LMFDB - Embedded newform 840.2.bj.b.517.37

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(13,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.13"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.bj (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [184] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			517.37
Character	$\chi$	$=$	840.517
Dual form			840.2.bj.b.13.37

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.361491 - 1.36723i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.73865 + 0.988485i) q^{4} +(-0.0291073 - 2.23588i) q^{5} +(1.22239 + 0.711166i) q^{6} +(-0.641375 - 2.56683i) q^{7} +(1.97999 + 2.01981i) q^{8} -1.00000i q^{9} +(-3.04644 + 0.848047i) q^{10} -3.14974i q^{11} +(0.530446 - 1.92837i) q^{12} +(-1.67579 + 1.67579i) q^{13} +(-3.27761 + 1.80480i) q^{14} +(1.60159 + 1.56042i) q^{15} +(2.04580 - 3.43725i) q^{16} +(0.426943 - 0.426943i) q^{17} +(-1.36723 + 0.361491i) q^{18} +4.04265i q^{19} +(2.26074 + 3.85863i) q^{20} +(2.26855 + 1.36151i) q^{21} +(-4.30643 + 1.13860i) q^{22} +(4.67491 - 4.67491i) q^{23} +(-2.82829 - 0.0281526i) q^{24} +(-4.99831 + 0.130161i) q^{25} +(2.89698 + 1.68541i) q^{26} +(0.707107 + 0.707107i) q^{27} +(3.65240 + 3.82883i) q^{28} -8.56714 q^{29} +(1.55450 - 2.75382i) q^{30} -3.09047i q^{31} +(-5.43906 - 1.55454i) q^{32} +(2.22720 + 2.22720i) q^{33} +(-0.738066 - 0.429394i) q^{34} +(-5.72046 + 1.50875i) q^{35} +(0.988485 + 1.73865i) q^{36} +(-2.50081 + 2.50081i) q^{37} +(5.52724 - 1.46138i) q^{38} -2.36993i q^{39} +(4.45841 - 4.48582i) q^{40} +11.9718i q^{41} +(1.04144 - 3.59380i) q^{42} +(-7.74027 - 7.74027i) q^{43} +(3.11347 + 5.47629i) q^{44} +(-2.23588 + 0.0291073i) q^{45} +(-8.08163 - 4.70175i) q^{46} +(0.967892 - 0.967892i) q^{47} +(0.983909 + 3.87710i) q^{48} +(-6.17728 + 3.29261i) q^{49} +(1.98480 + 6.78679i) q^{50} +0.603788i q^{51} +(1.25712 - 4.57011i) q^{52} +(-2.85984 - 2.85984i) q^{53} +(0.711166 - 1.22239i) q^{54} +(-7.04243 + 0.0916805i) q^{55} +(3.91459 - 6.37777i) q^{56} +(-2.85859 - 2.85859i) q^{57} +(3.09694 + 11.7133i) q^{58} +14.1712i q^{59} +(-4.32705 - 1.12988i) q^{60} -7.18773 q^{61} +(-4.22539 + 1.11718i) q^{62} +(-2.56683 + 0.641375i) q^{63} +(-0.159247 + 7.99841i) q^{64} +(3.79564 + 3.69809i) q^{65} +(2.23999 - 3.85022i) q^{66} +(-6.73219 + 6.73219i) q^{67} +(-0.320277 + 1.16433i) q^{68} +6.61132i q^{69} +(4.13071 + 7.27580i) q^{70} +10.2152 q^{71} +(2.01981 - 1.97999i) q^{72} +(-4.40775 - 4.40775i) q^{73} +(4.32321 + 2.51517i) q^{74} +(3.44230 - 3.62637i) q^{75} +(-3.99610 - 7.02875i) q^{76} +(-8.08486 + 2.02016i) q^{77} +(-3.24024 + 0.856708i) q^{78} -6.04794i q^{79} +(-7.74483 - 4.47410i) q^{80} -1.00000 q^{81} +(16.3682 - 4.32769i) q^{82} +(2.97764 - 2.97764i) q^{83} +(-5.29003 - 0.124756i) q^{84} +(-0.967019 - 0.942165i) q^{85} +(-7.78471 + 13.3808i) q^{86} +(6.05788 - 6.05788i) q^{87} +(6.36187 - 6.23647i) q^{88} -14.6515 q^{89} +(0.848047 + 3.04644i) q^{90} +(5.37629 + 3.22667i) q^{91} +(-3.50695 + 12.7491i) q^{92} +(2.18529 + 2.18529i) q^{93} +(-1.67322 - 0.973449i) q^{94} +(9.03887 - 0.117671i) q^{95} +(4.94523 - 2.74677i) q^{96} +(10.6973 - 10.6973i) q^{97} +(6.73479 + 7.25553i) q^{98} -3.14974 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) $ 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.361491	−	1.36723i	−0.255613	−	0.966779i
$2$	−0.361491	−	1.36723i	−0.255613	−	0.966779i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−1.73865	+	0.988485i	−0.869324	+	0.494242i
$5$	−0.0291073	−	2.23588i	−0.0130172	−	0.999915i
$5$	−0.0291073	−	2.23588i	−0.0130172	−	0.999915i
$6$	1.22239	+	0.711166i	0.499039	+	0.290332i
$7$	−0.641375	−	2.56683i	−0.242417	−	0.970172i
$7$	−0.641375	−	2.56683i	−0.242417	−	0.970172i
$8$	1.97999	+	2.01981i	0.700034	+	0.714110i
$9$		−	1.00000i		−	0.333333i
$10$	−3.04644	+	0.848047i	−0.963370	+	0.268176i
$11$		−	3.14974i		−	0.949682i	−0.880072	−	0.474841i	$-0.842506\pi$
$11$		−	3.14974i		−	0.949682i	0.880072	−	0.474841i	$-0.157494\pi$
$12$	0.530446	−	1.92837i	0.153127	−	0.556674i
$13$	−1.67579	+	1.67579i	−0.464781	+	0.464781i	−0.900219	−	0.435438i	$-0.856594\pi$
$13$	−1.67579	+	1.67579i	−0.464781	+	0.464781i	0.435438	+	0.900219i	$0.356594\pi$
$14$	−3.27761	+	1.80480i	−0.875977	+	0.482352i
$15$	1.60159	+	1.56042i	0.413528	+	0.402899i
$16$	2.04580	−	3.43725i	0.511449	−	0.859314i
$17$	0.426943	−	0.426943i	0.103549	−	0.103549i	−0.653434	−	0.756983i	$-0.726672\pi$
$17$	0.426943	−	0.426943i	0.103549	−	0.103549i	0.756983	+	0.653434i	$0.226672\pi$
$18$	−1.36723	+	0.361491i	−0.322260	+	0.0852043i
$19$			4.04265i			0.927447i	0.885980	+	0.463724i	$0.153487\pi$
$19$			4.04265i			0.927447i	−0.885980	+	0.463724i	$0.846513\pi$
$20$	2.26074	+	3.85863i	0.505517	+	0.862817i
$21$	2.26855	+	1.36151i	0.495037	+	0.297105i
$22$	−4.30643	+	1.13860i	−0.918133	+	0.242751i
$23$	4.67491	−	4.67491i	0.974786	−	0.974786i	−0.0249038	−	0.999690i	$-0.507928\pi$
$23$	4.67491	−	4.67491i	0.974786	−	0.974786i	0.999690	+	0.0249038i	$0.00792794\pi$
$24$	−2.82829	−	0.0281526i	−0.577322	−	0.00574663i
$25$	−4.99831	+	0.130161i	−0.999661	+	0.0260322i
$26$	2.89698	+	1.68541i	0.568145	+	0.330537i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	3.65240	+	3.82883i	0.690239	+	0.723581i
$29$	−8.56714			−1.59088			−0.795439	−	0.606034i	$-0.792759\pi$
$29$	−8.56714			−1.59088			−0.795439	+	0.606034i	$0.792759\pi$
$30$	1.55450	−	2.75382i	0.283812	−	0.502776i
$31$		−	3.09047i		−	0.555064i	−0.960716	−	0.277532i	$-0.910484\pi$
$31$		−	3.09047i		−	0.555064i	0.960716	−	0.277532i	$-0.0895165\pi$
$32$	−5.43906	−	1.55454i	−0.961499	−	0.274807i
$33$	2.22720	+	2.22720i	0.387706	+	0.387706i
$34$	−0.738066	−	0.429394i	−0.126577	−	0.0736404i
$35$	−5.72046	+	1.50875i	−0.966934	+	0.255025i
$36$	0.988485	+	1.73865i	0.164747	+	0.289775i
$37$	−2.50081	+	2.50081i	−0.411130	+	0.411130i	−0.882132	−	0.471002i	$-0.843893\pi$
$37$	−2.50081	+	2.50081i	−0.411130	+	0.411130i	0.471002	+	0.882132i	$0.343893\pi$
$38$	5.52724	−	1.46138i	0.896637	−	0.237067i
$39$		−	2.36993i		−	0.379492i
$40$	4.45841	−	4.48582i	0.704937	−	0.709270i
$41$			11.9718i			1.86968i	0.355072	+	0.934839i	$0.384456\pi$
$41$			11.9718i			1.86968i	−0.355072	+	0.934839i	$0.615544\pi$
$42$	1.04144	−	3.59380i	0.160697	−	0.554536i
$43$	−7.74027	−	7.74027i	−1.18038	−	1.18038i	−0.979646	−	0.200735i	$-0.935667\pi$
$43$	−7.74027	−	7.74027i	−1.18038	−	1.18038i	−0.200735	−	0.979646i	$-0.564333\pi$
$44$	3.11347	+	5.47629i	0.469373	+	0.825582i
$45$	−2.23588	+	0.0291073i	−0.333305	+	0.00433906i
$46$	−8.08163	−	4.70175i	−1.19157	−	0.693235i
$47$	0.967892	−	0.967892i	0.141182	−	0.141182i	−0.632984	−	0.774165i	$-0.718170\pi$
$47$	0.967892	−	0.967892i	0.141182	−	0.141182i	0.774165	+	0.632984i	$0.218170\pi$
$48$	0.983909	+	3.87710i	0.142015	+	0.559612i
$49$	−6.17728	+	3.29261i	−0.882468	+	0.470372i
$50$	1.98480	+	6.78679i	0.280694	+	0.959797i
$51$			0.603788i			0.0845473i
$52$	1.25712	−	4.57011i	0.174331	−	0.633760i
$53$	−2.85984	−	2.85984i	−0.392829	−	0.392829i	0.482866	−	0.875695i	$-0.339596\pi$
$53$	−2.85984	−	2.85984i	−0.392829	−	0.392829i	−0.875695	+	0.482866i	$0.839596\pi$
$54$	0.711166	−	1.22239i	0.0967775	−	0.166346i
$55$	−7.04243	+	0.0916805i	−0.949602	+	0.0123622i
$56$	3.91459	−	6.37777i	0.523110	−	0.852265i
$57$	−2.85859	−	2.85859i	−0.378629	−	0.378629i
$58$	3.09694	+	11.7133i	0.406649	+	1.53803i
$59$			14.1712i			1.84493i	0.386081	+	0.922465i	$0.373829\pi$
$59$			14.1712i			1.84493i	−0.386081	+	0.922465i	$0.626171\pi$
$60$	−4.32705	−	1.12988i	−0.558620	−	0.145867i
$61$	−7.18773			−0.920294			−0.460147	−	0.887843i	$-0.652203\pi$
$61$	−7.18773			−0.920294			−0.460147	+	0.887843i	$0.652203\pi$
$62$	−4.22539	+	1.11718i	−0.536625	+	0.141882i
$63$	−2.56683	+	0.641375i	−0.323391	+	0.0808056i
$64$	−0.159247	+	7.99841i	−0.0199059	+	0.999802i
$65$	3.79564	+	3.69809i	0.470792	+	0.458692i
$66$	2.23999	−	3.85022i	0.275724	−	0.473929i
$67$	−6.73219	+	6.73219i	−0.822468	+	0.822468i	−0.986461	−	0.163993i	$-0.947562\pi$
$67$	−6.73219	+	6.73219i	−0.822468	+	0.822468i	0.163993	+	0.986461i	$0.447562\pi$
$68$	−0.320277	+	1.16433i	−0.0388393	+	0.141196i
$69$			6.61132i			0.795910i
$70$	4.13071	+	7.27580i	0.493714	+	0.869624i
$71$	10.2152			1.21232			0.606159	−	0.795343i	$-0.292709\pi$
$71$	10.2152			1.21232			0.606159	+	0.795343i	$0.292709\pi$
$72$	2.01981	−	1.97999i	0.238037	−	0.233345i
$73$	−4.40775	−	4.40775i	−0.515888	−	0.515888i	0.400437	−	0.916324i	$-0.368858\pi$
$73$	−4.40775	−	4.40775i	−0.515888	−	0.515888i	−0.916324	+	0.400437i	$0.868858\pi$
$74$	4.32321	+	2.51517i	0.502562	+	0.292382i
$75$	3.44230	−	3.62637i	0.397482	−	0.418738i
$76$	−3.99610	−	7.02875i	−0.458384	−	0.806253i
$77$	−8.08486	+	2.02016i	−0.921355	+	0.230219i
$78$	−3.24024	+	0.856708i	−0.366885	+	0.0970031i
$79$		−	6.04794i		−	0.680447i	−0.940345	−	0.340223i	$-0.889497\pi$
$79$		−	6.04794i		−	0.680447i	0.940345	−	0.340223i	$-0.110503\pi$
$80$	−7.74483	−	4.47410i	−0.865898	−	0.500220i
$81$	−1.00000			−0.111111
$82$	16.3682	−	4.32769i	1.80757	−	0.477914i
$83$	2.97764	−	2.97764i	0.326838	−	0.326838i	−0.524545	−	0.851383i	$-0.675764\pi$
$83$	2.97764	−	2.97764i	0.326838	−	0.326838i	0.851383	+	0.524545i	$0.175764\pi$
$84$	−5.29003	−	0.124756i	−0.577190	−	0.0136120i
$85$	−0.967019	−	0.942165i	−0.104888	−	0.102192i
$86$	−7.78471	+	13.3808i	−0.839447	+	1.44289i
$87$	6.05788	−	6.05788i	0.649473	−	0.649473i
$88$	6.36187	−	6.23647i	0.678177	−	0.664809i
$89$	−14.6515			−1.55306			−0.776529	−	0.630082i	$-0.783021\pi$
$89$	−14.6515			−1.55306			−0.776529	+	0.630082i	$0.783021\pi$
$90$	0.848047	+	3.04644i	0.0893920	+	0.321123i
$91$	5.37629	+	3.22667i	0.563588	+	0.338247i
$92$	−3.50695	+	12.7491i	−0.365625	+	1.32919i
$93$	2.18529	+	2.18529i	0.226604	+	0.226604i
$94$	−1.67322	−	0.973449i	−0.172579	−	0.100404i
$95$	9.03887	−	0.117671i	0.927369	−	0.0120728i
$96$	4.94523	−	2.74677i	0.504720	−	0.280341i
$97$	10.6973	−	10.6973i	1.08615	−	1.08615i	0.0902239	−	0.995922i	$-0.471242\pi$
$97$	10.6973	−	10.6973i	1.08615	−	1.08615i	0.995922	−	0.0902239i	$-0.0287583\pi$
$98$	6.73479	+	7.25553i	0.680316	+	0.732919i
$99$	−3.14974			−0.316561
$100$	8.56163	−	5.16705i	0.856163	−	0.516705i
$101$	9.80142			0.975278			0.487639	−	0.873045i	$-0.337858\pi$
$101$	9.80142			0.975278			0.487639	+	0.873045i	$0.337858\pi$
$102$	0.825519	−	0.218264i	0.0817385	−	0.0216114i
$103$	−6.35740	−	6.35740i	−0.626413	−	0.626413i	0.320750	−	0.947164i	$-0.396065\pi$
$103$	−6.35740	−	6.35740i	−0.626413	−	0.626413i	−0.947164	+	0.320750i	$0.896065\pi$
$104$	−6.70284	−	0.0667196i	−0.657267	−	0.00654240i
$105$	2.97813	−	5.11182i	0.290636	−	0.498863i
$106$	−2.87626	+	4.94387i	−0.279367	+	0.480191i
$107$	11.6251	−	11.6251i	1.12384	−	1.12384i	0.132679	−	0.991159i	$-0.457642\pi$
$107$	11.6251	−	11.6251i	1.12384	−	1.12384i	0.991159	−	0.132679i	$-0.0423581\pi$
$108$	−1.92837	−	0.530446i	−0.185558	−	0.0510422i
$109$	−2.83769			−0.271802			−0.135901	−	0.990722i	$-0.543393\pi$
$109$	−2.83769			−0.271802			−0.135901	+	0.990722i	$0.543393\pi$
$110$	2.67113	+	9.59550i	0.254682	+	0.914895i
$111$		−	3.53668i		−	0.335687i
$112$	−10.1350	−	3.04665i	−0.957666	−	0.287882i
$113$	−2.36881	+	2.36881i	−0.222839	+	0.222839i	−0.809693	−	0.586854i	$-0.800366\pi$
$113$	−2.36881	+	2.36881i	−0.222839	+	0.222839i	0.586854	+	0.809693i	$0.300366\pi$
$114$	−2.87500	+	4.94170i	−0.269268	+	0.462833i
$115$	−10.5886	−	10.3165i	−0.987392	−	0.962015i
$116$	14.8952	−	8.46848i	1.38299	−	0.786279i
$117$	1.67579	+	1.67579i	0.154927	+	0.154927i
$118$	19.3753	−	5.12275i	1.78364	−	0.471588i
$119$	−1.36972	−	0.822061i	−0.125562	−	0.0753582i
$120$	0.0193781	+	6.32453i	0.00176897	+	0.577348i
$121$	1.07914			0.0981037
$122$	2.59830	+	9.82730i	0.235239	+	0.889722i
$123$	−8.46533	−	8.46533i	−0.763293	−	0.763293i
$124$	3.05488	+	5.37323i	0.274336	+	0.482531i
$125$	0.436511	+	11.1718i	0.0390428	+	0.999238i
$126$	1.80480	+	3.27761i	0.160784	+	0.291992i
$127$	7.88082	+	7.88082i	0.699310	+	0.699310i	0.964262	−	0.264952i	$-0.0853560\pi$
$127$	7.88082	+	7.88082i	0.699310	+	0.699310i	−0.264952	+	0.964262i	$0.585356\pi$
$128$	10.9933	−	2.67363i	0.971676	−	0.236318i
$129$	10.9464			0.963777
$130$	3.68406	−	6.52635i	0.323113	−	0.572399i
$131$	−11.4551			−1.00084			−0.500420	−	0.865783i	$-0.666821\pi$
$131$	−11.4551			−1.00084			−0.500420	+	0.865783i	$0.666821\pi$
$132$	−6.07388	−	1.67077i	−0.528663	−	0.145422i
$133$	10.3768	−	2.59285i	0.899784	−	0.224829i
$134$	11.6381	+	6.77084i	1.00538	+	0.584912i
$135$	1.56042	−	1.60159i	0.134300	−	0.137843i
$136$	1.70769	+	0.0169982i	0.146433	+	0.00145758i
$137$	−8.35810	−	8.35810i	−0.714080	−	0.714080i	0.253306	−	0.967386i	$-0.418482\pi$
$137$	−8.35810	−	8.35810i	−0.714080	−	0.714080i	−0.967386	+	0.253306i	$0.918482\pi$
$138$	9.03921	−	2.38993i	0.769469	−	0.203445i
$139$		−	11.9838i		−	1.01645i	−0.861223	−	0.508227i	$-0.830301\pi$
$139$		−	11.9838i		−	1.01645i	0.861223	−	0.508227i	$-0.169699\pi$
$140$	8.45449	−	8.27777i	0.714535	−	0.699599i
$141$			1.36881i			0.115274i
$142$	−3.69270	−	13.9665i	−0.309884	−	1.17204i
$143$	5.27831	+	5.27831i	0.441394	+	0.441394i
$144$	−3.43725	−	2.04580i	−0.286438	−	0.170483i
$145$	0.249366	+	19.1551i	0.0207088	+	1.59074i
$146$	−4.43305	+	7.61977i	−0.366882	+	0.630617i
$147$	2.03977	−	6.69622i	0.168237	−	0.552295i
$148$	1.87602	−	6.82004i	0.154208	−	0.560604i
$149$	11.6260			0.952439			0.476220	−	0.879326i	$-0.342007\pi$
$149$	11.6260			0.952439			0.476220	+	0.879326i	$0.342007\pi$
$150$	−6.20245	−	3.39552i	−0.506428	−	0.277243i
$151$	−2.85178			−0.232075			−0.116037	−	0.993245i	$-0.537019\pi$
$151$	−2.85178			−0.232075			−0.116037	+	0.993245i	$0.537019\pi$
$152$	−8.16538	+	8.00442i	−0.662299	+	0.649244i
$153$	−0.426943	−	0.426943i	−0.0345163	−	0.0345163i
$154$	5.68464	+	10.3236i	0.458081	+	0.831900i
$155$	−6.90991	+	0.0899552i	−0.555017	+	0.00722538i
$156$	2.34264	+	4.12047i	0.187561	+	0.329902i
$157$	8.00296	+	8.00296i	0.638706	+	0.638706i	0.950236	−	0.311530i	$-0.100842\pi$
$157$	8.00296	+	8.00296i	0.638706	+	0.638706i	−0.311530	+	0.950236i	$0.600842\pi$
$158$	−8.26894	+	2.18628i	−0.657842	+	0.173931i
$159$	4.04442			0.320744
$160$	−3.31745	+	12.2063i	−0.262267	+	0.964995i
$161$	−14.9981	−	9.00135i	−1.18201	−	0.709406i
$162$	0.361491	+	1.36723i	0.0284014	+	0.107420i
$163$	−2.97555	−	2.97555i	−0.233063	−	0.233063i	0.580907	−	0.813970i	$-0.302698\pi$
$163$	−2.97555	−	2.97555i	−0.233063	−	0.233063i	−0.813970	+	0.580907i	$0.802698\pi$
$164$	−11.8339	−	20.8147i	−0.924074	−	1.62536i
$165$	4.91493	−	5.04458i	0.382626	−	0.392720i
$166$	−5.14751	−	2.99473i	−0.399524	−	0.232436i
$167$	10.5871	−	10.5871i	0.819255	−	0.819255i	−0.166745	−	0.986000i	$-0.553326\pi$
$167$	10.5871	−	10.5871i	0.819255	−	0.819255i	0.986000	+	0.166745i	$0.0533257\pi$
$168$	1.74173	+	7.27780i	0.134377	+	0.561495i
$169$			7.38344i			0.567957i
$170$	−0.938589	+	1.66272i	−0.0719865	+	0.127525i
$171$	4.04265			0.309149
$172$	21.1088	+	5.80647i	1.60953	+	0.442739i
$173$	7.17872	−	7.17872i	0.545788	−	0.545788i	−0.379432	−	0.925220i	$-0.623880\pi$
$173$	7.17872	−	7.17872i	0.545788	−	0.545788i	0.925220	+	0.379432i	$0.123880\pi$
$174$	−10.4724	−	6.09266i	−0.793911	−	0.461883i
$175$	3.53989	+	12.7463i	0.267590	+	0.963533i
$176$	−10.8265	−	6.44373i	−0.816075	−	0.485714i
$177$	−10.0205	−	10.0205i	−0.753189	−	0.753189i
$178$	5.29639	+	20.0320i	0.396981	+	1.50146i
$179$	1.20525			0.0900845			0.0450422	−	0.998985i	$-0.485658\pi$
$179$	1.20525			0.0900845			0.0450422	+	0.998985i	$0.485658\pi$
$180$	3.85863	−	2.26074i	0.287606	−	0.168506i
$181$	−6.00674			−0.446477			−0.223239	−	0.974764i	$-0.571663\pi$
$181$	−6.00674			−0.446477			−0.223239	+	0.974764i	$0.571663\pi$
$182$	2.46813	−	8.51705i	0.182950	−	0.631326i
$183$	5.08249	−	5.08249i	0.375709	−	0.375709i
$184$	18.6987	+	0.186126i	1.37849	+	0.0137214i
$185$	5.66430	+	5.51871i	0.416447	+	0.405744i
$186$	2.19784	−	3.77776i	0.161153	−	0.276999i
$187$	−1.34476	−	1.34476i	−0.0983385	−	0.0983385i
$188$	−0.726078	+	2.63957i	−0.0529547	+	0.192511i
$189$	1.36151	−	2.26855i	0.0990350	−	0.165012i
$190$	−3.42836	−	12.3157i	−0.248719	−	0.893475i
$191$	−6.92005			−0.500717			−0.250359	−	0.968153i	$-0.580549\pi$
$191$	−6.92005			−0.500717			−0.250359	+	0.968153i	$0.580549\pi$
$192$	−5.54313	−	5.76834i	−0.400041	−	0.416294i
$193$	0.257652	−	0.257652i	0.0185462	−	0.0185462i	−0.697773	−	0.716319i	$-0.745826\pi$
$193$	0.257652	−	0.257652i	0.0185462	−	0.0185462i	0.716319	+	0.697773i	$0.245826\pi$
$194$	−18.4927	−	10.7587i	−1.32770	−	0.772430i
$195$	−5.29887	+	0.0689823i	−0.379460	+	0.00493992i
$196$	7.48542	−	11.8308i	0.534673	−	0.845059i
$197$	6.99522	−	6.99522i	0.498389	−	0.498389i	−0.412547	−	0.910936i	$-0.635361\pi$
$197$	6.99522	−	6.99522i	0.498389	−	0.498389i	0.910936	+	0.412547i	$0.135361\pi$
$198$	1.13860	+	4.30643i	0.0809170	+	0.306044i
$199$	−13.1934			−0.935254			−0.467627	−	0.883926i	$-0.654891\pi$
$199$	−13.1934			−0.935254			−0.467627	+	0.883926i	$0.654891\pi$
$200$	−10.1595	−	9.83790i	−0.718386	−	0.695644i
$201$		−	9.52076i		−	0.671542i
$202$	−3.54313	−	13.4008i	−0.249293	−	0.942878i
$203$	5.49474	+	21.9904i	0.385655	+	1.54342i
$204$	−0.596835	−	1.04978i	−0.0417868	−	0.0734990i
$205$	26.7674	−	0.348467i	1.86952	−	0.0243380i
$206$	−6.39390	+	10.9902i	−0.445484	+	0.765723i
$207$	−4.67491	−	4.67491i	−0.324929	−	0.324929i
$208$	2.33179	+	9.18845i	0.161681	+	0.637105i
$209$	12.7333			0.880780
$210$	−8.06562	−	2.22392i	−0.556581	−	0.153465i
$211$		−	24.3710i		−	1.67777i	−0.544310	−	0.838884i	$-0.683209\pi$
$211$		−	24.3710i		−	1.67777i	0.544310	−	0.838884i	$-0.316791\pi$
$212$	7.79916	+	2.14535i	0.535648	+	0.147343i
$213$	−7.22322	+	7.22322i	−0.494927	+	0.494927i
$214$	−20.0965	−	11.6918i	−1.37377	−	0.799236i
$215$	−17.0810	+	17.5316i	−1.16492	+	1.19565i
$216$	−0.0281526	+	2.82829i	−0.00191554	+	0.192441i
$217$	−7.93272	+	1.98215i	−0.538508	+	0.134557i
$218$	1.02580	+	3.87978i	0.0694759	+	0.262772i
$219$	6.23349			0.421220
$220$	12.1537	−	7.12074i	0.819402	−	0.480080i
$221$			1.43093i			0.0962551i
$222$	−4.83546	+	1.27848i	−0.324535	+	0.0858058i
$223$	−10.5418	−	10.5418i	−0.705931	−	0.705931i	0.259746	−	0.965677i	$-0.416361\pi$
$223$	−10.5418	−	10.5418i	−0.705931	−	0.705931i	−0.965677	+	0.259746i	$0.916361\pi$
$224$	−0.501775	+	14.9582i	−0.0335262	+	0.999438i
$225$	0.130161	+	4.99831i	0.00867739	+	0.333220i
$226$	4.09501	+	2.38241i	0.272396	+	0.158475i
$227$	−11.0334	−	11.0334i	−0.732312	−	0.732312i	0.238766	−	0.971077i	$-0.423257\pi$
$227$	−11.0334	−	11.0334i	−0.732312	−	0.732312i	−0.971077	+	0.238766i	$0.923257\pi$
$228$	7.79574	+	2.14441i	0.516286	+	0.142017i
$229$		−	14.1494i		−	0.935017i	−0.883989	−	0.467509i	$-0.845152\pi$
$229$		−	14.1494i		−	0.935017i	0.883989	−	0.467509i	$-0.154848\pi$
$230$	−10.2773	+	18.2064i	−0.677665	+	1.20049i
$231$	4.28839	−	7.14533i	0.282155	−	0.470128i
$232$	−16.9629	−	17.3040i	−1.11367	−	1.13606i
$233$	−5.57671	+	5.57671i	−0.365342	+	0.365342i	−0.865775	−	0.500433i	$-0.833174\pi$
$233$	−5.57671	+	5.57671i	−0.365342	+	0.365342i	0.500433	+	0.865775i	$0.333174\pi$
$234$	1.68541	−	2.89698i	0.110179	−	0.189382i
$235$	−2.19226	−	2.13592i	−0.143007	−	0.139332i
$236$	−14.0080	−	24.6387i	−0.911842	−	1.60384i
$237$	4.27654	+	4.27654i	0.277791	+	0.277791i
$238$	−0.628806	+	2.16990i	−0.0407595	+	0.140653i
$239$		−	16.6027i		−	1.07394i	−0.843602	−	0.536969i	$-0.819569\pi$
$239$		−	16.6027i		−	1.07394i	0.843602	−	0.536969i	$-0.180431\pi$
$240$	8.64009	−	2.31275i	0.557715	−	0.149288i
$241$			14.1668i			0.912562i	0.889836	+	0.456281i	$0.150819\pi$
$241$			14.1668i			0.912562i	−0.889836	+	0.456281i	$0.849181\pi$
$242$	−0.390100	−	1.47544i	−0.0250766	−	0.0948447i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	12.4969	−	7.10496i	0.800034	−	0.454848i
$245$	7.54167	+	13.7158i	0.481820	+	0.876270i
$246$	−8.51393	+	14.6342i	−0.542828	+	0.933043i
$247$	−6.77464	−	6.77464i	−0.431060	−	0.431060i
$248$	6.24215	−	6.11911i	0.396377	−	0.388564i
$249$			4.21101i			0.266862i
$250$	15.1167	−	4.63532i	0.956062	−	0.293164i
$251$	12.3831			0.781613			0.390807	−	0.920473i	$-0.372196\pi$
$251$	12.3831			0.781613			0.390807	+	0.920473i	$0.372196\pi$
$252$	3.82883	−	3.65240i	0.241194	−	0.230080i
$253$	−14.7247	−	14.7247i	−0.925737	−	0.925737i
$254$	7.92607	−	13.6238i	0.497326	−	0.854831i
$255$	1.35000	−	0.0175747i	0.0845401	−	0.00110057i
$256$	−7.62944	−	14.0638i	−0.476840	−	0.878990i
$257$	−3.19011	+	3.19011i	−0.198993	+	0.198993i	−0.799568	−	0.600575i	$-0.794938\pi$
$257$	−3.19011	+	3.19011i	−0.198993	+	0.198993i	0.600575	+	0.799568i	$0.294938\pi$
$258$	−3.95703	−	14.9663i	−0.246354	−	0.931759i
$259$	8.02312	+	4.81521i	0.498532	+	0.299202i
$260$	−10.2548	−	2.67774i	−0.635975	−	0.166066i
$261$			8.56714i			0.530292i
$262$	4.14093	+	15.6618i	0.255828	+	0.967592i
$263$	0.748111	−	0.748111i	0.0461305	−	0.0461305i	−0.683665	−	0.729796i	$-0.739615\pi$
$263$	0.748111	−	0.748111i	0.0461305	−	0.0461305i	0.729796	+	0.683665i	$0.239615\pi$
$264$	−0.0886734	+	8.90837i	−0.00545747	+	0.548272i
$265$	−6.31101	+	6.47749i	−0.387682	+	0.397909i
$266$	−7.29616	−	13.2502i	−0.447356	−	0.812423i
$267$	10.3602	−	10.3602i	0.634033	−	0.634033i
$268$	5.05025	−	18.3596i	0.308493	−	1.12149i
$269$		−	16.9512i		−	1.03353i	−0.856126	−	0.516767i	$-0.827135\pi$
$269$		−	16.9512i		−	1.03353i	0.856126	−	0.516767i	$-0.172865\pi$
$270$	−2.75382	−	1.55450i	−0.167592	−	0.0946039i
$271$		−	4.28643i		−	0.260382i	−0.991489	−	0.130191i	$-0.958441\pi$
$271$		−	4.28643i		−	0.260382i	0.991489	−	0.130191i	$-0.0415591\pi$
$272$	−0.594073	−	2.34095i	−0.0360210	−	0.141941i
$273$	−6.08321	+	1.52001i	−0.368173	+	0.0919953i
$274$	−8.40608	+	14.4488i	−0.507830	+	0.872886i
$275$	0.409973	+	15.7434i	0.0247223	+	0.949360i
$276$	−6.53519	−	11.4948i	−0.393372	−	0.691903i
$277$	−8.88967	+	8.88967i	−0.534128	+	0.534128i	−0.921798	−	0.387670i	$-0.873280\pi$
$277$	−8.88967	+	8.88967i	−0.534128	+	0.534128i	0.387670	+	0.921798i	$0.373280\pi$
$278$	−16.3846	+	4.33204i	−0.982686	+	0.259818i
$279$	−3.09047			−0.185021
$280$	−14.3739	−	8.56692i	−0.859003	−	0.511971i
$281$	−6.48286			−0.386735			−0.193368	−	0.981126i	$-0.561941\pi$
$281$	−6.48286			−0.386735			−0.193368	+	0.981126i	$0.561941\pi$
$282$	1.87148	−	0.494811i	0.111445	−	0.0294656i
$283$	2.08317	−	2.08317i	0.123832	−	0.123832i	−0.642475	−	0.766307i	$-0.722092\pi$
$283$	2.08317	−	2.08317i	0.123832	−	0.123832i	0.766307	+	0.642475i	$0.222092\pi$
$284$	−17.7606	+	10.0975i	−1.05390	+	0.599179i
$285$	−6.30824	+	6.47465i	−0.373668	+	0.383525i
$286$	5.30861	−	9.12473i	0.313905	−	0.539557i
$287$	30.7296	−	7.67840i	1.81391	−	0.453241i
$288$	−1.55454	+	5.43906i	−0.0916023	+	0.320500i
$289$			16.6354i			0.978555i
$290$	26.0993	−	7.26533i	1.53260	−	0.426635i
$291$			15.1283i			0.886834i
$292$	12.0205	+	3.30653i	0.703447	+	0.193500i
$293$	17.2751	−	17.2751i	1.00922	−	1.00922i	0.00926472	−	0.999957i	$-0.497051\pi$
$293$	17.2751	−	17.2751i	1.00922	−	1.00922i	0.999957	−	0.00926472i	$-0.00294909\pi$
$294$	−9.89264	−	0.368218i	−0.576951	−	0.0214749i
$295$	31.6850	−	0.412485i	1.84477	−	0.0240158i
$296$	−10.0027	−	0.0995667i	−0.581397	−	0.00578719i
$297$	2.22720	−	2.22720i	0.129235	−	0.129235i
$298$	−4.20270	−	15.8955i	−0.243456	−	0.920799i
$299$			15.6684i			0.906124i
$300$	−2.40033	+	9.70765i	−0.138583	+	0.560471i
$301$	−14.9036	+	24.8324i	−0.859028	+	1.43132i
$302$	1.03089	+	3.89905i	0.0593213	+	0.224365i
$303$	−6.93065	+	6.93065i	−0.398155	+	0.398155i
$304$	13.8956	+	8.27044i	0.796968	+	0.474342i
$305$	0.209216	+	16.0709i	0.0119797	+	0.920217i
$306$	−0.429394	+	0.738066i	−0.0245468	+	0.0421924i
$307$	−3.11129	−	3.11129i	−0.177570	−	0.177570i	0.612725	−	0.790296i	$-0.290073\pi$
$307$	−3.11129	−	3.11129i	−0.177570	−	0.177570i	−0.790296	+	0.612725i	$0.790073\pi$
$308$	12.0598	−	11.5041i	0.687172	−	0.655508i
$309$	8.99072			0.511464
$310$	2.62086	+	9.41493i	0.148855	+	0.534732i
$311$			7.70349i			0.436825i	0.975857	+	0.218412i	$0.0700878\pi$
$311$			7.70349i			0.436825i	−0.975857	+	0.218412i	$0.929912\pi$
$312$	4.78680	−	4.69244i	0.270999	−	0.265657i
$313$	7.57505	+	7.57505i	0.428167	+	0.428167i	0.888004	−	0.459837i	$-0.152092\pi$
$313$	7.57505	+	7.57505i	0.428167	+	0.428167i	−0.459837	+	0.888004i	$0.652092\pi$
$314$	8.04891	−	13.8349i	0.454226	−	0.780749i
$315$	1.50875	+	5.72046i	0.0850084	+	0.322311i
$316$	5.97830	+	10.5152i	0.336306	+	0.591529i
$317$	19.0557	−	19.0557i	1.07028	−	1.07028i	0.0729409	−	0.997336i	$-0.476762\pi$
$317$	19.0557	−	19.0557i	1.07028	−	1.07028i	0.997336	−	0.0729409i	$-0.0232385\pi$
$318$	−1.46202	−	5.52966i	−0.0819862	−	0.310088i
$319$			26.9842i			1.51083i
$320$	17.8881	+	0.123245i	0.999976	+	0.00688961i
$321$			16.4403i			0.917610i
$322$	−6.88526	+	23.7598i	−0.383701	+	1.32408i
$323$	1.72598	+	1.72598i	0.0960361	+	0.0960361i
$324$	1.73865	−	0.988485i	0.0965916	−	0.0549158i
$325$	8.15800	−	8.59424i	0.452524	−	0.476723i
$326$	−2.99263	+	5.14390i	−0.165747	+	0.284894i
$327$	2.00655	−	2.00655i	0.110962	−	0.110962i
$328$	−24.1807	+	23.7041i	−1.33516	+	1.30884i
$329$	−3.10520	−	1.86364i	−0.171195	−	0.102746i
$330$	−8.67382	−	4.89627i	−0.477478	−	0.269531i
$331$			15.3548i			0.843977i	0.906601	+	0.421988i	$0.138668\pi$
$331$			15.3548i			0.843977i	−0.906601	+	0.421988i	$0.861332\pi$
$332$	−2.23371	+	8.12041i	−0.122591	+	0.445665i
$333$	2.50081	+	2.50081i	0.137043	+	0.137043i
$334$	−18.3022	−	10.6479i	−1.00145	−	0.582626i
$335$	15.2483	+	14.8564i	0.833105	+	0.811692i
$336$	9.32082	−	5.01221i	0.508493	−	0.273438i
$337$	−15.3814	−	15.3814i	−0.837877	−	0.837877i	0.150703	−	0.988579i	$-0.451846\pi$
$337$	−15.3814	−	15.3814i	−0.837877	−	0.837877i	−0.988579	+	0.150703i	$0.951846\pi$
$338$	10.0949	−	2.66905i	0.549089	−	0.145177i
$339$		−	3.35000i		−	0.181947i
$340$	2.61262	+	0.682210i	0.141689	+	0.0369980i
$341$	−9.73416			−0.527135
$342$	−1.46138	−	5.52724i	−0.0790225	−	0.298879i
$343$	12.4135	+	13.7443i	0.670267	+	0.742120i
$344$	0.308170	−	30.9596i	0.0166154	−	1.66923i
$345$	14.7821	−	0.192438i	0.795842	−	0.0103605i
$346$	−12.4100	−	7.21994i	−0.667167	−	0.388146i
$347$	−2.60251	+	2.60251i	−0.139710	+	0.139710i	−0.773503	−	0.633793i	$-0.781497\pi$
$347$	−2.60251	+	2.60251i	−0.139710	+	0.139710i	0.633793	+	0.773503i	$0.281497\pi$
$348$	−4.54440	+	16.5206i	−0.243606	+	0.885600i
$349$			4.01988i			0.215179i	0.994195	+	0.107590i	$0.0343133\pi$
$349$			4.01988i			0.215179i	−0.994195	+	0.107590i	$0.965687\pi$
$350$	16.1476	−	9.44754i	0.863124	−	0.504992i
$351$	−2.36993			−0.126497
$352$	−4.89640	+	17.1316i	−0.260979	+	0.913119i
$353$	−10.3871	−	10.3871i	−0.552850	−	0.552850i	0.374412	−	0.927262i	$-0.377844\pi$
$353$	−10.3871	−	10.3871i	−0.552850	−	0.552850i	−0.927262	+	0.374412i	$0.877844\pi$
$354$	−10.0781	+	17.3227i	−0.535643	+	0.920693i
$355$	−0.297337	−	22.8399i	−0.0157810	−	1.21222i
$356$	25.4738	−	14.4828i	1.35011	−	0.767587i
$357$	1.54982	−	0.387254i	0.0820254	−	0.0204957i
$358$	−0.435687	−	1.64785i	−0.0230268	−	0.0870918i
$359$		−	8.85420i		−	0.467307i	−0.972320	−	0.233653i	$-0.924932\pi$
$359$		−	8.85420i		−	0.467307i	0.972320	−	0.233653i	$-0.0750681\pi$
$360$	−4.48582	−	4.45841i	−0.236423	−	0.234979i
$361$	2.65698			0.139841
$362$	2.17138	+	8.21261i	0.114125	+	0.431645i
$363$	−0.763068	+	0.763068i	−0.0400507	+	0.0400507i
$364$	−12.5370	−	0.295663i	−0.657117	−	0.0154970i
$365$	−9.72689	+	9.98348i	−0.509128	+	0.522559i
$366$	−8.78622	−	5.11167i	−0.459263	−	0.267191i
$367$	−18.1267	+	18.1267i	−0.946204	+	0.946204i	−0.998625	−	0.0524208i	$-0.983306\pi$
$367$	−18.1267	+	18.1267i	−0.946204	+	0.946204i	0.0524208	+	0.998625i	$0.483306\pi$
$368$	−6.50494	−	25.6328i	−0.339093	−	1.33620i
$369$	11.9718			0.623226
$370$	5.49777	−	9.73937i	0.285815	−	0.506326i
$371$	−5.50650	+	9.17496i	−0.285883	+	0.476340i
$372$	−5.95958	−	1.63933i	−0.308990	−	0.0849951i
$373$	−12.4629	−	12.4629i	−0.645305	−	0.645305i	0.306550	−	0.951855i	$-0.400825\pi$
$373$	−12.4629	−	12.4629i	−0.645305	−	0.645305i	−0.951855	+	0.306550i	$0.900825\pi$
$374$	−1.35248	+	2.32472i	−0.0699350	+	0.120208i
$375$	−8.20833	−	7.59101i	−0.423876	−	0.391998i
$376$	3.87138	+	0.0385355i	0.199651	+	0.00198731i
$377$	14.3567	−	14.3567i	0.739410	−	0.739410i
$378$	−3.59380	−	1.04144i	−0.184845	−	0.0535656i
$379$	5.54879			0.285022			0.142511	−	0.989793i	$-0.454482\pi$
$379$	5.54879			0.285022			0.142511	+	0.989793i	$0.454482\pi$
$380$	−15.5991	+	9.13938i	−0.800217	+	0.468840i
$381$	−11.1452			−0.570984
$382$	2.50154	+	9.46132i	0.127990	+	0.484083i
$383$	5.77404	+	5.77404i	0.295040	+	0.295040i	0.839067	−	0.544028i	$-0.183101\pi$
$383$	5.77404	+	5.77404i	0.295040	+	0.295040i	−0.544028	+	0.839067i	$0.683101\pi$
$384$	−5.88287	+	9.66395i	−0.300209	+	0.493161i
$385$	4.75217	+	18.0180i	0.242193	+	0.918280i
$386$	−0.445410	−	0.259132i	−0.0226708	−	0.0131895i
$387$	−7.74027	+	7.74027i	−0.393460	+	0.393460i
$388$	−8.02472	+	29.1729i	−0.407393	+	1.48103i
$389$	−20.8524			−1.05726			−0.528629	−	0.848853i	$-0.677294\pi$
$389$	−20.8524			−1.05726			−0.528629	+	0.848853i	$0.677294\pi$
$390$	2.00981	+	7.21985i	0.101771	+	0.365591i
$391$		−	3.99184i		−	0.201876i
$392$	−18.8814	−	5.95757i	−0.953655	−	0.300903i
$393$	8.10001	−	8.10001i	0.408591	−	0.408591i
$394$	−12.0928	−	7.03538i	−0.609227	−	0.354437i
$395$	−13.5225	+	0.176039i	−0.680389	+	0.00885751i
$396$	5.47629	−	3.11347i	0.275194	−	0.156458i
$397$	12.8380	+	12.8380i	0.644320	+	0.644320i	0.951614	−	0.307295i	$-0.0994238\pi$
$397$	12.8380	+	12.8380i	0.644320	+	0.644320i	−0.307295	+	0.951614i	$0.599424\pi$
$398$	4.76929	+	18.0384i	0.239063	+	0.904184i
$399$	−5.50409	+	9.17094i	−0.275549	+	0.459121i
$400$	−9.77812	+	17.4467i	−0.488906	+	0.872337i
$401$	32.9376			1.64483			0.822414	−	0.568890i	$-0.192627\pi$
$401$	32.9376			1.64483			0.822414	+	0.568890i	$0.192627\pi$
$402$	−13.0171	+	3.44167i	−0.649233	+	0.171655i
$403$	5.17898	+	5.17898i	0.257983	+	0.257983i
$404$	−17.0412	+	9.68855i	−0.847833	+	0.482024i
$405$	0.0291073	+	2.23588i	0.00144635	+	0.111102i
$406$	28.0797	−	15.4619i	1.39357	−	0.767363i
$407$	7.87689	+	7.87689i	0.390443	+	0.390443i
$408$	−1.21954	+	1.19550i	−0.0603760	+	0.0591859i
$409$	−12.5472			−0.620422			−0.310211	−	0.950668i	$-0.600400\pi$
$409$	−12.5472			−0.620422			−0.310211	+	0.950668i	$0.600400\pi$
$410$	−10.1526	−	36.4714i	−0.501403	−	1.80119i
$411$	11.8201			0.583044
$412$	17.3375	+	4.76909i	0.854156	+	0.234956i
$413$	36.3751	−	9.08903i	1.78990	−	0.447242i
$414$	−4.70175	+	8.08163i	−0.231078	+	0.397190i
$415$	−6.74430	−	6.57096i	−0.331065	−	0.322556i
$416$	11.7198	−	6.50965i	0.574612	−	0.319162i
$417$	8.47383	+	8.47383i	0.414965	+	0.414965i
$418$	−4.60297	−	17.4094i	−0.225139	−	0.851520i
$419$			18.0734i			0.882943i	0.897275	+	0.441472i	$0.145543\pi$
$419$			18.0734i			0.882943i	−0.897275	+	0.441472i	$0.854457\pi$
$420$	−0.124961	+	11.8315i	−0.00609748	+	0.577318i
$421$		−	2.50726i		−	0.122196i	−0.998132	−	0.0610982i	$-0.980540\pi$
$421$		−	2.50726i		−	0.122196i	0.998132	−	0.0610982i	$-0.0194603\pi$
$422$	−33.3208	+	8.80989i	−1.62203	+	0.428859i
$423$	−0.967892	−	0.967892i	−0.0470605	−	0.0470605i
$424$	0.113861	−	11.4388i	0.00552958	−	0.555517i
$425$	−2.07842	+	2.18956i	−0.100818	+	0.106209i
$426$	12.4870	+	7.26469i	0.604995	+	0.351975i
$427$	4.61003	+	18.4497i	0.223095	+	0.892844i
$428$	−8.72071	+	31.7031i	−0.421531	+	1.53243i
$429$	−7.46465			−0.360397
$430$	30.1444	+	17.0162i	1.45369	+	0.820593i
$431$	−29.0477			−1.39918			−0.699588	−	0.714546i	$-0.746633\pi$
$431$	−29.0477			−1.39918			−0.699588	+	0.714546i	$0.746633\pi$
$432$	3.87710	−	0.983909i	0.186537	−	0.0473384i
$433$	−28.2701	−	28.2701i	−1.35857	−	1.35857i	−0.875678	−	0.482895i	$-0.839585\pi$
$433$	−28.2701	−	28.2701i	−1.35857	−	1.35857i	−0.482895	−	0.875678i	$-0.660415\pi$
$434$	5.57766	+	10.1293i	0.267736	+	0.486224i
$435$	−13.7210	−	13.3684i	−0.657872	−	0.640964i
$436$	4.93375	−	2.80501i	0.236284	−	0.134336i
$437$	18.8990	+	18.8990i	0.904063	+	0.904063i
$438$	−2.25335	−	8.52263i	−0.107669	−	0.407227i
$439$	32.1011			1.53210			0.766052	−	0.642779i	$-0.222219\pi$
$439$	32.1011			1.53210			0.766052	+	0.642779i	$0.222219\pi$
$440$	−14.1292	−	14.0428i	−0.673581	−	0.669466i
$441$	3.29261	+	6.17728i	0.156791	+	0.294156i
$442$	1.95642	−	0.517270i	0.0930574	−	0.0246040i
$443$	16.1970	+	16.1970i	0.769544	+	0.769544i	0.978026	−	0.208482i	$-0.0668523\pi$
$443$	16.1970	+	16.1970i	0.769544	+	0.769544i	−0.208482	+	0.978026i	$0.566852\pi$
$444$	3.49595	+	6.14904i	0.165910	+	0.291820i
$445$	0.426466	+	32.7590i	0.0202164	+	1.55293i
$446$	−10.6023	+	18.2238i	−0.502034	+	0.862924i
$447$	−8.22083	+	8.22083i	−0.388832	+	0.388832i
$448$	20.6327	−	4.72122i	0.974805	−	0.223057i
$449$		−	16.7065i		−	0.788428i	−0.919019	−	0.394214i	$-0.871017\pi$
$449$		−	16.7065i		−	0.788428i	0.919019	−	0.394214i	$-0.128983\pi$
$450$	6.78679	−	1.98480i	0.319932	−	0.0935645i
$451$	37.7080			1.77560
$452$	1.77699	−	6.46005i	0.0835828	−	0.303855i
$453$	2.01651	−	2.01651i	0.0947441	−	0.0947441i
$454$	−11.0967	+	19.0737i	−0.520795	+	0.895172i
$455$	7.05795	−	12.1147i	0.330882	−	0.567944i
$456$	0.113811	−	11.4338i	0.00532969	−	0.535436i
$457$	22.1542	+	22.1542i	1.03633	+	1.03633i	0.999315	+	0.0370143i	$0.0117847\pi$
$457$	22.1542	+	22.1542i	1.03633	+	1.03633i	0.0370143	+	0.999315i	$0.488215\pi$
$458$	−19.3455	+	5.11487i	−0.903955	+	0.239002i
$459$	0.603788			0.0281824
$460$	28.6075	+	7.47002i	1.33383	+	0.348291i
$461$	−30.4640			−1.41885			−0.709425	−	0.704781i	$-0.751045\pi$
$461$	−30.4640			−1.41885			−0.709425	+	0.704781i	$0.751045\pi$
$462$	−11.3195	−	3.28025i	−0.526633	−	0.152611i
$463$	−23.0766	+	23.0766i	−1.07246	+	1.07246i	−0.0752994	+	0.997161i	$0.523991\pi$
$463$	−23.0766	+	23.0766i	−1.07246	+	1.07246i	−0.997161	+	0.0752994i	$0.976009\pi$
$464$	−17.5266	+	29.4474i	−0.813653	+	1.36706i
$465$	4.82243	−	4.94965i	0.223635	−	0.229535i
$466$	9.64059	+	5.60873i	0.446592	+	0.259819i
$467$	15.6460	+	15.6460i	0.724010	+	0.724010i	0.969420	−	0.245409i	$-0.0789224\pi$
$467$	15.6460	+	15.6460i	0.724010	+	0.724010i	−0.245409	+	0.969420i	$0.578922\pi$
$468$	−4.57011	−	1.25712i	−0.211253	−	0.0581103i
$469$	21.5983	+	12.9626i	0.997316	+	0.598556i
$470$	−2.12781	+	3.76945i	−0.0981486	+	0.173872i
$471$	−11.3179			−0.521501
$472$	−28.6231	+	28.0588i	−1.31748	+	1.29151i
$473$	−24.3798	+	24.3798i	−1.12099	+	1.12099i
$474$	4.30109	−	7.39296i	0.197556	−	0.339570i
$475$	−0.526195	−	20.2064i	−0.0241435	−	0.927133i
$476$	3.19406	+	0.0753264i	0.146399	+	0.00345258i
$477$	−2.85984	+	2.85984i	−0.130943	+	0.130943i
$478$	−22.6997	+	6.00172i	−1.03826	+	0.274512i
$479$	32.2323			1.47273			0.736366	−	0.676583i	$-0.236540\pi$
$479$	32.2323			1.47273			0.736366	+	0.676583i	$0.236540\pi$
$480$	−6.28539	−	10.9770i	−0.286887	−	0.501028i
$481$		−	8.38167i		−	0.382171i
$482$	19.3693	−	5.12116i	0.882246	−	0.233263i
$483$	16.9702	−	4.24033i	0.772169	−	0.192942i
$484$	−1.87625	+	1.06671i	−0.0852840	+	0.0484870i
$485$	−24.2292	−	23.6065i	−1.10019	−	1.07191i
$486$	−1.22239	−	0.711166i	−0.0554488	−	0.0322592i
$487$	−12.3205	−	12.3205i	−0.558294	−	0.558294i	0.370527	−	0.928822i	$-0.379177\pi$
$487$	−12.3205	−	12.3205i	−0.558294	−	0.558294i	−0.928822	+	0.370527i	$0.879177\pi$
$488$	−14.2317	−	14.5178i	−0.644237	−	0.657191i
$489$	4.20806			0.190295
$490$	16.0264	−	15.2694i	0.724001	−	0.689799i
$491$		−	40.1506i		−	1.81197i	−0.423307	−	0.905986i	$-0.639131\pi$
$491$		−	40.1506i		−	1.81197i	0.423307	−	0.905986i	$-0.360869\pi$
$492$	23.0861	+	6.35038i	1.04080	+	0.286297i
$493$	−3.65768	+	3.65768i	−0.164733	+	0.164733i
$494$	−6.81353	+	11.7115i	−0.306555	+	0.526924i
$495$	0.0916805	+	7.04243i	0.00412073	+	0.316534i
$496$	−10.6227	−	6.32247i	−0.476974	−	0.283887i
$497$	−6.55176	−	26.2207i	−0.293886	−	1.17616i
$498$	5.75743	−	1.52224i	0.257997	−	0.0682134i
$499$	−4.38696			−0.196387			−0.0981937	−	0.995167i	$-0.531306\pi$
$499$	−4.38696			−0.196387			−0.0981937	+	0.995167i	$0.531306\pi$
$500$	−11.8021	−	18.9924i	−0.527806	−	0.849365i
$501$			14.9724i			0.668919i
$502$	−4.47637	−	16.9306i	−0.199790	−	0.755647i
$503$	−25.5699	−	25.5699i	−1.14010	−	1.14010i	−0.988431	−	0.151674i	$-0.951533\pi$
$503$	−25.5699	−	25.5699i	−1.14010	−	1.14010i	−0.151674	−	0.988431i	$-0.548467\pi$
$504$	−6.37777	−	3.91459i	−0.284088	−	0.174370i
$505$	−0.285293	−	21.9148i	−0.0126954	−	0.975195i
$506$	−14.8093	+	25.4550i	−0.658353	+	1.13161i
$507$	−5.22088	−	5.22088i	−0.231868	−	0.231868i
$508$	−21.4920	−	5.91191i	−0.953555	−	0.262298i
$509$		−	0.00249713i		−	0.000110683i	−1.00000		5.53417e-5i	$-0.999982\pi$
$509$		−	0.00249713i		−	0.000110683i	1.00000		5.53417e-5i	$-1.76158e-5\pi$
$510$	−0.512041	−	1.83941i	−0.0226735	−	0.0814503i
$511$	−8.48694	+	14.1410i	−0.375440	+	0.625560i
$512$	−16.4706	+	15.5152i	−0.727903	+	0.685680i
$513$	−2.85859	+	2.85859i	−0.126210	+	0.126210i
$514$	5.51481	+	3.20842i	0.243248	+	0.141517i
$515$	−14.0293	+	14.3994i	−0.618206	+	0.634515i
$516$	−19.0319	+	10.8203i	−0.837834	+	0.476339i
$517$	−3.04861	−	3.04861i	−0.134078	−	0.134078i
$518$	3.68322	−	12.7101i	0.161831	−	0.558450i
$519$			10.1522i			0.445634i
$520$	0.0459247	+	14.9887i	0.00201393	+	0.657297i
$521$		−	18.2393i		−	0.799080i	−0.916716	−	0.399540i	$-0.869170\pi$
$521$		−	18.2393i		−	0.799080i	0.916716	−	0.399540i	$-0.130830\pi$
$522$	11.7133	−	3.09694i	0.512676	−	0.135550i
$523$	−13.3588	+	13.3588i	−0.584139	+	0.584139i	−0.936038	−	0.351899i	$-0.885536\pi$
$523$	−13.3588	+	13.3588i	−0.584139	+	0.584139i	0.351899	+	0.936038i	$0.385536\pi$
$524$	19.9165	−	11.3232i	0.870055	−	0.494658i
$525$	−11.5161	−	6.50994i	−0.502604	−	0.284117i
$526$	−1.29328	−	0.752406i	−0.0563896	−	0.0328065i
$527$	−1.31945	−	1.31945i	−0.0574762	−	0.0574762i
$528$	12.2119	−	3.09906i	0.531453	−	0.134869i
$529$		−	20.7096i		−	0.900416i
$530$	11.1376	+	6.28706i	0.483787	+	0.273092i
$531$	14.1712			0.614977
$532$	−15.4786	+	14.7654i	−0.671084	+	0.640160i
$533$	−20.0622	−	20.0622i	−0.868991	−	0.868991i
$534$	−17.9099	−	10.4197i	−0.775037	−	0.450903i
$535$	−26.3306	−	25.6539i	−1.13837	−	1.10911i
$536$	−26.9274	−	0.268034i	−1.16309	−	0.0115773i
$537$	−0.852239	+	0.852239i	−0.0367768	+	0.0367768i
$538$	−23.1763	+	6.12772i	−0.999199	+	0.264185i
$539$	10.3708	+	19.4568i	0.446704	+	0.838064i
$540$	−1.12988	+	4.32705i	−0.0486224	+	0.186207i
$541$			6.62287i			0.284739i	0.989814	+	0.142370i	$0.0454722\pi$
$541$			6.62287i			0.284739i	−0.989814	+	0.142370i	$0.954528\pi$
$542$	−5.86054	+	1.54951i	−0.251732	+	0.0665570i
$543$	4.24741	−	4.24741i	0.182274	−	0.182274i
$544$	−2.98587	+	1.65847i	−0.128018	+	0.0711062i
$545$	0.0825976	+	6.34473i	0.00353809	+	0.271778i
$546$	4.27724	+	7.76769i	0.183049	+	0.332427i
$547$	7.91721	−	7.91721i	0.338516	−	0.338516i	−0.517293	−	0.855808i	$-0.673060\pi$
$547$	7.91721	−	7.91721i	0.338516	−	0.338516i	0.855808	+	0.517293i	$0.173060\pi$
$548$	22.7936	+	6.26994i	0.973696	+	0.267839i
$549$			7.18773i			0.306765i
$550$	21.3766	−	6.25161i	0.911503	−	0.266570i
$551$		−	34.6339i		−	1.47546i
$552$	−13.3536	+	13.0904i	−0.568367	+	0.557163i
$553$	−15.5241	+	3.87900i	−0.660151	+	0.164952i
$554$	15.3678	+	8.94070i	0.652914	+	0.379854i
$555$	−7.90758	+	0.102943i	−0.335658	+	0.00436970i
$556$	11.8458	+	20.8356i	0.502374	+	0.883627i
$557$	1.18911	−	1.18911i	0.0503840	−	0.0503840i	−0.681466	−	0.731850i	$-0.738657\pi$
$557$	1.18911	−	1.18911i	0.0503840	−	0.0503840i	0.731850	+	0.681466i	$0.238657\pi$
$558$	1.11718	+	4.22539i	0.0472938	+	0.178875i
$559$	25.9422			1.09724
$560$	−6.51694	+	22.7493i	−0.275391	+	0.961332i
$561$	1.90178			0.0802930
$562$	2.34350	+	8.86358i	0.0988545	+	0.373887i
$563$	−9.59824	+	9.59824i	−0.404517	+	0.404517i	−0.879822	−	0.475304i	$-0.842338\pi$
$563$	−9.59824	+	9.59824i	−0.404517	+	0.404517i	0.475304	+	0.879822i	$0.342338\pi$
$564$	−1.35304	−	2.37987i	−0.0569734	−	0.100211i
$565$	5.36532	+	5.22742i	0.225721	+	0.219919i
$566$	−3.60123	−	2.09513i	−0.151371	−	0.0880649i
$567$	0.641375	+	2.56683i	0.0269352	+	0.107797i
$568$	20.2260	+	20.6327i	0.848664	+	0.865729i
$569$		−	1.12649i		−	0.0472248i	−0.999721	−	0.0236124i	$-0.992483\pi$
$569$		−	1.12649i		−	0.0472248i	0.999721	−	0.0236124i	$-0.00751675\pi$
$570$	11.1327	+	6.28430i	0.466299	+	0.263221i
$571$		−	17.5232i		−	0.733321i	−0.930355	−	0.366661i	$-0.880501\pi$
$571$		−	17.5232i		−	0.733321i	0.930355	−	0.366661i	$-0.119499\pi$
$572$	−14.3946	−	3.95960i	−0.601870	−	0.165559i
$573$	4.89322	−	4.89322i	0.204417	−	0.204417i
$574$	−21.6066	−	39.2388i	−0.901843	−	1.63780i
$575$	−22.7581	+	23.9751i	−0.949080	+	0.999832i
$576$	7.99841	+	0.159247i	0.333267	+	0.00663530i
$577$	−11.7714	+	11.7714i	−0.490048	+	0.490048i	−0.908321	−	0.418273i	$-0.862635\pi$
$577$	−11.7714	+	11.7714i	−0.490048	+	0.490048i	0.418273	+	0.908321i	$0.362635\pi$
$578$	22.7445	−	6.01356i	0.946047	−	0.250131i
$579$			0.364376i			0.0151429i
$580$	−19.3681	−	33.0574i	−0.804215	−	1.37264i
$581$	−9.55288	−	5.73332i	−0.396320	−	0.237858i
$582$	20.6838	−	5.46873i	0.857373	−	0.226686i
$583$	−9.00775	+	9.00775i	−0.373063	+	0.373063i
$584$	0.175489	−	17.6301i	0.00726179	−	0.729539i
$585$	3.69809	−	3.79564i	0.152897	−	0.156931i
$586$	−29.8639	−	17.3743i	−1.23366	−	0.717725i
$587$	−1.08650	−	1.08650i	−0.0448446	−	0.0448446i	0.684329	−	0.729173i	$-0.260095\pi$
$587$	−1.08650	−	1.08650i	−0.0448446	−	0.0448446i	−0.729173	+	0.684329i	$0.760095\pi$
$588$	3.07266	+	13.6587i	0.126715	+	0.563273i
$589$	12.4937			0.514793
$590$	−12.0178	−	43.1717i	−0.494766	−	1.77735i
$591$			9.89274i			0.406933i
$592$	3.47977	+	13.7121i	0.143018	+	0.563562i
$593$	−32.0658	−	32.0658i	−1.31678	−	1.31678i	−0.916307	−	0.400477i	$-0.868844\pi$
$593$	−32.0658	−	32.0658i	−1.31678	−	1.31678i	−0.400477	−	0.916307i	$-0.631156\pi$
$594$	−3.85022	−	2.23999i	−0.157976	−	0.0919079i
$595$	−1.79816	+	3.08646i	−0.0737174	+	0.126532i
$596$	−20.2135	+	11.4921i	−0.827979	+	0.470736i
$597$	9.32913	−	9.32913i	0.381816	−	0.381816i
$598$	21.4223	−	5.66397i	0.876022	−	0.231617i
$599$		−	30.2406i		−	1.23560i	−0.786336	−	0.617800i	$-0.788024\pi$
$599$		−	30.2406i		−	1.23560i	0.786336	−	0.617800i	$-0.211976\pi$
$600$	14.1403	−	0.227417i	0.577276	−	0.00928426i
$601$			18.8997i			0.770937i	0.922721	+	0.385468i	$0.125960\pi$
$601$			18.8997i			0.770937i	−0.922721	+	0.385468i	$0.874040\pi$
$602$	39.3392	+	11.4000i	1.60335	+	0.464628i
$603$	6.73219	+	6.73219i	0.274156	+	0.274156i
$604$	4.95825	−	2.81894i	0.201748	−	0.114701i
$605$	−0.0314109	−	2.41283i	−0.00127704	−	0.0980954i
$606$	11.9812	+	6.97044i	0.486702	+	0.283155i
$607$	8.49695	−	8.49695i	0.344881	−	0.344881i	−0.513318	−	0.858198i	$-0.671584\pi$
$607$	8.49695	−	8.49695i	0.344881	−	0.344881i	0.858198	+	0.513318i	$0.171584\pi$
$608$	6.28447	−	21.9882i	0.254869	−	0.891740i
$609$	−19.4349	−	11.6642i	−0.787544	−	0.472657i
$610$	21.8970	−	6.09553i	0.886584	−	0.246801i
$611$			3.24397i			0.131237i
$612$	1.16433	+	0.320277i	0.0470652	+	0.0129464i
$613$	−16.4600	−	16.4600i	−0.664812	−	0.664812i	0.291698	−	0.956510i	$-0.405780\pi$
$613$	−16.4600	−	16.4600i	−0.664812	−	0.664812i	−0.956510	+	0.291698i	$0.905780\pi$
$614$	−3.12915	+	5.37855i	−0.126282	+	0.217061i
$615$	−18.6810	+	19.1738i	−0.753292	+	0.773164i
$616$	−20.0883	−	12.3300i	−0.809381	−	0.496788i
$617$	6.09244	+	6.09244i	0.245272	+	0.245272i	0.819027	−	0.573755i	$-0.194514\pi$
$617$	6.09244	+	6.09244i	0.245272	+	0.245272i	−0.573755	+	0.819027i	$0.694514\pi$
$618$	−3.25007	−	12.2924i	−0.130737	−	0.494473i
$619$		−	36.7201i		−	1.47591i	−0.674853	−	0.737953i	$-0.735793\pi$
$619$		−	36.7201i		−	1.47591i	0.674853	−	0.737953i	$-0.264207\pi$
$620$	11.9250	−	6.98674i	0.478919	−	0.280594i
$621$	6.61132			0.265303
$622$	10.5325	−	2.78474i	0.422313	−	0.111658i
$623$	9.39711	+	37.6080i	0.376487	+	1.50673i
$624$	−8.14604	−	4.84839i	−0.326103	−	0.194091i
$625$	24.9661	−	1.30117i	0.998645	−	0.0520467i
$626$	7.61854	−	13.0952i	0.304498	−	0.523388i
$627$	−9.00380	+	9.00380i	−0.359577	+	0.359577i
$628$	−21.8251	−	6.00353i	−0.870918	−	0.239567i
$629$			2.13540i			0.0851441i
$630$	7.27580	−	4.13071i	0.289875	−	0.164571i
$631$	36.9096			1.46935			0.734673	−	0.678421i	$-0.237336\pi$
$631$	36.9096			1.46935			0.734673	+	0.678421i	$0.237336\pi$
$632$	12.2157	−	11.9749i	0.485914	−	0.476336i
$633$	17.2329	+	17.2329i	0.684946	+	0.684946i
$634$	−32.9421	−	19.1651i	−1.30830	−	0.761145i
$635$	17.3912	−	17.8499i	0.690148	−	0.708354i
$636$	−7.03183	+	3.99785i	−0.278830	+	0.158525i
$637$	4.83411	−	15.8696i	0.191534	−	0.628775i
$638$	36.8937	−	9.75457i	1.46064	−	0.386187i
$639$		−	10.2152i		−	0.404106i
$640$	−6.29789	−	24.5018i	−0.248946	−	0.968517i
$641$	49.0296			1.93655			0.968277	−	0.249878i	$-0.0803905\pi$
$641$	49.0296			1.93655			0.968277	+	0.249878i	$0.0803905\pi$
$642$	22.4778	−	5.94304i	0.887126	−	0.234553i
$643$	3.86309	−	3.86309i	0.152345	−	0.152345i	−0.626819	−	0.779165i	$-0.715644\pi$
$643$	3.86309	−	3.86309i	0.152345	−	0.152345i	0.779165	+	0.626819i	$0.215644\pi$
$644$	34.9741	+	0.824804i	1.37817	+	0.0325018i
$645$	−0.318620	−	24.4748i	−0.0125457	−	0.963695i
$646$	1.73589	−	2.98374i	0.0682976	−	0.117394i
$647$	−20.8703	+	20.8703i	−0.820498	+	0.820498i	−0.986179	−	0.165682i	$-0.947018\pi$
$647$	−20.8703	+	20.8703i	−0.820498	+	0.820498i	0.165682	+	0.986179i	$0.447018\pi$
$648$	−1.97999	−	2.01981i	−0.0777815	−	0.0793455i
$649$	44.6355			1.75210
$650$	−14.6994	−	8.04714i	−0.576557	−	0.315635i
$651$	4.20769	−	7.01087i	0.164912	−	0.274778i
$652$	8.11472	+	2.23215i	0.317797	+	0.0874177i
$653$	−4.22670	−	4.22670i	−0.165404	−	0.165404i	0.619552	−	0.784956i	$-0.287314\pi$
$653$	−4.22670	−	4.22670i	−0.165404	−	0.165404i	−0.784956	+	0.619552i	$0.787314\pi$
$654$	−3.46877	−	2.01807i	−0.135640	−	0.0789128i
$655$	0.333429	+	25.6123i	0.0130281	+	1.00076i
$656$	41.1501	+	24.4918i	1.60664	+	0.956245i
$657$	−4.40775	+	4.40775i	−0.171963	+	0.171963i
$658$	−1.42552	+	4.91922i	−0.0555727	+	0.191771i
$659$	27.5321			1.07250			0.536249	−	0.844060i	$-0.319841\pi$
$659$	27.5321			1.07250			0.536249	+	0.844060i	$0.319841\pi$
$660$	−3.55884	+	13.6291i	−0.138528	+	0.530511i
$661$	−38.0353			−1.47940			−0.739701	−	0.672936i	$-0.765033\pi$
$661$	−38.0353			−1.47940			−0.739701	+	0.672936i	$0.765033\pi$
$662$	20.9936	−	5.55063i	0.815939	−	0.215731i
$663$	−1.01182	−	1.01182i	−0.0392960	−	0.0392960i
$664$	11.9100	+	0.118551i	0.462196	+	0.00460067i
$665$	−6.09935	−	23.1258i	−0.236522	−	0.896781i
$666$	2.51517	−	4.32321i	0.0974607	−	0.167521i
$667$	−40.0506	+	40.0506i	−1.55077	+	1.55077i
$668$	−7.94206	+	28.8724i	−0.307288	+	1.11711i
$669$	14.9083			0.576390
$670$	14.8000	−	26.2185i	0.571775	−	1.01291i
$671$			22.6395i			0.873987i
$672$	−10.2222	−	10.9319i	−0.394332	−	0.421706i
$673$	8.31772	−	8.31772i	0.320625	−	0.320625i	−0.528382	−	0.849007i	$-0.677201\pi$
$673$	8.31772	−	8.31772i	0.320625	−	0.320625i	0.849007	+	0.528382i	$0.177201\pi$
$674$	−15.4697	+	26.5901i	−0.595870	+	1.02421i
$675$	−3.62637	−	3.44230i	−0.139579	−	0.132494i
$676$	−7.29842	−	12.8372i	−0.280708	−	0.493739i
$677$	−22.3917	−	22.3917i	−0.860585	−	0.860585i	0.130821	−	0.991406i	$-0.458239\pi$
$677$	−22.3917	−	22.3917i	−0.860585	−	0.860585i	−0.991406	+	0.130821i	$0.958239\pi$
$678$	−4.58023	+	1.21100i	−0.175903	+	0.0465080i
$679$	−34.3191	−	20.5972i	−1.31705	−	0.790448i
$680$	−0.0117003	−	3.81867i	−0.000448684	−	0.146439i
$681$	15.6036			0.597930
$682$	3.51881	+	13.3089i	0.134742	+	0.509623i
$683$	21.8152	+	21.8152i	0.834737	+	0.834737i	0.988161	−	0.153423i	$-0.0490298\pi$
$683$	21.8152	+	21.8152i	0.834737	+	0.834737i	−0.153423	+	0.988161i	$0.549030\pi$
$684$	−7.02875	+	3.99610i	−0.268751	+	0.152795i
$685$	−18.4444	+	18.9310i	−0.704725	+	0.723315i
$686$	14.3042	−	21.9406i	0.546137	−	0.837696i
$687$	10.0051	+	10.0051i	0.381719	+	0.381719i
$688$	−42.4403	+	10.7703i	−1.61802	+	0.410612i
$689$	9.58499			0.365159
$690$	−5.60671	−	20.1410i	−0.213444	−	0.766755i
$691$	−0.0391809			−0.00149051			−0.000745256	−	1.00000i	$-0.500237\pi$
$691$	−0.0391809			−0.00149051			−0.000745256		1.00000i	$0.500237\pi$
$692$	−5.38522	+	19.5773i	−0.204715	+	0.744219i
$693$	2.02016	+	8.08486i	0.0767397	+	0.307118i
$694$	4.49903	+	2.61746i	0.170781	+	0.0993573i
$695$	−26.7943	+	0.348817i	−1.01637	+	0.0132314i
$696$	24.2303	+	0.241187i	0.918448	+	0.00914218i
$697$	5.11126	+	5.11126i	0.193603	+	0.193603i
$698$	5.49612	−	1.45315i	0.208031	−	0.0550026i
$699$		−	7.88666i		−	0.298301i
$700$	−18.7542	−	18.6623i	−0.708841	−	0.705368i
$701$		−	25.0705i		−	0.946899i	−0.880821	−	0.473450i	$-0.843009\pi$
$701$		−	25.0705i		−	0.946899i	0.880821	−	0.473450i	$-0.156991\pi$
$702$	0.856708	+	3.24024i	0.0323344	+	0.122295i
$703$	−10.1099	−	10.1099i	−0.381302	−	0.381302i
$704$	25.1929	+	0.501587i	0.949494	+	0.0189043i
$705$	3.06049	−	0.0398423i	0.115265	−	0.00150055i
$706$	−10.4467	+	17.9564i	−0.393168	+	0.675799i
$707$	−6.28638	−	25.1586i	−0.236424	−	0.946187i
$708$	27.3273	+	7.51704i	1.02702	+	0.282508i
$709$	15.5764			0.584985			0.292493	−	0.956268i	$-0.405515\pi$
$709$	15.5764			0.584985			0.292493	+	0.956268i	$0.405515\pi$
$710$	−31.1200	+	8.66295i	−1.16791	+	0.325115i
$711$	−6.04794			−0.226816
$712$	−29.0099	−	29.5932i	−1.08719	−	1.10905i
$713$	−14.4477	−	14.4477i	−0.541069	−	0.541069i
$714$	−1.08971	−	1.97898i	−0.0407815	−	0.0740615i
$715$	11.6480	−	11.9553i	0.435611	−	0.447103i
$716$	−2.09550	+	1.19137i	−0.0783126	+	0.0445236i
$717$	11.7399	+	11.7399i	0.438433	+	0.438433i
$718$	−12.1057	+	3.20071i	−0.451782	+	0.119450i
$719$	−7.05434			−0.263082			−0.131541	−	0.991311i	$-0.541993\pi$
$719$	−7.05434			−0.263082			−0.131541	+	0.991311i	$0.541993\pi$
$720$	−4.47410	+	7.74483i	−0.166740	+	0.288633i
$721$	−12.2409	+	20.3959i	−0.455876	+	0.759582i
$722$	−0.960475	−	3.63271i	−0.0357452	−	0.135196i
$723$	−10.0174	−	10.0174i	−0.372552	−	0.372552i
$724$	10.4436	−	5.93757i	0.388134	−	0.220668i
$725$	42.8212	−	1.11511i	1.59034	−	0.0414140i
$726$	1.31913	+	0.767449i	0.0489576	+	0.0284827i
$727$	−19.6404	+	19.6404i	−0.728420	+	0.728420i	−0.970305	−	0.241885i	$-0.922234\pi$
$727$	−19.6404	+	19.6404i	−0.728420	+	0.728420i	0.241885	+	0.970305i	$0.422234\pi$
$728$	4.12777	+	17.2479i	0.152985	+	0.639248i
$729$			1.00000i			0.0370370i
$730$	17.1659	+	9.68997i	0.635339	+	0.358642i
$731$	−6.60931			−0.244454
$732$	−3.81270	+	13.8606i	−0.140922	+	0.512304i
$733$	−16.4484	+	16.4484i	−0.607534	+	0.607534i	−0.942301	−	0.334767i	$-0.891342\pi$
$733$	−16.4484	+	16.4484i	−0.607534	+	0.607534i	0.334767	+	0.942301i	$0.391342\pi$
$734$	31.3360	+	18.2307i	1.15663	+	0.672909i
$735$	−15.0313	−	4.36577i	−0.554438	−	0.161034i
$736$	−32.6945	+	18.1598i	−1.20513	+	0.669378i
$737$	21.2047	+	21.2047i	0.781083	+	0.781083i
$738$	−4.32769	−	16.3682i	−0.159305	−	0.602522i
$739$	21.5632			0.793216			0.396608	−	0.917988i	$-0.370187\pi$
$739$	21.5632			0.793216			0.396608	+	0.917988i	$0.370187\pi$
$740$	−15.3034	−	3.99603i	−0.562563	−	0.146897i
$741$	9.58079			0.351959
$742$	14.5349	+	4.21200i	0.533591	+	0.154628i
$743$	35.4825	−	35.4825i	1.30173	−	1.30173i	0.374501	−	0.927226i	$-0.377814\pi$
$743$	35.4825	−	35.4825i	1.30173	−	1.30173i	0.927226	−	0.374501i	$-0.122186\pi$
$744$	−0.0870047	+	8.74073i	−0.00318975	+	0.320451i
$745$	−0.338402	−	25.9943i	−0.0123981	−	0.952359i
$746$	−12.5345	+	21.5449i	−0.458919	+	0.788815i
$747$	−2.97764	−	2.97764i	−0.108946	−	0.108946i
$748$	3.66733	+	1.00879i	0.134091	+	0.0368850i
$749$	−37.2957	−	22.3836i	−1.36275	−	0.817879i
$750$	−7.41143	+	13.9668i	−0.270627	+	0.509994i
$751$	−38.4718			−1.40386			−0.701928	−	0.712248i	$-0.747677\pi$
$751$	−38.4718			−1.40386			−0.701928	+	0.712248i	$0.747677\pi$
$752$	−1.34678	−	5.30700i	−0.0491121	−	0.193526i
$753$	−8.75616	+	8.75616i	−0.319092	+	0.319092i
$754$	−24.8188	−	14.4392i	−0.903848	−	0.525843i
$755$	0.0830077	+	6.37624i	0.00302096	+	0.232055i
$756$	−0.124756	+	5.29003i	−0.00453734	+	0.192397i
$757$	−14.2962	+	14.2962i	−0.519605	+	0.519605i	−0.917452	−	0.397847i	$-0.869757\pi$
$757$	−14.2962	+	14.2962i	−0.519605	+	0.519605i	0.397847	+	0.917452i	$0.369757\pi$
$758$	−2.00584	−	7.58649i	−0.0728554	−	0.275554i
$759$	20.8239			0.755861
$760$	18.1346	+	18.0238i	0.657811	+	0.653792i
$761$			4.28764i			0.155427i	0.996976	+	0.0777134i	$0.0247619\pi$
$761$			4.28764i			0.155427i	−0.996976	+	0.0777134i	$0.975238\pi$
$762$	4.02888	+	15.2380i	0.145951	+	0.552016i
$763$	1.82002	+	7.28388i	0.0658893	+	0.263694i
$764$	12.0315	−	6.84036i	0.435286	−	0.247476i
$765$	−0.942165	+	0.967019i	−0.0340640	+	0.0349627i
$766$	5.80719	−	9.98172i	0.209822	−	0.360654i
$767$	−23.7479	−	23.7479i	−0.857488	−	0.857488i
$768$	15.3395	+	4.54981i	0.553515	+	0.164177i
$769$	−2.19684			−0.0792201			−0.0396100	−	0.999215i	$-0.512612\pi$
$769$	−2.19684			−0.0792201			−0.0396100	+	0.999215i	$0.512612\pi$
$770$	22.9169	−	13.0107i	0.825867	−	0.468871i
$771$		−	4.51149i		−	0.162477i
$772$	−0.193282	+	0.702652i	−0.00695635	+	0.0252890i
$773$	16.5613	−	16.5613i	0.595667	−	0.595667i	−0.343489	−	0.939157i	$-0.611609\pi$
$773$	16.5613	−	16.5613i	0.595667	−	0.595667i	0.939157	+	0.343489i	$0.111609\pi$
$774$	13.3808	+	7.78471i	0.480963	+	0.279816i
$775$	0.402258	+	15.4471i	0.0144495	+	0.554876i
$776$	42.7870	+	0.425900i	1.53597	+	0.0152889i
$777$	−9.07806	+	2.26834i	−0.325674	+	0.0813761i
$778$	7.53796	+	28.5101i	0.270249	+	1.02214i
$779$	−48.3977			−1.73403
$780$	9.14468	−	5.35779i	0.327432	−	0.191840i
$781$		−	32.1751i		−	1.15132i
$782$	−5.45777	+	1.44301i	−0.195169	+	0.0516021i
$783$	−6.05788	−	6.05788i	−0.216491	−	0.216491i
$784$	−1.31993	+	27.9689i	−0.0471403	+	0.998888i
$785$	17.6607	−	18.1266i	0.630338	−	0.646966i
$786$	−14.0027	−	8.14651i	−0.499459	−	0.290577i
$787$	13.0264	+	13.0264i	0.464340	+	0.464340i	0.900075	−	0.435735i	$-0.143511\pi$
$787$	13.0264	+	13.0264i	0.464340	+	0.464340i	−0.435735	+	0.900075i	$0.643511\pi$
$788$	−5.24756	+	19.0769i	−0.186937	+	0.679586i
$789$			1.05799i			0.0376654i
$790$	5.12894	+	18.4247i	0.182479	+	0.655522i
$791$	7.59963	+	4.56104i	0.270212	+	0.162172i
$792$	−6.23647	−	6.36187i	−0.221603	−	0.226059i
$793$	12.0451	−	12.0451i	0.427735	−	0.427735i
$794$	12.9117	−	22.1933i	0.458218	−	0.787611i
$795$	−0.117722	−	9.04284i	−0.00417518	−	0.320716i
$796$	22.9387	−	13.0415i	0.813039	−	0.462242i
$797$	−2.39422	−	2.39422i	−0.0848076	−	0.0848076i	0.663430	−	0.748238i	$-0.269100\pi$
$797$	−2.39422	−	2.39422i	−0.0848076	−	0.0848076i	−0.748238	+	0.663430i	$0.769100\pi$
$798$	14.5285	+	4.21016i	0.514303	+	0.149038i
$799$		−	0.826469i		−	0.0292384i
$800$	27.3884	+	7.06212i	0.968327	+	0.249684i
$801$			14.6515i			0.517686i
$802$	−11.9067	−	45.0334i	−0.420439	−	1.59018i
$803$	−13.8833	+	13.8833i	−0.489929	+	0.489929i
$804$	9.41112	+	16.5532i	0.331905	+	0.583788i
$805$	−19.6894	+	33.7959i	−0.693959	+	1.19115i
$806$	5.20871	−	8.95302i	0.183469	−	0.315357i
$807$	11.9863	+	11.9863i	0.421939	+	0.421939i
$808$	19.4068	+	19.7970i	0.682727	+	0.696455i
$809$			3.72661i			0.131021i	0.997852	+	0.0655104i	$0.0208676\pi$
$809$			3.72661i			0.131021i	−0.997852	+	0.0655104i	$0.979132\pi$
$810$	3.04644	−	0.848047i	0.107041	−	0.0297973i
$811$	−23.5676			−0.827569			−0.413785	−	0.910375i	$-0.635793\pi$
$811$	−23.5676			−0.827569			−0.413785	+	0.910375i	$0.635793\pi$
$812$	−31.2906	−	32.8021i	−1.09809	−	1.15113i
$813$	3.03096	+	3.03096i	0.106301	+	0.106301i
$814$	7.92212	−	13.6170i	0.277670	−	0.477275i
$815$	−6.56635	+	6.73957i	−0.230009	+	0.236077i
$816$	2.07537	+	1.23523i	0.0726526	+	0.0432416i
$817$	31.2912	−	31.2912i	1.09474	−	1.09474i
$818$	4.53572	+	17.1550i	0.158588	+	0.599811i
$819$	3.22667	−	5.37629i	0.112749	−	0.187863i
$820$	−46.1947	+	27.0651i	−1.61319	+	0.945153i
$821$		−	8.26755i		−	0.288540i	−0.989538	−	0.144270i	$-0.953917\pi$
$821$		−	8.26755i		−	0.288540i	0.989538	−	0.144270i	$-0.0460833\pi$
$822$	−4.27287	−	16.1609i	−0.149034	−	0.563675i
$823$	−10.9990	+	10.9990i	−0.383402	+	0.383402i	−0.872326	−	0.488924i	$-0.837389\pi$
$823$	−10.9990	+	10.9990i	−0.383402	+	0.383402i	0.488924	+	0.872326i	$0.337389\pi$
$824$	0.253112	−	25.4284i	0.00881758	−	0.885839i
$825$	−11.4221	−	10.8423i	−0.397668	−	0.377482i
$826$	−25.5761	−	46.4476i	−0.889906	−	1.61612i
$827$	3.99650	−	3.99650i	0.138972	−	0.138972i	−0.634198	−	0.773170i	$-0.718670\pi$
$827$	3.99650	−	3.99650i	0.138972	−	0.138972i	0.773170	+	0.634198i	$0.218670\pi$
$828$	12.7491	+	3.50695i	0.443062	+	0.121875i
$829$		−	26.5322i		−	0.921500i	−0.887530	−	0.460750i	$-0.847581\pi$
$829$		−	26.5322i		−	0.921500i	0.887530	−	0.460750i	$-0.152419\pi$
$830$	−6.54602	+	11.5964i	−0.227216	+	0.402516i
$831$		−	12.5719i		−	0.436114i
$832$	−13.1368	−	13.6705i	−0.455437	−	0.473941i
$833$	−1.23159	+	4.04310i	−0.0426721	+	0.140085i
$834$	8.52248	−	14.6489i	0.295109	−	0.507250i
$835$	−23.9796	−	23.3633i	−0.829850	−	0.808521i
$836$	−22.1387	+	12.5867i	−0.765684	+	0.435319i
$837$	2.18529	−	2.18529i	0.0755347	−	0.0755347i
$838$	24.7105	−	6.53337i	0.853611	−	0.225692i
$839$	53.6879			1.85351			0.926756	−	0.375663i	$-0.122585\pi$
$839$	53.6879			1.85351			0.926756	+	0.375663i	$0.122585\pi$
$840$	16.2216	−	4.10613i	0.559698	−	0.141675i
$841$	44.3958			1.53089
$842$	−3.42800	+	0.906352i	−0.118137	+	0.0312349i
$843$	4.58408	−	4.58408i	0.157884	−	0.157884i
$844$	24.0903	+	42.3726i	0.829224	+	1.45852i
$845$	16.5085	−	0.214912i	0.567909	−	0.00739321i
$846$	−0.973449	+	1.67322i	−0.0334679	+	0.0575264i
$847$	−0.692134	−	2.76998i	−0.0237820	−	0.0951775i
$848$	−15.6806	+	3.97935i	−0.538475	+	0.136651i
$849$			2.94605i			0.101108i
$850$	3.74497	+	2.05017i	0.128451	+	0.0703204i
$851$			23.3821i			0.801528i
$852$	5.41860	−	19.6987i	0.185638	−	0.674866i
$853$	19.9799	−	19.9799i	0.684100	−	0.684100i	−0.276821	−	0.960921i	$-0.589281\pi$
$853$	19.9799	−	19.9799i	0.684100	−	0.684100i	0.960921	+	0.276821i	$0.0892810\pi$
$854$	23.5586	−	12.9724i	0.806157	−	0.443906i
$855$	−0.117671	−	9.03887i	−0.00402425	−	0.309123i
$856$	46.4980	+	0.462838i	1.58927	+	0.0158195i
$857$	−11.0856	+	11.0856i	−0.378677	+	0.378677i	−0.870625	−	0.491947i	$-0.836285\pi$
$857$	−11.0856	+	11.0856i	−0.378677	+	0.378677i	0.491947	+	0.870625i	$0.336285\pi$
$858$	2.69841	+	10.2059i	0.0921221	+	0.348424i
$859$			39.4596i			1.34634i	0.739487	+	0.673171i	$0.235068\pi$
$859$			39.4596i			1.34634i	−0.739487	+	0.673171i	$0.764932\pi$
$860$	12.3681	−	47.3656i	0.421750	−	1.61515i
$861$	−16.2996	+	27.1585i	−0.555490	+	0.925561i
$862$	10.5005	+	39.7149i	0.357648	+	1.35270i
$863$	−9.22558	+	9.22558i	−0.314042	+	0.314042i	−0.846473	−	0.532431i	$-0.821279\pi$
$863$	−9.22558	+	9.22558i	−0.314042	+	0.314042i	0.532431	+	0.846473i	$0.321279\pi$
$864$	−2.74677	−	4.94523i	−0.0934470	−	0.168240i
$865$	−16.2597	−	15.8418i	−0.552847	−	0.538637i
$866$	−28.4324	+	48.8711i	−0.966172	+	1.66071i
$867$	−11.7630	−	11.7630i	−0.399494	−	0.399494i
$868$	11.8329	−	11.2876i	0.401634	−	0.383127i
$869$	−19.0494			−0.646208
$870$	−13.3176	+	23.5924i	−0.451510	+	0.799856i
$871$		−	22.5635i		−	0.764535i
$872$	−5.61861	−	5.73159i	−0.190270	−	0.194096i
$873$	−10.6973	−	10.6973i	−0.362048	−	0.362048i
$874$	19.0075	−	32.6712i	0.642939	−	1.10512i
$875$	28.3962	−	8.28577i	0.959968	−	0.280110i
$876$	−10.8379	+	6.16171i	−0.366177	+	0.208185i
$877$	17.5598	−	17.5598i	0.592954	−	0.592954i	−0.345474	−	0.938428i	$-0.612282\pi$
$877$	17.5598	−	17.5598i	0.592954	−	0.592954i	0.938428	+	0.345474i	$0.112282\pi$
$878$	−11.6043	−	43.8897i	−0.391625	−	1.48121i
$879$			24.4307i			0.824026i
$880$	−14.0923	+	24.3942i	−0.475050	+	0.822328i
$881$			44.0876i			1.48535i	0.669653	+	0.742674i	$0.266443\pi$
$881$			44.0876i			1.48535i	−0.669653	+	0.742674i	$0.733557\pi$
$882$	7.25553	−	6.73479i	0.244306	−	0.226772i
$883$	−0.361877	−	0.361877i	−0.0121781	−	0.0121781i	0.700992	−	0.713170i	$-0.252741\pi$
$883$	−0.361877	−	0.361877i	−0.0121781	−	0.0121781i	−0.713170	+	0.700992i	$0.752741\pi$
$884$	−1.41446	−	2.48789i	−0.0475733	−	0.0836768i
$885$	−22.1130	+	22.6964i	−0.743321	+	0.762930i
$886$	16.2900	−	28.0002i	0.547274	−	0.940684i
$887$	−12.6903	+	12.6903i	−0.426100	+	0.426100i	−0.887298	−	0.461197i	$-0.847420\pi$
$887$	−12.6903	+	12.6903i	−0.426100	+	0.426100i	0.461197	+	0.887298i	$0.347420\pi$
$888$	7.14341	−	7.00260i	0.239717	−	0.234992i
$889$	15.1742	−	25.2833i	0.508926	−	0.847975i
$890$	44.6350	−	12.4252i	1.49617	−	0.416493i
$891$			3.14974i			0.105520i
$892$	28.7489	+	7.90807i	0.962583	+	0.264782i
$893$	3.91285	+	3.91285i	0.130939	+	0.130939i
$894$	14.2115	+	8.26802i	0.475305	+	0.276524i
$895$	−0.0350816	−	2.69479i	−0.00117265	−	0.0900769i
$896$	−13.9136	−	26.5031i	−0.464819	−	0.885406i
$897$	−11.0792	−	11.0792i	−0.369924	−	0.369924i
$898$	−22.8417	+	6.03925i	−0.762236	+	0.201532i
$899$			26.4764i			0.883039i
$900$	−5.16705	−	8.56163i	−0.172235	−	0.285388i
$901$	−2.44197			−0.0813540
$902$	−13.6311	−	51.5556i	−0.453866	−	1.71661i
$903$	−7.02074	−	28.0976i	−0.233636	−	0.935029i
$904$	−9.47476	−	0.0943112i	−0.315126	−	0.00313674i
$905$	0.174840	+	13.4303i	0.00581188	+	0.446440i
$906$	−3.48600	−	2.02809i	−0.115814	−	0.0673788i
$907$	−23.9572	+	23.9572i	−0.795485	+	0.795485i	−0.982380	−	0.186895i	$-0.940158\pi$
$907$	−23.9572	+	23.9572i	−0.795485	+	0.795485i	0.186895	+	0.982380i	$0.440158\pi$
$908$	30.0895	+	8.27685i	0.998555	+	0.274677i
$909$		−	9.80142i		−	0.325093i
$910$	−19.1149	−	5.27052i	−0.633654	−	0.174716i
$911$	23.9927			0.794912			0.397456	−	0.917621i	$-0.369893\pi$
$911$	23.9927			0.794912			0.397456	+	0.917621i	$0.369893\pi$
$912$	−15.6738	+	3.97760i	−0.519010	+	0.131712i
$913$	−9.37878	−	9.37878i	−0.310392	−	0.310392i
$914$	22.2814	−	38.2985i	0.737002	−	1.26680i
$915$	−11.5118	−	11.2159i	−0.380567	−	0.370786i
$916$	13.9864	+	24.6008i	0.462125	+	0.812833i
$917$	7.34704	+	29.4035i	0.242621	+	0.970988i
$918$	−0.218264	−	0.825519i	−0.00720379	−	0.0272462i
$919$		−	58.5349i		−	1.93089i	−0.260611	−	0.965444i	$-0.583924\pi$
$919$		−	58.5349i		−	1.93089i	0.260611	−	0.965444i	$-0.416076\pi$
$920$	−0.128115	−	41.8135i	−0.00422382	−	1.37855i
$921$	4.40002			0.144986
$922$	11.0125	+	41.6514i	0.362676	+	1.37172i
$923$	−17.1185	+	17.1185i	−0.563463	+	0.563463i
$924$	−0.392950	+	16.6622i	−0.0129271	+	0.548147i
$925$	12.1743	−	12.8253i	0.400288	−	0.421694i
$926$	39.8931	+	23.2091i	1.31097	+	0.762698i
$927$	−6.35740	+	6.35740i	−0.208804	+	0.208804i
$928$	46.5972	+	13.3180i	1.52963	+	0.437184i
$929$	−44.8190			−1.47046			−0.735232	−	0.677815i	$-0.762927\pi$
$929$	−44.8190			−1.47046			−0.735232	+	0.677815i	$0.762927\pi$
$930$	−8.51059	−	4.80413i	−0.279073	−	0.157534i
$931$	−13.3108	−	24.9726i	−0.436245	−	0.818443i
$932$	4.18345	−	15.2084i	0.137033	−	0.498169i
$933$	−5.44719	−	5.44719i	−0.178333	−	0.178333i
$934$	15.7358	−	27.0476i	0.514892	−	0.885024i
$935$	−2.96757	+	3.04586i	−0.0970500	+	0.0996102i
$936$	−0.0667196	+	6.70284i	−0.00218080	+	0.219089i
$937$	26.1359	−	26.1359i	0.853823	−	0.853823i	−0.136779	−	0.990602i	$-0.543675\pi$
$937$	26.1359	−	26.1359i	0.853823	−	0.853823i	0.990602	+	0.136779i	$0.0436750\pi$
$938$	9.91525	−	34.2157i	0.323744	−	1.11718i
$939$	−10.7127			−0.349597
$940$	5.92290	+	1.54659i	0.193184	+	0.0504442i
$941$	−37.0773			−1.20869			−0.604343	−	0.796724i	$-0.706564\pi$
$941$	−37.0773			−1.20869			−0.604343	+	0.796724i	$0.706564\pi$
$942$	4.09132	+	15.4742i	0.133302	+	0.504176i
$943$	55.9670	+	55.9670i	1.82254	+	1.82254i
$944$	48.7099	+	28.9913i	1.58537	+	0.943588i
$945$	−5.11182	−	2.97813i	−0.166288	−	0.0968786i
$946$	42.1460	+	24.5198i	1.37028	+	0.797208i
$947$	28.7081	−	28.7081i	0.932888	−	0.932888i	−0.0649972	−	0.997885i	$-0.520704\pi$
$947$	28.7081	−	28.7081i	0.932888	−	0.932888i	0.997885	+	0.0649972i	$0.0207038\pi$
$948$	−11.6627	−	3.20811i	−0.378787	−	0.104194i
$949$	14.7729			0.479550
$950$	−27.4366	+	8.02386i	−0.890162	+	0.260329i
$951$			26.9489i			0.873878i
$952$	−1.05164	−	4.39425i	−0.0340837	−	0.142418i
$953$	−6.16298	+	6.16298i	−0.199639	+	0.199639i	−0.799845	−	0.600207i	$-0.795085\pi$
$953$	−6.16298	+	6.16298i	−0.199639	+	0.199639i	0.600207	+	0.799845i	$0.295085\pi$
$954$	4.94387	+	2.87626i	0.160064	+	0.0931223i
$955$	0.201424	+	15.4724i	0.00651793	+	0.500675i
$956$	16.4115	+	28.8662i	0.530785	+	0.933600i
$957$	−19.0807	−	19.0807i	−0.616793	−	0.616793i
$958$	−11.6517	−	44.0691i	−0.376449	−	1.42381i
$959$	−16.0932	+	26.8145i	−0.519676	+	0.865886i
$960$	−12.7360	+	12.5617i	−0.411051	+	0.405426i
$961$	21.4490			0.691904
$962$	−11.4597	+	3.02990i	−0.369475	+	0.0976879i
$963$	−11.6251	−	11.6251i	−0.374613	−	0.374613i
$964$	−14.0036	−	24.6310i	−0.451027	−	0.793313i
$965$	−0.583579	−	0.568580i	−0.0187861	−	0.0183032i
$966$	−11.9321	−	21.6693i	−0.383909	−	0.697199i
$967$	−12.1324	−	12.1324i	−0.390153	−	0.390153i	0.484589	−	0.874742i	$-0.338969\pi$
$967$	−12.1324	−	12.1324i	−0.390153	−	0.390153i	−0.874742	+	0.484589i	$0.838969\pi$
$968$	2.13669	+	2.17966i	0.0686759	+	0.0700569i
$969$	−2.44090			−0.0784131
$970$	−23.5169	+	41.6605i	−0.755082	+	1.33764i
$971$	41.1699			1.32121			0.660603	−	0.750735i	$-0.270301\pi$
$971$	41.1699			1.32121			0.660603	+	0.750735i	$0.270301\pi$
$972$	−0.530446	+	1.92837i	−0.0170141	+	0.0618526i
$973$	−30.7604	+	7.68611i	−0.986134	+	0.246405i
$974$	−12.3912	+	21.2987i	−0.397040	+	0.682455i
$975$	0.308472	+	11.8456i	0.00987901	+	0.379364i
$976$	−14.7046	+	24.7061i	−0.470684	+	0.790822i
$977$	11.8932	+	11.8932i	0.380498	+	0.380498i	0.871281	−	0.490784i	$-0.163289\pi$
$977$	11.8932	+	11.8932i	0.380498	+	0.380498i	−0.490784	+	0.871281i	$0.663289\pi$
$978$	−1.52118	−	5.75340i	−0.0486419	−	0.183973i
$979$			46.1485i			1.47491i
$980$	−26.6702	−	16.3921i	−0.851947	−	0.523627i
$981$			2.83769i			0.0906005i
$982$	−54.8952	+	14.5141i	−1.75178	+	0.463163i
$983$	16.7725	+	16.7725i	0.534959	+	0.534959i	0.922044	−	0.387085i	$-0.126518\pi$
$983$	16.7725	+	16.7725i	0.534959	+	0.534959i	−0.387085	+	0.922044i	$0.626518\pi$
$984$	0.337037	−	33.8596i	0.0107443	−	1.07941i
$985$	−15.8441	−	15.4369i	−0.504834	−	0.491859i
$986$	6.32311	+	3.67868i	0.201369	+	0.117153i
$987$	3.51350	−	0.877918i	0.111836	−	0.0279444i
$988$	18.4753	+	5.08209i	0.587779	+	0.161683i
$989$	−72.3701			−2.30124
$990$	9.59550	−	2.67113i	0.304965	−	0.0848940i
$991$	−14.4146			−0.457895			−0.228948	−	0.973439i	$-0.573528\pi$
$991$	−14.4146			−0.457895			−0.228948	+	0.973439i	$0.573528\pi$
$992$	−4.80426	+	16.8092i	−0.152535	+	0.533694i
$993$	−10.8575	−	10.8575i	−0.344552	−	0.344552i
$994$	−33.4813	+	18.4363i	−1.06196	+	0.584764i
$995$	0.384024	+	29.4988i	0.0121744	+	0.935175i
$996$	−4.16252	−	7.32147i	−0.131895	−	0.231990i
$997$	23.7945	+	23.7945i	0.753580	+	0.753580i	0.975146	−	0.221565i	$-0.0711166\pi$
$997$	23.7945	+	23.7945i	0.753580	+	0.753580i	−0.221565	+	0.975146i	$0.571117\pi$
$998$	1.58585	+	5.99800i	0.0501991	+	0.189863i
$999$	−3.53668			−0.111896

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bj.b.517.37	yes	184
5.3	odd	4	inner	840.2.bj.b.13.9	✓	184
7.6	odd	2	inner	840.2.bj.b.517.38	yes	184
8.5	even	2	inner	840.2.bj.b.517.10	yes	184
35.13	even	4	inner	840.2.bj.b.13.10	yes	184
40.13	odd	4	inner	840.2.bj.b.13.38	yes	184
56.13	odd	2	inner	840.2.bj.b.517.9	yes	184
280.13	even	4	inner	840.2.bj.b.13.37	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bj.b.13.9	✓	184	5.3	odd	4	inner
840.2.bj.b.13.10	yes	184	35.13	even	4	inner
840.2.bj.b.13.37	yes	184	280.13	even	4	inner
840.2.bj.b.13.38	yes	184	40.13	odd	4	inner
840.2.bj.b.517.9	yes	184	56.13	odd	2	inner
840.2.bj.b.517.10	yes	184	8.5	even	2	inner
840.2.bj.b.517.37	yes	184	1.1	even	1	trivial
840.2.bj.b.517.38	yes	184	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bj (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.361491 - 1.36723i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.73865 + 0.988485i) q^{4} +(-0.0291073 - 2.23588i) q^{5} +(1.22239 + 0.711166i) q^{6} +(-0.641375 - 2.56683i) q^{7} +(1.97999 + 2.01981i) q^{8} -1.00000i q^{9} +(-3.04644 + 0.848047i) q^{10} -3.14974i q^{11} +(0.530446 - 1.92837i) q^{12} +(-1.67579 + 1.67579i) q^{13} +(-3.27761 + 1.80480i) q^{14} +(1.60159 + 1.56042i) q^{15} +(2.04580 - 3.43725i) q^{16} +(0.426943 - 0.426943i) q^{17} +(-1.36723 + 0.361491i) q^{18} +4.04265i q^{19} +(2.26074 + 3.85863i) q^{20} +(2.26855 + 1.36151i) q^{21} +(-4.30643 + 1.13860i) q^{22} +(4.67491 - 4.67491i) q^{23} +(-2.82829 - 0.0281526i) q^{24} +(-4.99831 + 0.130161i) q^{25} +(2.89698 + 1.68541i) q^{26} +(0.707107 + 0.707107i) q^{27} +(3.65240 + 3.82883i) q^{28} -8.56714 q^{29} +(1.55450 - 2.75382i) q^{30} -3.09047i q^{31} +(-5.43906 - 1.55454i) q^{32} +(2.22720 + 2.22720i) q^{33} +(-0.738066 - 0.429394i) q^{34} +(-5.72046 + 1.50875i) q^{35} +(0.988485 + 1.73865i) q^{36} +(-2.50081 + 2.50081i) q^{37} +(5.52724 - 1.46138i) q^{38} -2.36993i q^{39} +(4.45841 - 4.48582i) q^{40} +11.9718i q^{41} +(1.04144 - 3.59380i) q^{42} +(-7.74027 - 7.74027i) q^{43} +(3.11347 + 5.47629i) q^{44} +(-2.23588 + 0.0291073i) q^{45} +(-8.08163 - 4.70175i) q^{46} +(0.967892 - 0.967892i) q^{47} +(0.983909 + 3.87710i) q^{48} +(-6.17728 + 3.29261i) q^{49} +(1.98480 + 6.78679i) q^{50} +0.603788i q^{51} +(1.25712 - 4.57011i) q^{52} +(-2.85984 - 2.85984i) q^{53} +(0.711166 - 1.22239i) q^{54} +(-7.04243 + 0.0916805i) q^{55} +(3.91459 - 6.37777i) q^{56} +(-2.85859 - 2.85859i) q^{57} +(3.09694 + 11.7133i) q^{58} +14.1712i q^{59} +(-4.32705 - 1.12988i) q^{60} -7.18773 q^{61} +(-4.22539 + 1.11718i) q^{62} +(-2.56683 + 0.641375i) q^{63} +(-0.159247 + 7.99841i) q^{64} +(3.79564 + 3.69809i) q^{65} +(2.23999 - 3.85022i) q^{66} +(-6.73219 + 6.73219i) q^{67} +(-0.320277 + 1.16433i) q^{68} +6.61132i q^{69} +(4.13071 + 7.27580i) q^{70} +10.2152 q^{71} +(2.01981 - 1.97999i) q^{72} +(-4.40775 - 4.40775i) q^{73} +(4.32321 + 2.51517i) q^{74} +(3.44230 - 3.62637i) q^{75} +(-3.99610 - 7.02875i) q^{76} +(-8.08486 + 2.02016i) q^{77} +(-3.24024 + 0.856708i) q^{78} -6.04794i q^{79} +(-7.74483 - 4.47410i) q^{80} -1.00000 q^{81} +(16.3682 - 4.32769i) q^{82} +(2.97764 - 2.97764i) q^{83} +(-5.29003 - 0.124756i) q^{84} +(-0.967019 - 0.942165i) q^{85} +(-7.78471 + 13.3808i) q^{86} +(6.05788 - 6.05788i) q^{87} +(6.36187 - 6.23647i) q^{88} -14.6515 q^{89} +(0.848047 + 3.04644i) q^{90} +(5.37629 + 3.22667i) q^{91} +(-3.50695 + 12.7491i) q^{92} +(2.18529 + 2.18529i) q^{93} +(-1.67322 - 0.973449i) q^{94} +(9.03887 - 0.117671i) q^{95} +(4.94523 - 2.74677i) q^{96} +(10.6973 - 10.6973i) q^{97} +(6.73479 + 7.25553i) q^{98} -3.14974 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) \) 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Introduction

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