LMFDB - Embedded newform 1170.2.bj.c.829.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(199,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1170.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bj (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:	$9.34249703649$
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:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			829.3
Root			$-0.330925 + 1.46916i$ of defining polynomial
Character	$\chi$	$=$	1170.829
Dual form			1170.2.bj.c.199.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.571769 + 2.16173i) q^{5} +(0.603137 - 1.04466i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.571769 + 2.16173i) q^{5} +(0.603137 - 1.04466i) q^{7} +1.00000 q^{8} +(2.15800 - 0.585699i) q^{10} +(-4.46182 + 2.57603i) q^{11} +(2.24511 + 2.82126i) q^{13} -1.20627 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.10150 - 2.36800i) q^{17} +(-1.84474 - 1.06506i) q^{19} +(-1.58623 - 1.57603i) q^{20} +(4.46182 + 2.57603i) q^{22} +(1.88293 - 1.08711i) q^{23} +(-4.34616 - 2.47202i) q^{25} +(1.32073 - 3.35495i) q^{26} +(0.603137 + 1.04466i) q^{28} +(-2.38346 - 4.12828i) q^{29} -5.91046i q^{31} +(-0.500000 + 0.866025i) q^{32} +4.73601i q^{34} +(1.91343 + 1.90113i) q^{35} +(-2.20034 - 3.81110i) q^{37} +2.13012i q^{38} +(-0.571769 + 2.16173i) q^{40} +(-4.10150 + 2.36800i) q^{41} +(1.70944 + 0.986944i) q^{43} -5.15206i q^{44} +(-1.88293 - 1.08711i) q^{46} -0.852296 q^{47} +(2.77245 + 4.80203i) q^{49} +(0.0322474 + 4.99990i) q^{50} +(-3.56583 + 0.533691i) q^{52} -4.48042i q^{53} +(-3.01756 - 11.1181i) q^{55} +(0.603137 - 1.04466i) q^{56} +(-2.38346 + 4.12828i) q^{58} +(-1.68133 - 0.970715i) q^{59} +(-1.53795 + 2.66381i) q^{61} +(-5.11861 + 2.95523i) q^{62} +1.00000 q^{64} +(-7.38248 + 3.24021i) q^{65} +(-7.02765 - 12.1723i) q^{67} +(4.10150 - 2.36800i) q^{68} +(0.689710 - 2.60764i) q^{70} +(0.298707 + 0.172459i) q^{71} -15.7228 q^{73} +(-2.20034 + 3.81110i) q^{74} +(1.84474 - 1.06506i) q^{76} +6.21480i q^{77} -13.5863 q^{79} +(2.15800 - 0.585699i) q^{80} +(4.10150 + 2.36800i) q^{82} +10.2045 q^{83} +(7.46410 - 7.51240i) q^{85} -1.97389i q^{86} +(-4.46182 + 2.57603i) q^{88} +(-14.1941 + 8.19497i) q^{89} +(4.30137 - 0.643777i) q^{91} +2.17422i q^{92} +(0.426148 + 0.738110i) q^{94} +(3.35713 - 3.37886i) q^{95} +(-4.24139 + 7.34631i) q^{97} +(2.77245 - 4.80203i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	$ 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{23} - 10 q^{25} + 2 q^{26} + 2 q^{28} - 14 q^{29} - 6 q^{32} + 22 q^{35} + 12 q^{37} - 2 q^{40} + 18 q^{41} + 36 q^{43} - 6 q^{46} + 16 q^{47} + 8 q^{49} + 20 q^{50} - 10 q^{52} + 8 q^{55} + 2 q^{56} - 14 q^{58} + 36 q^{59} + 10 q^{61} + 6 q^{62} + 12 q^{64} + 44 q^{65} - 4 q^{67} - 18 q^{68} + 4 q^{70} + 12 q^{71} - 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 4 q^{80} - 18 q^{82} + 72 q^{83} + 48 q^{85} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} - 18 q^{95} + 48 q^{97} + 8 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 4 * q^10 - 6 * q^11 + 8 * q^13 - 4 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 - 2 * q^20 + 6 * q^22 + 6 * q^23 - 10 * q^25 + 2 * q^26 + 2 * q^28 - 14 * q^29 - 6 * q^32 + 22 * q^35 + 12 * q^37 - 2 * q^40 + 18 * q^41 + 36 * q^43 - 6 * q^46 + 16 * q^47 + 8 * q^49 + 20 * q^50 - 10 * q^52 + 8 * q^55 + 2 * q^56 - 14 * q^58 + 36 * q^59 + 10 * q^61 + 6 * q^62 + 12 * q^64 + 44 * q^65 - 4 * q^67 - 18 * q^68 + 4 * q^70 + 12 * q^71 - 28 * q^73 + 12 * q^74 + 6 * q^76 + 4 * q^79 + 4 * q^80 - 18 * q^82 + 72 * q^83 + 48 * q^85 - 6 * q^88 - 18 * q^89 + 2 * q^91 - 8 * q^94 - 18 * q^95 + 48 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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			0
$3$		0			0
$4$	−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			0
$7$	0.603137	−	1.04466i	0.227964	−	0.394846i	−0.729240	−	0.684258i	$-0.760126\pi$
$7$	0.603137	−	1.04466i	0.227964	−	0.394846i	0.957205	+	0.289412i	$0.0934597\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	2.15800	−	0.585699i	0.682419	−	0.185214i
$11$	−4.46182	+	2.57603i	−1.34529	+	0.776703i	−0.987578	−	0.157130i	$-0.949776\pi$
$11$	−4.46182	+	2.57603i	−1.34529	+	0.776703i	−0.357711	+	0.933832i	$0.616443\pi$
$12$		0			0
$13$	2.24511	+	2.82126i	0.622681	+	0.782476i
$13$	2.24511	+	2.82126i	0.622681	+	0.782476i
$14$	−1.20627			−0.322390
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.10150	−	2.36800i	−0.994761	−	0.574326i	−0.0880670	−	0.996115i	$-0.528069\pi$
$17$	−4.10150	−	2.36800i	−0.994761	−	0.574326i	−0.906694	+	0.421789i	$0.861402\pi$
$18$		0			0
$19$	−1.84474	−	1.06506i	−0.423212	−	0.244341i	0.273239	−	0.961946i	$-0.411905\pi$
$19$	−1.84474	−	1.06506i	−0.423212	−	0.244341i	−0.696450	+	0.717605i	$0.745238\pi$
$20$	−1.58623	−	1.57603i	−0.354692	−	0.352411i
$21$		0			0
$22$	4.46182	+	2.57603i	0.951263	+	0.549212i
$23$	1.88293	−	1.08711i	0.392618	−	0.226678i	−0.290676	−	0.956822i	$-0.593880\pi$
$23$	1.88293	−	1.08711i	0.392618	−	0.226678i	0.683294	+	0.730144i	$0.260547\pi$
$24$		0			0
$25$	−4.34616	−	2.47202i	−0.869232	−	0.494404i
$26$	1.32073	−	3.35495i	0.259016	−	0.657960i
$27$		0			0
$28$	0.603137	+	1.04466i	0.113982	+	0.197423i
$29$	−2.38346	−	4.12828i	−0.442598	−	0.766602i	0.555283	−	0.831661i	$-0.312610\pi$
$29$	−2.38346	−	4.12828i	−0.442598	−	0.766602i	−0.997881	+	0.0650589i	$0.979276\pi$
$30$		0			0
$31$		−	5.91046i		−	1.06155i	−0.847513	−	0.530775i	$-0.821901\pi$
$31$		−	5.91046i		−	1.06155i	0.847513	−	0.530775i	$-0.178099\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$			4.73601i			0.812219i
$35$	1.91343	+	1.90113i	0.323428	+	0.321349i
$36$		0			0
$37$	−2.20034	−	3.81110i	−0.361734	−	0.626541i	0.626513	−	0.779411i	$-0.284482\pi$
$37$	−2.20034	−	3.81110i	−0.361734	−	0.626541i	−0.988246	+	0.152870i	$0.951148\pi$
$38$			2.13012i			0.345551i
$39$		0			0
$40$	−0.571769	+	2.16173i	−0.0904046	+	0.341800i
$41$	−4.10150	+	2.36800i	−0.640547	+	0.369820i	−0.784825	−	0.619717i	$-0.787247\pi$
$41$	−4.10150	+	2.36800i	−0.640547	+	0.369820i	0.144278	+	0.989537i	$0.453914\pi$
$42$		0			0
$43$	1.70944	+	0.986944i	0.260687	+	0.150508i	0.624648	−	0.780907i	$-0.285243\pi$
$43$	1.70944	+	0.986944i	0.260687	+	0.150508i	−0.363961	+	0.931414i	$0.618576\pi$
$44$		−	5.15206i		−	0.776703i
$45$		0			0
$46$	−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			0
$49$	2.77245	+	4.80203i	0.396065	+	0.686004i
$50$	0.0322474	+	4.99990i	0.00456046	+	0.707092i
$51$		0			0
$52$	−3.56583	+	0.533691i	−0.494492	+	0.0740096i
$53$		−	4.48042i		−	0.615433i	−0.951478	−	0.307716i	$-0.900435\pi$
$53$		−	4.48042i		−	0.615433i	0.951478	−	0.307716i	$-0.0995648\pi$
$54$		0			0
$55$	−3.01756	−	11.1181i	−0.406888	−	1.49917i
$56$	0.603137	−	1.04466i	0.0805976	−	0.139599i
$57$		0			0
$58$	−2.38346	+	4.12828i	−0.312964	+	0.542070i
$59$	−1.68133	−	0.970715i	−0.218890	−	0.126376i	0.386546	−	0.922270i	$-0.373668\pi$
$59$	−1.68133	−	0.970715i	−0.218890	−	0.126376i	−0.605436	+	0.795894i	$0.707001\pi$
$60$		0			0
$61$	−1.53795	+	2.66381i	−0.196915	+	0.341066i	−0.947527	−	0.319677i	$-0.896426\pi$
$61$	−1.53795	+	2.66381i	−0.196915	+	0.341066i	0.750612	+	0.660744i	$0.229759\pi$
$62$	−5.11861	+	2.95523i	−0.650064	+	0.375315i
$63$		0			0
$64$	1.00000			0.125000
$65$	−7.38248	+	3.24021i	−0.915684	+	0.401899i
$66$		0			0
$67$	−7.02765	−	12.1723i	−0.858564	−	1.48708i	−0.873298	−	0.487186i	$-0.838023\pi$
$67$	−7.02765	−	12.1723i	−0.858564	−	1.48708i	0.0147340	−	0.999891i	$-0.495310\pi$
$68$	4.10150	−	2.36800i	0.497380	−	0.287163i
$69$		0			0
$70$	0.689710	−	2.60764i	0.0824361	−	0.311673i
$71$	0.298707	+	0.172459i	0.0354500	+	0.0204671i	0.517620	−	0.855610i	$-0.326818\pi$
$71$	0.298707	+	0.172459i	0.0354500	+	0.0204671i	−0.482170	+	0.876078i	$0.660151\pi$
$72$		0			0
$73$	−15.7228			−1.84022			−0.920109	−	0.391662i	$-0.871900\pi$
$73$	−15.7228			−1.84022			−0.920109	+	0.391662i	$0.871900\pi$
$74$	−2.20034	+	3.81110i	−0.255784	+	0.443031i
$75$		0			0
$76$	1.84474	−	1.06506i	0.211606	−	0.122171i
$77$			6.21480i			0.708242i
$78$		0			0
$79$	−13.5863			−1.52858			−0.764290	−	0.644873i	$-0.776910\pi$
$79$	−13.5863			−1.52858			−0.764290	+	0.644873i	$0.776910\pi$
$80$	2.15800	−	0.585699i	0.241272	−	0.0654831i
$81$		0			0
$82$	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	$0.310784\pi$
$84$		0			0
$85$	7.46410	−	7.51240i	0.809595	−	0.814834i
$86$		−	1.97389i		−	0.212850i
$87$		0			0
$88$	−4.46182	+	2.57603i	−0.475631	+	0.274606i
$89$	−14.1941	+	8.19497i	−1.50457	+	0.868665i	−0.504586	+	0.863361i	$0.668355\pi$
$89$	−14.1941	+	8.19497i	−1.50457	+	0.868665i	−0.999986	+	0.00530346i	$0.998312\pi$
$90$		0			0
$91$	4.30137	−	0.643777i	0.450906	−	0.0674862i
$92$			2.17422i			0.226678i
$93$		0			0
$94$	0.426148	+	0.738110i	0.0439538	+	0.0761302i
$95$	3.35713	−	3.37886i	0.344435	−	0.346663i
$96$		0			0
$97$	−4.24139	+	7.34631i	−0.430648	+	0.745904i	−0.996929	−	0.0783078i	$-0.975048\pi$
$97$	−4.24139	+	7.34631i	−0.430648	+	0.745904i	0.566281	+	0.824212i	$0.308382\pi$
$98$	2.77245	−	4.80203i	0.280060	−	0.485078i
$99$		0			0
$100$	4.31391	−	2.52788i	0.431391	−	0.252788i
$101$	−6.79121	−	11.7627i	−0.675751	−	1.17044i	−0.976249	−	0.216653i	$-0.930486\pi$
$101$	−6.79121	−	11.7627i	−0.675751	−	1.17044i	0.300498	−	0.953783i	$-0.402847\pi$
$102$		0			0
$103$			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
$105$		0			0
$106$	−3.88016	+	2.24021i	−0.376874	+	0.217588i
$107$	7.00959	−	4.04699i	0.677642	−	0.391237i	−0.121324	−	0.992613i	$-0.538714\pi$
$107$	7.00959	−	4.04699i	0.677642	−	0.391237i	0.798966	+	0.601376i	$0.205381\pi$
$108$		0			0
$109$			16.8839i			1.61718i	0.588370	+	0.808592i	$0.299770\pi$
$109$			16.8839i			1.61718i	−0.588370	+	0.808592i	$0.700230\pi$
$110$	−8.11982	+	8.17235i	−0.774194	+	0.779203i
$111$		0			0
$112$	−1.20627			−0.113982
$113$	4.28771	+	2.47551i	0.403354	+	0.232876i	0.687930	−	0.725777i	$-0.258520\pi$
$113$	4.28771	+	2.47551i	0.403354	+	0.232876i	−0.284576	+	0.958653i	$0.591853\pi$
$114$		0			0
$115$	1.27344	+	4.69196i	0.118749	+	0.437527i
$116$	4.76693			0.442598
$117$		0			0
$118$			1.94143i			0.178723i
$119$	−4.94754	+	2.85646i	−0.453540	+	0.261851i
$120$		0			0
$121$	7.77188	−	13.4613i	0.706535	−	1.22375i
$122$	3.07591			0.278480
$123$		0			0
$124$	5.11861	+	2.95523i	0.459665	+	0.265388i
$125$	7.82884	−	7.98180i	0.700233	−	0.713914i
$126$		0			0
$127$	1.04089	−	0.600957i	0.0923639	−	0.0533263i	−0.453107	−	0.891456i	$-0.649684\pi$
$127$	1.04089	−	0.600957i	0.0923639	−	0.0533263i	0.545471	+	0.838130i	$0.316351\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	6.49734	+	4.77331i	0.569855	+	0.418647i
$131$	6.65149			0.581143			0.290572	−	0.956853i	$-0.406155\pi$
$131$	6.65149			0.581143			0.290572	+	0.956853i	$0.406155\pi$
$132$		0			0
$133$	−2.22526	+	1.28475i	−0.192954	+	0.111402i
$134$	−7.02765	+	12.1723i	−0.607097	+	1.05152i
$135$		0			0
$136$	−4.10150	−	2.36800i	−0.351701	−	0.203055i
$137$	−7.35746	+	12.7435i	−0.628590	+	1.08875i	0.359245	+	0.933243i	$0.383034\pi$
$137$	−7.35746	+	12.7435i	−0.628590	+	1.08875i	−0.987835	+	0.155507i	$0.950299\pi$
$138$		0			0
$139$	−7.82540	+	13.5540i	−0.663742	+	1.14963i	0.315883	+	0.948798i	$0.397699\pi$
$139$	−7.82540	+	13.5540i	−0.663742	+	1.14963i	−0.979625	+	0.200837i	$0.935634\pi$
$140$	−2.60314	+	0.706513i	−0.220005	+	0.0597113i
$141$		0			0
$142$		−	0.344918i		−	0.0289448i
$143$	−17.2849	−	6.80447i	−1.44544	−	0.569018i
$144$		0			0
$145$	10.2870	−	2.79198i	0.854290	−	0.231862i
$146$	7.86142	+	13.6164i	0.650615	+	1.12690i
$147$		0			0
$148$	4.40068			0.361734
$149$	19.7555	+	11.4058i	1.61843	+	0.934401i	0.987327	+	0.158702i	$0.0507309\pi$
$149$	19.7555	+	11.4058i	1.61843	+	0.934401i	0.631103	+	0.775699i	$0.282602\pi$
$150$		0			0
$151$			19.8995i			1.61940i	0.586845	+	0.809699i	$0.300370\pi$
$151$			19.8995i			1.61940i	−0.586845	+	0.809699i	$0.699630\pi$
$152$	−1.84474	−	1.06506i	−0.149628	−	0.0863877i
$153$		0			0
$154$	5.38217	−	3.10740i	0.433708	−	0.250401i
$155$	12.7768	+	3.37942i	1.02626	+	0.271442i
$156$		0			0
$157$		−	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
$159$		0			0
$160$	−1.58623	−	1.57603i	−0.125402	−	0.124596i
$161$		−	2.62270i		−	0.206698i
$162$		0			0
$163$	−1.93329	+	3.34855i	−0.151427	+	0.262279i	−0.931752	−	0.363095i	$-0.881720\pi$
$163$	−1.93329	+	3.34855i	−0.151427	+	0.262279i	0.780325	+	0.625374i	$0.215053\pi$
$164$		−	4.73601i		−	0.369820i
$165$		0			0
$166$	−5.10226	−	8.83737i	−0.396012	−	0.685913i
$167$	−11.3614	−	19.6785i	−0.879173	−	1.52277i	−0.852250	−	0.523134i	$-0.824763\pi$
$167$	−11.3614	−	19.6785i	−0.879173	−	1.52277i	−0.0269225	−	0.999638i	$-0.508571\pi$
$168$		0			0
$169$	−2.91899	+	12.6681i	−0.224538	+	0.974465i
$170$	−10.2380	−	2.70790i	−0.785217	−	0.207687i
$171$		0			0
$172$	−1.70944	+	0.986944i	−0.130343	+	0.0752538i
$173$	−4.06859	−	2.34900i	−0.309329	−	0.178591i	0.337297	−	0.941398i	$-0.390487\pi$
$173$	−4.06859	−	2.34900i	−0.309329	−	0.178591i	−0.646626	+	0.762807i	$0.723821\pi$
$174$		0			0
$175$	−5.20376	+	3.04931i	−0.393367	+	0.230506i
$176$	4.46182	+	2.57603i	0.336322	+	0.194176i
$177$		0			0
$178$	14.1941	+	8.19497i	1.06389	+	0.614239i
$179$	4.34913	+	7.53292i	0.325069	+	0.563037i	0.981526	−	0.191327i	$-0.0612790\pi$
$179$	4.34913	+	7.53292i	0.325069	+	0.563037i	−0.656457	+	0.754363i	$0.727946\pi$
$180$		0			0
$181$	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
$183$		0			0
$184$	1.88293	−	1.08711i	0.138811	−	0.0801427i
$185$	9.49666	−	2.57747i	0.698208	−	0.189500i
$186$		0			0
$187$	24.4002			1.78432
$188$	0.426148	−	0.738110i	0.0310800	−	0.0538322i
$189$		0			0
$190$	−4.60474	−	1.21794i	−0.334063	−	0.0883583i
$191$	5.77729	−	10.0066i	0.418030	−	0.724049i	−0.577711	−	0.816241i	$-0.696054\pi$
$191$	5.77729	−	10.0066i	0.418030	−	0.724049i	0.995741	+	0.0921920i	$0.0293874\pi$
$192$		0			0
$193$	−5.23154	−	9.06130i	−0.376575	−	0.652247i	0.613987	−	0.789316i	$-0.289565\pi$
$193$	−5.23154	−	9.06130i	−0.376575	−	0.652247i	−0.990561	+	0.137070i	$0.956232\pi$
$194$	8.48278			0.609028
$195$		0			0
$196$	−5.54490			−0.396065
$197$	−8.79472	−	15.2329i	−0.626598	−	1.08530i	−0.988230	−	0.152978i	$-0.951113\pi$
$197$	−8.79472	−	15.2329i	−0.626598	−	1.08530i	0.361632	−	0.932321i	$-0.382220\pi$
$198$		0			0
$199$	12.7858	−	22.1457i	0.906362	−	1.56986i	0.0872828	−	0.996184i	$-0.472182\pi$
$199$	12.7858	−	22.1457i	0.906362	−	1.56986i	0.819079	−	0.573681i	$-0.194485\pi$
$200$	−4.34616	−	2.47202i	−0.307320	−	0.174798i
$201$		0			0
$202$	−6.79121	+	11.7627i	−0.477828	+	0.827623i
$203$	−5.75022			−0.403586
$204$		0			0
$205$	−2.77388	−	10.2203i	−0.193736	−	0.713817i
$206$	1.86798	−	1.07848i	0.130148	−	0.0751412i
$207$		0			0
$208$	1.32073	−	3.35495i	0.0915760	−	0.232624i
$209$	10.9745			0.759122
$210$		0			0
$211$	−6.45984	−	11.1888i	−0.444714	−	0.770267i	0.553318	−	0.832970i	$-0.313361\pi$
$211$	−6.45984	−	11.1888i	−0.444714	−	0.770267i	−0.998032	+	0.0627029i	$0.980028\pi$
$212$	3.88016	+	2.24021i	0.266490	+	0.153858i
$213$		0			0
$214$	−7.00959	−	4.04699i	−0.479165	−	0.276646i
$215$	−3.11091	+	3.13104i	−0.212162	+	0.213535i
$216$		0			0
$217$	−6.17445	−	3.56482i	−0.419149	−	0.241996i
$218$	14.6219	−	8.44195i	0.990319	−	0.571761i
$219$		0			0
$220$	11.1374	+	2.94579i	0.750882	+	0.198605i
$221$	−2.52757	−	16.8878i	−0.170022	−	1.13600i
$222$		0			0
$223$	3.57679	+	6.19518i	0.239519	+	0.414860i	0.960576	−	0.278016i	$-0.0896768\pi$
$223$	3.57679	+	6.19518i	0.239519	+	0.414860i	−0.721057	+	0.692876i	$0.756343\pi$
$224$	0.603137	+	1.04466i	0.0402988	+	0.0697995i
$225$		0			0
$226$		−	4.95102i		−	0.329337i
$227$	12.9192	−	22.3768i	0.857480	−	1.48520i	−0.0168460	−	0.999858i	$-0.505362\pi$
$227$	12.9192	−	22.3768i	0.857480	−	1.48520i	0.874325	−	0.485340i	$-0.161304\pi$
$228$		0			0
$229$			8.95153i			0.591533i	0.955260	+	0.295767i	$0.0955751\pi$
$229$			8.95153i			0.591533i	−0.955260	+	0.295767i	$0.904425\pi$
$230$	3.42664	−	3.44881i	0.225946	−	0.227408i
$231$		0			0
$232$	−2.38346	−	4.12828i	−0.156482	−	0.271035i
$233$		−	3.86657i		−	0.253308i	−0.991947	−	0.126654i	$-0.959576\pi$
$233$		−	3.86657i		−	0.253308i	0.991947	−	0.126654i	$-0.0404237\pi$
$234$		0			0
$235$	0.487316	−	1.84243i	0.0317890	−	0.120187i
$236$	1.68133	−	0.970715i	0.109445	−	0.0631882i
$237$		0			0
$238$	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			0
$241$	9.76603	+	5.63842i	0.629085	+	0.363203i	0.780398	−	0.625283i	$-0.215017\pi$
$241$	9.76603	+	5.63842i	0.629085	+	0.363203i	−0.151312	+	0.988486i	$0.548350\pi$
$242$	−15.5438			−0.999191
$243$		0			0
$244$	−1.53795	−	2.66381i	−0.0984574	−	0.170533i
$245$	−11.9659	+	3.24764i	−0.764473	+	0.207484i
$246$		0			0
$247$	−1.13682	−	7.59565i	−0.0723344	−	0.483299i
$248$		−	5.91046i		−	0.375315i
$249$		0			0
$250$	−10.8269	−	2.78907i	−0.684751	−	0.176397i
$251$	−6.15329	+	10.6578i	−0.388392	+	0.672715i	−0.992233	−	0.124390i	$-0.960303\pi$
$251$	−6.15329	+	10.6578i	−0.388392	+	0.672715i	0.603841	+	0.797104i	$0.293636\pi$
$252$		0			0
$253$	−5.60085	+	9.70096i	−0.352123	+	0.609894i
$254$	−1.04089	−	0.600957i	−0.0653112	−	0.0377074i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−24.3239	+	14.0434i	−1.51728	+	0.876004i	−0.517490	+	0.855689i	$0.673134\pi$
$257$	−24.3239	+	14.0434i	−1.51728	+	0.876004i	−0.999794	+	0.0203154i	$0.993533\pi$
$258$		0			0
$259$	−5.30842			−0.329849
$260$	0.885137	−	8.01352i	0.0548939	−	0.496978i
$261$		0			0
$262$	−3.32575	−	5.76036i	−0.205465	−	0.355876i
$263$	−6.56756	+	3.79178i	−0.404973	+	0.233811i	−0.688628	−	0.725115i	$-0.741787\pi$
$263$	−6.56756	+	3.79178i	−0.404973	+	0.233811i	0.283654	+	0.958927i	$0.408453\pi$
$264$		0			0
$265$	9.68546	+	2.56176i	0.594973	+	0.157368i
$266$	2.22526	+	1.28475i	0.136439	+	0.0787732i
$267$		0			0
$268$	14.0553			0.858564
$269$	12.2355	−	21.1924i	0.746010	−	1.29213i	−0.203712	−	0.979031i	$-0.565301\pi$
$269$	12.2355	−	21.1924i	0.746010	−	1.29213i	0.949722	−	0.313096i	$-0.101366\pi$
$270$		0			0
$271$	10.0199	−	5.78497i	0.608664	−	0.351412i	−0.163779	−	0.986497i	$-0.552368\pi$
$271$	10.0199	−	5.78497i	0.608664	−	0.351412i	0.772442	+	0.635085i	$0.219035\pi$
$272$			4.73601i			0.287163i
$273$		0			0
$274$	14.7149			0.888961
$275$	25.7598	−	0.166140i	1.55337	−	0.0100186i
$276$		0			0
$277$	−11.2111	−	6.47271i	−0.673608	−	0.388908i	0.123835	−	0.992303i	$-0.460481\pi$
$277$	−11.2111	−	6.47271i	−0.673608	−	0.388908i	−0.797442	+	0.603395i	$0.793814\pi$
$278$	15.6508			0.938673
$279$		0			0
$280$	1.91343	+	1.90113i	0.114349	+	0.113614i
$281$			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			0
$283$	−4.80517	+	2.77427i	−0.285638	+	0.164913i	−0.635973	−	0.771711i	$-0.719401\pi$
$283$	−4.80517	+	2.77427i	−0.285638	+	0.164913i	0.350335	+	0.936624i	$0.386068\pi$
$284$	−0.298707	+	0.172459i	−0.0177250	+	0.0102335i
$285$		0			0
$286$	2.74961	+	18.3714i	0.162588	+	1.08632i
$287$			5.71292i			0.337223i
$288$		0			0
$289$	2.71489	+	4.70233i	0.159700	+	0.276608i
$290$	−7.56144	−	7.51283i	−0.444023	−	0.441168i
$291$		0			0
$292$	7.86142	−	13.6164i	0.460055	−	0.796838i
$293$	−12.0658	+	20.8986i	−0.704891	+	1.22091i	0.261840	+	0.965111i	$0.415671\pi$
$293$	−12.0658	+	20.8986i	−0.704891	+	1.22091i	−0.966731	+	0.255795i	$0.917663\pi$
$294$		0			0
$295$	3.05976	−	3.07955i	0.178146	−	0.179299i
$296$	−2.20034	−	3.81110i	−0.127892	−	0.221516i
$297$		0			0
$298$		−	22.8116i		−	1.32144i
$299$	7.29439	+	2.87155i	0.421845	+	0.166066i
$300$		0			0
$301$	2.06205	−	1.19052i	0.118855	−	0.0686207i
$302$	17.2335	−	9.94975i	0.991675	−	0.572544i
$303$		0			0
$304$			2.13012i			0.122171i
$305$	−4.87910	−	4.84773i	−0.279376	−	0.277580i
$306$		0			0
$307$	30.3243			1.73070			0.865348	−	0.501171i	$-0.167097\pi$
$307$	30.3243			1.73070			0.865348	+	0.501171i	$0.167097\pi$
$308$	−5.38217	−	3.10740i	−0.306678	−	0.177061i
$309$		0			0
$310$	−3.46175	−	12.7548i	−0.196614	−	0.724422i
$311$	−8.76406			−0.496964			−0.248482	−	0.968636i	$-0.579932\pi$
$311$	−8.76406			−0.496964			−0.248482	+	0.968636i	$0.579932\pi$
$312$		0			0
$313$		−	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
$315$		0			0
$316$	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	$0.239489\pi$
$318$		0			0
$319$	21.2692	+	12.2798i	1.19084	+	0.687534i
$320$	−0.571769	+	2.16173i	−0.0319629	+	0.120844i
$321$		0			0
$322$	−2.27133	+	1.31135i	−0.126576	+	0.0730787i
$323$	5.04413	+	8.73669i	0.280663	+	0.486122i
$324$		0			0
$325$	−2.78339	−	17.8116i	−0.154395	−	0.988009i
$326$	3.86657			0.214150
$327$		0			0
$328$	−4.10150	+	2.36800i	−0.226468	+	0.130751i
$329$	−0.514051	+	0.890362i	−0.0283405	+	0.0490873i
$330$		0			0
$331$	−9.56025	−	5.51961i	−0.525479	−	0.303385i	0.213694	−	0.976901i	$-0.431450\pi$
$331$	−9.56025	−	5.51961i	−0.525479	−	0.303385i	−0.739173	+	0.673515i	$0.764784\pi$
$332$	−5.10226	+	8.83737i	−0.280023	+	0.485014i
$333$		0			0
$334$	−11.3614	+	19.6785i	−0.621669	+	1.07676i
$335$	30.3313	−	8.23218i	1.65718	−	0.449772i
$336$		0			0
$337$			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
$339$		0			0
$340$	2.77388	+	10.2203i	0.150435	+	0.554274i
$341$	15.2255	+	26.3714i	0.824509	+	1.42809i
$342$		0			0
$343$	15.1326			0.817083
$344$	1.70944	+	0.986944i	0.0921667	+	0.0532124i
$345$		0			0
$346$			4.69800i			0.252566i
$347$	30.0526	+	17.3509i	1.61331	+	0.931443i	0.988597	+	0.150587i	$0.0481162\pi$
$347$	30.0526	+	17.3509i	1.61331	+	0.931443i	0.624710	+	0.780857i	$0.285217\pi$
$348$		0			0
$349$	−30.4563	+	17.5840i	−1.63029	+	0.941249i	−0.646288	+	0.763093i	$0.723680\pi$
$349$	−30.4563	+	17.5840i	−1.63029	+	0.941249i	−0.984002	+	0.178156i	$0.942987\pi$
$350$	5.24266	+	2.98193i	0.280232	+	0.159391i
$351$		0			0
$352$		−	5.15206i		−	0.274606i
$353$	−5.54542	−	9.60495i	−0.295153	−	0.511220i	0.679868	−	0.733335i	$-0.262037\pi$
$353$	−5.54542	−	9.60495i	−0.295153	−	0.511220i	−0.975020	+	0.222115i	$0.928704\pi$
$354$		0			0
$355$	−0.543601	+	0.547118i	−0.0288513	+	0.0290380i
$356$		−	16.3899i		−	0.868665i
$357$		0			0
$358$	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	$0.757492\pi$
$360$		0			0
$361$	−7.23130	−	12.5250i	−0.380595	−	0.659209i
$362$	−4.87740	−	8.44791i	−0.256351	−	0.444012i
$363$		0			0
$364$	−1.59316	+	4.04699i	−0.0835042	+	0.212120i
$365$	8.98983	−	33.9885i	0.470549	−	1.77904i
$366$		0			0
$367$	−13.4988	+	7.79352i	−0.704630	+	0.406818i	−0.809070	−	0.587713i	$-0.800028\pi$
$367$	−13.4988	+	7.79352i	−0.704630	+	0.406818i	0.104440	+	0.994531i	$0.466695\pi$
$368$	−1.88293	−	1.08711i	−0.0981544	−	0.0566695i
$369$		0			0
$370$	−6.98049	−	6.93561i	−0.362898	−	0.360565i
$371$	−4.68053	−	2.70231i	−0.243001	−	0.140297i
$372$		0			0
$373$	−0.860358	−	0.496728i	−0.0445476	−	0.0257196i	0.477561	−	0.878599i	$-0.341521\pi$
$373$	−0.860358	−	0.496728i	−0.0445476	−	0.0257196i	−0.522108	+	0.852879i	$0.674854\pi$
$374$	−12.2001	−	21.1312i	−0.630853	−	1.09267i
$375$		0			0
$376$	−0.852296			−0.0439538
$377$	6.29581	−	15.9928i	0.324251	−	0.823671i
$378$		0			0
$379$	23.7856	−	13.7326i	1.22178	−	0.705398i	0.256486	−	0.966548i	$-0.417435\pi$
$379$	23.7856	−	13.7326i	1.22178	−	0.705398i	0.965298	+	0.261150i	$0.0841018\pi$
$380$	1.24761	+	4.59679i	0.0640009	+	0.235810i
$381$		0			0
$382$	−11.5546			−0.591184
$383$	−16.2851	+	28.2067i	−0.832132	+	1.44130i	0.0642122	+	0.997936i	$0.479547\pi$
$383$	−16.2851	+	28.2067i	−0.832132	+	1.44130i	−0.896344	+	0.443359i	$0.853787\pi$
$384$		0			0
$385$	−13.4347	−	3.55343i	−0.684697	−	0.181100i
$386$	−5.23154	+	9.06130i	−0.266279	+	0.461208i
$387$		0			0
$388$	−4.24139	−	7.34631i	−0.215324	−	0.372952i
$389$	16.9110			0.857421			0.428710	−	0.903442i	$-0.358968\pi$
$389$	16.9110			0.857421			0.428710	+	0.903442i	$0.358968\pi$
$390$		0			0
$391$	−10.2971			−0.520747
$392$	2.77245	+	4.80203i	0.140030	+	0.242539i
$393$		0			0
$394$	−8.79472	+	15.2329i	−0.443072	+	0.767423i
$395$	7.76823	−	29.3699i	0.390862	−	1.47776i
$396$		0			0
$397$	−16.1198	+	27.9204i	−0.809031	+	1.40128i	0.104504	+	0.994524i	$0.466674\pi$
$397$	−16.1198	+	27.9204i	−0.809031	+	1.40128i	−0.913536	+	0.406759i	$0.866659\pi$
$398$	−25.5716			−1.28179
$399$		0			0
$400$	0.0322474	+	4.99990i	0.00161237	+	0.249995i
$401$	−28.0082	+	16.1705i	−1.39866	+	0.807518i	−0.994253	−	0.107060i	$-0.965856\pi$
$401$	−28.0082	+	16.1705i	−1.39866	+	0.807518i	−0.404410	+	0.914578i	$0.632523\pi$
$402$		0			0
$403$	16.6749	−	13.2696i	0.830638	−	0.661007i
$404$	13.5824			0.675751
$405$		0			0
$406$	2.87511	+	4.97984i	0.142689	+	0.247145i
$407$	19.6350	+	11.3363i	0.973272	+	0.561919i
$408$		0			0
$409$	1.00971	+	0.582957i	0.0499270	+	0.0288254i	0.524756	−	0.851253i	$-0.324157\pi$
$409$	1.00971	+	0.582957i	0.0499270	+	0.0288254i	−0.474829	+	0.880078i	$0.657490\pi$
$410$	−7.46410	+	7.51240i	−0.368626	+	0.371011i
$411$		0			0
$412$	−1.86798	−	1.07848i	−0.0920288	−	0.0531328i
$413$	−2.02814	+	1.17095i	−0.0997984	+	0.0576186i
$414$		0			0
$415$	−5.83462	+	22.0594i	−0.286410	+	1.08285i
$416$	−3.56583	+	0.533691i	−0.174829	+	0.0261663i
$417$		0			0
$418$	−5.48725	−	9.50420i	−0.268390	−	0.464866i
$419$	−5.91396	−	10.2433i	−0.288916	−	0.500417i	0.684635	−	0.728886i	$-0.259961\pi$
$419$	−5.91396	−	10.2433i	−0.288916	−	0.500417i	−0.973551	+	0.228469i	$0.926628\pi$
$420$		0			0
$421$			23.9102i			1.16531i	0.812719	+	0.582655i	$0.197986\pi$
$421$			23.9102i			1.16531i	−0.812719	+	0.582655i	$0.802014\pi$
$422$	−6.45984	+	11.1888i	−0.314460	+	0.544661i
$423$		0			0
$424$		−	4.48042i		−	0.217588i
$425$	11.9720	+	20.4307i	0.580729	+	0.991036i
$426$		0			0
$427$	1.85519	+	3.21329i	0.0897791	+	0.155502i
$428$			8.09397i			0.391237i
$429$		0			0
$430$	4.26701	+	1.12861i	0.205774	+	0.0544263i
$431$	22.8082	−	13.1683i	1.09863	−	0.634294i	0.162769	−	0.986664i	$-0.447957\pi$
$431$	22.8082	−	13.1683i	1.09863	−	0.634294i	0.935861	+	0.352370i	$0.114624\pi$
$432$		0			0
$433$	−11.2232	−	6.47972i	−0.539353	−	0.311396i	0.205464	−	0.978665i	$-0.434130\pi$
$433$	−11.2232	−	6.47972i	−0.539353	−	0.311396i	−0.744817	+	0.667269i	$0.767463\pi$
$434$			7.12964i			0.342234i
$435$		0			0
$436$	−14.6219	−	8.44195i	−0.700261	−	0.404296i
$437$	−4.63134			−0.221547
$438$		0			0
$439$	11.6234	+	20.1324i	0.554756	+	0.960865i	0.997922	+	0.0644259i	$0.0205216\pi$
$439$	11.6234	+	20.1324i	0.554756	+	0.960865i	−0.443167	+	0.896439i	$0.646145\pi$
$440$	−3.01756	−	11.1181i	−0.143856	−	0.530037i
$441$		0			0
$442$	−13.3615	+	10.6328i	−0.635542	+	0.505753i
$443$			23.3728i			1.11047i	0.831692	+	0.555237i	$0.187373\pi$
$443$			23.3728i			1.11047i	−0.831692	+	0.555237i	$0.812627\pi$
$444$		0			0
$445$	−9.59957	−	35.3695i	−0.455063	−	1.67667i
$446$	3.57679	−	6.19518i	0.169366	−	0.293350i
$447$		0			0
$448$	0.603137	−	1.04466i	0.0284955	−	0.0493557i
$449$	−1.20931	−	0.698196i	−0.0570709	−	0.0329499i	0.471193	−	0.882030i	$-0.343824\pi$
$449$	−1.20931	−	0.698196i	−0.0570709	−	0.0329499i	−0.528264	+	0.849080i	$0.677157\pi$
$450$		0			0
$451$	12.2001	−	21.1312i	0.574481	−	0.995030i
$452$	−4.28771	+	2.47551i	−0.201677	+	0.116438i
$453$		0			0
$454$	−25.8385			−1.21266
$455$	−1.06772	+	9.66650i	−0.0500554	+	0.453173i
$456$		0			0
$457$	−3.60093	−	6.23699i	−0.168444	−	0.291754i	0.769429	−	0.638733i	$-0.220541\pi$
$457$	−3.60093	−	6.23699i	−0.168444	−	0.291754i	−0.937873	+	0.346979i	$0.887208\pi$
$458$	7.75225	−	4.47576i	0.362239	−	0.209139i
$459$		0			0
$460$	−4.70007	−	1.24315i	−0.219142	−	0.0579622i
$461$	4.10920	+	2.37245i	0.191384	+	0.110496i	0.592630	−	0.805474i	$-0.298089\pi$
$461$	4.10920	+	2.37245i	0.191384	+	0.110496i	−0.401246	+	0.915970i	$0.631423\pi$
$462$		0			0
$463$	−15.7510			−0.732012			−0.366006	−	0.930612i	$-0.619275\pi$
$463$	−15.7510			−0.732012			−0.366006	+	0.930612i	$0.619275\pi$
$464$	−2.38346	+	4.12828i	−0.110650	+	0.191651i
$465$		0			0
$466$	−3.34855	+	1.93329i	−0.155119	+	0.0895578i
$467$		−	17.9789i		−	0.831962i	−0.909373	−	0.415981i	$-0.863438\pi$
$467$		−	17.9789i		−	0.831962i	0.909373	−	0.415981i	$-0.136562\pi$
$468$		0			0
$469$	−16.9545			−0.782888
$470$	−1.83925	+	0.499189i	−0.0848384	+	0.0230259i
$471$		0			0
$472$	−1.68133	−	0.970715i	−0.0773894	−	0.0446808i
$473$	−10.1696			−0.467598
$474$		0			0
$475$	5.38467	+	9.18914i	0.247066	+	0.421627i
$476$		−	5.71292i		−	0.261851i
$477$		0			0
$478$	13.3521	−	7.70884i	0.610711	−	0.352594i
$479$	−2.83964	+	1.63947i	−0.129747	+	0.0749093i	−0.563468	−	0.826138i	$-0.690533\pi$
$479$	−2.83964	+	1.63947i	−0.129747	+	0.0749093i	0.433722	+	0.901047i	$0.357200\pi$
$480$		0			0
$481$	5.81210	−	14.7640i	0.265009	−	0.673183i
$482$		−	11.2768i		−	0.513646i
$483$		0			0
$484$	7.77188	+	13.4613i	0.353267	+	0.611877i
$485$	−13.4556	−	13.3691i	−0.610989	−	0.607061i
$486$		0			0
$487$	4.98852	−	8.64037i	0.226052	−	0.391533i	−0.730583	−	0.682824i	$-0.760752\pi$
$487$	4.98852	−	8.64037i	0.226052	−	0.391533i	0.956634	+	0.291291i	$0.0940849\pi$
$488$	−1.53795	+	2.66381i	−0.0696199	+	0.120585i
$489$		0			0
$490$	8.79549	+	8.73894i	0.397340	+	0.394785i
$491$	−10.0376	−	17.3857i	−0.452992	−	0.784605i	0.545578	−	0.838060i	$-0.316310\pi$
$491$	−10.0376	−	17.3857i	−0.452992	−	0.784605i	−0.998570	+	0.0534548i	$0.982977\pi$
$492$		0			0
$493$			22.5762i			1.01678i
$494$	−6.00961	+	4.78234i	−0.270385	+	0.215168i
$495$		0			0
$496$	−5.11861	+	2.95523i	−0.229832	+	0.132694i
$497$	0.360323	−	0.208033i	0.0161627	−	0.00933153i
$498$		0			0
$499$		−	23.9474i		−	1.07203i	−0.844208	−	0.536016i	$-0.819929\pi$
$499$		−	23.9474i		−	1.07203i	0.844208	−	0.536016i	$-0.180071\pi$
$500$	2.99802	+	10.7709i	0.134076	+	0.481688i
$501$		0			0
$502$	12.3066			0.549269
$503$	10.5377	+	6.08395i	0.469853	+	0.271270i	0.716178	−	0.697917i	$-0.245890\pi$
$503$	10.5377	+	6.08395i	0.469853	+	0.271270i	−0.246325	+	0.969187i	$0.579223\pi$
$504$		0			0
$505$	29.3109	−	7.95522i	1.30432	−	0.354002i
$506$	11.2017			0.497977
$507$		0			0
$508$			1.20191i			0.0533263i
$509$	−34.9666	+	20.1880i	−1.54987	+	0.894817i	−0.551717	+	0.834031i	$0.686027\pi$
$509$	−34.9666	+	20.1880i	−1.54987	+	0.894817i	−0.998151	+	0.0607857i	$0.980639\pi$
$510$		0			0
$511$	−9.48302	+	16.4251i	−0.419504	+	0.726602i
$512$	1.00000			0.0441942
$513$		0			0
$514$	24.3239	+	14.0434i	1.07288	+	0.619429i
$515$	−4.66276	−	1.23328i	−0.205466	−	0.0543449i
$516$		0			0
$517$	3.80279	−	2.19554i	0.167246	−	0.0965598i
$518$	2.65421	+	4.59723i	0.116619	+	0.201991i
$519$		0			0
$520$	−7.38248	+	3.24021i	−0.323743	+	0.142093i
$521$	0.259356			0.0113626			0.00568129	−	0.999984i	$-0.498192\pi$
$521$	0.259356			0.0113626			0.00568129	+	0.999984i	$0.498192\pi$
$522$		0			0
$523$	33.4527	−	19.3139i	1.46278	−	0.844539i	0.463645	−	0.886021i	$-0.346541\pi$
$523$	33.4527	−	19.3139i	1.46278	−	0.844539i	0.999139	+	0.0414825i	$0.0132081\pi$
$524$	−3.32575	+	5.76036i	−0.145286	+	0.251642i
$525$		0			0
$526$	6.56756	+	3.79178i	0.286359	+	0.165330i
$527$	−13.9960	+	24.2418i	−0.609676	+	1.05599i
$528$		0			0
$529$	−9.13639	+	15.8247i	−0.397234	+	0.688030i
$530$	−2.62418	−	9.66874i	−0.113987	−	0.419983i
$531$		0			0
$532$		−	2.56951i		−	0.111402i
$533$	−15.8891	−	6.25498i	−0.688232	−	0.270933i
$534$		0			0
$535$	4.74063	+	17.4668i	0.204955	+	0.755155i
$536$	−7.02765	−	12.1723i	−0.303548	−	0.525761i
$537$		0			0
$538$	−24.4709			−1.05502
$539$	−24.7403	−	14.2838i	−1.06564	−	0.615249i
$540$		0			0
$541$		−	19.4443i		−	0.835975i	−0.908453	−	0.417988i	$-0.862736\pi$
$541$		−	19.4443i		−	0.835975i	0.908453	−	0.417988i	$-0.137264\pi$
$542$	−10.0199	−	5.78497i	−0.430390	−	0.248486i
$543$		0			0
$544$	4.10150	−	2.36800i	0.175851	−	0.101527i
$545$	−36.4984	−	9.65369i	−1.56342	−	0.413518i
$546$		0			0
$547$			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
$549$		0			0
$550$	−13.0238	−	22.2256i	−0.555336	−	0.947701i
$551$			10.1541i			0.432580i
$552$		0			0
$553$	−8.19440	+	14.1931i	−0.348462	+	0.603553i
$554$			12.9454i			0.549998i
$555$		0			0
$556$	−7.82540	−	13.5540i	−0.331871	−	0.574817i
$557$	5.63445	+	9.75916i	0.238739	+	0.413509i	0.960353	−	0.278787i	$-0.0899325\pi$
$557$	5.63445	+	9.75916i	0.238739	+	0.413509i	−0.721613	+	0.692296i	$0.756599\pi$
$558$		0			0
$559$	1.05345	+	7.03856i	0.0445560	+	0.297699i
$560$	0.689710	−	2.60764i	0.0291456	−	0.110193i
$561$		0			0
$562$	2.22730	−	1.28593i	0.0939531	−	0.0542439i
$563$	−14.2495	−	8.22694i	−0.600544	−	0.346724i	0.168712	−	0.985665i	$-0.446039\pi$
$563$	−14.2495	−	8.22694i	−0.600544	−	0.346724i	−0.769256	+	0.638941i	$0.779373\pi$
$564$		0			0
$565$	−7.80296	+	7.85345i	−0.328273	+	0.330397i
$566$	4.80517	+	2.77427i	0.201976	+	0.116611i
$567$		0			0
$568$	0.298707	+	0.172459i	0.0125335	+	0.00723621i
$569$	−15.2444	−	26.4040i	−0.639077	−	1.10691i	−0.985636	−	0.168886i	$-0.945983\pi$
$569$	−15.2444	−	26.4040i	−0.639077	−	1.10691i	0.346558	−	0.938028i	$-0.387350\pi$
$570$		0			0
$571$	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
$573$		0			0
$574$	4.94754	−	2.85646i	0.206506	−	0.119226i
$575$	−10.8709	+	0.0701128i	−0.453346	+	0.00292390i
$576$		0			0
$577$	−13.1315			−0.546670			−0.273335	−	0.961919i	$-0.588127\pi$
$577$	−13.1315			−0.546670			−0.273335	+	0.961919i	$0.588127\pi$
$578$	2.71489	−	4.70233i	0.112925	−	0.195591i
$579$		0			0
$580$	−2.72558	+	10.3048i	−0.113174	+	0.427884i
$581$	6.15472	−	10.6603i	0.255341	−	0.442263i
$582$		0			0
$583$	11.5417	+	19.9908i	0.478009	+	0.827935i
$584$	−15.7228			−0.650615
$585$		0			0
$586$	24.1316			0.996866
$587$	−3.03785	−	5.26171i	−0.125386	−	0.217174i	0.796498	−	0.604641i	$-0.206683\pi$
$587$	−3.03785	−	5.26171i	−0.125386	−	0.217174i	−0.921884	+	0.387467i	$0.873350\pi$
$588$		0			0
$589$	−6.29499	+	10.9032i	−0.259381	+	0.449260i
$590$	−4.19685	−	1.11005i	−0.172782	−	0.0457000i
$591$		0			0
$592$	−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	$0.623043\pi$
$594$		0			0
$595$	−3.34605	−	12.3285i	−0.137175	−	0.505418i
$596$	−19.7555	+	11.4058i	−0.809215	+	0.467200i
$597$		0			0
$598$	−1.16036	−	7.75290i	−0.0474507	−	0.317040i
$599$	−22.1098			−0.903382			−0.451691	−	0.892174i	$-0.649179\pi$
$599$	−22.1098			−0.903382			−0.451691	+	0.892174i	$0.649179\pi$
$600$		0			0
$601$	−5.90349	−	10.2251i	−0.240808	−	0.417092i	0.720136	−	0.693832i	$-0.244079\pi$
$601$	−5.90349	−	10.2251i	−0.240808	−	0.417092i	−0.960945	+	0.276740i	$0.910746\pi$
$602$	−2.06205	−	1.19052i	−0.0840428	−	0.0485222i
$603$		0			0
$604$	−17.2335	−	9.94975i	−0.701220	−	0.404850i
$605$	24.6560	+	24.4975i	1.00241	+	0.995963i
$606$		0			0
$607$	22.3119	+	12.8818i	0.905612	+	0.522856i	0.879017	−	0.476791i	$-0.158200\pi$
$607$	22.3119	+	12.8818i	0.905612	+	0.522856i	0.0265955	+	0.999646i	$0.491533\pi$
$608$	1.84474	−	1.06506i	0.0748139	−	0.0431938i
$609$		0			0
$610$	−1.75871	+	6.64928i	−0.0712080	+	0.269222i
$611$	−1.91349	−	2.40455i	−0.0774117	−	0.0972775i
$612$		0			0
$613$	6.54178	+	11.3307i	0.264220	+	0.457642i	0.967359	−	0.253410i	$-0.0815522\pi$
$613$	6.54178	+	11.3307i	0.264220	+	0.457642i	−0.703139	+	0.711052i	$0.748219\pi$
$614$	−15.1621	−	26.2616i	−0.611894	−	1.05983i
$615$		0			0
$616$			6.21480i			0.250401i
$617$	2.20914	−	3.82634i	0.0889366	−	0.154043i	−0.818125	−	0.575040i	$-0.804986\pi$
$617$	2.20914	−	3.82634i	0.0889366	−	0.154043i	0.907062	+	0.420997i	$0.138320\pi$
$618$		0			0
$619$			1.12760i			0.0453220i	0.999743	+	0.0226610i	$0.00721383\pi$
$619$			1.12760i			0.0453220i	−0.999743	+	0.0226610i	$0.992786\pi$
$620$	−9.31508	+	9.37535i	−0.374103	+	0.376523i
$621$		0			0
$622$	4.38203	+	7.58990i	0.175703	+	0.304327i
$623$			19.7708i			0.792099i
$624$		0			0
$625$	12.7782	+	21.4876i	0.511129	+	0.859504i
$626$	−25.1282	+	14.5077i	−1.00432	+	0.579846i
$627$		0			0
$628$	4.10836	+	2.37196i	0.163941	+	0.0946515i
$629$			20.8417i			0.831011i
$630$		0			0
$631$	−14.3916	−	8.30898i	−0.572920	−	0.330775i	0.185395	−	0.982664i	$-0.440644\pi$
$631$	−14.3916	−	8.30898i	−0.572920	−	0.330775i	−0.758315	+	0.651889i	$0.773977\pi$
$632$	−13.5863			−0.540434
$633$		0			0
$634$	−12.9985	−	22.5140i	−0.516236	−	0.894147i
$635$	0.703960	+	2.59373i	0.0279358	+	0.102929i
$636$		0			0
$637$	−7.32331	+	18.6029i	−0.290160	+	0.737072i
$638$		−	24.5595i		−	0.972320i
$639$		0			0
$640$	2.15800	−	0.585699i	0.0853024	−	0.0231518i
$641$	−5.05184	+	8.75005i	−0.199536	+	0.345606i	−0.948378	−	0.317142i	$-0.897277\pi$
$641$	−5.05184	+	8.75005i	−0.199536	+	0.345606i	0.748842	+	0.662748i	$0.230610\pi$
$642$		0			0
$643$	−17.5208	+	30.3469i	−0.690951	+	1.19676i	0.280575	+	0.959832i	$0.409475\pi$
$643$	−17.5208	+	30.3469i	−0.690951	+	1.19676i	−0.971526	+	0.236931i	$0.923858\pi$
$644$	2.27133	+	1.31135i	0.0895028	+	0.0516745i
$645$		0			0
$646$	5.04413	−	8.73669i	0.198459	−	0.343740i
$647$	17.2864	−	9.98031i	0.679598	−	0.392366i	−0.120105	−	0.992761i	$-0.538323\pi$
$647$	17.2864	−	9.98031i	0.679598	−	0.392366i	0.799704	+	0.600395i	$0.204990\pi$
$648$		0			0
$649$	10.0024			0.392628
$650$	−14.0336	+	11.3163i	−0.550443	+	0.443861i
$651$		0			0
$652$	−1.93329	−	3.34855i	−0.0757133	−	0.131139i
$653$	−4.51410	+	2.60621i	−0.176650	+	0.101989i	−0.585718	−	0.810515i	$-0.699187\pi$
$653$	−4.51410	+	2.60621i	−0.176650	+	0.101989i	0.409068	+	0.912504i	$0.365854\pi$
$654$		0			0
$655$	−3.80312	+	14.3787i	−0.148600	+	0.561824i
$656$	4.10150	+	2.36800i	0.160137	+	0.0924551i
$657$		0			0
$658$	1.02810			0.0400796
$659$	−3.66183	+	6.34248i	−0.142645	+	0.247068i	−0.928492	−	0.371353i	$-0.878894\pi$
$659$	−3.66183	+	6.34248i	−0.142645	+	0.247068i	0.785847	+	0.618421i	$0.212227\pi$
$660$		0			0
$661$	−31.7189	+	18.3129i	−1.23372	+	0.712289i	−0.967803	−	0.251707i	$-0.919008\pi$
$661$	−31.7189	+	18.3129i	−1.23372	+	0.712289i	−0.265917	+	0.963996i	$0.585675\pi$
$662$			11.0392i			0.429052i
$663$		0			0
$664$	10.2045			0.396012
$665$	−1.50496	−	5.54499i	−0.0583597	−	0.215025i
$666$		0			0
$667$	−8.97578	−	5.18217i	−0.347543	−	0.200654i
$668$	22.7228			0.879173
$669$		0			0
$670$	−22.2949	−	22.1516i	−0.861329	−	0.855791i
$671$		−	15.8473i		−	0.611777i
$672$		0			0
$673$	29.4292	−	16.9909i	1.13441	−	0.654952i	0.189370	−	0.981906i	$-0.439355\pi$
$673$	29.4292	−	16.9909i	1.13441	−	0.654952i	0.945041	+	0.326953i	$0.106022\pi$
$674$	15.3380	−	8.85540i	0.590798	−	0.341097i
$675$		0			0
$676$	−9.51136	−	8.86194i	−0.365822	−	0.340844i
$677$			41.7902i			1.60613i	0.595894	+	0.803063i	$0.296798\pi$
$677$			41.7902i			1.60613i	−0.595894	+	0.803063i	$0.703202\pi$
$678$		0			0
$679$	5.11628	+	8.86166i	0.196345	+	0.340079i
$680$	7.46410	−	7.51240i	0.286235	−	0.288087i
$681$		0			0
$682$	15.2255	−	26.3714i	0.583016	−	1.00981i
$683$	−24.2071	+	41.9280i	−0.926260	+	1.60433i	−0.136737	+	0.990607i	$0.543662\pi$
$683$	−24.2071	+	41.9280i	−0.926260	+	1.60433i	−0.789523	+	0.613721i	$0.789672\pi$
$684$		0			0
$685$	−23.3412	−	23.1912i	−0.891823	−	0.886089i
$686$	−7.56629	−	13.1052i	−0.288882	−	0.500359i
$687$		0			0
$688$		−	1.97389i		−	0.0752538i
$689$	12.6404	−	10.0590i	0.481562	−	0.383218i
$690$		0			0
$691$	−23.8905	+	13.7932i	−0.908837	+	0.524717i	−0.880057	−	0.474868i	$-0.842496\pi$
$691$	−23.8905	+	13.7932i	−0.908837	+	0.524717i	−0.0287804	+	0.999586i	$0.509162\pi$
$692$	4.06859	−	2.34900i	0.154664	−	0.0892955i
$693$		0			0
$694$		−	34.7017i		−	1.31726i
$695$	−24.8258	−	24.6662i	−0.941695	−	0.935641i
$696$		0			0
$697$	22.4298			0.849589
$698$	30.4563	+	17.5840i	1.15279	+	0.665563i
$699$		0			0
$700$	−0.0388991	−	6.03124i	−0.00147025	−	0.227960i
$701$	19.7883			0.747392			0.373696	−	0.927551i	$-0.378090\pi$
$701$	19.7883			0.747392			0.373696	+	0.927551i	$0.378090\pi$
$702$		0			0
$703$			9.37396i			0.353546i
$704$	−4.46182	+	2.57603i	−0.168161	+	0.0970879i
$705$		0			0
$706$	−5.54542	+	9.60495i	−0.208705	+	0.361487i
$707$	−16.3841			−0.616189
$708$		0			0
$709$	−6.09389	−	3.51831i	−0.228861	−	0.132133i	0.381186	−	0.924499i	$-0.375516\pi$
$709$	−6.09389	−	3.51831i	−0.228861	−	0.132133i	−0.610046	+	0.792366i	$0.708849\pi$
$710$	0.745619	+	0.197213i	0.0279826	+	0.00740128i
$711$		0			0
$712$	−14.1941	+	8.19497i	−0.531946	+	0.307119i
$713$	−6.42532	−	11.1290i	−0.240630	−	0.416783i
$714$		0			0
$715$	24.5924	−	33.4747i	0.919704	−	1.25188i
$716$	−8.69827			−0.325069
$717$		0			0
$718$	22.6531	−	13.0788i	0.845405	−	0.488095i
$719$	5.52118	−	9.56296i	0.205905	−	0.356638i	−0.744516	−	0.667605i	$-0.767319\pi$
$719$	5.52118	−	9.56296i	0.205905	−	0.356638i	0.950421	+	0.310967i	$0.100653\pi$
$720$		0			0
$721$	2.25330	+	1.30094i	0.0839171	+	0.0484496i
$722$	−7.23130	+	12.5250i	−0.269121	+	0.466131i
$723$		0			0
$724$	−4.87740	+	8.44791i	−0.181267	+	0.313964i
$725$	0.153721	+	23.8341i	0.00570905	+	0.885178i
$726$		0			0
$727$			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
$729$		0			0
$730$	−33.9298	+	9.20885i	−1.25580	+	0.340835i
$731$	−4.67418	−	8.09591i	−0.172881	−	0.299438i
$732$		0			0
$733$	−11.3855			−0.420535			−0.210267	−	0.977644i	$-0.567433\pi$
$733$	−11.3855			−0.420535			−0.210267	+	0.977644i	$0.567433\pi$
$734$	13.4988	+	7.79352i	0.498249	+	0.287664i
$735$		0			0
$736$			2.17422i			0.0801427i
$737$	62.7122	+	36.2069i	2.31003	+	1.33370i
$738$		0			0
$739$	−7.93251	+	4.57983i	−0.291802	+	0.168472i	−0.638754	−	0.769411i	$-0.720550\pi$
$739$	−7.93251	+	4.57983i	−0.291802	+	0.168472i	0.346952	+	0.937883i	$0.387217\pi$
$740$	−2.51617	+	9.51308i	−0.0924963	+	0.349708i
$741$		0			0
$742$			5.40461i			0.198410i
$743$	−19.9566	−	34.5658i	−0.732135	−	1.26809i	−0.955969	−	0.293468i	$-0.905191\pi$
$743$	−19.9566	−	34.5658i	−0.732135	−	1.26809i	0.223834	−	0.974627i	$-0.428143\pi$
$744$		0			0
$745$	−35.9519	+	36.1845i	−1.31717	+	1.32570i
$746$			0.993455i			0.0363730i
$747$		0			0
$748$	−12.2001	+	21.1312i	−0.446080	+	0.772634i
$749$		−	9.76355i		−	0.356752i
$750$		0			0
$751$	8.79993	+	15.2419i	0.321114	+	0.556186i	0.980718	−	0.195427i	$-0.0626094\pi$
$751$	8.79993	+	15.2419i	0.321114	+	0.556186i	−0.659604	+	0.751613i	$0.729276\pi$
$752$	0.426148	+	0.738110i	0.0155400	+	0.0269161i
$753$		0			0
$754$	−16.9981	+	2.54407i	−0.619033	+	0.0926494i
$755$	−43.0174	−	11.3779i	−1.56556	−	0.414085i
$756$		0			0
$757$	19.1099	−	11.0331i	0.694560	−	0.401004i	−0.110758	−	0.993847i	$-0.535328\pi$
$757$	19.1099	−	11.0331i	0.694560	−	0.401004i	0.805318	+	0.592843i	$0.201995\pi$
$758$	−23.7856	−	13.7326i	−0.863932	−	0.498791i
$759$		0			0
$760$	3.35713	−	3.37886i	0.121776	−	0.122564i
$761$	17.4454	+	10.0721i	0.632394	+	0.365113i	0.781678	−	0.623682i	$-0.214364\pi$
$761$	17.4454	+	10.0721i	0.632394	+	0.365113i	−0.149285	+	0.988794i	$0.547697\pi$
$762$		0			0
$763$	17.6380	+	10.1833i	0.638538	+	0.368660i
$764$	5.77729	+	10.0066i	0.209015	+	0.362025i
$765$		0			0
$766$	32.5703			1.17681
$767$	−1.03612	−	6.92282i	−0.0374123	−	0.249969i
$768$		0			0
$769$	26.9356	−	15.5513i	0.971323	−	0.560794i	0.0716840	−	0.997427i	$-0.477163\pi$
$769$	26.9356	−	15.5513i	0.971323	−	0.560794i	0.899639	+	0.436634i	$0.143829\pi$
$770$	3.64000	+	13.4115i	0.131177	+	0.483318i
$771$		0			0
$772$	10.4631			0.376575
$773$	−0.416119	+	0.720739i	−0.0149668	+	0.0259232i	−0.873412	−	0.486982i	$-0.838098\pi$
$773$	−0.416119	+	0.720739i	−0.0149668	+	0.0259232i	0.858445	+	0.512906i	$0.171431\pi$
$774$		0			0
$775$	−14.6108	+	25.6878i	−0.524835	+	0.922734i
$776$	−4.24139	+	7.34631i	−0.152257	+	0.263717i
$777$		0			0
$778$	−8.45549	−	14.6453i	−0.303144	−	0.525061i
$779$	10.0883			0.361449
$780$		0			0
$781$	−1.77704			−0.0635874
$782$	5.14856	+	8.91756i	0.184112	+	0.318891i
$783$		0			0
$784$	2.77245	−	4.80203i	0.0990161	−	0.171501i
$785$	10.2551	+	2.71243i	0.366019	+	0.0968106i
$786$		0			0
$787$	12.4115	−	21.4974i	0.442422	−	0.766298i	−0.555446	−	0.831552i	$-0.687453\pi$
$787$	12.4115	−	21.4974i	0.442422	−	0.766298i	0.997869	+	0.0652545i	$0.0207859\pi$
$788$	17.5894			0.626598
$789$		0			0
$790$	−29.3192	+	7.95749i	−1.04313	+	0.283115i
$791$	5.17215	−	2.98614i	0.183900	−	0.106175i
$792$		0			0
$793$	−10.9682	+	1.64158i	−0.389491	+	0.0582944i
$794$	32.2397			1.14414
$795$		0			0
$796$	12.7858	+	22.1457i	0.453181	+	0.784932i
$797$	−20.5483	−	11.8636i	−0.727858	−	0.420229i	0.0897802	−	0.995962i	$-0.471384\pi$
$797$	−20.5483	−	11.8636i	−0.727858	−	0.420229i	−0.817638	+	0.575733i	$0.804717\pi$
$798$		0			0
$799$	3.49569	+	2.01824i	0.123669	+	0.0714002i
$800$	4.31391	−	2.52788i	0.152520	−	0.0893739i
$801$		0			0
$802$	28.0082	+	16.1705i	0.989003	+	0.571001i
$803$	70.1524	−	40.5025i	2.47562	−	1.42930i
$804$		0			0
$805$	5.66958	+	1.49958i	0.199826	+	0.0528532i
$806$	−19.8293	−	7.80611i	−0.698457	−	0.274959i
$807$		0			0
$808$	−6.79121	−	11.7627i	−0.238914	−	0.413811i
$809$	−18.7196	−	32.4233i	−0.658145	−	1.13994i	−0.981095	−	0.193525i	$-0.938008\pi$
$809$	−18.7196	−	32.4233i	−0.658145	−	1.13994i	0.322950	−	0.946416i	$-0.395325\pi$
$810$		0			0
$811$			40.2205i			1.41233i	0.708046	+	0.706166i	$0.249577\pi$
$811$			40.2205i			1.41233i	−0.708046	+	0.706166i	$0.750423\pi$
$812$	2.87511	−	4.97984i	0.100897	−	0.174758i
$813$		0			0
$814$		−	22.6726i		−	0.794673i
$815$	−6.13327	−	6.09384i	−0.214839	−	0.213458i
$816$		0			0
$817$	−2.10231	−	3.64130i	−0.0735504	−	0.127393i
$818$		−	1.16591i		−	0.0407652i
$819$		0			0
$820$	10.2380	+	2.70790i	0.357526	+	0.0945641i
$821$	24.5442	−	14.1706i	0.856598	−	0.494557i	−0.00627372	−	0.999980i	$-0.501997\pi$
$821$	24.5442	−	14.1706i	0.856598	−	0.494557i	0.862872	+	0.505423i	$0.168664\pi$
$822$		0			0
$823$	−41.0437	−	23.6966i	−1.43069	−	0.826011i	−0.433520	−	0.901144i	$-0.642729\pi$
$823$	−41.0437	−	23.6966i	−1.43069	−	0.826011i	−0.997174	+	0.0751325i	$0.976062\pi$
$824$			2.15696i			0.0751412i
$825$		0			0
$826$	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	$0.485042\pi$
$828$		0			0
$829$	−10.4285	−	18.0627i	−0.362197	−	0.627343i	0.626125	−	0.779722i	$-0.284640\pi$
$829$	−10.4285	−	18.0627i	−0.362197	−	0.627343i	−0.988322	+	0.152379i	$0.951307\pi$
$830$	22.0213	−	5.97677i	0.764371	−	0.207457i
$831$		0			0
$832$	2.24511	+	2.82126i	0.0778351	+	0.0978095i
$833$		−	26.2607i		−	0.909880i
$834$		0			0
$835$	49.0358	−	13.3087i	1.69695	−	0.460568i
$836$	−5.48725	+	9.50420i	−0.189781	+	0.328710i
$837$		0			0
$838$	−5.91396	+	10.2433i	−0.204294	+	0.353848i
$839$	−5.34438	−	3.08558i	−0.184508	−	0.106526i	0.404901	−	0.914361i	$-0.367306\pi$
$839$	−5.34438	−	3.08558i	−0.184508	−	0.106526i	−0.589409	+	0.807835i	$0.700639\pi$
$840$		0			0
$841$	3.13821	−	5.43553i	0.108214	−	0.187432i
$842$	20.7068	−	11.9551i	0.713604	−	0.412000i
$843$		0			0
$844$	12.9197			0.444714
$845$	−25.7159	−	13.5533i	−0.884655	−	0.466247i
$846$		0			0
$847$	−9.37502	−	16.2380i	−0.322129	−	0.557944i
$848$	−3.88016	+	2.24021i	−0.133245	+	0.0769291i
$849$		0			0
$850$	11.7075	−	20.5835i	0.401564	−	0.706007i
$851$	−8.28616	−	4.78402i	−0.284046	−	0.163994i
$852$		0			0
$853$	−52.4997			−1.79756			−0.898778	−	0.438405i	$-0.855544\pi$
$853$	−52.4997			−1.79756			−0.898778	+	0.438405i	$0.855544\pi$
$854$	1.85519	−	3.21329i	0.0634834	−	0.109956i
$855$		0			0
$856$	7.00959	−	4.04699i	0.239583	−	0.138323i
$857$			23.9128i			0.816846i	0.912793	+	0.408423i	$0.133921\pi$
$857$			23.9128i			0.816846i	−0.912793	+	0.408423i	$0.866079\pi$
$858$		0			0
$859$	−35.2521			−1.20279			−0.601393	−	0.798953i	$-0.705387\pi$
$859$	−35.2521			−1.20279			−0.601393	+	0.798953i	$0.705387\pi$
$860$	−1.15610	−	4.25965i	−0.0394228	−	0.145253i
$861$		0			0
$862$	−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			0
$865$	7.40419	−	7.45210i	0.251750	−	0.253379i
$866$			12.9594i			0.440380i
$867$		0			0
$868$	6.17445	−	3.56482i	0.209574	−	0.120998i
$869$	60.6196	−	34.9988i	2.05638	−	1.18725i
$870$		0			0
$871$	18.5632	−	47.1548i	0.628991	−	1.59778i
$872$			16.8839i			0.571761i
$873$		0			0
$874$	2.31567	+	4.01086i	0.0783287	+	0.135669i
$875$	−3.61644	−	12.9926i	−0.122258	−	0.439231i
$876$		0			0
$877$	8.42697	−	14.5959i	0.284559	−	0.492870i	−0.687943	−	0.725764i	$-0.741486\pi$
$877$	8.42697	−	14.5959i	0.284559	−	0.492870i	0.972502	+	0.232894i	$0.0748196\pi$
$878$	11.6234	−	20.1324i	0.392272	−	0.679434i
$879$		0			0
$880$	−8.11982	+	8.17235i	−0.273719	+	0.275490i
$881$	24.0475	+	41.6516i	0.810182	+	1.40328i	0.912736	+	0.408550i	$0.133965\pi$
$881$	24.0475	+	41.6516i	0.810182	+	1.40328i	−0.102554	+	0.994727i	$0.532701\pi$
$882$		0			0
$883$		−	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
$885$		0			0
$886$	20.2414	−	11.6864i	0.680024	−	0.392612i
$887$	16.2697	−	9.39331i	0.546283	−	0.315396i	−0.201339	−	0.979522i	$-0.564529\pi$
$887$	16.2697	−	9.39331i	0.546283	−	0.315396i	0.747621	+	0.664125i	$0.231196\pi$
$888$		0			0
$889$		−	1.44984i		−	0.0486260i
$890$	−25.8311	+	25.9982i	−0.865859	+	0.871462i
$891$		0			0
$892$	−7.15357			−0.239519
$893$	1.57226	+	0.907745i	0.0526137	+	0.0303765i
$894$		0			0
$895$	−18.7708	+	5.09457i	−0.627440	+	0.170293i
$896$	−1.20627			−0.0402988
$897$		0			0
$898$			1.39639i			0.0465982i
$899$	−24.4000	+	14.0874i	−0.813787	+	0.469840i
$900$		0			0
$901$	−10.6097	+	18.3765i	−0.353459	+	0.612209i
$902$	−24.4002			−0.812439
$903$		0			0
$904$	4.28771	+	2.47551i	0.142607	+	0.0823342i
$905$	−5.57749	+	21.0873i	−0.185402	+	0.700964i
$906$		0			0
$907$	18.2967	−	10.5636i	0.607532	−	0.350759i	−0.164467	−	0.986383i	$-0.552590\pi$
$907$	18.2967	−	10.5636i	0.607532	−	0.350759i	0.771999	+	0.635624i	$0.219257\pi$
$908$	12.9192	+	22.3768i	0.428740	+	0.742599i
$909$		0			0
$910$	8.90530	−	3.90858i	0.295208	−	0.129568i
$911$	−19.2766			−0.638664			−0.319332	−	0.947643i	$-0.603458\pi$
$911$	−19.2766			−0.638664			−0.319332	+	0.947643i	$0.603458\pi$
$912$		0			0
$913$	−45.5307	+	26.2872i	−1.50685	+	0.869978i
$914$	−3.60093	+	6.23699i	−0.119108	+	0.206301i
$915$		0			0
$916$	−7.75225	−	4.47576i	−0.256142	−	0.147883i
$917$	4.01176	−	6.94857i	0.132480	−	0.229462i
$918$		0			0
$919$	17.8995	−	31.0028i	0.590450	−	1.02269i	−0.403722	−	0.914882i	$-0.632284\pi$
$919$	17.8995	−	31.0028i	0.590450	−	1.02269i	0.994172	−	0.107807i	$-0.0343830\pi$
$920$	1.27344	+	4.69196i	0.0419840	+	0.154689i
$921$		0			0
$922$		−	4.74489i		−	0.156265i
$923$	0.184079	+	1.22992i	0.00605905	+	0.0404833i
$924$		0			0
$925$	0.141910	+	22.0029i	0.00466598	+	0.723452i
$926$	7.87551	+	13.6408i	0.258805	+	0.448264i
$927$		0			0
$928$	4.76693			0.156482
$929$	13.4933	+	7.79033i	0.442699	+	0.255593i	0.704742	−	0.709464i	$-0.251063\pi$
$929$	13.4933	+	7.79033i	0.442699	+	0.255593i	−0.262043	+	0.965056i	$0.584396\pi$
$930$		0			0
$931$		−	11.8113i		−	0.387100i
$932$	3.34855	+	1.93329i	0.109685	+	0.0633269i
$933$		0			0
$934$	−15.5701	+	8.98943i	−0.509471	+	0.294143i
$935$	−13.9513	+	52.7467i	−0.456256	+	1.72500i
$936$		0			0
$937$		−	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
$939$		0			0
$940$	1.35194	+	1.34324i	0.0440953	+	0.0438118i
$941$		−	5.01957i		−	0.163633i	−0.996647	−	0.0818167i	$-0.973928\pi$
$941$		−	5.01957i		−	0.163633i	0.996647	−	0.0818167i	$-0.0260722\pi$
$942$		0			0
$943$	−5.14856	+	8.91756i	−0.167660	+	0.290396i
$944$			1.94143i			0.0631882i
$945$		0			0
$946$	5.08480	+	8.80713i	0.165321	+	0.286344i
$947$	−20.0915	−	34.7995i	−0.652886	−	1.13083i	−0.982419	−	0.186688i	$-0.940225\pi$
$947$	−20.0915	−	34.7995i	−0.652886	−	1.13083i	0.329534	−	0.944144i	$-0.393109\pi$
$948$		0			0
$949$	−35.2994	−	44.3582i	−1.14587	−	1.43993i
$950$	5.26570	−	9.25783i	0.170842	−	0.300364i
$951$		0			0
$952$	−4.94754	+	2.85646i	−0.160351	+	0.0925785i
$953$	9.42493	+	5.44149i	0.305304	+	0.176267i	0.644823	−	0.764332i	$-0.276931\pi$
$953$	9.42493	+	5.44149i	0.305304	+	0.176267i	−0.339519	+	0.940599i	$0.610264\pi$
$954$		0			0
$955$	18.3282	+	18.2104i	0.593087	+	0.589274i
$956$	−13.3521	−	7.70884i	−0.431838	−	0.249322i
$957$		0			0
$958$	2.83964	+	1.63947i	0.0917447	+	0.0529688i
$959$	8.87511	+	15.3721i	0.286592	+	0.496392i
$960$		0			0
$961$	−3.93359			−0.126890
$962$	−15.6921	+	2.34860i	−0.505933	+	0.0757220i
$963$		0			0
$964$	−9.76603	+	5.63842i	−0.314543	+	0.181601i
$965$	22.5793	−	6.12822i	0.726854	−	0.197274i
$966$		0			0
$967$	−2.14376			−0.0689387			−0.0344693	−	0.999406i	$-0.510974\pi$
$967$	−2.14376			−0.0689387			−0.0344693	+	0.999406i	$0.510974\pi$
$968$	7.77188	−	13.4613i	0.249798	−	0.432662i
$969$		0			0
$970$	−4.85019	+	18.3375i	−0.155730	+	0.588781i
$971$	4.57889	−	7.93087i	0.146944	−	0.254514i	−0.783153	−	0.621829i	$-0.786390\pi$
$971$	4.57889	−	7.93087i	0.146944	−	0.254514i	0.930096	+	0.367316i	$0.119723\pi$
$972$		0			0
$973$	9.43958	+	16.3498i	0.302619	+	0.524151i
$974$	−9.97704			−0.319685
$975$		0			0
$976$	3.07591			0.0984574
$977$	7.16508	+	12.4103i	0.229231	+	0.397040i	0.957581	−	0.288166i	$-0.0930454\pi$
$977$	7.16508	+	12.4103i	0.229231	+	0.397040i	−0.728349	+	0.685206i	$0.759712\pi$
$978$		0			0
$979$	42.2210	−	73.1289i	1.34939	−	2.33721i
$980$	3.17040	−	11.9866i	0.101275	−	0.382898i
$981$		0			0
$982$	−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	$0.611994\pi$
$984$		0			0
$985$	37.9580	−	10.3021i	1.20944	−	0.328253i
$986$	19.5516	−	11.2881i	0.622649	−	0.359486i
$987$		0			0
$988$	7.14644	+	2.81330i	0.227358	+	0.0895031i
$989$	4.29166			0.136467
$990$		0			0
$991$	−11.9222	−	20.6499i	−0.378722	−	0.655966i	0.612154	−	0.790738i	$-0.290303\pi$
$991$	−11.9222	−	20.6499i	−0.378722	−	0.655966i	−0.990877	+	0.134772i	$0.956970\pi$
$992$	5.11861	+	2.95523i	0.162516	+	0.0938287i
$993$		0			0
$994$	−0.360323	−	0.208033i	−0.0114287	−	0.00659839i
$995$	40.5624	+	40.3017i	1.28592	+	1.27765i
$996$		0			0
$997$	25.5772	+	14.7670i	0.810037	+	0.467675i	0.846969	−	0.531642i	$-0.178425\pi$
$997$	25.5772	+	14.7670i	0.810037	+	0.467675i	−0.0369315	+	0.999318i	$0.511758\pi$
$998$	−20.7390	+	11.9737i	−0.656482	+	0.379020i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bj.c.829.3		12
3.2	odd	2		390.2.x.b.49.3	yes	12
5.4	even	2		1170.2.bj.d.829.4		12
13.4	even	6		1170.2.bj.d.199.4		12
15.2	even	4		1950.2.bc.j.751.3		12
15.8	even	4		1950.2.bc.i.751.4		12
15.14	odd	2		390.2.x.a.49.4	✓	12
39.17	odd	6		390.2.x.a.199.4	yes	12
65.4	even	6	inner	1170.2.bj.c.199.3		12
195.17	even	12		1950.2.bc.j.901.3		12
195.134	odd	6		390.2.x.b.199.3	yes	12
195.173	even	12		1950.2.bc.i.901.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.4	✓	12	15.14	odd	2
390.2.x.a.199.4	yes	12	39.17	odd	6
390.2.x.b.49.3	yes	12	3.2	odd	2
390.2.x.b.199.3	yes	12	195.134	odd	6
1170.2.bj.c.199.3		12	65.4	even	6	inner
1170.2.bj.c.829.3		12	1.1	even	1	trivial
1170.2.bj.d.199.4		12	13.4	even	6
1170.2.bj.d.829.4		12	5.4	even	2
1950.2.bc.i.751.4		12	15.8	even	4
1950.2.bc.i.901.4		12	195.173	even	12
1950.2.bc.j.751.3		12	15.2	even	4
1950.2.bc.j.901.3		12	195.17	even	12

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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.571769 + 2.16173i) q^{5} +(0.603137 - 1.04466i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.571769 + 2.16173i) q^{5} +(0.603137 - 1.04466i) q^{7} +1.00000 q^{8} +(2.15800 - 0.585699i) q^{10} +(-4.46182 + 2.57603i) q^{11} +(2.24511 + 2.82126i) q^{13} -1.20627 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.10150 - 2.36800i) q^{17} +(-1.84474 - 1.06506i) q^{19} +(-1.58623 - 1.57603i) q^{20} +(4.46182 + 2.57603i) q^{22} +(1.88293 - 1.08711i) q^{23} +(-4.34616 - 2.47202i) q^{25} +(1.32073 - 3.35495i) q^{26} +(0.603137 + 1.04466i) q^{28} +(-2.38346 - 4.12828i) q^{29} -5.91046i q^{31} +(-0.500000 + 0.866025i) q^{32} +4.73601i q^{34} +(1.91343 + 1.90113i) q^{35} +(-2.20034 - 3.81110i) q^{37} +2.13012i q^{38} +(-0.571769 + 2.16173i) q^{40} +(-4.10150 + 2.36800i) q^{41} +(1.70944 + 0.986944i) q^{43} -5.15206i q^{44} +(-1.88293 - 1.08711i) q^{46} -0.852296 q^{47} +(2.77245 + 4.80203i) q^{49} +(0.0322474 + 4.99990i) q^{50} +(-3.56583 + 0.533691i) q^{52} -4.48042i q^{53} +(-3.01756 - 11.1181i) q^{55} +(0.603137 - 1.04466i) q^{56} +(-2.38346 + 4.12828i) q^{58} +(-1.68133 - 0.970715i) q^{59} +(-1.53795 + 2.66381i) q^{61} +(-5.11861 + 2.95523i) q^{62} +1.00000 q^{64} +(-7.38248 + 3.24021i) q^{65} +(-7.02765 - 12.1723i) q^{67} +(4.10150 - 2.36800i) q^{68} +(0.689710 - 2.60764i) q^{70} +(0.298707 + 0.172459i) q^{71} -15.7228 q^{73} +(-2.20034 + 3.81110i) q^{74} +(1.84474 - 1.06506i) q^{76} +6.21480i q^{77} -13.5863 q^{79} +(2.15800 - 0.585699i) q^{80} +(4.10150 + 2.36800i) q^{82} +10.2045 q^{83} +(7.46410 - 7.51240i) q^{85} -1.97389i q^{86} +(-4.46182 + 2.57603i) q^{88} +(-14.1941 + 8.19497i) q^{89} +(4.30137 - 0.643777i) q^{91} +2.17422i q^{92} +(0.426148 + 0.738110i) q^{94} +(3.35713 - 3.37886i) q^{95} +(-4.24139 + 7.34631i) q^{97} +(2.77245 - 4.80203i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	\( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{23} - 10 q^{25} + 2 q^{26} + 2 q^{28} - 14 q^{29} - 6 q^{32} + 22 q^{35} + 12 q^{37} - 2 q^{40} + 18 q^{41} + 36 q^{43} - 6 q^{46} + 16 q^{47} + 8 q^{49} + 20 q^{50} - 10 q^{52} + 8 q^{55} + 2 q^{56} - 14 q^{58} + 36 q^{59} + 10 q^{61} + 6 q^{62} + 12 q^{64} + 44 q^{65} - 4 q^{67} - 18 q^{68} + 4 q^{70} + 12 q^{71} - 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 4 q^{80} - 18 q^{82} + 72 q^{83} + 48 q^{85} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} - 18 q^{95} + 48 q^{97} + 8 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 4 * q^10 - 6 * q^11 + 8 * q^13 - 4 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 - 2 * q^20 + 6 * q^22 + 6 * q^23 - 10 * q^25 + 2 * q^26 + 2 * q^28 - 14 * q^29 - 6 * q^32 + 22 * q^35 + 12 * q^37 - 2 * q^40 + 18 * q^41 + 36 * q^43 - 6 * q^46 + 16 * q^47 + 8 * q^49 + 20 * q^50 - 10 * q^52 + 8 * q^55 + 2 * q^56 - 14 * q^58 + 36 * q^59 + 10 * q^61 + 6 * q^62 + 12 * q^64 + 44 * q^65 - 4 * q^67 - 18 * q^68 + 4 * q^70 + 12 * q^71 - 28 * q^73 + 12 * q^74 + 6 * q^76 + 4 * q^79 + 4 * q^80 - 18 * q^82 + 72 * q^83 + 48 * q^85 - 6 * q^88 - 18 * q^89 + 2 * q^91 - 8 * q^94 - 18 * q^95 + 48 * q^97 + 8 * q^98

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