LMFDB - Embedded newform 390.2.x.a.199.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(49,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("390.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.x (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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 $ x^12 - 2x^11 - 8x^10 + 34x^9 + 8x^8 - 134x^7 + 98x^6 + 154x^5 + 104x^4 + 190x^3 - 1196x^2 - 338*x + 2197
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.4
Root			$-0.330925 - 1.46916i$ of defining polynomial
Character	$\chi$	$=$	390.199
Dual form			390.2.x.a.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.571769 + 2.16173i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.603137 - 1.04466i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.58623 - 1.57603i) q^{10} +(4.46182 + 2.57603i) q^{11} -1.00000i q^{12} +(-2.24511 + 2.82126i) q^{13} +1.20627 q^{14} +(-1.57603 + 1.58623i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.10150 + 2.36800i) q^{17} -1.00000 q^{18} +(-1.84474 + 1.06506i) q^{19} +(2.15800 - 0.585699i) q^{20} -1.20627i q^{21} +(-4.46182 + 2.57603i) q^{22} +(1.88293 + 1.08711i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-4.34616 - 2.47202i) q^{25} +(-1.32073 - 3.35495i) q^{26} +1.00000i q^{27} +(-0.603137 + 1.04466i) q^{28} +(2.38346 - 4.12828i) q^{29} +(-0.585699 - 2.15800i) q^{30} +5.91046i q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.57603 + 4.46182i) q^{33} -4.73601i q^{34} +(2.60314 - 0.706513i) q^{35} +(0.500000 - 0.866025i) q^{36} +(2.20034 - 3.81110i) q^{37} -2.13012i q^{38} +(-3.35495 + 1.32073i) q^{39} +(-0.571769 + 2.16173i) q^{40} +(4.10150 + 2.36800i) q^{41} +(1.04466 + 0.603137i) q^{42} +(-1.70944 + 0.986944i) q^{43} -5.15206i q^{44} +(-2.15800 + 0.585699i) q^{45} +(-1.88293 + 1.08711i) q^{46} -0.852296 q^{47} +(-0.866025 + 0.500000i) q^{48} +(2.77245 - 4.80203i) q^{49} +(4.31391 - 2.52788i) q^{50} -4.73601 q^{51} +(3.56583 + 0.533691i) q^{52} +4.48042i q^{53} +(-0.866025 - 0.500000i) q^{54} +(-8.11982 + 8.17235i) q^{55} +(-0.603137 - 1.04466i) q^{56} -2.13012 q^{57} +(2.38346 + 4.12828i) q^{58} +(1.68133 - 0.970715i) q^{59} +(2.16173 + 0.571769i) q^{60} +(-1.53795 - 2.66381i) q^{61} +(-5.11861 - 2.95523i) q^{62} +(0.603137 - 1.04466i) q^{63} +1.00000 q^{64} +(-4.81512 - 6.46642i) q^{65} -5.15206 q^{66} +(7.02765 - 12.1723i) q^{67} +(4.10150 + 2.36800i) q^{68} +(1.08711 + 1.88293i) q^{69} +(-0.689710 + 2.60764i) q^{70} +(-0.298707 + 0.172459i) q^{71} +(0.500000 + 0.866025i) q^{72} +15.7228 q^{73} +(2.20034 + 3.81110i) q^{74} +(-2.52788 - 4.31391i) q^{75} +(1.84474 + 1.06506i) q^{76} -6.21480i q^{77} +(0.533691 - 3.56583i) q^{78} -13.5863 q^{79} +(-1.58623 - 1.57603i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.10150 + 2.36800i) q^{82} +10.2045 q^{83} +(-1.04466 + 0.603137i) q^{84} +(-2.77388 - 10.2203i) q^{85} -1.97389i q^{86} +(4.12828 - 2.38346i) q^{87} +(4.46182 + 2.57603i) q^{88} +(14.1941 + 8.19497i) q^{89} +(0.571769 - 2.16173i) q^{90} +(4.30137 + 0.643777i) q^{91} -2.17422i q^{92} +(-2.95523 + 5.11861i) q^{93} +(0.426148 - 0.738110i) q^{94} +(-1.24761 - 4.59679i) q^{95} -1.00000i q^{96} +(4.24139 + 7.34631i) q^{97} +(2.77245 + 4.80203i) q^{98} +5.15206i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} - 2 q^{7} + 12 q^{8} + 6 q^{9} - 2 q^{10} + 6 q^{11} - 8 q^{13} + 4 q^{14} + 6 q^{15} - 6 q^{16} + 18 q^{17} - 12 q^{18} - 6 q^{19} + 4 q^{20} - 6 q^{22} + 6 q^{23} - 10 q^{25}+ \cdots + 8 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 - 2 * q^7 + 12 * q^8 + 6 * q^9 - 2 * q^10 + 6 * q^11 - 8 * q^13 + 4 * q^14 + 6 * q^15 - 6 * q^16 + 18 * q^17 - 12 * q^18 - 6 * q^19 + 4 * q^20 - 6 * q^22 + 6 * q^23 - 10 * q^25 - 2 * q^26 - 2 * q^28 + 14 * q^29 - 6 * q^30 - 6 * q^32 + 6 * q^33 + 26 * q^35 + 6 * q^36 - 12 * q^37 - 2 * q^39 - 2 * q^40 - 18 * q^41 - 12 * q^42 - 36 * q^43 - 4 * q^45 - 6 * q^46 + 16 * q^47 + 8 * q^49 - 10 * q^50 + 16 * q^51 + 10 * q^52 - 28 * q^55 - 2 * q^56 - 8 * q^57 + 14 * q^58 - 36 * q^59 + 10 * q^61 + 6 * q^62 + 2 * q^63 + 12 * q^64 + 6 * q^65 - 12 * q^66 + 4 * q^67 - 18 * q^68 + 16 * q^69 - 4 * q^70 - 12 * q^71 + 6 * q^72 + 28 * q^73 - 12 * q^74 - 8 * q^75 + 6 * q^76 - 2 * q^78 + 4 * q^79 - 2 * q^80 - 6 * q^81 + 18 * q^82 + 72 * q^83 + 12 * q^84 + 18 * q^85 + 6 * q^87 + 6 * q^88 + 18 * q^89 + 2 * q^90 + 2 * q^91 - 16 * q^93 - 8 * q^94 - 42 * q^95 - 48 * q^97 + 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.571769	+	2.16173i	−0.255703	+	0.966755i
$5$	−0.571769	+	2.16173i	−0.255703	+	0.966755i
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−0.603137	−	1.04466i	−0.227964	−	0.394846i	0.729240	−	0.684258i	$-0.239874\pi$
$7$	−0.603137	−	1.04466i	−0.227964	−	0.394846i	−0.957205	+	0.289412i	$0.906540\pi$
$8$	1.00000			0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.58623	−	1.57603i	−0.501610	−	0.498385i
$11$	4.46182	+	2.57603i	1.34529	+	0.776703i	0.987578	−	0.157130i	$-0.0502240\pi$
$11$	4.46182	+	2.57603i	1.34529	+	0.776703i	0.357711	+	0.933832i	$0.383557\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−2.24511	+	2.82126i	−0.622681	+	0.782476i
$13$	−2.24511	+	2.82126i	−0.622681	+	0.782476i
$14$	1.20627			0.322390
$15$	−1.57603	+	1.58623i	−0.406930	+	0.409563i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.10150	+	2.36800i	−0.994761	+	0.574326i	−0.906694	−	0.421789i	$-0.861402\pi$
$17$	−4.10150	+	2.36800i	−0.994761	+	0.574326i	−0.0880670	+	0.996115i	$0.528069\pi$
$18$	−1.00000			−0.235702
$19$	−1.84474	+	1.06506i	−0.423212	+	0.244341i	−0.696450	−	0.717605i	$-0.745238\pi$
$19$	−1.84474	+	1.06506i	−0.423212	+	0.244341i	0.273239	+	0.961946i	$0.411905\pi$
$20$	2.15800	−	0.585699i	0.482543	−	0.130966i
$21$		−	1.20627i		−	0.263231i
$22$	−4.46182	+	2.57603i	−0.951263	+	0.549212i
$23$	1.88293	+	1.08711i	0.392618	+	0.226678i	0.683294	−	0.730144i	$-0.260547\pi$
$23$	1.88293	+	1.08711i	0.392618	+	0.226678i	−0.290676	+	0.956822i	$0.593880\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−4.34616	−	2.47202i	−0.869232	−	0.494404i
$26$	−1.32073	−	3.35495i	−0.259016	−	0.657960i
$27$			1.00000i			0.192450i
$28$	−0.603137	+	1.04466i	−0.113982	+	0.197423i
$29$	2.38346	−	4.12828i	0.442598	−	0.766602i	−0.555283	−	0.831661i	$-0.687390\pi$
$29$	2.38346	−	4.12828i	0.442598	−	0.766602i	0.997881	+	0.0650589i	$0.0207235\pi$
$30$	−0.585699	−	2.15800i	−0.106934	−	0.393995i
$31$			5.91046i			1.06155i	0.847513	+	0.530775i	$0.178099\pi$
$31$			5.91046i			1.06155i	−0.847513	+	0.530775i	$0.821901\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.57603	+	4.46182i	0.448430	+	0.776703i
$34$		−	4.73601i		−	0.812219i
$35$	2.60314	−	0.706513i	0.440010	−	0.119423i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	2.20034	−	3.81110i	0.361734	−	0.626541i	−0.626513	−	0.779411i	$-0.715518\pi$
$37$	2.20034	−	3.81110i	0.361734	−	0.626541i	0.988246	+	0.152870i	$0.0488517\pi$
$38$		−	2.13012i		−	0.345551i
$39$	−3.35495	+	1.32073i	−0.537222	+	0.211486i
$40$	−0.571769	+	2.16173i	−0.0904046	+	0.341800i
$41$	4.10150	+	2.36800i	0.640547	+	0.369820i	0.784825	−	0.619717i	$-0.212753\pi$
$41$	4.10150	+	2.36800i	0.640547	+	0.369820i	−0.144278	+	0.989537i	$0.546086\pi$
$42$	1.04466	+	0.603137i	0.161195	+	0.0930660i
$43$	−1.70944	+	0.986944i	−0.260687	+	0.150508i	−0.624648	−	0.780907i	$-0.714757\pi$
$43$	−1.70944	+	0.986944i	−0.260687	+	0.150508i	0.363961	+	0.931414i	$0.381424\pi$
$44$		−	5.15206i		−	0.776703i
$45$	−2.15800	+	0.585699i	−0.321695	+	0.0873109i
$46$	−1.88293	+	1.08711i	−0.277623	+	0.160285i
$47$	−0.852296			−0.124320			−0.0621600	−	0.998066i	$-0.519799\pi$
$47$	−0.852296			−0.124320			−0.0621600	+	0.998066i	$0.519799\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	2.77245	−	4.80203i	0.396065	−	0.686004i
$50$	4.31391	−	2.52788i	0.610079	−	0.357496i
$51$	−4.73601			−0.663174
$52$	3.56583	+	0.533691i	0.494492	+	0.0740096i
$53$			4.48042i			0.615433i	0.951478	+	0.307716i	$0.0995648\pi$
$53$			4.48042i			0.615433i	−0.951478	+	0.307716i	$0.900435\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−8.11982	+	8.17235i	−1.09488	+	1.10196i
$56$	−0.603137	−	1.04466i	−0.0805976	−	0.139599i
$57$	−2.13012			−0.282141
$58$	2.38346	+	4.12828i	0.312964	+	0.542070i
$59$	1.68133	−	0.970715i	0.218890	−	0.126376i	−0.386546	−	0.922270i	$-0.626332\pi$
$59$	1.68133	−	0.970715i	0.218890	−	0.126376i	0.605436	+	0.795894i	$0.292999\pi$
$60$	2.16173	+	0.571769i	0.279078	+	0.0738150i
$61$	−1.53795	−	2.66381i	−0.196915	−	0.341066i	0.750612	−	0.660744i	$-0.229759\pi$
$61$	−1.53795	−	2.66381i	−0.196915	−	0.341066i	−0.947527	+	0.319677i	$0.896426\pi$
$62$	−5.11861	−	2.95523i	−0.650064	−	0.375315i
$63$	0.603137	−	1.04466i	0.0759881	−	0.131615i
$64$	1.00000			0.125000
$65$	−4.81512	−	6.46642i	−0.597242	−	0.802061i
$66$	−5.15206			−0.634175
$67$	7.02765	−	12.1723i	0.858564	−	1.48708i	−0.0147340	−	0.999891i	$-0.504690\pi$
$67$	7.02765	−	12.1723i	0.858564	−	1.48708i	0.873298	−	0.487186i	$-0.161977\pi$
$68$	4.10150	+	2.36800i	0.497380	+	0.287163i
$69$	1.08711	+	1.88293i	0.130873	+	0.226678i
$70$	−0.689710	+	2.60764i	−0.0824361	+	0.311673i
$71$	−0.298707	+	0.172459i	−0.0354500	+	0.0204671i	−0.517620	−	0.855610i	$-0.673182\pi$
$71$	−0.298707	+	0.172459i	−0.0354500	+	0.0204671i	0.482170	+	0.876078i	$0.339849\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	15.7228			1.84022			0.920109	−	0.391662i	$-0.128100\pi$
$73$	15.7228			1.84022			0.920109	+	0.391662i	$0.128100\pi$
$74$	2.20034	+	3.81110i	0.255784	+	0.443031i
$75$	−2.52788	−	4.31391i	−0.291894	−	0.498128i
$76$	1.84474	+	1.06506i	0.211606	+	0.122171i
$77$		−	6.21480i		−	0.708242i
$78$	0.533691	−	3.56583i	0.0604286	−	0.403751i
$79$	−13.5863			−1.52858			−0.764290	−	0.644873i	$-0.776910\pi$
$79$	−13.5863			−1.52858			−0.764290	+	0.644873i	$0.776910\pi$
$80$	−1.58623	−	1.57603i	−0.177346	−	0.176206i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.10150	+	2.36800i	−0.452935	+	0.261502i
$83$	10.2045			1.12009			0.560046	−	0.828462i	$-0.310784\pi$
$83$	10.2045			1.12009			0.560046	+	0.828462i	$0.310784\pi$
$84$	−1.04466	+	0.603137i	−0.113982	+	0.0658076i
$85$	−2.77388	−	10.2203i	−0.300869	−	1.10855i
$86$		−	1.97389i		−	0.212850i
$87$	4.12828	−	2.38346i	0.442598	−	0.255534i
$88$	4.46182	+	2.57603i	0.475631	+	0.274606i
$89$	14.1941	+	8.19497i	1.50457	+	0.868665i	0.999986	+	0.00530346i	$0.00168815\pi$
$89$	14.1941	+	8.19497i	1.50457	+	0.868665i	0.504586	+	0.863361i	$0.331645\pi$
$90$	0.571769	−	2.16173i	0.0602697	−	0.227866i
$91$	4.30137	+	0.643777i	0.450906	+	0.0674862i
$92$		−	2.17422i		−	0.226678i
$93$	−2.95523	+	5.11861i	−0.306443	+	0.530775i
$94$	0.426148	−	0.738110i	0.0439538	−	0.0761302i
$95$	−1.24761	−	4.59679i	−0.128002	−	0.471621i
$96$		−	1.00000i		−	0.102062i
$97$	4.24139	+	7.34631i	0.430648	+	0.745904i	0.996929	−	0.0783078i	$-0.0249517\pi$
$97$	4.24139	+	7.34631i	0.430648	+	0.745904i	−0.566281	+	0.824212i	$0.691618\pi$
$98$	2.77245	+	4.80203i	0.280060	+	0.485078i
$99$			5.15206i			0.517802i
$100$	0.0322474	+	4.99990i	0.00322474	+	0.499990i
$101$	6.79121	−	11.7627i	0.675751	−	1.17044i	−0.300498	−	0.953783i	$-0.597153\pi$
$101$	6.79121	−	11.7627i	0.675751	−	1.17044i	0.976249	−	0.216653i	$-0.0695139\pi$
$102$	2.36800	−	4.10150i	0.234467	−	0.406109i
$103$			2.15696i			0.212531i	0.994338	+	0.106266i	$0.0338894\pi$
$103$			2.15696i			0.212531i	−0.994338	+	0.106266i	$0.966111\pi$
$104$	−2.24511	+	2.82126i	−0.220151	+	0.276647i
$105$	2.60764	+	0.689710i	0.254480	+	0.0673088i
$106$	−3.88016	−	2.24021i	−0.376874	−	0.217588i
$107$	7.00959	+	4.04699i	0.677642	+	0.391237i	0.798966	−	0.601376i	$-0.205381\pi$
$107$	7.00959	+	4.04699i	0.677642	+	0.391237i	−0.121324	+	0.992613i	$0.538714\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$		−	16.8839i		−	1.61718i	−0.588370	−	0.808592i	$-0.700230\pi$
$109$		−	16.8839i		−	1.61718i	0.588370	−	0.808592i	$-0.299770\pi$
$110$	−3.01756	−	11.1181i	−0.287713	−	1.06007i
$111$	3.81110	−	2.20034i	0.361734	−	0.208847i
$112$	1.20627			0.113982
$113$	4.28771	−	2.47551i	0.403354	−	0.232876i	−0.284576	−	0.958653i	$-0.591853\pi$
$113$	4.28771	−	2.47551i	0.403354	−	0.232876i	0.687930	+	0.725777i	$0.258520\pi$
$114$	1.06506	−	1.84474i	0.0997519	−	0.172775i
$115$	−3.42664	+	3.44881i	−0.319535	+	0.321603i
$116$	−4.76693			−0.442598
$117$	−3.56583	−	0.533691i	−0.329661	−	0.0493397i
$118$			1.94143i			0.178723i
$119$	4.94754	+	2.85646i	0.453540	+	0.261851i
$120$	−1.57603	+	1.58623i	−0.143871	+	0.144802i
$121$	7.77188	+	13.4613i	0.706535	+	1.22375i
$122$	3.07591			0.278480
$123$	2.36800	+	4.10150i	0.213516	+	0.369820i
$124$	5.11861	−	2.95523i	0.459665	−	0.265388i
$125$	7.82884	−	7.98180i	0.700233	−	0.713914i
$126$	0.603137	+	1.04466i	0.0537317	+	0.0930660i
$127$	−1.04089	−	0.600957i	−0.0923639	−	0.0533263i	0.453107	−	0.891456i	$-0.350316\pi$
$127$	−1.04089	−	0.600957i	−0.0923639	−	0.0533263i	−0.545471	+	0.838130i	$0.683649\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−1.97389			−0.173791
$130$	8.00765	−	0.936802i	0.702317	−	0.0821629i
$131$	−6.65149			−0.581143			−0.290572	−	0.956853i	$-0.593845\pi$
$131$	−6.65149			−0.581143			−0.290572	+	0.956853i	$0.593845\pi$
$132$	2.57603	−	4.46182i	0.224215	−	0.388351i
$133$	2.22526	+	1.28475i	0.192954	+	0.111402i
$134$	7.02765	+	12.1723i	0.607097	+	1.05152i
$135$	−2.16173	−	0.571769i	−0.186052	−	0.0492100i
$136$	−4.10150	+	2.36800i	−0.351701	+	0.203055i
$137$	−7.35746	−	12.7435i	−0.628590	−	1.08875i	−0.987835	−	0.155507i	$-0.950299\pi$
$137$	−7.35746	−	12.7435i	−0.628590	−	1.08875i	0.359245	−	0.933243i	$-0.383034\pi$
$138$	−2.17422			−0.185082
$139$	−7.82540	−	13.5540i	−0.663742	−	1.14963i	−0.979625	−	0.200837i	$-0.935634\pi$
$139$	−7.82540	−	13.5540i	−0.663742	−	1.14963i	0.315883	−	0.948798i	$-0.397699\pi$
$140$	−1.91343	−	1.90113i	−0.161714	−	0.160674i
$141$	−0.738110	−	0.426148i	−0.0621600	−	0.0358881i
$142$		−	0.344918i		−	0.0289448i
$143$	−17.2849	+	6.80447i	−1.44544	+	0.569018i
$144$	−1.00000			−0.0833333
$145$	7.56144	+	7.51283i	0.627943	+	0.623906i
$146$	−7.86142	+	13.6164i	−0.650615	+	1.12690i
$147$	4.80203	−	2.77245i	0.396065	−	0.228668i
$148$	−4.40068			−0.361734
$149$	−19.7555	+	11.4058i	−1.61843	+	0.934401i	−0.631103	+	0.775699i	$0.717398\pi$
$149$	−19.7555	+	11.4058i	−1.61843	+	0.934401i	−0.987327	+	0.158702i	$0.949269\pi$
$150$	4.99990	−	0.0322474i	0.408240	−	0.00263299i
$151$		−	19.8995i		−	1.61940i	−0.586845	−	0.809699i	$-0.699630\pi$
$151$		−	19.8995i		−	1.61940i	0.586845	−	0.809699i	$-0.300370\pi$
$152$	−1.84474	+	1.06506i	−0.149628	+	0.0863877i
$153$	−4.10150	−	2.36800i	−0.331587	−	0.191442i
$154$	5.38217	+	3.10740i	0.433708	+	0.250401i
$155$	−12.7768	−	3.37942i	−1.02626	−	0.271442i
$156$	2.82126	+	2.24511i	0.225881	+	0.179752i
$157$		−	4.74392i		−	0.378606i	−0.981919	−	0.189303i	$-0.939377\pi$
$157$		−	4.74392i		−	0.378606i	0.981919	−	0.189303i	$-0.0606228\pi$
$158$	6.79315	−	11.7661i	0.540434	−	0.936060i
$159$	−2.24021	+	3.88016i	−0.177660	+	0.307716i
$160$	2.15800	−	0.585699i	0.170605	−	0.0463036i
$161$		−	2.62270i		−	0.206698i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	1.93329	+	3.34855i	0.151427	+	0.262279i	0.931752	−	0.363095i	$-0.118280\pi$
$163$	1.93329	+	3.34855i	0.151427	+	0.262279i	−0.780325	+	0.625374i	$0.784947\pi$
$164$		−	4.73601i		−	0.369820i
$165$	−11.1181	+	3.01756i	−0.865546	+	0.234917i
$166$	−5.10226	+	8.83737i	−0.396012	+	0.685913i
$167$	−11.3614	+	19.6785i	−0.879173	+	1.52277i	−0.0269225	+	0.999638i	$0.508571\pi$
$167$	−11.3614	+	19.6785i	−0.879173	+	1.52277i	−0.852250	+	0.523134i	$0.824763\pi$
$168$		−	1.20627i		−	0.0930660i
$169$	−2.91899	−	12.6681i	−0.224538	−	0.974465i
$170$	10.2380	+	2.70790i	0.785217	+	0.207687i
$171$	−1.84474	−	1.06506i	−0.141071	−	0.0814471i
$172$	1.70944	+	0.986944i	0.130343	+	0.0752538i
$173$	−4.06859	+	2.34900i	−0.309329	+	0.178591i	−0.646626	−	0.762807i	$-0.723821\pi$
$173$	−4.06859	+	2.34900i	−0.309329	+	0.178591i	0.337297	+	0.941398i	$0.390487\pi$
$174$			4.76693i			0.361380i
$175$	0.0388991	+	6.03124i	0.00294050	+	0.455919i
$176$	−4.46182	+	2.57603i	−0.336322	+	0.194176i
$177$	1.94143			0.145927
$178$	−14.1941	+	8.19497i	−1.06389	+	0.614239i
$179$	−4.34913	+	7.53292i	−0.325069	+	0.563037i	−0.981526	−	0.191327i	$-0.938721\pi$
$179$	−4.34913	+	7.53292i	−0.325069	+	0.563037i	0.656457	+	0.754363i	$0.272054\pi$
$180$	1.58623	+	1.57603i	0.118231	+	0.117470i
$181$	9.75480			0.725069			0.362534	−	0.931970i	$-0.381912\pi$
$181$	9.75480			0.725069			0.362534	+	0.931970i	$0.381912\pi$
$182$	−2.70821	+	3.40321i	−0.200746	+	0.252263i
$183$		−	3.07591i		−	0.227378i
$184$	1.88293	+	1.08711i	0.138811	+	0.0801427i
$185$	6.98049	+	6.93561i	0.513215	+	0.509916i
$186$	−2.95523	−	5.11861i	−0.216688	−	0.375315i
$187$	−24.4002			−1.78432
$188$	0.426148	+	0.738110i	0.0310800	+	0.0538322i
$189$	1.04466	−	0.603137i	0.0759881	−	0.0438718i
$190$	4.60474	+	1.21794i	0.334063	+	0.0883583i
$191$	−5.77729	−	10.0066i	−0.418030	−	0.724049i	0.577711	−	0.816241i	$-0.303946\pi$
$191$	−5.77729	−	10.0066i	−0.418030	−	0.724049i	−0.995741	+	0.0921920i	$0.970613\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	5.23154	−	9.06130i	0.376575	−	0.652247i	−0.613987	−	0.789316i	$-0.710435\pi$
$193$	5.23154	−	9.06130i	0.376575	−	0.652247i	0.990561	+	0.137070i	$0.0437685\pi$
$194$	−8.48278			−0.609028
$195$	−0.936802	−	8.00765i	−0.0670858	−	0.573439i
$196$	−5.54490			−0.396065
$197$	−8.79472	+	15.2329i	−0.626598	+	1.08530i	0.361632	+	0.932321i	$0.382220\pi$
$197$	−8.79472	+	15.2329i	−0.626598	+	1.08530i	−0.988230	+	0.152978i	$0.951113\pi$
$198$	−4.46182	−	2.57603i	−0.317088	−	0.183071i
$199$	12.7858	+	22.1457i	0.906362	+	1.56986i	0.819079	+	0.573681i	$0.194485\pi$
$199$	12.7858	+	22.1457i	0.906362	+	1.56986i	0.0872828	+	0.996184i	$0.472182\pi$
$200$	−4.34616	−	2.47202i	−0.307320	−	0.174798i
$201$	12.1723	−	7.02765i	0.858564	−	0.495692i
$202$	6.79121	+	11.7627i	0.477828	+	0.827623i
$203$	−5.75022			−0.403586
$204$	2.36800	+	4.10150i	0.165793	+	0.287163i
$205$	−7.46410	+	7.51240i	−0.521315	+	0.524689i
$206$	−1.86798	−	1.07848i	−0.130148	−	0.0751412i
$207$			2.17422i			0.151119i
$208$	−1.32073	−	3.35495i	−0.0915760	−	0.232624i
$209$	−10.9745			−0.759122
$210$	−1.90113	+	1.91343i	−0.131190	+	0.132039i
$211$	−6.45984	+	11.1888i	−0.444714	+	0.770267i	−0.998032	−	0.0627029i	$-0.980028\pi$
$211$	−6.45984	+	11.1888i	−0.444714	+	0.770267i	0.553318	+	0.832970i	$0.313361\pi$
$212$	3.88016	−	2.24021i	0.266490	−	0.153858i
$213$	−0.344918			−0.0236334
$214$	−7.00959	+	4.04699i	−0.479165	+	0.276646i
$215$	−1.15610	−	4.25965i	−0.0788456	−	0.290505i
$216$			1.00000i			0.0680414i
$217$	6.17445	−	3.56482i	0.419149	−	0.241996i
$218$	14.6219	+	8.44195i	0.990319	+	0.571761i
$219$	13.6164	+	7.86142i	0.920109	+	0.531225i
$220$	11.1374	+	2.94579i	0.750882	+	0.198605i
$221$	2.52757	−	16.8878i	0.170022	−	1.13600i
$222$			4.40068i			0.295354i
$223$	−3.57679	+	6.19518i	−0.239519	+	0.414860i	−0.960576	−	0.278016i	$-0.910323\pi$
$223$	−3.57679	+	6.19518i	−0.239519	+	0.414860i	0.721057	+	0.692876i	$0.243657\pi$
$224$	−0.603137	+	1.04466i	−0.0402988	+	0.0697995i
$225$	−0.0322474	−	4.99990i	−0.00214982	−	0.333326i
$226$			4.95102i			0.329337i
$227$	12.9192	+	22.3768i	0.857480	+	1.48520i	0.874325	+	0.485340i	$0.161304\pi$
$227$	12.9192	+	22.3768i	0.857480	+	1.48520i	−0.0168460	+	0.999858i	$0.505362\pi$
$228$	1.06506	+	1.84474i	0.0705353	+	0.122171i
$229$		−	8.95153i		−	0.591533i	−0.955260	−	0.295767i	$-0.904425\pi$
$229$		−	8.95153i		−	0.591533i	0.955260	−	0.295767i	$-0.0955751\pi$
$230$	−1.27344	−	4.69196i	−0.0839680	−	0.309379i
$231$	3.10740	−	5.38217i	0.204452	−	0.354121i
$232$	2.38346	−	4.12828i	0.156482	−	0.271035i
$233$			3.86657i			0.253308i	0.991947	+	0.126654i	$0.0404237\pi$
$233$			3.86657i			0.253308i	−0.991947	+	0.126654i	$0.959576\pi$
$234$	2.24511	−	2.82126i	0.146767	−	0.184431i
$235$	0.487316	−	1.84243i	0.0317890	−	0.120187i
$236$	−1.68133	−	0.970715i	−0.109445	−	0.0631882i
$237$	−11.7661	−	6.79315i	−0.764290	−	0.441263i
$238$	−4.94754	+	2.85646i	−0.320701	+	0.185157i
$239$			15.4177i			0.997286i	0.866807	+	0.498643i	$0.166168\pi$
$239$			15.4177i			0.997286i	−0.866807	+	0.498643i	$0.833832\pi$
$240$	−0.585699	−	2.15800i	−0.0378067	−	0.139298i
$241$	9.76603	−	5.63842i	0.629085	−	0.363203i	−0.151312	−	0.988486i	$-0.548350\pi$
$241$	9.76603	−	5.63842i	0.629085	−	0.363203i	0.780398	+	0.625283i	$0.215017\pi$
$242$	−15.5438			−0.999191
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−1.53795	+	2.66381i	−0.0984574	+	0.170533i
$245$	8.79549	+	8.73894i	0.561923	+	0.558311i
$246$	−4.73601			−0.301957
$247$	1.13682	−	7.59565i	0.0723344	−	0.483299i
$248$			5.91046i			0.375315i
$249$	8.83737	+	5.10226i	0.560046	+	0.323342i
$250$	2.99802	+	10.7709i	0.189612	+	0.681210i
$251$	6.15329	+	10.6578i	0.388392	+	0.672715i	0.992233	−	0.124390i	$-0.0396973\pi$
$251$	6.15329	+	10.6578i	0.388392	+	0.672715i	−0.603841	+	0.797104i	$0.706364\pi$
$252$	−1.20627			−0.0759881
$253$	5.60085	+	9.70096i	0.352123	+	0.609894i
$254$	1.04089	−	0.600957i	0.0653112	−	0.0377074i
$255$	2.70790	−	10.2380i	0.169575	−	0.641127i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−24.3239	−	14.0434i	−1.51728	−	0.876004i	−0.999794	−	0.0203154i	$-0.993533\pi$
$257$	−24.3239	−	14.0434i	−1.51728	−	0.876004i	−0.517490	−	0.855689i	$-0.673134\pi$
$258$	0.986944	−	1.70944i	0.0614444	−	0.106425i
$259$	−5.30842			−0.329849
$260$	−3.19253	+	7.40323i	−0.197992	+	0.459129i
$261$	4.76693			0.295065
$262$	3.32575	−	5.76036i	0.205465	−	0.355876i
$263$	−6.56756	−	3.79178i	−0.404973	−	0.233811i	0.283654	−	0.958927i	$-0.408453\pi$
$263$	−6.56756	−	3.79178i	−0.404973	−	0.233811i	−0.688628	+	0.725115i	$0.741787\pi$
$264$	2.57603	+	4.46182i	0.158544	+	0.274606i
$265$	−9.68546	−	2.56176i	−0.594973	−	0.157368i
$266$	−2.22526	+	1.28475i	−0.136439	+	0.0787732i
$267$	8.19497	+	14.1941i	0.501524	+	0.868665i
$268$	−14.0553			−0.858564
$269$	−12.2355	−	21.1924i	−0.746010	−	1.29213i	−0.949722	−	0.313096i	$-0.898634\pi$
$269$	−12.2355	−	21.1924i	−0.746010	−	1.29213i	0.203712	−	0.979031i	$-0.434699\pi$
$270$	1.57603	−	1.58623i	0.0959142	−	0.0965348i
$271$	10.0199	+	5.78497i	0.608664	+	0.351412i	0.772442	−	0.635085i	$-0.219035\pi$
$271$	10.0199	+	5.78497i	0.608664	+	0.351412i	−0.163779	+	0.986497i	$0.552368\pi$
$272$		−	4.73601i		−	0.287163i
$273$	3.40321	+	2.70821i	0.205972	+	0.163909i
$274$	14.7149			0.888961
$275$	−13.0238	−	22.2256i	−0.785363	−	1.34025i
$276$	1.08711	−	1.88293i	0.0654363	−	0.113339i
$277$	11.2111	−	6.47271i	0.673608	−	0.388908i	−0.123835	−	0.992303i	$-0.539519\pi$
$277$	11.2111	−	6.47271i	0.673608	−	0.388908i	0.797442	+	0.603395i	$0.206186\pi$
$278$	15.6508			0.938673
$279$	−5.11861	+	2.95523i	−0.306443	+	0.176925i
$280$	2.60314	−	0.706513i	0.155567	−	0.0422223i
$281$			2.57187i			0.153425i	0.997053	+	0.0767124i	$0.0244423\pi$
$281$			2.57187i			0.153425i	−0.997053	+	0.0767124i	$0.975558\pi$
$282$	0.738110	−	0.426148i	0.0439538	−	0.0253767i
$283$	4.80517	+	2.77427i	0.285638	+	0.164913i	0.635973	−	0.771711i	$-0.280599\pi$
$283$	4.80517	+	2.77427i	0.285638	+	0.164913i	−0.350335	+	0.936624i	$0.613932\pi$
$284$	0.298707	+	0.172459i	0.0177250	+	0.0102335i
$285$	1.21794	−	4.60474i	0.0721443	−	0.272761i
$286$	2.74961	−	18.3714i	0.162588	−	1.08632i
$287$		−	5.71292i		−	0.337223i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	2.71489	−	4.70233i	0.159700	−	0.276608i
$290$	−10.2870	+	2.79198i	−0.604075	+	0.163951i
$291$			8.48278i			0.497270i
$292$	−7.86142	−	13.6164i	−0.460055	−	0.796838i
$293$	−12.0658	−	20.8986i	−0.704891	−	1.22091i	−0.966731	−	0.255795i	$-0.917663\pi$
$293$	−12.0658	−	20.8986i	−0.704891	−	1.22091i	0.261840	−	0.965111i	$-0.415671\pi$
$294$			5.54490i			0.323385i
$295$	1.13709	+	4.18960i	0.0662042	+	0.243928i
$296$	2.20034	−	3.81110i	0.127892	−	0.221516i
$297$	−2.57603	+	4.46182i	−0.149477	+	0.258901i
$298$		−	22.8116i		−	1.32144i
$299$	−7.29439	+	2.87155i	−0.421845	+	0.166066i
$300$	−2.47202	+	4.34616i	−0.142722	+	0.250926i
$301$	2.06205	+	1.19052i	0.118855	+	0.0686207i
$302$	17.2335	+	9.94975i	0.991675	+	0.572544i
$303$	11.7627	−	6.79121i	0.675751	−	0.390145i
$304$		−	2.13012i		−	0.122171i
$305$	6.63780	−	1.80156i	0.380080	−	0.103157i
$306$	4.10150	−	2.36800i	0.234467	−	0.135370i
$307$	−30.3243			−1.73070			−0.865348	−	0.501171i	$-0.832903\pi$
$307$	−30.3243			−1.73070			−0.865348	+	0.501171i	$0.832903\pi$
$308$	−5.38217	+	3.10740i	−0.306678	+	0.177061i
$309$	−1.07848	+	1.86798i	−0.0613525	+	0.106266i
$310$	9.31508	−	9.37535i	0.529061	−	0.532484i
$311$	8.76406			0.496964			0.248482	−	0.968636i	$-0.420068\pi$
$311$	8.76406			0.496964			0.248482	+	0.968636i	$0.420068\pi$
$312$	−3.35495	+	1.32073i	−0.189937	+	0.0747715i
$313$		−	29.0155i		−	1.64005i	−0.572326	−	0.820026i	$-0.693959\pi$
$313$		−	29.0155i		−	1.64005i	0.572326	−	0.820026i	$-0.306041\pi$
$314$	4.10836	+	2.37196i	0.231848	+	0.133857i
$315$	1.91343	+	1.90113i	0.107809	+	0.107116i
$316$	6.79315	+	11.7661i	0.382145	+	0.661894i
$317$	25.9970			1.46014			0.730068	−	0.683375i	$-0.239489\pi$
$317$	25.9970			1.46014			0.730068	+	0.683375i	$0.239489\pi$
$318$	−2.24021	−	3.88016i	−0.125625	−	0.217588i
$319$	21.2692	−	12.2798i	1.19084	−	0.687534i
$320$	−0.571769	+	2.16173i	−0.0319629	+	0.120844i
$321$	4.04699	+	7.00959i	0.225881	+	0.391237i
$322$	2.27133	+	1.31135i	0.126576	+	0.0730787i
$323$	5.04413	−	8.73669i	0.280663	−	0.486122i
$324$	1.00000			0.0555556
$325$	16.7318	−	6.71169i	0.928113	−	0.372297i
$326$	−3.86657			−0.214150
$327$	8.44195	−	14.6219i	0.466841	−	0.808592i
$328$	4.10150	+	2.36800i	0.226468	+	0.130751i
$329$	0.514051	+	0.890362i	0.0283405	+	0.0490873i
$330$	2.94579	−	11.1374i	0.162160	−	0.613092i
$331$	−9.56025	+	5.51961i	−0.525479	+	0.303385i	−0.739173	−	0.673515i	$-0.764784\pi$
$331$	−9.56025	+	5.51961i	−0.525479	+	0.303385i	0.213694	+	0.976901i	$0.431450\pi$
$332$	−5.10226	−	8.83737i	−0.280023	−	0.485014i
$333$	4.40068			0.241156
$334$	−11.3614	−	19.6785i	−0.621669	−	1.07676i
$335$	22.2949	+	22.1516i	1.21810	+	1.21027i
$336$	1.04466	+	0.603137i	0.0569911	+	0.0329038i
$337$			17.7108i			0.964769i	0.875960	+	0.482384i	$0.160229\pi$
$337$			17.7108i			0.964769i	−0.875960	+	0.482384i	$0.839771\pi$
$338$	12.4303	+	3.80611i	0.676122	+	0.207025i
$339$	4.95102			0.268902
$340$	−7.46410	+	7.51240i	−0.404798	+	0.407417i
$341$	−15.2255	+	26.3714i	−0.824509	+	1.42809i
$342$	1.84474	−	1.06506i	0.0997519	−	0.0575918i
$343$	−15.1326			−0.817083
$344$	−1.70944	+	0.986944i	−0.0921667	+	0.0532124i
$345$	−4.69196	+	1.27344i	−0.252607	+	0.0685595i
$346$		−	4.69800i		−	0.252566i
$347$	30.0526	−	17.3509i	1.61331	−	0.931443i	0.624710	−	0.780857i	$-0.285217\pi$
$347$	30.0526	−	17.3509i	1.61331	−	0.931443i	0.988597	−	0.150587i	$-0.0481162\pi$
$348$	−4.12828	−	2.38346i	−0.221299	−	0.127767i
$349$	−30.4563	−	17.5840i	−1.63029	−	0.941249i	−0.984002	−	0.178156i	$-0.942987\pi$
$349$	−30.4563	−	17.5840i	−1.63029	−	0.941249i	−0.646288	−	0.763093i	$-0.723680\pi$
$350$	−5.24266	−	2.98193i	−0.280232	−	0.159391i
$351$	−2.82126	−	2.24511i	−0.150588	−	0.119835i
$352$		−	5.15206i		−	0.274606i
$353$	−5.54542	+	9.60495i	−0.295153	+	0.511220i	−0.975020	−	0.222115i	$-0.928704\pi$
$353$	−5.54542	+	9.60495i	−0.295153	+	0.511220i	0.679868	+	0.733335i	$0.262037\pi$
$354$	−0.970715	+	1.68133i	−0.0515929	+	0.0893616i
$355$	−0.202018	−	0.744332i	−0.0107220	−	0.0395050i
$356$		−	16.3899i		−	0.868665i
$357$	2.85646	+	4.94754i	0.151180	+	0.261851i
$358$	−4.34913	−	7.53292i	−0.229859	−	0.398127i
$359$			26.1575i			1.38054i	0.723552	+	0.690270i	$0.242508\pi$
$359$			26.1575i			1.38054i	−0.723552	+	0.690270i	$0.757492\pi$
$360$	−2.15800	+	0.585699i	−0.113736	+	0.0308690i
$361$	−7.23130	+	12.5250i	−0.380595	+	0.659209i
$362$	−4.87740	+	8.44791i	−0.256351	+	0.444012i
$363$			15.5438i			0.815836i
$364$	−1.59316	−	4.04699i	−0.0835042	−	0.212120i
$365$	−8.98983	+	33.9885i	−0.470549	+	1.77904i
$366$	2.66381	+	1.53795i	0.139240	+	0.0803901i
$367$	13.4988	+	7.79352i	0.704630	+	0.406818i	0.809070	−	0.587713i	$-0.199972\pi$
$367$	13.4988	+	7.79352i	0.704630	+	0.406818i	−0.104440	+	0.994531i	$0.533305\pi$
$368$	−1.88293	+	1.08711i	−0.0981544	+	0.0566695i
$369$			4.73601i			0.246547i
$370$	−9.49666	+	2.57747i	−0.493708	+	0.133996i
$371$	4.68053	−	2.70231i	0.243001	−	0.140297i
$372$	5.91046			0.306443
$373$	0.860358	−	0.496728i	0.0445476	−	0.0257196i	−0.477561	−	0.878599i	$-0.658479\pi$
$373$	0.860358	−	0.496728i	0.0445476	−	0.0257196i	0.522108	+	0.852879i	$0.325146\pi$
$374$	12.2001	−	21.1312i	0.630853	−	1.09267i
$375$	10.7709	−	2.99802i	0.556206	−	0.154817i
$376$	−0.852296			−0.0439538
$377$	6.29581	+	15.9928i	0.324251	+	0.823671i
$378$			1.20627i			0.0620440i
$379$	23.7856	+	13.7326i	1.22178	+	0.705398i	0.965298	−	0.261150i	$-0.0841018\pi$
$379$	23.7856	+	13.7326i	1.22178	+	0.705398i	0.256486	+	0.966548i	$0.417435\pi$
$380$	−3.35713	+	3.37886i	−0.172217	+	0.173332i
$381$	−0.600957	−	1.04089i	−0.0307880	−	0.0533263i
$382$	11.5546			0.591184
$383$	−16.2851	−	28.2067i	−0.832132	−	1.44130i	−0.896344	−	0.443359i	$-0.853787\pi$
$383$	−16.2851	−	28.2067i	−0.832132	−	1.44130i	0.0642122	−	0.997936i	$-0.479547\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$	13.4347	+	3.55343i	0.684697	+	0.181100i
$386$	5.23154	+	9.06130i	0.266279	+	0.461208i
$387$	−1.70944	−	0.986944i	−0.0868956	−	0.0501692i
$388$	4.24139	−	7.34631i	0.215324	−	0.372952i
$389$	−16.9110			−0.857421			−0.428710	−	0.903442i	$-0.641032\pi$
$389$	−16.9110			−0.857421			−0.428710	+	0.903442i	$0.641032\pi$
$390$	7.40323	+	3.19253i	0.374877	+	0.161660i
$391$	−10.2971			−0.520747
$392$	2.77245	−	4.80203i	0.140030	−	0.242539i
$393$	−5.76036	−	3.32575i	−0.290572	−	0.167762i
$394$	−8.79472	−	15.2329i	−0.443072	−	0.767423i
$395$	7.76823	−	29.3699i	0.390862	−	1.47776i
$396$	4.46182	−	2.57603i	0.224215	−	0.129450i
$397$	16.1198	+	27.9204i	0.809031	+	1.40128i	0.913536	+	0.406759i	$0.133341\pi$
$397$	16.1198	+	27.9204i	0.809031	+	1.40128i	−0.104504	+	0.994524i	$0.533326\pi$
$398$	−25.5716			−1.28179
$399$	1.28475	+	2.22526i	0.0643181	+	0.111402i
$400$	4.31391	−	2.52788i	0.215696	−	0.126394i
$401$	28.0082	+	16.1705i	1.39866	+	0.807518i	0.994253	−	0.107060i	$-0.0341437\pi$
$401$	28.0082	+	16.1705i	1.39866	+	0.807518i	0.404410	+	0.914578i	$0.367477\pi$
$402$			14.0553i			0.701015i
$403$	−16.6749	−	13.2696i	−0.830638	−	0.661007i
$404$	−13.5824			−0.675751
$405$	−1.58623	−	1.57603i	−0.0788204	−	0.0783137i
$406$	2.87511	−	4.97984i	0.142689	−	0.247145i
$407$	19.6350	−	11.3363i	0.973272	−	0.561919i
$408$	−4.73601			−0.234467
$409$	1.00971	−	0.582957i	0.0499270	−	0.0288254i	−0.474829	−	0.880078i	$-0.657490\pi$
$409$	1.00971	−	0.582957i	0.0499270	−	0.0288254i	0.524756	+	0.851253i	$0.324157\pi$
$410$	−2.77388	−	10.2203i	−0.136992	−	0.504745i
$411$		−	14.7149i		−	0.725833i
$412$	1.86798	−	1.07848i	0.0920288	−	0.0531328i
$413$	−2.02814	−	1.17095i	−0.0997984	−	0.0576186i
$414$	−1.88293	−	1.08711i	−0.0925408	−	0.0534285i
$415$	−5.83462	+	22.0594i	−0.286410	+	1.08285i
$416$	3.56583	+	0.533691i	0.174829	+	0.0261663i
$417$		−	15.6508i		−	0.766423i
$418$	5.48725	−	9.50420i	0.268390	−	0.464866i
$419$	5.91396	−	10.2433i	0.288916	−	0.500417i	−0.684635	−	0.728886i	$-0.740039\pi$
$419$	5.91396	−	10.2433i	0.288916	−	0.500417i	0.973551	+	0.228469i	$0.0733719\pi$
$420$	−0.706513	−	2.60314i	−0.0344743	−	0.127020i
$421$		−	23.9102i		−	1.16531i	−0.812719	−	0.582655i	$-0.802014\pi$
$421$		−	23.9102i		−	1.16531i	0.812719	−	0.582655i	$-0.197986\pi$
$422$	−6.45984	−	11.1888i	−0.314460	−	0.544661i
$423$	−0.426148	−	0.738110i	−0.0207200	−	0.0358881i
$424$			4.48042i			0.217588i
$425$	23.6796	−	0.152724i	1.14863	−	0.00740819i
$426$	0.172459	−	0.298707i	0.00835566	−	0.0144724i
$427$	−1.85519	+	3.21329i	−0.0897791	+	0.155502i
$428$		−	8.09397i		−	0.391237i
$429$	−18.3714	−	2.74961i	−0.886980	−	0.132752i
$430$	4.26701	+	1.12861i	0.205774	+	0.0544263i
$431$	−22.8082	−	13.1683i	−1.09863	−	0.634294i	−0.162769	−	0.986664i	$-0.552043\pi$
$431$	−22.8082	−	13.1683i	−1.09863	−	0.634294i	−0.935861	+	0.352370i	$0.885376\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	11.2232	−	6.47972i	0.539353	−	0.311396i	−0.205464	−	0.978665i	$-0.565870\pi$
$433$	11.2232	−	6.47972i	0.539353	−	0.311396i	0.744817	+	0.667269i	$0.232537\pi$
$434$			7.12964i			0.342234i
$435$	2.79198	+	10.2870i	0.133865	+	0.493225i
$436$	−14.6219	+	8.44195i	−0.700261	+	0.404296i
$437$	−4.63134			−0.221547
$438$	−13.6164	+	7.86142i	−0.650615	+	0.375633i
$439$	11.6234	−	20.1324i	0.554756	−	0.960865i	−0.443167	−	0.896439i	$-0.646145\pi$
$439$	11.6234	−	20.1324i	0.554756	−	0.960865i	0.997922	−	0.0644259i	$-0.0205216\pi$
$440$	−8.11982	+	8.17235i	−0.387097	+	0.389602i
$441$	5.54490			0.264043
$442$	13.3615	+	10.6328i	0.635542	+	0.505753i
$443$		−	23.3728i		−	1.11047i	−0.831692	−	0.555237i	$-0.812627\pi$
$443$		−	23.3728i		−	1.11047i	0.831692	−	0.555237i	$-0.187373\pi$
$444$	−3.81110	−	2.20034i	−0.180867	−	0.104423i
$445$	−25.8311	+	25.9982i	−1.22451	+	1.23243i
$446$	−3.57679	−	6.19518i	−0.169366	−	0.293350i
$447$	−22.8116			−1.07895
$448$	−0.603137	−	1.04466i	−0.0284955	−	0.0493557i
$449$	1.20931	−	0.698196i	0.0570709	−	0.0329499i	−0.471193	−	0.882030i	$-0.656176\pi$
$449$	1.20931	−	0.698196i	0.0570709	−	0.0329499i	0.528264	+	0.849080i	$0.322843\pi$
$450$	4.34616	+	2.47202i	0.204880	+	0.116532i
$451$	12.2001	+	21.1312i	0.574481	+	0.995030i
$452$	−4.28771	−	2.47551i	−0.201677	−	0.116438i
$453$	9.94975	−	17.2335i	0.467480	−	0.809699i
$454$	−25.8385			−1.21266
$455$	−3.85106	+	8.93032i	−0.180541	+	0.418660i
$456$	−2.13012			−0.0997519
$457$	3.60093	−	6.23699i	0.168444	−	0.291754i	−0.769429	−	0.638733i	$-0.779459\pi$
$457$	3.60093	−	6.23699i	0.168444	−	0.291754i	0.937873	+	0.346979i	$0.112792\pi$
$458$	7.75225	+	4.47576i	0.362239	+	0.209139i
$459$	−2.36800	−	4.10150i	−0.110529	−	0.191442i
$460$	4.70007	+	1.24315i	0.219142	+	0.0579622i
$461$	−4.10920	+	2.37245i	−0.191384	+	0.110496i	−0.592630	−	0.805474i	$-0.701911\pi$
$461$	−4.10920	+	2.37245i	−0.191384	+	0.110496i	0.401246	+	0.915970i	$0.368577\pi$
$462$	3.10740	+	5.38217i	0.144569	+	0.250401i
$463$	15.7510			0.732012			0.366006	−	0.930612i	$-0.380725\pi$
$463$	15.7510			0.732012			0.366006	+	0.930612i	$0.380725\pi$
$464$	2.38346	+	4.12828i	0.110650	+	0.191651i
$465$	−9.37535	−	9.31508i	−0.434772	−	0.431976i
$466$	−3.34855	−	1.93329i	−0.155119	−	0.0895578i
$467$			17.9789i			0.831962i	0.909373	+	0.415981i	$0.136562\pi$
$467$			17.9789i			0.831962i	−0.909373	+	0.415981i	$0.863438\pi$
$468$	1.32073	+	3.35495i	0.0610506	+	0.155083i
$469$	−16.9545			−0.782888
$470$	1.35194	+	1.34324i	0.0623602	+	0.0619593i
$471$	2.37196	−	4.10836i	0.109294	−	0.189303i
$472$	1.68133	−	0.970715i	0.0773894	−	0.0446808i
$473$	−10.1696			−0.467598
$474$	11.7661	−	6.79315i	0.540434	−	0.312020i
$475$	10.6504	−	0.0686907i	0.488672	−	0.00315174i
$476$		−	5.71292i		−	0.261851i
$477$	−3.88016	+	2.24021i	−0.177660	+	0.102572i
$478$	−13.3521	−	7.70884i	−0.610711	−	0.352594i
$479$	2.83964	+	1.63947i	0.129747	+	0.0749093i	0.563468	−	0.826138i	$-0.309467\pi$
$479$	2.83964	+	1.63947i	0.129747	+	0.0749093i	−0.433722	+	0.901047i	$0.642800\pi$
$480$	2.16173	+	0.571769i	0.0986691	+	0.0260976i
$481$	5.81210	+	14.7640i	0.265009	+	0.673183i
$482$			11.2768i			0.513646i
$483$	1.31135	−	2.27133i	0.0596685	−	0.103349i
$484$	7.77188	−	13.4613i	0.353267	−	0.611877i
$485$	−18.3058	+	4.96836i	−0.831225	+	0.225601i
$486$		−	1.00000i		−	0.0453609i
$487$	−4.98852	−	8.64037i	−0.226052	−	0.391533i	0.730583	−	0.682824i	$-0.239248\pi$
$487$	−4.98852	−	8.64037i	−0.226052	−	0.391533i	−0.956634	+	0.291291i	$0.905915\pi$
$488$	−1.53795	−	2.66381i	−0.0696199	−	0.120585i
$489$			3.86657i			0.174852i
$490$	−11.9659	+	3.24764i	−0.540564	+	0.146714i
$491$	10.0376	−	17.3857i	0.452992	−	0.784605i	−0.545578	−	0.838060i	$-0.683690\pi$
$491$	10.0376	−	17.3857i	0.452992	−	0.784605i	0.998570	+	0.0534548i	$0.0170233\pi$
$492$	2.36800	−	4.10150i	0.106758	−	0.184910i
$493$			22.5762i			1.01678i
$494$	6.00961	+	4.78234i	0.270385	+	0.215168i
$495$	−11.1374	−	2.94579i	−0.500588	−	0.132403i
$496$	−5.11861	−	2.95523i	−0.229832	−	0.132694i
$497$	0.360323	+	0.208033i	0.0161627	+	0.00933153i
$498$	−8.83737	+	5.10226i	−0.396012	+	0.228638i
$499$			23.9474i			1.07203i	0.844208	+	0.536016i	$0.180071\pi$
$499$			23.9474i			1.07203i	−0.844208	+	0.536016i	$0.819929\pi$
$500$	−10.8269	−	2.78907i	−0.484192	−	0.124731i
$501$	−19.6785	+	11.3614i	−0.879173	+	0.507591i
$502$	−12.3066			−0.549269
$503$	10.5377	−	6.08395i	0.469853	−	0.271270i	−0.246325	−	0.969187i	$-0.579223\pi$
$503$	10.5377	−	6.08395i	0.469853	−	0.271270i	0.716178	+	0.697917i	$0.245890\pi$
$504$	0.603137	−	1.04466i	0.0268659	−	0.0465330i
$505$	21.5448	+	21.4063i	0.958733	+	0.952570i
$506$	−11.2017			−0.497977
$507$	3.80611	−	12.4303i	0.169035	−	0.552051i
$508$			1.20191i			0.0533263i
$509$	34.9666	+	20.1880i	1.54987	+	0.894817i	0.998151	+	0.0607857i	$0.0193606\pi$
$509$	34.9666	+	20.1880i	1.54987	+	0.894817i	0.551717	+	0.834031i	$0.313973\pi$
$510$	7.51240	+	7.46410i	0.332655	+	0.330516i
$511$	−9.48302	−	16.4251i	−0.419504	−	0.726602i
$512$	1.00000			0.0441942
$513$	−1.06506	−	1.84474i	−0.0470235	−	0.0814471i
$514$	24.3239	−	14.0434i	1.07288	−	0.619429i
$515$	−4.66276	−	1.23328i	−0.205466	−	0.0543449i
$516$	0.986944	+	1.70944i	0.0434478	+	0.0752538i
$517$	−3.80279	−	2.19554i	−0.167246	−	0.0965598i
$518$	2.65421	−	4.59723i	0.116619	−	0.201991i
$519$	−4.69800			−0.206219
$520$	−4.81512	−	6.46642i	−0.211157	−	0.283571i
$521$	−0.259356			−0.0113626			−0.00568129	−	0.999984i	$-0.501808\pi$
$521$	−0.259356			−0.0113626			−0.00568129	+	0.999984i	$0.501808\pi$
$522$	−2.38346	+	4.12828i	−0.104321	+	0.180690i
$523$	−33.4527	−	19.3139i	−1.46278	−	0.844539i	−0.463645	−	0.886021i	$-0.653459\pi$
$523$	−33.4527	−	19.3139i	−1.46278	−	0.844539i	−0.999139	+	0.0414825i	$0.986792\pi$
$524$	3.32575	+	5.76036i	0.145286	+	0.251642i
$525$	−2.98193	+	5.24266i	−0.130142	+	0.228808i
$526$	6.56756	−	3.79178i	0.286359	−	0.165330i
$527$	−13.9960	−	24.2418i	−0.609676	−	1.05599i
$528$	−5.15206			−0.224215
$529$	−9.13639	−	15.8247i	−0.397234	−	0.688030i
$530$	7.06128	−	7.10697i	0.306723	−	0.308707i
$531$	1.68133	+	0.970715i	0.0729634	+	0.0421255i
$532$		−	2.56951i		−	0.111402i
$533$	−15.8891	+	6.25498i	−0.688232	+	0.270933i
$534$	−16.3899			−0.709262
$535$	−12.7564	+	12.8389i	−0.551506	+	0.555074i
$536$	7.02765	−	12.1723i	0.303548	−	0.525761i
$537$	−7.53292	+	4.34913i	−0.325069	+	0.187679i
$538$	24.4709			1.05502
$539$	24.7403	−	14.2838i	1.06564	−	0.615249i
$540$	0.585699	+	2.15800i	0.0252045	+	0.0928655i
$541$			19.4443i			0.835975i	0.908453	+	0.417988i	$0.137264\pi$
$541$			19.4443i			0.835975i	−0.908453	+	0.417988i	$0.862736\pi$
$542$	−10.0199	+	5.78497i	−0.430390	+	0.248486i
$543$	8.44791	+	4.87740i	0.362534	+	0.209309i
$544$	4.10150	+	2.36800i	0.175851	+	0.101527i
$545$	36.4984	+	9.65369i	1.56342	+	0.413518i
$546$	−4.04699	+	1.59316i	−0.173195	+	0.0681809i
$547$			25.2121i			1.07799i	0.842308	+	0.538997i	$0.181197\pi$
$547$			25.2121i			1.07799i	−0.842308	+	0.538997i	$0.818803\pi$
$548$	−7.35746	+	12.7435i	−0.314295	+	0.544375i
$549$	1.53795	−	2.66381i	0.0656383	−	0.113689i
$550$	25.7598	−	0.166140i	1.09840	−	0.00708425i
$551$			10.1541i			0.432580i
$552$	1.08711	+	1.88293i	0.0462704	+	0.0801427i
$553$	8.19440	+	14.1931i	0.348462	+	0.603553i
$554$			12.9454i			0.549998i
$555$	2.57747	+	9.49666i	0.109408	+	0.403111i
$556$	−7.82540	+	13.5540i	−0.331871	+	0.574817i
$557$	5.63445	−	9.75916i	0.238739	−	0.413509i	−0.721613	−	0.692296i	$-0.756599\pi$
$557$	5.63445	−	9.75916i	0.238739	−	0.413509i	0.960353	+	0.278787i	$0.0899325\pi$
$558$		−	5.91046i		−	0.250210i
$559$	1.05345	−	7.03856i	0.0445560	−	0.297699i
$560$	−0.689710	+	2.60764i	−0.0291456	+	0.110193i
$561$	−21.1312	−	12.2001i	−0.892160	−	0.515089i
$562$	−2.22730	−	1.28593i	−0.0939531	−	0.0542439i
$563$	−14.2495	+	8.22694i	−0.600544	+	0.346724i	−0.769256	−	0.638941i	$-0.779373\pi$
$563$	−14.2495	+	8.22694i	−0.600544	+	0.346724i	0.168712	+	0.985665i	$0.446039\pi$
$564$			0.852296i			0.0358881i
$565$	2.89981	+	10.6843i	0.121996	+	0.449491i
$566$	−4.80517	+	2.77427i	−0.201976	+	0.116611i
$567$	1.20627			0.0506587
$568$	−0.298707	+	0.172459i	−0.0125335	+	0.00723621i
$569$	15.2444	−	26.4040i	0.639077	−	1.10691i	−0.346558	−	0.938028i	$-0.612650\pi$
$569$	15.2444	−	26.4040i	0.639077	−	1.10691i	0.985636	−	0.168886i	$-0.0540170\pi$
$570$	3.37886	+	3.35713i	0.141525	+	0.140615i
$571$	13.0909			0.547836			0.273918	−	0.961753i	$-0.411680\pi$
$571$	13.0909			0.547836			0.273918	+	0.961753i	$0.411680\pi$
$572$	14.5353	+	11.5669i	0.607751	+	0.483638i
$573$		−	11.5546i		−	0.482699i
$574$	4.94754	+	2.85646i	0.206506	+	0.119226i
$575$	−5.49615	−	9.37939i	−0.229205	−	0.391147i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	13.1315			0.546670			0.273335	−	0.961919i	$-0.411873\pi$
$577$	13.1315			0.546670			0.273335	+	0.961919i	$0.411873\pi$
$578$	2.71489	+	4.70233i	0.112925	+	0.195591i
$579$	9.06130	−	5.23154i	0.376575	−	0.217416i
$580$	2.72558	−	10.3048i	0.113174	−	0.427884i
$581$	−6.15472	−	10.6603i	−0.255341	−	0.442263i
$582$	−7.34631	−	4.24139i	−0.304514	−	0.175811i
$583$	−11.5417	+	19.9908i	−0.478009	+	0.827935i
$584$	15.7228			0.650615
$585$	3.19253	−	7.40323i	0.131995	−	0.306086i
$586$	24.1316			0.996866
$587$	−3.03785	+	5.26171i	−0.125386	+	0.217174i	−0.921884	−	0.387467i	$-0.873350\pi$
$587$	−3.03785	+	5.26171i	−0.125386	+	0.217174i	0.796498	+	0.604641i	$0.206683\pi$
$588$	−4.80203	−	2.77245i	−0.198032	−	0.114334i
$589$	−6.29499	−	10.9032i	−0.259381	−	0.449260i
$590$	−4.19685	−	1.11005i	−0.172782	−	0.0457000i
$591$	−15.2329	+	8.79472i	−0.626598	+	0.361767i
$592$	2.20034	+	3.81110i	0.0904334	+	0.156635i
$593$	−18.3609			−0.753990			−0.376995	−	0.926215i	$-0.623043\pi$
$593$	−18.3609			−0.753990			−0.376995	+	0.926215i	$0.623043\pi$
$594$	−2.57603	−	4.46182i	−0.105696	−	0.183071i
$595$	−9.00375	+	9.06201i	−0.369118	+	0.371506i
$596$	19.7555	+	11.4058i	0.809215	+	0.467200i
$597$			25.5716i			1.04658i
$598$	1.16036	−	7.75290i	0.0474507	−	0.317040i
$599$	22.1098			0.903382			0.451691	−	0.892174i	$-0.350821\pi$
$599$	22.1098			0.903382			0.451691	+	0.892174i	$0.350821\pi$
$600$	−2.52788	−	4.31391i	−0.103200	−	0.176115i
$601$	−5.90349	+	10.2251i	−0.240808	+	0.417092i	−0.960945	−	0.276740i	$-0.910746\pi$
$601$	−5.90349	+	10.2251i	−0.240808	+	0.417092i	0.720136	+	0.693832i	$0.244079\pi$
$602$	−2.06205	+	1.19052i	−0.0840428	+	0.0485222i
$603$	14.0553			0.572376
$604$	−17.2335	+	9.94975i	−0.701220	+	0.404850i
$605$	−33.5434	+	9.10397i	−1.36373	+	0.370129i
$606$			13.5824i			0.551748i
$607$	−22.3119	+	12.8818i	−0.905612	+	0.522856i	−0.879017	−	0.476791i	$-0.841800\pi$
$607$	−22.3119	+	12.8818i	−0.905612	+	0.522856i	−0.0265955	+	0.999646i	$0.508467\pi$
$608$	1.84474	+	1.06506i	0.0748139	+	0.0431938i
$609$	−4.97984	−	2.87511i	−0.201793	−	0.116505i
$610$	−1.75871	+	6.64928i	−0.0712080	+	0.269222i
$611$	1.91349	−	2.40455i	0.0774117	−	0.0972775i
$612$			4.73601i			0.191442i
$613$	−6.54178	+	11.3307i	−0.264220	+	0.457642i	−0.967359	−	0.253410i	$-0.918448\pi$
$613$	−6.54178	+	11.3307i	−0.264220	+	0.457642i	0.703139	+	0.711052i	$0.251781\pi$
$614$	15.1621	−	26.2616i	0.611894	−	1.05983i
$615$	−10.2203	+	2.77388i	−0.412122	+	0.111853i
$616$		−	6.21480i		−	0.250401i
$617$	2.20914	+	3.82634i	0.0889366	+	0.154043i	0.907062	−	0.420997i	$-0.138320\pi$
$617$	2.20914	+	3.82634i	0.0889366	+	0.154043i	−0.818125	+	0.575040i	$0.804986\pi$
$618$	−1.07848	−	1.86798i	−0.0433828	−	0.0751412i
$619$		−	1.12760i		−	0.0453220i	−0.999743	−	0.0226610i	$-0.992786\pi$
$619$		−	1.12760i		−	0.0453220i	0.999743	−	0.0226610i	$-0.00721383\pi$
$620$	3.46175	+	12.7548i	0.139027	+	0.512244i
$621$	−1.08711	+	1.88293i	−0.0436242	+	0.0755593i
$622$	−4.38203	+	7.58990i	−0.175703	+	0.304327i
$623$		−	19.7708i		−	0.792099i
$624$	0.533691	−	3.56583i	0.0213647	−	0.142748i
$625$	12.7782	+	21.4876i	0.511129	+	0.859504i
$626$	25.1282	+	14.5077i	1.00432	+	0.579846i
$627$	−9.50420	−	5.48725i	−0.379561	−	0.219140i
$628$	−4.10836	+	2.37196i	−0.163941	+	0.0946515i
$629$			20.8417i			0.831011i
$630$	−2.60314	+	0.706513i	−0.103711	+	0.0281482i
$631$	−14.3916	+	8.30898i	−0.572920	+	0.330775i	−0.758315	−	0.651889i	$-0.773977\pi$
$631$	−14.3916	+	8.30898i	−0.572920	+	0.330775i	0.185395	+	0.982664i	$0.440644\pi$
$632$	−13.5863			−0.540434
$633$	−11.1888	+	6.45984i	−0.444714	+	0.256756i
$634$	−12.9985	+	22.5140i	−0.516236	+	0.894147i
$635$	1.89426	−	1.90651i	0.0751712	−	0.0756576i
$636$	4.48042			0.177660
$637$	7.32331	+	18.6029i	0.290160	+	0.737072i
$638$			24.5595i			0.972320i
$639$	−0.298707	−	0.172459i	−0.0118167	−	0.00682236i
$640$	−1.58623	−	1.57603i	−0.0627012	−	0.0622981i
$641$	5.05184	+	8.75005i	0.199536	+	0.345606i	0.948378	−	0.317142i	$-0.102723\pi$
$641$	5.05184	+	8.75005i	0.199536	+	0.345606i	−0.748842	+	0.662748i	$0.769390\pi$
$642$	−8.09397			−0.319444
$643$	17.5208	+	30.3469i	0.690951	+	1.19676i	0.971526	+	0.236931i	$0.0761415\pi$
$643$	17.5208	+	30.3469i	0.690951	+	1.19676i	−0.280575	+	0.959832i	$0.590525\pi$
$644$	−2.27133	+	1.31135i	−0.0895028	+	0.0516745i
$645$	1.12861	−	4.26701i	0.0444389	−	0.168014i
$646$	5.04413	+	8.73669i	0.198459	+	0.343740i
$647$	17.2864	+	9.98031i	0.679598	+	0.392366i	0.799704	−	0.600395i	$-0.204990\pi$
$647$	17.2864	+	9.98031i	0.679598	+	0.392366i	−0.120105	+	0.992761i	$0.538323\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	10.0024			0.392628
$650$	−2.55341	+	17.8460i	−0.100153	+	0.699978i
$651$	7.12964			0.279433
$652$	1.93329	−	3.34855i	0.0757133	−	0.131139i
$653$	−4.51410	−	2.60621i	−0.176650	−	0.101989i	0.409068	−	0.912504i	$-0.365854\pi$
$653$	−4.51410	−	2.60621i	−0.176650	−	0.101989i	−0.585718	+	0.810515i	$0.699187\pi$
$654$	8.44195	+	14.6219i	0.330106	+	0.571761i
$655$	3.80312	−	14.3787i	0.148600	−	0.561824i
$656$	−4.10150	+	2.36800i	−0.160137	+	0.0924551i
$657$	7.86142	+	13.6164i	0.306703	+	0.531225i
$658$	−1.02810			−0.0400796
$659$	3.66183	+	6.34248i	0.142645	+	0.247068i	0.928492	−	0.371353i	$-0.121106\pi$
$659$	3.66183	+	6.34248i	0.142645	+	0.247068i	−0.785847	+	0.618421i	$0.787773\pi$
$660$	8.17235	+	8.11982i	0.318108	+	0.316063i
$661$	−31.7189	−	18.3129i	−1.23372	−	0.712289i	−0.265917	−	0.963996i	$-0.585675\pi$
$661$	−31.7189	−	18.3129i	−1.23372	−	0.712289i	−0.967803	+	0.251707i	$0.919008\pi$
$662$		−	11.0392i		−	0.429052i
$663$	10.6328	−	13.3615i	0.412946	−	0.518918i
$664$	10.2045			0.396012
$665$	−4.04962	+	4.07583i	−0.157038	+	0.158054i
$666$	−2.20034	+	3.81110i	−0.0852614	+	0.147677i
$667$	8.97578	−	5.18217i	0.347543	−	0.200654i
$668$	22.7228			0.879173
$669$	−6.19518	+	3.57679i	−0.239519	+	0.138287i
$670$	−30.3313	+	8.23218i	−1.17180	+	0.318037i
$671$		−	15.8473i		−	0.611777i
$672$	−1.04466	+	0.603137i	−0.0402988	+	0.0232665i
$673$	−29.4292	−	16.9909i	−1.13441	−	0.654952i	−0.189370	−	0.981906i	$-0.560645\pi$
$673$	−29.4292	−	16.9909i	−1.13441	−	0.654952i	−0.945041	+	0.326953i	$0.893978\pi$
$674$	−15.3380	−	8.85540i	−0.590798	−	0.341097i
$675$	2.47202	−	4.34616i	0.0951481	−	0.167284i
$676$	−9.51136	+	8.86194i	−0.365822	+	0.340844i
$677$		−	41.7902i		−	1.60613i	−0.595894	−	0.803063i	$-0.703202\pi$
$677$		−	41.7902i		−	1.60613i	0.595894	−	0.803063i	$-0.296798\pi$
$678$	−2.47551	+	4.28771i	−0.0950713	+	0.164668i
$679$	5.11628	−	8.86166i	0.196345	−	0.340079i
$680$	−2.77388	−	10.2203i	−0.106373	−	0.391931i
$681$			25.8385i			0.990132i
$682$	−15.2255	−	26.3714i	−0.583016	−	1.00981i
$683$	−24.2071	−	41.9280i	−0.926260	−	1.60433i	−0.789523	−	0.613721i	$-0.789672\pi$
$683$	−24.2071	−	41.9280i	−0.926260	−	1.60433i	−0.136737	−	0.990607i	$-0.543662\pi$
$684$			2.13012i			0.0814471i
$685$	31.7548	−	8.61851i	1.21329	−	0.329296i
$686$	7.56629	−	13.1052i	0.288882	−	0.500359i
$687$	4.47576	−	7.75225i	0.170761	−	0.295767i
$688$		−	1.97389i		−	0.0752538i
$689$	−12.6404	−	10.0590i	−0.481562	−	0.383218i
$690$	1.24315	−	4.70007i	0.0473259	−	0.178929i
$691$	−23.8905	−	13.7932i	−0.908837	−	0.524717i	−0.0287804	−	0.999586i	$-0.509162\pi$
$691$	−23.8905	−	13.7932i	−0.908837	−	0.524717i	−0.880057	+	0.474868i	$0.842496\pi$
$692$	4.06859	+	2.34900i	0.154664	+	0.0892955i
$693$	5.38217	−	3.10740i	0.204452	−	0.118040i
$694$			34.7017i			1.31726i
$695$	33.7744	−	9.16666i	1.28114	−	0.347711i
$696$	4.12828	−	2.38346i	0.156482	−	0.0903449i
$697$	−22.4298			−0.849589
$698$	30.4563	−	17.5840i	1.15279	−	0.665563i
$699$	−1.93329	+	3.34855i	−0.0731236	+	0.126654i
$700$	5.20376	−	3.04931i	0.196684	−	0.115253i
$701$	−19.7883			−0.747392			−0.373696	−	0.927551i	$-0.621910\pi$
$701$	−19.7883			−0.747392			−0.373696	+	0.927551i	$0.621910\pi$
$702$	3.35495	−	1.32073i	0.126624	−	0.0498476i
$703$			9.37396i			0.353546i
$704$	4.46182	+	2.57603i	0.168161	+	0.0970879i
$705$	1.34324	−	1.35194i	0.0505895	−	0.0509169i
$706$	−5.54542	−	9.60495i	−0.208705	−	0.361487i
$707$	−16.3841			−0.616189
$708$	−0.970715	−	1.68133i	−0.0364817	−	0.0631882i
$709$	−6.09389	+	3.51831i	−0.228861	+	0.132133i	−0.610046	−	0.792366i	$-0.708849\pi$
$709$	−6.09389	+	3.51831i	−0.228861	+	0.132133i	0.381186	+	0.924499i	$0.375516\pi$
$710$	0.745619	+	0.197213i	0.0279826	+	0.00740128i
$711$	−6.79315	−	11.7661i	−0.254763	−	0.441263i
$712$	14.1941	+	8.19497i	0.531946	+	0.307119i
$713$	−6.42532	+	11.1290i	−0.240630	+	0.416783i
$714$	−5.71292			−0.213801
$715$	−4.82646	−	41.2559i	−0.180499	−	1.54288i
$716$	8.69827			0.325069
$717$	−7.70884	+	13.3521i	−0.287892	+	0.498643i
$718$	−22.6531	−	13.0788i	−0.845405	−	0.488095i
$719$	−5.52118	−	9.56296i	−0.205905	−	0.356638i	0.744516	−	0.667605i	$-0.232681\pi$
$719$	−5.52118	−	9.56296i	−0.205905	−	0.356638i	−0.950421	+	0.310967i	$0.899347\pi$
$720$	0.571769	−	2.16173i	0.0213086	−	0.0805630i
$721$	2.25330	−	1.30094i	0.0839171	−	0.0484496i
$722$	−7.23130	−	12.5250i	−0.269121	−	0.466131i
$723$	11.2768			0.419390
$724$	−4.87740	−	8.44791i	−0.181267	−	0.313964i
$725$	−20.5641	+	12.0502i	−0.763732	+	0.447533i
$726$	−13.4613	−	7.77188i	−0.499595	−	0.288442i
$727$			14.1056i			0.523147i	0.965184	+	0.261573i	$0.0842414\pi$
$727$			14.1056i			0.523147i	−0.965184	+	0.261573i	$0.915759\pi$
$728$	4.30137	+	0.643777i	0.159419	+	0.0238600i
$729$	−1.00000			−0.0370370
$730$	−24.9400	−	24.7797i	−0.923071	−	0.917137i
$731$	4.67418	−	8.09591i	0.172881	−	0.299438i
$732$	−2.66381	+	1.53795i	−0.0984574	+	0.0568444i
$733$	11.3855			0.420535			0.210267	−	0.977644i	$-0.432567\pi$
$733$	11.3855			0.420535			0.210267	+	0.977644i	$0.432567\pi$
$734$	−13.4988	+	7.79352i	−0.498249	+	0.287664i
$735$	3.24764	+	11.9659i	0.119791	+	0.441369i
$736$		−	2.17422i		−	0.0801427i
$737$	62.7122	−	36.2069i	2.31003	−	1.33370i
$738$	−4.10150	−	2.36800i	−0.150978	−	0.0871675i
$739$	−7.93251	−	4.57983i	−0.291802	−	0.168472i	0.346952	−	0.937883i	$-0.387217\pi$
$739$	−7.93251	−	4.57983i	−0.291802	−	0.168472i	−0.638754	+	0.769411i	$0.720550\pi$
$740$	2.51617	−	9.51308i	0.0924963	−	0.349708i
$741$	4.78234	−	6.00961i	0.175684	−	0.220769i
$742$			5.40461i			0.198410i
$743$	−19.9566	+	34.5658i	−0.732135	+	1.26809i	0.223834	+	0.974627i	$0.428143\pi$
$743$	−19.9566	+	34.5658i	−0.732135	+	1.26809i	−0.955969	+	0.293468i	$0.905191\pi$
$744$	−2.95523	+	5.11861i	−0.108344	+	0.187657i
$745$	−13.3607	−	49.2275i	−0.489500	−	1.80355i
$746$			0.993455i			0.0363730i
$747$	5.10226	+	8.83737i	0.186682	+	0.323342i
$748$	12.2001	+	21.1312i	0.446080	+	0.772634i
$749$		−	9.76355i		−	0.356752i
$750$	−2.78907	+	10.8269i	−0.101843	+	0.395341i
$751$	8.79993	−	15.2419i	0.321114	−	0.556186i	−0.659604	−	0.751613i	$-0.729276\pi$
$751$	8.79993	−	15.2419i	0.321114	−	0.556186i	0.980718	+	0.195427i	$0.0626094\pi$
$752$	0.426148	−	0.738110i	0.0155400	−	0.0269161i
$753$			12.3066i			0.448476i
$754$	−16.9981	−	2.54407i	−0.619033	−	0.0926494i
$755$	43.0174	+	11.3779i	1.56556	+	0.414085i
$756$	−1.04466	−	0.603137i	−0.0379941	−	0.0219359i
$757$	−19.1099	−	11.0331i	−0.694560	−	0.401004i	0.110758	−	0.993847i	$-0.464672\pi$
$757$	−19.1099	−	11.0331i	−0.694560	−	0.401004i	−0.805318	+	0.592843i	$0.798005\pi$
$758$	−23.7856	+	13.7326i	−0.863932	+	0.498791i
$759$			11.2017i			0.406596i
$760$	−1.24761	−	4.59679i	−0.0452555	−	0.166743i
$761$	−17.4454	+	10.0721i	−0.632394	+	0.365113i	−0.781678	−	0.623682i	$-0.785636\pi$
$761$	−17.4454	+	10.0721i	−0.632394	+	0.365113i	0.149285	+	0.988794i	$0.452303\pi$
$762$	1.20191			0.0435408
$763$	−17.6380	+	10.1833i	−0.638538	+	0.368660i
$764$	−5.77729	+	10.0066i	−0.209015	+	0.362025i
$765$	7.46410	−	7.51240i	0.269865	−	0.271611i
$766$	32.5703			1.17681
$767$	−1.03612	+	6.92282i	−0.0374123	+	0.249969i
$768$		−	1.00000i		−	0.0360844i
$769$	26.9356	+	15.5513i	0.971323	+	0.560794i	0.899639	−	0.436634i	$-0.143829\pi$
$769$	26.9356	+	15.5513i	0.971323	+	0.560794i	0.0716840	+	0.997427i	$0.477163\pi$
$770$	−9.79472	+	9.85810i	−0.352977	+	0.355261i
$771$	−14.0434	−	24.3239i	−0.505761	−	0.876004i
$772$	−10.4631			−0.376575
$773$	−0.416119	−	0.720739i	−0.0149668	−	0.0259232i	0.858445	−	0.512906i	$-0.171431\pi$
$773$	−0.416119	−	0.720739i	−0.0149668	−	0.0259232i	−0.873412	+	0.486982i	$0.838098\pi$
$774$	1.70944	−	0.986944i	0.0614444	−	0.0354750i
$775$	14.6108	−	25.6878i	0.524835	−	0.922734i
$776$	4.24139	+	7.34631i	0.152257	+	0.263717i
$777$	−4.59723	−	2.65421i	−0.164925	−	0.0952193i
$778$	8.45549	−	14.6453i	0.303144	−	0.525061i
$779$	−10.0883			−0.361449
$780$	−6.46642	+	4.81512i	−0.231535	+	0.172409i
$781$	−1.77704			−0.0635874
$782$	5.14856	−	8.91756i	0.184112	−	0.318891i
$783$	4.12828	+	2.38346i	0.147533	+	0.0851780i
$784$	2.77245	+	4.80203i	0.0990161	+	0.171501i
$785$	10.2551	+	2.71243i	0.366019	+	0.0968106i
$786$	5.76036	−	3.32575i	0.205465	−	0.118625i
$787$	−12.4115	−	21.4974i	−0.442422	−	0.766298i	0.555446	−	0.831552i	$-0.312547\pi$
$787$	−12.4115	−	21.4974i	−0.442422	−	0.766298i	−0.997869	+	0.0652545i	$0.979214\pi$
$788$	17.5894			0.626598
$789$	−3.79178	−	6.56756i	−0.134991	−	0.233811i
$790$	21.5510	+	21.4125i	0.766750	+	0.761821i
$791$	−5.17215	−	2.98614i	−0.183900	−	0.106175i
$792$			5.15206i			0.183071i
$793$	10.9682	+	1.64158i	0.389491	+	0.0582944i
$794$	−32.2397			−1.14414
$795$	−7.10697	−	7.06128i	−0.252058	−	0.250438i
$796$	12.7858	−	22.1457i	0.453181	−	0.784932i
$797$	−20.5483	+	11.8636i	−0.727858	+	0.420229i	−0.817638	−	0.575733i	$-0.804717\pi$
$797$	−20.5483	+	11.8636i	−0.727858	+	0.420229i	0.0897802	+	0.995962i	$0.471384\pi$
$798$	−2.56951			−0.0909595
$799$	3.49569	−	2.01824i	0.123669	−	0.0714002i
$800$	0.0322474	+	4.99990i	0.00114012	+	0.176773i
$801$			16.3899i			0.579110i
$802$	−28.0082	+	16.1705i	−0.989003	+	0.571001i
$803$	70.1524	+	40.5025i	2.47562	+	1.42930i
$804$	−12.1723	−	7.02765i	−0.429282	−	0.247846i
$805$	5.66958	+	1.49958i	0.199826	+	0.0528532i
$806$	19.8293	−	7.80611i	0.698457	−	0.274959i
$807$		−	24.4709i		−	0.861418i
$808$	6.79121	−	11.7627i	0.238914	−	0.413811i
$809$	18.7196	−	32.4233i	0.658145	−	1.13994i	−0.322950	−	0.946416i	$-0.604675\pi$
$809$	18.7196	−	32.4233i	0.658145	−	1.13994i	0.981095	−	0.193525i	$-0.0619921\pi$
$810$	2.15800	−	0.585699i	0.0758243	−	0.0205794i
$811$		−	40.2205i		−	1.41233i	−0.708046	−	0.706166i	$-0.750423\pi$
$811$		−	40.2205i		−	1.41233i	0.708046	−	0.706166i	$-0.249577\pi$
$812$	2.87511	+	4.97984i	0.100897	+	0.174758i
$813$	5.78497	+	10.0199i	0.202888	+	0.351412i
$814$			22.6726i			0.794673i
$815$	−8.34406	+	2.26465i	−0.292280	+	0.0793272i
$816$	2.36800	−	4.10150i	0.0828967	−	0.143581i
$817$	2.10231	−	3.64130i	0.0735504	−	0.127393i
$818$			1.16591i			0.0407652i
$819$	1.59316	+	4.04699i	0.0556695	+	0.141413i
$820$	10.2380	+	2.70790i	0.357526	+	0.0945641i
$821$	−24.5442	−	14.1706i	−0.856598	−	0.494557i	0.00627372	−	0.999980i	$-0.498003\pi$
$821$	−24.5442	−	14.1706i	−0.856598	−	0.494557i	−0.862872	+	0.505423i	$0.831336\pi$
$822$	12.7435	+	7.35746i	0.444480	+	0.256621i
$823$	41.0437	−	23.6966i	1.43069	−	0.826011i	0.433520	−	0.901144i	$-0.357271\pi$
$823$	41.0437	−	23.6966i	1.43069	−	0.826011i	0.997174	+	0.0751325i	$0.0239380\pi$
$824$			2.15696i			0.0751412i
$825$	−0.166140	−	25.7598i	−0.00578427	−	0.896841i
$826$	2.02814	−	1.17095i	0.0705681	−	0.0407425i
$827$	2.70177			0.0939496			0.0469748	−	0.998896i	$-0.485042\pi$
$827$	2.70177			0.0939496			0.0469748	+	0.998896i	$0.485042\pi$
$828$	1.88293	−	1.08711i	0.0654363	−	0.0377796i
$829$	−10.4285	+	18.0627i	−0.362197	+	0.627343i	−0.988322	−	0.152379i	$-0.951307\pi$
$829$	−10.4285	+	18.0627i	−0.362197	+	0.627343i	0.626125	+	0.779722i	$0.284640\pi$
$830$	−16.1867	−	16.0826i	−0.561849	−	0.558237i
$831$	12.9454			0.449072
$832$	−2.24511	+	2.82126i	−0.0778351	+	0.0978095i
$833$			26.2607i			0.909880i
$834$	13.5540	+	7.82540i	0.469336	+	0.270972i
$835$	−36.0436	−	35.8119i	−1.24734	−	1.23932i
$836$	5.48725	+	9.50420i	0.189781	+	0.328710i
$837$	−5.91046			−0.204296
$838$	5.91396	+	10.2433i	0.204294	+	0.353848i
$839$	5.34438	−	3.08558i	0.184508	−	0.106526i	−0.404901	−	0.914361i	$-0.632694\pi$
$839$	5.34438	−	3.08558i	0.184508	−	0.106526i	0.589409	+	0.807835i	$0.299361\pi$
$840$	2.60764	+	0.689710i	0.0899721	+	0.0237973i
$841$	3.13821	+	5.43553i	0.108214	+	0.187432i
$842$	20.7068	+	11.9551i	0.713604	+	0.412000i
$843$	−1.28593	+	2.22730i	−0.0442899	+	0.0767124i
$844$	12.9197			0.444714
$845$	29.0539	+	0.933129i	0.999485	+	0.0321006i
$846$	0.852296			0.0293025
$847$	9.37502	−	16.2380i	0.322129	−	0.557944i
$848$	−3.88016	−	2.24021i	−0.133245	−	0.0769291i
$849$	2.77427	+	4.80517i	0.0952125	+	0.164913i
$850$	−11.7075	+	20.5835i	−0.401564	+	0.706007i
$851$	8.28616	−	4.78402i	0.284046	−	0.163994i
$852$	0.172459	+	0.298707i	0.00590834	+	0.0102335i
$853$	52.4997			1.79756			0.898778	−	0.438405i	$-0.144456\pi$
$853$	52.4997			1.79756			0.898778	+	0.438405i	$0.144456\pi$
$854$	−1.85519	−	3.21329i	−0.0634834	−	0.109956i
$855$	3.35713	−	3.37886i	0.114812	−	0.115554i
$856$	7.00959	+	4.04699i	0.239583	+	0.138323i
$857$		−	23.9128i		−	0.816846i	−0.912793	−	0.408423i	$-0.866079\pi$
$857$		−	23.9128i		−	0.816846i	0.912793	−	0.408423i	$-0.133921\pi$
$858$	11.5669	−	14.5353i	0.394889	−	0.496227i
$859$	−35.2521			−1.20279			−0.601393	−	0.798953i	$-0.705387\pi$
$859$	−35.2521			−1.20279			−0.601393	+	0.798953i	$0.705387\pi$
$860$	−3.11091	+	3.13104i	−0.106081	+	0.106768i
$861$	2.85646	−	4.94754i	0.0973480	−	0.168612i
$862$	22.8082	−	13.1683i	0.776849	−	0.448514i
$863$	7.68909			0.261740			0.130870	−	0.991400i	$-0.458223\pi$
$863$	7.68909			0.261740			0.130870	+	0.991400i	$0.458223\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	−2.75161	−	10.1383i	−0.0935576	−	0.344712i
$866$			12.9594i			0.440380i
$867$	4.70233	−	2.71489i	0.159700	−	0.0922026i
$868$	−6.17445	−	3.56482i	−0.209574	−	0.120998i
$869$	−60.6196	−	34.9988i	−2.05638	−	1.18725i
$870$	−10.3048	−	2.72558i	−0.349366	−	0.0924058i
$871$	18.5632	+	47.1548i	0.628991	+	1.59778i
$872$		−	16.8839i		−	0.571761i
$873$	−4.24139	+	7.34631i	−0.143549	+	0.248635i
$874$	2.31567	−	4.01086i	0.0783287	−	0.135669i
$875$	−13.0602	−	3.36439i	−0.441514	−	0.113737i
$876$		−	15.7228i		−	0.531225i
$877$	−8.42697	−	14.5959i	−0.284559	−	0.492870i	0.687943	−	0.725764i	$-0.258514\pi$
$877$	−8.42697	−	14.5959i	−0.284559	−	0.492870i	−0.972502	+	0.232894i	$0.925180\pi$
$878$	11.6234	+	20.1324i	0.392272	+	0.679434i
$879$		−	24.1316i		−	0.813938i
$880$	−3.01756	−	11.1181i	−0.101722	−	0.374793i
$881$	−24.0475	+	41.6516i	−0.810182	+	1.40328i	0.102554	+	0.994727i	$0.467299\pi$
$881$	−24.0475	+	41.6516i	−0.810182	+	1.40328i	−0.912736	+	0.408550i	$0.866035\pi$
$882$	−2.77245	+	4.80203i	−0.0933533	+	0.161693i
$883$		−	38.3641i		−	1.29105i	−0.763737	−	0.645527i	$-0.776638\pi$
$883$		−	38.3641i		−	1.29105i	0.763737	−	0.645527i	$-0.223362\pi$
$884$	−15.8891	+	6.25498i	−0.534407	+	0.210378i
$885$	−1.11005	+	4.19685i	−0.0373139	+	0.141076i
$886$	20.2414	+	11.6864i	0.680024	+	0.392612i
$887$	16.2697	+	9.39331i	0.546283	+	0.315396i	0.747621	−	0.664125i	$-0.231196\pi$
$887$	16.2697	+	9.39331i	0.546283	+	0.315396i	−0.201339	+	0.979522i	$0.564529\pi$
$888$	3.81110	−	2.20034i	0.127892	−	0.0738385i
$889$			1.44984i			0.0486260i
$890$	−9.59957	−	35.3695i	−0.321778	−	1.18559i
$891$	−4.46182	+	2.57603i	−0.149477	+	0.0863003i
$892$	7.15357			0.239519
$893$	1.57226	−	0.907745i	0.0526137	−	0.0303765i
$894$	11.4058	−	19.7555i	0.381468	−	0.660721i
$895$	−13.7974	−	13.7087i	−0.461198	−	0.458233i
$896$	1.20627			0.0402988
$897$	−7.75290	−	1.16036i	−0.258862	−	0.0387433i
$898$			1.39639i			0.0465982i
$899$	24.4000	+	14.0874i	0.813787	+	0.469840i
$900$	−4.31391	+	2.52788i	−0.143797	+	0.0842625i
$901$	−10.6097	−	18.3765i	−0.353459	−	0.612209i
$902$	−24.4002			−0.812439
$903$	1.19052	+	2.06205i	0.0396182	+	0.0686207i
$904$	4.28771	−	2.47551i	0.142607	−	0.0823342i
$905$	−5.57749	+	21.0873i	−0.185402	+	0.700964i
$906$	9.94975	+	17.2335i	0.330558	+	0.572544i
$907$	−18.2967	−	10.5636i	−0.607532	−	0.350759i	0.164467	−	0.986383i	$-0.447410\pi$
$907$	−18.2967	−	10.5636i	−0.607532	−	0.350759i	−0.771999	+	0.635624i	$0.780743\pi$
$908$	12.9192	−	22.3768i	0.428740	−	0.742599i
$909$	13.5824			0.450501
$910$	−5.80835	−	7.80028i	−0.192545	−	0.258577i
$911$	19.2766			0.638664			0.319332	−	0.947643i	$-0.396542\pi$
$911$	19.2766			0.638664			0.319332	+	0.947643i	$0.396542\pi$
$912$	1.06506	−	1.84474i	0.0352676	−	0.0610853i
$913$	45.5307	+	26.2872i	1.50685	+	0.869978i
$914$	3.60093	+	6.23699i	0.119108	+	0.206301i
$915$	6.64928	+	1.75871i	0.219819	+	0.0581411i
$916$	−7.75225	+	4.47576i	−0.256142	+	0.147883i
$917$	4.01176	+	6.94857i	0.132480	+	0.229462i
$918$	4.73601			0.156312
$919$	17.8995	+	31.0028i	0.590450	+	1.02269i	0.994172	+	0.107807i	$0.0343830\pi$
$919$	17.8995	+	31.0028i	0.590450	+	1.02269i	−0.403722	+	0.914882i	$0.632284\pi$
$920$	−3.42664	+	3.44881i	−0.112973	+	0.113704i
$921$	−26.2616	−	15.1621i	−0.865348	−	0.499609i
$922$		−	4.74489i		−	0.156265i
$923$	0.184079	−	1.22992i	0.00605905	−	0.0404833i
$924$	−6.21480			−0.204452
$925$	−18.9841	+	11.1244i	−0.624195	+	0.365767i
$926$	−7.87551	+	13.6408i	−0.258805	+	0.448264i
$927$	−1.86798	+	1.07848i	−0.0613525	+	0.0354219i
$928$	−4.76693			−0.156482
$929$	−13.4933	+	7.79033i	−0.442699	+	0.255593i	−0.704742	−	0.709464i	$-0.748937\pi$
$929$	−13.4933	+	7.79033i	−0.442699	+	0.255593i	0.262043	+	0.965056i	$0.415604\pi$
$930$	12.7548	−	3.46175i	0.418245	−	0.113515i
$931$			11.8113i			0.387100i
$932$	3.34855	−	1.93329i	0.109685	−	0.0633269i
$933$	7.58990	+	4.38203i	0.248482	+	0.143461i
$934$	−15.5701	−	8.98943i	−0.509471	−	0.294143i
$935$	13.9513	−	52.7467i	0.456256	−	1.72500i
$936$	−3.56583	−	0.533691i	−0.116553	−	0.0174442i
$937$		−	27.4692i		−	0.897381i	−0.893687	−	0.448690i	$-0.851891\pi$
$937$		−	27.4692i		−	0.897381i	0.893687	−	0.448690i	$-0.148109\pi$
$938$	8.47727	−	14.6831i	0.276793	−	0.479419i
$939$	14.5077	−	25.1282i	0.473442	−	0.820026i
$940$	−1.83925	+	0.499189i	−0.0599898	+	0.0162817i
$941$		−	5.01957i		−	0.163633i	−0.996647	−	0.0818167i	$-0.973928\pi$
$941$		−	5.01957i		−	0.163633i	0.996647	−	0.0818167i	$-0.0260722\pi$
$942$	2.37196	+	4.10836i	0.0772826	+	0.133857i
$943$	5.14856	+	8.91756i	0.167660	+	0.290396i
$944$			1.94143i			0.0631882i
$945$	0.706513	+	2.60314i	0.0229829	+	0.0846801i
$946$	5.08480	−	8.80713i	0.165321	−	0.286344i
$947$	−20.0915	+	34.7995i	−0.652886	+	1.13083i	0.329534	+	0.944144i	$0.393109\pi$
$947$	−20.0915	+	34.7995i	−0.652886	+	1.13083i	−0.982419	+	0.186688i	$0.940225\pi$
$948$			13.5863i			0.441263i
$949$	−35.2994	+	44.3582i	−1.14587	+	1.43993i
$950$	−5.26570	+	9.25783i	−0.170842	+	0.300364i
$951$	22.5140	+	12.9985i	0.730068	+	0.421505i
$952$	4.94754	+	2.85646i	0.160351	+	0.0925785i
$953$	9.42493	−	5.44149i	0.305304	−	0.176267i	−0.339519	−	0.940599i	$-0.610264\pi$
$953$	9.42493	−	5.44149i	0.305304	−	0.176267i	0.644823	+	0.764332i	$0.276931\pi$
$954$		−	4.48042i		−	0.145059i
$955$	24.9348	−	6.76751i	0.806870	−	0.218991i
$956$	13.3521	−	7.70884i	0.431838	−	0.249322i
$957$	24.5595			0.793896
$958$	−2.83964	+	1.63947i	−0.0917447	+	0.0529688i
$959$	−8.87511	+	15.3721i	−0.286592	+	0.496392i
$960$	−1.57603	+	1.58623i	−0.0508662	+	0.0511953i
$961$	−3.93359			−0.126890
$962$	−15.6921	−	2.34860i	−0.505933	−	0.0757220i
$963$			8.09397i			0.260825i
$964$	−9.76603	−	5.63842i	−0.314543	−	0.181601i
$965$	16.5969	+	16.4902i	0.534272	+	0.530837i
$966$	1.31135	+	2.27133i	0.0421920	+	0.0730787i
$967$	2.14376			0.0689387			0.0344693	−	0.999406i	$-0.489026\pi$
$967$	2.14376			0.0689387			0.0344693	+	0.999406i	$0.489026\pi$
$968$	7.77188	+	13.4613i	0.249798	+	0.432662i
$969$	8.73669	−	5.04413i	0.280663	−	0.162041i
$970$	4.85019	−	18.3375i	0.155730	−	0.588781i
$971$	−4.57889	−	7.93087i	−0.146944	−	0.254514i	0.783153	−	0.621829i	$-0.213610\pi$
$971$	−4.57889	−	7.93087i	−0.146944	−	0.254514i	−0.930096	+	0.367316i	$0.880277\pi$
$972$	0.866025	+	0.500000i	0.0277778	+	0.0160375i
$973$	−9.43958	+	16.3498i	−0.302619	+	0.524151i
$974$	9.97704			0.319685
$975$	17.8460	+	2.55341i	0.571530	+	0.0817746i
$976$	3.07591			0.0984574
$977$	7.16508	−	12.4103i	0.229231	−	0.397040i	−0.728349	−	0.685206i	$-0.759712\pi$
$977$	7.16508	−	12.4103i	0.229231	−	0.397040i	0.957581	+	0.288166i	$0.0930454\pi$
$978$	−3.34855	−	1.93329i	−0.107075	−	0.0618197i
$979$	42.2210	+	73.1289i	1.34939	+	2.33721i
$980$	3.17040	−	11.9866i	0.101275	−	0.382898i
$981$	14.6219	−	8.44195i	0.466841	−	0.269531i
$982$	10.0376	+	17.3857i	0.320314	+	0.554800i
$983$	−21.6099			−0.689250			−0.344625	−	0.938740i	$-0.611994\pi$
$983$	−21.6099			−0.689250			−0.344625	+	0.938740i	$0.611994\pi$
$984$	2.36800	+	4.10150i	0.0754892	+	0.130751i
$985$	−27.9009	−	27.7215i	−0.888996	−	0.883281i
$986$	−19.5516	−	11.2881i	−0.622649	−	0.359486i
$987$			1.02810i			0.0327248i
$988$	−7.14644	+	2.81330i	−0.227358	+	0.0895031i
$989$	−4.29166			−0.136467
$990$	8.11982	−	8.17235i	0.258065	−	0.259734i
$991$	−11.9222	+	20.6499i	−0.378722	+	0.655966i	−0.990877	−	0.134772i	$-0.956970\pi$
$991$	−11.9222	+	20.6499i	−0.378722	+	0.655966i	0.612154	+	0.790738i	$0.290303\pi$
$992$	5.11861	−	2.95523i	0.162516	−	0.0938287i
$993$	−11.0392			−0.350319
$994$	−0.360323	+	0.208033i	−0.0114287	+	0.00659839i
$995$	−55.1835	+	14.9773i	−1.74943	+	0.474811i
$996$		−	10.2045i		−	0.323342i
$997$	−25.5772	+	14.7670i	−0.810037	+	0.467675i	−0.846969	−	0.531642i	$-0.821575\pi$
$997$	−25.5772	+	14.7670i	−0.810037	+	0.467675i	0.0369315	+	0.999318i	$0.488242\pi$
$998$	−20.7390	−	11.9737i	−0.656482	−	0.379020i
$999$	3.81110	+	2.20034i	0.120578	+	0.0696157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.x.a.199.4	yes	12
3.2	odd	2		1170.2.bj.d.199.4		12
5.2	odd	4		1950.2.bc.j.901.3		12
5.3	odd	4		1950.2.bc.i.901.4		12
5.4	even	2		390.2.x.b.199.3	yes	12
13.10	even	6		390.2.x.b.49.3	yes	12
15.14	odd	2		1170.2.bj.c.199.3		12
39.23	odd	6		1170.2.bj.c.829.3		12
65.23	odd	12		1950.2.bc.i.751.4		12
65.49	even	6	inner	390.2.x.a.49.4	✓	12
65.62	odd	12		1950.2.bc.j.751.3		12
195.179	odd	6		1170.2.bj.d.829.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.4	✓	12	65.49	even	6	inner
390.2.x.a.199.4	yes	12	1.1	even	1	trivial
390.2.x.b.49.3	yes	12	13.10	even	6
390.2.x.b.199.3	yes	12	5.4	even	2
1170.2.bj.c.199.3		12	15.14	odd	2
1170.2.bj.c.829.3		12	39.23	odd	6
1170.2.bj.d.199.4		12	3.2	odd	2
1170.2.bj.d.829.4		12	195.179	odd	6
1950.2.bc.i.751.4		12	65.23	odd	12
1950.2.bc.i.901.4		12	5.3	odd	4
1950.2.bc.j.751.3		12	65.62	odd	12
1950.2.bc.j.901.3		12	5.2	odd	4

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.571769 + 2.16173i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.603137 - 1.04466i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.58623 - 1.57603i) q^{10} +(4.46182 + 2.57603i) q^{11} -1.00000i q^{12} +(-2.24511 + 2.82126i) q^{13} +1.20627 q^{14} +(-1.57603 + 1.58623i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.10150 + 2.36800i) q^{17} -1.00000 q^{18} +(-1.84474 + 1.06506i) q^{19} +(2.15800 - 0.585699i) q^{20} -1.20627i q^{21} +(-4.46182 + 2.57603i) q^{22} +(1.88293 + 1.08711i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-4.34616 - 2.47202i) q^{25} +(-1.32073 - 3.35495i) q^{26} +1.00000i q^{27} +(-0.603137 + 1.04466i) q^{28} +(2.38346 - 4.12828i) q^{29} +(-0.585699 - 2.15800i) q^{30} +5.91046i q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.57603 + 4.46182i) q^{33} -4.73601i q^{34} +(2.60314 - 0.706513i) q^{35} +(0.500000 - 0.866025i) q^{36} +(2.20034 - 3.81110i) q^{37} -2.13012i q^{38} +(-3.35495 + 1.32073i) q^{39} +(-0.571769 + 2.16173i) q^{40} +(4.10150 + 2.36800i) q^{41} +(1.04466 + 0.603137i) q^{42} +(-1.70944 + 0.986944i) q^{43} -5.15206i q^{44} +(-2.15800 + 0.585699i) q^{45} +(-1.88293 + 1.08711i) q^{46} -0.852296 q^{47} +(-0.866025 + 0.500000i) q^{48} +(2.77245 - 4.80203i) q^{49} +(4.31391 - 2.52788i) q^{50} -4.73601 q^{51} +(3.56583 + 0.533691i) q^{52} +4.48042i q^{53} +(-0.866025 - 0.500000i) q^{54} +(-8.11982 + 8.17235i) q^{55} +(-0.603137 - 1.04466i) q^{56} -2.13012 q^{57} +(2.38346 + 4.12828i) q^{58} +(1.68133 - 0.970715i) q^{59} +(2.16173 + 0.571769i) q^{60} +(-1.53795 - 2.66381i) q^{61} +(-5.11861 - 2.95523i) q^{62} +(0.603137 - 1.04466i) q^{63} +1.00000 q^{64} +(-4.81512 - 6.46642i) q^{65} -5.15206 q^{66} +(7.02765 - 12.1723i) q^{67} +(4.10150 + 2.36800i) q^{68} +(1.08711 + 1.88293i) q^{69} +(-0.689710 + 2.60764i) q^{70} +(-0.298707 + 0.172459i) q^{71} +(0.500000 + 0.866025i) q^{72} +15.7228 q^{73} +(2.20034 + 3.81110i) q^{74} +(-2.52788 - 4.31391i) q^{75} +(1.84474 + 1.06506i) q^{76} -6.21480i q^{77} +(0.533691 - 3.56583i) q^{78} -13.5863 q^{79} +(-1.58623 - 1.57603i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.10150 + 2.36800i) q^{82} +10.2045 q^{83} +(-1.04466 + 0.603137i) q^{84} +(-2.77388 - 10.2203i) q^{85} -1.97389i q^{86} +(4.12828 - 2.38346i) q^{87} +(4.46182 + 2.57603i) q^{88} +(14.1941 + 8.19497i) q^{89} +(0.571769 - 2.16173i) q^{90} +(4.30137 + 0.643777i) q^{91} -2.17422i q^{92} +(-2.95523 + 5.11861i) q^{93} +(0.426148 - 0.738110i) q^{94} +(-1.24761 - 4.59679i) q^{95} -1.00000i q^{96} +(4.24139 + 7.34631i) q^{97} +(2.77245 + 4.80203i) q^{98} +5.15206i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} - 2 q^{7} + 12 q^{8} + 6 q^{9} - 2 q^{10} + 6 q^{11} - 8 q^{13} + 4 q^{14} + 6 q^{15} - 6 q^{16} + 18 q^{17} - 12 q^{18} - 6 q^{19} + 4 q^{20} - 6 q^{22} + 6 q^{23} - 10 q^{25}+ \cdots + 8 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 - 2 * q^7 + 12 * q^8 + 6 * q^9 - 2 * q^10 + 6 * q^11 - 8 * q^13 + 4 * q^14 + 6 * q^15 - 6 * q^16 + 18 * q^17 - 12 * q^18 - 6 * q^19 + 4 * q^20 - 6 * q^22 + 6 * q^23 - 10 * q^25 - 2 * q^26 - 2 * q^28 + 14 * q^29 - 6 * q^30 - 6 * q^32 + 6 * q^33 + 26 * q^35 + 6 * q^36 - 12 * q^37 - 2 * q^39 - 2 * q^40 - 18 * q^41 - 12 * q^42 - 36 * q^43 - 4 * q^45 - 6 * q^46 + 16 * q^47 + 8 * q^49 - 10 * q^50 + 16 * q^51 + 10 * q^52 - 28 * q^55 - 2 * q^56 - 8 * q^57 + 14 * q^58 - 36 * q^59 + 10 * q^61 + 6 * q^62 + 2 * q^63 + 12 * q^64 + 6 * q^65 - 12 * q^66 + 4 * q^67 - 18 * q^68 + 16 * q^69 - 4 * q^70 - 12 * q^71 + 6 * q^72 + 28 * q^73 - 12 * q^74 - 8 * q^75 + 6 * q^76 - 2 * q^78 + 4 * q^79 - 2 * q^80 - 6 * q^81 + 18 * q^82 + 72 * q^83 + 12 * q^84 + 18 * q^85 + 6 * q^87 + 6 * q^88 + 18 * q^89 + 2 * q^90 + 2 * q^91 - 16 * q^93 - 8 * q^94 - 42 * q^95 - 48 * q^97 + 8 * q^98

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