LMFDB - Embedded newform 840.2.bj.b.517.10

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			517.10
Character	$\chi$	$=$	840.517
Dual form			840.2.bj.b.13.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36723 - 0.361491i) 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} +(-2.01981 - 1.97999i) q^{8} -1.00000i q^{9} +(0.768454 - 3.06749i) q^{10} +3.14974i q^{11} +(1.92837 - 0.530446i) q^{12} +(1.67579 - 1.67579i) q^{13} +(-0.0509796 + 3.74131i) q^{14} +(1.60159 + 1.56042i) q^{15} +(2.04580 + 3.43725i) q^{16} +(0.426943 - 0.426943i) q^{17} +(-0.361491 + 1.36723i) q^{18} -4.04265i q^{19} +(-2.15952 + 3.91618i) q^{20} +(-2.26855 - 1.36151i) q^{21} +(1.13860 - 4.30643i) 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} +(1.42215 - 5.09681i) q^{28} +8.56714 q^{29} +(-1.62566 - 2.71242i) q^{30} -3.09047i q^{31} +(-1.55454 - 5.43906i) 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} +(-1.46138 + 5.52724i) q^{38} -2.36993i q^{39} +(4.36823 - 4.57368i) q^{40} +11.9718i q^{41} +(2.60946 + 2.68155i) 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} +(3.87710 + 0.983909i) q^{48} +(-6.17728 + 3.29261i) q^{49} +(6.88090 + 1.62888i) q^{50} -0.603788i q^{51} +(4.57011 - 1.25712i) q^{52} +(2.85984 + 2.85984i) q^{53} +(0.711166 + 1.22239i) q^{54} +(-7.04243 + 0.0916805i) q^{55} +(-3.78686 + 6.45443i) q^{56} +(-2.85859 - 2.85859i) q^{57} +(-11.7133 - 3.09694i) q^{58} -14.1712i q^{59} +(1.24214 + 4.29617i) q^{60} +7.18773 q^{61} +(-1.11718 + 4.22539i) 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} +(1.16433 - 0.320277i) q^{68} -6.61132i q^{69} +(-8.36660 - 0.00508468i) q^{70} +10.2152 q^{71} +(-1.97999 + 2.01981i) 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} +(-0.856708 + 3.24024i) q^{78} -6.04794i q^{79} +(-7.62574 + 4.67420i) q^{80} -1.00000 q^{81} +(4.32769 - 16.3682i) q^{82} +(-2.97764 + 2.97764i) q^{83} +(-2.59838 - 4.60960i) q^{84} +(0.967019 + 0.942165i) q^{85} +(-7.78471 - 13.3808i) q^{86} +(6.05788 - 6.05788i) q^{87} +(6.23647 - 6.36187i) q^{88} -14.6515 q^{89} +(-3.06749 - 0.768454i) q^{90} +(-5.37629 - 3.22667i) q^{91} +(12.7491 - 3.50695i) 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} +(9.63602 - 2.26873i) 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 $

$2$	−1.36723	−	0.361491i	−0.966779	−	0.255613i
$2$	−1.36723	−	0.361491i	−0.966779	−	0.255613i
$3$	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
$8$	−2.01981	−	1.97999i	−0.714110	−	0.700034i
$9$		−	1.00000i		−	0.333333i
$10$	0.768454	−	3.06749i	0.243006	−	0.970025i
$11$			3.14974i			0.949682i	0.880072	+	0.474841i	$0.157494\pi$
$11$			3.14974i			0.949682i	−0.880072	+	0.474841i	$0.842506\pi$
$12$	1.92837	−	0.530446i	0.556674	−	0.153127i
$13$	1.67579	−	1.67579i	0.464781	−	0.464781i	−0.435438	−	0.900219i	$-0.643406\pi$
$13$	1.67579	−	1.67579i	0.464781	−	0.464781i	0.900219	+	0.435438i	$0.143406\pi$
$14$	−0.0509796	+	3.74131i	−0.0136249	+	0.999907i
$15$	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	$0.226672\pi$
$18$	−0.361491	+	1.36723i	−0.0852043	+	0.322260i
$19$		−	4.04265i		−	0.927447i	−0.885980	−	0.463724i	$-0.846513\pi$
$19$		−	4.04265i		−	0.927447i	0.885980	−	0.463724i	$-0.153487\pi$
$20$	−2.15952	+	3.91618i	−0.482884	+	0.875684i
$21$	−2.26855	−	1.36151i	−0.495037	−	0.297105i
$22$	1.13860	−	4.30643i	0.242751	−	0.918133i
$23$	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
$28$	1.42215	−	5.09681i	0.268761	−	0.963207i
$29$	8.56714			1.59088			0.795439	−	0.606034i	$-0.207241\pi$
$29$	8.56714			1.59088			0.795439	+	0.606034i	$0.207241\pi$
$30$	−1.62566	−	2.71242i	−0.296804	−	0.495218i
$31$		−	3.09047i		−	0.555064i	−0.960716	−	0.277532i	$-0.910484\pi$
$31$		−	3.09047i		−	0.555064i	0.960716	−	0.277532i	$-0.0895165\pi$
$32$	−1.55454	−	5.43906i	−0.274807	−	0.961499i
$33$	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	−0.471002	−	0.882132i	$-0.656107\pi$
$37$	2.50081	−	2.50081i	0.411130	−	0.411130i	0.882132	+	0.471002i	$0.156107\pi$
$38$	−1.46138	+	5.52724i	−0.237067	+	0.896637i
$39$		−	2.36993i		−	0.379492i
$40$	4.36823	−	4.57368i	0.690679	−	0.723162i
$41$			11.9718i			1.86968i	0.355072	+	0.934839i	$0.384456\pi$
$41$			11.9718i			1.86968i	−0.355072	+	0.934839i	$0.615544\pi$
$42$	2.60946	+	2.68155i	0.402648	+	0.413773i
$43$	7.74027	+	7.74027i	1.18038	+	1.18038i	0.979646	+	0.200735i	$0.0643329\pi$
$43$	7.74027	+	7.74027i	1.18038	+	1.18038i	0.200735	+	0.979646i	$0.435667\pi$
$44$	−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	$0.218170\pi$
$48$	3.87710	+	0.983909i	0.559612	+	0.142015i
$49$	−6.17728	+	3.29261i	−0.882468	+	0.470372i
$50$	6.88090	+	1.62888i	0.973106	+	0.230359i
$51$		−	0.603788i		−	0.0845473i
$52$	4.57011	−	1.25712i	0.633760	−	0.174331i
$53$	2.85984	+	2.85984i	0.392829	+	0.392829i	0.875695	−	0.482866i	$-0.160404\pi$
$53$	2.85984	+	2.85984i	0.392829	+	0.392829i	−0.482866	+	0.875695i	$0.660404\pi$
$54$	0.711166	+	1.22239i	0.0967775	+	0.166346i
$55$	−7.04243	+	0.0916805i	−0.949602	+	0.0123622i
$56$	−3.78686	+	6.45443i	−0.506041	+	0.862510i
$57$	−2.85859	−	2.85859i	−0.378629	−	0.378629i
$58$	−11.7133	−	3.09694i	−1.53803	−	0.406649i
$59$		−	14.1712i		−	1.84493i	−0.386081	−	0.922465i	$-0.626171\pi$
$59$		−	14.1712i		−	1.84493i	0.386081	−	0.922465i	$-0.373829\pi$
$60$	1.24214	+	4.29617i	0.160360	+	0.554633i
$61$	7.18773			0.920294			0.460147	−	0.887843i	$-0.347797\pi$
$61$	7.18773			0.920294			0.460147	+	0.887843i	$0.347797\pi$
$62$	−1.11718	+	4.22539i	−0.141882	+	0.536625i
$63$	−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	−0.163993	−	0.986461i	$-0.552438\pi$
$67$	6.73219	−	6.73219i	0.822468	−	0.822468i	0.986461	+	0.163993i	$0.0524375\pi$
$68$	1.16433	−	0.320277i	0.141196	−	0.0388393i
$69$		−	6.61132i		−	0.795910i
$70$	−8.36660	−	0.00508468i	−1.00000	−	0.000607736i
$71$	10.2152			1.21232			0.606159	−	0.795343i	$-0.292709\pi$
$71$	10.2152			1.21232			0.606159	+	0.795343i	$0.292709\pi$
$72$	−1.97999	+	2.01981i	−0.233345	+	0.238037i
$73$	−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
$78$	−0.856708	+	3.24024i	−0.0970031	+	0.366885i
$79$		−	6.04794i		−	0.680447i	−0.940345	−	0.340223i	$-0.889497\pi$
$79$		−	6.04794i		−	0.680447i	0.940345	−	0.340223i	$-0.110503\pi$
$80$	−7.62574	+	4.67420i	−0.852583	+	0.522592i
$81$	−1.00000			−0.111111
$82$	4.32769	−	16.3682i	0.477914	−	1.80757i
$83$	−2.97764	+	2.97764i	−0.326838	+	0.326838i	−0.851383	−	0.524545i	$-0.824236\pi$
$83$	−2.97764	+	2.97764i	−0.326838	+	0.326838i	0.524545	+	0.851383i	$0.324236\pi$
$84$	−2.59838	−	4.60960i	−0.283506	−	0.502949i
$85$	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
$88$	6.23647	−	6.36187i	0.664809	−	0.678177i
$89$	−14.6515			−1.55306			−0.776529	−	0.630082i	$-0.783021\pi$
$89$	−14.6515			−1.55306			−0.776529	+	0.630082i	$0.783021\pi$
$90$	−3.06749	−	0.768454i	−0.323342	−	0.0810021i
$91$	−5.37629	−	3.22667i	−0.563588	−	0.338247i
$92$	12.7491	−	3.50695i	1.32919	−	0.365625i
$93$	−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	$-0.0287583\pi$
$98$	9.63602	−	2.26873i	0.973385	−	0.229176i
$99$	3.14974			0.316561
$100$	−8.81896	−	4.71444i	−0.881896	−	0.471444i
$101$	−9.80142			−0.975278			−0.487639	−	0.873045i	$-0.662142\pi$
$101$	−9.80142			−0.975278			−0.487639	+	0.873045i	$0.662142\pi$
$102$	−0.218264	+	0.825519i	−0.0216114	+	0.0817385i
$103$	−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	$0.542358\pi$
$107$	−11.6251	+	11.6251i	−1.12384	+	1.12384i	−0.991159	+	0.132679i	$0.957642\pi$
$108$	−0.530446	−	1.92837i	−0.0510422	−	0.185558i
$109$	2.83769			0.271802			0.135901	−	0.990722i	$-0.456607\pi$
$109$	2.83769			0.271802			0.135901	+	0.990722i	$0.456607\pi$
$110$	9.66179	+	2.42043i	0.921215	+	0.230779i
$111$		−	3.53668i		−	0.335687i
$112$	7.51074	−	7.45579i	0.709698	−	0.704506i
$113$	−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
$118$	−5.12275	+	19.3753i	−0.471588	+	1.78364i
$119$	−1.36972	−	0.822061i	−0.125562	−	0.0753582i
$120$	−0.145270	−	6.32289i	−0.0132612	−	0.577198i
$121$	1.07914			0.0981037
$122$	−9.82730	−	2.59830i	−0.889722	−	0.235239i
$123$	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
$126$	3.74131	+	0.0509796i	0.333302	+	0.00454162i
$127$	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	$0.585356\pi$
$128$	2.67363	−	10.9933i	0.236318	−	0.971676i
$129$	10.9464			0.963777
$130$	−3.85270	−	6.42824i	−0.337904	−	0.563794i
$131$	11.4551			1.00084			0.500420	−	0.865783i	$-0.333179\pi$
$131$	11.4551			1.00084			0.500420	+	0.865783i	$0.333179\pi$
$132$	1.67077	+	6.07388i	0.145422	+	0.528663i
$133$	−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	$0.918482\pi$
$138$	−2.38993	+	9.03921i	−0.203445	+	0.769469i
$139$			11.9838i			1.01645i	0.861223	+	0.508227i	$0.169699\pi$
$139$			11.9838i			1.01645i	−0.861223	+	0.508227i	$0.830301\pi$
$140$	11.4372	+	3.03140i	0.966624	+	0.256200i
$141$		−	1.36881i		−	0.115274i
$142$	−13.9665	−	3.69270i	−1.17204	−	0.309884i
$143$	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
$148$	6.82004	−	1.87602i	0.560604	−	0.154208i
$149$	−11.6260			−0.952439			−0.476220	−	0.879326i	$-0.657993\pi$
$149$	−11.6260			−0.952439			−0.476220	+	0.879326i	$0.657993\pi$
$150$	6.01732	−	3.71373i	0.491312	−	0.303225i
$151$	−2.85178			−0.232075			−0.116037	−	0.993245i	$-0.537019\pi$
$151$	−2.85178			−0.232075			−0.116037	+	0.993245i	$0.537019\pi$
$152$	−8.00442	+	8.16538i	−0.649244	+	0.662299i
$153$	−0.426943	−	0.426943i	−0.0345163	−	0.0345163i
$154$	−11.7842	−	0.160572i	−0.949594	−	0.0129393i
$155$	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	0.311530	−	0.950236i	$-0.399158\pi$
$157$	−8.00296	−	8.00296i	−0.638706	−	0.638706i	−0.950236	+	0.311530i	$0.899158\pi$
$158$	−2.18628	+	8.26894i	−0.173931	+	0.657842i
$159$	4.04442			0.320744
$160$	12.1158	−	3.63408i	0.957841	−	0.287300i
$161$	−14.9981	−	9.00135i	−1.18201	−	0.709406i
$162$	1.36723	+	0.361491i	0.107420	+	0.0284014i
$163$	2.97555	+	2.97555i	0.233063	+	0.233063i	0.813970	−	0.580907i	$-0.197302\pi$
$163$	2.97555	+	2.97555i	0.233063	+	0.233063i	−0.580907	+	0.813970i	$0.697302\pi$
$164$	−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	$0.0533257\pi$
$168$	1.88625	+	7.24169i	0.145528	+	0.558708i
$169$			7.38344i			0.567957i
$170$	−0.981556	−	1.63773i	−0.0752819	−	0.125608i
$171$	−4.04265			−0.309149
$172$	5.80647	+	21.1088i	0.442739	+	1.60953i
$173$	−7.17872	+	7.17872i	−0.545788	+	0.545788i	−0.925220	−	0.379432i	$-0.876120\pi$
$173$	−7.17872	+	7.17872i	−0.545788	+	0.545788i	0.379432	+	0.925220i	$0.376120\pi$
$174$	−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
$178$	20.0320	+	5.29639i	1.50146	+	0.396981i
$179$	−1.20525			−0.0900845			−0.0450422	−	0.998985i	$-0.514342\pi$
$179$	−1.20525			−0.0900845			−0.0450422	+	0.998985i	$0.514342\pi$
$180$	3.91618	+	2.15952i	0.291895	+	0.160961i
$181$	6.00674			0.446477			0.223239	−	0.974764i	$-0.428337\pi$
$181$	6.00674			0.446477			0.223239	+	0.974764i	$0.428337\pi$
$182$	6.18423	+	6.35509i	0.458405	+	0.471070i
$183$	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
$188$	2.63957	−	0.726078i	0.192511	−	0.0529547i
$189$	−1.36151	+	2.26855i	−0.0990350	+	0.165012i
$190$	−12.4008	−	3.10659i	−0.899647	−	0.225376i
$191$	−6.92005			−0.500717			−0.250359	−	0.968153i	$-0.580549\pi$
$191$	−6.92005			−0.500717			−0.250359	+	0.968153i	$0.580549\pi$
$192$	5.76834	+	5.54313i	0.416294	+	0.400041i
$193$	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
$196$	−13.9948	−	0.381461i	−0.999629	−	0.0272472i
$197$	−6.99522	+	6.99522i	−0.498389	+	0.498389i	−0.910936	−	0.412547i	$-0.864639\pi$
$197$	−6.99522	+	6.99522i	−0.498389	+	0.498389i	0.412547	+	0.910936i	$0.364639\pi$
$198$	−4.30643	−	1.13860i	−0.306044	−	0.0809170i
$199$	−13.1934			−0.935254			−0.467627	−	0.883926i	$-0.654891\pi$
$199$	−13.1934			−0.935254			−0.467627	+	0.883926i	$0.654891\pi$
$200$	10.3533	+	9.63372i	0.732091	+	0.681207i
$201$		−	9.52076i		−	0.671542i
$202$	13.4008	+	3.54313i	0.942878	+	0.249293i
$203$	−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
$208$	9.18845	+	2.33179i	0.637105	+	0.161681i
$209$	12.7333			0.880780
$210$	−5.91967	+	5.91248i	−0.408496	+	0.408000i
$211$			24.3710i			1.67777i	0.544310	+	0.838884i	$0.316791\pi$
$211$			24.3710i			1.67777i	−0.544310	+	0.838884i	$0.683209\pi$
$212$	2.14535	+	7.79916i	0.147343	+	0.535648i
$213$	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
$218$	−3.87978	−	1.02580i	−0.262772	−	0.0694759i
$219$	−6.23349			−0.421220
$220$	−12.3349	−	6.80194i	−0.831622	−	0.458587i
$221$		−	1.43093i		−	0.0962551i
$222$	−1.27848	+	4.83546i	−0.0858058	+	0.324535i
$223$	−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	$0.916361\pi$
$224$	−12.9641	+	7.47873i	−0.866202	+	0.499694i
$225$	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	0.971077	−	0.238766i	$-0.0767428\pi$
$227$	11.0334	+	11.0334i	0.732312	+	0.732312i	−0.238766	+	0.971077i	$0.576743\pi$
$228$	−2.14441	−	7.79574i	−0.142017	−	0.516286i
$229$			14.1494i			0.935017i	0.883989	+	0.467509i	$0.154848\pi$
$229$			14.1494i			0.935017i	−0.883989	+	0.467509i	$0.845152\pi$
$230$	−10.7478	−	17.9327i	−0.708687	−	1.18245i
$231$	4.28839	−	7.14533i	0.282155	−	0.470128i
$232$	−17.3040	−	16.9629i	−1.13606	−	1.11367i
$233$	−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
$238$	1.57556	+	1.61909i	0.102128	+	0.104950i
$239$		−	16.6027i		−	1.07394i	−0.843602	−	0.536969i	$-0.819569\pi$
$239$		−	16.6027i		−	1.07394i	0.843602	−	0.536969i	$-0.180431\pi$
$240$	−2.08705	+	8.69737i	−0.134718	+	0.561413i
$241$			14.1668i			0.912562i	0.889836	+	0.456281i	$0.150819\pi$
$241$			14.1668i			0.912562i	−0.889836	+	0.456281i	$0.849181\pi$
$242$	−1.47544	−	0.390100i	−0.0948447	−	0.0250766i
$243$	−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
$248$	−6.11911	+	6.24215i	−0.388564	+	0.396377i
$249$			4.21101i			0.266862i
$250$	−3.44170	+	15.4323i	−0.217672	+	0.976022i
$251$	−12.3831			−0.781613			−0.390807	−	0.920473i	$-0.627804\pi$
$251$	−12.3831			−0.781613			−0.390807	+	0.920473i	$0.627804\pi$
$252$	−5.09681	−	1.42215i	−0.321069	−	0.0895871i
$253$	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	$0.294938\pi$
$258$	−14.9663	−	3.95703i	−0.931759	−	0.246354i
$259$	−8.02312	−	4.81521i	−0.498532	−	0.299202i
$260$	2.94379	+	10.1816i	0.182566	+	0.631437i
$261$		−	8.56714i		−	0.530292i
$262$	−15.6618	−	4.14093i	−0.967592	−	0.255828i
$263$	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
$266$	15.1248	+	0.206093i	0.927361	+	0.0126364i
$267$	−10.3602	+	10.3602i	−0.634033	+	0.634033i
$268$	18.3596	−	5.05025i	1.12149	−	0.308493i
$269$			16.9512i			1.03353i	0.856126	+	0.516767i	$0.172865\pi$
$269$			16.9512i			1.03353i	−0.856126	+	0.516767i	$0.827135\pi$
$270$	−2.71242	+	1.62566i	−0.165073	+	0.0989347i
$271$		−	4.28643i		−	0.260382i	−0.991489	−	0.130191i	$-0.958441\pi$
$271$		−	4.28643i		−	0.260382i	0.991489	−	0.130191i	$-0.0415591\pi$
$272$	2.34095	+	0.594073i	0.141941	+	0.0360210i
$273$	−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	−0.387670	−	0.921798i	$-0.626720\pi$
$277$	8.88967	−	8.88967i	0.534128	−	0.534128i	0.921798	+	0.387670i	$0.126720\pi$
$278$	4.33204	−	16.3846i	0.259818	−	0.982686i
$279$	−3.09047			−0.185021
$280$	−14.5415	−	8.27909i	−0.869024	−	0.494771i
$281$	−6.48286			−0.386735			−0.193368	−	0.981126i	$-0.561941\pi$
$281$	−6.48286			−0.386735			−0.193368	+	0.981126i	$0.561941\pi$
$282$	−0.494811	+	1.87148i	−0.0294656	+	0.111445i
$283$	−2.08317	+	2.08317i	−0.123832	+	0.123832i	−0.766307	−	0.642475i	$-0.777908\pi$
$283$	−2.08317	+	2.08317i	−0.123832	+	0.123832i	0.642475	+	0.766307i	$0.277908\pi$
$284$	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
$288$	−5.43906	+	1.55454i	−0.320500	+	0.0916023i
$289$			16.6354i			0.978555i
$290$	6.58345	−	26.2796i	0.386593	−	1.54319i
$291$		−	15.1283i		−	0.886834i
$292$	−3.30653	−	12.0205i	−0.193500	−	0.703447i
$293$	−17.2751	+	17.2751i	−1.00922	+	1.00922i	−0.00926472	+	0.999957i	$0.502949\pi$
$293$	−17.2751	+	17.2751i	−1.00922	+	1.00922i	−0.999957	+	0.00926472i	$0.997051\pi$
$294$	5.20946	−	8.41793i	0.303822	−	0.490943i
$295$	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
$298$	15.8955	+	4.20270i	0.920799	+	0.243456i
$299$		−	15.6684i		−	0.906124i
$300$	−9.56956	+	2.90233i	−0.552499	+	0.167566i
$301$	14.9036	−	24.8324i	0.859028	−	1.43132i
$302$	3.89905	+	1.03089i	0.224365	+	0.0593213i
$303$	−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	0.790296	−	0.612725i	$-0.209927\pi$
$307$	3.11129	+	3.11129i	0.177570	+	0.177570i	−0.612725	+	0.790296i	$0.709927\pi$
$308$	16.0536	+	4.47941i	0.914740	+	0.255238i
$309$	−8.99072			−0.511464
$310$	−9.47997	−	2.37488i	−0.538426	−	0.134884i
$311$			7.70349i			0.436825i	0.975857	+	0.218412i	$0.0700878\pi$
$311$			7.70349i			0.436825i	−0.975857	+	0.218412i	$0.929912\pi$
$312$	−4.69244	+	4.78680i	−0.265657	+	0.270999i
$313$	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	$0.523238\pi$
$317$	−19.0557	+	19.0557i	−1.07028	+	1.07028i	−0.997336	+	0.0729409i	$0.976762\pi$
$318$	−5.52966	−	1.46202i	−0.310088	−	0.0819862i
$319$			26.9842i			1.51083i
$320$	−17.8788	+	0.588870i	−0.999458	+	0.0329188i
$321$			16.4403i			0.917610i
$322$	17.2520	+	17.7286i	0.961414	+	0.987977i
$323$	−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
$328$	23.7041	−	24.1807i	1.30884	−	1.33516i
$329$	−3.10520	−	1.86364i	−0.171195	−	0.102746i
$330$	8.54342	−	5.12041i	0.470300	−	0.281869i
$331$		−	15.3548i		−	0.843977i	−0.906601	−	0.421988i	$-0.861332\pi$
$331$		−	15.3548i		−	0.843977i	0.906601	−	0.421988i	$-0.138668\pi$
$332$	−8.12041	+	2.23371i	−0.445665	+	0.122591i
$333$	−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
$336$	0.0388574	−	10.5829i	0.00211984	−	0.577346i
$337$	−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	$0.951846\pi$
$338$	2.66905	−	10.0949i	0.145177	−	0.549089i
$339$			3.35000i			0.181947i
$340$	0.749991	+	2.59398i	0.0406740	+	0.140678i
$341$	9.73416			0.527135
$342$	5.52724	+	1.46138i	0.298879	+	0.0790225i
$343$	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	−0.633793	−	0.773503i	$-0.718503\pi$
$347$	2.60251	−	2.60251i	0.139710	−	0.139710i	0.773503	+	0.633793i	$0.218503\pi$
$348$	16.5206	−	4.54440i	0.885600	−	0.243606i
$349$		−	4.01988i		−	0.215179i	−0.994195	−	0.107590i	$-0.965687\pi$
$349$		−	4.01988i		−	0.215179i	0.994195	−	0.107590i	$-0.0343133\pi$
$350$	−0.232161	−	18.7068i	−0.0124095	−	0.999923i
$351$	−2.36993			−0.126497
$352$	17.1316	−	4.89640i	0.913119	−	0.260979i
$353$	−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
$358$	1.64785	+	0.435687i	0.0870918	+	0.0230268i
$359$		−	8.85420i		−	0.467307i	−0.972320	−	0.233653i	$-0.924932\pi$
$359$		−	8.85420i		−	0.467307i	0.972320	−	0.233653i	$-0.0750681\pi$
$360$	−4.57368	−	4.36823i	−0.241054	−	0.230226i
$361$	2.65698			0.139841
$362$	−8.21261	−	2.17138i	−0.431645	−	0.114125i
$363$	0.763068	−	0.763068i	0.0400507	−	0.0400507i
$364$	−6.15797	−	10.9244i	−0.322765	−	0.572595i
$365$	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	$0.483306\pi$
$368$	25.6328	+	6.50494i	1.33620	+	0.339093i
$369$	11.9718			0.623226
$370$	−5.74944	−	9.59295i	−0.298899	−	0.498714i
$371$	5.50650	−	9.17496i	0.285883	−	0.476340i
$372$	−1.63933	−	5.95958i	−0.0849951	−	0.308990i
$373$	12.4629	+	12.4629i	0.645305	+	0.645305i	0.951855	−	0.306550i	$-0.0991747\pi$
$373$	12.4629	+	12.4629i	0.645305	+	0.645305i	−0.306550	+	0.951855i	$0.599175\pi$
$374$	−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
$378$	2.68155	−	2.60946i	0.137924	−	0.134216i
$379$	−5.54879			−0.285022			−0.142511	−	0.989793i	$-0.545518\pi$
$379$	−5.54879			−0.285022			−0.142511	+	0.989793i	$0.545518\pi$
$380$	15.8317	+	8.73020i	0.812151	+	0.447850i
$381$	11.1452			0.570984
$382$	9.46132	+	2.50154i	0.484083	+	0.127990i
$383$	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
$388$	29.1729	−	8.02472i	1.48103	−	0.407393i
$389$	20.8524			1.05726			0.528629	−	0.848853i	$-0.322706\pi$
$389$	20.8524			1.05726			0.528629	+	0.848853i	$0.322706\pi$
$390$	−7.26972	−	1.82118i	−0.368117	−	0.0922190i
$391$		−	3.99184i		−	0.201876i
$392$	18.9963	+	5.58054i	0.959456	+	0.281860i
$393$	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	0.307295	−	0.951614i	$-0.400576\pi$
$397$	−12.8380	−	12.8380i	−0.644320	−	0.644320i	−0.951614	+	0.307295i	$0.900576\pi$
$398$	18.0384	+	4.76929i	0.904184	+	0.239063i
$399$	−5.50409	+	9.17094i	−0.275549	+	0.459121i
$400$	−10.6729	−	16.9142i	−0.533646	−	0.845708i
$401$	32.9376			1.64483			0.822414	−	0.568890i	$-0.192627\pi$
$401$	32.9376			1.64483			0.822414	+	0.568890i	$0.192627\pi$
$402$	−3.44167	+	13.0171i	−0.171655	+	0.649233i
$403$	−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
$406$	−0.436749	+	32.0523i	−0.0216755	+	1.59073i
$407$	7.87689	+	7.87689i	0.390443	+	0.390443i
$408$	−1.19550	+	1.21954i	−0.0591859	+	0.0603760i
$409$	−12.5472			−0.620422			−0.310211	−	0.950668i	$-0.600400\pi$
$409$	−12.5472			−0.620422			−0.310211	+	0.950668i	$0.600400\pi$
$410$	36.7233	+	9.19976i	1.81363	+	0.454344i
$411$	−11.8201			−0.583044
$412$	−4.76909	−	17.3375i	−0.234956	−	0.854156i
$413$	−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
$418$	−17.4094	−	4.60297i	−0.851520	−	0.225139i
$419$		−	18.0734i		−	0.882943i	−0.897275	−	0.441472i	$-0.854457\pi$
$419$		−	18.0734i		−	0.882943i	0.897275	−	0.441472i	$-0.145543\pi$
$420$	10.2309	−	5.94383i	0.499216	−	0.290029i
$421$			2.50726i			0.122196i	0.998132	+	0.0610982i	$0.0194603\pi$
$421$			2.50726i			0.122196i	−0.998132	+	0.0610982i	$0.980540\pi$
$422$	8.80989	−	33.3208i	0.428859	−	1.62203i
$423$	−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
$428$	−31.7031	+	8.72071i	−1.53243	+	0.421531i
$429$	7.46465			0.360397
$430$	29.6912	−	17.7951i	1.43184	−	0.858158i
$431$	−29.0477			−1.39918			−0.699588	−	0.714546i	$-0.746633\pi$
$431$	−29.0477			−1.39918			−0.699588	+	0.714546i	$0.746633\pi$
$432$	0.983909	−	3.87710i	0.0473384	−	0.186537i
$433$	−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	$-0.660415\pi$
$434$	11.5624	+	0.157551i	0.555013	+	0.00756268i
$435$	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
$438$	8.52263	+	2.25335i	0.407227	+	0.107669i
$439$	32.1011			1.53210			0.766052	−	0.642779i	$-0.222219\pi$
$439$	32.1011			1.53210			0.766052	+	0.642779i	$0.222219\pi$
$440$	14.4059	+	13.7588i	0.686774	+	0.655925i
$441$	3.29261	+	6.17728i	0.156791	+	0.294156i
$442$	−0.517270	+	1.95642i	−0.0246040	+	0.0930574i
$443$	−16.1970	−	16.1970i	−0.769544	−	0.769544i	0.208482	−	0.978026i	$-0.433148\pi$
$443$	−16.1970	−	16.1970i	−0.769544	−	0.769544i	−0.978026	+	0.208482i	$0.933148\pi$
$444$	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
$448$	20.4285	−	5.53874i	0.965154	−	0.261681i
$449$		−	16.7065i		−	0.788428i	−0.919019	−	0.394214i	$-0.871017\pi$
$449$		−	16.7065i		−	0.788428i	0.919019	−	0.394214i	$-0.128983\pi$
$450$	1.62888	−	6.88090i	0.0767863	−	0.324369i
$451$	−37.7080			−1.77560
$452$	−6.46005	+	1.77699i	−0.303855	+	0.0835828i
$453$	−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	$0.488215\pi$
$458$	5.11487	−	19.3455i	0.239002	−	0.903955i
$459$	−0.603788			−0.0281824
$460$	8.21220	+	28.4034i	0.382896	+	1.32431i
$461$	30.4640			1.41885			0.709425	−	0.704781i	$-0.248955\pi$
$461$	30.4640			1.41885			0.709425	+	0.704781i	$0.248955\pi$
$462$	−8.44620	+	8.21911i	−0.392953	+	0.382388i
$463$	−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	0.245409	−	0.969420i	$-0.421078\pi$
$467$	−15.6460	−	15.6460i	−0.724010	−	0.724010i	−0.969420	+	0.245409i	$0.921078\pi$
$468$	−1.25712	−	4.57011i	−0.0581103	−	0.211253i
$469$	−21.5983	−	12.9626i	−0.997316	−	0.598556i
$470$	−2.22522	−	3.71278i	−0.102642	−	0.171258i
$471$	−11.3179			−0.521501
$472$	−28.0588	+	28.6231i	−1.29151	+	1.31748i
$473$	−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
$476$	−1.56887	−	2.78322i	−0.0719090	−	0.127569i
$477$	2.85984	−	2.85984i	0.130943	−	0.130943i
$478$	−6.00172	+	22.6997i	−0.274512	+	1.03826i
$479$	32.2323			1.47273			0.736366	−	0.676583i	$-0.236540\pi$
$479$	32.2323			1.47273			0.736366	+	0.676583i	$0.236540\pi$
$480$	5.99750	−	11.1369i	0.273747	−	0.508326i
$481$		−	8.38167i		−	0.382171i
$482$	5.12116	−	19.3693i	0.233263	−	0.882246i
$483$	−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	$0.879177\pi$
$488$	−14.5178	−	14.2317i	−0.657191	−	0.644237i
$489$	4.20806			0.190295
$490$	5.35307	+	21.4789i	0.241827	+	0.970319i
$491$			40.1506i			1.81197i	0.423307	+	0.905986i	$0.360869\pi$
$491$			40.1506i			1.81197i	−0.423307	+	0.905986i	$0.639131\pi$
$492$	6.35038	+	23.0861i	0.286297	+	1.04080i
$493$	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
$498$	1.52224	−	5.75743i	0.0682134	−	0.257997i
$499$	4.38696			0.196387			0.0981937	−	0.995167i	$-0.468694\pi$
$499$	4.38696			0.196387			0.0981937	+	0.995167i	$0.468694\pi$
$500$	10.2842	−	19.8553i	0.459925	−	0.887958i
$501$		−	14.9724i		−	0.668919i
$502$	16.9306	+	4.47637i	0.755647	+	0.199790i
$503$	−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	$-0.548467\pi$
$504$	6.45443	+	3.78686i	0.287503	+	0.168680i
$505$	−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
$508$	5.91191	+	21.4920i	0.262298	+	0.953555i
$509$			0.00249713i			0.000110683i	1.00000		5.53417e-5i	$1.76158e-5\pi$
$509$			0.00249713i			0.000110683i	−1.00000		5.53417e-5i	$0.999982\pi$
$510$	−1.85211	−	0.463983i	−0.0820129	−	0.0205455i
$511$	−8.48694	+	14.1410i	−0.375440	+	0.625560i
$512$	15.5152	−	16.4706i	0.685680	−	0.727903i
$513$	−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
$518$	9.22881	+	9.48379i	0.405491	+	0.416694i
$519$			10.1522i			0.445634i
$520$	−0.344279	−	14.9848i	−0.0150976	−	0.657126i
$521$		−	18.2393i		−	0.799080i	−0.916716	−	0.399540i	$-0.869170\pi$
$521$		−	18.2393i		−	0.799080i	0.916716	−	0.399540i	$-0.130830\pi$
$522$	−3.09694	+	11.7133i	−0.135550	+	0.512676i
$523$	13.3588	−	13.3588i	0.584139	−	0.584139i	−0.351899	−	0.936038i	$-0.614464\pi$
$523$	13.3588	−	13.3588i	0.584139	−	0.584139i	0.936038	+	0.351899i	$0.114464\pi$
$524$	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
$528$	−3.09906	+	12.2119i	−0.134869	+	0.531453i
$529$		−	20.7096i		−	0.900416i
$530$	10.9702	−	6.57486i	0.476514	−	0.285594i
$531$	−14.1712			−0.614977
$532$	−20.6046	−	5.74926i	−0.893324	−	0.249262i
$533$	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
$538$	6.12772	−	23.1763i	0.264185	−	0.999199i
$539$	−10.3708	−	19.4568i	−0.446704	−	0.838064i
$540$	4.29617	−	1.24214i	0.184878	−	0.0534533i
$541$		−	6.62287i		−	0.284739i	−0.989814	−	0.142370i	$-0.954528\pi$
$541$		−	6.62287i		−	0.284739i	0.989814	−	0.142370i	$-0.0454722\pi$
$542$	−1.54951	+	5.86054i	−0.0665570	+	0.251732i
$543$	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
$546$	8.86663	+	0.120818i	0.379457	+	0.00517053i
$547$	−7.91721	+	7.91721i	−0.338516	+	0.338516i	−0.855808	−	0.517293i	$-0.826940\pi$
$547$	−7.91721	+	7.91721i	−0.338516	+	0.338516i	0.517293	+	0.855808i	$0.326940\pi$
$548$	−6.26994	−	22.7936i	−0.267839	−	0.973696i
$549$		−	7.18773i		−	0.306765i
$550$	−5.13056	+	21.6730i	−0.218768	+	0.924141i
$551$		−	34.6339i		−	1.47546i
$552$	−13.0904	+	13.3536i	−0.557163	+	0.568367i
$553$	−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	−0.731850	−	0.681466i	$-0.761343\pi$
$557$	−1.18911	+	1.18911i	−0.0503840	+	0.0503840i	0.681466	+	0.731850i	$0.261343\pi$
$558$	4.22539	+	1.11718i	0.178875	+	0.0472938i
$559$	25.9422			1.09724
$560$	16.8889	+	16.5761i	0.713684	+	0.700467i
$561$	1.90178			0.0802930
$562$	8.86358	+	2.34350i	0.373887	+	0.0988545i
$563$	9.59824	−	9.59824i	0.404517	−	0.404517i	−0.475304	−	0.879822i	$-0.657662\pi$
$563$	9.59824	−	9.59824i	0.404517	−	0.404517i	0.879822	+	0.475304i	$0.157662\pi$
$564$	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
$568$	−20.6327	−	20.2260i	−0.865729	−	0.848664i
$569$		−	1.12649i		−	0.0472248i	−0.999721	−	0.0236124i	$-0.992483\pi$
$569$		−	1.12649i		−	0.0472248i	0.999721	−	0.0236124i	$-0.00751675\pi$
$570$	−10.9654	+	6.57198i	−0.459289	+	0.275270i
$571$			17.5232i			0.733321i	0.930355	+	0.366661i	$0.119499\pi$
$571$			17.5232i			0.733321i	−0.930355	+	0.366661i	$0.880501\pi$
$572$	3.95960	+	14.3946i	0.165559	+	0.601870i
$573$	−4.89322	+	4.89322i	−0.204417	+	0.204417i
$574$	−44.7901	−	0.610317i	−1.86950	−	0.0254741i
$575$	−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	$0.362635\pi$
$578$	6.01356	−	22.7445i	0.250131	−	0.946047i
$579$		−	0.364376i		−	0.0151429i
$580$	−18.5009	+	33.5504i	−0.768210	+	1.39311i
$581$	9.55288	+	5.73332i	0.396320	+	0.237858i
$582$	−5.46873	+	20.6838i	−0.226686	+	0.857373i
$583$	−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	0.729173	−	0.684329i	$-0.239905\pi$
$587$	1.08650	+	1.08650i	0.0448446	+	0.0448446i	−0.684329	+	0.729173i	$0.739905\pi$
$588$	−10.1656	+	9.62609i	−0.419220	+	0.396973i
$589$	−12.4937			−0.514793
$590$	−43.4699	−	10.8899i	−1.78963	−	0.448330i
$591$			9.89274i			0.406933i
$592$	13.7121	+	3.47977i	0.563562	+	0.143018i
$593$	−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
$598$	−5.66397	+	21.4223i	−0.231617	+	0.876022i
$599$		−	30.2406i		−	1.23560i	−0.786336	−	0.617800i	$-0.788024\pi$
$599$		−	30.2406i		−	1.23560i	0.786336	−	0.617800i	$-0.211976\pi$
$600$	14.1330	−	0.508848i	0.576976	−	0.0207736i
$601$			18.8997i			0.770937i	0.922721	+	0.385468i	$0.125960\pi$
$601$			18.8997i			0.770937i	−0.922721	+	0.385468i	$0.874040\pi$
$602$	−29.3534	+	28.5642i	−1.19635	+	1.16419i
$603$	−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	$0.171584\pi$
$608$	−21.9882	+	6.28447i	−0.891740	+	0.254869i
$609$	−19.4349	−	11.6642i	−0.787544	−	0.472657i
$610$	5.52344	−	22.0483i	0.223637	−	0.892708i
$611$		−	3.24397i		−	0.131237i
$612$	−0.320277	−	1.16433i	−0.0129464	−	0.0470652i
$613$	16.4600	+	16.4600i	0.664812	+	0.664812i	0.956510	−	0.291698i	$-0.0942203\pi$
$613$	16.4600	+	16.4600i	0.664812	+	0.664812i	−0.291698	+	0.956510i	$0.594220\pi$
$614$	−3.12915	−	5.37855i	−0.126282	−	0.217061i
$615$	−18.6810	+	19.1738i	−0.753292	+	0.773164i
$616$	−20.3298	−	11.9276i	−0.819110	−	0.480578i
$617$	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	$0.694514\pi$
$618$	12.2924	+	3.25007i	0.494473	+	0.130737i
$619$			36.7201i			1.47591i	0.674853	+	0.737953i	$0.264207\pi$
$619$			36.7201i			1.47591i	−0.674853	+	0.737953i	$0.735793\pi$
$620$	12.1028	+	6.67394i	0.486061	+	0.268032i
$621$	−6.61132			−0.265303
$622$	2.78474	−	10.5325i	0.111658	−	0.422313i
$623$	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
$628$	−6.00353	−	21.8251i	−0.239567	−	0.870918i
$629$		−	2.13540i		−	0.0851441i
$630$	−0.00508468	+	8.36660i	−0.000202579	+	0.333333i
$631$	36.9096			1.46935			0.734673	−	0.678421i	$-0.237336\pi$
$631$	36.9096			1.46935			0.734673	+	0.678421i	$0.237336\pi$
$632$	−11.9749	+	12.2157i	−0.476336	+	0.485914i
$633$	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
$638$	9.75457	−	36.8937i	0.386187	−	1.46064i
$639$		−	10.2152i		−	0.404106i
$640$	24.6574	+	5.65792i	0.974670	+	0.223649i
$641$	49.0296			1.93655			0.968277	−	0.249878i	$-0.0803905\pi$
$641$	49.0296			1.93655			0.968277	+	0.249878i	$0.0803905\pi$
$642$	5.94304	−	22.4778i	0.234553	−	0.887126i
$643$	−3.86309	+	3.86309i	−0.152345	+	0.152345i	−0.779165	−	0.626819i	$-0.784356\pi$
$643$	−3.86309	+	3.86309i	−0.152345	+	0.152345i	0.626819	+	0.779165i	$0.284356\pi$
$644$	−17.1787	−	30.4756i	−0.676936	−	1.20091i
$645$	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	$0.447018\pi$
$648$	2.01981	+	1.97999i	0.0793455	+	0.0777815i
$649$	44.6355			1.75210
$650$	14.2606	−	8.80128i	0.559348	−	0.345215i
$651$	−4.20769	+	7.01087i	−0.164912	+	0.274778i
$652$	2.23215	+	8.11472i	0.0874177	+	0.317797i
$653$	4.22670	+	4.22670i	0.165404	+	0.165404i	0.784956	−	0.619552i	$-0.212686\pi$
$653$	4.22670	+	4.22670i	0.165404	+	0.165404i	−0.619552	+	0.784956i	$0.712686\pi$
$654$	−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
$658$	3.57184	+	3.67053i	0.139245	+	0.143092i
$659$	−27.5321			−1.07250			−0.536249	−	0.844060i	$-0.680159\pi$
$659$	−27.5321			−1.07250			−0.536249	+	0.844060i	$0.680159\pi$
$660$	−13.5318	+	3.91242i	−0.526725	+	0.152291i
$661$	38.0353			1.47940			0.739701	−	0.672936i	$-0.234967\pi$
$661$	38.0353			1.47940			0.739701	+	0.672936i	$0.234967\pi$
$662$	−5.55063	+	20.9936i	−0.215731	+	0.815939i
$663$	−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
$668$	28.8724	−	7.94206i	1.11711	−	0.307288i
$669$	−14.9083			−0.576390
$670$	−15.4775	−	25.8243i	−0.597949	−	0.997679i
$671$			22.6395i			0.873987i
$672$	−3.87876	+	14.4553i	−0.149627	+	0.557625i
$673$	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	0.991406	−	0.130821i	$-0.0417614\pi$
$677$	22.3917	+	22.3917i	0.860585	+	0.860585i	−0.130821	+	0.991406i	$0.541761\pi$
$678$	1.21100	−	4.58023i	0.0465080	−	0.175903i
$679$	−34.3191	−	20.5972i	−1.31705	−	0.790448i
$680$	−0.0877121	−	3.81768i	−0.00336361	−	0.146402i
$681$	15.6036			0.597930
$682$	−13.3089	−	3.51881i	−0.509623	−	0.134742i
$683$	−21.8152	−	21.8152i	−0.834737	−	0.834737i	0.153423	−	0.988161i	$-0.450970\pi$
$683$	−21.8152	−	21.8152i	−0.834737	−	0.834737i	−0.988161	+	0.153423i	$0.950970\pi$
$684$	−7.02875	−	3.99610i	−0.268751	−	0.152795i
$685$	18.4444	−	18.9310i	0.704725	−	0.723315i
$686$	−12.0037	−	23.2790i	−0.458305	−	0.888795i
$687$	10.0051	+	10.0051i	0.381719	+	0.381719i
$688$	−10.7703	+	42.4403i	−0.410612	+	1.61802i
$689$	9.58499			0.365159
$690$	−20.2801	−	5.08049i	−0.772052	−	0.193411i
$691$	0.0391809			0.00149051			0.000745256	−	1.00000i	$-0.499763\pi$
$691$	0.0391809			0.00149051			0.000745256		1.00000i	$0.499763\pi$
$692$	−19.5773	+	5.38522i	−0.744219	+	0.204715i
$693$	−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
$698$	−1.45315	+	5.49612i	−0.0550026	+	0.208031i
$699$			7.88666i			0.298301i
$700$	−6.44494	+	25.6605i	−0.243596	+	0.969877i
$701$			25.0705i			0.946899i	0.880821	+	0.473450i	$0.156991\pi$
$701$			25.0705i			0.946899i	−0.880821	+	0.473450i	$0.843009\pi$
$702$	3.24024	+	0.856708i	0.122295	+	0.0323344i
$703$	−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
$708$	−7.51704	−	27.3273i	−0.282508	−	1.02702i
$709$	−15.5764			−0.584985			−0.292493	−	0.956268i	$-0.594485\pi$
$709$	−15.5764			−0.584985			−0.292493	+	0.956268i	$0.594485\pi$
$710$	7.84989	−	31.3349i	0.294601	−	1.17598i
$711$	−6.04794			−0.226816
$712$	29.5932	+	29.0099i	1.10905	+	1.08719i
$713$	−14.4477	−	14.4477i	−0.541069	−	0.541069i
$714$	2.25896	+	0.0307809i	0.0845394	+	0.00115195i
$715$	−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
$718$	−3.20071	+	12.1057i	−0.119450	+	0.451782i
$719$	−7.05434			−0.263082			−0.131541	−	0.991311i	$-0.541993\pi$
$719$	−7.05434			−0.263082			−0.131541	+	0.991311i	$0.541993\pi$
$720$	4.67420	+	7.62574i	0.174197	+	0.284194i
$721$	−12.2409	+	20.3959i	−0.455876	+	0.759582i
$722$	−3.63271	−	0.960475i	−0.135196	−	0.0357452i
$723$	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	$0.422234\pi$
$728$	4.47029	+	17.1623i	0.165680	+	0.636076i
$729$			1.00000i			0.0370370i
$730$	−16.9079	+	10.1336i	−0.625788	+	0.375060i
$731$	6.60931			0.244454
$732$	13.8606	−	3.81270i	0.512304	−	0.140922i
$733$	16.4484	−	16.4484i	0.607534	−	0.607534i	−0.334767	−	0.942301i	$-0.608658\pi$
$733$	16.4484	−	16.4484i	0.607534	−	0.607534i	0.942301	+	0.334767i	$0.108658\pi$
$734$	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
$738$	−16.3682	−	4.32769i	−0.602522	−	0.159305i
$739$	−21.5632			−0.793216			−0.396608	−	0.917988i	$-0.629813\pi$
$739$	−21.5632			−0.793216			−0.396608	+	0.917988i	$0.629813\pi$
$740$	4.39306	+	15.1942i	0.161492	+	0.558549i
$741$	−9.58079			−0.351959
$742$	−10.8453	+	10.5537i	−0.398145	+	0.387440i
$743$	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
$748$	1.00879	+	3.66733i	0.0368850	+	0.134091i
$749$	37.2957	+	22.3836i	1.36275	+	0.817879i
$750$	8.47861	+	13.3459i	0.309595	+	0.487324i
$751$	−38.4718			−1.40386			−0.701928	−	0.712248i	$-0.747677\pi$
$751$	−38.4718			−1.40386			−0.701928	+	0.712248i	$0.747677\pi$
$752$	5.30700	+	1.34678i	0.193526	+	0.0491121i
$753$	−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
$756$	−4.60960	+	2.59838i	−0.167650	+	0.0945021i
$757$	14.2962	−	14.2962i	0.519605	−	0.519605i	−0.397847	−	0.917452i	$-0.630243\pi$
$757$	14.2962	−	14.2962i	0.519605	−	0.519605i	0.917452	+	0.397847i	$0.130243\pi$
$758$	7.58649	+	2.00584i	0.275554	+	0.0728554i
$759$	20.8239			0.755861
$760$	−18.4898	−	17.6592i	−0.670695	−	0.640568i
$761$			4.28764i			0.155427i	0.996976	+	0.0777134i	$0.0247619\pi$
$761$			4.28764i			0.155427i	−0.996976	+	0.0777134i	$0.975238\pi$
$762$	−15.2380	−	4.02888i	−0.552016	−	0.145951i
$763$	−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
$768$	4.54981	+	15.3395i	0.164177	+	0.553515i
$769$	−2.19684			−0.0792201			−0.0396100	−	0.999215i	$-0.512612\pi$
$769$	−2.19684			−0.0792201			−0.0396100	+	0.999215i	$0.512612\pi$
$770$	0.0160154	−	26.3526i	0.000577156	−	0.949682i
$771$			4.51149i			0.162477i
$772$	0.702652	−	0.193282i	0.0252890	−	0.00695635i
$773$	−16.5613	+	16.5613i	−0.595667	+	0.595667i	−0.939157	−	0.343489i	$-0.888391\pi$
$773$	−16.5613	+	16.5613i	−0.595667	+	0.595667i	0.343489	+	0.939157i	$0.388391\pi$
$774$	−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
$778$	−28.5101	−	7.53796i	−1.02214	−	0.270249i
$779$	48.3977			1.73403
$780$	9.28106	+	5.11792i	0.332315	+	0.183251i
$781$			32.1751i			1.15132i
$782$	−1.44301	+	5.45777i	−0.0516021	+	0.195169i
$783$	−6.05788	−	6.05788i	−0.216491	−	0.216491i
$784$	−23.9550	−	14.4969i	−0.855535	−	0.517745i
$785$	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	0.435735	−	0.900075i	$-0.356489\pi$
$787$	−13.0264	−	13.0264i	−0.464340	−	0.464340i	−0.900075	+	0.435735i	$0.856489\pi$
$788$	−19.0769	+	5.24756i	−0.679586	+	0.186937i
$789$		−	1.05799i		−	0.0376654i
$790$	−18.5520	−	4.64756i	−0.660050	−	0.165353i
$791$	7.59963	+	4.56104i	0.270212	+	0.162172i
$792$	−6.36187	−	6.23647i	−0.226059	−	0.221603i
$793$	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	0.748238	−	0.663430i	$-0.230900\pi$
$797$	2.39422	+	2.39422i	0.0848076	+	0.0848076i	−0.663430	+	0.748238i	$0.730900\pi$
$798$	10.8406	−	10.5491i	0.383752	−	0.373435i
$799$		−	0.826469i		−	0.0292384i
$800$	8.47803	+	26.9838i	0.299744	+	0.954020i
$801$			14.6515i			0.517686i
$802$	−45.0334	−	11.9067i	−1.59018	−	0.420439i
$803$	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
$808$	19.7970	+	19.4068i	0.696455	+	0.682727i
$809$			3.72661i			0.131021i	0.997852	+	0.0655104i	$0.0208676\pi$
$809$			3.72661i			0.131021i	−0.997852	+	0.0655104i	$0.979132\pi$
$810$	−0.768454	+	3.06749i	−0.0270007	+	0.107781i
$811$	23.5676			0.827569			0.413785	−	0.910375i	$-0.364207\pi$
$811$	23.5676			0.827569			0.413785	+	0.910375i	$0.364207\pi$
$812$	12.1838	−	43.6651i	0.427566	−	1.53234i
$813$	−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
$818$	17.1550	+	4.53572i	0.599811	+	0.158588i
$819$	−3.22667	+	5.37629i	−0.112749	+	0.187863i
$820$	−46.8836	−	25.8533i	−1.63725	−	0.902838i
$821$			8.26755i			0.288540i	0.989538	+	0.144270i	$0.0460833\pi$
$821$			8.26755i			0.288540i	−0.989538	+	0.144270i	$0.953917\pi$
$822$	16.1609	+	4.27287i	0.563675	+	0.149034i
$823$	−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
$826$	53.0188	+	0.722441i	1.84476	+	0.0251369i
$827$	−3.99650	+	3.99650i	−0.138972	+	0.138972i	−0.773170	−	0.634198i	$-0.781330\pi$
$827$	−3.99650	+	3.99650i	−0.138972	+	0.138972i	0.634198	+	0.773170i	$0.281330\pi$
$828$	−3.50695	−	12.7491i	−0.121875	−	0.443062i
$829$			26.5322i			0.921500i	0.887530	+	0.460750i	$0.152419\pi$
$829$			26.5322i			0.921500i	−0.887530	+	0.460750i	$0.847581\pi$
$830$	6.84569	+	11.4220i	0.237617	+	0.396465i
$831$		−	12.5719i		−	0.436114i
$832$	13.6705	+	13.1368i	0.473941	+	0.455437i
$833$	−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
$838$	−6.53337	+	24.7105i	−0.225692	+	0.853611i
$839$	53.6879			1.85351			0.926756	−	0.375663i	$-0.122585\pi$
$839$	53.6879			1.85351			0.926756	+	0.375663i	$0.122585\pi$
$840$	−16.1366	+	4.42822i	−0.556767	+	0.152788i
$841$	44.3958			1.53089
$842$	0.906352	−	3.42800i	0.0312349	−	0.118137i
$843$	−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
$848$	−3.97935	+	15.6806i	−0.136651	+	0.538475i
$849$			2.94605i			0.101108i
$850$	3.63319	−	2.24231i	0.124617	−	0.0769106i
$851$		−	23.3821i		−	0.801528i
$852$	19.6987	−	5.41860i	0.674866	−	0.185638i
$853$	−19.9799	+	19.9799i	−0.684100	+	0.684100i	−0.960921	−	0.276821i	$-0.910719\pi$
$853$	−19.9799	+	19.9799i	−0.684100	+	0.684100i	0.276821	+	0.960921i	$0.410719\pi$
$854$	−0.366428	+	26.8915i	−0.0125389	+	0.920209i
$855$	−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	$0.336285\pi$
$858$	−10.2059	−	2.69841i	−0.348424	−	0.0921221i
$859$		−	39.4596i		−	1.34634i	−0.739487	−	0.673171i	$-0.764932\pi$
$859$		−	39.4596i		−	1.34634i	0.739487	−	0.673171i	$-0.235068\pi$
$860$	−47.0276	+	13.5970i	−1.60363	+	0.463653i
$861$	16.2996	−	27.1585i	0.555490	−	0.925561i
$862$	39.7149	+	10.5005i	1.35270	+	0.357648i
$863$	−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
$868$	−15.7515	−	4.39511i	−0.534642	−	0.149180i
$869$	19.0494			0.646208
$870$	−13.9273	−	23.2377i	−0.472179	−	0.787831i
$871$		−	22.5635i		−	0.764535i
$872$	−5.73159	−	5.61861i	−0.194096	−	0.190270i
$873$	−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	−0.938428	−	0.345474i	$-0.887718\pi$
$877$	−17.5598	+	17.5598i	−0.592954	+	0.592954i	0.345474	+	0.938428i	$0.387718\pi$
$878$	−43.8897	−	11.6043i	−1.48121	−	0.391625i
$879$			24.4307i			0.824026i
$880$	−14.7225	−	24.0191i	−0.496296	−	0.809683i
$881$			44.0876i			1.48535i	0.669653	+	0.742674i	$0.266443\pi$
$881$			44.0876i			1.48535i	−0.669653	+	0.742674i	$0.733557\pi$
$882$	−2.26873	−	9.63602i	−0.0763920	−	0.324462i
$883$	0.361877	+	0.361877i	0.0121781	+	0.0121781i	0.713170	−	0.700992i	$-0.247259\pi$
$883$	0.361877	+	0.361877i	0.0121781	+	0.0121781i	−0.700992	+	0.713170i	$0.747259\pi$
$884$	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	$0.347420\pi$
$888$	−7.00260	+	7.14341i	−0.234992	+	0.239717i
$889$	15.1742	−	25.2833i	0.508926	−	0.847975i
$890$	−11.2590	+	44.9433i	−0.377403	+	1.50650i
$891$		−	3.14974i		−	0.105520i
$892$	−7.90807	−	28.7489i	−0.264782	−	0.962583i
$893$	−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
$896$	−29.9327	+	0.188037i	−0.999980	+	0.00628189i
$897$	−11.0792	−	11.0792i	−0.369924	−	0.369924i
$898$	−6.03925	+	22.8417i	−0.201532	+	0.762236i
$899$		−	26.4764i		−	0.883039i
$900$	−4.71444	+	8.81896i	−0.157148	+	0.293965i
$901$	2.44197			0.0813540
$902$	51.5556	+	13.6311i	1.71661	+	0.453866i
$903$	−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	−0.186895	−	0.982380i	$-0.559842\pi$
$907$	23.9572	−	23.9572i	0.795485	−	0.795485i	0.982380	+	0.186895i	$0.0598423\pi$
$908$	8.27685	+	30.0895i	0.274677	+	0.998555i
$909$			9.80142i			0.325093i
$910$	−14.0292	+	14.0122i	−0.465063	+	0.464498i
$911$	23.9927			0.794912			0.397456	−	0.917621i	$-0.369893\pi$
$911$	23.9927			0.794912			0.397456	+	0.917621i	$0.369893\pi$
$912$	3.97760	−	15.6738i	0.131712	−	0.519010i
$913$	−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
$918$	0.825519	+	0.218264i	0.0272462	+	0.00720379i
$919$		−	58.5349i		−	1.93089i	−0.260611	−	0.965444i	$-0.583924\pi$
$919$		−	58.5349i		−	1.93089i	0.260611	−	0.965444i	$-0.416076\pi$
$920$	−0.960424	−	41.8026i	−0.0316643	−	1.37819i
$921$	4.40002			0.144986
$922$	−41.6514	−	11.0125i	−1.37172	−	0.362676i
$923$	17.1185	−	17.1185i	0.563463	−	0.563463i
$924$	14.5190	−	8.18421i	0.477642	−	0.269241i
$925$	−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
$928$	−13.3180	−	46.5972i	−0.437184	−	1.52963i
$929$	−44.8190			−1.47046			−0.735232	−	0.677815i	$-0.762927\pi$
$929$	−44.8190			−1.47046			−0.735232	+	0.677815i	$0.762927\pi$
$930$	−8.38264	+	5.02406i	−0.274878	+	0.164745i
$931$	13.3108	+	24.9726i	0.436245	+	0.818443i
$932$	−15.2084	+	4.18345i	−0.498169	+	0.137033i
$933$	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	$0.0436750\pi$
$938$	24.8440	+	25.5304i	0.811186	+	0.833598i
$939$	10.7127			0.349597
$940$	1.70025	+	5.88063i	0.0554561	+	0.191805i
$941$	37.0773			1.20869			0.604343	−	0.796724i	$-0.293436\pi$
$941$	37.0773			1.20869			0.604343	+	0.796724i	$0.293436\pi$
$942$	15.4742	+	4.09132i	0.504176	+	0.133302i
$943$	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	−0.997885	−	0.0649972i	$-0.979296\pi$
$947$	−28.7081	+	28.7081i	−0.932888	+	0.932888i	0.0649972	+	0.997885i	$0.479296\pi$
$948$	−3.20811	−	11.6627i	−0.104194	−	0.378787i
$949$	−14.7729			−0.479550
$950$	6.58500	−	27.8171i	0.213646	−	0.902504i
$951$			26.9489i			0.873878i
$952$	1.13890	+	4.37245i	0.0369119	+	0.141712i
$953$	−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
$958$	−44.0691	−	11.6517i	−1.42381	−	0.376449i
$959$	−16.0932	+	26.8145i	−0.519676	+	0.865886i
$960$	−12.2259	+	13.0586i	−0.394588	+	0.421466i
$961$	21.4490			0.691904
$962$	−3.02990	+	11.4597i	−0.0976879	+	0.369475i
$963$	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
$966$	24.7350	+	0.337043i	0.795836	+	0.0108442i
$967$	−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	$0.838969\pi$
$968$	−2.17966	−	2.13669i	−0.0700569	−	0.0686759i
$969$	−2.44090			−0.0784131
$970$	−24.5934	−	41.0342i	−0.789648	−	1.31753i
$971$	−41.1699			−1.32121			−0.660603	−	0.750735i	$-0.729699\pi$
$971$	−41.1699			−1.32121			−0.660603	+	0.750735i	$0.729699\pi$
$972$	−1.92837	+	0.530446i	−0.0618526	+	0.0170141i
$973$	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	$0.663289\pi$
$978$	−5.75340	−	1.52118i	−0.183973	−	0.0486419i
$979$		−	46.1485i		−	1.47491i
$980$	0.445549	−	31.3018i	0.0142326	−	0.999899i
$981$		−	2.83769i		−	0.0906005i
$982$	14.5141	−	54.8952i	0.463163	−	1.75178i
$983$	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
$988$	−5.08209	−	18.4753i	−0.161683	−	0.587779i
$989$	72.3701			2.30124
$990$	2.42043	−	9.66179i	0.0769263	−	0.307072i
$991$	−14.4146			−0.457895			−0.228948	−	0.973439i	$-0.573528\pi$
$991$	−14.4146			−0.457895			−0.228948	+	0.973439i	$0.573528\pi$
$992$	−16.8092	+	4.80426i	−0.533694	+	0.152535i
$993$	−10.8575	−	10.8575i	−0.344552	−	0.344552i
$994$	−0.520766	+	38.2181i	−0.0165177	+	1.21221i
$995$	−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	0.221565	−	0.975146i	$-0.428883\pi$
$997$	−23.7945	−	23.7945i	−0.753580	−	0.753580i	−0.975146	+	0.221565i	$0.928883\pi$
$998$	−5.99800	−	1.58585i	−0.189863	−	0.0501991i
$999$	−3.53668			−0.111896

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bj.b.13.9	✓	184	40.13	odd	4	inner
840.2.bj.b.13.10	yes	184	280.13	even	4	inner
840.2.bj.b.13.37	yes	184	35.13	even	4	inner
840.2.bj.b.13.38	yes	184	5.3	odd	4	inner
840.2.bj.b.517.9	yes	184	7.6	odd	2	inner
840.2.bj.b.517.10	yes	184	1.1	even	1	trivial
840.2.bj.b.517.37	yes	184	8.5	even	2	inner
840.2.bj.b.517.38	yes	184	56.13	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+(-1.36723 - 0.361491i) 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} +(-2.01981 - 1.97999i) q^{8} -1.00000i q^{9} +(0.768454 - 3.06749i) q^{10} +3.14974i q^{11} +(1.92837 - 0.530446i) q^{12} +(1.67579 - 1.67579i) q^{13} +(-0.0509796 + 3.74131i) q^{14} +(1.60159 + 1.56042i) q^{15} +(2.04580 + 3.43725i) q^{16} +(0.426943 - 0.426943i) q^{17} +(-0.361491 + 1.36723i) q^{18} -4.04265i q^{19} +(-2.15952 + 3.91618i) q^{20} +(-2.26855 - 1.36151i) q^{21} +(1.13860 - 4.30643i) 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} +(1.42215 - 5.09681i) q^{28} +8.56714 q^{29} +(-1.62566 - 2.71242i) q^{30} -3.09047i q^{31} +(-1.55454 - 5.43906i) 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} +(-1.46138 + 5.52724i) q^{38} -2.36993i q^{39} +(4.36823 - 4.57368i) q^{40} +11.9718i q^{41} +(2.60946 + 2.68155i) 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} +(3.87710 + 0.983909i) q^{48} +(-6.17728 + 3.29261i) q^{49} +(6.88090 + 1.62888i) q^{50} -0.603788i q^{51} +(4.57011 - 1.25712i) q^{52} +(2.85984 + 2.85984i) q^{53} +(0.711166 + 1.22239i) q^{54} +(-7.04243 + 0.0916805i) q^{55} +(-3.78686 + 6.45443i) q^{56} +(-2.85859 - 2.85859i) q^{57} +(-11.7133 - 3.09694i) q^{58} -14.1712i q^{59} +(1.24214 + 4.29617i) q^{60} +7.18773 q^{61} +(-1.11718 + 4.22539i) 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} +(1.16433 - 0.320277i) q^{68} -6.61132i q^{69} +(-8.36660 - 0.00508468i) q^{70} +10.2152 q^{71} +(-1.97999 + 2.01981i) 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} +(-0.856708 + 3.24024i) q^{78} -6.04794i q^{79} +(-7.62574 + 4.67420i) q^{80} -1.00000 q^{81} +(4.32769 - 16.3682i) q^{82} +(-2.97764 + 2.97764i) q^{83} +(-2.59838 - 4.60960i) q^{84} +(0.967019 + 0.942165i) q^{85} +(-7.78471 - 13.3808i) q^{86} +(6.05788 - 6.05788i) q^{87} +(6.23647 - 6.36187i) q^{88} -14.6515 q^{89} +(-3.06749 - 0.768454i) q^{90} +(-5.37629 - 3.22667i) q^{91} +(12.7491 - 3.50695i) 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} +(9.63602 - 2.26873i) 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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