LMFDB - Embedded newform 360.2.bk.a.229.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(229,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 3]))

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

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

chi := DirichletCharacter("360.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.20
Character	$\chi$	$=$	360.229
Dual form			360.2.bk.a.349.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.888188 + 1.10051i) q^{2} +(1.67702 - 0.433134i) q^{3} +(-0.422246 - 1.95492i) q^{4} +(1.45294 + 1.69970i) q^{5} +(-1.01284 + 2.23028i) q^{6} +(-0.435632 + 0.251512i) q^{7} +(2.52644 + 1.27165i) q^{8} +(2.62479 - 1.45275i) q^{9} +O(q^{10})$	\(q+(-0.888188 + 1.10051i) q^{2} +(1.67702 - 0.433134i) q^{3} +(-0.422246 - 1.95492i) q^{4} +(1.45294 + 1.69970i) q^{5} +(-1.01284 + 2.23028i) q^{6} +(-0.435632 + 0.251512i) q^{7} +(2.52644 + 1.27165i) q^{8} +(2.62479 - 1.45275i) q^{9} +(-3.16102 + 0.0893258i) q^{10} +(1.50457 - 0.868661i) q^{11} +(-1.55486 - 3.09555i) q^{12} +(-1.03049 + 1.78486i) q^{13} +(0.110131 - 0.702807i) q^{14} +(3.17280 + 2.22111i) q^{15} +(-3.64342 + 1.65091i) q^{16} +1.74463i q^{17} +(-0.732541 + 4.17892i) q^{18} -4.71652i q^{19} +(2.70927 - 3.55807i) q^{20} +(-0.621625 + 0.610478i) q^{21} +(-0.380365 + 2.42732i) q^{22} +(2.61329 + 1.50878i) q^{23} +(4.78769 + 1.03829i) q^{24} +(-0.777934 + 4.93911i) q^{25} +(-1.04899 - 2.71935i) q^{26} +(3.77259 - 3.57317i) q^{27} +(0.675630 + 0.745425i) q^{28} +(5.76129 - 3.32629i) q^{29} +(-5.26240 + 1.51894i) q^{30} +(-3.09242 + 5.35623i) q^{31} +(1.41919 - 5.47594i) q^{32} +(2.14694 - 2.10844i) q^{33} +(-1.91999 - 1.54956i) q^{34} +(-1.06044 - 0.375010i) q^{35} +(-3.94831 - 4.51783i) q^{36} +0.268484 q^{37} +(5.19058 + 4.18915i) q^{38} +(-0.955067 + 3.43958i) q^{39} +(1.50935 + 6.14181i) q^{40} +(-1.43762 + 2.49003i) q^{41} +(-0.119718 - 1.22632i) q^{42} +(-2.88016 - 4.98857i) q^{43} +(-2.33346 - 2.57451i) q^{44} +(6.28289 + 2.35059i) q^{45} +(-3.98152 + 1.53587i) q^{46} +(-3.28509 + 1.89665i) q^{47} +(-5.39502 + 4.34670i) q^{48} +(-3.37348 + 5.84304i) q^{49} +(-4.74459 - 5.24298i) q^{50} +(0.755660 + 2.92579i) q^{51} +(3.92437 + 1.26087i) q^{52} -9.62677 q^{53} +(0.581546 + 7.32542i) q^{54} +(3.66250 + 1.29519i) q^{55} +(-1.42043 + 0.0814603i) q^{56} +(-2.04288 - 7.90970i) q^{57} +(-1.45650 + 9.29473i) q^{58} +(-1.68133 - 0.970719i) q^{59} +(3.00238 - 7.14043i) q^{60} +(-9.20522 + 5.31464i) q^{61} +(-3.14794 - 8.16058i) q^{62} +(-0.778058 + 1.29303i) q^{63} +(4.76582 + 6.42549i) q^{64} +(-4.53095 + 0.841774i) q^{65} +(0.413476 + 4.23542i) q^{66} +(7.17786 - 12.4324i) q^{67} +(3.41062 - 0.736665i) q^{68} +(5.03604 + 1.39835i) q^{69} +(1.35457 - 0.833947i) q^{70} +13.9805 q^{71} +(8.47877 - 0.332473i) q^{72} -14.8657i q^{73} +(-0.238464 + 0.295469i) q^{74} +(0.834685 + 8.61994i) q^{75} +(-9.22041 + 1.99153i) q^{76} +(-0.436958 + 0.756833i) q^{77} +(-2.93702 - 4.10605i) q^{78} +(-6.80294 - 11.7830i) q^{79} +(-8.09971 - 3.79403i) q^{80} +(4.77905 - 7.62632i) q^{81} +(-1.46343 - 3.79374i) q^{82} +(-4.12946 - 7.15243i) q^{83} +(1.45591 + 0.957454i) q^{84} +(-2.96535 + 2.53485i) q^{85} +(8.04810 + 1.26115i) q^{86} +(8.22108 - 8.07366i) q^{87} +(4.90583 - 0.281344i) q^{88} -13.2772 q^{89} +(-8.16723 + 4.82662i) q^{90} -1.03672i q^{91} +(1.84610 - 5.74584i) q^{92} +(-2.86609 + 10.3219i) q^{93} +(0.830496 - 5.29986i) q^{94} +(8.01665 - 6.85282i) q^{95} +(0.00819559 - 9.79796i) q^{96} +(-3.21307 + 1.85507i) q^{97} +(-3.43404 - 8.90227i) q^{98} +(2.68722 - 4.46581i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 2 q^{4} - 8 q^{9}+O(q^{10}) $ 136 * q - 2 * q^4 - 8 * q^9	$ 136 q - 2 q^{4} - 8 q^{9} - 10 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{20} - 38 q^{24} - 2 q^{25} + 16 q^{26} - 12 q^{30} - 4 q^{31} + 8 q^{34} - 24 q^{36} + 4 q^{39} - 6 q^{40} - 4 q^{41} - 56 q^{44} - 28 q^{46} + 40 q^{49} - 12 q^{50} + 10 q^{54} - 28 q^{55} + 26 q^{56} - 58 q^{60} - 20 q^{64} + 18 q^{65} + 16 q^{66} - 6 q^{70} - 128 q^{71} + 36 q^{74} + 12 q^{76} - 4 q^{79} - 36 q^{80} - 16 q^{81} - 110 q^{84} + 44 q^{86} - 32 q^{89} + 32 q^{90} - 34 q^{94} + 8 q^{95} - 2 q^{96}+O(q^{100}) $ 136 * q - 2 * q^4 - 8 * q^9 - 10 * q^14 + 2 * q^15 - 2 * q^16 - 2 * q^20 - 38 * q^24 - 2 * q^25 + 16 * q^26 - 12 * q^30 - 4 * q^31 + 8 * q^34 - 24 * q^36 + 4 * q^39 - 6 * q^40 - 4 * q^41 - 56 * q^44 - 28 * q^46 + 40 * q^49 - 12 * q^50 + 10 * q^54 - 28 * q^55 + 26 * q^56 - 58 * q^60 - 20 * q^64 + 18 * q^65 + 16 * q^66 - 6 * q^70 - 128 * q^71 + 36 * q^74 + 12 * q^76 - 4 * q^79 - 36 * q^80 - 16 * q^81 - 110 * q^84 + 44 * q^86 - 32 * q^89 + 32 * q^90 - 34 * q^94 + 8 * q^95 - 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.888188	+	1.10051i	−0.628043	+	0.778178i
$2$	−0.888188	+	1.10051i	−0.628043	+	0.778178i
$3$	1.67702	−	0.433134i	0.968228	−	0.250070i
$3$	1.67702	−	0.433134i	0.968228	−	0.250070i
$4$	−0.422246	−	1.95492i	−0.211123	−	0.977460i
$5$	1.45294	+	1.69970i	0.649774	+	0.760127i
$5$	1.45294	+	1.69970i	0.649774	+	0.760127i
$6$	−1.01284	+	2.23028i	−0.413490	+	0.910509i
$7$	−0.435632	+	0.251512i	−0.164653	+	0.0950627i	−0.580062	−	0.814572i	$-0.696972\pi$
$7$	−0.435632	+	0.251512i	−0.164653	+	0.0950627i	0.415409	+	0.909635i	$0.363638\pi$
$8$	2.52644	+	1.27165i	0.893232	+	0.449596i
$9$	2.62479	−	1.45275i	0.874930	−	0.484249i
$10$	−3.16102	+	0.0893258i	−0.999601	+	0.0282473i
$11$	1.50457	−	0.868661i	0.453643	−	0.261911i	−0.255724	−	0.966750i	$-0.582314\pi$
$11$	1.50457	−	0.868661i	0.453643	−	0.261911i	0.709368	+	0.704839i	$0.248981\pi$
$12$	−1.55486	−	3.09555i	−0.448848	−	0.893608i
$13$	−1.03049	+	1.78486i	−0.285806	+	0.495031i	−0.972804	−	0.231628i	$-0.925595\pi$
$13$	−1.03049	+	1.78486i	−0.285806	+	0.495031i	0.686998	+	0.726659i	$0.258928\pi$
$14$	0.110131	−	0.702807i	0.0294338	−	0.187833i
$15$	3.17280	+	2.22111i	0.819214	+	0.573487i
$16$	−3.64342	+	1.65091i	−0.910854	+	0.412728i
$17$			1.74463i			0.423136i	0.977363	+	0.211568i	$0.0678570\pi$
$17$			1.74463i			0.423136i	−0.977363	+	0.211568i	$0.932143\pi$
$18$	−0.732541	+	4.17892i	−0.172662	+	0.984981i
$19$		−	4.71652i		−	1.08204i	−0.841009	−	0.541022i	$-0.818038\pi$
$19$		−	4.71652i		−	1.08204i	0.841009	−	0.541022i	$-0.181962\pi$
$20$	2.70927	−	3.55807i	0.605811	−	0.795608i
$21$	−0.621625	+	0.610478i	−0.135650	+	0.133217i
$22$	−0.380365	+	2.42732i	−0.0810942	+	0.517507i
$23$	2.61329	+	1.50878i	0.544908	+	0.314603i	0.747066	−	0.664750i	$-0.231462\pi$
$23$	2.61329	+	1.50878i	0.544908	+	0.314603i	−0.202158	+	0.979353i	$0.564795\pi$
$24$	4.78769	+	1.03829i	0.977283	+	0.211940i
$25$	−0.777934	+	4.93911i	−0.155587	+	0.987822i
$26$	−1.04899	−	2.71935i	−0.205723	−	0.533309i
$27$	3.77259	−	3.57317i	0.726035	−	0.687657i
$28$	0.675630	+	0.745425i	0.127682	+	0.140872i
$29$	5.76129	−	3.32629i	1.06985	−	0.617676i	0.141706	−	0.989909i	$-0.454741\pi$
$29$	5.76129	−	3.32629i	1.06985	−	0.617676i	0.928139	+	0.372233i	$0.121408\pi$
$30$	−5.26240	+	1.51894i	−0.960778	+	0.277320i
$31$	−3.09242	+	5.35623i	−0.555415	+	0.962007i	0.442456	+	0.896790i	$0.354107\pi$
$31$	−3.09242	+	5.35623i	−0.555415	+	0.962007i	−0.997871	+	0.0652169i	$0.979226\pi$
$32$	1.41919	−	5.47594i	0.250880	−	0.968018i
$33$	2.14694	−	2.10844i	0.373734	−	0.367032i
$34$	−1.91999	−	1.54956i	−0.329275	−	0.265748i
$35$	−1.06044	−	0.375010i	−0.179247	−	0.0633883i
$36$	−3.94831	−	4.51783i	−0.658052	−	0.752972i
$37$	0.268484			0.0441385			0.0220692	−	0.999756i	$-0.492975\pi$
$37$	0.268484			0.0441385			0.0220692	+	0.999756i	$0.492975\pi$
$38$	5.19058	+	4.18915i	0.842023	+	0.679570i
$39$	−0.955067	+	3.43958i	−0.152933	+	0.550774i
$40$	1.50935	+	6.14181i	0.238649	+	0.971106i
$41$	−1.43762	+	2.49003i	−0.224519	+	0.388878i	−0.956175	−	0.292796i	$-0.905414\pi$
$41$	−1.43762	+	2.49003i	−0.224519	+	0.388878i	0.731656	+	0.681674i	$0.238748\pi$
$42$	−0.119718	−	1.22632i	−0.0184729	−	0.189226i
$43$	−2.88016	−	4.98857i	−0.439220	−	0.760751i	0.558410	−	0.829565i	$-0.311412\pi$
$43$	−2.88016	−	4.98857i	−0.439220	−	0.760751i	−0.997629	+	0.0688146i	$0.978078\pi$
$44$	−2.33346	−	2.57451i	−0.351782	−	0.388123i
$45$	6.28289	+	2.35059i	0.936598	+	0.350405i
$46$	−3.98152	+	1.53587i	−0.587043	+	0.226451i
$47$	−3.28509	+	1.89665i	−0.479180	+	0.276655i	−0.720075	−	0.693897i	$-0.755892\pi$
$47$	−3.28509	+	1.89665i	−0.479180	+	0.276655i	0.240895	+	0.970551i	$0.422559\pi$
$48$	−5.39502	+	4.34670i	−0.778703	+	0.627392i
$49$	−3.37348	+	5.84304i	−0.481926	+	0.834721i
$50$	−4.74459	−	5.24298i	−0.670986	−	0.741470i
$51$	0.755660	+	2.92579i	0.105814	+	0.409692i
$52$	3.92437	+	1.26087i	0.544213	+	0.174852i
$53$	−9.62677			−1.32234			−0.661169	−	0.750237i	$-0.729939\pi$
$53$	−9.62677			−1.32234			−0.661169	+	0.750237i	$0.729939\pi$
$54$	0.581546	+	7.32542i	0.0791384	+	0.996864i
$55$	3.66250	+	1.29519i	0.493852	+	0.174644i
$56$	−1.42043	+	0.0814603i	−0.189813	+	0.0108856i
$57$	−2.04288	−	7.90970i	−0.270587	−	1.04766i
$58$	−1.45650	+	9.29473i	−0.191248	+	1.22046i
$59$	−1.68133	−	0.970719i	−0.218891	−	0.126377i	0.386546	−	0.922270i	$-0.373668\pi$
$59$	−1.68133	−	0.970719i	−0.218891	−	0.126377i	−0.605437	+	0.795893i	$0.707002\pi$
$60$	3.00238	−	7.14043i	0.387606	−	0.921825i
$61$	−9.20522	+	5.31464i	−1.17861	+	0.680470i	−0.955692	−	0.294368i	$-0.904891\pi$
$61$	−9.20522	+	5.31464i	−1.17861	+	0.680470i	−0.222916	+	0.974838i	$0.571558\pi$
$62$	−3.14794	−	8.16058i	−0.399788	−	1.03639i
$63$	−0.778058	+	1.29303i	−0.0980261	+	0.162906i
$64$	4.76582	+	6.42549i	0.595727	+	0.803187i
$65$	−4.53095	+	0.841774i	−0.561996	+	0.104409i
$66$	0.413476	+	4.23542i	0.0508953	+	0.521344i
$67$	7.17786	−	12.4324i	0.876915	−	1.51886i	0.0222060	−	0.999753i	$-0.492931\pi$
$67$	7.17786	−	12.4324i	0.876915	−	1.51886i	0.854709	−	0.519108i	$-0.173736\pi$
$68$	3.41062	−	0.736665i	0.413598	−	0.0893337i
$69$	5.03604	+	1.39835i	0.606268	+	0.168342i
$70$	1.35457	−	0.833947i	0.161902	−	0.0996758i
$71$	13.9805			1.65918			0.829592	−	0.558370i	$-0.188573\pi$
$71$	13.9805			1.65918			0.829592	+	0.558370i	$0.188573\pi$
$72$	8.47877	−	0.332473i	0.999232	−	0.0391824i
$73$		−	14.8657i		−	1.73989i	−0.493144	−	0.869947i	$-0.664153\pi$
$73$		−	14.8657i		−	1.73989i	0.493144	−	0.869947i	$-0.335847\pi$
$74$	−0.238464	+	0.295469i	−0.0277209	+	0.0343476i
$75$	0.834685	+	8.61994i	0.0963811	+	0.995345i
$76$	−9.22041	+	1.99153i	−1.05765	+	0.228444i
$77$	−0.436958	+	0.756833i	−0.0497960	+	0.0862491i
$78$	−2.93702	−	4.10605i	−0.332552	−	0.464919i
$79$	−6.80294	−	11.7830i	−0.765391	−	1.32570i	−0.940040	−	0.341065i	$-0.889212\pi$
$79$	−6.80294	−	11.7830i	−0.765391	−	1.32570i	0.174649	−	0.984631i	$-0.444121\pi$
$80$	−8.09971	−	3.79403i	−0.905576	−	0.424185i
$81$	4.77905	−	7.62632i	0.531005	−	0.847369i
$82$	−1.46343	−	3.79374i	−0.161609	−	0.418948i
$83$	−4.12946	−	7.15243i	−0.453267	−	0.785082i	0.545320	−	0.838228i	$-0.316408\pi$
$83$	−4.12946	−	7.15243i	−0.453267	−	0.785082i	−0.998587	+	0.0531466i	$0.983075\pi$
$84$	1.45591	+	0.957454i	0.158853	+	0.104467i
$85$	−2.96535	+	2.53485i	−0.321637	+	0.274943i
$86$	8.04810	+	1.26115i	0.867849	+	0.135993i
$87$	8.22108	−	8.07366i	0.881392	−	0.865587i
$88$	4.90583	−	0.281344i	0.522963	−	0.0299913i
$89$	−13.2772			−1.40738			−0.703692	−	0.710506i	$-0.748466\pi$
$89$	−13.2772			−1.40738			−0.703692	+	0.710506i	$0.748466\pi$
$90$	−8.16723	+	4.82662i	−0.860902	+	0.508771i
$91$		−	1.03672i		−	0.108678i
$92$	1.84610	−	5.74584i	0.192469	−	0.599045i
$93$	−2.86609	+	10.3219i	−0.297199	+	1.07033i
$94$	0.830496	−	5.29986i	0.0856591	−	0.546639i
$95$	8.01665	−	6.85282i	0.822491	−	0.703084i
$96$	0.00819559	−	9.79796i	0.000836459	−	1.00000i
$97$	−3.21307	+	1.85507i	−0.326238	+	0.188354i	−0.654170	−	0.756348i	$-0.726982\pi$
$97$	−3.21307	+	1.85507i	−0.326238	+	0.188354i	0.327932	+	0.944701i	$0.393648\pi$
$98$	−3.43404	−	8.90227i	−0.346891	−	0.899265i
$99$	2.68722	−	4.46581i	0.270076	−	0.448831i
$100$	9.98404	−	0.564721i	0.998404	−	0.0564721i
$101$	−0.585395	+	0.337978i	−0.0582490	+	0.0336301i	−0.528842	−	0.848721i	$-0.677373\pi$
$101$	−0.585395	+	0.337978i	−0.0582490	+	0.0336301i	0.470593	+	0.882351i	$0.344040\pi$
$102$	−3.89102	−	1.76703i	−0.385269	−	0.174962i
$103$	−10.4794	−	6.05027i	−1.03256	−	0.596151i	−0.114845	−	0.993383i	$-0.536637\pi$
$103$	−10.4794	−	6.05027i	−1.03256	−	0.596151i	−0.917718	+	0.397233i	$0.869971\pi$
$104$	−4.87318	+	3.19892i	−0.477855	+	0.313680i
$105$	−1.94081	−	0.169586i	−0.189404	−	0.0165499i
$106$	8.55037	−	10.5944i	0.830486	−	1.02901i
$107$	3.81648			0.368953			0.184477	−	0.982837i	$-0.440941\pi$
$107$	3.81648			0.368953			0.184477	+	0.982837i	$0.440941\pi$
$108$	−8.57822	−	5.86635i	−0.825440	−	0.564490i
$109$		−	6.82828i		−	0.654031i	−0.945019	−	0.327015i	$-0.893957\pi$
$109$		−	6.82828i		−	0.654031i	0.945019	−	0.327015i	$-0.106043\pi$
$110$	−4.67836	+	2.88025i	−0.446064	+	0.274621i
$111$	0.450253	−	0.116289i	0.0427361	−	0.0110377i
$112$	1.17196	−	1.63555i	0.110740	−	0.154545i
$113$	16.5011	+	9.52694i	1.55230	+	0.896219i	0.997954	+	0.0639312i	$0.0203638\pi$
$113$	16.5011	+	9.52694i	1.55230	+	0.896219i	0.554343	+	0.832288i	$0.312970\pi$
$114$	10.5192	+	4.77708i	0.985210	+	0.447414i
$115$	1.23248	+	6.63396i	0.114929	+	0.618620i
$116$	−8.93530	−	9.85835i	−0.829622	−	0.915325i
$117$	−0.111866	+	6.18192i	−0.0103420	+	0.571519i
$118$	2.56163	−	0.988146i	0.235817	−	0.0909662i
$119$	−0.438797	−	0.760018i	−0.0402244	−	0.0696708i
$120$	5.19144	+	9.64619i	0.473911	+	0.880573i
$121$	−3.99086	+	6.91236i	−0.362805	+	0.628397i
$122$	2.32715	−	14.8508i	0.210690	−	1.34453i
$123$	−1.33240	+	4.79852i	−0.120139	+	0.432668i
$124$	11.7768	+	3.78379i	1.05758	+	0.339794i
$125$	−9.52528	+	5.85398i	−0.851967	+	0.523596i
$126$	−0.731931	−	2.00471i	−0.0652056	−	0.178594i
$127$			3.04051i			0.269802i	0.990859	+	0.134901i	$0.0430716\pi$
$127$			3.04051i			0.269802i	−0.990859	+	0.134901i	$0.956928\pi$
$128$	−11.3043	−	0.462210i	−0.999165	−	0.0408539i
$129$	−6.99080	−	7.11845i	−0.615505	−	0.626744i
$130$	3.09796	−	5.73401i	0.271709	−	0.502906i
$131$	7.80100	+	4.50391i	0.681576	+	0.393508i	0.800449	−	0.599401i	$-0.204595\pi$
$131$	7.80100	+	4.50391i	0.681576	+	0.393508i	−0.118872	+	0.992910i	$0.537928\pi$
$132$	−5.02837	−	3.30681i	−0.437663	−	0.287821i
$133$	1.18626	+	2.05467i	0.102862	+	0.178162i
$134$	7.30672	+	18.9416i	0.631204	+	1.63631i
$135$	11.5547	+	1.22065i	0.994466	+	0.105057i
$136$	−2.21856	+	4.40772i	−0.190240	+	0.377959i
$137$	−15.5954	+	9.00404i	−1.33241	+	0.769267i	−0.985668	−	0.168694i	$-0.946045\pi$
$137$	−15.5954	+	9.00404i	−1.33241	+	0.769267i	−0.346741	+	0.937961i	$0.612712\pi$
$138$	−6.01185	+	4.30021i	−0.511763	+	0.366058i
$139$	−8.82834	−	5.09704i	−0.748810	−	0.432325i	0.0764540	−	0.997073i	$-0.475640\pi$
$139$	−8.82834	−	5.09704i	−0.748810	−	0.432325i	−0.825264	+	0.564748i	$0.808974\pi$
$140$	−0.285347	+	2.23142i	−0.0241162	+	0.188590i
$141$	−4.68766	+	4.60360i	−0.394772	+	0.387693i
$142$	−12.4173	+	15.3857i	−1.04204	+	1.29114i
$143$			3.58058i			0.299423i
$144$	−7.16484	+	9.62627i	−0.597070	+	0.802189i
$145$	14.0245	+	4.95956i	1.16467	+	0.411869i
$146$	16.3598	+	13.2035i	1.35395	+	1.09273i
$147$	−3.12658	+	11.2601i	−0.257876	+	0.928715i
$148$	−0.113366	−	0.524864i	−0.00931864	−	0.0431436i
$149$	−13.7787	−	7.95513i	−1.12879	−	0.651709i	−0.185162	−	0.982708i	$-0.559281\pi$
$149$	−13.7787	−	7.95513i	−1.12879	−	0.651709i	−0.943631	+	0.330999i	$0.892614\pi$
$150$	−10.2277	−	6.73754i	−0.835087	−	0.550118i
$151$	−9.52878	−	16.5043i	−0.775441	−	1.34310i	−0.934546	−	0.355842i	$-0.884194\pi$
$151$	−9.52878	−	16.5043i	−0.775441	−	1.34310i	0.159105	−	0.987262i	$-0.449139\pi$
$152$	5.99776	−	11.9160i	0.486482	−	0.966516i
$153$	2.53451	+	4.57930i	0.204903	+	0.370214i
$154$	−0.444802	−	1.15309i	−0.0358432	−	0.0929183i
$155$	−13.5971	+	2.52610i	−1.09214	+	0.202901i
$156$	7.12738	+	0.414729i	0.570647	+	0.0332049i
$157$	9.28260	−	16.0779i	0.740832	−	1.28316i	−0.211285	−	0.977424i	$-0.567765\pi$
$157$	9.28260	−	16.0779i	0.740832	−	1.28316i	0.952117	−	0.305734i	$-0.0989018\pi$
$158$	19.0096	+	2.97884i	1.51233	+	0.236984i
$159$	−16.1443	+	4.16968i	−1.28032	+	0.330677i
$160$	11.3694	−	5.54401i	0.898832	−	0.438293i
$161$	−1.51791			−0.119628
$162$	4.14815	+	12.0330i	0.325910	+	0.945401i
$163$	5.53167			0.433273			0.216637	−	0.976252i	$-0.430491\pi$
$163$	5.53167			0.433273			0.216637	+	0.976252i	$0.430491\pi$
$164$	5.47485	+	1.75903i	0.427514	+	0.137357i
$165$	6.70308	+	0.585708i	0.521834	+	0.0455973i
$166$	11.5391	+	1.80819i	0.895605	+	0.140343i
$167$	−1.98143	−	1.14398i	−0.153328	−	0.0885239i	0.421373	−	0.906887i	$-0.361548\pi$
$167$	−1.98143	−	1.14398i	−0.153328	−	0.0885239i	−0.574701	+	0.818363i	$0.694882\pi$
$168$	−2.34681	+	0.751849i	−0.181061	+	0.0580064i
$169$	4.37619	+	7.57978i	0.336630	+	0.583060i
$170$	−0.155841	−	5.51482i	−0.0119524	−	0.422967i
$171$	−6.85192	−	12.3799i	−0.523979	−	0.946713i
$172$	−8.53613	+	7.73688i	−0.650874	+	0.589931i
$173$	6.78414	+	11.7505i	0.515789	+	0.893373i	0.999832	+	0.0183285i	$0.00583446\pi$
$173$	6.78414	+	11.7505i	0.515789	+	0.893373i	−0.484043	+	0.875044i	$0.660832\pi$
$174$	1.58328	+	16.2183i	0.120029	+	1.22951i
$175$	−0.903354	−	2.34729i	−0.0682871	−	0.177439i
$176$	−4.04767	+	5.64880i	−0.305105	+	0.425794i
$177$	−3.24008	−	0.899672i	−0.243540	−	0.0676235i
$178$	11.7927	−	14.6117i	0.883898	−	1.09520i
$179$			17.4696i			1.30574i	0.757471	+	0.652868i	$0.226435\pi$
$179$			17.4696i			1.30574i	−0.757471	+	0.652868i	$0.773565\pi$
$180$	1.94229	−	13.2751i	0.144770	−	0.989465i
$181$			2.03919i			0.151572i	0.997124	+	0.0757860i	$0.0241466\pi$
$181$			2.03919i			0.151572i	−0.997124	+	0.0757860i	$0.975853\pi$
$182$	1.14092	+	0.920803i	0.0845708	+	0.0682545i
$183$	−13.1354	+	12.8998i	−0.970996	+	0.953584i
$184$	4.68368	+	7.13503i	0.345285	+	0.526002i
$185$	0.390091	+	0.456341i	0.0286800	+	0.0335508i
$186$	−8.81377	−	12.3220i	−0.646257	−	0.903491i
$187$	1.51550	+	2.62492i	0.110824	+	0.191953i
$188$	5.09491	+	5.62124i	0.371585	+	0.409971i
$189$	−0.744764	+	2.50544i	−0.0541736	+	0.182244i
$190$	0.421307	+	14.9090i	0.0305648	+	1.08161i
$191$	8.28507	+	14.3502i	0.599487	+	1.03834i	0.992897	+	0.118978i	$0.0379618\pi$
$191$	8.28507	+	14.3502i	0.599487	+	1.03834i	−0.393410	+	0.919363i	$0.628705\pi$
$192$	10.7755	+	8.71144i	0.777653	+	0.628694i
$193$	7.22695	+	4.17248i	0.520207	+	0.300342i	0.737020	−	0.675871i	$-0.236233\pi$
$193$	7.22695	+	4.17248i	0.520207	+	0.300342i	−0.216812	+	0.976213i	$0.569566\pi$
$194$	0.812289	−	5.18367i	0.0583189	−	0.372166i
$195$	−7.23390	+	3.37418i	−0.518030	+	0.241630i
$196$	12.8471	+	4.12768i	0.917651	+	0.294835i
$197$	−2.07500			−0.147838			−0.0739190	−	0.997264i	$-0.523551\pi$
$197$	−2.07500			−0.147838			−0.0739190	+	0.997264i	$0.523551\pi$
$198$	2.52791	+	6.92379i	0.179651	+	0.492052i
$199$	−1.94866			−0.138137			−0.0690683	−	0.997612i	$-0.522003\pi$
$199$	−1.94866			−0.138137			−0.0690683	+	0.997612i	$0.522003\pi$
$200$	−8.24622	+	11.4891i	−0.583096	+	0.812403i
$201$	6.65251	−	23.9584i	0.469232	−	1.68989i
$202$	0.147992	−	0.944421i	0.0104127	−	0.0664492i
$203$	−1.67320	+	2.89807i	−0.117436	+	0.203405i
$204$	5.40060	−	2.71266i	0.378118	−	0.189924i
$205$	−6.32108	+	1.17435i	−0.441483	+	0.0820201i
$206$	15.9660	−	6.15888i	1.11241	−	0.429110i
$207$	9.05121	+	0.163788i	0.629102	+	0.0113840i
$208$	0.807853	−	8.20423i	0.0560145	−	0.568861i
$209$	−4.09706	−	7.09631i	−0.283399	−	0.490862i
$210$	1.91043	−	1.98526i	0.131833	−	0.136996i
$211$	22.4326	+	12.9514i	1.54432	+	0.891614i	0.998558	+	0.0536743i	$0.0170933\pi$
$211$	22.4326	+	12.9514i	1.54432	+	0.891614i	0.545763	+	0.837940i	$0.316240\pi$
$212$	4.06486	+	18.8195i	0.279176	+	1.29253i
$213$	23.4456	−	6.05544i	1.60647	−	0.414912i
$214$	−3.38975	+	4.20008i	−0.231719	+	0.287112i
$215$	4.29437	−	12.1435i	0.292874	−	0.828179i
$216$	14.0751	−	4.23001i	0.957686	−	0.287815i
$217$		−	3.11113i		−	0.211197i
$218$	7.51460	+	6.06480i	0.508953	+	0.410760i
$219$	−6.43883	−	24.9300i	−0.435096	−	1.68461i
$220$	0.985519	−	7.70678i	0.0664437	−	0.519591i
$221$	−3.11392	−	1.79783i	−0.209465	−	0.120935i
$222$	−0.271931	+	0.598794i	−0.0182508	+	0.0401885i
$223$	−23.0116	+	13.2858i	−1.54097	+	0.889681i	−0.542195	+	0.840253i	$0.682407\pi$
$223$	−23.0116	+	13.2858i	−1.54097	+	0.889681i	−0.998778	+	0.0494283i	$0.984260\pi$
$224$	0.759021	+	2.74244i	0.0507142	+	0.183237i
$225$	5.13337	+	14.0943i	0.342225	+	0.939618i
$226$	−25.1406	+	9.69797i	−1.67233	+	0.645100i
$227$	6.24360	+	10.8142i	0.414402	+	0.717766i	0.995365	−	0.0961642i	$-0.0306574\pi$
$227$	6.24360	+	10.8142i	0.414402	+	0.717766i	−0.580963	+	0.813930i	$0.697324\pi$
$228$	−14.6002	+	7.33351i	−0.966923	+	0.485674i
$229$	17.3208	+	10.0002i	1.14459	+	0.660831i	0.947564	−	0.319567i	$-0.103537\pi$
$229$	17.3208	+	10.0002i	1.14459	+	0.660831i	0.197029	+	0.980398i	$0.436871\pi$
$230$	−8.39541	−	4.53585i	−0.553577	−	0.299085i
$231$	−0.404977	+	1.45849i	−0.0266455	+	0.0959613i
$232$	18.7854	−	1.07732i	1.23332	−	0.0707298i
$233$		−	5.36527i		−	0.351491i	−0.984436	−	0.175745i	$-0.943766\pi$
$233$		−	5.36527i		−	0.351491i	0.984436	−	0.175745i	$-0.0562335\pi$
$234$	−6.70391	−	5.61381i	−0.438248	−	0.366986i
$235$	−7.99677	−	2.82794i	−0.521652	−	0.184475i
$236$	−1.18774	+	3.69676i	−0.0773153	+	0.240638i
$237$	−16.5123	−	16.8138i	−1.07259	−	1.09217i
$238$	1.22614	+	0.192138i	0.0794790	+	0.0124545i
$239$	4.10846	−	7.11607i	0.265754	−	0.460300i	−0.702007	−	0.712171i	$-0.747712\pi$
$239$	4.10846	−	7.11607i	0.265754	−	0.460300i	0.967761	+	0.251870i	$0.0810456\pi$
$240$	−15.2267	−	2.85439i	−0.982879	−	0.184250i
$241$	2.79374	+	4.83889i	0.179960	+	0.311700i	0.941867	−	0.335987i	$-0.109070\pi$
$241$	2.79374	+	4.83889i	0.179960	+	0.311700i	−0.761906	+	0.647687i	$0.775736\pi$
$242$	−4.06250	−	10.5315i	−0.261147	−	0.676987i
$243$	4.71134	−	14.8595i	0.302232	−	0.953234i
$244$	14.2766	+	15.7514i	0.913963	+	1.00838i
$245$	−14.8329	+	2.75569i	−0.947637	+	0.176055i
$246$	−4.09740	−	5.72831i	−0.261241	−	0.365224i
$247$	8.41832	+	4.86032i	0.535645	+	0.309255i
$248$	−14.6241	+	9.59973i	−0.928629	+	0.609583i
$249$	−10.0231	−	10.2062i	−0.635191	−	0.646789i
$250$	2.01787	−	15.6821i	0.127621	−	0.991823i
$251$		−	4.38308i		−	0.276658i	−0.990386	−	0.138329i	$-0.955827\pi$
$251$		−	4.38308i		−	0.276658i	0.990386	−	0.138329i	$-0.0441731\pi$
$252$	2.85630	+	0.975065i	0.179930	+	0.0614233i
$253$	5.24248			0.329592
$254$	−3.34611	−	2.70054i	−0.209954	−	0.169447i
$255$	−3.87502	+	5.53538i	−0.242663	+	0.346639i
$256$	10.5490	−	12.0299i	0.659311	−	0.751871i
$257$	−0.235944	−	0.136223i	−0.0147178	−	0.00849733i	0.492623	−	0.870243i	$-0.336038\pi$
$257$	−0.235944	−	0.136223i	−0.0147178	−	0.00849733i	−0.507341	+	0.861745i	$0.669371\pi$
$258$	14.0431	−	1.37093i	0.874283	−	0.0853504i
$259$	−0.116960	+	0.0675270i	−0.00726755	+	0.00419592i
$260$	3.55878	+	8.50221i	0.220706	+	0.527285i
$261$	10.2899	−	17.1005i	0.636931	−	1.05849i
$262$	−11.8853	+	4.58476i	−0.734279	+	0.283248i
$263$	−6.05619	+	3.49654i	−0.373441	+	0.215606i	−0.674961	−	0.737854i	$-0.735839\pi$
$263$	−6.05619	+	3.49654i	−0.373441	+	0.215606i	0.301520	+	0.953460i	$0.402506\pi$
$264$	8.10531	−	2.59670i	0.498847	−	0.159816i
$265$	−13.9871	−	16.3626i	−0.859221	−	1.00515i
$266$	−3.31481	−	0.519435i	−0.203244	−	0.0318486i
$267$	−22.2662	+	5.75082i	−1.36267	+	0.351944i
$268$	−27.3352	−	8.78259i	−1.66976	−	0.536482i
$269$		−	19.1427i		−	1.16715i	−0.812059	−	0.583576i	$-0.801653\pi$
$269$		−	19.1427i		−	1.16715i	0.812059	−	0.583576i	$-0.198347\pi$
$270$	−11.6060	+	11.6318i	−0.706321	+	0.707892i
$271$	−10.6402			−0.646345			−0.323172	−	0.946340i	$-0.604749\pi$
$271$	−10.6402			−0.646345			−0.323172	+	0.946340i	$0.604749\pi$
$272$	−2.88024	−	6.35643i	−0.174640	−	0.385415i
$273$	−0.449039	−	1.73860i	−0.0271771	−	0.105225i
$274$	3.94265	−	25.1602i	0.238184	−	1.51998i
$275$	3.11996	+	8.10698i	0.188141	+	0.488869i
$276$	0.607222	−	10.4355i	0.0365505	−	0.628143i
$277$	−0.767384	−	1.32915i	−0.0461076	−	0.0798607i	0.842051	−	0.539399i	$-0.181348\pi$
$277$	−0.767384	−	1.32915i	−0.0461076	−	0.0798607i	−0.888158	+	0.459538i	$0.848015\pi$
$278$	13.4506	−	5.18855i	0.806711	−	0.311188i
$279$	−0.335702	+	18.5515i	−0.0200979	+	1.11065i
$280$	−2.20226	−	2.29595i	−0.131610	−	0.137209i
$281$	5.97183	+	10.3435i	0.356249	+	0.617042i	0.987331	−	0.158675i	$-0.0507221\pi$
$281$	5.97183	+	10.3435i	0.356249	+	0.617042i	−0.631082	+	0.775716i	$0.717389\pi$
$282$	−0.902790	−	9.24768i	−0.0537603	−	0.550691i
$283$	−8.04280	+	13.9305i	−0.478095	+	0.828084i	−0.999685	−	0.0251120i	$-0.992006\pi$
$283$	−8.04280	+	13.9305i	−0.478095	+	0.828084i	0.521590	+	0.853196i	$0.325339\pi$
$284$	−5.90322	−	27.3308i	−0.350292	−	1.62179i
$285$	10.4759	−	14.9646i	0.620538	−	0.886426i
$286$	−3.94047	−	3.18023i	−0.233005	−	0.188051i
$287$		−	1.44632i		−	0.0853735i
$288$	−4.23008	−	16.4349i	−0.249260	−	0.968437i
$289$	13.9563			0.820956
$290$	−17.9144	+	11.0291i	−1.05197	+	0.647649i
$291$	−4.58489	+	4.50268i	−0.268771	+	0.263952i
$292$	−29.0612	+	6.27697i	−1.70068	+	0.367332i
$293$	10.2218	−	17.7047i	0.597165	−	1.03432i	−0.396072	−	0.918220i	$-0.629627\pi$
$293$	10.2218	−	17.7047i	0.597165	−	1.03432i	0.993237	−	0.116101i	$-0.0370398\pi$
$294$	−9.61484	−	13.4419i	−0.560749	−	0.783947i
$295$	−0.792950	−	4.26815i	−0.0461673	−	0.248502i
$296$	0.678309	+	0.341417i	0.0394259	+	0.0198445i
$297$	2.57223	−	8.65317i	0.149256	−	0.502108i
$298$	20.9928	−	8.09794i	1.21608	−	0.469101i
$299$	−5.38592	+	3.10956i	−0.311476	+	0.179831i
$300$	16.4988	−	5.27147i	0.952561	−	0.304349i
$301$	2.50938	+	1.44879i	0.144638	+	0.0835068i
$302$	26.6265	+	4.17242i	1.53219	+	0.240096i
$303$	−0.835329	+	0.820350i	−0.0479884	+	0.0471279i
$304$	7.78656	+	17.1842i	0.446590	+	0.985584i
$305$	−22.4079	−	7.92424i	−1.28307	−	0.453741i
$306$	−7.29069	−	1.27802i	−0.416781	−	0.0730593i
$307$	−16.0132			−0.913924			−0.456962	−	0.889486i	$-0.651062\pi$
$307$	−16.0132			−0.913924			−0.456962	+	0.889486i	$0.651062\pi$
$308$	1.66405	+	0.534647i	0.0948181	+	0.0304644i
$309$	−20.1947	−	5.60745i	−1.14884	−	0.318997i
$310$	9.29674	−	17.2074i	0.528019	−	0.977312i
$311$	−2.37874	+	4.12011i	−0.134886	+	0.233630i	−0.925554	−	0.378616i	$-0.876400\pi$
$311$	−2.37874	+	4.12011i	−0.134886	+	0.233630i	0.790668	+	0.612245i	$0.209734\pi$
$312$	−6.78686	+	7.47540i	−0.384230	+	0.423211i
$313$	16.3775	−	9.45556i	0.925711	−	0.534460i	0.0402587	−	0.999189i	$-0.487182\pi$
$313$	16.3775	−	9.45556i	0.925711	−	0.534460i	0.885453	+	0.464730i	$0.153848\pi$
$314$	9.44924	+	24.4958i	0.533251	+	1.38238i
$315$	−3.32823	+	0.556232i	−0.187525	+	0.0313401i
$316$	−20.1624	+	18.2745i	−1.13422	+	1.02802i
$317$	12.5942	+	21.8139i	0.707363	+	1.22519i	0.965832	+	0.259169i	$0.0834487\pi$
$317$	12.5942	+	21.8139i	0.707363	+	1.22519i	−0.258469	+	0.966020i	$0.583218\pi$
$318$	9.75037	−	21.4704i	0.546774	−	1.20400i
$319$	5.77883	−	10.0092i	0.323552	−	0.560409i
$320$	−3.99694	+	17.4363i	−0.223436	+	0.974719i
$321$	6.40032	−	1.65305i	0.357231	−	0.0922642i
$322$	1.34819	−	1.67047i	0.0751315	−	0.0930919i
$323$	8.22860			0.457852
$324$	−16.9268	−	6.12247i	−0.940376	−	0.340137i
$325$	−8.01396	−	6.47820i	−0.444535	−	0.359346i
$326$	−4.91316	+	6.08766i	−0.272115	+	0.337164i
$327$	−2.95756	−	11.4512i	−0.163553	−	0.633251i
$328$	−6.79852	+	4.46278i	−0.375385	+	0.246416i
$329$	0.954061	−	1.65248i	0.0525991	−	0.0911043i
$330$	−6.59817	+	6.85659i	−0.363217	+	0.377443i
$331$	−1.63622	+	0.944669i	−0.0899345	+	0.0519237i	−0.544293	−	0.838895i	$-0.683202\pi$
$331$	−1.63622	+	0.944669i	−0.0899345	+	0.0519237i	0.454358	+	0.890819i	$0.349869\pi$
$332$	−12.2388	+	11.0928i	−0.671690	+	0.608799i
$333$	0.704714	−	0.390039i	0.0386181	−	0.0213740i
$334$	3.01885	−	1.16452i	0.165184	−	0.0637196i
$335$	31.5603	−	5.86337i	1.72432	−	0.320350i
$336$	1.25699	−	3.25047i	0.0685746	−	0.177328i
$337$	29.7751	+	17.1906i	1.62195	+	0.936434i	0.986397	+	0.164378i	$0.0525617\pi$
$337$	29.7751	+	17.1906i	1.62195	+	0.936434i	0.635554	+	0.772056i	$0.280772\pi$
$338$	−12.2285	−	1.91623i	−0.665143	−	0.104229i
$339$	31.7992	+	8.82966i	1.72710	+	0.479561i
$340$	6.20753	+	4.72669i	0.336650	+	0.256341i
$341$			10.7451i			0.581878i
$342$	19.7100	+	3.45505i	1.06579	+	0.186827i
$343$		−	6.91506i		−	0.373378i
$344$	−0.932830	−	16.2659i	−0.0502948	−	0.876998i
$345$	4.94028	+	10.5915i	0.265976	+	0.570225i
$346$	−18.9571	−	2.97061i	−1.01914	−	0.159701i
$347$	−13.4247	+	23.2523i	−0.720678	+	1.24825i	0.240050	+	0.970761i	$0.422836\pi$
$347$	−13.4247	+	23.2523i	−0.720678	+	1.24825i	−0.960728	+	0.277491i	$0.910497\pi$
$348$	−19.2547	−	12.6625i	−1.03216	−	0.678780i
$349$	−1.24539	+	0.719029i	−0.0666644	+	0.0384887i	−0.532962	−	0.846139i	$-0.678921\pi$
$349$	−1.24539	+	0.719029i	−0.0666644	+	0.0384887i	0.466297	+	0.884628i	$0.345588\pi$
$350$	3.38557	+	1.09069i	0.180966	+	0.0582997i
$351$	2.49000	+	10.4157i	0.132906	+	0.555946i
$352$	−2.62147	−	9.47170i	−0.139725	−	0.504843i
$353$	23.5951	−	13.6227i	1.25584	−	0.725061i	0.283579	−	0.958949i	$-0.408478\pi$
$353$	23.5951	−	13.6227i	1.25584	−	0.725061i	0.972264	+	0.233888i	$0.0751447\pi$
$354$	3.86790	−	2.76667i	0.205577	−	0.147047i
$355$	20.3129	+	23.7627i	1.07810	+	1.26119i
$356$	5.60625	+	25.9559i	0.297131	+	1.37566i
$357$	−1.06506	−	1.08451i	−0.0563690	−	0.0573982i
$358$	−19.2254	−	15.5163i	−1.01610	−	0.820059i
$359$	−4.01647			−0.211981			−0.105991	−	0.994367i	$-0.533801\pi$
$359$	−4.01647			−0.211981			−0.105991	+	0.994367i	$0.533801\pi$
$360$	12.8842	+	13.9283i	0.679059	+	0.734084i
$361$	−3.24556			−0.170819
$362$	−2.24415	−	1.81119i	−0.117950	−	0.0951939i
$363$	−3.69876	+	13.3207i	−0.194135	+	0.699158i
$364$	−2.02671	+	0.437751i	−0.106228	+	0.0229444i
$365$	25.2671	−	21.5989i	1.32254	−	1.13054i
$366$	−2.52973	−	25.9131i	−0.132231	−	1.35450i
$367$	24.2221	−	13.9846i	1.26438	−	0.729992i	0.290464	−	0.956886i	$-0.406190\pi$
$367$	24.2221	−	13.9846i	1.26438	−	0.729992i	0.973920	+	0.226893i	$0.0728569\pi$
$368$	−12.0122	−	1.18281i	−0.626177	−	0.0616583i
$369$	−0.156063	+	8.62432i	−0.00812432	+	0.448964i
$370$	−0.848681	+	0.0239825i	−0.0441209	+	0.00124679i
$371$	4.19373	−	2.42125i	0.217727	−	0.125705i
$372$	21.3887	+	1.24457i	1.10895	+	0.0645280i
$373$	−6.59924	+	11.4302i	−0.341696	+	0.591835i	−0.984748	−	0.173988i	$-0.944335\pi$
$373$	−6.59924	+	11.4302i	−0.341696	+	0.591835i	0.643052	+	0.765823i	$0.277668\pi$
$374$	−4.23479	−	0.663599i	−0.218976	−	0.0343139i
$375$	−13.4385	+	13.9430i	−0.693963	+	0.720011i
$376$	−10.7115	+	0.614290i	−0.552402	+	0.0316796i
$377$			13.7108i			0.706142i
$378$	−2.09577	−	3.04492i	−0.107795	−	0.156614i
$379$		−	21.8404i		−	1.12187i	−0.827861	−	0.560933i	$-0.810443\pi$
$379$		−	21.8404i		−	1.12187i	0.827861	−	0.560933i	$-0.189557\pi$
$380$	−16.7817	−	12.7783i	−0.860883	−	0.655514i
$381$	1.31695	+	5.09900i	0.0674693	+	0.261229i
$382$	−23.1512	−	3.62783i	−1.18452	−	0.185616i
$383$	−29.9233	−	17.2762i	−1.52901	−	0.882775i	−0.999404	−	0.0345315i	$-0.989006\pi$
$383$	−29.9233	−	17.2762i	−1.52901	−	0.882775i	−0.529607	−	0.848243i	$-0.677661\pi$
$384$	−19.1577	+	4.12112i	−0.977636	+	0.210305i
$385$	−1.92126	+	0.356937i	−0.0979164	+	0.0181912i
$386$	−11.0108	+	4.24739i	−0.560432	+	0.216186i
$387$	−14.8069	−	8.90982i	−0.752679	−	0.452912i
$388$	4.98321	+	5.49800i	0.252984	+	0.279119i
$389$	15.2716	−	8.81709i	0.774303	−	0.447044i	−0.0601045	−	0.998192i	$-0.519143\pi$
$389$	15.2716	−	8.81709i	0.774303	−	0.447044i	0.834407	+	0.551148i	$0.185810\pi$
$390$	2.71174	−	10.9579i	0.137314	−	0.554874i
$391$	−2.63227	+	4.55923i	−0.133120	+	0.230570i
$392$	−15.9532	+	10.4722i	−0.805759	+	0.528927i
$393$	15.0332	+	4.17427i	0.758326	+	0.210564i
$394$	1.84299	−	2.28356i	0.0928487	−	0.115044i
$395$	10.1433	−	28.6830i	0.510366	−	1.44320i
$396$	−9.86496	−	3.36763i	−0.495733	−	0.169230i
$397$	2.85912			0.143495			0.0717475	−	0.997423i	$-0.477142\pi$
$397$	2.85912			0.143495			0.0717475	+	0.997423i	$0.477142\pi$
$398$	1.73077	−	2.14452i	0.0867558	−	0.107495i
$399$	2.87933	+	2.93191i	0.144147	+	0.146779i
$400$	−5.31970	−	19.2795i	−0.265985	−	0.963977i
$401$	−10.5817	+	18.3281i	−0.528427	+	0.915262i	0.471024	+	0.882120i	$0.343885\pi$
$401$	−10.5817	+	18.3281i	−0.528427	+	0.915262i	−0.999451	+	0.0331417i	$0.989449\pi$
$402$	20.4578	+	28.6007i	1.02034	+	1.42647i
$403$	−6.37341	−	11.0391i	−0.317482	−	0.549895i
$404$	0.907900	+	1.00169i	0.0451697	+	0.0498359i
$405$	19.9061	−	2.95765i	0.989141	−	0.146967i
$406$	−1.70324	−	4.41541i	−0.0845304	−	0.219133i
$407$	0.403951	−	0.233221i	0.0200231	−	0.0115604i
$408$	−1.81144	+	8.35276i	−0.0896796	+	0.413523i
$409$	−7.26975	+	12.5916i	−0.359466	+	0.622614i	−0.987872	−	0.155272i	$-0.950375\pi$
$409$	−7.26975	+	12.5916i	−0.359466	+	0.622614i	0.628406	+	0.777886i	$0.283708\pi$
$410$	4.32192	−	7.99946i	0.213445	−	0.395065i
$411$	−22.2539	+	21.8549i	−1.09770	+	1.07802i
$412$	−7.40291	+	23.0410i	−0.364715	+	1.13515i
$413$	0.976591			0.0480549
$414$	−8.21942	+	9.81547i	−0.403962	+	0.482404i
$415$	6.15711	−	17.4109i	0.302241	−	0.854666i
$416$	8.31131	+	8.17594i	0.407496	+	0.400859i
$417$	−17.0130	−	4.72399i	−0.833130	−	0.231335i
$418$	11.4485	+	1.79400i	0.559965	+	0.0877475i
$419$	21.5050	+	12.4159i	1.05059	+	0.606558i	0.922814	−	0.385245i	$-0.125883\pi$
$419$	21.5050	+	12.4159i	1.05059	+	0.606558i	0.127775	+	0.991803i	$0.459216\pi$
$420$	0.487972	+	3.86573i	0.0238106	+	0.188628i
$421$	−6.27837	+	3.62482i	−0.305989	+	0.176663i	−0.645130	−	0.764073i	$-0.723197\pi$
$421$	−6.27837	+	3.62482i	−0.305989	+	0.176663i	0.339141	+	0.940735i	$0.389864\pi$
$422$	−34.1775	+	13.1840i	−1.66374	+	0.641785i
$423$	−5.86732	+	9.75072i	−0.285279	+	0.474096i
$424$	−24.3215	−	12.2419i	−1.18115	−	0.594518i
$425$	−8.61694	−	1.35721i	−0.417983	−	0.0658344i
$426$	−14.1600	+	31.1805i	−0.686056	+	1.51070i
$427$	2.67339	−	4.63045i	0.129375	−	0.224083i
$428$	−1.61150	−	7.46092i	−0.0778946	−	0.360637i
$429$	1.55087	+	6.00470i	0.0748768	+	0.289910i
$430$	9.54982	+	15.5117i	0.460533	+	0.748040i
$431$	17.9970			0.866883			0.433441	−	0.901182i	$-0.357299\pi$
$431$	17.9970			0.866883			0.433441	+	0.901182i	$0.357299\pi$
$432$	−7.84612	+	19.2468i	−0.377497	+	0.926011i
$433$			20.0151i			0.961864i	0.876758	+	0.480932i	$0.159702\pi$
$433$			20.0151i			0.961864i	−0.876758	+	0.480932i	$0.840298\pi$
$434$	3.42383	+	2.76326i	0.164349	+	0.132641i
$435$	25.6675	+	2.24280i	1.23066	+	0.107534i
$436$	−13.3487	+	2.88321i	−0.639289	+	0.138081i
$437$	7.11620	−	12.3256i	0.340414	−	0.589614i
$438$	33.1546	+	15.0565i	1.58419	+	0.719429i
$439$	3.14969	+	5.45542i	0.150326	+	0.260373i	0.931347	−	0.364132i	$-0.118634\pi$
$439$	3.14969	+	5.45542i	0.150326	+	0.260373i	−0.781021	+	0.624505i	$0.785301\pi$
$440$	7.60607	+	7.92964i	0.362605	+	0.378031i
$441$	−0.366213	+	20.2376i	−0.0174387	+	0.963695i
$442$	4.74427	−	1.83010i	0.225662	−	0.0870490i
$443$	−10.7427	−	18.6069i	−0.510402	−	0.884041i	−0.999927	−	0.0120526i	$-0.996163\pi$
$443$	−10.7427	−	18.6069i	−0.510402	−	0.884041i	0.489526	−	0.871989i	$-0.337170\pi$
$444$	−0.417454	−	0.831105i	−0.0198115	−	0.0394425i
$445$	−19.2910	−	22.5673i	−0.914481	−	1.06979i
$446$	5.81751	−	37.1248i	0.275467	−	1.75791i
$447$	−26.5528	−	7.37289i	−1.25590	−	0.348726i
$448$	−3.69223	−	1.60049i	−0.174442	−	0.0756160i
$449$	11.5159			0.543470			0.271735	−	0.962372i	$-0.412403\pi$
$449$	11.5159			0.543470			0.271735	+	0.962372i	$0.412403\pi$
$450$	−20.0703	−	6.86903i	−0.946122	−	0.323809i
$451$			4.99523i			0.235216i
$452$	11.6569	−	36.2811i	0.548293	−	1.70652i
$453$	−23.1285	−	23.5509i	−1.08667	−	1.10652i
$454$	−17.4467	−	2.73392i	−0.818812	−	0.128309i
$455$	1.76211	−	1.50629i	0.0826091	−	0.0706161i
$456$	4.89712	−	22.5812i	0.229329	−	1.05746i
$457$	6.86274	−	3.96220i	0.321025	−	0.185344i	−0.330824	−	0.943692i	$-0.607327\pi$
$457$	6.86274	−	3.96220i	0.321025	−	0.185344i	0.651850	+	0.758348i	$0.273993\pi$
$458$	−26.3894	+	10.1797i	−1.23310	+	0.475667i
$459$	6.23388	+	6.58179i	0.290973	+	0.307212i
$460$	12.4485	−	5.21055i	0.580412	−	0.242943i
$461$	26.0633	−	15.0477i	1.21389	−	0.700840i	0.250285	−	0.968172i	$-0.419476\pi$
$461$	26.0633	−	15.0477i	1.21389	−	0.700840i	0.963604	+	0.267333i	$0.0861422\pi$
$462$	−1.24538	−	1.74109i	−0.0579404	−	0.0810028i
$463$	13.7372	+	7.93120i	0.638424	+	0.368594i	0.784007	−	0.620752i	$-0.213173\pi$
$463$	13.7372	+	7.93120i	0.638424	+	0.368594i	−0.145583	+	0.989346i	$0.546506\pi$
$464$	−15.4994	+	21.6304i	−0.719541	+	1.00417i
$465$	−21.7084	+	10.1257i	−1.00670	+	0.469567i
$466$	5.90454	+	4.76537i	0.273522	+	0.220751i
$467$	30.3428			1.40410			0.702048	−	0.712130i	$-0.252269\pi$
$467$	30.3428			1.40410			0.702048	+	0.712130i	$0.252269\pi$
$468$	12.1324	−	2.39160i	0.560820	−	0.110552i
$469$			7.22128i			0.333448i
$470$	10.2148	−	6.28878i	0.471174	−	0.290080i
$471$	8.60320	−	30.9836i	0.396415	−	1.42765i
$472$	−3.01338	−	4.59053i	−0.138702	−	0.211296i
$473$	−8.66676	−	5.00376i	−0.398498	−	0.230073i
$474$	33.1698	−	3.23814i	1.52354	−	0.148733i
$475$	23.2954	+	3.66914i	1.06887	+	0.168352i
$476$	−1.30049	+	1.17873i	−0.0596080	+	0.0540268i
$477$	−25.2682	+	13.9853i	−1.15695	+	0.640341i
$478$	4.18222	+	10.8418i	0.191290	+	0.495893i
$479$	−9.13692	−	15.8256i	−0.417477	−	0.723091i	0.578208	−	0.815889i	$-0.303752\pi$
$479$	−9.13692	−	15.8256i	−0.417477	−	0.723091i	−0.995685	+	0.0927984i	$0.970419\pi$
$480$	16.6655	−	14.2219i	0.760670	−	0.649138i
$481$	−0.276669	+	0.479206i	−0.0126150	+	0.0218499i
$482$	−7.80661	−	1.22331i	−0.355581	−	0.0557202i
$483$	−2.54556	+	0.657457i	−0.115827	+	0.0299154i
$484$	15.1982	+	4.88308i	0.690829	+	0.221958i
$485$	−7.82145	−	2.76594i	−0.355154	−	0.125595i
$486$	12.1684	+	18.3829i	0.551971	+	0.833863i
$487$			26.6684i			1.20846i	0.796810	+	0.604230i	$0.206519\pi$
$487$			26.6684i			1.20846i	−0.796810	+	0.604230i	$0.793481\pi$
$488$	−30.0148	+	1.72132i	−1.35871	+	0.0779203i
$489$	9.27671	−	2.39595i	0.419507	−	0.108349i
$490$	10.1417	−	18.7713i	0.458155	−	0.848001i
$491$	−28.5106	−	16.4606i	−1.28667	−	0.742858i	−0.308609	−	0.951189i	$-0.599863\pi$
$491$	−28.5106	−	16.4606i	−1.28667	−	0.742858i	−0.978058	+	0.208332i	$0.933197\pi$
$492$	9.94332	+	0.578583i	0.448279	+	0.0260845i
$493$	5.80315	+	10.0514i	0.261361	+	0.452690i
$494$	−12.8259	+	4.94757i	−0.577063	+	0.222602i
$495$	11.4949	−	1.92109i	0.516657	−	0.0863464i
$496$	2.42431	−	24.6203i	0.108855	−	1.10548i
$497$	−6.09037	+	3.51627i	−0.273190	+	0.157726i
$498$	20.1344	−	1.96559i	0.902245	−	0.0880802i
$499$	−9.66780	−	5.58171i	−0.432790	−	0.249872i	0.267744	−	0.963490i	$-0.413722\pi$
$499$	−9.66780	−	5.58171i	−0.432790	−	0.249872i	−0.700535	+	0.713618i	$0.747055\pi$
$500$	15.4661	+	16.1493i	0.691663	+	0.722220i
$501$	−3.81840	−	1.06025i	−0.170593	−	0.0473686i
$502$	4.82363	+	3.89300i	0.215289	+	0.173753i
$503$		−	4.26695i		−	0.190254i	−0.995465	−	0.0951269i	$-0.969674\pi$
$503$		−	4.26695i		−	0.190254i	0.995465	−	0.0951269i	$-0.0303257\pi$
$504$	−3.61000	+	2.27735i	−0.160802	+	0.101441i
$505$	−1.42500	−	0.503932i	−0.0634118	−	0.0224247i
$506$	−4.65631	+	5.76940i	−0.206998	+	0.256481i
$507$	10.6220	+	10.8160i	0.471740	+	0.480354i
$508$	5.94395	−	1.28384i	0.263720	−	0.0569613i
$509$	−17.0145	−	9.82330i	−0.754152	−	0.435410i	0.0730399	−	0.997329i	$-0.476730\pi$
$509$	−17.0145	−	9.82330i	−0.754152	−	0.435410i	−0.827192	+	0.561919i	$0.810063\pi$
$510$	−2.65000	−	9.18095i	−0.117344	−	0.406539i
$511$	3.73890	+	6.47596i	0.165399	+	0.286480i
$512$	3.86960	+	22.2941i	0.171014	+	0.985269i
$513$	−16.8529	−	17.7935i	−0.744075	−	0.785602i
$514$	0.359477	−	0.138668i	0.0158559	−	0.00611639i
$515$	−4.94227	−	26.6024i	−0.217783	−	1.17224i
$516$	−10.9641	+	16.6722i	−0.482670	+	0.733952i
$517$	−3.29509	+	5.70726i	−0.144918	+	0.251005i
$518$	0.0295684	−	0.188692i	0.00129916	−	0.00829067i
$519$	16.4667	+	16.7673i	0.722807	+	0.736005i
$520$	−12.5176	−	3.63509i	−0.548935	−	0.159409i
$521$	−1.83732			−0.0804943			−0.0402472	−	0.999190i	$-0.512815\pi$
$521$	−1.83732			−0.0804943			−0.0402472	+	0.999190i	$0.512815\pi$
$522$	9.67990	+	26.5126i	0.423678	+	1.16043i
$523$	−0.387484			−0.0169435			−0.00847175	−	0.999964i	$-0.502697\pi$
$523$	−0.387484			−0.0169435			−0.00847175	+	0.999964i	$0.502697\pi$
$524$	5.51084	−	17.1521i	0.240742	−	0.749292i
$525$	−2.53163	−	3.54519i	−0.110490	−	0.154725i
$526$	1.53105	−	9.77049i	0.0667570	−	0.426014i
$527$	−9.34466	−	5.39514i	−0.407060	−	0.235016i
$528$	−4.34134	+	11.2263i	−0.188933	+	0.488564i
$529$	−6.94716	−	12.0328i	−0.302050	−	0.523166i
$530$	30.4304	−	0.859919i	1.32181	−	0.0373525i
$531$	−5.82336	−	0.105378i	−0.252712	−	0.00457300i
$532$	3.51581	−	3.18662i	0.152430	−	0.138158i
$533$	−2.96291	−	5.13190i	−0.128338	−	0.222287i
$534$	13.4477	−	29.6120i	0.581939	−	1.28143i
$535$	5.54512	+	6.48686i	0.239736	+	0.280452i
$536$	33.9441	−	22.2821i	1.46616	−	0.962438i
$537$	7.56666	+	29.2968i	0.326526	+	1.26425i
$538$	21.0668	+	17.0023i	0.908252	+	0.733022i
$539$			11.7217i			0.504887i
$540$	−2.49263	−	23.1038i	−0.107266	−	0.994230i
$541$		−	10.1969i		−	0.438399i	−0.975680	−	0.219199i	$-0.929655\pi$
$541$		−	10.1969i		−	0.438399i	0.975680	−	0.219199i	$-0.0703445\pi$
$542$	9.45047	−	11.7096i	0.405932	−	0.502971i
$543$	0.883244	+	3.41977i	0.0379036	+	0.146756i
$544$	9.55351	+	2.47597i	0.409603	+	0.106156i
$545$	11.6060	−	9.92108i	0.497147	−	0.424972i
$546$	2.31218	+	1.05003i	0.0989522	+	0.0449373i
$547$	5.88185	+	10.1877i	0.251490	+	0.435593i	0.963936	−	0.266133i	$-0.0857461\pi$
$547$	5.88185	+	10.1877i	0.251490	+	0.435593i	−0.712446	+	0.701727i	$0.752413\pi$
$548$	24.1873	+	26.6859i	1.03323	+	1.13997i
$549$	−16.4410	+	27.3227i	−0.701683	+	1.16610i
$550$	−11.6929	−	3.76697i	−0.498588	−	0.160624i
$551$	−15.6885	−	27.1733i	−0.668352	−	1.15762i
$552$	10.9450	+	9.93693i	0.465852	+	0.422944i
$553$	5.92716	+	3.42205i	0.252048	+	0.145520i
$554$	2.14432	+	0.336019i	0.0911035	+	0.0142761i
$555$	0.851846	+	0.596331i	0.0361589	+	0.0253128i
$556$	−6.23658	+	19.4109i	−0.264490	+	0.823205i
$557$	0.900940			0.0381741			0.0190870	−	0.999818i	$-0.493924\pi$
$557$	0.900940			0.0381741			0.0190870	+	0.999818i	$0.493924\pi$
$558$	−20.1179	−	16.8466i	−0.851660	−	0.713175i
$559$	11.8719			0.502126
$560$	4.48274	−	0.384379i	0.189430	−	0.0162430i
$561$	3.67846	+	3.74562i	0.155305	+	0.158140i
$562$	−16.6872	−	2.61492i	−0.703909	−	0.110304i
$563$	−0.0255347	+	0.0442275i	−0.00107616	+	0.00186397i	−0.866563	−	0.499068i	$-0.833676\pi$
$563$	−0.0255347	+	0.0442275i	−0.00107616	+	0.00186397i	0.865487	+	0.500932i	$0.167009\pi$
$564$	10.9790	+	7.22015i	0.462300	+	0.304023i
$565$	7.78226	+	41.8890i	0.327402	+	1.76228i
$566$	−8.18718	−	21.2241i	−0.344133	−	0.892116i
$567$	−0.163793	+	4.52426i	−0.00687865	+	0.190001i
$568$	35.3210	+	17.7783i	1.48204	+	0.745962i
$569$	9.22321	+	15.9751i	0.386657	+	0.669709i	0.991998	−	0.126257i	$-0.0402964\pi$
$569$	9.22321	+	15.9751i	0.386657	+	0.669709i	−0.605341	+	0.795967i	$0.706963\pi$
$570$	7.16413	+	24.8202i	0.300072	+	1.03960i
$571$	−21.7726	−	12.5704i	−0.911155	−	0.526055i	−0.0303522	−	0.999539i	$-0.509663\pi$
$571$	−21.7726	−	12.5704i	−0.911155	−	0.526055i	−0.880802	+	0.473484i	$0.842996\pi$
$572$	6.99975	−	1.51189i	0.292674	−	0.0632151i
$573$	20.1098	+	20.4770i	0.840097	+	0.855437i
$574$	1.59169	+	1.28460i	0.0664358	+	0.0536182i
$575$	−9.48501	+	11.7336i	−0.395552	+	0.489324i
$576$	21.8439	+	9.94204i	0.910162	+	0.414251i
$577$			8.02957i			0.334275i	0.985934	+	0.167138i	$0.0534525\pi$
$577$			8.02957i			0.334275i	−0.985934	+	0.167138i	$0.946548\pi$
$578$	−12.3958	+	15.3590i	−0.515596	+	0.638850i
$579$	13.9270	+	3.86710i	0.578786	+	0.160711i
$580$	3.77376	−	29.5109i	0.156697	−	1.22537i
$581$	3.59785	+	2.07722i	0.149264	+	0.0861776i
$582$	−0.882997	−	9.04494i	−0.0366014	−	0.374925i
$583$	−14.4841	+	8.36240i	−0.599870	+	0.346335i
$584$	18.9039	−	37.5573i	0.782249	−	1.55413i
$585$	−10.6699	+	8.79181i	−0.441147	+	0.363497i
$586$	10.4053	+	26.9743i	0.429840	+	1.11430i
$587$	−0.302735	−	0.524352i	−0.0124952	−	0.0216423i	0.859710	−	0.510782i	$-0.170644\pi$
$587$	−0.302735	−	0.524352i	−0.0124952	−	0.0216423i	−0.872205	+	0.489140i	$0.837311\pi$
$588$	23.3327	+	1.35769i	0.962225	+	0.0559900i
$589$	25.2628	+	14.5855i	1.04093	+	0.600983i
$590$	5.40144	+	2.91827i	0.222374	+	0.120143i
$591$	−3.47982	+	0.898755i	−0.143141	+	0.0369698i
$592$	−0.978198	+	0.443243i	−0.0402037	+	0.0182172i
$593$		−	35.0785i		−	1.44050i	−0.693714	−	0.720251i	$-0.744027\pi$
$593$		−	35.0785i		−	1.44050i	0.693714	−	0.720251i	$-0.255973\pi$
$594$	7.23828	+	10.5164i	0.296990	+	0.431493i
$595$	0.654255	−	1.85008i	0.0268218	−	0.0758460i
$596$	−9.73364	+	30.2952i	−0.398705	+	1.24094i
$597$	−3.26794	+	0.844030i	−0.133748	+	0.0345438i
$598$	1.36160	−	8.68914i	0.0556801	−	0.355325i
$599$	−13.4116	+	23.2297i	−0.547985	+	0.949138i	0.450427	+	0.892813i	$0.351272\pi$
$599$	−13.4116	+	23.2297i	−0.547985	+	0.949138i	−0.998412	+	0.0563249i	$0.982062\pi$
$600$	−8.85275	+	22.8392i	−0.361412	+	0.932406i
$601$	−11.8445	−	20.5153i	−0.483147	−	0.836835i	0.516666	−	0.856187i	$-0.327173\pi$
$601$	−11.8445	−	20.5153i	−0.483147	−	0.836835i	−0.999813	+	0.0193524i	$0.993840\pi$
$602$	−3.82320	+	1.47480i	−0.155822	+	0.0601083i
$603$	0.779202	−	43.0601i	0.0317316	−	1.75354i
$604$	−28.2412	+	25.5969i	−1.14912	+	1.04152i
$605$	−17.5474	+	3.26000i	−0.713403	+	0.132538i
$606$	−0.160875	−	1.64791i	−0.00653509	−	0.0669419i
$607$	11.6807	+	6.74385i	0.474104	+	0.273724i	0.717956	−	0.696088i	$-0.245078\pi$
$607$	11.6807	+	6.74385i	0.474104	+	0.273724i	−0.243852	+	0.969812i	$0.578411\pi$
$608$	−25.8274	−	6.69364i	−1.04744	−	0.271463i
$609$	−1.55074	+	5.58484i	−0.0628392	+	0.226309i
$610$	28.6231	−	17.6219i	1.15892	−	0.713491i
$611$		−	7.81790i		−	0.316278i
$612$	7.88197	−	6.88836i	0.318610	−	0.278445i
$613$	7.59381			0.306711			0.153356	−	0.988171i	$-0.450992\pi$
$613$	7.59381			0.306711			0.153356	+	0.988171i	$0.450992\pi$
$614$	14.2228	−	17.6227i	0.573984	−	0.711195i
$615$	−10.0919	+	4.70728i	−0.406946	+	0.189816i
$616$	−2.06637	+	1.35644i	−0.0832566	+	0.0546524i
$617$	−11.6982	−	6.75399i	−0.470954	−	0.271905i	0.245685	−	0.969350i	$-0.420987\pi$
$617$	−11.6982	−	6.75399i	−0.470954	−	0.271905i	−0.716639	+	0.697444i	$0.754320\pi$
$618$	24.1077	−	17.2440i	0.969755	−	0.693655i
$619$	−38.8056	+	22.4044i	−1.55973	+	0.900510i	−0.562447	+	0.826833i	$0.690140\pi$
$619$	−38.8056	+	22.4044i	−1.55973	+	0.900510i	−0.997282	+	0.0736773i	$0.976527\pi$
$620$	10.6796	+	25.5145i	0.428904	+	1.02469i
$621$	15.2500	−	3.64571i	0.611961	−	0.146297i
$622$	−2.42145	−	6.27726i	−0.0970912	−	0.251695i
$623$	5.78398	−	3.33938i	0.231730	−	0.133790i
$624$	−2.19874	−	14.1086i	−0.0880202	−	0.564795i
$625$	−23.7896	−	7.68461i	−0.951585	−	0.307384i
$626$	−4.14036	+	26.4219i	−0.165482	+	1.05603i
$627$	−9.94450	−	10.1261i	−0.397145	−	0.404397i
$628$	−35.3506	−	11.3579i	−1.41064	−	0.453229i
$629$			0.468406i			0.0186766i
$630$	2.34395	−	4.15679i	0.0933854	−	0.165610i
$631$	4.17763			0.166309			0.0831543	−	0.996537i	$-0.473501\pi$
$631$	4.17763			0.166309			0.0831543	+	0.996537i	$0.473501\pi$
$632$	−2.20335	−	38.4201i	−0.0876446	−	1.52827i
$633$	43.2296	+	12.0035i	1.71822	+	0.477097i
$634$	−35.1924	−	5.51471i	−1.39767	−	0.219017i
$635$	−5.16794	+	4.41768i	−0.205084	+	0.175310i
$636$	14.9682	+	29.8001i	0.593529	+	1.18165i
$637$	−6.95267	−	12.0424i	−0.275475	−	0.477136i
$638$	5.88257	+	15.2497i	0.232893	+	0.603743i
$639$	36.6960	−	20.3102i	1.45167	−	0.803459i
$640$	−15.6388	−	19.8854i	−0.618178	−	0.786038i
$641$	−19.5410	−	33.8460i	−0.771824	−	1.33684i	−0.936562	−	0.350501i	$-0.886011\pi$
$641$	−19.5410	−	33.8460i	−0.771824	−	1.33684i	0.164738	−	0.986337i	$-0.447322\pi$
$642$	−3.86549	+	8.51184i	−0.152559	+	0.335935i
$643$	−5.11302	+	8.85601i	−0.201638	+	0.349247i	−0.949056	−	0.315107i	$-0.897960\pi$
$643$	−5.11302	+	8.85601i	−0.201638	+	0.349247i	0.747419	+	0.664353i	$0.231293\pi$
$644$	0.640931	+	2.96739i	0.0252562	+	0.116931i
$645$	1.94199	−	22.2249i	0.0764658	−	0.875105i
$646$	−7.30854	+	9.05566i	−0.287551	+	0.356290i
$647$			23.8427i			0.937353i	0.883370	+	0.468676i	$0.155269\pi$
$647$			23.8427i			0.937353i	−0.883370	+	0.468676i	$0.844731\pi$
$648$	21.7720	−	13.1902i	0.855284	−	0.518159i
$649$	−3.37290			−0.132398
$650$	14.2472	−	3.06559i	0.558822	−	0.120242i
$651$	−1.34753	−	5.21742i	−0.0528140	−	0.204487i
$652$	−2.33572	−	10.8140i	−0.0914740	−	0.423507i
$653$	−7.25898	+	12.5729i	−0.284066	+	0.492017i	−0.972382	−	0.233394i	$-0.925017\pi$
$653$	−7.25898	+	12.5729i	−0.284066	+	0.492017i	0.688316	+	0.725411i	$0.258350\pi$
$654$	15.2290	+	6.91596i	0.595501	+	0.270435i
$655$	3.67910	+	19.8032i	0.143754	+	0.773776i
$656$	1.12703	−	11.4456i	0.0440030	−	0.446877i
$657$	−21.5961	−	39.0193i	−0.842543	−	1.52229i
$658$	0.971188	+	2.51767i	0.0378609	+	0.0981489i
$659$	−12.5315	+	7.23505i	−0.488157	+	0.281837i	−0.723809	−	0.690000i	$-0.757611\pi$
$659$	−12.5315	+	7.23505i	−0.488157	+	0.281837i	0.235653	+	0.971837i	$0.424277\pi$
$660$	−1.68534	−	13.3513i	−0.0656016	−	0.519698i
$661$	−7.14171	−	4.12327i	−0.277780	−	0.160377i	0.354638	−	0.935004i	$-0.384604\pi$
$661$	−7.14171	−	4.12327i	−0.277780	−	0.160377i	−0.632418	+	0.774627i	$0.717938\pi$
$662$	0.413648	−	2.63972i	0.0160769	−	0.102595i
$663$	−6.00081	−	1.66624i	−0.233052	−	0.0647115i
$664$	−1.33746	−	23.3214i	−0.0519034	−	0.905047i
$665$	−1.76874	+	5.00159i	−0.0685889	+	0.193953i
$666$	−0.196675	+	1.12197i	−0.00762102	+	0.0434756i
$667$	20.0746			0.777290
$668$	−1.39974	+	4.35658i	−0.0541575	+	0.168561i
$669$	−32.8364	+	32.2476i	−1.26953	+	1.24676i
$670$	−21.5788	+	39.9402i	−0.833661	+	1.54303i
$671$	−9.23324	+	15.9924i	−0.356445	+	0.617381i
$672$	2.46074	+	4.27036i	0.0949249	+	0.164733i
$673$	−8.28497	+	4.78333i	−0.319362	+	0.184384i	−0.651108	−	0.758985i	$-0.725696\pi$
$673$	−8.28497	+	4.78333i	−0.319362	+	0.184384i	0.331746	+	0.943369i	$0.392362\pi$
$674$	−45.3643	+	17.4993i	−1.74737	+	0.674046i
$675$	14.7135	+	21.4129i	0.566322	+	0.824184i
$676$	12.9700	−	11.7556i	0.498847	−	0.452139i
$677$	16.5451	+	28.6570i	0.635881	+	1.10138i	0.986328	+	0.164795i	$0.0526963\pi$
$677$	16.5451	+	28.6570i	0.635881	+	1.10138i	−0.350447	+	0.936583i	$0.613970\pi$
$678$	−37.9608	+	27.1529i	−1.45788	+	1.04280i
$679$	0.933144	−	1.61625i	0.0358108	−	0.0620261i
$680$	−10.7152	+	2.63326i	−0.410910	+	0.100981i
$681$	15.1546	+	15.4314i	0.580727	+	0.591331i
$682$	−11.8251	−	9.54363i	−0.452805	−	0.365444i
$683$	12.2144			0.467370			0.233685	−	0.972312i	$-0.424922\pi$
$683$	12.2144			0.467370			0.233685	+	0.972312i	$0.424922\pi$
$684$	−21.3085	+	18.6223i	−0.814749	+	0.712041i
$685$	−37.9634	−	13.4252i	−1.45051	−	0.512951i
$686$	7.61009	+	6.14187i	0.290555	+	0.234498i
$687$	33.3788	+	9.26827i	1.27348	+	0.353606i
$688$	18.7293	+	13.4206i	0.714048	+	0.511655i
$689$	9.92027	−	17.1824i	0.377932	−	0.654598i
$690$	−16.0439	−	3.97037i	−0.610781	−	0.151149i
$691$	−7.72260	+	4.45864i	−0.293781	+	0.169615i	−0.639646	−	0.768670i	$-0.720919\pi$
$691$	−7.72260	+	4.45864i	−0.293781	+	0.169615i	0.345865	+	0.938284i	$0.387586\pi$
$692$	20.1067	−	18.2240i	0.764341	−	0.692774i
$693$	−0.0474345	+	2.62132i	−0.00180189	+	0.0995756i
$694$	−13.6658	−	35.4265i	−0.518745	−	1.34477i
$695$	−4.16361	−	22.4112i	−0.157935	−	0.850105i
$696$	31.0369	−	9.94331i	1.17645	−	0.376900i
$697$	−4.34420	−	2.50812i	−0.164548	−	0.0950020i
$698$	0.314845	−	2.00920i	0.0119171	−	0.0760494i
$699$	−2.32388	−	8.99767i	−0.0878973	−	0.340323i
$700$	−4.20733	+	2.75712i	−0.159022	+	0.104209i
$701$			24.5732i			0.928117i	0.885805	+	0.464059i	$0.153607\pi$
$701$			24.5732i			0.928117i	−0.885805	+	0.464059i	$0.846393\pi$
$702$	−13.6741	−	6.51078i	−0.516096	−	0.245734i
$703$		−	1.26631i		−	0.0477597i
$704$	12.7521	+	5.52769i	0.480611	+	0.208333i
$705$	−14.6356	−	1.27885i	−0.551209	−	0.0481641i
$706$	−5.96503	+	38.0662i	−0.224497	+	1.43264i
$707$	0.170011	−	0.294468i	0.00639393	−	0.0110746i
$708$	−0.390674	+	6.71398i	−0.0146824	+	0.252327i
$709$	20.5390	−	11.8582i	0.771360	−	0.445345i	−0.0619997	−	0.998076i	$-0.519748\pi$
$709$	20.5390	−	11.8582i	0.771360	−	0.445345i	0.833359	+	0.552731i	$0.186414\pi$
$710$	−44.1927	+	1.24882i	−1.65852	+	0.0468675i
$711$	−34.9741	−	21.0450i	−1.31163	−	0.789251i
$712$	−33.5441	−	16.8840i	−1.25712	−	0.632753i
$713$	−16.1628	+	9.33157i	−0.605300	+	0.349470i
$714$	2.13949	−	0.208864i	0.0800682	−	0.00781653i
$715$	−6.08590	+	5.20237i	−0.227600	+	0.194557i
$716$	34.1516	−	7.37645i	1.27630	−	0.275671i
$717$	3.80776	−	13.7133i	0.142204	−	0.512133i
$718$	3.56738	−	4.42017i	0.133134	−	0.164959i
$719$	−34.9158			−1.30214			−0.651071	−	0.759017i	$-0.725680\pi$
$719$	−34.9158			−1.30214			−0.651071	+	0.759017i	$0.725680\pi$
$720$	−26.7718	+	1.80833i	−0.997727	+	0.0673923i
$721$	6.08686			0.226687
$722$	2.88266	−	3.57177i	0.107282	−	0.132927i
$723$	6.78104	+	6.90486i	0.252190	+	0.256794i
$724$	3.98646	−	0.861041i	0.148156	−	0.0320003i
$725$	11.9470	+	31.0433i	0.443700	+	1.15292i
$726$	−11.3744	−	15.9018i	−0.422144	−	0.590173i
$727$	21.9078	−	12.6484i	0.812514	−	0.469105i	−0.0353143	−	0.999376i	$-0.511243\pi$
$727$	21.9078	−	12.6484i	0.812514	−	0.469105i	0.847828	+	0.530271i	$0.177910\pi$
$728$	1.31835	−	2.61922i	0.0488611	−	0.0970747i
$729$	1.46487	−	26.9602i	0.0542545	−	0.998527i
$730$	1.32789	+	46.9906i	0.0491473	+	1.73920i
$731$	8.70324	−	5.02482i	0.321901	−	0.185850i
$732$	30.7645	+	20.2317i	1.13709	+	0.747786i
$733$	−23.3250	+	40.4001i	−0.861529	+	1.49221i	0.00892310	+	0.999960i	$0.497160\pi$
$733$	−23.3250	+	40.4001i	−0.861529	+	1.49221i	−0.870452	+	0.492252i	$0.836174\pi$
$734$	−6.12353	+	39.0777i	−0.226024	+	1.44238i
$735$	−23.6814	+	11.0460i	−0.873503	+	0.407437i
$736$	11.9707	−	12.1689i	0.441248	−	0.448553i
$737$		−	24.9405i		−	0.918695i
$738$	−9.35254	−	7.83176i	−0.344272	−	0.288291i
$739$			7.30748i			0.268810i	0.990926	+	0.134405i	$0.0429123\pi$
$739$			7.30748i			0.268810i	−0.990926	+	0.134405i	$0.957088\pi$
$740$	0.727395	−	0.955284i	0.0267396	−	0.0351169i
$741$	16.2229	+	4.50459i	0.595961	+	0.165480i
$742$	−1.06021	+	6.76576i	−0.0389214	+	0.248379i
$743$	3.92012	+	2.26328i	0.143815	+	0.0830318i	0.570181	−	0.821519i	$-0.306873\pi$
$743$	3.92012	+	2.26328i	0.143815	+	0.0830318i	−0.426366	+	0.904551i	$0.640206\pi$
$744$	−20.3669	+	22.4331i	−0.746686	+	0.822438i
$745$	−6.49829	−	34.9779i	−0.238079	−	1.28149i
$746$	−6.71771	−	17.4147i	−0.245953	−	0.637598i
$747$	−21.2296	−	12.7746i	−0.776752	−	0.467397i
$748$	4.49159	−	4.07103i	0.164229	−	0.148852i
$749$	−1.66258	+	0.959892i	−0.0607494	+	0.0350737i
$750$	−3.40844	−	27.1732i	−0.124458	−	0.992225i
$751$	−1.77769	+	3.07904i	−0.0648687	+	0.112356i	−0.896636	−	0.442769i	$-0.853996\pi$
$751$	−1.77769	+	3.07904i	−0.0648687	+	0.112356i	0.831767	+	0.555125i	$0.187330\pi$
$752$	8.83776	−	12.3337i	0.322280	−	0.449763i
$753$	−1.89846	−	7.35052i	−0.0691838	−	0.267868i
$754$	−15.0889	−	12.1778i	−0.549504	−	0.443488i
$755$	14.2076	−	40.1758i	0.517068	−	1.46215i
$756$	5.21241	+	0.398041i	0.189573	+	0.0144766i
$757$	−11.5482			−0.419728			−0.209864	−	0.977731i	$-0.567302\pi$
$757$	−11.5482			−0.419728			−0.209864	+	0.977731i	$0.567302\pi$
$758$	24.0356	+	19.3984i	0.873012	+	0.704580i
$759$	8.79174	−	2.27070i	0.319120	−	0.0824210i
$760$	28.9680	−	7.11888i	1.05078	−	0.258229i
$761$	3.58913	−	6.21655i	0.130106	−	0.225350i	−0.793611	−	0.608425i	$-0.791802\pi$
$761$	3.58913	−	6.21655i	0.130106	−	0.225350i	0.923717	+	0.383075i	$0.125135\pi$
$762$	−6.78119	−	3.07955i	−0.245657	−	0.111560i
$763$	1.71740	+	2.97462i	0.0621739	+	0.107688i
$764$	24.5551	−	22.2559i	0.888371	−	0.805191i
$765$	−4.10092	+	10.9613i	−0.148269	+	0.396308i
$766$	45.5902	−	17.5864i	1.64724	−	0.635422i
$767$	3.46519	−	2.00063i	0.125121	−	0.0722385i
$768$	12.4803	−	24.7435i	0.450343	−	0.892856i
$769$	4.22086	−	7.31075i	0.152208	−	0.263632i	−0.779831	−	0.625990i	$-0.784695\pi$
$769$	4.22086	−	7.31075i	0.152208	−	0.263632i	0.932039	+	0.362358i	$0.118028\pi$
$770$	1.31363	−	2.43139i	0.0473398	−	0.0876213i
$771$	−0.454686	−	0.126252i	−0.0163751	−	0.00454687i
$772$	5.10532	−	15.8899i	0.183744	−	0.571891i
$773$	−18.3196			−0.658909			−0.329455	−	0.944171i	$-0.606865\pi$
$773$	−18.3196			−0.658909			−0.329455	+	0.944171i	$0.606865\pi$
$774$	22.9567	−	8.38160i	0.825161	−	0.301271i
$775$	−24.0493	−	19.4406i	−0.863877	−	0.698327i
$776$	−10.4766	+	0.600823i	−0.376089	+	0.0215683i
$777$	−0.166896	+	0.163903i	−0.00598737	+	0.00588000i
$778$	−3.86079	+	24.6378i	−0.138416	+	0.883309i
$779$	11.7443	+	6.78057i	0.420783	+	0.242939i
$780$	9.65073	+	12.7170i	0.345552	+	0.455340i
$781$	21.0346	−	12.1443i	0.752678	−	0.434559i
$782$	−2.67953	−	6.94629i	−0.0958197	−	0.248399i
$783$	9.84961	−	33.1348i	0.351996	−	1.18414i
$784$	2.64465	−	26.8580i	0.0944517	−	0.959213i
$785$	40.8146	−	7.58266i	1.45674	−	0.270637i
$786$	−17.9461	+	12.8367i	−0.640118	+	0.457869i
$787$	16.6441	−	28.8284i	0.593298	−	1.02762i	−0.400486	−	0.916303i	$-0.631159\pi$
$787$	16.6441	−	28.8284i	0.593298	−	1.02762i	0.993785	−	0.111320i	$-0.0355079\pi$
$788$	0.876162	+	4.05647i	0.0312120	+	0.144506i
$789$	−8.64188	+	8.48692i	−0.307659	+	0.302142i
$790$	22.5567	+	36.6387i	0.802532	+	1.30355i
$791$	−9.58457			−0.340788
$792$	12.4680	−	7.86540i	0.443033	−	0.279485i
$793$		−	21.9067i		−	0.777930i
$794$	−2.53943	+	3.14649i	−0.0901211	+	0.111665i
$795$	−30.5438	−	21.3821i	−1.08328	−	0.758344i
$796$	0.822813	+	3.80947i	0.0291638	+	0.135023i
$797$	−6.41956	+	11.1190i	−0.227393	+	0.393855i	−0.957035	−	0.289974i	$-0.906353\pi$
$797$	−6.41956	+	11.1190i	−0.227393	+	0.393855i	0.729642	+	0.683829i	$0.239687\pi$
$798$	−5.78398	+	0.564651i	−0.204751	+	0.0199884i
$799$	−3.30896	−	5.73128i	−0.117063	−	0.202758i
$800$	25.9422	+	11.2695i	0.917196	+	0.398436i
$801$	−34.8499	+	19.2885i	−1.23136	+	0.681524i
$802$	−10.7717	−	27.9241i	−0.380362	−	0.986035i
$803$	−12.9132	−	22.3664i	−0.455698	−	0.789292i
$804$	−49.6457	−	2.88879i	−1.75087	−	0.101880i
$805$	−2.20543	−	2.57998i	−0.0777311	−	0.0909324i
$806$	17.8094	+	2.79076i	0.627309	+	0.0983003i
$807$	−8.29136	−	32.1027i	−0.291870	−	1.13007i
$808$	−1.90876	+	0.109465i	−0.0671498	+	0.00385096i
$809$	50.7647			1.78479			0.892396	−	0.451252i	$-0.149023\pi$
$809$	50.7647			1.78479			0.892396	+	0.451252i	$0.149023\pi$
$810$	−14.4254	+	24.5338i	−0.506857	+	0.862030i
$811$			4.21883i			0.148143i	0.997253	+	0.0740716i	$0.0235993\pi$
$811$			4.21883i			0.148143i	−0.997253	+	0.0740716i	$0.976401\pi$
$812$	6.37200	+	2.04728i	0.223613	+	0.0718453i
$813$	−17.8438	+	4.60862i	−0.625809	+	0.161631i
$814$	−0.102122	+	0.651697i	−0.00357937	+	0.0228420i
$815$	8.03717	+	9.40215i	0.281530	+	0.329343i
$816$	−7.58340	−	9.41233i	−0.265472	−	0.329497i
$817$	−23.5287	+	13.5843i	−0.823165	+	0.475255i
$818$	−7.40026	−	19.1841i	−0.258744	−	0.670757i
$819$	−1.50610	−	2.72118i	−0.0526272	−	0.0950856i
$820$	4.96481	+	11.8613i	0.173379	+	0.414216i
$821$	−6.28399	+	3.62806i	−0.219313	+	0.126620i	−0.605632	−	0.795745i	$-0.707080\pi$
$821$	−6.28399	+	3.62806i	−0.219313	+	0.126620i	0.386319	+	0.922365i	$0.373746\pi$
$822$	−4.28585	−	43.9019i	−0.149486	−	1.53125i
$823$	23.2064	+	13.3982i	0.808926	+	0.467033i	0.846583	−	0.532257i	$-0.178656\pi$
$823$	23.2064	+	13.3982i	0.808926	+	0.467033i	−0.0376570	+	0.999291i	$0.511989\pi$
$824$	−18.7817	−	28.6117i	−0.654292	−	0.996737i
$825$	8.74364	+	12.2442i	0.304415	+	0.426288i
$826$	−0.867396	+	1.07475i	−0.0301806	+	0.0373953i
$827$	29.5351			1.02704			0.513518	−	0.858079i	$-0.328342\pi$
$827$	29.5351			1.02704			0.513518	+	0.858079i	$0.328342\pi$
$828$	−3.50164	−	17.7635i	−0.121691	−	0.617326i
$829$			40.9548i			1.42242i	0.702981	+	0.711209i	$0.251852\pi$
$829$			40.9548i			1.42242i	−0.702981	+	0.711209i	$0.748148\pi$
$830$	13.6922	+	22.2401i	0.475263	+	0.771965i
$831$	−1.86262	−	1.89663i	−0.0646135	−	0.0657933i
$832$	−16.3797	+	1.88492i	−0.567865	+	0.0653477i
$833$	−10.1940	−	5.88549i	−0.353200	−	0.203920i
$834$	20.3095	−	14.5272i	0.703261	−	0.503035i
$835$	−0.934482	−	5.02997i	−0.0323391	−	0.174069i
$836$	−12.1427	+	11.0058i	−0.419966	+	0.380644i
$837$	7.47230	+	31.2566i	0.258280	+	1.08039i
$838$	−32.7644	+	12.6388i	−1.13183	+	0.436601i
$839$	18.2689	+	31.6427i	0.630714	+	1.09243i	0.987406	+	0.158207i	$0.0505713\pi$
$839$	18.2689	+	31.6427i	0.630714	+	1.09243i	−0.356692	+	0.934222i	$0.616095\pi$
$840$	−4.68769	−	2.89648i	−0.161741	−	0.0999380i
$841$	7.62834	−	13.2127i	0.263046	−	0.455610i
$842$	1.58722	−	10.1289i	0.0546992	−	0.349066i
$843$	14.4950	+	14.7597i	0.499234	+	0.508350i
$844$	15.8470	−	49.3225i	0.545475	−	1.69775i
$845$	−6.52499	+	18.4511i	−0.224466	+	0.634739i
$846$	−5.51948	−	15.1175i	−0.189764	−	0.519751i
$847$		−	4.01500i		−	0.137957i
$848$	35.0743	−	15.8930i	1.20446	−	0.545766i
$849$	−7.45414	+	26.8454i	−0.255826	+	0.921331i
$850$	9.14708	−	8.27757i	0.313742	−	0.283918i
$851$	0.701625	+	0.405083i	0.0240514	+	0.0138861i
$852$	−21.7377	−	43.2774i	−0.744722	−	1.48266i
$853$	−23.7918	−	41.2086i	−0.814615	−	1.41095i	−0.909604	−	0.415476i	$-0.863615\pi$
$853$	−23.7918	−	41.2086i	−0.814615	−	1.41095i	0.0949894	−	0.995478i	$-0.469718\pi$
$854$	2.72139	+	7.05481i	0.0931239	+	0.241411i
$855$	11.0866	−	29.6334i	0.379154	−	1.01344i
$856$	9.64213	+	4.85323i	0.329561	+	0.165880i
$857$	−25.3467	+	14.6339i	−0.865828	+	0.499886i	−0.865960	−	0.500114i	$-0.833291\pi$
$857$	−25.3467	+	14.6339i	−0.865828	+	0.499886i	0.000131580		1.00000i	$0.499958\pi$
$858$	−7.98570	−	3.62655i	−0.272627	−	0.123809i
$859$	−30.5267	−	17.6246i	−1.04156	−	0.601343i	−0.121282	−	0.992618i	$-0.538701\pi$
$859$	−30.5267	−	17.6246i	−1.04156	−	0.601343i	−0.920274	+	0.391275i	$0.872034\pi$
$860$	−25.5528	−	3.26761i	−0.871344	−	0.111425i
$861$	−0.626449	−	2.42550i	−0.0213493	−	0.0826610i
$862$	−15.9847	+	19.8058i	−0.544440	+	0.674590i
$863$			16.7375i			0.569752i	0.958564	+	0.284876i	$0.0919525\pi$
$863$			16.7375i			0.569752i	−0.958564	+	0.284876i	$0.908048\pi$
$864$	−14.2125	−	25.7295i	−0.483517	−	0.875335i
$865$	−10.1153	+	28.6037i	−0.343931	+	0.972556i
$866$	−22.0268	−	17.7772i	−0.748502	−	0.604092i
$867$	23.4049	−	6.04493i	0.794872	−	0.205296i
$868$	−6.08200	+	1.31366i	−0.206436	+	0.0445885i
$869$	−20.4709	−	11.8189i	−0.694429	−	0.400929i
$870$	−25.2658	+	26.2553i	−0.856590	+	0.890138i
$871$	14.7934	+	25.6229i	0.501255	+	0.868199i
$872$	8.68318	−	17.2513i	0.294049	−	0.584201i
$873$	−5.73869	+	9.53695i	−0.194225	+	0.322777i
$874$	7.24395	+	18.7789i	0.245030	+	0.635206i
$875$	2.67717	−	4.94590i	0.0905048	−	0.167202i
$876$	−46.0174	+	23.1140i	−1.55478	+	0.780949i
$877$	15.5923	−	27.0067i	0.526515	−	0.911950i	−0.473008	−	0.881058i	$-0.656832\pi$
$877$	15.5923	−	27.0067i	0.526515	−	0.911950i	0.999523	−	0.0308920i	$-0.00983478\pi$
$878$	−8.80125	−	1.37917i	−0.297028	−	0.0465448i
$879$	9.47369	−	34.1186i	0.319540	−	1.15079i
$880$	−15.4823	+	1.32755i	−0.521907	+	0.0447517i
$881$	41.3042			1.39158			0.695788	−	0.718248i	$-0.255055\pi$
$881$	41.3042			1.39158			0.695788	+	0.718248i	$0.255055\pi$
$882$	−21.9464	−	18.3778i	−0.738974	−	0.618812i
$883$	10.5777			0.355969			0.177985	−	0.984033i	$-0.443042\pi$
$883$	10.5777			0.355969			0.177985	+	0.984033i	$0.443042\pi$
$884$	−2.19976	+	6.84659i	−0.0739860	+	0.230276i
$885$	−3.17848	−	6.81433i	−0.106843	−	0.229061i
$886$	30.0186	+	4.70397i	1.00850	+	0.158033i
$887$	0.596498	+	0.344388i	0.0200284	+	0.0115634i	0.509981	−	0.860186i	$-0.329652\pi$
$887$	0.596498	+	0.344388i	0.0200284	+	0.0115634i	−0.489952	+	0.871749i	$0.662986\pi$
$888$	1.28542	+	0.278765i	0.0431358	+	0.00935473i
$889$	−0.764725	−	1.32454i	−0.0256481	−	0.0444238i
$890$	41.9695	−	1.18600i	1.40682	−	0.0397548i
$891$	0.565700	−	15.6257i	0.0189516	−	0.523479i
$892$	35.6892	+	39.3760i	1.19496	+	1.31841i
$893$	8.94558	+	15.4942i	0.299352	+	0.518494i
$894$	31.6978	−	22.6731i	1.06013	−	0.758301i
$895$	−29.6930	+	25.3822i	−0.992526	+	0.848434i
$896$	5.04075	−	2.64181i	0.168400	−	0.0882566i
$897$	−7.68544	+	7.54763i	−0.256609	+	0.252008i
$898$	−10.2283	+	12.6734i	−0.341323	+	0.422916i
$899$			41.1451i			1.37227i
$900$	25.3856	−	15.9866i	0.846187	−	0.532886i
$901$		−	16.7952i		−	0.559529i
$902$	−5.49730	−	4.43670i	−0.183040	−	0.147726i
$903$	4.83579	+	1.34275i	0.160925	+	0.0446840i
$904$	29.5743	+	45.0529i	0.983626	+	1.49844i
$905$	−3.46601	+	2.96283i	−0.115214	+	0.0984876i
$906$	46.4605	−	4.53562i	1.54355	−	0.150686i
$907$	−14.0381	−	24.3148i	−0.466129	−	0.807358i	0.533123	−	0.846038i	$-0.321018\pi$
$907$	−14.0381	−	24.3148i	−0.466129	−	0.807358i	−0.999252	+	0.0386793i	$0.987685\pi$
$908$	18.5046	−	16.7720i	0.614097	−	0.556598i
$909$	−1.04554	+	1.73755i	−0.0346784	+	0.0576310i
$910$	0.0926060	+	3.27709i	0.00306986	+	0.108635i
$911$	−20.0103	−	34.6589i	−0.662971	−	1.14830i	−0.979831	−	0.199827i	$-0.935962\pi$
$911$	−20.0103	−	34.6589i	−0.662971	−	1.14830i	0.316860	−	0.948472i	$-0.397371\pi$
$912$	20.5013	+	25.4457i	0.678866	+	0.842591i
$913$	−12.4261	−	7.17420i	−0.411243	−	0.237431i
$914$	−1.73495	+	11.0717i	−0.0573871	+	0.366219i
$915$	−41.0108	−	3.58348i	−1.35577	−	0.118466i
$916$	12.2359	−	38.0833i	0.404286	−	1.25831i
$917$	−4.53115			−0.149632
$918$	−12.7802	+	1.01459i	−0.421809	+	0.0334863i
$919$	44.2057			1.45821			0.729105	−	0.684402i	$-0.239936\pi$
$919$	44.2057			1.45821			0.729105	+	0.684402i	$0.239936\pi$
$920$	−5.32229	+	18.3276i	−0.175471	+	0.604243i
$921$	−26.8545	+	6.93587i	−0.884886	+	0.228545i
$922$	−6.58900	+	42.0481i	−0.216997	+	1.38478i
$923$	−14.4068	+	24.9533i	−0.474205	+	0.821347i
$924$	3.02222	+	0.175857i	0.0994237	+	0.00578528i
$925$	−0.208863	+	1.32607i	−0.00686737	+	0.0436010i
$926$	−20.9296	+	8.07358i	−0.687790	+	0.265314i
$927$	−36.2957	−	0.656795i	−1.19211	−	0.0215720i
$928$	−10.0382	−	36.2691i	−0.329519	−	1.19059i
$929$	18.1652	+	31.4631i	0.595981	+	1.03227i	0.993408	+	0.114636i	$0.0365702\pi$
$929$	18.1652	+	31.4631i	0.595981	+	1.03227i	−0.397426	+	0.917634i	$0.630097\pi$
$930$	8.13773	−	32.8838i	0.266847	−	1.07830i
$931$	27.5588	+	15.9111i	0.903204	+	0.521465i
$932$	−10.4887	+	2.26546i	−0.343568	+	0.0742077i
$933$	−2.20464	+	7.93981i	−0.0721768	+	0.259938i
$934$	−26.9501	+	33.3925i	−0.881833	+	1.09264i
$935$	−2.25964	+	6.38973i	−0.0738980	+	0.208966i
$936$	−8.14385	+	15.4760i	−0.266190	+	0.505849i
$937$		−	33.9924i		−	1.11048i	−0.831689	−	0.555242i	$-0.812626\pi$
$937$		−	33.9924i		−	1.11048i	0.831689	−	0.555242i	$-0.187374\pi$
$938$	−7.94709	−	6.41385i	−0.259482	−	0.209420i
$939$	23.3699	−	22.9508i	0.762647	−	0.748971i
$940$	−2.15180	+	16.8271i	−0.0701839	+	0.548840i
$941$	−11.8245	−	6.82689i	−0.385468	−	0.222550i	0.294726	−	0.955582i	$-0.404771\pi$
$941$	−11.8245	−	6.82689i	−0.385468	−	0.222550i	−0.680195	+	0.733031i	$0.738105\pi$
$942$	26.4565	+	36.9872i	0.862000	+	1.20511i
$943$	−7.51384	+	4.33812i	−0.244684	+	0.141269i
$944$	7.72838	+	0.760997i	0.251537	+	0.0247683i
$945$	−5.34059	+	2.37438i	−0.173729	+	0.0772386i
$946$	13.2044	−	5.09359i	0.429312	−	0.165607i
$947$	−14.1775	−	24.5562i	−0.460707	−	0.797969i	0.538289	−	0.842760i	$-0.319071\pi$
$947$	−14.1775	−	24.5562i	−0.460707	−	0.797969i	−0.998996	+	0.0447918i	$0.985738\pi$
$948$	−25.8974	+	39.3798i	−0.841108	+	1.27900i
$949$	26.5331	+	15.3189i	0.861301	+	0.497273i
$950$	−24.7286	+	22.3780i	−0.802303	+	0.726037i
$951$	30.5691	+	31.1273i	0.991271	+	1.00937i
$952$	−0.142118	−	2.47814i	−0.00460608	−	0.0803169i
$953$			39.9460i			1.29398i	0.762499	+	0.646990i	$0.223972\pi$
$953$			39.9460i			1.29398i	−0.762499	+	0.646990i	$0.776028\pi$
$954$	7.05200	−	40.2295i	0.228317	−	1.30248i
$955$	−12.3532	+	34.9320i	−0.399740	+	1.13037i
$956$	−15.6461	−	5.02698i	−0.506032	−	0.162584i
$957$	5.35588	−	19.2887i	0.173131	−	0.623514i
$958$	25.5316	+	4.00084i	0.824887	+	0.129261i
$959$	4.52925	−	7.84489i	0.146257	−	0.253325i
$960$	0.849304	+	30.9722i	0.0274112	+	0.999624i
$961$	−3.62612	−	6.28063i	−0.116972	−	0.202601i
$962$	−0.281636	−	0.730102i	−0.00908032	−	0.0235394i
$963$	10.0175	−	5.54439i	0.322808	−	0.178666i
$964$	8.28000	−	7.50473i	0.266681	−	0.241711i
$965$	3.40837	+	18.3460i	0.109719	+	0.590578i
$966$	1.53740	−	3.38536i	0.0494650	−	0.108922i
$967$	−41.4550	−	23.9341i	−1.33310	−	0.769668i	−0.347329	−	0.937743i	$-0.612911\pi$
$967$	−41.4550	−	23.9341i	−1.33310	−	0.769668i	−0.985774	+	0.168076i	$0.946245\pi$
$968$	−18.8728	+	12.3887i	−0.606594	+	0.398189i
$969$	13.7995	−	3.56409i	0.443305	−	0.114495i
$970$	9.99086	−	6.15091i	0.320787	−	0.197494i
$971$		−	30.7092i		−	0.985506i	−0.870169	−	0.492753i	$-0.835991\pi$
$971$		−	30.7092i		−	0.985506i	0.870169	−	0.492753i	$-0.164009\pi$
$972$	−31.0384	−	2.93594i	−0.995556	−	0.0941703i
$973$	5.12787			0.164392
$974$	−29.3488	−	23.6865i	−0.940397	−	0.758965i
$975$	−16.2455	−	7.39295i	−0.520272	−	0.236764i
$976$	24.7645	−	34.5605i	0.792691	−	1.10625i
$977$	7.48586	+	4.32196i	0.239494	+	0.138272i	0.614944	−	0.788571i	$-0.289179\pi$
$977$	7.48586	+	4.32196i	0.239494	+	0.138272i	−0.375450	+	0.926843i	$0.622512\pi$
$978$	−5.60269	+	12.3372i	−0.179154	+	0.394499i
$979$	−19.9765	+	11.5334i	−0.638450	+	0.368609i
$980$	11.6503	+	27.8335i	0.372154	+	0.889108i
$981$	−9.91978	−	17.9228i	−0.316714	−	0.572231i
$982$	43.4379	−	16.7561i	1.38616	−	0.534710i
$983$	16.3223	−	9.42371i	0.520602	−	0.300570i	−0.216579	−	0.976265i	$-0.569490\pi$
$983$	16.3223	−	9.42371i	0.520602	−	0.300570i	0.737181	+	0.675695i	$0.236157\pi$
$984$	−9.46827	+	10.4288i	−0.301837	+	0.332459i
$985$	−3.01486	−	3.52688i	−0.0960613	−	0.112376i
$986$	−16.2159	−	2.54106i	−0.516419	−	0.0809238i
$987$	0.884233	−	3.18448i	0.0281454	−	0.101363i
$988$	5.94693	−	18.5094i	0.189197	−	0.588862i
$989$		−	17.3821i		−	0.552719i
$990$	−8.09544	+	14.3565i	−0.257290	+	0.456280i
$991$	33.6365			1.06850			0.534249	−	0.845327i	$-0.320595\pi$
$991$	33.6365			1.06850			0.534249	+	0.845327i	$0.320595\pi$
$992$	24.9416	+	24.5354i	0.791898	+	0.779000i
$993$	−2.33480	+	2.29293i	−0.0740926	+	0.0727639i
$994$	1.53969	−	9.82562i	0.0488360	−	0.311650i
$995$	−2.83128	−	3.31213i	−0.0897577	−	0.105001i
$996$	−15.7200	+	23.9040i	−0.498107	+	0.757426i
$997$	−9.43539	−	16.3426i	−0.298822	−	0.517574i	0.677045	−	0.735942i	$-0.263260\pi$
$997$	−9.43539	−	16.3426i	−0.298822	−	0.517574i	−0.975867	+	0.218367i	$0.929927\pi$
$998$	14.7296	−	5.68191i	0.466256	−	0.179858i
$999$	1.01288	−	0.959339i	0.0320461	−	0.0303521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bk.a.229.20	yes	136
5.4	even	2	inner	360.2.bk.a.229.49	yes	136
8.5	even	2	inner	360.2.bk.a.229.3	✓	136
9.7	even	3	inner	360.2.bk.a.349.66	yes	136
40.29	even	2	inner	360.2.bk.a.229.66	yes	136
45.34	even	6	inner	360.2.bk.a.349.3	yes	136
72.61	even	6	inner	360.2.bk.a.349.49	yes	136
360.349	even	6	inner	360.2.bk.a.349.20	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bk.a.229.3	✓	136	8.5	even	2	inner
360.2.bk.a.229.20	yes	136	1.1	even	1	trivial
360.2.bk.a.229.49	yes	136	5.4	even	2	inner
360.2.bk.a.229.66	yes	136	40.29	even	2	inner
360.2.bk.a.349.3	yes	136	45.34	even	6	inner
360.2.bk.a.349.20	yes	136	360.349	even	6	inner
360.2.bk.a.349.49	yes	136	72.61	even	6	inner
360.2.bk.a.349.66	yes	136	9.7	even	3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.888188 + 1.10051i) q^{2} +(1.67702 - 0.433134i) q^{3} +(-0.422246 - 1.95492i) q^{4} +(1.45294 + 1.69970i) q^{5} +(-1.01284 + 2.23028i) q^{6} +(-0.435632 + 0.251512i) q^{7} +(2.52644 + 1.27165i) q^{8} +(2.62479 - 1.45275i) q^{9} +O(q^{10})\)	\(q+(-0.888188 + 1.10051i) q^{2} +(1.67702 - 0.433134i) q^{3} +(-0.422246 - 1.95492i) q^{4} +(1.45294 + 1.69970i) q^{5} +(-1.01284 + 2.23028i) q^{6} +(-0.435632 + 0.251512i) q^{7} +(2.52644 + 1.27165i) q^{8} +(2.62479 - 1.45275i) q^{9} +(-3.16102 + 0.0893258i) q^{10} +(1.50457 - 0.868661i) q^{11} +(-1.55486 - 3.09555i) q^{12} +(-1.03049 + 1.78486i) q^{13} +(0.110131 - 0.702807i) q^{14} +(3.17280 + 2.22111i) q^{15} +(-3.64342 + 1.65091i) q^{16} +1.74463i q^{17} +(-0.732541 + 4.17892i) q^{18} -4.71652i q^{19} +(2.70927 - 3.55807i) q^{20} +(-0.621625 + 0.610478i) q^{21} +(-0.380365 + 2.42732i) q^{22} +(2.61329 + 1.50878i) q^{23} +(4.78769 + 1.03829i) q^{24} +(-0.777934 + 4.93911i) q^{25} +(-1.04899 - 2.71935i) q^{26} +(3.77259 - 3.57317i) q^{27} +(0.675630 + 0.745425i) q^{28} +(5.76129 - 3.32629i) q^{29} +(-5.26240 + 1.51894i) q^{30} +(-3.09242 + 5.35623i) q^{31} +(1.41919 - 5.47594i) q^{32} +(2.14694 - 2.10844i) q^{33} +(-1.91999 - 1.54956i) q^{34} +(-1.06044 - 0.375010i) q^{35} +(-3.94831 - 4.51783i) q^{36} +0.268484 q^{37} +(5.19058 + 4.18915i) q^{38} +(-0.955067 + 3.43958i) q^{39} +(1.50935 + 6.14181i) q^{40} +(-1.43762 + 2.49003i) q^{41} +(-0.119718 - 1.22632i) q^{42} +(-2.88016 - 4.98857i) q^{43} +(-2.33346 - 2.57451i) q^{44} +(6.28289 + 2.35059i) q^{45} +(-3.98152 + 1.53587i) q^{46} +(-3.28509 + 1.89665i) q^{47} +(-5.39502 + 4.34670i) q^{48} +(-3.37348 + 5.84304i) q^{49} +(-4.74459 - 5.24298i) q^{50} +(0.755660 + 2.92579i) q^{51} +(3.92437 + 1.26087i) q^{52} -9.62677 q^{53} +(0.581546 + 7.32542i) q^{54} +(3.66250 + 1.29519i) q^{55} +(-1.42043 + 0.0814603i) q^{56} +(-2.04288 - 7.90970i) q^{57} +(-1.45650 + 9.29473i) q^{58} +(-1.68133 - 0.970719i) q^{59} +(3.00238 - 7.14043i) q^{60} +(-9.20522 + 5.31464i) q^{61} +(-3.14794 - 8.16058i) q^{62} +(-0.778058 + 1.29303i) q^{63} +(4.76582 + 6.42549i) q^{64} +(-4.53095 + 0.841774i) q^{65} +(0.413476 + 4.23542i) q^{66} +(7.17786 - 12.4324i) q^{67} +(3.41062 - 0.736665i) q^{68} +(5.03604 + 1.39835i) q^{69} +(1.35457 - 0.833947i) q^{70} +13.9805 q^{71} +(8.47877 - 0.332473i) q^{72} -14.8657i q^{73} +(-0.238464 + 0.295469i) q^{74} +(0.834685 + 8.61994i) q^{75} +(-9.22041 + 1.99153i) q^{76} +(-0.436958 + 0.756833i) q^{77} +(-2.93702 - 4.10605i) q^{78} +(-6.80294 - 11.7830i) q^{79} +(-8.09971 - 3.79403i) q^{80} +(4.77905 - 7.62632i) q^{81} +(-1.46343 - 3.79374i) q^{82} +(-4.12946 - 7.15243i) q^{83} +(1.45591 + 0.957454i) q^{84} +(-2.96535 + 2.53485i) q^{85} +(8.04810 + 1.26115i) q^{86} +(8.22108 - 8.07366i) q^{87} +(4.90583 - 0.281344i) q^{88} -13.2772 q^{89} +(-8.16723 + 4.82662i) q^{90} -1.03672i q^{91} +(1.84610 - 5.74584i) q^{92} +(-2.86609 + 10.3219i) q^{93} +(0.830496 - 5.29986i) q^{94} +(8.01665 - 6.85282i) q^{95} +(0.00819559 - 9.79796i) q^{96} +(-3.21307 + 1.85507i) q^{97} +(-3.43404 - 8.90227i) q^{98} +(2.68722 - 4.46581i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 2 q^{4} - 8 q^{9}+O(q^{10}) \) 136 * q - 2 * q^4 - 8 * q^9	\( 136 q - 2 q^{4} - 8 q^{9} - 10 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{20} - 38 q^{24} - 2 q^{25} + 16 q^{26} - 12 q^{30} - 4 q^{31} + 8 q^{34} - 24 q^{36} + 4 q^{39} - 6 q^{40} - 4 q^{41} - 56 q^{44} - 28 q^{46} + 40 q^{49} - 12 q^{50} + 10 q^{54} - 28 q^{55} + 26 q^{56} - 58 q^{60} - 20 q^{64} + 18 q^{65} + 16 q^{66} - 6 q^{70} - 128 q^{71} + 36 q^{74} + 12 q^{76} - 4 q^{79} - 36 q^{80} - 16 q^{81} - 110 q^{84} + 44 q^{86} - 32 q^{89} + 32 q^{90} - 34 q^{94} + 8 q^{95} - 2 q^{96}+O(q^{100}) \) 136 * q - 2 * q^4 - 8 * q^9 - 10 * q^14 + 2 * q^15 - 2 * q^16 - 2 * q^20 - 38 * q^24 - 2 * q^25 + 16 * q^26 - 12 * q^30 - 4 * q^31 + 8 * q^34 - 24 * q^36 + 4 * q^39 - 6 * q^40 - 4 * q^41 - 56 * q^44 - 28 * q^46 + 40 * q^49 - 12 * q^50 + 10 * q^54 - 28 * q^55 + 26 * q^56 - 58 * q^60 - 20 * q^64 + 18 * q^65 + 16 * q^66 - 6 * q^70 - 128 * q^71 + 36 * q^74 + 12 * q^76 - 4 * q^79 - 36 * q^80 - 16 * q^81 - 110 * q^84 + 44 * q^86 - 32 * q^89 + 32 * q^90 - 34 * q^94 + 8 * q^95 - 2 * q^96

Introduction

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