LMFDB - Embedded newform 819.2.n.e.172.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(100,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("819.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.n (of order $3$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			172.2
Root			$0.857510 - 1.48525i$ of defining polynomial
Character	$\chi$	$=$	819.172
Dual form			819.2.n.e.100.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.857510 + 1.48525i) q^{2} +(-0.470647 - 0.815185i) q^{4} +(-1.22863 - 2.12806i) q^{5} +(2.18175 + 1.49666i) q^{7} -1.81570 q^{8} +O(q^{10})$	\(q+(-0.857510 + 1.48525i) q^{2} +(-0.470647 - 0.815185i) q^{4} +(-1.22863 - 2.12806i) q^{5} +(2.18175 + 1.49666i) q^{7} -1.81570 q^{8} +4.21426 q^{10} +1.03816 q^{11} +(-3.36305 + 1.29996i) q^{13} +(-4.09378 + 1.95704i) q^{14} +(2.49828 - 4.32714i) q^{16} +(1.50975 + 2.61496i) q^{17} +3.19341 q^{19} +(-1.15651 + 2.00313i) q^{20} +(-0.890235 + 1.54193i) q^{22} +(-1.73601 + 3.00685i) q^{23} +(-0.519081 + 0.899075i) q^{25} +(0.953083 - 6.10970i) q^{26} +(0.193220 - 2.48292i) q^{28} +(4.01417 + 6.95275i) q^{29} +(-3.48074 + 6.02882i) q^{31} +(2.46889 + 4.27625i) q^{32} -5.17850 q^{34} +(0.504403 - 6.48172i) q^{35} +(-1.41332 + 2.44794i) q^{37} +(-2.73838 + 4.74302i) q^{38} +(2.23083 + 3.86391i) q^{40} +(2.54107 + 4.40125i) q^{41} +(-3.21838 + 5.57439i) q^{43} +(-0.488608 - 0.846294i) q^{44} +(-2.97729 - 5.15682i) q^{46} +(-4.88951 - 8.46887i) q^{47} +(2.52003 + 6.53065i) q^{49} +(-0.890235 - 1.54193i) q^{50} +(2.64252 + 2.12969i) q^{52} +(-5.90947 + 10.2355i) q^{53} +(-1.27552 - 2.20927i) q^{55} +(-3.96140 - 2.71748i) q^{56} -13.7688 q^{58} +(4.47070 + 7.74348i) q^{59} -2.60893 q^{61} +(-5.96954 - 10.3396i) q^{62} +1.52470 q^{64} +(6.89834 + 5.55958i) q^{65} -11.2200 q^{67} +(1.42112 - 2.46145i) q^{68} +(9.19445 + 6.30731i) q^{70} +(1.63013 - 2.82347i) q^{71} +(7.50717 - 13.0028i) q^{73} +(-2.42387 - 4.19827i) q^{74} +(-1.50297 - 2.60322i) q^{76} +(2.26501 + 1.55377i) q^{77} +(-0.211818 - 0.366880i) q^{79} -12.2779 q^{80} -8.71596 q^{82} +1.34088 q^{83} +(3.70986 - 6.42567i) q^{85} +(-5.51958 - 9.56019i) q^{86} -1.88499 q^{88} +(2.65247 - 4.59421i) q^{89} +(-9.28292 - 2.19715i) q^{91} +3.26819 q^{92} +16.7712 q^{94} +(-3.92353 - 6.79576i) q^{95} +(2.92406 - 5.06463i) q^{97} +(-11.8606 - 1.85722i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} + q^{7} - 12 q^{8}+O(q^{10}) $ 16 * q - 6 * q^4 + q^7 - 12 * q^8	$ 16 q - 6 q^{4} + q^{7} - 12 q^{8} + 8 q^{10} - 4 q^{11} + 5 q^{13} + 7 q^{14} - 6 q^{16} + 2 q^{17} + 22 q^{19} + 20 q^{20} + 7 q^{22} - 4 q^{23} + 2 q^{25} + 6 q^{26} - 7 q^{28} - 15 q^{29} + 3 q^{31} - 3 q^{32} - 68 q^{34} + 12 q^{35} + 4 q^{37} - 2 q^{38} - 25 q^{40} - 19 q^{41} + 11 q^{43} + 16 q^{44} + 2 q^{46} - 5 q^{47} + 13 q^{49} + 7 q^{50} + 36 q^{52} - 36 q^{53} - 15 q^{55} - 39 q^{56} - 40 q^{58} + 17 q^{59} + 44 q^{61} + 6 q^{62} - 20 q^{64} + 21 q^{65} - 52 q^{67} - 5 q^{68} + 46 q^{70} - 9 q^{71} - 6 q^{73} - 15 q^{74} - 16 q^{76} + 36 q^{77} + 16 q^{79} - 56 q^{80} + 2 q^{82} - 36 q^{83} - 4 q^{85} - 16 q^{86} - 48 q^{88} - 20 q^{89} - 7 q^{91} + 94 q^{92} + 40 q^{94} + 7 q^{97} + 3 q^{98}+O(q^{100}) $ 16 * q - 6 * q^4 + q^7 - 12 * q^8 + 8 * q^10 - 4 * q^11 + 5 * q^13 + 7 * q^14 - 6 * q^16 + 2 * q^17 + 22 * q^19 + 20 * q^20 + 7 * q^22 - 4 * q^23 + 2 * q^25 + 6 * q^26 - 7 * q^28 - 15 * q^29 + 3 * q^31 - 3 * q^32 - 68 * q^34 + 12 * q^35 + 4 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 + 2 * q^46 - 5 * q^47 + 13 * q^49 + 7 * q^50 + 36 * q^52 - 36 * q^53 - 15 * q^55 - 39 * q^56 - 40 * q^58 + 17 * q^59 + 44 * q^61 + 6 * q^62 - 20 * q^64 + 21 * q^65 - 52 * q^67 - 5 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 - 15 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 - 56 * q^80 + 2 * q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 - 48 * q^88 - 20 * q^89 - 7 * q^91 + 94 * q^92 + 40 * q^94 + 7 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.857510	+	1.48525i	−0.606351	+	1.05023i	0.385485	+	0.922714i	$0.374034\pi$
$2$	−0.857510	+	1.48525i	−0.606351	+	1.05023i	−0.991836	+	0.127517i	$0.959299\pi$
$3$		0			0
$3$		0			0
$4$	−0.470647	−	0.815185i	−0.235324	−	0.407592i
$5$	−1.22863	−	2.12806i	−0.549462	−	0.951695i	−0.998311	−	0.0580883i	$-0.981500\pi$
$5$	−1.22863	−	2.12806i	−0.549462	−	0.951695i	0.448850	−	0.893607i	$-0.351834\pi$
$6$		0			0
$7$	2.18175	+	1.49666i	0.824623	+	0.565683i
$7$	2.18175	+	1.49666i	0.824623	+	0.565683i
$8$	−1.81570			−0.641947
$9$		0			0
$10$	4.21426			1.33267
$11$	1.03816			0.313018			0.156509	−	0.987677i	$-0.449976\pi$
$11$	1.03816			0.313018			0.156509	+	0.987677i	$0.449976\pi$
$12$		0			0
$13$	−3.36305	+	1.29996i	−0.932742	+	0.360544i
$13$	−3.36305	+	1.29996i	−0.932742	+	0.360544i
$14$	−4.09378	+	1.95704i	−1.09411	+	0.523042i
$15$		0			0
$16$	2.49828	−	4.32714i	0.624569	−	1.08179i
$17$	1.50975	+	2.61496i	0.366168	+	0.634222i	0.988963	−	0.148163i	$-0.0473361\pi$
$17$	1.50975	+	2.61496i	0.366168	+	0.634222i	−0.622795	+	0.782385i	$0.714003\pi$
$18$		0			0
$19$	3.19341			0.732619			0.366310	−	0.930493i	$-0.380621\pi$
$19$	3.19341			0.732619			0.366310	+	0.930493i	$0.380621\pi$
$20$	−1.15651	+	2.00313i	−0.258603	+	0.447913i
$21$		0			0
$22$	−0.890235	+	1.54193i	−0.189799	+	0.328741i
$23$	−1.73601	+	3.00685i	−0.361983	+	0.626972i	−0.988287	−	0.152606i	$-0.951233\pi$
$23$	−1.73601	+	3.00685i	−0.361983	+	0.626972i	0.626304	+	0.779579i	$0.284567\pi$
$24$		0			0
$25$	−0.519081	+	0.899075i	−0.103816	+	0.179815i
$26$	0.953083	−	6.10970i	0.186915	−	1.19821i
$27$		0			0
$28$	0.193220	−	2.48292i	0.0365151	−	0.469229i
$29$	4.01417	+	6.95275i	0.745413	+	1.29109i	0.950002	+	0.312245i	$0.101081\pi$
$29$	4.01417	+	6.95275i	0.745413	+	1.29109i	−0.204589	+	0.978848i	$0.565586\pi$
$30$		0			0
$31$	−3.48074	+	6.02882i	−0.625160	+	1.08281i	0.363350	+	0.931653i	$0.381633\pi$
$31$	−3.48074	+	6.02882i	−0.625160	+	1.08281i	−0.988510	+	0.151156i	$0.951700\pi$
$32$	2.46889	+	4.27625i	0.436443	+	0.755941i
$33$		0			0
$34$	−5.17850			−0.888106
$35$	0.504403	−	6.48172i	0.0852598	−	1.09561i
$36$		0			0
$37$	−1.41332	+	2.44794i	−0.232348	+	0.402439i	−0.958499	−	0.285097i	$-0.907974\pi$
$37$	−1.41332	+	2.44794i	−0.232348	+	0.402439i	0.726151	+	0.687536i	$0.241308\pi$
$38$	−2.73838	+	4.74302i	−0.444225	+	0.769419i
$39$		0			0
$40$	2.23083	+	3.86391i	0.352725	+	0.610938i
$41$	2.54107	+	4.40125i	0.396848	+	0.687360i	0.993335	−	0.115262i	$-0.0367708\pi$
$41$	2.54107	+	4.40125i	0.396848	+	0.687360i	−0.596487	+	0.802622i	$0.703437\pi$
$42$		0			0
$43$	−3.21838	+	5.57439i	−0.490798	+	0.850087i	−0.999944	−	0.0105935i	$-0.996628\pi$
$43$	−3.21838	+	5.57439i	−0.490798	+	0.850087i	0.509146	+	0.860680i	$0.329961\pi$
$44$	−0.488608	−	0.846294i	−0.0736605	−	0.127584i
$45$		0			0
$46$	−2.97729	−	5.15682i	−0.438977	−	0.760331i
$47$	−4.88951	−	8.46887i	−0.713208	−	1.23531i	−0.963647	−	0.267180i	$-0.913908\pi$
$47$	−4.88951	−	8.46887i	−0.713208	−	1.23531i	0.250439	−	0.968132i	$-0.419425\pi$
$48$		0			0
$49$	2.52003	+	6.53065i	0.360005	+	0.932950i
$50$	−0.890235	−	1.54193i	−0.125898	−	0.218062i
$51$		0			0
$52$	2.64252	+	2.12969i	0.366451	+	0.295334i
$53$	−5.90947	+	10.2355i	−0.811728	+	1.40595i	0.0999257	+	0.994995i	$0.468139\pi$
$53$	−5.90947	+	10.2355i	−0.811728	+	1.40595i	−0.911654	+	0.410959i	$0.865194\pi$
$54$		0			0
$55$	−1.27552	−	2.20927i	−0.171991	−	0.297898i
$56$	−3.96140	−	2.71748i	−0.529364	−	0.363139i
$57$		0			0
$58$	−13.7688			−1.80793
$59$	4.47070	+	7.74348i	0.582036	+	1.00812i	0.995238	+	0.0974764i	$0.0310770\pi$
$59$	4.47070	+	7.74348i	0.582036	+	1.00812i	−0.413202	+	0.910639i	$0.635590\pi$
$60$		0			0
$61$	−2.60893			−0.334039			−0.167019	−	0.985954i	$-0.553414\pi$
$61$	−2.60893			−0.334039			−0.167019	+	0.985954i	$0.553414\pi$
$62$	−5.96954	−	10.3396i	−0.758133	−	1.31312i
$63$		0			0
$64$	1.52470			0.190588
$65$	6.89834	+	5.55958i	0.855634	+	0.689581i
$66$		0			0
$67$	−11.2200			−1.37074			−0.685371	−	0.728194i	$-0.740360\pi$
$67$	−11.2200			−1.37074			−0.685371	+	0.728194i	$0.740360\pi$
$68$	1.42112	−	2.46145i	0.172336	−	0.298495i
$69$		0			0
$70$	9.19445	+	6.30731i	1.09895	+	0.753867i
$71$	1.63013	−	2.82347i	0.193461	−	0.335085i	−0.752934	−	0.658096i	$-0.771362\pi$
$71$	1.63013	−	2.82347i	0.193461	−	0.335085i	0.946395	+	0.323012i	$0.104695\pi$
$72$		0			0
$73$	7.50717	−	13.0028i	0.878648	−	1.52186i	0.0258228	−	0.999667i	$-0.491779\pi$
$73$	7.50717	−	13.0028i	0.878648	−	1.52186i	0.852825	−	0.522196i	$-0.174887\pi$
$74$	−2.42387	−	4.19827i	−0.281769	−	0.488038i
$75$		0			0
$76$	−1.50297	−	2.60322i	−0.172403	−	0.298610i
$77$	2.26501	+	1.55377i	0.258121	+	0.177069i
$78$		0			0
$79$	−0.211818	−	0.366880i	−0.0238314	−	0.0412773i	0.853864	−	0.520497i	$-0.174253\pi$
$79$	−0.211818	−	0.366880i	−0.0238314	−	0.0412773i	−0.877695	+	0.479219i	$0.840920\pi$
$80$	−12.2779			−1.37271
$81$		0			0
$82$	−8.71596			−0.962516
$83$	1.34088			0.147181			0.0735904	−	0.997289i	$-0.476554\pi$
$83$	1.34088			0.147181			0.0735904	+	0.997289i	$0.476554\pi$
$84$		0			0
$85$	3.70986	−	6.42567i	0.402391	−	0.696961i
$86$	−5.51958	−	9.56019i	−0.595192	−	1.03090i
$87$		0			0
$88$	−1.88499			−0.200941
$89$	2.65247	−	4.59421i	0.281161	−	0.486985i	−0.690510	−	0.723323i	$-0.742614\pi$
$89$	2.65247	−	4.59421i	0.281161	−	0.486985i	0.971671	+	0.236338i	$0.0759472\pi$
$90$		0			0
$91$	−9.28292	−	2.19715i	−0.973114	−	0.230324i
$92$	3.26819			0.340732
$93$		0			0
$94$	16.7712			1.72982
$95$	−3.92353	−	6.79576i	−0.402546	−	0.697230i
$96$		0			0
$97$	2.92406	−	5.06463i	0.296894	−	0.514235i	−0.678530	−	0.734573i	$-0.737383\pi$
$97$	2.92406	−	5.06463i	0.296894	−	0.514235i	0.975424	+	0.220338i	$0.0707159\pi$
$98$	−11.8606	−	1.85722i	−1.19810	−	0.187607i
$99$		0			0
$100$	0.977216			0.0977216
$101$	18.5287			1.84368			0.921840	−	0.387572i	$-0.126686\pi$
$101$	18.5287			1.84368			0.921840	+	0.387572i	$0.126686\pi$
$102$		0			0
$103$	−1.01571	−	1.75926i	−0.100081	−	0.173345i	0.811637	−	0.584162i	$-0.198577\pi$
$103$	−1.01571	−	1.75926i	−0.100081	−	0.173345i	−0.911718	+	0.410817i	$0.865243\pi$
$104$	6.10629	−	2.36034i	0.598771	−	0.231450i
$105$		0			0
$106$	−10.1349	−	17.5541i	−0.984385	−	1.70500i
$107$	−1.21833	+	2.11021i	−0.117781	+	0.204002i	−0.918888	−	0.394519i	$-0.870911\pi$
$107$	−1.21833	+	2.11021i	−0.117781	+	0.204002i	0.801107	+	0.598521i	$0.204245\pi$
$108$		0			0
$109$	−7.85642	+	13.6077i	−0.752508	+	1.30338i	0.194095	+	0.980983i	$0.437823\pi$
$109$	−7.85642	+	13.6077i	−0.752508	+	1.30338i	−0.946604	+	0.322400i	$0.895510\pi$
$110$	4.37509			0.417148
$111$		0			0
$112$	11.9269	−	5.70166i	1.12698	−	0.538756i
$113$	−2.52708	+	4.37702i	−0.237727	+	0.411756i	−0.960062	−	0.279788i	$-0.909736\pi$
$113$	−2.52708	+	4.37702i	−0.237727	+	0.411756i	0.722335	+	0.691544i	$0.243069\pi$
$114$		0			0
$115$	8.53167			0.795582
$116$	3.77852	−	6.54458i	0.350826	−	0.607649i
$117$		0			0
$118$	−15.3347			−1.41167
$119$	−0.619813	+	7.96477i	−0.0568182	+	0.730129i
$120$		0			0
$121$	−9.92222			−0.902020
$122$	2.23718	−	3.87491i	0.202545	−	0.350818i
$123$		0			0
$124$	6.55281			0.588459
$125$	−9.73529			−0.870751
$126$		0			0
$127$	1.84246	+	3.19124i	0.163492	+	0.283177i	0.936119	−	0.351684i	$-0.114391\pi$
$127$	1.84246	+	3.19124i	0.163492	+	0.283177i	−0.772627	+	0.634861i	$0.781058\pi$
$128$	−6.24523	+	10.8171i	−0.552006	+	0.956102i
$129$		0			0
$130$	−14.1728	+	5.47837i	−1.24303	+	0.480485i
$131$	0.924144	+	1.60066i	0.0807428	+	0.139851i	0.903569	−	0.428442i	$-0.140937\pi$
$131$	0.924144	+	1.60066i	0.0807428	+	0.139851i	−0.822826	+	0.568293i	$0.807604\pi$
$132$		0			0
$133$	6.96722	+	4.77944i	0.604134	+	0.414430i
$134$	9.62127	−	16.6645i	0.831151	−	1.43960i
$135$		0			0
$136$	−2.74126	−	4.74799i	−0.235061	−	0.407137i
$137$	1.40759	+	2.43802i	0.120259	+	0.208294i	0.919870	−	0.392224i	$-0.128294\pi$
$137$	1.40759	+	2.43802i	0.120259	+	0.208294i	−0.799611	+	0.600518i	$0.794961\pi$
$138$		0			0
$139$	1.87848	−	3.25363i	0.159331	−	0.275969i	−0.775297	−	0.631597i	$-0.782400\pi$
$139$	1.87848	−	3.25363i	0.159331	−	0.275969i	0.934628	+	0.355628i	$0.115733\pi$
$140$	−5.52120	+	2.63942i	−0.466626	+	0.223072i
$141$		0			0
$142$	2.79571	+	4.84232i	0.234611	+	0.406358i
$143$	−3.49139	+	1.34957i	−0.291965	+	0.112857i
$144$		0			0
$145$	9.86389	−	17.0848i	0.819151	−	1.41881i
$146$	12.8750	+	22.3001i	1.06554	+	1.84557i
$147$		0			0
$148$	2.66070			0.218708
$149$	−6.73683			−0.551902			−0.275951	−	0.961172i	$-0.588993\pi$
$149$	−6.73683			−0.551902			−0.275951	+	0.961172i	$0.588993\pi$
$150$		0			0
$151$	−2.70020	+	4.67689i	−0.219739	+	0.380600i	−0.954728	−	0.297479i	$-0.903854\pi$
$151$	−2.70020	+	4.67689i	−0.219739	+	0.380600i	0.734989	+	0.678079i	$0.237187\pi$
$152$	−5.79828			−0.470303
$153$		0			0
$154$	−4.25001	+	2.03173i	−0.342475	+	0.163721i
$155$	17.1062			1.37401
$156$		0			0
$157$	−5.82721	+	10.0930i	−0.465062	+	0.805512i	−0.999204	−	0.0398832i	$-0.987301\pi$
$157$	−5.82721	+	10.0930i	−0.465062	+	0.805512i	0.534142	+	0.845395i	$0.320635\pi$
$158$	0.726546			0.0578009
$159$		0			0
$160$	6.06673	−	10.5079i	0.479617	−	0.830722i
$161$	−8.28776	+	3.96198i	−0.653167	+	0.312248i
$162$		0			0
$163$	24.2516			1.89953			0.949766	−	0.312960i	$-0.101321\pi$
$163$	24.2516			1.89953			0.949766	+	0.312960i	$0.101321\pi$
$164$	2.39189	−	4.14288i	0.186775	−	0.323504i
$165$		0			0
$166$	−1.14982	+	1.99154i	−0.0892433	+	0.154574i
$167$	−8.23216	−	14.2585i	−0.637024	−	1.10336i	−0.986083	−	0.166257i	$-0.946832\pi$
$167$	−8.23216	−	14.2585i	−0.637024	−	1.10336i	0.349059	−	0.937101i	$-0.386501\pi$
$168$		0			0
$169$	9.62021	−	8.74366i	0.740016	−	0.672589i
$170$	6.36248	+	11.0201i	0.487980	+	0.845207i
$171$		0			0
$172$	6.05888			0.461985
$173$	20.0405			1.52365			0.761827	−	0.647781i	$-0.224303\pi$
$173$	20.0405			1.52365			0.761827	+	0.647781i	$0.224303\pi$
$174$		0			0
$175$	−2.47811	+	1.18467i	−0.187328	+	0.0895524i
$176$	2.59362	−	4.49228i	0.195501	−	0.338618i
$177$		0			0
$178$	4.54903	+	7.87915i	0.340964	+	0.590568i
$179$	10.0951			0.754546			0.377273	−	0.926102i	$-0.376862\pi$
$179$	10.0951			0.754546			0.377273	+	0.926102i	$0.376862\pi$
$180$		0			0
$181$	19.8959			1.47885			0.739426	−	0.673238i	$-0.235097\pi$
$181$	19.8959			1.47885			0.739426	+	0.673238i	$0.235097\pi$
$182$	11.2235	−	11.9034i	0.831942	−	0.882337i
$183$		0			0
$184$	3.15207	−	5.45955i	0.232374	−	0.402483i
$185$	6.94580			0.510666
$186$		0			0
$187$	1.56737	+	2.71476i	0.114617	+	0.198523i
$188$	−4.60246	+	7.97170i	−0.335669	+	0.581396i
$189$		0			0
$190$	13.4579			0.976337
$191$	−15.2774			−1.10543			−0.552715	−	0.833370i	$-0.686408\pi$
$191$	−15.2774			−1.10543			−0.552715	+	0.833370i	$0.686408\pi$
$192$		0			0
$193$	25.6681			1.84763			0.923814	−	0.382843i	$-0.125055\pi$
$193$	25.6681			1.84763			0.923814	+	0.382843i	$0.125055\pi$
$194$	5.01483	+	8.68594i	0.360044	+	0.623614i
$195$		0			0
$196$	4.13764	−	5.12793i	0.295546	−	0.366281i
$197$	−7.84255	−	13.5837i	−0.558759	−	0.967798i	−0.997600	−	0.0692340i	$-0.977944\pi$
$197$	−7.84255	−	13.5837i	−0.558759	−	0.967798i	0.438842	−	0.898564i	$-0.355389\pi$
$198$		0			0
$199$	2.87545	+	4.98042i	0.203835	+	0.353052i	0.949761	−	0.312976i	$-0.101326\pi$
$199$	2.87545	+	4.98042i	0.203835	+	0.353052i	−0.745926	+	0.666029i	$0.767993\pi$
$200$	0.942496	−	1.63245i	0.0666445	−	0.115432i
$201$		0			0
$202$	−15.8886	+	27.5198i	−1.11792	+	1.93629i
$203$	−1.64798	+	21.1770i	−0.115665	+	1.48633i
$204$		0			0
$205$	6.24408	−	10.8151i	0.436105	−	0.755356i
$206$	3.48392			0.242737
$207$		0			0
$208$	−2.77672	+	17.8001i	−0.192531	+	1.23421i
$209$	3.31528			0.229323
$210$		0			0
$211$	10.3771	+	17.9736i	0.714387	+	1.23735i	0.963196	+	0.268802i	$0.0866276\pi$
$211$	10.3771	+	17.9736i	0.714387	+	1.23735i	−0.248809	+	0.968553i	$0.580039\pi$
$212$	11.1251			0.764075
$213$		0			0
$214$	−2.08946	−	3.61906i	−0.142833	−	0.247394i
$215$	15.8168			1.07870
$216$		0			0
$217$	−16.6172	+	7.94388i	−1.12805	+	0.539266i
$218$	−13.4739	−	23.3375i	−0.912569	−	1.58062i
$219$		0			0
$220$	−1.20064	+	2.07957i	−0.0809472	+	0.140205i
$221$	−8.47671	−	6.83164i	−0.570205	−	0.459546i
$222$		0			0
$223$	5.68668	+	9.84963i	0.380809	+	0.659580i	0.991178	−	0.132537i	$-0.0423123\pi$
$223$	5.68668	+	9.84963i	0.380809	+	0.659580i	−0.610369	+	0.792117i	$0.708979\pi$
$224$	−1.01358	+	13.0248i	−0.0677227	+	0.870255i
$225$		0			0
$226$	−4.33399	−	7.50668i	−0.288292	−	0.499337i
$227$	−2.71464	−	4.70189i	−0.180177	−	0.312075i	0.761764	−	0.647855i	$-0.224334\pi$
$227$	−2.71464	−	4.70189i	−0.180177	−	0.312075i	−0.941941	+	0.335779i	$0.891000\pi$
$228$		0			0
$229$	−8.67170	−	15.0198i	−0.573042	−	0.992538i	−0.996251	−	0.0865059i	$-0.972430\pi$
$229$	−8.67170	−	15.0198i	−0.573042	−	0.992538i	0.423209	−	0.906032i	$-0.360903\pi$
$230$	−7.31599	+	12.6717i	−0.482402	+	0.835545i
$231$		0			0
$232$	−7.28853	−	12.6241i	−0.478516	−	0.828813i
$233$	−10.0164	−	17.3490i	−0.656199	−	1.13657i	−0.981592	−	0.190991i	$-0.938830\pi$
$233$	−10.0164	−	17.3490i	−0.656199	−	1.13657i	0.325393	−	0.945579i	$-0.394504\pi$
$234$		0			0
$235$	−12.0148	+	20.8103i	−0.783761	+	1.35751i
$236$	4.20825	−	7.28890i	0.273934	−	0.474467i
$237$		0			0
$238$	−11.2982	−	7.75045i	−0.732352	−	0.502387i
$239$	8.30497			0.537204			0.268602	−	0.963251i	$-0.413438\pi$
$239$	8.30497			0.537204			0.268602	+	0.963251i	$0.413438\pi$
$240$		0			0
$241$	−10.2953	−	17.8320i	−0.663178	−	1.14866i	−0.979776	−	0.200099i	$-0.935874\pi$
$241$	−10.2953	−	17.8320i	−0.663178	−	1.14866i	0.316597	−	0.948560i	$-0.397460\pi$
$242$	8.50840	−	14.7370i	0.546941	−	0.947329i
$243$		0			0
$244$	1.22788	+	2.12676i	0.0786073	+	0.136152i
$245$	10.8014	−	13.3866i	0.690076	−	0.855235i
$246$		0			0
$247$	−10.7396	+	4.15131i	−0.683345	+	0.264141i
$248$	6.31999	−	10.9465i	0.401320	−	0.695106i
$249$		0			0
$250$	8.34811	−	14.4594i	0.527981	−	0.914490i
$251$	−5.22288	+	9.04629i	−0.329665	+	0.570997i	−0.982445	−	0.186550i	$-0.940269\pi$
$251$	−5.22288	+	9.04629i	−0.329665	+	0.570997i	0.652780	+	0.757547i	$0.273603\pi$
$252$		0			0
$253$	−1.80226	+	3.12160i	−0.113307	+	0.196253i
$254$	−6.31972			−0.396534
$255$		0			0
$256$	−9.18600	−	15.9106i	−0.574125	−	0.994414i
$257$	3.61689	−	6.26463i	0.225615	−	0.390777i	−0.730889	−	0.682497i	$-0.760894\pi$
$257$	3.61689	−	6.26463i	0.225615	−	0.390777i	0.956504	+	0.291720i	$0.0942275\pi$
$258$		0			0
$259$	−6.74723	+	3.22553i	−0.419252	+	0.200425i
$260$	1.28540	−	8.24003i	0.0797173	−	0.511025i
$261$		0			0
$262$	−3.16985			−0.195834
$263$	1.70621			0.105209			0.0526047	−	0.998615i	$-0.483248\pi$
$263$	1.70621			0.105209			0.0526047	+	0.998615i	$0.483248\pi$
$264$		0			0
$265$	29.0423			1.78405
$266$	−13.0731	+	6.24964i	−0.801565	+	0.383190i
$267$		0			0
$268$	5.28067	+	9.14638i	0.322568	+	0.558704i
$269$	10.9941	+	19.0424i	0.670324	+	1.16104i	0.977812	+	0.209483i	$0.0671782\pi$
$269$	10.9941	+	19.0424i	0.670324	+	1.16104i	−0.307488	+	0.951552i	$0.599488\pi$
$270$		0			0
$271$	11.8251	−	20.4817i	0.718324	−	1.24417i	−0.243340	−	0.969941i	$-0.578243\pi$
$271$	11.8251	−	20.4817i	0.718324	−	1.24417i	0.961664	−	0.274232i	$-0.0884236\pi$
$272$	15.0871			0.914790
$273$		0			0
$274$	−4.82810			−0.291676
$275$	−0.538890	+	0.933385i	−0.0324963	+	0.0562853i
$276$		0			0
$277$	14.9643	+	25.9190i	0.899119	+	1.55732i	0.828622	+	0.559809i	$0.189125\pi$
$277$	14.9643	+	25.9190i	0.899119	+	1.55732i	0.0704974	+	0.997512i	$0.477541\pi$
$278$	3.22164	+	5.58004i	0.193221	+	0.334669i
$279$		0			0
$280$	−0.915846	+	11.7689i	−0.0547323	+	0.703325i
$281$	27.8636			1.66220			0.831102	−	0.556120i	$-0.187711\pi$
$281$	27.8636			1.66220			0.831102	+	0.556120i	$0.187711\pi$
$282$		0			0
$283$	−19.4075			−1.15366			−0.576829	−	0.816865i	$-0.695710\pi$
$283$	−19.4075			−1.15366			−0.576829	+	0.816865i	$0.695710\pi$
$284$	−3.06887			−0.182104
$285$		0			0
$286$	0.989454	−	6.34286i	0.0585077	−	0.375061i
$287$	−1.04321	+	13.4055i	−0.0615787	+	0.791303i
$288$		0			0
$289$	3.94131	−	6.82655i	0.231842	−	0.401562i
$290$	16.9168	+	29.3007i	0.993387	+	1.72060i
$291$		0			0
$292$	−14.1329			−0.827067
$293$	2.20711	−	3.82282i	0.128940	−	0.223331i	−0.794326	−	0.607492i	$-0.792176\pi$
$293$	2.20711	−	3.82282i	0.128940	−	0.223331i	0.923266	+	0.384160i	$0.125509\pi$
$294$		0			0
$295$	10.9857	−	19.0278i	0.639613	−	1.10784i
$296$	2.56616	−	4.44473i	0.149155	−	0.258344i
$297$		0			0
$298$	5.77690	−	10.0059i	0.334647	−	0.579625i
$299$	1.92949	−	12.3689i	0.111585	−	0.715314i
$300$		0			0
$301$	−15.3646	+	7.34510i	−0.885603	+	0.423364i
$302$	−4.63090	−	8.02096i	−0.266479	−	0.461554i
$303$		0			0
$304$	7.97803	−	13.8184i	0.457571	−	0.792537i
$305$	3.20542	+	5.55194i	0.183542	+	0.317903i
$306$		0			0
$307$	−9.06995			−0.517649			−0.258825	−	0.965924i	$-0.583335\pi$
$307$	−9.06995			−0.517649			−0.258825	+	0.965924i	$0.583335\pi$
$308$	0.200593	−	2.57768i	0.0114299	−	0.146877i
$309$		0			0
$310$	−14.6688	+	25.4070i	−0.833130	+	1.44302i
$311$	11.8691	−	20.5579i	0.673037	−	1.16573i	−0.304002	−	0.952671i	$-0.598323\pi$
$311$	11.8691	−	20.5579i	0.673037	−	1.16573i	0.977039	−	0.213062i	$-0.0683437\pi$
$312$		0			0
$313$	−6.48059	−	11.2247i	−0.366304	−	0.634458i	0.622680	−	0.782476i	$-0.286044\pi$
$313$	−6.48059	−	11.2247i	−0.366304	−	0.634458i	−0.988985	+	0.148019i	$0.952710\pi$
$314$	−9.99379	−	17.3098i	−0.563982	−	0.976846i
$315$		0			0
$316$	−0.199384	+	0.345342i	−0.0112162	+	0.0194270i
$317$	−15.7012	−	27.1953i	−0.881867	−	1.52744i	−0.849263	−	0.527971i	$-0.822953\pi$
$317$	−15.7012	−	27.1953i	−0.881867	−	1.52744i	−0.0326048	−	0.999468i	$-0.510380\pi$
$318$		0			0
$319$	4.16736	+	7.21808i	0.233327	+	0.404135i
$320$	−1.87330	−	3.24465i	−0.104721	−	0.181381i
$321$		0			0
$322$	1.22230	−	15.7068i	0.0681159	−	0.875308i
$323$	4.82126	+	8.35066i	0.268262	+	0.464643i
$324$		0			0
$325$	0.576934	−	3.69842i	0.0320026	−	0.205151i
$326$	−20.7960	+	36.0197i	−1.15178	+	1.99495i
$327$		0			0
$328$	−4.61382	−	7.99136i	−0.254755	−	0.441249i
$329$	2.00734	−	25.7948i	0.110668	−	1.42212i
$330$		0			0
$331$	−11.5233			−0.633378			−0.316689	−	0.948529i	$-0.602571\pi$
$331$	−11.5233			−0.633378			−0.316689	+	0.948529i	$0.602571\pi$
$332$	−0.631082	−	1.09307i	−0.0346351	−	0.0599898i
$333$		0			0
$334$	28.2366			1.54504
$335$	13.7853	+	23.8768i	0.753170	+	1.30453i
$336$		0			0
$337$	−17.7823			−0.968665			−0.484332	−	0.874884i	$-0.660937\pi$
$337$	−17.7823			−0.968665			−0.484332	+	0.874884i	$0.660937\pi$
$338$	4.73710	+	21.7862i	0.257664	+	1.18501i
$339$		0			0
$340$	−6.98414			−0.378768
$341$	−3.61357	+	6.25890i	−0.195686	+	0.338938i
$342$		0			0
$343$	−4.27608	+	18.0199i	−0.230886	+	0.972981i
$344$	5.84361	−	10.1214i	0.315066	−	0.545711i
$345$		0			0
$346$	−17.1850	+	29.7652i	−0.923869	+	1.60019i
$347$	−6.16001	−	10.6694i	−0.330687	−	0.572766i	0.651960	−	0.758253i	$-0.273947\pi$
$347$	−6.16001	−	10.6694i	−0.330687	−	0.572766i	−0.982647	+	0.185487i	$0.940614\pi$
$348$		0			0
$349$	−4.29722	−	7.44301i	−0.230025	−	0.398415i	0.727790	−	0.685800i	$-0.240548\pi$
$349$	−4.29722	−	7.44301i	−0.230025	−	0.398415i	−0.957815	+	0.287385i	$0.907214\pi$
$350$	0.365477	−	4.69648i	0.0195356	−	0.251037i
$351$		0			0
$352$	2.56311	+	4.43944i	0.136614	+	0.236623i
$353$	−29.1648			−1.55229			−0.776144	−	0.630556i	$-0.782827\pi$
$353$	−29.1648			−1.55229			−0.776144	+	0.630556i	$0.782827\pi$
$354$		0			0
$355$	−8.01135			−0.425198
$356$	−4.99350			−0.264655
$357$		0			0
$358$	−8.65668	+	14.9938i	−0.457520	+	0.792448i
$359$	1.79924	+	3.11637i	0.0949602	+	0.164476i	0.909592	−	0.415503i	$-0.136394\pi$
$359$	1.79924	+	3.11637i	0.0949602	+	0.164476i	−0.814632	+	0.579979i	$0.803061\pi$
$360$		0			0
$361$	−8.80212			−0.463269
$362$	−17.0609	+	29.5504i	−0.896703	+	1.55314i
$363$		0			0
$364$	2.57789	+	8.60138i	0.135118	+	0.450835i
$365$	−36.8943			−1.93113
$366$		0			0
$367$	31.0655			1.62161			0.810803	−	0.585319i	$-0.199031\pi$
$367$	31.0655			1.62161			0.810803	+	0.585319i	$0.199031\pi$
$368$	8.67406	+	15.0239i	0.452167	+	0.783175i
$369$		0			0
$370$	−5.95610	+	10.3163i	−0.309643	+	0.536317i
$371$	−28.2120	+	13.4868i	−1.46469	+	0.700201i
$372$		0			0
$373$	−23.4625			−1.21484			−0.607421	−	0.794380i	$-0.707796\pi$
$373$	−23.4625			−1.21484			−0.607421	+	0.794380i	$0.707796\pi$
$374$	−5.37613			−0.277993
$375$		0			0
$376$	8.87788	+	15.3769i	0.457842	+	0.793005i
$377$	−22.5381	−	18.1642i	−1.16077	−	0.935502i
$378$		0			0
$379$	4.67032	+	8.08923i	0.239898	+	0.415516i	0.960685	−	0.277641i	$-0.0895526\pi$
$379$	4.67032	+	8.08923i	0.239898	+	0.415516i	−0.720787	+	0.693157i	$0.756219\pi$
$380$	−3.69320	+	6.39681i	−0.189457	+	0.328150i
$381$		0			0
$382$	13.1005	−	22.6907i	0.670279	−	1.16096i
$383$	−11.6813			−0.596889			−0.298444	−	0.954427i	$-0.596468\pi$
$383$	−11.6813			−0.596889			−0.298444	+	0.954427i	$0.596468\pi$
$384$		0			0
$385$	0.523653	−	6.72908i	0.0266878	−	0.342946i
$386$	−22.0106	+	38.1235i	−1.12031	+	1.94044i
$387$		0			0
$388$	−5.50481			−0.279464
$389$	−9.34341	+	16.1833i	−0.473730	+	0.820524i	−0.999548	−	0.0300730i	$-0.990426\pi$
$389$	−9.34341	+	16.1833i	−0.473730	+	0.820524i	0.525818	+	0.850597i	$0.323759\pi$
$390$		0			0
$391$	−10.4838			−0.530186
$392$	−4.57563	−	11.8577i	−0.231104	−	0.598905i
$393$		0			0
$394$	26.9003			1.35522
$395$	−0.520495	+	0.901523i	−0.0261889	+	0.0453605i
$396$		0			0
$397$	9.44412			0.473987			0.236993	−	0.971511i	$-0.423838\pi$
$397$	9.44412			0.473987			0.236993	+	0.971511i	$0.423838\pi$
$398$	−9.86289			−0.494382
$399$		0			0
$400$	2.59362	+	4.49228i	0.129681	+	0.224614i
$401$	5.18622	−	8.98279i	0.258987	−	0.448579i	−0.706984	−	0.707230i	$-0.749945\pi$
$401$	5.18622	−	8.98279i	0.258987	−	0.448579i	0.965971	+	0.258651i	$0.0832779\pi$
$402$		0			0
$403$	3.86868	−	24.8001i	0.192713	−	1.23538i
$404$	−8.72050	−	15.1044i	−0.433861	−	0.751470i
$405$		0			0
$406$	−30.0400	−	20.6071i	−1.49086	−	1.02271i
$407$	−1.46725	+	2.54136i	−0.0727291	+	0.125970i
$408$		0			0
$409$	−11.4435	−	19.8207i	−0.565844	−	0.980071i	−0.996971	−	0.0777796i	$-0.975217\pi$
$409$	−11.4435	−	19.8207i	−0.565844	−	0.980071i	0.431126	−	0.902292i	$-0.358116\pi$
$410$	10.7087	+	18.5480i	0.528866	+	0.916023i
$411$		0			0
$412$	−0.956082	+	1.65598i	−0.0471028	+	0.0815844i
$413$	−1.83540	+	23.5854i	−0.0903143	+	1.16056i
$414$		0			0
$415$	−1.64745	−	2.85347i	−0.0808702	−	0.140071i
$416$	−13.8620	−	11.1718i	−0.679639	−	0.547742i
$417$		0			0
$418$	−2.84289	+	4.92402i	−0.139050	+	0.240842i
$419$	−4.33086	−	7.50127i	−0.211576	−	0.366461i	0.740632	−	0.671911i	$-0.234526\pi$
$419$	−4.33086	−	7.50127i	−0.211576	−	0.366461i	−0.952208	+	0.305450i	$0.901193\pi$
$420$		0			0
$421$	−1.15030			−0.0560620			−0.0280310	−	0.999607i	$-0.508924\pi$
$421$	−1.15030			−0.0560620			−0.0280310	+	0.999607i	$0.508924\pi$
$422$	−35.5938			−1.73268
$423$		0			0
$424$	10.7298	−	18.5846i	0.521087	−	0.902549i
$425$	−3.13473			−0.152057
$426$		0			0
$427$	−5.69202	−	3.90467i	−0.275456	−	0.188960i
$428$	2.29362			0.110866
$429$		0			0
$430$	−13.5631	+	23.4919i	−0.654070	+	1.13288i
$431$	−8.76048			−0.421977			−0.210989	−	0.977489i	$-0.567668\pi$
$431$	−8.76048			−0.421977			−0.210989	+	0.977489i	$0.567668\pi$
$432$		0			0
$433$	0.463102	−	0.802117i	0.0222553	−	0.0385473i	−0.854683	−	0.519150i	$-0.826249\pi$
$433$	0.463102	−	0.802117i	0.0222553	−	0.0385473i	0.876939	+	0.480603i	$0.159582\pi$
$434$	2.45074	−	31.4926i	0.117639	−	1.51170i
$435$		0			0
$436$	14.7904			0.708332
$437$	−5.54379	+	9.60213i	−0.265195	+	0.459332i
$438$		0			0
$439$	−6.20418	+	10.7460i	−0.296109	+	0.512877i	−0.975242	−	0.221139i	$-0.929023\pi$
$439$	−6.20418	+	10.7460i	−0.296109	+	0.512877i	0.679133	+	0.734015i	$0.262356\pi$
$440$	2.31597	+	4.01137i	0.110409	+	0.191235i
$441$		0			0
$442$	17.4156	−	6.73185i	0.828374	−	0.320201i
$443$	1.61468	+	2.79670i	0.0767156	+	0.132875i	0.901831	−	0.432089i	$-0.142223\pi$
$443$	1.61468	+	2.79670i	0.0767156	+	0.132875i	−0.825115	+	0.564964i	$0.808890\pi$
$444$		0			0
$445$	−13.0356			−0.617948
$446$	−19.5056			−0.923615
$447$		0			0
$448$	3.32651	+	2.28195i	0.157163	+	0.107812i
$449$	9.94344	−	17.2225i	0.469260	−	0.812782i	−0.530123	−	0.847921i	$-0.677854\pi$
$449$	9.94344	−	17.2225i	0.469260	−	0.812782i	0.999382	+	0.0351392i	$0.0111875\pi$
$450$		0			0
$451$	2.63804	+	4.56922i	0.124220	+	0.215156i
$452$	4.75744			0.223771
$453$		0			0
$454$	9.31132			0.437002
$455$	6.72964	+	22.4541i	0.315491	+	1.05266i
$456$		0			0
$457$	0.0394872	−	0.0683939i	0.00184713	−	0.00319933i	−0.865100	−	0.501599i	$-0.832745\pi$
$457$	0.0394872	−	0.0683939i	0.00184713	−	0.00319933i	0.866947	+	0.498399i	$0.166079\pi$
$458$	29.7443			1.38986
$459$		0			0
$460$	−4.01541	−	6.95489i	−0.187219	−	0.324273i
$461$	−2.45979	+	4.26049i	−0.114564	+	0.198431i	−0.917605	−	0.397493i	$-0.869880\pi$
$461$	−2.45979	+	4.26049i	−0.114564	+	0.198431i	0.803041	+	0.595923i	$0.203214\pi$
$462$		0			0
$463$	1.24837			0.0580166			0.0290083	−	0.999579i	$-0.490765\pi$
$463$	1.24837			0.0580166			0.0290083	+	0.999579i	$0.490765\pi$
$464$	40.1140			1.86225
$465$		0			0
$466$	34.3568			1.59155
$467$	14.3411	+	24.8395i	0.663628	+	1.14944i	0.979655	+	0.200687i	$0.0643173\pi$
$467$	14.3411	+	24.8395i	0.663628	+	1.14944i	−0.316028	+	0.948750i	$0.602349\pi$
$468$		0			0
$469$	−24.4792	−	16.7925i	−1.13035	−	0.775406i
$470$	−20.6057	−	35.6901i	−0.950468	−	1.64626i
$471$		0			0
$472$	−8.11746	−	14.0599i	−0.373636	−	0.647157i
$473$	−3.34120	+	5.78712i	−0.153628	+	0.266092i
$474$		0			0
$475$	−1.65764	+	2.87112i	−0.0760577	+	0.131736i
$476$	6.78447	−	3.24333i	0.310966	−	0.148658i
$477$		0			0
$478$	−7.12159	+	12.3350i	−0.325734	+	0.564188i
$479$	6.97871			0.318866			0.159433	−	0.987209i	$-0.449033\pi$
$479$	6.97871			0.318866			0.159433	+	0.987209i	$0.449033\pi$
$480$		0			0
$481$	1.57084	−	10.0698i	0.0716240	−	0.459143i
$482$	35.3133			1.60848
$483$		0			0
$484$	4.66987	+	8.08844i	0.212267	+	0.367657i
$485$	−14.3704			−0.652527
$486$		0			0
$487$	0.964157	+	1.66997i	0.0436901	+	0.0756735i	0.887044	−	0.461686i	$-0.152755\pi$
$487$	0.964157	+	1.66997i	0.0436901	+	0.0756735i	−0.843353	+	0.537359i	$0.819422\pi$
$488$	4.73703			0.214435
$489$		0			0
$490$	10.6201	+	27.5219i	0.479767	+	1.24331i
$491$	−14.6968	−	25.4556i	−0.663256	−	1.14879i	−0.979755	−	0.200200i	$-0.935841\pi$
$491$	−14.6968	−	25.4556i	−0.663256	−	1.14879i	0.316499	−	0.948593i	$-0.397493\pi$
$492$		0			0
$493$	−12.1208	+	20.9938i	−0.545893	+	0.945514i
$494$	3.04359	−	19.5108i	0.136937	−	0.877832i
$495$		0			0
$496$	17.3917	+	30.1233i	0.780911	+	1.35258i
$497$	7.78231	−	3.72035i	0.349084	−	0.166881i
$498$		0			0
$499$	−9.92902	−	17.1976i	−0.444484	−	0.769869i	0.553532	−	0.832828i	$-0.313280\pi$
$499$	−9.92902	−	17.1976i	−0.444484	−	0.769869i	−0.998016	+	0.0629592i	$0.979946\pi$
$500$	4.58189	+	7.93607i	0.204908	+	0.354912i
$501$		0			0
$502$	−8.95734	−	15.5146i	−0.399786	−	0.692449i
$503$	−13.3790	+	23.1731i	−0.596540	+	1.03324i	0.396787	+	0.917911i	$0.370125\pi$
$503$	−13.3790	+	23.1731i	−0.596540	+	1.03324i	−0.993328	+	0.115327i	$0.963208\pi$
$504$		0			0
$505$	−22.7650	−	39.4302i	−1.01303	−	1.75462i
$506$	−3.09091	−	5.35361i	−0.137408	−	0.237997i
$507$		0			0
$508$	1.73430	−	3.00389i	0.0769471	−	0.133276i
$509$	2.96465	−	5.13492i	0.131406	−	0.227601i	−0.792813	−	0.609465i	$-0.791384\pi$
$509$	2.96465	−	5.13492i	0.131406	−	0.227601i	0.924219	+	0.381864i	$0.124718\pi$
$510$		0			0
$511$	35.8395	−	17.1332i	1.58545	−	0.757926i
$512$	6.52743			0.288474
$513$		0			0
$514$	6.20303	+	10.7440i	0.273604	+	0.473896i
$515$	−2.49587	+	4.32297i	−0.109981	+	0.190493i
$516$		0			0
$517$	−5.07610	−	8.79206i	−0.223247	−	0.386674i
$518$	0.995096	−	12.7873i	0.0437220	−	0.561840i
$519$		0			0
$520$	−12.5253	−	10.0945i	−0.549272	−	0.442675i
$521$	16.7414	−	28.9969i	0.733453	−	1.27038i	−0.221946	−	0.975059i	$-0.571241\pi$
$521$	16.7414	−	28.9969i	0.733453	−	1.27038i	0.955399	−	0.295319i	$-0.0954259\pi$
$522$		0			0
$523$	−20.7273	+	35.9007i	−0.906341	+	1.56983i	−0.0872343	+	0.996188i	$0.527803\pi$
$523$	−20.7273	+	35.9007i	−0.906341	+	1.56983i	−0.819107	+	0.573641i	$0.805530\pi$
$524$	0.869892	−	1.50670i	0.0380014	−	0.0658203i
$525$		0			0
$526$	−1.46309	+	2.53415i	−0.0637938	+	0.110494i
$527$	−21.0202			−0.915655
$528$		0			0
$529$	5.47255	+	9.47874i	0.237937	+	0.412119i
$530$	−24.9041	+	43.1351i	−1.08176	+	1.87367i
$531$		0			0
$532$	0.617030	−	7.92900i	0.0267516	−	0.343766i
$533$	−14.2672	−	11.4984i	−0.617980	−	0.498049i
$534$		0			0
$535$	5.98753			0.258864
$536$	20.3722			0.879944
$537$		0			0
$538$	−37.7103			−1.62581
$539$	2.61620	+	6.77988i	0.112688	+	0.292030i
$540$		0			0
$541$	−14.7605	−	25.5660i	−0.634606	−	1.09917i	−0.986599	−	0.163166i	$-0.947829\pi$
$541$	−14.7605	−	25.5660i	−0.634606	−	1.09917i	0.351993	−	0.936003i	$-0.385504\pi$
$542$	20.2803	+	35.1265i	0.871113	+	1.50881i
$543$		0			0
$544$	−7.45483	+	12.9121i	−0.319623	+	0.553603i
$545$	38.6106			1.65390
$546$		0			0
$547$	34.6619			1.48203			0.741017	−	0.671486i	$-0.234344\pi$
$547$	34.6619			1.48203			0.741017	+	0.671486i	$0.234344\pi$
$548$	1.32496	−	2.29490i	0.0565995	−	0.0980332i
$549$		0			0
$550$	−0.924208	−	1.60077i	−0.0394084	−	0.0682573i
$551$	12.8189	+	22.2030i	0.546104	+	0.945879i
$552$		0			0
$553$	0.0869600	−	1.11746i	0.00369792	−	0.0475192i
$554$	−51.3283			−2.18073
$555$		0			0
$556$	−3.53641			−0.149977
$557$	15.0484			0.637623			0.318812	−	0.947818i	$-0.396716\pi$
$557$	15.0484			0.637623			0.318812	+	0.947818i	$0.396716\pi$
$558$		0			0
$559$	3.57707	−	22.9307i	0.151294	−	0.969866i
$560$	−26.7872	−	18.3758i	−1.13197	−	0.776518i
$561$		0			0
$562$	−23.8933	+	41.3845i	−1.00788	+	1.74570i
$563$	−0.728725	−	1.26219i	−0.0307121	−	0.0531949i	0.850261	−	0.526362i	$-0.176444\pi$
$563$	−0.728725	−	1.26219i	−0.0307121	−	0.0531949i	−0.880973	+	0.473167i	$0.843111\pi$
$564$		0			0
$565$	12.4194			0.522488
$566$	16.6422	−	28.8251i	0.699522	−	1.21161i
$567$		0			0
$568$	−2.95984	+	5.12659i	−0.124192	+	0.215107i
$569$	2.05326	−	3.55635i	0.0860770	−	0.149090i	−0.819773	−	0.572689i	$-0.805900\pi$
$569$	2.05326	−	3.55635i	0.0860770	−	0.149090i	0.905850	+	0.423599i	$0.139234\pi$
$570$		0			0
$571$	16.1753	−	28.0165i	0.676916	−	1.17245i	−0.298988	−	0.954257i	$-0.596649\pi$
$571$	16.1753	−	28.0165i	0.676916	−	1.17245i	0.975905	−	0.218197i	$-0.0700175\pi$
$572$	2.74336	+	2.21096i	0.114706	+	0.0924448i
$573$		0			0
$574$	−19.0160	−	13.0448i	−0.793713	−	0.544479i
$575$	−1.80226	−	3.12160i	−0.0751593	−	0.130180i
$576$		0			0
$577$	3.24107	−	5.61369i	0.134927	−	0.233701i	−0.790642	−	0.612278i	$-0.790253\pi$
$577$	3.24107	−	5.61369i	0.134927	−	0.233701i	0.925570	+	0.378577i	$0.123587\pi$
$578$	6.75942	+	11.7077i	0.281155	+	0.486975i
$579$		0			0
$580$	−18.5696			−0.771063
$581$	2.92546	+	2.00684i	0.121369	+	0.0832577i
$582$		0			0
$583$	−6.13499	+	10.6261i	−0.254085	+	0.440088i
$584$	−13.6308	+	23.6092i	−0.564046	+	0.976956i
$585$		0			0
$586$	3.78523	+	6.55621i	0.156366	+	0.270835i
$587$	−8.72720	−	15.1159i	−0.360210	−	0.623902i	0.627785	−	0.778387i	$-0.283962\pi$
$587$	−8.72720	−	15.1159i	−0.360210	−	0.623902i	−0.987995	+	0.154485i	$0.950628\pi$
$588$		0			0
$589$	−11.1154	+	19.2525i	−0.458004	+	0.793286i
$590$	18.8407	+	32.6331i	0.775660	+	1.34348i
$591$		0			0
$592$	7.06172	+	12.2313i	0.290235	+	0.502702i
$593$	5.07543	+	8.79090i	0.208423	+	0.360999i	0.951218	−	0.308520i	$-0.0998337\pi$
$593$	5.07543	+	8.79090i	0.208423	+	0.360999i	−0.742795	+	0.669519i	$0.766500\pi$
$594$		0			0
$595$	17.7110	−	8.46678i	0.726080	−	0.347104i
$596$	3.17067	+	5.49176i	0.129876	+	0.224951i
$597$		0			0
$598$	16.7164	+	13.4723i	0.683585	+	0.550922i
$599$	5.29665	−	9.17406i	0.216415	−	0.374842i	−0.737294	−	0.675572i	$-0.763897\pi$
$599$	5.29665	−	9.17406i	0.216415	−	0.374842i	0.953709	+	0.300730i	$0.0972302\pi$
$600$		0			0
$601$	5.08203	+	8.80234i	0.207300	+	0.359055i	0.950863	−	0.309611i	$-0.100199\pi$
$601$	5.08203	+	8.80234i	0.207300	+	0.359055i	−0.743563	+	0.668666i	$0.766866\pi$
$602$	2.26601	−	29.1188i	0.0923556	−	1.18680i
$603$		0			0
$604$	5.08337			0.206840
$605$	12.1908	+	21.1150i	0.495625	+	0.858448i
$606$		0			0
$607$	32.4478			1.31702			0.658508	−	0.752574i	$-0.271188\pi$
$607$	32.4478			1.31702			0.658508	+	0.752574i	$0.271188\pi$
$608$	7.88420	+	13.6558i	0.319746	+	0.553817i
$609$		0			0
$610$	−10.9947			−0.445163
$611$	27.4528	+	22.1251i	1.11062	+	0.895085i
$612$		0			0
$613$	−9.83642			−0.397289			−0.198645	−	0.980072i	$-0.563654\pi$
$613$	−9.83642			−0.397289			−0.198645	+	0.980072i	$0.563654\pi$
$614$	7.77757	−	13.4712i	0.313877	−	0.543651i
$615$		0			0
$616$	−4.11258	−	2.82119i	−0.165700	−	0.113669i
$617$	−17.6661	+	30.5985i	−0.711208	+	1.23185i	0.253195	+	0.967415i	$0.418518\pi$
$617$	−17.6661	+	30.5985i	−0.711208	+	1.23185i	−0.964404	+	0.264434i	$0.914815\pi$
$618$		0			0
$619$	−17.5126	+	30.3327i	−0.703892	+	1.21918i	0.263198	+	0.964742i	$0.415223\pi$
$619$	−17.5126	+	30.3327i	−0.703892	+	1.21918i	−0.967090	+	0.254434i	$0.918111\pi$
$620$	−8.05100	−	13.9447i	−0.323336	−	0.560034i
$621$		0			0
$622$	20.3558	+	35.2573i	0.816193	+	1.41369i
$623$	12.6630	−	6.05356i	0.507331	−	0.242531i
$624$		0			0
$625$	14.5565	+	25.2126i	0.582261	+	1.00850i
$626$	22.2287			0.888437
$627$		0			0
$628$	10.9702			0.437761
$629$	−8.53503			−0.340314
$630$		0			0
$631$	−10.2980	+	17.8367i	−0.409959	+	0.710069i	−0.994885	−	0.101017i	$-0.967790\pi$
$631$	−10.2980	+	17.8367i	−0.409959	+	0.710069i	0.584926	+	0.811087i	$0.301124\pi$
$632$	0.384599	+	0.666145i	0.0152985	+	0.0264978i
$633$		0			0
$634$	53.8558			2.13889
$635$	4.52742	−	7.84172i	0.179665	−	0.311189i
$636$		0			0
$637$	−16.9646	−	18.6870i	−0.672161	−	0.740405i
$638$	−14.2942			−0.565913
$639$		0			0
$640$	30.6924			1.21322
$641$	−17.5384	−	30.3774i	−0.692725	−	1.19983i	−0.970942	−	0.239316i	$-0.923077\pi$
$641$	−17.5384	−	30.3774i	−0.692725	−	1.19983i	0.278217	−	0.960518i	$-0.410256\pi$
$642$		0			0
$643$	−12.4615	+	21.5840i	−0.491435	+	0.851190i	−0.999951	−	0.00986235i	$-0.996861\pi$
$643$	−12.4615	+	21.5840i	−0.491435	+	0.851190i	0.508517	+	0.861052i	$0.330194\pi$
$644$	7.13036	+	4.89136i	0.280976	+	0.192747i
$645$		0			0
$646$	−16.5371			−0.650644
$647$	3.35518			0.131906			0.0659528	−	0.997823i	$-0.478991\pi$
$647$	3.35518			0.131906			0.0659528	+	0.997823i	$0.478991\pi$
$648$		0			0
$649$	4.64131	+	8.03899i	0.182188	+	0.315558i
$650$	4.99835	+	4.02832i	0.196052	+	0.158004i
$651$		0			0
$652$	−11.4140	−	19.7695i	−0.447005	−	0.774235i
$653$	2.54625	−	4.41024i	0.0996426	−	0.172586i	−0.811894	−	0.583805i	$-0.801563\pi$
$653$	2.54625	−	4.41024i	0.0996426	−	0.172586i	0.911537	+	0.411219i	$0.134897\pi$
$654$		0			0
$655$	2.27087	−	3.93326i	0.0887302	−	0.153685i
$656$	25.3931			0.991435
$657$		0			0
$658$	36.5905	+	25.1007i	1.42645	+	0.978529i
$659$	16.9148	−	29.2973i	0.658907	−	1.14126i	−0.321992	−	0.946742i	$-0.604352\pi$
$659$	16.9148	−	29.2973i	0.658907	−	1.14126i	0.980899	−	0.194518i	$-0.0623143\pi$
$660$		0			0
$661$	33.9014			1.31861			0.659306	−	0.751875i	$-0.270850\pi$
$661$	33.9014			1.31861			0.659306	+	0.751875i	$0.270850\pi$
$662$	9.88135	−	17.1150i	0.384050	−	0.665194i
$663$		0			0
$664$	−2.43464			−0.0944823
$665$	1.61077	−	20.6988i	0.0624629	−	0.802665i
$666$		0			0
$667$	−27.8745			−1.07931
$668$	−7.74889	+	13.4215i	−0.299813	+	0.519292i
$669$		0			0
$670$	−47.2841			−1.82674
$671$	−2.70849			−0.104560
$672$		0			0
$673$	−7.46805	−	12.9350i	−0.287872	−	0.498609i	0.685430	−	0.728139i	$-0.259614\pi$
$673$	−7.46805	−	12.9350i	−0.287872	−	0.498609i	−0.973302	+	0.229530i	$0.926281\pi$
$674$	15.2485	−	26.4112i	0.587351	−	1.01732i
$675$		0			0
$676$	−11.6554	−	3.72707i	−0.448286	−	0.143349i
$677$	−10.8470	−	18.7875i	−0.416883	−	0.722063i	0.578741	−	0.815512i	$-0.303544\pi$
$677$	−10.8470	−	18.7875i	−0.416883	−	0.722063i	−0.995624	+	0.0934485i	$0.970211\pi$
$678$		0			0
$679$	13.9596	−	6.67341i	0.535720	−	0.256102i
$680$	−6.73600	+	11.6671i	−0.258314	+	0.447412i
$681$		0			0
$682$	−6.19735	−	10.7341i	−0.237309	−	0.411031i
$683$	11.6479	+	20.1747i	0.445694	+	0.771965i	0.998100	−	0.0616101i	$-0.0196235\pi$
$683$	11.6479	+	20.1747i	0.445694	+	0.771965i	−0.552406	+	0.833575i	$0.686290\pi$
$684$		0			0
$685$	3.45883	−	5.99087i	0.132155	−	0.228900i
$686$	−23.0972	−	21.8033i	−0.881856	−	0.832452i
$687$		0			0
$688$	16.0808	+	27.8527i	0.613074	+	1.06188i
$689$	6.56810	−	42.1046i	0.250225	−	1.60406i
$690$		0			0
$691$	−15.6725	+	27.1456i	−0.596212	+	1.03267i	0.397163	+	0.917748i	$0.369995\pi$
$691$	−15.6725	+	27.1456i	−0.596212	+	1.03267i	−0.993375	+	0.114921i	$0.963339\pi$
$692$	−9.43202	−	16.3367i	−0.358552	−	0.621030i
$693$		0			0
$694$	21.1291			0.802049
$695$	−9.23188			−0.350185
$696$		0			0
$697$	−7.67275	+	13.2896i	−0.290626	+	0.503379i
$698$	14.7397			0.557904
$699$		0			0
$700$	2.13204	+	1.46256i	0.0805835	+	0.0552795i
$701$	36.5409			1.38013			0.690066	−	0.723746i	$-0.257581\pi$
$701$	36.5409			1.38013			0.690066	+	0.723746i	$0.257581\pi$
$702$		0			0
$703$	−4.51331	+	7.81728i	−0.170223	+	0.294834i
$704$	1.58289			0.0596573
$705$		0			0
$706$	25.0091	−	43.3171i	0.941232	−	1.63026i
$707$	40.4250	+	27.7312i	1.52034	+	1.04294i
$708$		0			0
$709$	32.9378			1.23700			0.618502	−	0.785783i	$-0.287740\pi$
$709$	32.9378			1.23700			0.618502	+	0.785783i	$0.287740\pi$
$710$	6.86981	−	11.8989i	0.257819	−	0.446556i
$711$		0			0
$712$	−4.81609	+	8.34170i	−0.180490	+	0.312619i
$713$	−12.0852	−	20.9322i	−0.452594	−	0.783916i
$714$		0			0
$715$	7.16160	+	5.77175i	0.267829	+	0.215851i
$716$	−4.75125	−	8.22941i	−0.177563	−	0.307547i
$717$		0			0
$718$	−6.17147			−0.230317
$719$	−8.58636			−0.320217			−0.160109	−	0.987099i	$-0.551184\pi$
$719$	−8.58636			−0.320217			−0.160109	+	0.987099i	$0.551184\pi$
$720$		0			0
$721$	0.416990	−	5.35843i	0.0155295	−	0.199558i
$722$	7.54790	−	13.0734i	0.280904	−	0.486540i
$723$		0			0
$724$	−9.36395	−	16.2188i	−0.348009	−	0.602769i
$725$	−8.33472			−0.309544
$726$		0			0
$727$	31.5760			1.17109			0.585545	−	0.810640i	$-0.300881\pi$
$727$	31.5760			1.17109			0.585545	+	0.810640i	$0.300881\pi$
$728$	16.8550	+	3.98937i	0.624688	+	0.147856i
$729$		0			0
$730$	31.6372	−	54.7972i	1.17095	−	2.02814i
$731$	−19.4358			−0.718858
$732$		0			0
$733$	7.35414	+	12.7377i	0.271631	+	0.470479i	0.969280	−	0.245961i	$-0.0791035\pi$
$733$	7.35414	+	12.7377i	0.271631	+	0.470479i	−0.697648	+	0.716440i	$0.745770\pi$
$734$	−26.6390	+	46.1401i	−0.983263	+	1.70306i
$735$		0			0
$736$	−17.1441			−0.631939
$737$	−11.6482			−0.429067
$738$		0			0
$739$	−14.1659			−0.521102			−0.260551	−	0.965460i	$-0.583904\pi$
$739$	−14.1659			−0.521102			−0.260551	+	0.965460i	$0.583904\pi$
$740$	−3.26902	−	5.66211i	−0.120172	−	0.208143i
$741$		0			0
$742$	4.16077	−	53.4670i	0.152747	−	1.96283i
$743$	21.4265	+	37.1119i	0.786063	+	1.36150i	0.928362	+	0.371678i	$0.121217\pi$
$743$	21.4265	+	37.1119i	0.786063	+	1.36150i	−0.142298	+	0.989824i	$0.545449\pi$
$744$		0			0
$745$	8.27709	+	14.3363i	0.303249	+	0.525243i
$746$	20.1193	−	34.8477i	0.736621	−	1.27586i
$747$		0			0
$748$	1.47535	−	2.55539i	0.0539442	−	0.0934342i
$749$	−5.81636	+	2.78052i	−0.212525	+	0.101598i
$750$		0			0
$751$	0.310328	−	0.537504i	0.0113240	−	0.0196138i	−0.860308	−	0.509775i	$-0.829729\pi$
$751$	0.310328	−	0.537504i	0.0113240	−	0.0196138i	0.871632	+	0.490161i	$0.163062\pi$
$752$	−48.8614			−1.78179
$753$		0			0
$754$	46.3050	−	17.8988i	1.68633	−	0.651837i
$755$	13.2702			0.482954
$756$		0			0
$757$	2.21558	+	3.83750i	0.0805266	+	0.139476i	0.903476	−	0.428638i	$-0.141006\pi$
$757$	2.21558	+	3.83750i	0.0805266	+	0.139476i	−0.822950	+	0.568114i	$0.807673\pi$
$758$	−16.0194			−0.581851
$759$		0			0
$760$	7.12397	+	12.3391i	0.258413	+	0.447585i
$761$	−21.0044			−0.761409			−0.380704	−	0.924697i	$-0.624318\pi$
$761$	−21.0044			−0.761409			−0.380704	+	0.924697i	$0.624318\pi$
$762$		0			0
$763$	−37.5068	+	17.9302i	−1.35784	+	0.649117i
$764$	7.19024	+	12.4539i	0.260134	+	0.450565i
$765$		0			0
$766$	10.0169	−	17.3497i	0.361924	−	0.626871i
$767$	−25.1014	−	20.2300i	−0.906360	−	0.730463i
$768$		0			0
$769$	−5.85570	−	10.1424i	−0.211162	−	0.365743i	0.740917	−	0.671597i	$-0.234391\pi$
$769$	−5.85570	−	10.1424i	−0.211162	−	0.365743i	−0.952078	+	0.305854i	$0.901058\pi$
$770$	9.54533	+	6.54801i	0.343990	+	0.235974i
$771$		0			0
$772$	−12.0806	−	20.9242i	−0.434790	−	0.753079i
$773$	4.02075	+	6.96415i	0.144616	+	0.250483i	0.929230	−	0.369502i	$-0.120472\pi$
$773$	4.02075	+	6.96415i	0.144616	+	0.250483i	−0.784613	+	0.619985i	$0.787139\pi$
$774$		0			0
$775$	−3.61357	−	6.25890i	−0.129803	−	0.224826i
$776$	−5.30923	+	9.19585i	−0.190590	+	0.330112i
$777$		0			0
$778$	−16.0241	−	27.7546i	−0.574493	−	0.995052i
$779$	8.11467	+	14.0550i	0.290738	+	0.503573i
$780$		0			0
$781$	1.69234	−	2.93122i	0.0605568	−	0.104887i
$782$	8.98993	−	15.5710i	0.321479	−	0.556818i
$783$		0			0
$784$	34.5548	+	5.41083i	1.23410	+	0.193244i
$785$	28.6380			1.02214
$786$		0			0
$787$	−22.0887	−	38.2587i	−0.787377	−	1.36378i	−0.927569	−	0.373653i	$-0.878105\pi$
$787$	−22.0887	−	38.2587i	−0.787377	−	1.36378i	0.140192	−	0.990124i	$-0.455228\pi$
$788$	−7.38215	+	12.7863i	−0.262978	+	0.455492i
$789$		0			0
$790$	−0.892659	−	1.54613i	−0.0317594	−	0.0550088i
$791$	−12.0643	+	5.76739i	−0.428959	+	0.205065i
$792$		0			0
$793$	8.77395	−	3.39150i	0.311572	−	0.120436i
$794$	−8.09843	+	14.0269i	−0.287403	+	0.497796i
$795$		0			0
$796$	2.70664	−	4.68804i	0.0959343	−	0.166163i
$797$	9.83025	−	17.0265i	0.348205	−	0.603109i	−0.637725	−	0.770264i	$-0.720125\pi$
$797$	9.83025	−	17.0265i	0.348205	−	0.603109i	0.985931	+	0.167155i	$0.0534579\pi$
$798$		0			0
$799$	14.7639	−	25.5718i	0.522308	−	0.904664i
$800$	−5.12622			−0.181239
$801$		0			0
$802$	8.89447	+	15.4057i	0.314075	+	0.543993i
$803$	7.79366	−	13.4990i	0.275032	−	0.476370i
$804$		0			0
$805$	18.6139	+	12.7690i	0.656055	+	0.450048i
$806$	33.5169	+	27.0123i	1.18058	+	0.951466i
$807$		0			0
$808$	−33.6427			−1.18355
$809$	0.872672			0.0306815			0.0153407	−	0.999882i	$-0.495117\pi$
$809$	0.872672			0.0306815			0.0153407	+	0.999882i	$0.495117\pi$
$810$		0			0
$811$	35.1149			1.23305			0.616526	−	0.787335i	$-0.288540\pi$
$811$	35.1149			1.23305			0.616526	+	0.787335i	$0.288540\pi$
$812$	18.0388	−	8.62347i	0.633036	−	0.302625i
$813$		0			0
$814$	−2.51637	−	4.35848i	−0.0881987	−	0.152765i
$815$	−29.7963	−	51.6088i	−1.04372	−	1.80778i
$816$		0			0
$817$	−10.2776	+	17.8013i	−0.359568	+	0.622790i
$818$	39.2517			1.37240
$819$		0			0
$820$	−11.7550			−0.410503
$821$	−10.1024	+	17.4978i	−0.352575	+	0.610678i	−0.986700	−	0.162553i	$-0.948027\pi$
$821$	−10.1024	+	17.4978i	−0.352575	+	0.610678i	0.634125	+	0.773231i	$0.281361\pi$
$822$		0			0
$823$	−13.9713	−	24.1991i	−0.487010	−	0.843526i	0.512878	−	0.858461i	$-0.328579\pi$
$823$	−13.9713	−	24.1991i	−0.487010	−	0.843526i	−0.999888	+	0.0149350i	$0.995246\pi$
$824$	1.84422	+	3.19429i	0.0642466	+	0.111278i
$825$		0			0
$826$	−33.4564	−	22.9508i	−1.16410	−	0.798560i
$827$	44.6141			1.55138			0.775692	−	0.631112i	$-0.217401\pi$
$827$	44.6141			1.55138			0.775692	+	0.631112i	$0.217401\pi$
$828$		0			0
$829$	−28.1051			−0.976129			−0.488065	−	0.872807i	$-0.662297\pi$
$829$	−28.1051			−0.976129			−0.488065	+	0.872807i	$0.662297\pi$
$830$	5.65082			0.196143
$831$		0			0
$832$	−5.12764	+	1.98205i	−0.177769	+	0.0687152i
$833$	−13.2728	+	16.4495i	−0.459875	+	0.569940i
$834$		0			0
$835$	−20.2286	+	35.0370i	−0.700040	+	1.21251i
$836$	−1.56033	−	2.70257i	−0.0539651	−	0.0934702i
$837$		0			0
$838$	14.8550			0.513158
$839$	−18.8751	+	32.6926i	−0.651640	+	1.12867i	0.331085	+	0.943601i	$0.392585\pi$
$839$	−18.8751	+	32.6926i	−0.651640	+	1.12867i	−0.982725	+	0.185072i	$0.940748\pi$
$840$		0			0
$841$	−17.7271	+	30.7043i	−0.611280	+	1.05877i
$842$	0.986390	−	1.70848i	0.0339933	−	0.0588780i
$843$		0			0
$844$	9.76788	−	16.9185i	0.336224	−	0.582357i
$845$	−30.4267	−	9.72959i	−1.04671	−	0.334708i
$846$		0			0
$847$	−21.6478	−	14.8502i	−0.743826	−	0.510258i
$848$	29.5270	+	51.1422i	1.01396	+	1.75623i
$849$		0			0
$850$	2.68806	−	4.65586i	0.0921998	−	0.159695i
$851$	−4.90706	−	8.49928i	−0.168212	−	0.291352i
$852$		0			0
$853$	7.52465			0.257639			0.128820	−	0.991668i	$-0.458881\pi$
$853$	7.52465			0.257639			0.128820	+	0.991668i	$0.458881\pi$
$854$	10.6804	−	5.10578i	0.365475	−	0.174716i
$855$		0			0
$856$	2.21213	−	3.83152i	0.0756089	−	0.130959i
$857$	−7.72284	+	13.3764i	−0.263807	+	0.456928i	−0.967250	−	0.253824i	$-0.918312\pi$
$857$	−7.72284	+	13.3764i	−0.263807	+	0.456928i	0.703443	+	0.710751i	$0.251645\pi$
$858$		0			0
$859$	4.27437	+	7.40343i	0.145840	+	0.252602i	0.929686	−	0.368353i	$-0.120078\pi$
$859$	4.27437	+	7.40343i	0.145840	+	0.252602i	−0.783846	+	0.620955i	$0.786745\pi$
$860$	−7.44414	−	12.8936i	−0.253843	−	0.439669i
$861$		0			0
$862$	7.51220	−	13.0115i	0.255866	−	0.443174i
$863$	27.6867	+	47.9548i	0.942468	+	1.63240i	0.760744	+	0.649052i	$0.224834\pi$
$863$	27.6867	+	47.9548i	0.942468	+	1.63240i	0.181724	+	0.983350i	$0.441832\pi$
$864$		0			0
$865$	−24.6225	−	42.6474i	−0.837189	−	1.45005i
$866$	0.794230	+	1.37565i	0.0269890	+	0.0467464i
$867$		0			0
$868$	14.2966	+	9.80731i	0.485257	+	0.332882i
$869$	−0.219902	−	0.380881i	−0.00745966	−	0.0129205i
$870$		0			0
$871$	37.7335	−	14.5856i	1.27855	−	0.494213i
$872$	14.2649	−	24.7075i	0.483071	−	0.836703i
$873$		0			0
$874$	−9.50771	−	16.4678i	−0.321603	−	0.557033i
$875$	−21.2399	−	14.5704i	−0.718041	−	0.492569i
$876$		0			0
$877$	49.1212			1.65870			0.829352	−	0.558726i	$-0.188710\pi$
$877$	49.1212			1.65870			0.829352	+	0.558726i	$0.188710\pi$
$878$	−10.6403	−	18.4295i	−0.359093	−	0.621967i
$879$		0			0
$880$	−12.7464			−0.429682
$881$	3.45324	+	5.98118i	0.116342	+	0.201511i	0.918316	−	0.395849i	$-0.129550\pi$
$881$	3.45324	+	5.98118i	0.116342	+	0.201511i	−0.801973	+	0.597360i	$0.796216\pi$
$882$		0			0
$883$	−25.4087			−0.855071			−0.427536	−	0.903998i	$-0.640618\pi$
$883$	−25.4087			−0.855071			−0.427536	+	0.903998i	$0.640618\pi$
$884$	−1.57951	+	10.1254i	−0.0531246	+	0.340553i
$885$		0			0
$886$	−5.53841			−0.186066
$887$	−21.0930	+	36.5342i	−0.708234	+	1.22670i	0.257277	+	0.966338i	$0.417175\pi$
$887$	−21.0930	+	36.5342i	−0.708234	+	1.22670i	−0.965512	+	0.260360i	$0.916159\pi$
$888$		0			0
$889$	−0.756405	+	9.72000i	−0.0253690	+	0.325998i
$890$	11.1782	−	19.3612i	0.374694	−	0.648989i
$891$		0			0
$892$	5.35285	−	9.27140i	0.179227	−	0.310429i
$893$	−15.6142	−	27.0446i	−0.522510	−	0.905013i
$894$		0			0
$895$	−12.4032	−	21.4830i	−0.414594	−	0.718098i
$896$	−29.8150	+	14.2531i	−0.996048	+	0.476163i
$897$		0			0
$898$	17.0532	+	29.5370i	0.569072	+	0.985662i
$899$	−55.8892			−1.86401
$900$		0			0
$901$	−35.6873			−1.18892
$902$	−9.04858			−0.301285
$903$		0			0
$904$	4.58841	−	7.94737i	0.152608	−	0.264325i
$905$	−24.4448	−	42.3396i	−0.812572	−	1.40742i
$906$		0			0
$907$	27.3859			0.909335			0.454667	−	0.890661i	$-0.349758\pi$
$907$	27.3859			0.909335			0.454667	+	0.890661i	$0.349758\pi$
$908$	−2.55527	+	4.42586i	−0.0847997	+	0.146877i
$909$		0			0
$910$	−39.1206	−	9.25937i	−1.29684	−	0.306945i
$911$	−46.0844			−1.52685			−0.763423	−	0.645899i	$-0.776483\pi$
$911$	−46.0844			−1.52685			−0.763423	+	0.645899i	$0.776483\pi$
$912$		0			0
$913$	1.39205			0.0460702
$914$	0.0677214	+	0.117297i	0.00224002	+	0.00387984i
$915$		0			0
$916$	−8.16262	+	14.1381i	−0.269701	+	0.467135i
$917$	−0.379398	+	4.87537i	−0.0125288	+	0.160999i
$918$		0			0
$919$	−40.1277			−1.32369			−0.661845	−	0.749641i	$-0.730226\pi$
$919$	−40.1277			−1.32369			−0.661845	+	0.749641i	$0.730226\pi$
$920$	−15.4910			−0.510722
$921$		0			0
$922$	−4.21860	−	7.30683i	−0.138932	−	0.240638i
$923$	−1.81182	+	11.6146i	−0.0596367	+	0.382299i
$924$		0			0
$925$	−1.46725	−	2.54136i	−0.0482430	−	0.0835593i
$926$	−1.07049	+	1.85414i	−0.0351784	+	0.0609308i
$927$		0			0
$928$	−19.8211	+	34.3312i	−0.650660	+	1.12698i
$929$	47.1060			1.54550			0.772750	−	0.634711i	$-0.218881\pi$
$929$	47.1060			1.54550			0.772750	+	0.634711i	$0.218881\pi$
$930$		0			0
$931$	8.04751	+	20.8551i	0.263746	+	0.683497i
$932$	−9.42842	+	16.3305i	−0.308838	+	0.534924i
$933$		0			0
$934$	−49.1906			−1.60957
$935$	3.85144	−	6.67088i	0.125955	−	0.218161i
$936$		0			0
$937$	43.2558			1.41310			0.706552	−	0.707661i	$-0.250249\pi$
$937$	43.2558			1.41310			0.706552	+	0.707661i	$0.250249\pi$
$938$	45.9323	−	21.9580i	1.49974	−	0.716955i
$939$		0			0
$940$	22.6190			0.737750
$941$	21.2053	−	36.7287i	0.691274	−	1.19732i	−0.280146	−	0.959957i	$-0.590383\pi$
$941$	21.2053	−	36.7287i	0.691274	−	1.19732i	0.971421	−	0.237365i	$-0.0762836\pi$
$942$		0			0
$943$	−17.6452			−0.574608
$944$	44.6762			1.45409
$945$		0			0
$946$	−5.73022	−	9.92503i	−0.186305	−	0.322691i
$947$	21.9080	−	37.9458i	0.711914	−	1.23307i	−0.252223	−	0.967669i	$-0.581162\pi$
$947$	21.9080	−	37.9458i	0.711914	−	1.23307i	0.964138	−	0.265403i	$-0.0855049\pi$
$948$		0			0
$949$	−8.34387	+	53.4881i	−0.270854	+	1.73630i
$950$	−2.84289	−	4.92402i	−0.0922354	−	0.159756i
$951$		0			0
$952$	1.12540	−	14.4616i	0.0364743	−	0.468704i
$953$	−8.09343	+	14.0182i	−0.262172	+	0.454095i	−0.966819	−	0.255463i	$-0.917772\pi$
$953$	−8.09343	+	14.0182i	−0.262172	+	0.454095i	0.704647	+	0.709558i	$0.251105\pi$
$954$		0			0
$955$	18.7703	+	32.5111i	0.607392	+	1.05203i
$956$	−3.90871	−	6.77008i	−0.126417	−	0.218960i
$957$		0			0
$958$	−5.98432	+	10.3651i	−0.193345	+	0.334883i
$959$	−0.577874	+	7.42583i	−0.0186605	+	0.239793i
$960$		0			0
$961$	−8.73113	−	15.1228i	−0.281649	−	0.487831i
$962$	13.6092	+	10.9680i	0.438777	+	0.353624i
$963$		0			0
$964$	−9.69091	+	16.7851i	−0.312123	+	0.540613i
$965$	−31.5366	−	54.6231i	−1.01520	−	1.75838i
$966$		0			0
$967$	−42.5994			−1.36990			−0.684952	−	0.728588i	$-0.740177\pi$
$967$	−42.5994			−1.36990			−0.684952	+	0.728588i	$0.740177\pi$
$968$	18.0158			0.579049
$969$		0			0
$970$	12.3228	−	21.3437i	0.395661	−	0.685304i
$971$	−3.00538			−0.0964472			−0.0482236	−	0.998837i	$-0.515356\pi$
$971$	−3.00538			−0.0964472			−0.0482236	+	0.998837i	$0.515356\pi$
$972$		0			0
$973$	8.96795	−	4.28715i	0.287499	−	0.137440i
$974$	−3.30710			−0.105966
$975$		0			0
$976$	−6.51782	+	11.2892i	−0.208630	+	0.361359i
$977$	40.8447			1.30674			0.653368	−	0.757040i	$-0.273355\pi$
$977$	40.8447			1.30674			0.653368	+	0.757040i	$0.273355\pi$
$978$		0			0
$979$	2.75369	−	4.76953i	0.0880083	−	0.152435i
$980$	−15.9962	−	2.50479i	−0.510979	−	0.0800126i
$981$		0			0
$982$	50.4105			1.60866
$983$	−30.1629	+	52.2437i	−0.962047	+	1.66631i	−0.244699	+	0.969599i	$0.578689\pi$
$983$	−30.1629	+	52.2437i	−0.962047	+	1.66631i	−0.717348	+	0.696715i	$0.754644\pi$
$984$		0			0
$985$	−19.2712	+	33.3788i	−0.614033	+	1.06354i
$986$	−20.7874	−	36.0048i	−0.662006	−	1.14663i
$987$		0			0
$988$	8.43865	+	6.80096i	0.268469	+	0.216367i
$989$	−11.1743	−	19.3544i	−0.355321	−	0.615433i
$990$		0			0
$991$	−45.9189			−1.45866			−0.729332	−	0.684160i	$-0.760169\pi$
$991$	−45.9189			−1.45866			−0.729332	+	0.684160i	$0.760169\pi$
$992$	−34.3743			−1.09139
$993$		0			0
$994$	−1.14775	+	14.7489i	−0.0364045	+	0.467808i
$995$	7.06574	−	12.2382i	0.223999	−	0.387978i
$996$		0			0
$997$	−13.2885	−	23.0163i	−0.420850	−	0.728934i	0.575172	−	0.818032i	$-0.304935\pi$
$997$	−13.2885	−	23.0163i	−0.420850	−	0.728934i	−0.996023	+	0.0890978i	$0.971602\pi$
$998$	34.0569			1.07805
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.n.e.172.2		16
3.2	odd	2		273.2.j.b.172.7	yes	16
7.2	even	3		819.2.s.e.289.7		16
13.9	even	3		819.2.s.e.802.7		16
21.2	odd	6		273.2.l.b.16.2	yes	16
39.35	odd	6		273.2.l.b.256.2	yes	16
91.9	even	3	inner	819.2.n.e.100.2		16
273.191	odd	6		273.2.j.b.100.7	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.7	✓	16	273.191	odd	6
273.2.j.b.172.7	yes	16	3.2	odd	2
273.2.l.b.16.2	yes	16	21.2	odd	6
273.2.l.b.256.2	yes	16	39.35	odd	6
819.2.n.e.100.2		16	91.9	even	3	inner
819.2.n.e.172.2		16	1.1	even	1	trivial
819.2.s.e.289.7		16	7.2	even	3
819.2.s.e.802.7		16	13.9	even	3

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.n (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.857510 + 1.48525i) q^{2} +(-0.470647 - 0.815185i) q^{4} +(-1.22863 - 2.12806i) q^{5} +(2.18175 + 1.49666i) q^{7} -1.81570 q^{8} +O(q^{10})\)	\(q+(-0.857510 + 1.48525i) q^{2} +(-0.470647 - 0.815185i) q^{4} +(-1.22863 - 2.12806i) q^{5} +(2.18175 + 1.49666i) q^{7} -1.81570 q^{8} +4.21426 q^{10} +1.03816 q^{11} +(-3.36305 + 1.29996i) q^{13} +(-4.09378 + 1.95704i) q^{14} +(2.49828 - 4.32714i) q^{16} +(1.50975 + 2.61496i) q^{17} +3.19341 q^{19} +(-1.15651 + 2.00313i) q^{20} +(-0.890235 + 1.54193i) q^{22} +(-1.73601 + 3.00685i) q^{23} +(-0.519081 + 0.899075i) q^{25} +(0.953083 - 6.10970i) q^{26} +(0.193220 - 2.48292i) q^{28} +(4.01417 + 6.95275i) q^{29} +(-3.48074 + 6.02882i) q^{31} +(2.46889 + 4.27625i) q^{32} -5.17850 q^{34} +(0.504403 - 6.48172i) q^{35} +(-1.41332 + 2.44794i) q^{37} +(-2.73838 + 4.74302i) q^{38} +(2.23083 + 3.86391i) q^{40} +(2.54107 + 4.40125i) q^{41} +(-3.21838 + 5.57439i) q^{43} +(-0.488608 - 0.846294i) q^{44} +(-2.97729 - 5.15682i) q^{46} +(-4.88951 - 8.46887i) q^{47} +(2.52003 + 6.53065i) q^{49} +(-0.890235 - 1.54193i) q^{50} +(2.64252 + 2.12969i) q^{52} +(-5.90947 + 10.2355i) q^{53} +(-1.27552 - 2.20927i) q^{55} +(-3.96140 - 2.71748i) q^{56} -13.7688 q^{58} +(4.47070 + 7.74348i) q^{59} -2.60893 q^{61} +(-5.96954 - 10.3396i) q^{62} +1.52470 q^{64} +(6.89834 + 5.55958i) q^{65} -11.2200 q^{67} +(1.42112 - 2.46145i) q^{68} +(9.19445 + 6.30731i) q^{70} +(1.63013 - 2.82347i) q^{71} +(7.50717 - 13.0028i) q^{73} +(-2.42387 - 4.19827i) q^{74} +(-1.50297 - 2.60322i) q^{76} +(2.26501 + 1.55377i) q^{77} +(-0.211818 - 0.366880i) q^{79} -12.2779 q^{80} -8.71596 q^{82} +1.34088 q^{83} +(3.70986 - 6.42567i) q^{85} +(-5.51958 - 9.56019i) q^{86} -1.88499 q^{88} +(2.65247 - 4.59421i) q^{89} +(-9.28292 - 2.19715i) q^{91} +3.26819 q^{92} +16.7712 q^{94} +(-3.92353 - 6.79576i) q^{95} +(2.92406 - 5.06463i) q^{97} +(-11.8606 - 1.85722i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} + q^{7} - 12 q^{8}+O(q^{10}) \) 16 * q - 6 * q^4 + q^7 - 12 * q^8	\( 16 q - 6 q^{4} + q^{7} - 12 q^{8} + 8 q^{10} - 4 q^{11} + 5 q^{13} + 7 q^{14} - 6 q^{16} + 2 q^{17} + 22 q^{19} + 20 q^{20} + 7 q^{22} - 4 q^{23} + 2 q^{25} + 6 q^{26} - 7 q^{28} - 15 q^{29} + 3 q^{31} - 3 q^{32} - 68 q^{34} + 12 q^{35} + 4 q^{37} - 2 q^{38} - 25 q^{40} - 19 q^{41} + 11 q^{43} + 16 q^{44} + 2 q^{46} - 5 q^{47} + 13 q^{49} + 7 q^{50} + 36 q^{52} - 36 q^{53} - 15 q^{55} - 39 q^{56} - 40 q^{58} + 17 q^{59} + 44 q^{61} + 6 q^{62} - 20 q^{64} + 21 q^{65} - 52 q^{67} - 5 q^{68} + 46 q^{70} - 9 q^{71} - 6 q^{73} - 15 q^{74} - 16 q^{76} + 36 q^{77} + 16 q^{79} - 56 q^{80} + 2 q^{82} - 36 q^{83} - 4 q^{85} - 16 q^{86} - 48 q^{88} - 20 q^{89} - 7 q^{91} + 94 q^{92} + 40 q^{94} + 7 q^{97} + 3 q^{98}+O(q^{100}) \) 16 * q - 6 * q^4 + q^7 - 12 * q^8 + 8 * q^10 - 4 * q^11 + 5 * q^13 + 7 * q^14 - 6 * q^16 + 2 * q^17 + 22 * q^19 + 20 * q^20 + 7 * q^22 - 4 * q^23 + 2 * q^25 + 6 * q^26 - 7 * q^28 - 15 * q^29 + 3 * q^31 - 3 * q^32 - 68 * q^34 + 12 * q^35 + 4 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 + 2 * q^46 - 5 * q^47 + 13 * q^49 + 7 * q^50 + 36 * q^52 - 36 * q^53 - 15 * q^55 - 39 * q^56 - 40 * q^58 + 17 * q^59 + 44 * q^61 + 6 * q^62 - 20 * q^64 + 21 * q^65 - 52 * q^67 - 5 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 - 15 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 - 56 * q^80 + 2 * q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 - 48 * q^88 - 20 * q^89 - 7 * q^91 + 94 * q^92 + 40 * q^94 + 7 * q^97 + 3 * q^98

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