$260$	12.4251	−	3.29680i	0.770569	−	0.204459i
$261$	−0.227072	−	1.14157i	−0.0140554	−	0.0706613i
$262$	−3.41496	−	17.1682i	−0.210977	−	1.06065i
$263$	−2.13884	−	5.16361i	−0.131886	−	0.318402i	0.844116	−	0.536160i	$-0.180126\pi$
$263$	−2.13884	−	5.16361i	−0.131886	−	0.318402i	−0.976003	+	0.217758i	$0.930126\pi$
$264$	−1.02260	+	2.46877i	−0.0629365	+	0.151942i
$265$	8.94313	+	11.7140i	0.549372	+	0.719586i
$266$	1.15440	−	0.229625i	0.0707811	−	0.0140792i
$267$	−1.97411	+	9.92451i	−0.120813	+	0.607370i
$268$	2.74638			0.167762
$269$	1.33070	−	6.68989i	0.0811343	−	0.407890i	−0.918780	−	0.394771i	$-0.870824\pi$
$269$	1.33070	−	6.68989i	0.0811343	−	0.407890i	0.999914	−	0.0131189i	$-0.00417601\pi$
$270$	−7.18009	+	8.14712i	−0.436967	+	0.495818i
$271$			0.568062i			0.0345073i	0.999851	+	0.0172537i	$0.00549229\pi$
$271$			0.568062i			0.0345073i	−0.999851	+	0.0172537i	$0.994508\pi$
$272$	−2.41983	+	3.33833i	−0.146723	+	0.202416i
$273$	−14.6415	+	14.6415i	−0.886146	+	0.886146i
$274$	−0.439861	−	1.06192i	−0.0265729	−	0.0641528i
$275$	9.18040	+	10.5719i	0.553599	+	0.637510i
$276$	3.22436	−	3.22436i	0.194084	−	0.194084i
$277$	19.7796	+	3.93441i	1.18844	+	0.236396i	0.749429	−	0.662085i	$-0.230328\pi$
$277$	19.7796	+	3.93441i	1.18844	+	0.236396i	0.439013	+	0.898480i	$0.355328\pi$
$278$	−5.49657	−	3.67269i	−0.329662	−	0.220273i
$279$	−5.91926	+	8.85880i	−0.354377	+	0.530363i
$280$	−0.531443	−	8.42326i	−0.0317598	−	0.503386i
$281$	−0.143711	−	0.0595269i	−0.00857306	−	0.00355108i	0.378393	−	0.925645i	$-0.376477\pi$
$281$	−0.143711	−	0.0595269i	−0.00857306	−	0.00355108i	−0.386966	+	0.922094i	$0.626477\pi$
$282$	−5.25298	+	1.04488i	−0.312810	+	0.0622218i
$283$	7.66884	−	11.4772i	0.455865	−	0.682250i	−0.530339	−	0.847786i	$-0.677935\pi$
$283$	7.66884	−	11.4772i	0.455865	−	0.682250i	0.986204	+	0.165535i	$0.0529352\pi$
$284$	3.33444	−	2.22800i	0.197863	−	0.132208i
$285$	0.292832	+	0.597476i	0.0173458	+	0.0353914i
$286$	15.7895	+	3.14073i	0.933654	+	0.185715i
$287$	13.3901	−	32.3265i	0.790392	−	1.90818i
$288$	−1.47745	−	1.47745i	−0.0870595	−	0.0870595i
$289$	5.28889	+	16.1563i	0.311111	+	0.950373i
$290$	−0.403269	+	1.17853i	−0.0236808	+	0.0692059i
$291$	−13.7679	+	5.70286i	−0.807089	+	0.334307i
$292$	−0.713404	+	0.476681i	−0.0417488	+	0.0278957i
$293$			23.1984i			1.35527i	0.735400	+	0.677633i	$0.236994\pi$
$293$			23.1984i			1.35527i	−0.735400	+	0.677633i	$0.763006\pi$
$294$	3.84183	+	5.74971i	0.224060	+	0.335330i
$295$	6.05566	−	4.62323i	0.352574	−	0.269175i
$296$	8.56427	+	5.72246i	0.497788	+	0.332611i
$297$	−12.5646	+	5.20444i	−0.729073	+	0.301992i
$298$	7.93030	−	3.28484i	0.459390	−	0.190286i
$299$	−22.8420	−	15.2626i	−1.32099	−	0.882657i
$300$	4.52542	−	1.51157i	0.261275	−	0.0872708i
$301$	−18.8851	−	28.2635i	−1.08852	−	1.62908i
$302$			4.42307i			0.254519i
$303$	−4.11946	+	2.75253i	−0.236657	+	0.158129i
$304$	−0.288099	+	0.119335i	−0.0165236	+	0.00684430i
$305$	−10.0450	−	20.4952i	−0.575173	−	1.17355i
$306$	−8.50738	+	1.35704i	−0.486335	+	0.0775771i
$307$	5.80418	+	5.80418i	0.331262	+	0.331262i	0.853066	−	0.521803i	$-0.174741\pi$
$307$	5.80418	+	5.80418i	0.331262	+	0.331262i	−0.521803	+	0.853066i	$0.674741\pi$
$308$	4.04488	−	9.76520i	0.230478	−	0.556424i
$309$	13.6443	+	2.71402i	0.776198	+	0.154395i
$310$	10.2385	−	5.01806i	0.581510	−	0.285006i
$311$	−19.7609	+	13.2038i	−1.12054	+	0.748721i	−0.970773	−	0.240000i	$-0.922852\pi$
$311$	−19.7609	+	13.2038i	−1.12054	+	0.748721i	−0.149767	+	0.988721i	$0.547852\pi$
$312$	3.04777	−	4.56132i	0.172546	−	0.258234i
$313$	−0.321242	+	0.0638990i	−0.0181577	+	0.00361179i	−0.204161	−	0.978937i	$-0.565447\pi$
$313$	−0.321242	+	0.0638990i	−0.0181577	+	0.00361179i	0.186003	+	0.982549i	$0.440447\pi$
$314$	12.2917	+	5.09137i	0.693659	+	0.287323i
$315$	11.6598	−	13.2301i	0.656953	−	0.745433i
$316$	2.48518	−	3.71934i	0.139802	−	0.209229i
$317$	−0.124348	−	0.0830869i	−0.00698410	−	0.00466663i	0.552073	−	0.833796i	$-0.313837\pi$
$317$	−0.124348	−	0.0830869i	−0.00698410	−	0.00466663i	−0.559057	+	0.829129i	$0.688837\pi$
$318$	6.16841	+	1.22697i	0.345907	+	0.0688052i
$319$	−1.10305	+	1.10305i	−0.0617587	+	0.0617587i
$320$	0.573463	+	2.16128i	0.0320576	+	0.120819i
$321$	−5.27113	−	12.7256i	−0.294206	−	0.710276i
$322$	−12.7539	+	12.7539i	−0.710749	+	0.710749i
$323$	−0.298771	+	1.25054i	−0.0166241	+	0.0695818i
$324$		−	1.63400i		−	0.0907778i
$325$	−14.2506	−	24.9635i	−0.790482	−	1.38472i
$326$	2.97940	−	14.9784i	0.165013	−	0.829579i
$327$	7.75577			0.428895
$328$	−1.80851	+	9.09201i	−0.0998585	+	0.502022i
$329$	20.7781	−	4.13303i	1.14554	−	0.227861i
$330$	5.92213	+	0.794374i	0.326002	+	0.0437289i
$331$	−11.8192	+	28.5341i	−0.649643	+	1.56838i	0.163646	+	0.986519i	$0.447674\pi$
$331$	−11.8192	+	28.5341i	−0.649643	+	1.56838i	−0.813290	+	0.581859i	$0.802326\pi$
$332$	−0.565299	−	1.36475i	−0.0310248	−	0.0749005i
$333$	4.19863	+	21.1079i	0.230083	+	1.15671i
$334$	−0.0921295	−	0.463166i	−0.00504110	−	0.0253433i
$335$	−1.57495	−	5.93570i	−0.0860486	−	0.324302i
$336$	−2.54683	−	2.54683i	−0.138941	−	0.138941i
$337$	−1.83165	−	2.74125i	−0.0997761	−	0.149325i	0.778223	−	0.627989i	$-0.216122\pi$
$337$	−1.83165	−	2.74125i	−0.0997761	−	0.149325i	−0.877999	+	0.478663i	$0.841122\pi$
$338$	−18.5240	−	7.67288i	−1.00757	−	0.417349i
$339$	−4.04927			−0.219926
$340$	8.60275	+	3.31552i	0.466550	+	0.179809i
$341$	14.2794			0.773271
$342$	−0.601962	−	0.249341i	−0.0325504	−	0.0134828i
$343$	−0.517415	−	0.774367i	−0.0279378	−	0.0418119i
$344$	6.36806	+	6.36806i	0.343343	+	0.343343i
$345$	−8.81780	−	5.11970i	−0.474735	−	0.275635i
$346$	1.74630	+	8.77923i	0.0938815	+	0.471974i
$347$	0.502701	+	2.52725i	0.0269864	+	0.135670i	0.991930	−	0.126788i	$-0.0404669\pi$
$347$	0.502701	+	2.52725i	0.0269864	+	0.135670i	−0.964943	+	0.262458i	$0.915467\pi$
$348$	0.203422	+	0.491103i	0.0109045	+	0.0263259i
$349$	−2.63485	+	6.36108i	−0.141040	+	0.340501i	−0.978577	−	0.205879i	$-0.933995\pi$
$349$	−2.63485	+	6.36108i	−0.141040	+	0.340501i	0.837537	+	0.546380i	$0.183995\pi$
$350$	−17.9003	+	5.97902i	−0.956810	+	0.319592i
$351$	27.3834	−	5.44689i	1.46162	−	0.290734i
$352$	−0.546316	+	2.74651i	−0.0291187	+	0.146390i
$353$	−25.0889			−1.33535			−0.667674	−	0.744454i	$-0.732710\pi$
$353$	−25.0889			−1.33535			−0.667674	+	0.744454i	$0.732710\pi$
$354$	0.634295	−	3.18882i	0.0337124	−	0.169484i
$355$	−6.72752	−	5.92899i	−0.357060	−	0.314678i
$356$			10.6042i			0.562022i
$357$	−14.6650	+	2.33927i	−0.776156	+	0.123808i
$358$	−5.15966	+	5.15966i	−0.272697	+	0.272697i
$359$	−3.72132	−	8.98407i	−0.196404	−	0.474161i	0.794741	−	0.606949i	$-0.207607\pi$
$359$	−3.72132	−	8.98407i	−0.196404	−	0.474161i	−0.991144	+	0.132788i	$0.957607\pi$
$360$	−2.34592	+	4.04045i	−0.123641	+	0.212950i
$361$	13.3663	−	13.3663i	0.703488	−	0.703488i
$362$	2.13090	+	0.423862i	0.111998	+	0.0222777i
$363$	−2.50578	−	1.67431i	−0.131519	−	0.0878783i
$364$	−12.0555	+	18.0423i	−0.631878	+	0.945672i
$365$	1.43935	+	1.26851i	0.0753392	+	0.0663968i
$366$	−8.99884	−	3.72744i	−0.470377	−	0.194837i
$367$	15.2095	−	3.02536i	0.793931	−	0.157923i	0.218569	−	0.975822i	$-0.429861\pi$
$367$	15.2095	−	3.02536i	0.793931	−	0.157923i	0.575362	+	0.817899i	$0.304861\pi$
$368$	2.65485	−	3.97327i	0.138394	−	0.207121i
$369$	−16.1050	+	10.7610i	−0.838392	+	0.560195i
$370$	7.45657	−	21.7914i	0.387648	−	1.13288i
$371$	−24.3991	−	4.85328i	−1.26674	−	0.251970i
$372$	1.86208	−	4.49545i	0.0965442	−	0.233078i
$373$	16.1984	+	16.1984i	0.838724	+	0.838724i	0.988691	−	0.149967i	$-0.0479169\pi$
$373$	16.1984	+	16.1984i	0.838724	+	0.838724i	−0.149967	+	0.988691i	$0.547917\pi$
$374$	7.84678	+	8.46987i	0.405748	+	0.437966i
$375$	−5.86210	−	8.91388i	−0.302717	−	0.460311i
$376$	−5.18549	+	2.14790i	−0.267421	+	0.110770i
$377$	2.66277	−	1.77921i	0.137140	−	0.0916338i
$378$		−	18.3309i		−	0.942840i
$379$	12.1871	+	18.2394i	0.626012	+	0.936893i	0.999955	+	0.00944122i	$0.00300528\pi$
$379$	12.1871	+	18.2394i	0.626012	+	0.936893i	−0.373944	+	0.927451i	$0.621995\pi$
$380$	0.423130	+	0.554229i	0.0217061	+	0.0284314i
$381$	15.9250	+	10.6408i	0.815865	+	0.545144i
$382$	−13.0634	+	5.41104i	−0.668382	+	0.276853i
$383$	−23.4891	+	9.72950i	−1.20024	+	0.497154i	−0.891075	−	0.453855i	$-0.850048\pi$
$383$	−23.4891	+	9.72950i	−1.20024	+	0.497154i	−0.309161	+	0.951010i	$0.600048\pi$
$384$	0.793420	+	0.530147i	0.0404891	+	0.0270539i
$385$	−23.4249	−	3.14214i	−1.19385	−	0.160138i
$386$	−0.735974	−	1.10146i	−0.0374601	−	0.0560630i
$387$			18.8170i			0.956520i
$388$	−12.9850	+	8.67631i	−0.659214	+	0.440473i
$389$	−14.6940	+	6.08645i	−0.745015	+	0.308595i	−0.722706	−	0.691156i	$-0.757102\pi$
$389$	−14.6940	+	6.08645i	−0.745015	+	0.308595i	−0.0223090	+	0.999751i	$0.507102\pi$
$390$	−11.6061	−	3.97135i	−0.587697	−	0.201097i
$391$	−6.83980	−	18.4774i	−0.345904	−	0.934442i
$392$	5.12422	+	5.12422i	0.258812	+	0.258812i
$393$	−6.39215	+	15.4320i	−0.322441	+	0.778442i
$394$	−1.71612	−	0.341358i	−0.0864571	−	0.0171974i
$395$	−9.46369	−	3.23828i	−0.476170	−	0.162935i
$396$	−4.86499	+	3.25068i	−0.244475	+	0.163353i
$397$	−7.31860	+	10.9531i	−0.367310	+	0.549718i	−0.968381	−	0.249478i	$-0.919741\pi$
$397$	−7.31860	+	10.9531i	−0.367310	+	0.549718i	0.601071	+	0.799196i	$0.294741\pi$
$398$	3.34115	−	0.664596i	0.167477	−	0.0333132i
$399$	−1.03766	−	0.429814i	−0.0519481	−	0.0215176i
$400$	4.34228	−	2.47883i	0.217114	−	0.123942i
$401$	2.27205	−	3.40036i	0.113461	−	0.169806i	−0.770393	−	0.637569i	$-0.779940\pi$
$401$	2.27205	−	3.40036i	0.113461	−	0.169806i	0.883854	+	0.467763i	$0.154940\pi$
$402$	−2.17903	−	1.45598i	−0.108680	−	0.0726179i
$403$	−28.7516	−	5.71905i	−1.43222	−	0.284886i
$404$	−3.67132	+	3.67132i	−0.182655	+	0.182655i
$405$	−3.53153	+	0.937038i	−0.175483	+	0.0465618i
$406$	−0.804633	−	1.94256i	−0.0399333	−	0.0964074i
$407$	20.3956	−	20.3956i	1.01097	−	1.01097i
$408$	3.68974	−	1.36584i	0.182669	−	0.0676190i
$409$		−	26.3322i		−	1.30204i	−0.759060	−	0.651021i	$-0.774341\pi$
$409$		−	26.3322i		−	1.30204i	0.759060	−	0.651021i	$-0.225659\pi$
$410$	20.6875	−	1.30522i	1.02168	−	0.0644604i
$411$	−0.213977	+	1.07574i	−0.0105547	+	0.0530622i
$412$	14.5788			0.718244
$413$	−2.50895	+	12.6133i	−0.123457	+	0.620662i
$414$	9.79272	−	1.94789i	0.481286	−	0.0957337i
$415$	−2.62544	+	2.00440i	−0.128878	+	0.0983923i
$416$	2.20002	−	5.31132i	0.107865	−	0.260409i
$417$	2.41403	+	5.82798i	0.118215	+	0.285397i
$418$	0.170361	+	0.856462i	0.00833263	+	0.0418910i
$419$	−1.24149	−	6.24139i	−0.0606508	−	0.304912i	0.938538	−	0.345175i	$-0.112180\pi$
$419$	−1.24149	−	6.24139i	−0.0606508	−	0.304912i	−0.999189	+	0.0402629i	$0.987180\pi$
$420$	−4.04390	+	6.96493i	−0.197322	+	0.339854i
$421$	−16.7929	−	16.7929i	−0.818436	−	0.818436i	0.167445	−	0.985881i	$-0.446448\pi$
$421$	−16.7929	−	16.7929i	−0.818436	−	0.818436i	−0.985881	+	0.167445i	$0.946448\pi$
$422$	0.275721	+	0.412646i	0.0134219	+	0.0200873i
$423$	−10.8347	−	4.48789i	−0.526802	−	0.218209i
$424$	6.59086			0.320081
$425$	2.23241	−	20.4943i	0.108288	−	0.994120i
$426$	−3.82678			−0.185408
$427$	35.5949	+	14.7439i	1.72256	+	0.713506i
$428$	−8.01948	−	12.0020i	−0.387636	−	0.580139i
$429$	−10.8627	−	10.8627i	−0.524455	−	0.524455i
$430$	10.1113	−	17.4150i	0.487611	−	0.839827i
$431$	4.77925	+	24.0269i	0.230208	+	1.15734i	0.906990	+	0.421152i	$0.138374\pi$
$431$	4.77925	+	24.0269i	0.230208	+	1.15734i	−0.676782	+	0.736184i	$0.736626\pi$
$432$	0.947462	+	4.76321i	0.0455848	+	0.229170i
$433$	−7.10985	−	17.1647i	−0.341678	−	0.824883i	−0.997546	−	0.0700080i	$-0.977698\pi$
$433$	−7.10985	−	17.1647i	−0.341678	−	0.824883i	0.655869	−	0.754875i	$-0.272302\pi$
$434$	−7.36544	+	17.7817i	−0.353552	+	0.853551i
$435$	0.944758	−	0.721281i	0.0452977	−	0.0345828i
$436$	7.97153	−	1.58564i	0.381767	−	0.0759382i
$437$	0.290713	−	1.46151i	0.0139067	−	0.0699135i
$438$	0.818740			0.0391209
$439$	6.96095	−	34.9950i	0.332228	−	1.67022i	−0.348210	−	0.937417i	$-0.613210\pi$
$439$	6.96095	−	34.9950i	0.332228	−	1.67022i	0.680438	−	0.732806i	$-0.261790\pi$
$440$	6.24929	−	0.394282i	0.297923	−	0.0187967i
$441$			15.1416i			0.721026i
$442$	−12.4073	−	20.1969i	−0.590154	−	0.960666i
$443$	−19.6949	+	19.6949i	−0.935735	+	0.935735i	−0.998056	−	0.0623210i	$-0.980150\pi$
$443$	−19.6949	+	19.6949i	−0.935735	+	0.935735i	0.0623210	+	0.998056i	$0.480150\pi$
$444$	−3.76132	−	9.08064i	−0.178505	−	0.430948i
$445$	22.9187	−	6.08112i	1.08645	−	0.288273i
$446$	−17.4063	+	17.4063i	−0.824212	+	0.824212i
$447$	−8.03351	−	1.59796i	−0.379972	−	0.0755811i
$448$	−3.13837	−	2.09699i	−0.148274	−	0.0990736i
$449$	10.1228	−	15.1498i	0.477724	−	0.714965i	−0.511836	−	0.859083i	$-0.671034\pi$
$449$	10.1228	−	15.1498i	0.477724	−	0.714965i	0.989561	+	0.144118i	$0.0460345\pi$
$450$	10.0778	+	2.75315i	0.475074	+	0.129785i
$451$	23.9833	+	9.93422i	1.12933	+	0.467784i
$452$	−4.16192	+	0.827857i	−0.195760	+	0.0389391i
$453$	2.34488	−	3.50936i	0.110172	−	0.164884i
$454$	19.9035	−	13.2991i	0.934120	−	0.624159i
$455$	45.9078	+	15.7087i	2.15219	+	0.736434i
$456$	0.291848	+	0.0580523i	0.0136671	+	0.00271855i
$457$	−9.80059	+	23.6607i	−0.458452	+	1.10680i	0.510572	+	0.859835i	$0.329434\pi$
$457$	−9.80059	+	23.6607i	−0.458452	+	1.10680i	−0.969024	+	0.246966i	$0.920566\pi$
$458$	−1.68157	−	1.68157i	−0.0785744	−	0.0785744i
$459$	18.1939	+	8.36320i	0.849217	+	0.390361i
$460$	−10.1098	−	3.45936i	−0.471373	−	0.161294i
$461$	30.2852	−	12.5445i	1.41052	−	0.584257i	0.458061	−	0.888921i	$-0.348544\pi$
$461$	30.2852	−	12.5445i	1.41052	−	0.584257i	0.952460	+	0.304664i	$0.0985441\pi$
$462$	−8.38628	+	5.60353i	−0.390165	+	0.260700i
$463$		−	2.18733i		−	0.101654i	−0.998707	−	0.0508269i	$-0.983814\pi$
$463$		−	2.18733i		−	0.101654i	0.998707	−	0.0508269i	$-0.0161857\pi$
$464$	0.309485	+	0.463177i	0.0143675	+	0.0215024i
$465$	−10.7838	−	1.44650i	−0.500085	−	0.0670798i
$466$	−8.93672	−	5.97133i	−0.413986	−	0.276616i
$467$	−28.6355	+	11.8612i	−1.32509	+	0.548872i	−0.929252	−	0.369447i	$-0.879547\pi$
$467$	−28.6355	+	11.8612i	−1.32509	+	0.548872i	−0.395841	+	0.918319i	$0.629547\pi$
$468$	11.0976	−	4.59679i	0.512988	−	0.212486i
$469$	8.61916	+	5.75914i	0.397996	+	0.265932i
$470$	7.61591	+	9.97557i	0.351296	+	0.460139i
$471$	−7.05328	−	10.5560i	−0.324998	−	0.486394i
$472$		−	3.40721i		−	0.156829i
$473$	20.9689	−	14.0110i	0.964153	−	0.644226i
$474$	−3.94359	+	1.63349i	−0.181135	+	0.0750285i
$475$	0.955197	−	1.23233i	0.0438274	−	0.0565433i
$476$	−14.5948	+	5.40256i	−0.668950	+	0.247626i
$477$	9.73767	+	9.73767i	0.445857	+	0.445857i
$478$	−7.69640	+	18.5807i	−0.352025	+	0.849863i
$479$	−30.9583	−	6.15799i	−1.41452	−	0.281366i	−0.572100	−	0.820184i	$-0.693871\pi$
$479$	−30.9583	−	6.15799i	−1.41452	−	0.281366i	−0.842422	+	0.538818i	$0.818871\pi$
$480$	0.690799	−	2.01882i	0.0315305	−	0.0921463i
$481$	−49.2354	+	32.8980i	−2.24494	+	1.50002i
$482$	2.51953	−	3.77074i	0.114761	−	0.171753i
$483$	16.8807	−	3.35778i	0.768098	−	0.152784i
$484$	−2.91779	−	1.20859i	−0.132627	−	0.0549359i
$485$	26.1984	+	23.0887i	1.18961	+	1.04841i
$486$	−8.96069	+	13.4106i	−0.406465	+	0.608318i
$487$	16.7437	+	11.1878i	0.758732	+	0.506968i	0.873738	−	0.486396i	$-0.161689\pi$
$487$	16.7437	+	11.1878i	0.758732	+	0.506968i	−0.115007	+	0.993365i	$0.536689\pi$
$488$	−10.0112	−	1.99136i	−0.453188	−	0.0901447i
$489$	−10.3047	+	10.3047i	−0.465994	+	0.465994i
$490$	8.13633	−	14.0134i	0.367562	−	0.633063i
$491$	9.38490	+	22.6571i	0.423534	+	1.02250i	0.981297	+	0.192502i	$0.0616601\pi$
$491$	9.38490	+	22.6571i	0.423534	+	1.02250i	−0.557762	+	0.830001i	$0.688340\pi$
$492$	6.25501	−	6.25501i	0.281998	−	0.281998i
$493$	2.29514	+	0.0876443i	0.103368	+	0.00394730i
$494$		−	1.79272i		−	0.0806585i
$495$	9.81553	+	8.65047i	0.441175	+	0.388810i
$496$	0.994802	−	5.00121i	0.0446679	−	0.224561i
$497$	15.1368			0.678979
$498$	−0.274999	+	1.38251i	−0.0123230	+	0.0619519i
$499$	36.9936	−	7.35849i	1.65606	−	0.329411i	0.723473	−	0.690353i	$-0.242545\pi$
$499$	36.9936	−	7.35849i	1.65606	−	0.329411i	0.932588	+	0.360942i	$0.117545\pi$
$500$	−7.84759	−	7.96338i	−0.350955	−	0.356133i
$501$	−0.172449	+	0.416328i	−0.00770444	+	0.0186002i
$502$	1.26662	+	3.05788i	0.0565319	+	0.136480i
$503$	1.32307	+	6.65150i	0.0589926	+	0.296576i	0.999007	−	0.0445597i	$-0.0141885\pi$
$503$	1.32307	+	6.65150i	0.0589926	+	0.296576i	−0.940014	+	0.341135i	$0.889189\pi$
$504$	−1.53858	−	7.73498i	−0.0685340	−	0.344543i
$505$	10.0401	+	5.82938i	0.446779	+	0.259404i
$506$	−9.46225	−	9.46225i	−0.420649	−	0.420649i
$507$	10.6295	+	15.9082i	0.472074	+	0.706509i
$508$	18.5435	+	7.68099i	0.822737	+	0.340789i
$509$	13.5968			0.602668			0.301334	−	0.953519i	$-0.402568\pi$
$509$	13.5968			0.602668			0.301334	+	0.953519i	$0.402568\pi$
$510$	−5.06789	−	7.19132i	−0.224410	−	0.318437i
$511$	−3.23852			−0.143264
$512$	0.923880	+	0.382683i	0.0408301	+	0.0169124i
$513$	0.841378	+	1.25921i	0.0371478	+	0.0555956i
$514$	−10.0900	−	10.0900i	−0.445049	−	0.445049i
$515$	−8.36038	−	31.5088i	−0.368403	−	1.38844i
$516$	−1.67654	−	8.42855i	−0.0738057	−	0.371046i
$517$	3.06633	+	15.4155i	0.134857	+	0.677971i
$518$	14.8779	+	35.9184i	0.653697	+	1.57816i
$519$	3.26873	−	7.89141i	0.143481	−	0.346394i
$520$	−12.7409	−	1.70902i	−0.558725	−	0.0749455i
$521$	32.2104	−	6.40706i	1.41117	−	0.280698i	0.570075	−	0.821593i	$-0.306914\pi$
$521$	32.2104	−	6.40706i	1.41117	−	0.280698i	0.841090	+	0.540895i	$0.181914\pi$
$522$	−0.227072	+	1.14157i	−0.00993867	+	0.0499651i
$523$	36.5024			1.59614			0.798070	−	0.602565i	$-0.205854\pi$
$523$	36.5024			1.59614			0.798070	+	0.602565i	$0.205854\pi$
$524$	−3.41496	+	17.1682i	−0.149183	+	0.749996i
$525$	17.3722	+	4.74589i	0.758185	+	0.207128i
$526$			5.58905i			0.243694i
$527$	−14.2884	−	15.4230i	−0.622414	−	0.671838i
$528$	1.88951	−	1.88951i	0.0822305	−	0.0822305i
$529$	−0.0630980	−	0.152332i	−0.00274339	−	0.00662313i
$530$	−3.77962	−	14.2447i	−0.164176	−	0.618751i
$531$	5.03398	−	5.03398i	0.218456	−	0.218456i
$532$	−1.15440	−	0.229625i	−0.0500498	−	0.00995552i
$533$	−44.3118	−	29.6082i	−1.91936	−	1.28247i
$534$	5.62179	−	8.41360i	0.243278	−	0.364092i
$535$	−21.3408	+	24.2151i	−0.922645	+	1.04691i
$536$	−2.53732	−	1.05099i	−0.109596	−	0.0453960i
$537$	6.82916	−	1.35840i	0.294700	−	0.0586195i
$538$	−3.78952	+	5.67141i	−0.163378	+	0.244512i
$539$	16.8732	−	11.2743i	0.726780	−	0.485619i
$540$	9.75131	−	4.77926i	0.419630	−	0.205667i
$541$	7.08352	+	1.40900i	0.304544	+	0.0605776i	0.344997	−	0.938604i	$-0.387880\pi$
$541$	7.08352	+	1.40900i	0.304544	+	0.0605776i	−0.0404526	+	0.999181i	$0.512880\pi$
$542$	0.217388	−	0.524821i	0.00933762	−	0.0225430i
$543$	−1.46599	−	1.46599i	−0.0629116	−	0.0629116i
$544$	3.51315	−	2.15819i	0.150625	−	0.0925315i
$545$	−7.99839	−	16.3194i	−0.342613	−	0.699048i
$546$	19.1301	−	7.92394i	0.818692	−	0.339113i
$547$	33.0002	−	22.0501i	1.41099	−	0.942792i	0.411481	−	0.911418i	$-0.365012\pi$
$547$	33.0002	−	22.0501i	1.41099	−	0.942792i	0.999508	−	0.0313741i	$-0.00998833\pi$
$548$			1.14941i			0.0491004i
$549$	−11.8490	−	17.7332i	−0.505702	−	0.756837i
$550$	−4.43589	−	13.2804i	−0.189147	−	0.566277i
$551$	0.144435	+	0.0965085i	0.00615315	+	0.00411140i
$552$	−4.21283	+	1.74501i	−0.179310	+	0.0742726i
$553$	15.5988	−	6.46125i	0.663330	−	0.274760i
$554$	−16.7684	−	11.2043i	−0.712419	−	0.476023i
$555$	−17.4688	+	13.3367i	−0.741511	+	0.566111i
$556$	3.67269	+	5.49657i	0.155757	+	0.233107i
$557$		−	29.8842i		−	1.26623i	−0.774056	−	0.633117i	$-0.781775\pi$
$557$		−	29.8842i		−	1.26623i	0.774056	−	0.633117i	$-0.218225\pi$
$558$	8.85880	−	5.91926i	0.375023	−	0.250582i
$559$	−47.8326	+	19.8129i	−2.02311	+	0.837998i
$560$	−2.73245	+	7.98545i	−0.115467	+	0.337447i
$561$	−1.73553	−	10.8801i	−0.0732740	−	0.459359i
$562$	0.109991	+	0.109991i	0.00463971	+	0.00463971i
$563$	1.18442	−	2.85945i	0.0499174	−	0.120511i	−0.896954	−	0.442124i	$-0.854225\pi$
$563$	1.18442	−	2.85945i	0.0499174	−	0.120511i	0.946871	+	0.321613i	$0.104225\pi$
$564$	5.25298	+	1.04488i	0.221190	+	0.0439975i
$565$	4.17594	+	8.52034i	0.175683	+	0.358453i
$566$	−11.4772	+	7.66884i	−0.482424	+	0.322345i
$567$	3.42648	−	5.12810i	0.143899	−	0.215360i
$568$	−3.93324	+	0.782371i	−0.165035	+	0.0328275i
$569$	22.5622	+	9.34559i	0.945859	+	0.391787i	0.801673	−	0.597763i	$-0.203944\pi$
$569$	22.5622	+	9.34559i	0.945859	+	0.391787i	0.144186	+	0.989551i	$0.453944\pi$
$570$	−0.0418969	−	0.664057i	−0.00175487	−	0.0278143i
$571$	−6.22109	+	9.31052i	−0.260345	+	0.389633i	−0.938497	−	0.345288i	$-0.887781\pi$
$571$	−6.22109	+	9.31052i	−0.260345	+	0.389633i	0.678152	+	0.734922i	$0.262781\pi$
$572$	−13.3857	−	8.94404i	−0.559685	−	0.373969i
$573$	13.2334	+	2.63229i	0.552834	+	0.109965i
$574$	−24.7417	+	24.7417i	−1.03270	+	1.03270i
$575$	−1.67906	+	23.8340i	−0.0700216	+	0.993946i
$576$	0.799590	+	1.93038i	0.0333162	+	0.0804325i
$577$	−3.62693	+	3.62693i	−0.150991	+	0.150991i	−0.778561	−	0.627569i	$-0.784050\pi$
$577$	−3.62693	+	3.62693i	−0.150991	+	0.150991i	0.627569	+	0.778561i	$0.284050\pi$
$578$	1.29647	−	16.9505i	0.0539259	−	0.705048i
$579$			1.26410i			0.0525341i
$580$	0.823578	−	0.934499i	0.0341972	−	0.0388029i
$581$	1.08776	−	5.46852i	0.0451277	−	0.226873i
$582$	14.9023			0.617719
$583$	3.60069	−	18.1019i	0.149125	−	0.749704i
$584$	0.841518	−	0.167388i	0.0348222	−	0.00692657i
$585$	−16.2990	−	21.3490i	−0.673882	−	0.882673i
$586$	8.87765	−	21.4325i	0.366732	−	0.885370i
$587$	1.02281	+	2.46929i	0.0422161	+	0.101919i	0.943581	−	0.331142i	$-0.107434\pi$
$587$	1.02281	+	2.46929i	0.0422161	+	0.101919i	−0.901365	+	0.433060i	$0.857434\pi$
$588$	−1.34907	−	6.78225i	−0.0556348	−	0.279695i
$589$	−0.310215	−	1.55956i	−0.0127822	−	0.0642605i
$590$	−7.36394	+	1.95391i	−0.303169	+	0.0804411i
$591$	1.18064	+	1.18064i	0.0485649	+	0.0485649i
$592$	−5.72246	−	8.56427i	−0.235192	−	0.351989i
$593$	36.5110	+	15.1234i	1.49933	+	0.621042i	0.973323	−	0.229440i	$-0.0736895\pi$
$593$	36.5110	+	15.1234i	1.49933	+	0.621042i	0.526004	+	0.850482i	$0.323690\pi$
$594$	13.5998			0.558008
$595$	20.0460	+	28.4452i	0.821806	+	1.16614i
$596$	−8.58370			−0.351602
$597$	−3.00327	−	1.24400i	−0.122916	−	0.0509133i
$598$	15.2626	+	22.8420i	0.624133	+	0.934081i
$599$	33.3470	+	33.3470i	1.36252	+	1.36252i	0.870689	+	0.491834i	$0.163673\pi$
$599$	33.3470	+	33.3470i	1.36252	+	1.36252i	0.491834	+	0.870689i	$0.336327\pi$
$600$	−4.75940	−	0.335290i	−0.194302	−	0.0136882i
$601$	−5.91062	−	29.7147i	−0.241099	−	1.21209i	−0.891685	−	0.452656i	$-0.850477\pi$
$601$	−5.91062	−	29.7147i	−0.241099	−	1.21209i	0.650586	−	0.759433i	$-0.274523\pi$
$602$	6.63156	+	33.3391i	0.270282	+	1.35880i
$603$	−2.19598	−	5.30156i	−0.0894271	−	0.215896i
$604$	1.69264	−	4.08639i	0.0688724	−	0.166273i
$605$	−0.938856	+	6.99925i	−0.0381699	+	0.284560i
$606$	4.85923	−	0.966561i	0.197393	−	0.0392639i
$607$	−3.03730	+	15.2695i	−0.123280	+	0.619771i	0.868903	+	0.494982i	$0.164825\pi$
$607$	−3.03730	+	15.2695i	−0.123280	+	0.619771i	−0.992183	+	0.124789i	$0.960175\pi$
$608$	0.311836			0.0126466
$609$	−0.391427	+	1.96784i	−0.0158614	+	0.0797408i
$610$	1.43719	+	22.7791i	0.0581900	+	0.922299i
$611$		−	32.2672i		−	1.30539i
$612$	8.37911	+	2.00189i	0.338706	+	0.0809216i
$613$	−15.5475	+	15.5475i	−0.627957	+	0.627957i	−0.947554	−	0.319597i	$-0.896453\pi$
$613$	−15.5475	+	15.5475i	−0.627957	+	0.627957i	0.319597	+	0.947554i	$0.396453\pi$
$614$	−3.14120	−	7.58353i	−0.126769	−	0.306046i
$615$	−17.1059	−	9.93183i	−0.689775	−	0.400490i
$616$	−7.47396	+	7.47396i	−0.301134	+	0.301134i
$617$	−16.5015	−	3.28236i	−0.664327	−	0.132143i	−0.148602	−	0.988897i	$-0.547477\pi$
$617$	−16.5015	−	3.28236i	−0.664327	−	0.132143i	−0.515725	+	0.856754i	$0.672477\pi$
$618$	−11.5671	−	7.72888i	−0.465297	−	0.310901i
$619$	−10.9909	+	16.4491i	−0.441763	+	0.661145i	−0.983812	−	0.179202i	$-0.942649\pi$
$619$	−10.9909	+	16.4491i	−0.441763	+	0.661145i	0.542049	+	0.840347i	$0.317649\pi$
$620$	−11.3795	+	0.717960i	−0.457012	+	0.0288340i
$621$	−21.4409	−	8.88111i	−0.860394	−	0.356387i
$622$	23.3096	−	4.63657i	0.934631	−	0.185910i
$623$	−22.2369	+	33.2799i	−0.890904	+	1.33333i
$624$	−4.56132	+	3.04777i	−0.182599	+	0.122009i
$625$	−12.7108	+	21.5276i	−0.508432	+	0.861102i
$626$	0.321242	+	0.0638990i	0.0128394	+	0.00255392i
$627$	0.318883	−	0.769851i	0.0127349	−	0.0307449i
$628$	−9.40763	−	9.40763i	−0.375405	−	0.375405i
$629$	−42.4377	−	1.62057i	−1.69210	−	0.0646163i
$630$	−15.8352	+	7.76104i	−0.630888	+	0.309207i
$631$	−19.6003	+	8.11870i	−0.780275	+	0.323200i	−0.737026	−	0.675864i	$-0.763771\pi$
$631$	−19.6003	+	8.11870i	−0.780275	+	0.323200i	−0.0432484	+	0.999064i	$0.513771\pi$
$632$	−3.71934	+	2.48518i	−0.147947	+	0.0988552i
$633$		−	0.473574i		−	0.0188229i
$634$	0.0830869	+	0.124348i	0.00329980	+	0.00493851i
$635$	5.96675	−	44.4826i	0.236783	−	1.76524i
$636$	−5.22932	−	3.49412i	−0.207356	−	0.138551i
$637$	−38.4898	+	15.9430i	−1.52502	+	0.631684i
$638$	1.44120	−	0.596964i	0.0570576	−	0.0236340i
$639$	−6.96708	−	4.65525i	−0.275613	−	0.184159i
$640$	0.297276	−	2.21622i	0.0117509	−	0.0876037i
$641$	3.29442	+	4.93045i	0.130122	+	0.194741i	0.890810	−	0.454377i	$-0.150138\pi$
$641$	3.29442	+	4.93045i	0.130122	+	0.194741i	−0.760688	+	0.649118i	$0.775138\pi$
$642$			13.7741i			0.543622i
$643$	−18.6025	+	12.4298i	−0.733612	+	0.490184i	−0.865392	−	0.501095i	$-0.832931\pi$
$643$	−18.6025	+	12.4298i	−0.733612	+	0.490184i	0.131780	+	0.991279i	$0.457931\pi$
$644$	16.6638	−	6.90238i	0.656647	−	0.271992i
$645$	−17.2550	+	8.45694i	−0.679417	+	0.332992i
$646$	0.754589	−	1.04101i	0.0296889	−	0.0409581i
$647$	−25.6959	−	25.6959i	−1.01021	−	1.01021i	−0.999947	−	0.0102608i	$-0.996734\pi$
$647$	−25.6959	−	25.6959i	−1.01021	−	1.01021i	−0.0102608	−	0.999947i	$-0.503266\pi$
$648$	−0.625305	+	1.50962i	−0.0245643	+	0.0593034i
$649$	−9.35795	−	1.86141i	−0.367332	−	0.0730668i
$650$	3.61275	+	28.5167i	0.141704	+	1.11852i
$651$	15.2708	−	10.2036i	0.598510	−	0.399912i
$652$	−8.48460	+	12.6981i	−0.332283	+	0.497296i
$653$	33.2017	−	6.60423i	1.29928	−	0.258443i	0.503484	−	0.864004i	$-0.332051\pi$
$653$	33.2017	−	6.60423i	1.29928	−	0.258443i	0.795799	+	0.605561i	$0.207051\pi$
$654$	−7.16540	−	2.96800i	−0.280189	−	0.116058i
$655$	39.0636	−	2.46462i	1.52634	−	0.0963005i
$656$	5.15021	−	7.70784i	0.201082	−	0.300940i
$657$	1.49061	+	0.995992i	0.0581541	+	0.0388573i
$658$	−20.7781	−	4.13303i	−0.810016	−	0.161122i
$659$	30.0602	−	30.0602i	1.17098	−	1.17098i	0.189001	−	0.981977i	$-0.439475\pi$
$659$	30.0602	−	30.0602i	1.17098	−	1.17098i	0.981977	−	0.189001i	$-0.0605250\pi$
$660$	−5.16734	−	3.00021i	−0.201138	−	0.116783i
$661$	−11.8936	−	28.7137i	−0.462608	−	1.11683i	−0.967323	−	0.253548i	$-0.918403\pi$
$661$	−11.8936	−	28.7137i	−0.462608	−	1.11683i	0.504715	−	0.863286i	$-0.331597\pi$
$662$	21.8391	−	21.8391i	0.848800	−	0.848800i
$663$	−0.863112	+	22.6023i	−0.0335205	+	0.877799i
$664$			1.47720i			0.0573263i
$665$	0.165723	+	2.62668i	0.00642647	+	0.101858i
$666$	4.19863	−	21.1079i	0.162694	−	0.817916i
$667$	−2.66196			−0.103072
$668$	−0.0921295	+	0.463166i	−0.00356460	+	0.0179204i
$669$	23.0384	−	4.58262i	0.890716	−	0.177174i
$670$	−0.816433	+	6.08658i	−0.0315416	+	0.235145i
$671$	−10.9386	+	26.4081i	−0.422280	+	1.01947i
$672$	1.37833	+	3.32759i	0.0531704	+	0.128365i
$673$	−6.29309	−	31.6375i	−0.242581	−	1.21954i	−0.889485	−	0.456964i	$-0.848937\pi$
$673$	−6.29309	−	31.6375i	−0.242581	−	1.21954i	0.646904	−	0.762571i	$-0.276063\pi$
$674$	0.643188	+	3.23353i	0.0247747	+	0.124551i
$675$	−15.9213	−	18.3346i	−0.612813	−	0.705699i
$676$	14.1776	+	14.1776i	0.545293	+	0.545293i
$677$	11.6902	+	17.4957i	0.449292	+	0.672413i	0.985111	−	0.171920i	$-0.0549970\pi$
$677$	11.6902	+	17.4957i	0.449292	+	0.672413i	−0.535819	+	0.844333i	$0.679997\pi$
$678$	3.74104	+	1.54959i	0.143674	+	0.0595116i
$679$	−58.9459			−2.26214
$680$	−6.67911	−	6.35527i	−0.256132	−	0.243713i
$681$	−22.8424			−0.875321
$682$	−13.1924	−	5.46448i	−0.505164	−	0.209246i
$683$	−24.8872	−	37.2464i	−0.952284	−	1.42519i	−0.904566	−	0.426333i	$-0.859805\pi$
$683$	−24.8872	−	37.2464i	−0.952284	−	1.42519i	−0.0477178	−	0.998861i	$-0.515195\pi$
$684$	0.460722	+	0.460722i	0.0176161	+	0.0176161i
$685$	2.48420	−	0.659145i	0.0949165	−	0.0251846i
$686$	0.181692	+	0.913428i	0.00693704	+	0.0348748i
$687$	0.442712	+	2.22567i	0.0168905	+	0.0849144i
$688$	−3.44637	−	8.32027i	−0.131392	−	0.317207i
$689$	−14.5000	+	35.0062i	−0.552407	+	1.33363i
$690$	6.18736	+	8.10441i	0.235549	+	0.308530i
$691$	−15.5942	+	3.10187i	−0.593230	+	0.118001i	−0.482570	−	0.875858i	$-0.660297\pi$
$691$	−15.5942	+	3.10187i	−0.593230	+	0.118001i	−0.110660	+	0.993858i	$0.535297\pi$
$692$	1.74630	−	8.77923i	0.0663842	−	0.333736i
$693$	−22.0848			−0.838932
$694$	0.502701	−	2.52725i	0.0190823	−	0.0959330i
$695$	9.77349	−	11.0898i	0.370730	−	0.420660i
$696$		−	0.531566i		−	0.0201490i
$697$	−13.2687	−	35.8447i	−0.502587	−	1.35772i
$698$	4.86856	−	4.86856i	0.184278	−	0.184278i
$699$	3.92490	+	9.47554i	0.148453	+	0.358398i
$700$	18.8258	+	1.32624i	0.711547	+	0.0501271i
$701$	−18.7261	+	18.7261i	−0.707276	+	0.707276i	−0.965961	−	0.258686i	$-0.916711\pi$
$701$	−18.7261	+	18.7261i	−0.707276	+	0.707276i	0.258686	+	0.965961i	$0.416711\pi$
$702$	−27.3834	−	5.44689i	−1.03352	−	0.205580i
$703$	−2.67065	−	1.78447i	−0.100725	−	0.0673026i
$704$	1.55578	−	2.32838i	0.0586355	−	0.0877542i
$705$	−0.754103	−	11.9524i	−0.0284012	−	0.450152i
$706$	23.1791	+	9.60111i	0.872358	+	0.361343i
$707$	−19.2207	+	3.82323i	−0.722867	+	0.143787i
$708$	−1.80632	+	2.70335i	−0.0678857	+	0.101598i
$709$	−10.9253	+	7.30008i	−0.410310	+	0.274160i	−0.743548	−	0.668682i	$-0.766859\pi$
$709$	−10.9253	+	7.30008i	−0.410310	+	0.274160i	0.333238	+	0.942843i	$0.391859\pi$
$710$	3.94649	+	8.05219i	0.148109	+	0.302193i
$711$	−9.16686	−	1.82340i	−0.343784	−	0.0683829i
$712$	4.05806	−	9.79701i	0.152082	−	0.367159i
$713$	17.2301	+	17.2301i	0.645272	+	0.645272i
$714$	14.4439	+	3.45086i	0.540550	+	0.129145i
$715$	−11.6544	+	34.0594i	−0.435850	+	1.27375i
$716$	6.74143	−	2.79239i	0.251939	−	0.104357i
$717$	15.9570	−	10.6621i	0.595925	−	0.398184i
$718$			9.72428i			0.362907i
$719$	28.8785	+	43.2197i	1.07698	+	1.61182i	0.743064	+	0.669220i	$0.233372\pi$
$719$	28.8785	+	43.2197i	1.07698	+	1.61182i	0.333921	+	0.942601i	$0.391628\pi$
$720$	3.71356	−	2.83514i	0.138396	−	0.105659i
$721$	45.7536	+	30.5716i	1.70395	+	1.13854i
$722$	−17.4639	+	7.23377i	−0.649938	+	0.269213i
$723$	−3.99809	+	1.65606i	−0.148691	+	0.0615897i
$724$	−1.80649	−	1.20706i	−0.0671376	−	0.0448599i
$725$	−2.49201	−	1.24408i	−0.0925508	−	0.0462041i
$726$	1.67431	+	2.50578i	0.0621393	+	0.0929981i
$727$			1.45820i			0.0540815i	0.999634	+	0.0270407i	$0.00860838\pi$
$727$			1.45820i			0.0540815i	−0.999634	+	0.0270407i	$0.991392\pi$
$728$	18.0423	−	12.0555i	0.668691	−	0.446805i
$729$	9.69033	−	4.01387i	0.358901	−	0.148662i
$730$	−0.844352	−	1.72277i	−0.0312509	−	0.0637624i
$731$	−36.1154	−	8.62848i	−1.33578	−	0.319136i
$732$	6.88741	+	6.88741i	0.254566	+	0.254566i
$733$	4.20864	−	10.1606i	0.155450	−	0.375289i	−0.826898	−	0.562351i	$-0.809897\pi$
$733$	4.20864	−	10.1606i	0.155450	−	0.375289i	0.982348	+	0.187063i	$0.0598968\pi$
$734$	−15.2095	−	3.02536i	−0.561394	−	0.111668i
$735$	−13.8847	+	6.80510i	−0.512145	+	0.251010i
$736$	−3.97327	+	2.65485i	−0.146457	+	0.0978592i
$737$	−4.27275	+	6.39463i	−0.157389	+	0.235549i
$738$	18.9971	−	3.77876i	0.699293	−	0.139098i
$739$	30.1250	+	12.4782i	1.10817	+	0.459017i	0.860306	−	0.509779i	$-0.170273\pi$
$739$	30.1250	+	12.4782i	1.10817	+	0.459017i	0.247860	+	0.968796i	$0.420273\pi$
$740$	−15.2282	+	17.2792i	−0.559799	+	0.635194i
$741$	−0.950406	+	1.42238i	−0.0349140	+	0.0522526i
$742$	20.6846	+	13.8210i	0.759354	+	0.507384i
$743$	44.2588	+	8.80362i	1.62370	+	0.322973i	0.921312	−	0.388824i	$-0.127119\pi$
$743$	44.2588	+	8.80362i	1.62370	+	0.322973i	0.702385	+	0.711797i	$0.252119\pi$
$744$	−3.44067	+	3.44067i	−0.126141	+	0.126141i
$745$	4.92243	+	18.5518i	0.180344	+	0.679685i
$746$	−8.76653	−	21.1643i	−0.320966	−	0.774880i
$747$	−2.18248	+	2.18248i	−0.0798529	+	0.0798529i
$748$	−4.00821	−	10.8280i	−0.146554	−	0.395910i
$749$		−	54.4835i		−	1.99078i
$750$	2.00468	+	10.4787i	0.0732006	+	0.382627i
$751$	7.33561	−	36.8786i	0.267680	−	1.34572i	−0.579742	−	0.814800i	$-0.696847\pi$
$751$	7.33561	−	36.8786i	0.267680	−	1.34572i	0.847422	−	0.530919i	$-0.178153\pi$
$752$	5.61274			0.204675
$753$	0.616167	−	3.09768i	0.0224544	−	0.112886i
$754$	−3.14095	+	0.624774i	−0.114387	+	0.0227529i
$755$	−9.80250	−	1.31487i	−0.356749	−	0.0478532i
$756$	−7.01493	+	16.9355i	−0.255131	+	0.615940i
$757$	−15.2554	−	36.8299i	−0.554469	−	1.33861i	−0.914091	−	0.405508i	$-0.867095\pi$
$757$	−15.2554	−	36.8299i	−0.554469	−	1.33861i	0.359623	−	0.933098i	$-0.382905\pi$
$758$	−4.27956	−	21.5148i	−0.155440	−	0.781452i
$759$	2.49116	+	12.5239i	0.0904235	+	0.454590i
$760$	−0.178826	−	0.673966i	−0.00648672	−	0.0244473i
$761$	19.4265	+	19.4265i	0.704212	+	0.704212i	0.965312	−	0.261100i	$-0.0840852\pi$
$761$	19.4265	+	19.4265i	0.704212	+	0.704212i	−0.261100	+	0.965312i	$0.584085\pi$
$762$	−10.6408	−	15.9250i	−0.385475	−	0.576904i
$763$	28.3427	+	11.7399i	1.02607	+	0.425014i
$764$	14.1397			0.511557
$765$	−0.478466	−	19.2576i	−0.0172990	−	0.696261i
$766$	25.4244			0.918621
$767$	18.0968	+	7.49593i	0.653436	+	0.270662i
$768$	−0.530147	−	0.793420i	−0.0191300	−	0.0286301i
$769$	−6.98576	−	6.98576i	−0.251913	−	0.251913i	0.569842	−	0.821755i	$-0.307005\pi$
$769$	−6.98576	−	6.98576i	−0.251913	−	0.251913i	−0.821755	+	0.569842i	$0.807005\pi$
$770$	20.4394	+	11.8673i	0.736584	+	0.427668i
$771$	2.65642	+	13.3547i	0.0956687	+	0.480959i
$772$	0.258440	+	1.29926i	0.00930145	+	0.0467615i
$773$	−2.37475	−	5.73316i	−0.0854140	−	0.206208i	0.875401	−	0.483397i	$-0.160597\pi$
$773$	−2.37475	−	5.73316i	−0.0854140	−	0.206208i	−0.960815	+	0.277189i	$0.910597\pi$
$774$	7.20094	−	17.3846i	0.258833	−	0.624877i
$775$	8.07744	+	24.1826i	0.290150	+	0.868665i
$776$	15.3169	−	3.04671i	0.549843	−	0.109371i
$777$	7.23760	−	36.3859i	0.259647	−	1.30534i
$778$	15.9047			0.570209
$779$	0.563960	−	2.83522i	0.0202060	−	0.101582i
$780$	9.20285	+	8.11051i	0.329515	+	0.290403i
$781$			11.2301i			0.401846i
$782$	−0.751839	+	19.6884i	−0.0268857	+	0.704055i
$783$	1.91298	−	1.91298i	0.0683645	−	0.0683645i
$784$	−2.77321	−	6.69512i	−0.0990431	−	0.239111i
$785$	−14.9376	+	25.7275i	−0.533146	+	0.918253i
$786$	11.8112	−	11.8112i	0.421290	−	0.421290i
$787$	−19.1406	−	3.80730i	−0.682288	−	0.135716i	−0.158235	−	0.987401i	$-0.550580\pi$
$787$	−19.1406	−	3.80730i	−0.682288	−	0.135716i	−0.524053	+	0.851686i	$0.675580\pi$
$788$	1.45486	+	0.972106i	0.0518272	+	0.0346298i
$789$	2.96302	−	4.43447i	0.105486	−	0.157871i
$790$	7.50408	+	6.61338i	0.266983	+	0.235293i
$791$	−14.7977	−	6.12939i	−0.526144	−	0.217936i
$792$	5.73865	−	1.14149i	0.203914	−	0.0405610i
$793$	32.6017	−	48.7919i	1.15772	−	1.73265i
$794$	10.9531	−	7.31860i	0.388709	−	0.259727i
$795$	−4.55296	+	13.3058i	−0.161477	+	0.471908i
$796$	−3.34115	−	0.664596i	−0.118424	−	0.0235560i
$797$	8.81871	−	21.2903i	0.312375	−	0.754140i	−0.687241	−	0.726429i	$-0.741178\pi$
$797$	8.81871	−	21.2903i	0.312375	−	0.754140i	0.999616	−	0.0277102i	$-0.00882157\pi$
$798$	0.794193	+	0.794193i	0.0281141	+	0.0281141i
$799$	13.5818	−	18.7372i	0.480491	−	0.662873i
$800$	−4.96035	+	0.628422i	−0.175375	+	0.0222181i
$801$	20.4702	−	8.47902i	0.723278	−	0.299591i
$802$	−3.40036	+	2.27205i	−0.120071	+	0.0802288i
$803$		−	2.40269i		−	0.0847890i
$804$	1.45598	+	2.17903i	0.0513486	+	0.0768486i
$805$	−24.4741	−	32.0570i	−0.862598	−	1.12986i
$806$	24.3744	+	16.2865i	0.858553	+	0.573667i
$807$	6.01336	−	2.49082i	0.211680	−	0.0876809i
$808$	4.79680	−	1.98690i	0.168751	−	0.0698990i
$809$	−25.3345	−	16.9279i	−0.890712	−	0.595155i	0.0237985	−	0.999717i	$-0.492424\pi$
$809$	−25.3345	−	16.9279i	−0.890712	−	0.595155i	−0.914511	+	0.404562i	$0.867424\pi$
$810$	3.62130	+	0.485749i	0.127240	+	0.0170675i
$811$	3.76345	+	5.63241i	0.132153	+	0.197781i	0.891644	−	0.452737i	$-0.149552\pi$
$811$	3.76345	+	5.63241i	0.132153	+	0.197781i	−0.759492	+	0.650517i	$0.774552\pi$
$812$			2.10261i			0.0737871i
$813$	−0.450712	+	0.301156i	−0.0158072	+	0.0105620i
$814$	−26.6482	+	11.0380i	−0.934018	+	0.386883i
$815$	32.3098	+	11.0557i	1.13176	+	0.387265i
$816$	−3.93156	−	0.150134i	−0.137632	−	0.00525576i
$817$	−1.98579	−	1.98579i	−0.0694740	−	0.0694740i
$818$	−10.0769	+	24.3277i	−0.352330	+	0.850600i
$819$	44.4679	+	8.84521i	1.55383	+	0.309077i
$820$	−19.6123	−	6.71090i	−0.684890	−	0.234355i
$821$	0.0491354	−	0.0328312i	0.00171484	−	0.00114582i	−0.554713	−	0.832042i	$-0.687172\pi$
$821$	0.0491354	−	0.0328312i	0.00171484	−	0.00114582i	0.556427	+	0.830896i	$0.312172\pi$
$822$	0.609356	−	0.911966i	0.0212537	−	0.0318085i
$823$	−27.4218	+	5.45454i	−0.955866	+	0.190133i	−0.648293	−	0.761391i	$-0.724517\pi$
$823$	−27.4218	+	5.45454i	−0.955866	+	0.190133i	−0.307573	+	0.951525i	$0.599517\pi$
$824$	−13.4690	−	5.57905i	−0.469216	−	0.194356i
$825$	−3.52101	+	12.8886i	−0.122586	+	0.448723i
$826$	7.14489	−	10.6931i	0.248602	−	0.372060i
$827$	−2.86713	−	1.91575i	−0.0996998	−	0.0666173i	0.504721	−	0.863283i	$-0.331595\pi$
$827$	−2.86713	−	1.91575i	−0.0996998	−	0.0666173i	−0.604421	+	0.796665i	$0.706595\pi$
$828$	−9.79272	−	1.94789i	−0.340320	−	0.0676939i
$829$	−20.0943	+	20.0943i	−0.697904	+	0.697904i	−0.963958	−	0.266054i	$-0.914280\pi$
$829$	−20.0943	+	20.0943i	−0.697904	+	0.697904i	0.266054	+	0.963958i	$0.414280\pi$
$830$	3.19264	−	0.847117i	0.110818	−	0.0294039i
$831$	7.36446	+	17.7794i	0.255470	+	0.616760i
$832$	−4.06511	+	4.06511i	−0.140932	+	0.140932i
$833$	−29.0612	−	6.94313i	−1.00691	−	0.240565i
$834$		−	6.30816i		−	0.218434i
$835$	1.05387	−	0.0664909i	0.0364705	−	0.00230101i
$836$	0.170361	−	0.856462i	0.00589206	−	0.0296214i
$837$	−24.7644			−0.855981
$838$	−1.24149	+	6.24139i	−0.0428866	+	0.215605i
$839$	16.6096	−	3.30385i	0.573426	−	0.114062i	0.100145	−	0.994973i	$-0.468069\pi$
$839$	16.6096	−	3.30385i	0.573426	−	0.114062i	0.473281	+	0.880911i	$0.343069\pi$
$840$	6.40144	−	4.88722i	0.220871	−	0.168625i
$841$	−10.9791	+	26.5058i	−0.378589	+	0.913994i
$842$	9.08826	+	21.9410i	0.313202	+	0.756137i
$843$	−0.0289578	−	0.145581i	−0.000997361	−	0.00501407i
$844$	−0.0968204	−	0.486749i	−0.00333270	−	0.0167546i
$845$	22.5115	−	38.7722i	0.774419	−	1.33380i
$846$	8.29253	+	8.29253i	0.285103	+	0.285103i
$847$	−6.62271	−	9.91159i	−0.227559	−	0.340566i
$848$	−6.08916	−	2.52221i	−0.209103	−	0.0866132i
$849$	13.1719			0.452058
$850$	−9.90530	+	18.0800i	−0.339749	+	0.620138i
$851$	49.2205			1.68726
$852$	3.53549	+	1.46445i	0.121124	+	0.0501711i
$853$	−10.6966	−	16.0086i	−0.366245	−	0.548124i	0.601882	−	0.798585i	$-0.294418\pi$
$853$	−10.6966	−	16.0086i	−0.366245	−	0.548124i	−0.968127	+	0.250461i	$0.919418\pi$
$854$	−27.2431	−	27.2431i	−0.932241	−	0.932241i
$855$	0.731543	−	1.25996i	0.0250183	−	0.0430896i
$856$	2.81607	+	14.1573i	0.0962512	+	0.483888i
$857$	−1.69936	−	8.54328i	−0.0580492	−	0.291833i	0.940846	−	0.338836i	$-0.110033\pi$
$857$	−1.69936	−	8.54328i	−0.0580492	−	0.291833i	−0.998895	+	0.0470027i	$0.985033\pi$
$858$	5.87884	+	14.1928i	0.200700	+	0.484533i
$859$	−19.4345	+	46.9191i	−0.663097	+	1.60086i	0.129826	+	0.991537i	$0.458558\pi$
$859$	−19.4345	+	46.9191i	−0.663097	+	1.60086i	−0.792923	+	0.609321i	$0.791442\pi$
$860$	−16.0061	+	12.2199i	−0.545803	+	0.416697i
$861$	32.7472	−	6.51383i	1.11602	−	0.221991i
$862$	4.77925	−	24.0269i	0.162782	−	0.818360i
$863$	19.7887			0.673617			0.336808	−	0.941573i	$-0.390653\pi$
$863$	19.7887			0.673617			0.336808	+	0.941573i	$0.390653\pi$
$864$	0.947462	−	4.76321i	0.0322333	−	0.162048i
$865$	−19.9758	+	1.26032i	−0.679198	+	0.0428522i
$866$			18.5789i			0.631338i
$867$	−10.0149	+	12.7615i	−0.340123	+	0.433405i
$868$	13.6096	−	13.6096i	0.461938	−	0.461938i
$869$	4.79365	+	11.5729i	0.162614	+	0.392584i
$870$	−1.14886	+	0.304834i	−0.0389502	+	0.0103348i
$871$	11.1643	−	11.1643i	0.378289	−	0.378289i
$872$	−7.97153	−	1.58564i	−0.269950	−	0.0536964i
$873$	27.1313	+	18.1285i	0.918254	+	0.613558i
$874$	−0.827879	+	1.23901i	−0.0280034	+	0.0419101i
$875$	−7.92950	−	41.4483i	−0.268066	−	1.40121i
$876$	−0.756417	−	0.313318i	−0.0255570	−	0.0105860i
$877$	−1.28871	+	0.256340i	−0.0435167	+	0.00865600i	−0.216801	−	0.976216i	$-0.569562\pi$
$877$	−1.28871	+	0.256340i	−0.0435167	+	0.00865600i	0.173284	+	0.984872i	$0.444562\pi$
$878$	−19.8231	+	29.6674i	−0.668997	+	1.00123i
$879$	−18.4061	+	12.2986i	−0.620822	+	0.414820i
$880$	−5.92447	−	2.02723i	−0.199714	−	0.0683379i
$881$	36.3159	+	7.22367i	1.22351	+	0.243372i	0.764245	−	0.644926i	$-0.223112\pi$
$881$	36.3159	+	7.22367i	1.22351	+	0.243372i	0.459268	+	0.888298i	$0.348112\pi$
$882$	5.79442	−	13.9890i	0.195108	−	0.471033i
$883$	−8.11148	−	8.11148i	−0.272973	−	0.272973i	0.557323	−	0.830296i	$-0.311829\pi$
$883$	−8.11148	−	8.11148i	−0.272973	−	0.272973i	−0.830296	+	0.557323i	$0.811829\pi$
$884$	3.73382	+	23.4075i	0.125582	+	0.787280i
$885$	6.87856	+	2.35370i	0.231220	+	0.0791186i
$886$	25.7327	−	10.6588i	0.864507	−	0.358090i
$887$	−26.1101	+	17.4462i	−0.876692	+	0.585787i	−0.910439	−	0.413643i	$-0.864256\pi$
$887$	−26.1101	+	17.4462i	−0.876692	+	0.585787i	0.0337466	+	0.999430i	$0.489256\pi$
$888$			9.82881i			0.329833i
$889$	42.0895	+	62.9914i	1.41164	+	2.11267i
$890$	−23.5013	−	3.15238i	−0.787764	−	0.105668i
$891$	3.80458	+	2.54214i	0.127458	+	0.0851648i
$892$	22.7424	−	9.42022i	0.761472	−	0.315412i
$893$	1.61702	−	0.669793i	0.0541116	−	0.0224138i
$894$	6.81048	+	4.55062i	0.227776	+	0.152195i
$895$	−9.90110	−	12.9688i	−0.330957	−	0.433499i
$896$	2.09699	+	3.13837i	0.0700556	+	0.104846i
$897$		−	26.2147i		−	0.875285i
$898$	−15.1498	+	10.1228i	−0.505557	+	0.337802i
$899$	−2.62432	+	1.08703i	−0.0875260	+	0.0362544i
$900$	−8.25713	−	6.40021i	−0.275238	−	0.213340i
$901$	−23.1547	+	14.2243i	−0.771395	+	0.473881i
$902$	−18.3560	−	18.3560i	−0.611189	−	0.611189i
$903$	12.4130	−	29.9676i	0.413078	−	0.997260i
$904$	4.16192	+	0.827857i	0.138423	+	0.0275341i
$905$	−1.57284	+	4.59654i	−0.0522829	+	0.152794i
$906$	−3.50936	+	2.34488i	−0.116591	+	0.0779033i
$907$	−19.1339	+	28.6359i	−0.635330	+	0.950839i	0.364477	+	0.931212i	$0.381248\pi$
$907$	−19.1339	+	28.6359i	−0.635330	+	0.950839i	−0.999807	+	0.0196268i	$0.993752\pi$
$908$	−23.4778	+	4.67003i	−0.779139	+	0.154980i
$909$	10.0226	+	4.15149i	0.332428	+	0.137696i
$910$	−36.4018	−	32.0811i	−1.20671	−	1.06348i
$911$	6.35786	−	9.51521i	0.210645	−	0.315253i	−0.711069	−	0.703122i	$-0.751789\pi$
$911$	6.35786	−	9.51521i	0.210645	−	0.315253i	0.921714	+	0.387869i	$0.126789\pi$
$912$	−0.247417	−	0.165319i	−0.00819280	−	0.00547425i
$913$	4.05714	+	0.807016i	0.134272	+	0.0267083i
$914$	18.1091	−	18.1091i	0.598997	−	0.598997i
$915$	10.9360	−	18.8353i	0.361532	−	0.622677i
$916$	0.910057	+	2.19707i	0.0300691	+	0.0725933i
$917$	−46.7190	+	46.7190i	−1.54280	+	1.54280i
$918$	−13.6085	−	14.6891i	−0.449147	−	0.484812i
$919$			19.9181i			0.657036i	0.944498	+	0.328518i	$0.106549\pi$
$919$			19.9181i			0.657036i	−0.944498	+	0.328518i	$0.893451\pi$
$920$	8.01641	+	7.06490i	0.264293	+	0.232923i
$921$	−1.52809	+	7.68223i	−0.0503523	+	0.253138i
$922$	−32.7804			−1.07957
$923$	4.49779	−	22.6119i	0.148047	−	0.744281i
$924$	9.89229	−	1.96770i	0.325432	−	0.0647325i
$925$	46.0779	+	23.0035i	1.51503	+	0.756349i
$926$	−0.837054	+	2.02083i	−0.0275073	+	0.0664085i
$927$	−11.6570	−	28.1426i	−0.382867	−	0.924323i
$928$	−0.108677	−	0.546354i	−0.00356748	−	0.0179350i
$929$	−4.63571	−	23.3053i	−0.152093	−	0.764621i	−0.979251	−	0.202652i	$-0.935044\pi$
$929$	−4.63571	−	23.3053i	−0.152093	−	0.764621i	0.827158	−	0.561969i	$-0.189956\pi$
$930$	9.40936	+	5.46316i	0.308545	+	0.179144i
$931$	−1.59792	−	1.59792i	−0.0523696	−	0.0523696i
$932$	5.97133	+	8.93672i	0.195597	+	0.292732i
$933$	−20.9524	−	8.67876i	−0.685950	−	0.284130i
$934$	30.9948			1.01418
$935$	−21.1037	+	14.8723i	−0.690166	+	0.486376i
$936$	−12.0120			−0.392624
$937$	−27.0210	−	11.1925i	−0.882738	−	0.365642i	−0.105180	−	0.994453i	$-0.533542\pi$
$937$	−27.0210	−	11.1925i	−0.882738	−	0.365642i	−0.777558	+	0.628811i	$0.783542\pi$
$938$	−5.75914	−	8.61916i	−0.188043	−	0.281425i
$939$	−0.221004	−	0.221004i	−0.00721220	−	0.00721220i
$940$	−3.21870	−	12.1307i	−0.104982	−	0.395660i
$941$	6.12322	+	30.7835i	0.199611	+	1.00351i	0.942527	+	0.334129i	$0.108442\pi$
$941$	6.12322	+	30.7835i	0.199611	+	1.00351i	−0.742916	+	0.669385i	$0.766558\pi$
$942$	2.47678	+	12.4516i	0.0806979	+	0.405696i
$943$	16.9523	+	40.9264i	0.552041	+	1.33275i
$944$	−1.30388	+	3.14785i	−0.0424378	+	0.102454i
$945$	40.6253	+	5.44934i	1.32154	+	0.177267i
$946$	−24.7345	+	4.92001i	−0.804190	+	0.159963i
$947$	3.88070	−	19.5096i	0.126106	−	0.633977i	−0.865095	−	0.501609i	$-0.832742\pi$
$947$	3.88070	−	19.5096i	0.126106	−	0.633977i	0.991201	−	0.132369i	$-0.0422582\pi$
$948$	4.26851			0.138635
$949$	−0.962303	+	4.83783i	−0.0312377	+	0.157042i
$950$	−1.35408	+	0.772989i	−0.0439322	+	0.0250791i
$951$		−	0.142709i		−	0.00462765i
$952$	15.5513	+	0.593856i	0.504020	+	0.0192470i
$953$	9.32003	−	9.32003i	0.301905	−	0.301905i	−0.539854	−	0.841759i	$-0.681520\pi$
$953$	9.32003	−	9.32003i	0.301905	−	0.301905i	0.841759	+	0.539854i	$0.181520\pi$
$954$	−5.26999	−	12.7229i	−0.170622	−	0.411918i
$955$	−8.10861	−	30.5599i	−0.262388	−	0.988896i
$956$	14.2211	−	14.2211i	0.459943	−	0.459943i
$957$	−1.45995	−	0.290403i	−0.0471936	−	0.00938740i
$958$	26.2452	+	17.5365i	0.847944	+	0.566578i
$959$	−2.41031	+	3.60728i	−0.0778328	+	0.116485i
$960$	−1.41079	+	1.60079i	−0.0455329	+	0.0516654i
$961$	−4.61780	−	1.91276i	−0.148961	−	0.0617018i
$962$	58.0771	−	11.5523i	1.87248	−	0.372460i
$963$	−16.7561	+	25.0773i	−0.539959	+	0.808106i
$964$	−3.77074	+	2.51953i	−0.121447	+	0.0811486i
$965$	2.65987	−	1.30364i	0.0856242	−	0.0419657i
$966$	−16.8807	−	3.35778i	−0.543127	−	0.108035i
$967$	−5.70914	+	13.7831i	−0.183594	+	0.443234i	−0.988702	−	0.149893i	$-0.952107\pi$
$967$	−5.70914	+	13.7831i	−0.183594	+	0.443234i	0.805109	+	0.593128i	$0.202107\pi$
$968$	2.23318	+	2.23318i	0.0717772	+	0.0717772i
$969$	−1.15059	+	0.425917i	−0.0369624	+	0.0136824i
$970$	−15.3685	−	31.3569i	−0.493452	−	1.00681i
$971$	−2.84225	+	1.17730i	−0.0912121	+	0.0377813i	−0.427823	−	0.903863i	$-0.640719\pi$
$971$	−2.84225	+	1.17730i	−0.0912121	+	0.0377813i	0.336611	+	0.941644i	$0.390719\pi$
$972$	13.4106	−	8.96069i	0.430146	−	0.287414i
$973$			24.9519i			0.799921i
$974$	−11.1878	−	16.7437i	−0.358481	−	0.536504i
$975$	12.2516	−	24.5410i	0.392365	−	0.785942i
$976$	8.48713	+	5.67092i	0.271666	+	0.181522i
$977$	4.32813	−	1.79277i	0.138469	−	0.0573558i	−0.312373	−	0.949960i	$-0.601124\pi$
$977$	4.32813	−	1.79277i	0.138469	−	0.0573558i	0.450842	+	0.892604i	$0.351124\pi$
$978$	13.4637	−	5.57685i	0.430522	−	0.178328i
$979$	−24.6907	−	16.4978i	−0.789117	−	0.527271i
$980$	−12.8797	+	9.83309i	−0.411427	+	0.314106i
$981$	−9.43484	−	14.1202i	−0.301231	−	0.450824i
$982$		−	24.5239i		−	0.782590i
$983$	20.5105	−	13.7047i	0.654185	−	0.437112i	−0.183683	−	0.982986i	$-0.558802\pi$
$983$	20.5105	−	13.7047i	0.654185	−	0.437112i	0.837868	+	0.545873i	$0.183802\pi$
$984$	−8.17256	+	3.38519i	−0.260532	+	0.107916i
$985$	1.26669	−	3.70183i	0.0403600	−	0.117950i
$986$	−2.08689	−	0.959283i	−0.0664601	−	0.0305498i
$987$	14.2947	+	14.2947i	0.455005	+	0.455005i
$988$	−0.686046	+	1.65626i	−0.0218260	+	0.0526927i
$989$	42.2083	+	8.39575i	1.34215	+	0.266969i
$990$	−5.75798	−	11.7482i	−0.183001	−	0.373383i
$991$	26.8671	−	17.9521i	0.853463	−	0.570266i	−0.0500887	−	0.998745i	$-0.515950\pi$
$991$	26.8671	−	17.9521i	0.853463	−	0.570266i	0.903552	+	0.428479i	$0.140950\pi$
$992$	−2.83296	+	4.23982i	−0.0899465	+	0.134614i
$993$	−28.9055	+	5.74966i	−0.917288	+	0.182460i
$994$	−13.9846	−	5.79261i	−0.443564	−	0.183730i
$995$	0.479646	+	7.60229i	0.0152058	+	0.241009i
$996$	0.783131	−	1.17204i	0.0248144	−	0.0371374i
$997$	48.8913	+	32.6681i	1.54840	+	1.03461i	0.976819	+	0.214066i	$0.0686706\pi$
$997$	48.8913	+	32.6681i	1.54840	+	1.03461i	0.571583	+	0.820544i	$0.306329\pi$
$998$	−36.9936	−	7.35849i	−1.17101	−	0.232929i
$999$	−35.3716	+	35.3716i	−1.11911	+	1.11911i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.r.b.167.4	yes	40
5.2	odd	4		850.2.s.d.643.4		40
5.3	odd	4		170.2.o.b.133.2	✓	40
5.4	even	2		850.2.v.d.507.2		40
17.11	odd	16		170.2.o.b.147.2	yes	40
85.28	even	16	inner	170.2.r.b.113.4	yes	40
85.62	even	16		850.2.v.d.793.2		40
85.79	odd	16		850.2.s.d.657.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.b.133.2	✓	40	5.3	odd	4
170.2.o.b.147.2	yes	40	17.11	odd	16
170.2.r.b.113.4	yes	40	85.28	even	16	inner
170.2.r.b.167.4	yes	40	1.1	even	1	trivial
850.2.s.d.643.4		40	5.2	odd	4
850.2.s.d.657.4		40	85.79	odd	16
850.2.v.d.507.2		40	5.4	even	2
850.2.v.d.793.2		40	85.62	even	16

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

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Newspace parameters

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$q$ -expansion

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Twists

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

Label	170.2.r.b.167.4

Level	$170$
Weight	$2$
Character	170.167
Analytic conductor	$1.357$
Analytic rank	$0$
Dimension	$40$
Inner twists	$2$