LMFDB - Embedded newform 855.2.da.b.784.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(199,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("855.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.da (of order $18$, degree $6$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			784.3
Character	$\chi$	$=$	855.784
Dual form			855.2.da.b.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.358233 - 0.984236i) q^{2} +(0.691698 - 0.580404i) q^{4} +(-2.23415 + 0.0926215i) q^{5} +(-2.37320 + 1.37016i) q^{7} +(-2.63320 - 1.52028i) q^{8} +O(q^{10})$	\(q+(-0.358233 - 0.984236i) q^{2} +(0.691698 - 0.580404i) q^{4} +(-2.23415 + 0.0926215i) q^{5} +(-2.37320 + 1.37016i) q^{7} +(-2.63320 - 1.52028i) q^{8} +(0.891507 + 2.16575i) q^{10} +(0.416418 - 0.721257i) q^{11} +(0.601551 - 0.106070i) q^{13} +(2.19872 + 1.84495i) q^{14} +(-0.239424 + 1.35784i) q^{16} +(1.65483 + 4.54662i) q^{17} +(-4.35537 + 0.175314i) q^{19} +(-1.49160 + 1.36077i) q^{20} +(-0.859062 - 0.151476i) q^{22} +(2.41106 + 2.87338i) q^{23} +(4.98284 - 0.413861i) q^{25} +(-0.319893 - 0.554071i) q^{26} +(-0.846286 + 2.32515i) q^{28} +(3.73543 + 1.35958i) q^{29} +(3.46338 + 5.99875i) q^{31} +(-4.56652 + 0.805200i) q^{32} +(3.88213 - 3.25750i) q^{34} +(5.17516 - 3.28096i) q^{35} +4.33071i q^{37} +(1.73279 + 4.22391i) q^{38} +(6.02377 + 3.15264i) q^{40} +(-0.923271 + 5.23613i) q^{41} +(-6.72257 + 8.01164i) q^{43} +(-0.130585 - 0.740582i) q^{44} +(1.96437 - 3.40239i) q^{46} +(-1.16292 + 3.19511i) q^{47} +(0.254704 - 0.441160i) q^{49} +(-2.19235 - 4.75604i) q^{50} +(0.354529 - 0.422511i) q^{52} +(-8.78556 - 10.4702i) q^{53} +(-0.863535 + 1.64996i) q^{55} +8.33212 q^{56} -4.16359i q^{58} +(-9.41315 + 3.42610i) q^{59} +(6.94990 - 5.83166i) q^{61} +(4.66350 - 5.55774i) q^{62} +(3.80717 + 6.59422i) q^{64} +(-1.33413 + 0.292692i) q^{65} +(3.73984 - 10.2751i) q^{67} +(3.78352 + 2.18442i) q^{68} +(-5.08316 - 3.91824i) q^{70} +(0.519169 + 0.435634i) q^{71} +(-6.90688 - 1.21787i) q^{73} +(4.26244 - 1.55140i) q^{74} +(-2.91085 + 2.64914i) q^{76} +2.28224i q^{77} +(-0.604220 + 3.42670i) q^{79} +(0.409144 - 3.05580i) q^{80} +(5.48434 - 0.967036i) q^{82} +(-4.30834 + 2.48742i) q^{83} +(-4.11826 - 10.0046i) q^{85} +(10.2936 + 3.74656i) q^{86} +(-2.19302 + 1.26614i) q^{88} +(-1.02256 - 5.79921i) q^{89} +(-1.28227 + 1.07595i) q^{91} +(3.33544 + 0.588129i) q^{92} +3.56134 q^{94} +(9.71431 - 0.795079i) q^{95} +(4.25430 + 11.6886i) q^{97} +(-0.525449 - 0.0926508i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) $ 48 * q - 18 * q^4 + 6 * q^5	$ 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49} + 18 q^{50} - 36 q^{56} + 36 q^{59} + 48 q^{61} + 18 q^{65} - 123 q^{70} + 24 q^{71} - 84 q^{74} + 66 q^{76} + 48 q^{79} + 39 q^{80} - 84 q^{85} + 42 q^{86} + 12 q^{89} - 30 q^{91} - 72 q^{94} + 63 q^{95}+O(q^{100}) $ 48 * q - 18 * q^4 + 6 * q^5 - 15 * q^10 + 12 * q^11 - 6 * q^14 - 42 * q^16 + 12 * q^19 - 42 * q^20 + 12 * q^25 - 12 * q^26 - 42 * q^31 - 36 * q^34 - 6 * q^35 + 66 * q^40 - 6 * q^41 + 6 * q^44 - 6 * q^46 + 12 * q^49 + 18 * q^50 - 36 * q^56 + 36 * q^59 + 48 * q^61 + 18 * q^65 - 123 * q^70 + 24 * q^71 - 84 * q^74 + 66 * q^76 + 48 * q^79 + 39 * q^80 - 84 * q^85 + 42 * q^86 + 12 * q^89 - 30 * q^91 - 72 * q^94 + 63 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−0.358233	−	0.984236i	−0.253309	−	0.695960i	−0.999542	−	0.0302752i	$-0.990362\pi$
$2$	−0.358233	−	0.984236i	−0.253309	−	0.695960i	0.746233	−	0.665685i	$-0.231861\pi$
$3$		0			0
$3$		0			0
$4$	0.691698	−	0.580404i	0.345849	−	0.290202i
$5$	−2.23415	+	0.0926215i	−0.999142	+	0.0414216i
$5$	−2.23415	+	0.0926215i	−0.999142	+	0.0414216i
$6$		0			0
$7$	−2.37320	+	1.37016i	−0.896983	+	0.517874i	−0.876220	−	0.481911i	$-0.839943\pi$
$7$	−2.37320	+	1.37016i	−0.896983	+	0.517874i	−0.0207632	+	0.999784i	$0.506610\pi$
$8$	−2.63320	−	1.52028i	−0.930976	−	0.537499i
$9$		0			0
$10$	0.891507	+	2.16575i	0.281919	+	0.684871i
$11$	0.416418	−	0.721257i	0.125555	−	0.217467i	−0.796395	−	0.604777i	$-0.793262\pi$
$11$	0.416418	−	0.721257i	0.125555	−	0.217467i	0.921950	+	0.387310i	$0.126596\pi$
$12$		0			0
$13$	0.601551	−	0.106070i	0.166840	−	0.0294185i	−0.0896039	−	0.995977i	$-0.528560\pi$
$13$	0.601551	−	0.106070i	0.166840	−	0.0294185i	0.256444	+	0.966559i	$0.417449\pi$
$14$	2.19872	+	1.84495i	0.587633	+	0.493083i
$15$		0			0
$16$	−0.239424	+	1.35784i	−0.0598561	+	0.339461i
$17$	1.65483	+	4.54662i	0.401356	+	1.10272i	0.961616	+	0.274400i	$0.0884792\pi$
$17$	1.65483	+	4.54662i	0.401356	+	1.10272i	−0.560259	+	0.828317i	$0.689299\pi$
$18$		0			0
$19$	−4.35537	+	0.175314i	−0.999191	+	0.0402198i
$19$	−4.35537	+	0.175314i	−0.999191	+	0.0402198i
$20$	−1.49160	+	1.36077i	−0.333532	+	0.304278i
$21$		0			0
$22$	−0.859062	−	0.151476i	−0.183153	−	0.0322947i
$23$	2.41106	+	2.87338i	0.502740	+	0.599142i	0.956410	−	0.292028i	$-0.0943300\pi$
$23$	2.41106	+	2.87338i	0.502740	+	0.599142i	−0.453670	+	0.891170i	$0.649886\pi$
$24$		0			0
$25$	4.98284	−	0.413861i	0.996569	−	0.0827721i
$26$	−0.319893	−	0.554071i	−0.0627362	−	0.108662i
$27$		0			0
$28$	−0.846286	+	2.32515i	−0.159933	+	0.439412i
$29$	3.73543	+	1.35958i	0.693651	+	0.252468i	0.664698	−	0.747112i	$-0.268560\pi$
$29$	3.73543	+	1.35958i	0.693651	+	0.252468i	0.0289533	+	0.999581i	$0.490783\pi$
$30$		0			0
$31$	3.46338	+	5.99875i	0.622042	+	1.07741i	0.989105	+	0.147212i	$0.0470300\pi$
$31$	3.46338	+	5.99875i	0.622042	+	1.07741i	−0.367063	+	0.930196i	$0.619637\pi$
$32$	−4.56652	+	0.805200i	−0.807254	+	0.142341i
$33$		0			0
$34$	3.88213	−	3.25750i	0.665780	−	0.558656i
$35$	5.17516	−	3.28096i	0.874762	−	0.554584i
$36$		0			0
$37$			4.33071i			0.711965i	0.934493	+	0.355982i	$0.115854\pi$
$37$			4.33071i			0.711965i	−0.934493	+	0.355982i	$0.884146\pi$
$38$	1.73279	+	4.22391i	0.281095	+	0.685209i
$39$		0			0
$40$	6.02377	+	3.15264i	0.952441	+	0.498475i
$41$	−0.923271	+	5.23613i	−0.144191	+	0.817746i	0.823823	+	0.566848i	$0.191837\pi$
$41$	−0.923271	+	5.23613i	−0.144191	+	0.817746i	−0.968013	+	0.250899i	$0.919274\pi$
$42$		0			0
$43$	−6.72257	+	8.01164i	−1.02518	+	1.22176i	−0.0503713	+	0.998731i	$0.516040\pi$
$43$	−6.72257	+	8.01164i	−1.02518	+	1.22176i	−0.974811	+	0.223034i	$0.928404\pi$
$44$	−0.130585	−	0.740582i	−0.0196864	−	0.111647i
$45$		0			0
$46$	1.96437	−	3.40239i	0.289631	−	0.501655i
$47$	−1.16292	+	3.19511i	−0.169630	+	0.466054i	−0.995156	−	0.0983098i	$-0.968656\pi$
$47$	−1.16292	+	3.19511i	−0.169630	+	0.466054i	0.825526	+	0.564364i	$0.190879\pi$
$48$		0			0
$49$	0.254704	−	0.441160i	0.0363862	−	0.0630228i
$50$	−2.19235	−	4.75604i	−0.310046	−	0.672605i
$51$		0			0
$52$	0.354529	−	0.422511i	0.0491643	−	0.0585917i
$53$	−8.78556	−	10.4702i	−1.20679	−	1.43820i	−0.867444	−	0.497535i	$-0.834239\pi$
$53$	−8.78556	−	10.4702i	−1.20679	−	1.43820i	−0.339346	−	0.940662i	$-0.610206\pi$
$54$		0			0
$55$	−0.863535	+	1.64996i	−0.116439	+	0.222481i
$56$	8.33212			1.11343
$57$		0			0
$58$		−	4.16359i		−	0.546706i
$59$	−9.41315	+	3.42610i	−1.22549	+	0.446041i	−0.872050	−	0.489417i	$-0.837210\pi$
$59$	−9.41315	+	3.42610i	−1.22549	+	0.446041i	−0.353437	+	0.935458i	$0.614987\pi$
$60$		0			0
$61$	6.94990	−	5.83166i	0.889844	−	0.746668i	−0.0783350	−	0.996927i	$-0.524960\pi$
$61$	6.94990	−	5.83166i	0.889844	−	0.746668i	0.968179	+	0.250260i	$0.0805159\pi$
$62$	4.66350	−	5.55774i	0.592265	−	0.705833i
$63$		0			0
$64$	3.80717	+	6.59422i	0.475897	+	0.824277i
$65$	−1.33413	+	0.292692i	−0.165479	+	0.0363040i
$66$		0			0
$67$	3.73984	−	10.2751i	0.456894	−	1.25531i	−0.470891	−	0.882191i	$-0.656067\pi$
$67$	3.73984	−	10.2751i	0.456894	−	1.25531i	0.927785	−	0.373115i	$-0.121710\pi$
$68$	3.78352	+	2.18442i	0.458819	+	0.264899i
$69$		0			0
$70$	−5.08316	−	3.91824i	−0.607553	−	0.468319i
$71$	0.519169	+	0.435634i	0.0616140	+	0.0517003i	0.673075	−	0.739575i	$-0.264973\pi$
$71$	0.519169	+	0.435634i	0.0616140	+	0.0517003i	−0.611461	+	0.791275i	$0.709418\pi$
$72$		0			0
$73$	−6.90688	−	1.21787i	−0.808389	−	0.142541i	−0.245846	−	0.969309i	$-0.579066\pi$
$73$	−6.90688	−	1.21787i	−0.808389	−	0.142541i	−0.562543	+	0.826768i	$0.690177\pi$
$74$	4.26244	−	1.55140i	0.495499	−	0.180347i
$75$		0			0
$76$	−2.91085	+	2.64914i	−0.333897	+	0.303877i
$77$			2.28224i			0.260086i
$78$		0			0
$79$	−0.604220	+	3.42670i	−0.0679801	+	0.385534i	0.931767	+	0.363056i	$0.118267\pi$
$79$	−0.604220	+	3.42670i	−0.0679801	+	0.385534i	−0.999747	+	0.0224781i	$0.992844\pi$
$80$	0.409144	−	3.05580i	0.0457437	−	0.341649i
$81$		0			0
$82$	5.48434	−	0.967036i	0.605644	−	0.106791i
$83$	−4.30834	+	2.48742i	−0.472902	+	0.273030i	−0.717454	−	0.696606i	$-0.754693\pi$
$83$	−4.30834	+	2.48742i	−0.472902	+	0.273030i	0.244552	+	0.969636i	$0.421359\pi$
$84$		0			0
$85$	−4.11826	−	10.0046i	−0.446688	−	1.08515i
$86$	10.2936	+	3.74656i	1.10999	+	0.404002i
$87$		0			0
$88$	−2.19302	+	1.26614i	−0.233777	+	0.134971i
$89$	−1.02256	−	5.79921i	−0.108391	−	0.614716i	−0.989812	−	0.142383i	$-0.954523\pi$
$89$	−1.02256	−	5.79921i	−0.108391	−	0.614716i	0.881421	−	0.472332i	$-0.156588\pi$
$90$		0			0
$91$	−1.28227	+	1.07595i	−0.134418	+	0.112790i
$92$	3.33544	+	0.588129i	0.347744	+	0.0613167i
$93$		0			0
$94$	3.56134			0.367324
$95$	9.71431	−	0.795079i	0.996667	−	0.0815734i
$96$		0			0
$97$	4.25430	+	11.6886i	0.431959	+	1.18680i	0.944608	+	0.328200i	$0.106442\pi$
$97$	4.25430	+	11.6886i	0.431959	+	1.18680i	−0.512649	+	0.858598i	$0.671336\pi$
$98$	−0.525449	−	0.0926508i	−0.0530783	−	0.00935914i
$99$		0			0
$100$	3.20642	−	3.17833i	0.320642	−	0.317833i
$101$	3.08004	+	17.4678i	0.306475	+	1.73811i	0.616478	+	0.787372i	$0.288559\pi$
$101$	3.08004	+	17.4678i	0.306475	+	1.73811i	−0.310003	+	0.950736i	$0.600330\pi$
$102$		0			0
$103$	−4.51935	−	2.60925i	−0.445305	−	0.257097i	0.260541	−	0.965463i	$-0.416099\pi$
$103$	−4.51935	−	2.60925i	−0.445305	−	0.257097i	−0.705845	+	0.708366i	$0.749433\pi$
$104$	−1.74526	−	0.635222i	−0.171137	−	0.0622887i
$105$		0			0
$106$	−7.15790	+	12.3979i	−0.695237	+	1.20419i
$107$	13.1524	−	7.59356i	1.27149	−	0.734097i	0.296225	−	0.955118i	$-0.404272\pi$
$107$	13.1524	−	7.59356i	1.27149	−	0.734097i	0.975269	+	0.221021i	$0.0709390\pi$
$108$		0			0
$109$	−3.00487	−	2.52138i	−0.287814	−	0.241505i	0.487437	−	0.873158i	$-0.337932\pi$
$109$	−3.00487	−	2.52138i	−0.287814	−	0.241505i	−0.775251	+	0.631654i	$0.782376\pi$
$110$	1.93330	+	0.258852i	0.184333	+	0.0246805i
$111$		0			0
$112$	−1.29227	−	3.55048i	−0.122108	−	0.335489i
$113$			3.97342i			0.373788i	0.982380	+	0.186894i	$0.0598421\pi$
$113$			3.97342i			0.373788i	−0.982380	+	0.186894i	$0.940158\pi$
$114$		0			0
$115$	−5.65279	−	6.19625i	−0.527126	−	0.577803i
$116$	3.37289	−	1.22763i	0.313165	−	0.113983i
$117$		0			0
$118$	6.74420	+	8.03742i	0.620853	+	0.739904i
$119$	−10.1569	−	8.52262i	−0.931078	−	0.781267i
$120$		0			0
$121$	5.15319	+	8.92559i	0.468472	+	0.811417i
$122$	−8.22942	−	4.75126i	−0.745056	−	0.430158i
$123$		0			0
$124$	5.87731	+	2.13917i	0.527798	+	0.192103i
$125$	−11.0941	+	1.38614i	−0.992285	+	0.123981i
$126$		0			0
$127$	−9.04543	+	1.59495i	−0.802652	+	0.141529i	−0.559901	−	0.828559i	$-0.689161\pi$
$127$	−9.04543	+	1.59495i	−0.802652	+	0.141529i	−0.242751	+	0.970089i	$0.578050\pi$
$128$	−0.834749	+	0.994815i	−0.0737821	+	0.0879301i
$129$		0			0
$130$	0.766008	+	1.20825i	0.0671833	+	0.105970i
$131$	−3.51355	+	1.27883i	−0.306980	+	0.111732i	−0.490917	−	0.871206i	$-0.663338\pi$
$131$	−3.51355	+	1.27883i	−0.306980	+	0.111732i	0.183936	+	0.982938i	$0.441116\pi$
$132$		0			0
$133$	10.0959	−	6.38363i	0.875429	−	0.553531i
$134$	−11.4529			−0.989379
$135$		0			0
$136$	2.55462	−	14.4880i	0.219057	−	1.24233i
$137$	−1.51913	−	1.81043i	−0.129788	−	0.154675i	0.697237	−	0.716841i	$-0.254413\pi$
$137$	−1.51913	−	1.81043i	−0.129788	−	0.154675i	−0.827025	+	0.562166i	$0.809968\pi$
$138$		0			0
$139$	−0.424186	−	2.40568i	−0.0359790	−	0.204047i	0.961519	−	0.274737i	$-0.0885909\pi$
$139$	−0.424186	−	2.40568i	−0.0359790	−	0.204047i	−0.997498	+	0.0706903i	$0.977480\pi$
$140$	1.67537	−	5.27312i	0.141595	−	0.445660i
$141$		0			0
$142$	0.242784	−	0.667043i	0.0203740	−	0.0559770i
$143$	0.173993	−	0.478042i	0.0145500	−	0.0399759i
$144$		0			0
$145$	−8.47142	−	2.69153i	−0.703513	−	0.223520i
$146$	1.27560	+	7.23428i	0.105569	+	0.598713i
$147$		0			0
$148$	2.51356	+	2.99555i	0.206613	+	0.246232i
$149$	2.47773	−	14.0519i	0.202984	−	1.15118i	−0.697598	−	0.716490i	$-0.745748\pi$
$149$	2.47773	−	14.0519i	0.202984	−	1.15118i	0.900581	−	0.434687i	$-0.143141\pi$
$150$		0			0
$151$	2.34319			0.190686			0.0953432	−	0.995444i	$-0.469605\pi$
$151$	2.34319			0.190686			0.0953432	+	0.995444i	$0.469605\pi$
$152$	11.7351	+	6.15974i	0.951841	+	0.499621i
$153$		0			0
$154$	2.24627	−	0.817575i	0.181009	−	0.0658820i
$155$	−8.29333	−	13.0813i	−0.666136	−	1.05072i
$156$		0			0
$157$	10.3969	−	12.3906i	0.829765	−	0.988875i	−0.170229	−	0.985405i	$-0.554451\pi$
$157$	10.3969	−	12.3906i	0.829765	−	0.988875i	0.999994	−	0.00347076i	$-0.00110478\pi$
$158$	3.58914	−	0.632862i	0.285536	−	0.0503478i
$159$		0			0
$160$	10.1277	−	2.22189i	0.800665	−	0.175656i
$161$	−9.65891	−	3.51556i	−0.761229	−	0.277065i
$162$		0			0
$163$	−13.8787	−	8.01289i	−1.08707	−	0.627618i	−0.154273	−	0.988028i	$-0.549303\pi$
$163$	−13.8787	−	8.01289i	−1.08707	−	0.627618i	−0.932794	+	0.360410i	$0.882637\pi$
$164$	2.40044	+	4.15769i	0.187443	+	0.324661i
$165$		0			0
$166$	3.99160	+	3.34935i	0.309809	+	0.259960i
$167$	−4.87006	−	5.80391i	−0.376856	−	0.449120i	0.543963	−	0.839109i	$-0.316923\pi$
$167$	−4.87006	−	5.80391i	−0.376856	−	0.449120i	−0.920819	+	0.389989i	$0.872479\pi$
$168$		0			0
$169$	−11.8654	+	4.31865i	−0.912722	+	0.332204i
$170$	−8.37155	+	7.63730i	−0.642069	+	0.585754i
$171$		0			0
$172$			9.44344i			0.720056i
$173$	3.03100	+	8.32761i	0.230443	+	0.633136i	0.999985	−	0.00545960i	$-0.00173785\pi$
$173$	3.03100	+	8.32761i	0.230443	+	0.633136i	−0.769542	+	0.638596i	$0.779516\pi$
$174$		0			0
$175$	−11.2582	+	7.80949i	−0.851040	+	0.590342i
$176$	0.879653	+	0.738116i	0.0663063	+	0.0556376i
$177$		0			0
$178$	−5.34148	+	3.08391i	−0.400361	+	0.231149i
$179$	−2.73273	+	4.73323i	−0.204254	+	0.353778i	−0.949895	−	0.312570i	$-0.898810\pi$
$179$	−2.73273	+	4.73323i	−0.204254	+	0.353778i	0.745641	+	0.666348i	$0.232143\pi$
$180$		0			0
$181$	−17.6816	−	6.43559i	−1.31427	−	0.478354i	−0.412650	−	0.910890i	$-0.635397\pi$
$181$	−17.6816	−	6.43559i	−1.31427	−	0.478354i	−0.901617	+	0.432536i	$0.857619\pi$
$182$	1.51834	+	0.876613i	0.112547	+	0.0649789i
$183$		0			0
$184$	−1.98044	−	11.2317i	−0.146000	−	0.828009i
$185$	−0.401117	−	9.67545i	−0.0294907	−	0.711354i
$186$		0			0
$187$	3.96838	+	0.699733i	0.290197	+	0.0511695i
$188$	1.05006	+	2.88502i	0.0765835	+	0.210411i
$189$		0			0
$190$	−4.26253	−	9.27636i	−0.309236	−	0.672978i
$191$	17.2606			1.24893			0.624465	−	0.781053i	$-0.285317\pi$
$191$	17.2606			1.24893			0.624465	+	0.781053i	$0.285317\pi$
$192$		0			0
$193$	−7.36067	−	1.29789i	−0.529833	−	0.0934238i	−0.0976691	−	0.995219i	$-0.531139\pi$
$193$	−7.36067	−	1.29789i	−0.529833	−	0.0934238i	−0.432164	+	0.901795i	$0.642250\pi$
$194$	9.98032	−	8.37448i	0.716545	−	0.601253i
$195$		0			0
$196$	−0.0798727	−	0.452980i	−0.00570519	−	0.0323557i
$197$	−10.5724	+	6.10400i	−0.753255	+	0.434892i	−0.826869	−	0.562395i	$-0.809880\pi$
$197$	−10.5724	+	6.10400i	−0.753255	+	0.434892i	0.0736138	+	0.997287i	$0.476547\pi$
$198$		0			0
$199$	−7.29002	−	2.65335i	−0.516776	−	0.188091i	0.0704481	−	0.997515i	$-0.477557\pi$
$199$	−7.29002	−	2.65335i	−0.516776	−	0.188091i	−0.587224	+	0.809424i	$0.699779\pi$
$200$	−13.7500	−	6.48553i	−0.972271	−	0.458596i
$201$		0			0
$202$	16.0890	−	9.28901i	1.13202	−	0.653573i
$203$	−10.7277	+	1.89159i	−0.752940	+	0.132764i
$204$		0			0
$205$	1.57775	−	11.7838i	0.110195	−	0.823017i
$206$	−0.949137	+	5.38282i	−0.0661295	+	0.375039i
$207$		0			0
$208$			0.842208i			0.0583966i
$209$	−1.68721	+	3.21434i	−0.116707	+	0.222341i
$210$		0			0
$211$	−9.45058	+	3.43973i	−0.650605	+	0.236801i	−0.646175	−	0.763190i	$-0.723632\pi$
$211$	−9.45058	+	3.43973i	−0.650605	+	0.236801i	−0.00442979	+	0.999990i	$0.501410\pi$
$212$	−12.1539	−	2.14306i	−0.834734	−	0.147186i
$213$		0			0
$214$	−12.1855	−	10.2248i	−0.832983	−	0.698956i
$215$	14.2772	−	18.5219i	0.973695	−	1.26318i
$216$		0			0
$217$	−16.4386	−	9.49081i	−1.11592	−	0.644278i
$218$	−1.40519	+	3.86074i	−0.0951718	+	0.261482i
$219$		0			0
$220$	0.360339	+	1.64248i	0.0242941	+	0.110736i
$221$	1.47773	+	2.55950i	0.0994027	+	0.172170i
$222$		0			0
$223$	18.2046	−	21.6954i	1.21907	−	1.45283i	0.366339	−	0.930482i	$-0.380611\pi$
$223$	18.2046	−	21.6954i	1.21907	−	1.45283i	0.852731	−	0.522350i	$-0.174944\pi$
$224$	9.73398	−	8.16778i	0.650379	−	0.545733i
$225$		0			0
$226$	3.91079	−	1.42341i	0.260142	−	0.0946839i
$227$			15.8786i			1.05390i	0.849897	+	0.526949i	$0.176664\pi$
$227$			15.8786i			1.05390i	−0.849897	+	0.526949i	$0.823336\pi$
$228$		0			0
$229$	−11.3865			−0.752438			−0.376219	−	0.926531i	$-0.622776\pi$
$229$	−11.3865			−0.752438			−0.376219	+	0.926531i	$0.622776\pi$
$230$	−4.07356	+	7.78339i	−0.268603	+	0.513221i
$231$		0			0
$232$	−7.76917	−	9.25894i	−0.510071	−	0.607879i
$233$	10.1973	−	12.1527i	0.668050	−	0.796151i	−0.320467	−	0.947260i	$-0.603840\pi$
$233$	10.1973	−	12.1527i	0.668050	−	0.796151i	0.988517	+	0.151109i	$0.0482843\pi$
$234$		0			0
$235$	2.30221	−	7.24606i	0.150180	−	0.472681i
$236$	−4.52253	+	7.83325i	−0.294392	+	0.509901i
$237$		0			0
$238$	−4.74975	+	13.0498i	−0.307881	+	0.845895i
$239$	−10.4324	+	18.0695i	−0.674817	+	1.16882i	0.301705	+	0.953401i	$0.402444\pi$
$239$	−10.4324	+	18.0695i	−0.674817	+	1.16882i	−0.976522	+	0.215416i	$0.930889\pi$
$240$		0			0
$241$	4.93664	+	27.9971i	0.317997	+	1.80345i	0.554899	+	0.831917i	$0.312757\pi$
$241$	4.93664	+	27.9971i	0.317997	+	1.80345i	−0.236902	+	0.971533i	$0.576132\pi$
$242$	6.93885	−	8.26940i	0.446046	−	0.531577i
$243$		0			0
$244$	1.42252	−	8.06750i	0.0910673	−	0.516469i
$245$	−0.528185	+	1.00921i	−0.0337445	+	0.0644759i
$246$		0			0
$247$	−2.60138	+	0.567434i	−0.165522	+	0.0361049i
$248$		−	21.0612i		−	1.33739i
$249$		0			0
$250$	5.33856	+	10.4226i	0.337640	+	0.659185i
$251$	−19.0083	+	15.9499i	−1.19979	+	1.00675i	−0.200157	+	0.979764i	$0.564145\pi$
$251$	−19.0083	+	15.9499i	−1.19979	+	1.00675i	−0.999636	+	0.0269823i	$0.991410\pi$
$252$		0			0
$253$	3.07645	−	0.542462i	0.193415	−	0.0341043i
$254$	4.81018	+	8.33148i	0.301818	+	0.522763i
$255$		0			0
$256$	15.5885	+	5.67373i	0.974279	+	0.354608i
$257$	1.86135	−	5.11403i	0.116108	−	0.319004i	−0.868003	−	0.496559i	$-0.834597\pi$
$257$	1.86135	−	5.11403i	0.116108	−	0.319004i	0.984111	+	0.177555i	$0.0568188\pi$
$258$		0			0
$259$	−5.93379	−	10.2776i	−0.368708	−	0.638620i
$260$	−0.752936	+	0.976789i	−0.0466951	+	0.0605779i
$261$		0			0
$262$	2.51734	+	3.00005i	0.155522	+	0.185344i
$263$	−19.2231	−	3.38955i	−1.18535	−	0.209009i	−0.453992	−	0.891006i	$-0.650001\pi$
$263$	−19.2231	−	3.38955i	−1.18535	−	0.209009i	−0.731355	+	0.681997i	$0.761112\pi$
$264$		0			0
$265$	20.5980	+	22.5783i	1.26533	+	1.38697i
$266$	−9.89970	−	7.64996i	−0.606990	−	0.469049i
$267$		0			0
$268$	−3.37688	−	9.27790i	−0.206276	−	0.566738i
$269$	3.22722	−	18.3025i	0.196767	−	1.11592i	−0.713113	−	0.701049i	$-0.752715\pi$
$269$	3.22722	−	18.3025i	0.196767	−	1.11592i	0.909880	−	0.414872i	$-0.136174\pi$
$270$		0			0
$271$	1.44946	+	1.21624i	0.0880485	+	0.0738815i	0.685749	−	0.727838i	$-0.259475\pi$
$271$	1.44946	+	1.21624i	0.0880485	+	0.0738815i	−0.597701	+	0.801719i	$0.703919\pi$
$272$	−6.56980	+	1.15843i	−0.398353	+	0.0702403i
$273$		0			0
$274$	−1.23769	+	2.14374i	−0.0747715	+	0.129508i
$275$	1.77644	−	3.76625i	0.107124	−	0.227113i
$276$		0			0
$277$	5.87068	+	3.38944i	0.352735	+	0.203652i	0.665889	−	0.746051i	$-0.268052\pi$
$277$	5.87068	+	3.38944i	0.352735	+	0.203652i	−0.313154	+	0.949702i	$0.601386\pi$
$278$	−2.21580	+	1.27929i	−0.132895	+	0.0767269i
$279$		0			0
$280$	−18.6152	+	0.771734i	−1.11247	+	0.0461199i
$281$	9.41170	−	7.89735i	0.561455	−	0.471116i	−0.317343	−	0.948311i	$-0.602791\pi$
$281$	9.41170	−	7.89735i	0.561455	−	0.471116i	0.878798	+	0.477194i	$0.158346\pi$
$282$		0			0
$283$	8.77851	+	24.1188i	0.521829	+	1.43371i	0.868483	+	0.495719i	$0.165095\pi$
$283$	8.77851	+	24.1188i	0.521829	+	1.43371i	−0.346654	+	0.937993i	$0.612682\pi$
$284$	0.611952			0.0363126
$285$		0			0
$286$	−0.532837			−0.0315073
$287$	−4.98326	−	13.6914i	−0.294152	−	0.808177i
$288$		0			0
$289$	−4.91052	+	4.12042i	−0.288854	+	0.242377i
$290$	0.385638	+	9.30208i	0.0226454	+	0.546237i
$291$		0			0
$292$	−5.48433	+	3.16638i	−0.320946	+	0.185298i
$293$	24.3458	+	14.0560i	1.42229	+	0.821162i	0.996495	−	0.0836552i	$-0.0266594\pi$
$293$	24.3458	+	14.0560i	1.42229	+	0.821162i	0.425800	+	0.904817i	$0.359993\pi$
$294$		0			0
$295$	20.7130	−	8.52629i	1.20596	−	0.496420i
$296$	6.58388	−	11.4036i	0.382680	−	0.662822i
$297$		0			0
$298$	−14.7180	+	2.59518i	−0.852591	+	0.150335i
$299$	1.75515	+	1.47275i	0.101503	+	0.0851712i
$300$		0			0
$301$	4.97669	−	28.2242i	0.286852	−	1.62682i
$302$	−0.839409	−	2.30626i	−0.0483025	−	0.132710i
$303$		0			0
$304$	0.804733	−	5.95588i	0.0461546	−	0.341593i
$305$	−14.9870	+	13.6725i	−0.858152	+	0.782886i
$306$		0			0
$307$	−2.53762	−	0.447450i	−0.144829	−	0.0255373i	0.100763	−	0.994910i	$-0.467872\pi$
$307$	−2.53762	−	0.447450i	−0.144829	−	0.0255373i	−0.245593	+	0.969373i	$0.578983\pi$
$308$	1.32462	+	1.57862i	0.0754774	+	0.0899504i
$309$		0			0
$310$	−9.90418	+	12.8488i	−0.562519	+	0.729760i
$311$	7.31837	+	12.6758i	0.414987	+	0.718778i	0.995427	−	0.0955246i	$-0.0304529\pi$
$311$	7.31837	+	12.6758i	0.414987	+	0.718778i	−0.580440	+	0.814303i	$0.697120\pi$
$312$		0			0
$313$	−0.511007	+	1.40398i	−0.0288838	+	0.0793577i	−0.953296	−	0.302036i	$-0.902334\pi$
$313$	−0.511007	+	1.40398i	−0.0288838	+	0.0793577i	0.924413	+	0.381394i	$0.124556\pi$
$314$	−15.9198	−	5.79432i	−0.898405	−	0.326993i
$315$		0			0
$316$	1.57093	+	2.72094i	0.0883719	+	0.153065i
$317$	5.55662	−	0.979782i	0.312091	−	0.0550301i	−0.0154089	−	0.999881i	$-0.504905\pi$
$317$	5.55662	−	0.979782i	0.312091	−	0.0550301i	0.327500	+	0.944851i	$0.393794\pi$
$318$		0			0
$319$	2.53611	−	2.12805i	0.141995	−	0.119148i
$320$	−9.11656	−	14.3798i	−0.509631	−	0.803857i
$321$		0			0
$322$			10.7660i			0.599968i
$323$	−8.00451	−	19.5121i	−0.445383	−	1.08568i
$324$		0			0
$325$	2.95354	−	0.777487i	0.163833	−	0.0431272i
$326$	−2.91476	+	16.5304i	−0.161434	+	0.915536i
$327$		0			0
$328$	10.3915	−	12.3841i	0.573776	−	0.683800i
$329$	−1.61798	−	9.17601i	−0.0892021	−	0.505890i
$330$		0			0
$331$	−15.9460	+	27.6193i	−0.876472	+	1.51809i	−0.0212866	+	0.999773i	$0.506776\pi$
$331$	−15.9460	+	27.6193i	−0.876472	+	1.51809i	−0.855186	+	0.518321i	$0.826557\pi$
$332$	−1.53636	+	4.22113i	−0.0843189	+	0.231664i
$333$		0			0
$334$	−3.96780	+	6.87244i	−0.217109	+	0.376043i
$335$	−7.40366	+	23.3026i	−0.404505	+	1.27315i
$336$		0			0
$337$	−9.85896	+	11.7495i	−0.537052	+	0.640033i	−0.964524	−	0.263995i	$-0.914960\pi$
$337$	−9.85896	+	11.7495i	−0.537052	+	0.640033i	0.427472	+	0.904029i	$0.359404\pi$
$338$	8.50114	+	10.1313i	0.462401	+	0.551068i
$339$		0			0
$340$	−8.65527	−	4.52988i	−0.469398	−	0.245667i
$341$	5.76886			0.312401
$342$		0			0
$343$		−	17.7864i		−	0.960373i
$344$	29.8818	−	10.8761i	1.61112	−	0.586399i
$345$		0			0
$346$	7.11053	−	5.96644i	0.382264	−	0.320758i
$347$	−0.0531571	+	0.0633501i	−0.00285362	+	0.00340081i	−0.767469	−	0.641086i	$-0.778484\pi$
$347$	−0.0531571	+	0.0633501i	−0.00285362	+	0.00340081i	0.764616	+	0.644486i	$0.222929\pi$
$348$		0			0
$349$	−2.32166	−	4.02124i	−0.124276	−	0.215252i	0.797174	−	0.603750i	$-0.206327\pi$
$349$	−2.32166	−	4.02124i	−0.124276	−	0.215252i	−0.921450	+	0.388498i	$0.872994\pi$
$350$	11.7194	+	8.28312i	0.626430	+	0.442751i
$351$		0			0
$352$	−1.32082	+	3.62893i	−0.0704001	+	0.193423i
$353$	−3.45892	−	1.99701i	−0.184100	−	0.106290i	0.405118	−	0.914265i	$-0.367231\pi$
$353$	−3.45892	−	1.99701i	−0.184100	−	0.106290i	−0.589218	+	0.807974i	$0.700564\pi$
$354$		0			0
$355$	−1.20025	−	0.925185i	−0.0637026	−	0.0491037i
$356$	−4.07319	−	3.41781i	−0.215878	−	0.181144i
$357$		0			0
$358$	5.63757	+	0.994055i	0.297955	+	0.0525374i
$359$	−28.3973	+	10.3358i	−1.49875	+	0.545502i	−0.955738	−	0.294220i	$-0.904940\pi$
$359$	−28.3973	+	10.3358i	−1.49875	+	0.545502i	−0.543017	+	0.839722i	$0.682718\pi$
$360$		0			0
$361$	18.9385	−	1.52712i	0.996765	−	0.0803746i
$362$			19.7084i			1.03585i
$363$		0			0
$364$	−0.262456	+	1.48846i	−0.0137564	+	0.0780167i
$365$	15.5438	+	2.08117i	0.813599	+	0.108934i
$366$		0			0
$367$	−17.8643	+	3.14996i	−0.932511	+	0.164427i	−0.619208	−	0.785227i	$-0.712546\pi$
$367$	−17.8643	+	3.14996i	−0.932511	+	0.164427i	−0.313302	+	0.949653i	$0.601435\pi$
$368$	−4.47887	+	2.58588i	−0.233477	+	0.134798i
$369$		0			0
$370$	−9.37924	+	3.86086i	−0.487604	+	0.200717i
$371$	35.1958	+	12.8102i	1.82727	+	0.665074i
$372$		0			0
$373$	21.8369	−	12.6075i	1.13067	−	0.652794i	0.186568	−	0.982442i	$-0.440264\pi$
$373$	21.8369	−	12.6075i	1.13067	−	0.652794i	0.944104	+	0.329648i	$0.106930\pi$
$374$	−0.732902	−	4.15649i	−0.0378975	−	0.214927i
$375$		0			0
$376$	7.91966	−	6.64538i	0.408425	−	0.342710i
$377$	2.39126	+	0.421644i	0.123156	+	0.0217158i
$378$		0			0
$379$	27.5634			1.41584			0.707918	−	0.706294i	$-0.249634\pi$
$379$	27.5634			1.41584			0.707918	+	0.706294i	$0.249634\pi$
$380$	6.25790	−	6.18818i	0.321024	−	0.317447i
$381$		0			0
$382$	−6.18330	−	16.9885i	−0.316365	−	0.869206i
$383$	18.0453	+	3.18187i	0.922072	+	0.162586i	0.614480	−	0.788932i	$-0.289366\pi$
$383$	18.0453	+	3.18187i	0.922072	+	0.162586i	0.307592	+	0.951518i	$0.400477\pi$
$384$		0			0
$385$	−0.211385	−	5.09887i	−0.0107732	−	0.259863i
$386$	1.35941	+	7.70959i	0.0691921	+	0.392408i
$387$		0			0
$388$	9.72680	+	5.61577i	0.493803	+	0.285098i
$389$	6.75172	+	2.45743i	0.342326	+	0.124596i	0.507461	−	0.861674i	$-0.330584\pi$
$389$	6.75172	+	2.45743i	0.342326	+	0.124596i	−0.165136	+	0.986271i	$0.552806\pi$
$390$		0			0
$391$	−9.07429	+	15.7171i	−0.458906	+	0.794849i
$392$	−1.34137	+	0.774441i	−0.0677495	+	0.0391152i
$393$		0			0
$394$	9.79517	+	8.21913i	0.493474	+	0.414074i
$395$	1.03253	−	7.71173i	0.0519523	−	0.388019i
$396$		0			0
$397$	4.00993	+	11.0172i	0.201252	+	0.552937i	0.998728	−	0.0504142i	$-0.0160541\pi$
$397$	4.00993	+	11.0172i	0.201252	+	0.552937i	−0.797476	+	0.603351i	$0.793832\pi$
$398$			8.12562i			0.407301i
$399$		0			0
$400$	−0.631056	+	6.86500i	−0.0315528	+	0.343250i
$401$	36.8475	−	13.4114i	1.84008	−	0.669734i	0.850455	−	0.526048i	$-0.176327\pi$
$401$	36.8475	−	13.4114i	1.84008	−	0.669734i	0.989623	−	0.143686i	$-0.0458954\pi$
$402$		0			0
$403$	2.71969	+	3.24120i	0.135477	+	0.161456i
$404$	12.2688	+	10.2948i	0.610396	+	0.512183i
$405$		0			0
$406$	5.70480	+	9.88101i	0.283125	+	0.490386i
$407$	3.12355	+	1.80339i	0.154829	+	0.0893905i
$408$		0			0
$409$	8.34099	+	3.03587i	0.412436	+	0.150114i	0.539901	−	0.841729i	$-0.318462\pi$
$409$	8.34099	+	3.03587i	0.412436	+	0.150114i	−0.127465	+	0.991843i	$0.540684\pi$
$410$	−12.1633	+	2.66847i	−0.600700	+	0.131786i
$411$		0			0
$412$	−4.64044	+	0.818235i	−0.228618	+	0.0403115i
$413$	17.6449	−	21.0284i	0.868249	−	1.03474i
$414$		0			0
$415$	9.39509	−	5.95632i	0.461187	−	0.292384i
$416$	−2.66159	+	0.968738i	−0.130495	+	0.0474963i
$417$		0			0
$418$	3.76809	+	0.509128i	0.184303	+	0.0249022i
$419$	−7.80196			−0.381151			−0.190575	−	0.981673i	$-0.561035\pi$
$419$	−7.80196			−0.381151			−0.190575	+	0.981673i	$0.561035\pi$
$420$		0			0
$421$	6.00077	−	34.0320i	0.292459	−	1.65862i	−0.384893	−	0.922961i	$-0.625762\pi$
$421$	6.00077	−	34.0320i	0.292459	−	1.65862i	0.677352	−	0.735659i	$-0.263127\pi$
$422$	6.77101	+	8.06938i	0.329608	+	0.392811i
$423$		0			0
$424$	7.21648	+	40.9267i	0.350463	+	1.98758i
$425$	10.1274	+	21.9702i	0.491253	+	1.06571i
$426$		0			0
$427$	−8.50314	+	23.3622i	−0.411496	+	1.13058i
$428$	4.69018	−	12.8862i	0.226709	−	0.622877i
$429$		0			0
$430$	−23.3444	−	7.41697i	−1.12577	−	0.357678i
$431$	−0.493077	−	2.79638i	−0.0237507	−	0.134697i	0.970627	−	0.240590i	$-0.0773409\pi$
$431$	−0.493077	−	2.79638i	−0.0237507	−	0.134697i	−0.994377	+	0.105893i	$0.966230\pi$
$432$		0			0
$433$	14.0467	+	16.7402i	0.675040	+	0.804481i	0.989461	−	0.144803i	$-0.0462548\pi$
$433$	14.0467	+	16.7402i	0.675040	+	0.804481i	−0.314421	+	0.949284i	$0.601810\pi$
$434$	−3.45237	+	19.5794i	−0.165719	+	0.939839i
$435$		0			0
$436$	−3.54188			−0.169625
$437$	−11.0048	−	12.0920i	−0.526430	−	0.578437i
$438$		0			0
$439$	30.6114	−	11.1416i	1.46100	−	0.531761i	0.515361	−	0.856973i	$-0.327658\pi$
$439$	30.6114	−	11.1416i	1.46100	−	0.531761i	0.945641	+	0.325212i	$0.105436\pi$
$440$	4.78226	−	3.03187i	0.227985	−	0.144539i
$441$		0			0
$442$	1.98978	−	2.37133i	0.0946442	−	0.112793i
$443$	−7.64381	+	1.34781i	−0.363169	+	0.0640364i	−0.352255	−	0.935904i	$-0.614585\pi$
$443$	−7.64381	+	1.34781i	−0.363169	+	0.0640364i	−0.0109135	+	0.999940i	$0.503474\pi$
$444$		0			0
$445$	2.82168	+	12.8616i	0.133760	+	0.609698i
$446$	−27.8749	−	10.1456i	−1.31991	−	0.480409i
$447$		0			0
$448$	−18.0703	−	10.4329i	−0.853743	−	0.492909i
$449$	−11.4911	−	19.9031i	−0.542296	−	0.939285i	−0.998772	−	0.0495489i	$-0.984222\pi$
$449$	−11.4911	−	19.9031i	−0.542296	−	0.939285i	0.456475	−	0.889736i	$-0.349112\pi$
$450$		0			0
$451$	3.39213	+	2.84633i	0.159729	+	0.134029i
$452$	2.30619	+	2.74841i	0.108474	+	0.129274i
$453$		0			0
$454$	15.6283	−	5.68822i	0.733470	−	0.266961i
$455$	2.76512	−	2.52260i	0.129631	−	0.118261i
$456$		0			0
$457$			3.38866i			0.158515i	0.996854	+	0.0792573i	$0.0252549\pi$
$457$			3.38866i			0.158515i	−0.996854	+	0.0792573i	$0.974745\pi$
$458$	4.07900	+	11.2070i	0.190599	+	0.523667i
$459$		0			0
$460$	−7.50635	−	1.00503i	−0.349986	−	0.0468599i
$461$	8.31382	+	6.97612i	0.387213	+	0.324910i	0.815526	−	0.578720i	$-0.196448\pi$
$461$	8.31382	+	6.97612i	0.387213	+	0.324910i	−0.428313	+	0.903630i	$0.640892\pi$
$462$		0			0
$463$	−6.33213	+	3.65586i	−0.294279	+	0.169902i	−0.639870	−	0.768483i	$-0.721012\pi$
$463$	−6.33213	+	3.65586i	−0.294279	+	0.169902i	0.345591	+	0.938385i	$0.387678\pi$
$464$	−2.74045	+	4.74660i	−0.127222	+	0.220355i
$465$		0			0
$466$	−15.6142	−	5.68309i	−0.723313	−	0.263264i
$467$	−9.38929	−	5.42091i	−0.434484	−	0.250850i	0.266771	−	0.963760i	$-0.414043\pi$
$467$	−9.38929	−	5.42091i	−0.434484	−	0.250850i	−0.701255	+	0.712910i	$0.747377\pi$
$468$		0			0
$469$	5.20325	+	29.5091i	0.240264	+	1.36260i
$470$	−7.95656	+	0.329857i	−0.367009	+	0.0152152i
$471$		0			0
$472$	29.9953	+	5.28898i	1.38065	+	0.243445i
$473$	2.97906	+	8.18489i	0.136977	+	0.376342i
$474$		0			0
$475$	−21.6296	+	2.67608i	−0.992433	+	0.122787i
$476$	−11.9720			−0.548738
$477$		0			0
$478$	21.5219	+	3.79489i	0.984388	+	0.173574i
$479$	2.64084	−	2.21593i	0.120663	−	0.101249i	−0.580459	−	0.814289i	$-0.697127\pi$
$479$	2.64084	−	2.21593i	0.120663	−	0.101249i	0.701123	+	0.713041i	$0.252683\pi$
$480$		0			0
$481$	0.459357	+	2.60515i	0.0209449	+	0.118784i
$482$	25.7873	−	14.8883i	1.17458	−	0.678143i
$483$		0			0
$484$	8.74490	+	3.18288i	0.397495	+	0.144677i
$485$	−10.5874	−	25.7200i	−0.480747	−	1.16789i
$486$		0			0
$487$	23.3802	−	13.4986i	1.05946	−	0.611680i	0.134177	−	0.990957i	$-0.457161\pi$
$487$	23.3802	−	13.4986i	1.05946	−	0.611680i	0.925283	+	0.379278i	$0.123828\pi$
$488$	−27.1662	+	4.79014i	−1.22976	+	0.216839i
$489$		0			0
$490$	1.18251	+	0.158328i	0.0534205	+	0.00715252i
$491$	−0.0423665	+	0.240272i	−0.00191197	+	0.0108433i	−0.985749	−	0.168224i	$-0.946197\pi$
$491$	−0.0423665	+	0.240272i	−0.00191197	+	0.0108433i	0.983837	+	0.179067i	$0.0573080\pi$
$492$		0			0
$493$			19.2334i			0.866231i
$494$	1.49039	+	2.35710i	0.0670558	+	0.106051i
$495$		0			0
$496$	−8.97458	+	3.26648i	−0.402971	+	0.146669i
$497$	−1.82898	−	0.322498i	−0.0820409	−	0.0144660i
$498$		0			0
$499$	2.48864	+	2.08821i	0.111407	+	0.0934813i	0.696789	−	0.717276i	$-0.254611\pi$
$499$	2.48864	+	2.08821i	0.111407	+	0.0934813i	−0.585383	+	0.810757i	$0.699056\pi$
$500$	−6.86923	+	7.39784i	−0.307201	+	0.330841i
$501$		0			0
$502$	22.5078	+	12.9949i	1.00457	+	0.579991i
$503$	2.43705	−	6.69573i	0.108663	−	0.298548i	−0.873429	−	0.486951i	$-0.838109\pi$
$503$	2.43705	−	6.69573i	0.108663	−	0.298548i	0.982092	+	0.188403i	$0.0603312\pi$
$504$		0			0
$505$	−8.49915	−	38.7403i	−0.378207	−	1.72392i
$506$	−1.63600	−	2.83363i	−0.0727289	−	0.125970i
$507$		0			0
$508$	−5.33099	+	6.35323i	−0.236524	+	0.281879i
$509$	1.32543	−	1.11216i	0.0587485	−	0.0492958i	−0.612941	−	0.790129i	$-0.710014\pi$
$509$	1.32543	−	1.11216i	0.0587485	−	0.0492958i	0.671689	+	0.740833i	$0.265569\pi$
$510$		0			0
$511$	18.0600	−	6.57332i	0.798929	−	0.290787i
$512$		−	14.7780i		−	0.653100i
$513$		0			0
$514$	−5.70021			−0.251426
$515$	10.3386	+	5.41086i	0.455572	+	0.238431i
$516$		0			0
$517$	1.82023	+	2.16927i	0.0800537	+	0.0954042i
$518$	−7.98993	+	9.52203i	−0.351058	+	0.418374i
$519$		0			0
$520$	3.95800	+	1.25753i	0.173570	+	0.0551465i
$521$	6.40164	−	11.0880i	0.280461	−	0.485773i	−0.691037	−	0.722819i	$-0.742846\pi$
$521$	6.40164	−	11.0880i	0.280461	−	0.485773i	0.971498	+	0.237046i	$0.0761794\pi$
$522$		0			0
$523$	−2.98119	+	8.19075i	−0.130358	+	0.358157i	−0.987650	−	0.156674i	$-0.949923\pi$
$523$	−2.98119	+	8.19075i	−0.130358	+	0.358157i	0.857292	+	0.514830i	$0.172145\pi$
$524$	−1.68808	+	2.92384i	−0.0737441	+	0.127729i
$525$		0			0
$526$	3.55023	+	20.1343i	0.154797	+	0.877898i
$527$	−21.5427	+	25.6736i	−0.938416	+	1.11836i
$528$		0			0
$529$	1.55076	−	8.79481i	0.0674244	−	0.382383i
$530$	14.8435	−	28.3616i	0.644761	−	1.23195i
$531$		0			0
$532$	3.27826	−	10.2753i	0.142131	−	0.445489i
$533$			3.24773i			0.140675i
$534$		0			0
$535$	−28.6812	+	18.1833i	−1.23999	+	0.786135i
$536$	−25.4688	+	21.3708i	−1.10008	+	0.923080i
$537$		0			0
$538$	−19.1701	+	3.38020i	−0.826480	+	0.145731i
$539$	−0.212126	−	0.367414i	−0.00913693	−	0.0158256i
$540$		0			0
$541$	−10.3511	−	3.76748i	−0.445027	−	0.161977i	0.109780	−	0.993956i	$-0.464985\pi$
$541$	−10.3511	−	3.76748i	−0.445027	−	0.161977i	−0.554806	+	0.831979i	$0.687208\pi$
$542$	0.677825	−	1.86231i	0.0291151	−	0.0799931i
$543$		0			0
$544$	−11.2178	−	19.4297i	−0.480958	−	0.833043i
$545$	6.94685	+	5.35483i	0.297570	+	0.229376i
$546$		0			0
$547$	−11.8246	−	14.0921i	−0.505585	−	0.602533i	0.451525	−	0.892259i	$-0.350880\pi$
$547$	−11.8246	−	14.0921i	−0.505585	−	0.602533i	−0.957110	+	0.289726i	$0.906436\pi$
$548$	−2.10156	−	0.370562i	−0.0897741	−	0.0158296i
$549$		0			0
$550$	−4.34326	−	0.399248i	−0.185197	−	0.0170240i
$551$	−16.5075	−	5.26662i	−0.703244	−	0.224366i
$552$		0			0
$553$	−3.26122	−	8.96012i	−0.138681	−	0.381023i
$554$	1.23294	−	6.99234i	0.0523825	−	0.297076i
$555$		0			0
$556$	−1.68967	−	1.41780i	−0.0716581	−	0.0601283i
$557$	0.199028	−	0.0350939i	0.00843307	−	0.00148698i	−0.169430	−	0.985542i	$-0.554193\pi$
$557$	0.199028	−	0.0350939i	0.00843307	−	0.00148698i	0.177863	+	0.984055i	$0.443082\pi$
$558$		0			0
$559$	−3.19418	+	5.53248i	−0.135099	+	0.233999i
$560$	3.21597	+	7.81260i	0.135900	+	0.330143i
$561$		0			0
$562$	−11.1444	−	6.43424i	−0.470100	−	0.271412i
$563$	−5.85758	+	3.38187i	−0.246867	+	0.142529i	−0.618329	−	0.785919i	$-0.712190\pi$
$563$	−5.85758	+	3.38187i	−0.246867	+	0.142529i	0.371462	+	0.928448i	$0.378857\pi$
$564$		0			0
$565$	−0.368025	−	8.87722i	−0.0154829	−	0.373468i
$566$	20.5938	−	17.2803i	0.865623	−	0.726344i
$567$		0			0
$568$	−0.704789	−	1.93639i	−0.0295723	−	0.0812492i
$569$	7.15701			0.300038			0.150019	−	0.988683i	$-0.452067\pi$
$569$	7.15701			0.300038			0.150019	+	0.988683i	$0.452067\pi$
$570$		0			0
$571$	−18.3153			−0.766471			−0.383236	−	0.923651i	$-0.625190\pi$
$571$	−18.3153			−0.766471			−0.383236	+	0.923651i	$0.625190\pi$
$572$	−0.157107	−	0.431647i	−0.00656896	−	0.0180481i
$573$		0			0
$574$	−11.6904	+	9.80941i	−0.487948	+	0.409437i
$575$	13.2031	+	13.3198i	0.550607	+	0.555473i
$576$		0			0
$577$	−18.6883	+	10.7897i	−0.778006	+	0.449182i	−0.835723	−	0.549151i	$-0.814951\pi$
$577$	−18.6883	+	10.7897i	−0.778006	+	0.449182i	0.0577173	+	0.998333i	$0.481618\pi$
$578$	5.81457	+	3.35704i	0.241854	+	0.139635i
$579$		0			0
$580$	−7.42184	+	3.05512i	−0.308175	+	0.126857i
$581$	6.81636	−	11.8063i	0.282790	−	0.489807i
$582$		0			0
$583$	−11.2102	+	1.97666i	−0.464278	+	0.0818648i
$584$	16.3357	+	13.7073i	0.675975	+	0.567210i
$585$		0			0
$586$	5.11301	−	28.9973i	0.211216	−	1.19787i
$587$	9.89913	+	27.1976i	0.408581	+	1.12257i	0.957937	+	0.286978i	$0.0926508\pi$
$587$	9.89913	+	27.1976i	0.408581	+	1.12257i	−0.549356	+	0.835588i	$0.685127\pi$
$588$		0			0
$589$	−16.1360	−	25.5196i	−0.664872	−	1.05152i
$590$	−15.8120	−	17.3321i	−0.650969	−	0.713553i
$591$		0			0
$592$	−5.88043	−	1.03688i	−0.241684	−	0.0426154i
$593$	11.4565	+	13.6533i	0.470461	+	0.560674i	0.948137	−	0.317863i	$-0.102965\pi$
$593$	11.4565	+	13.6533i	0.470461	+	0.560674i	−0.477676	+	0.878536i	$0.658521\pi$
$594$		0			0
$595$	23.4813	+	18.1001i	0.962640	+	0.742030i
$596$	−6.44194	−	11.1578i	−0.263872	−	0.457040i
$597$		0			0
$598$	0.820779	−	2.25507i	0.0335642	−	0.0922167i
$599$	8.03512	+	2.92455i	0.328306	+	0.119494i	0.500914	−	0.865497i	$-0.332997\pi$
$599$	8.03512	+	2.92455i	0.328306	+	0.119494i	−0.172608	+	0.984991i	$0.555219\pi$
$600$		0			0
$601$	2.09514	+	3.62889i	0.0854627	+	0.148026i	0.905588	−	0.424158i	$-0.139430\pi$
$601$	2.09514	+	3.62889i	0.0854627	+	0.148026i	−0.820126	+	0.572184i	$0.806096\pi$
$602$	−29.5621	+	5.21260i	−1.20486	+	0.212450i
$603$		0			0
$604$	1.62078	−	1.36000i	0.0659487	−	0.0553375i
$605$	−12.3397	−	19.4638i	−0.501680	−	0.791316i
$606$		0			0
$607$			7.59458i			0.308254i	0.988051	+	0.154127i	$0.0492566\pi$
$607$			7.59458i			0.308254i	−0.988051	+	0.154127i	$0.950743\pi$
$608$	19.7477	−	4.30752i	0.800876	−	0.174693i
$609$		0			0
$610$	18.8258	+	9.85279i	0.762235	+	0.398928i
$611$	−0.360654	+	2.04537i	−0.0145905	+	0.0827469i
$612$		0			0
$613$	11.5348	−	13.7466i	0.465885	−	0.555220i	−0.481030	−	0.876704i	$-0.659737\pi$
$613$	11.5348	−	13.7466i	0.465885	−	0.555220i	0.946915	+	0.321484i	$0.104182\pi$
$614$	0.468661	+	2.65791i	0.0189136	+	0.107264i
$615$		0			0
$616$	3.46964	−	6.00960i	0.139796	−	0.242134i
$617$	−13.8805	+	38.1365i	−0.558809	+	1.53532i	0.262558	+	0.964916i	$0.415434\pi$
$617$	−13.8805	+	38.1365i	−0.558809	+	1.53532i	−0.821367	+	0.570400i	$0.806788\pi$
$618$		0			0
$619$	−12.7804	+	22.1363i	−0.513688	+	0.889733i	0.486186	+	0.873855i	$0.338388\pi$
$619$	−12.7804	+	22.1363i	−0.513688	+	0.889733i	−0.999874	+	0.0158781i	$0.994946\pi$
$620$	−13.3289	−	4.23485i	−0.535303	−	0.170076i
$621$		0			0
$622$	9.85430	−	11.7439i	0.395121	−	0.470887i
$623$	10.3726	+	12.3616i	0.415570	+	0.495257i
$624$		0			0
$625$	24.6574	−	4.12440i	0.986298	−	0.164976i
$626$	1.56491			0.0625463
$627$		0			0
$628$		−	14.6049i		−	0.582801i
$629$	−19.6901	+	7.16661i	−0.785096	+	0.285751i
$630$		0			0
$631$	3.55051	−	2.97923i	0.141344	−	0.118601i	−0.569375	−	0.822078i	$-0.692815\pi$
$631$	3.55051	−	2.97923i	0.141344	−	0.118601i	0.710718	+	0.703477i	$0.248370\pi$
$632$	6.80057	−	8.10461i	0.270512	−	0.322384i
$633$		0			0
$634$	−2.95490	−	5.11804i	−0.117354	−	0.203263i
$635$	20.0611	−	4.40116i	0.796101	−	0.174655i
$636$		0			0
$637$	0.106424	−	0.292397i	0.00421666	−	0.0115852i
$638$	−3.00302	−	1.73379i	−0.118891	−	0.0686415i
$639$		0			0
$640$	1.77281	−	2.29988i	0.0700766	−	0.0909108i
$641$	−17.7783	−	14.9178i	−0.702201	−	0.589217i	0.220198	−	0.975455i	$-0.429330\pi$
$641$	−17.7783	−	14.9178i	−0.702201	−	0.589217i	−0.922399	+	0.386239i	$0.873774\pi$
$642$		0			0
$643$	−15.0138	−	2.64733i	−0.592086	−	0.104401i	−0.130426	−	0.991458i	$-0.541635\pi$
$643$	−15.0138	−	2.64733i	−0.592086	−	0.104401i	−0.461659	+	0.887057i	$0.652746\pi$
$644$	−8.72149	+	3.17436i	−0.343675	+	0.125087i
$645$		0			0
$646$	−16.3370	+	14.8682i	−0.642773	+	0.584982i
$647$		−	17.6749i		−	0.694872i	−0.937704	−	0.347436i	$-0.887052\pi$
$647$		−	17.6749i		−	0.694872i	0.937704	−	0.347436i	$-0.112948\pi$
$648$		0			0
$649$	−1.44870	+	8.21599i	−0.0568664	+	0.322506i
$650$	−1.82329	−	2.62846i	−0.0715151	−	0.103097i
$651$		0			0
$652$	−14.2506	+	2.51277i	−0.558097	+	0.0984075i
$653$	−5.94488	+	3.43228i	−0.232641	+	0.134315i	−0.611790	−	0.791020i	$-0.709550\pi$
$653$	−5.94488	+	3.43228i	−0.232641	+	0.134315i	0.379149	+	0.925336i	$0.376217\pi$
$654$		0			0
$655$	7.73135	−	3.18252i	0.302089	−	0.124351i
$656$	−6.88879	−	2.50731i	−0.268962	−	0.0978941i
$657$		0			0
$658$	−8.45175	+	4.87962i	−0.329484	+	0.190227i
$659$	4.75738	+	26.9804i	0.185321	+	1.05101i	0.925542	+	0.378645i	$0.123610\pi$
$659$	4.75738	+	26.9804i	0.185321	+	1.05101i	−0.740221	+	0.672364i	$0.765279\pi$
$660$		0			0
$661$	21.8707	−	18.3517i	0.850673	−	0.713800i	−0.109265	−	0.994013i	$-0.534850\pi$
$661$	21.8707	−	18.3517i	0.850673	−	0.713800i	0.959938	+	0.280213i	$0.0904051\pi$
$662$	32.8963	+	5.80051i	1.27855	+	0.225443i
$663$		0			0
$664$	15.1263			0.587014
$665$	−21.9646	+	15.1971i	−0.851749	+	0.589318i
$666$		0			0
$667$	5.09971	+	14.0113i	0.197462	+	0.542521i
$668$	−6.73722	−	1.18795i	−0.260671	−	0.0459633i
$669$		0			0
$670$	25.5875	−	1.06078i	0.988530	−	0.0409817i
$671$	−1.31206	−	7.44107i	−0.0506516	−	0.287259i
$672$		0			0
$673$	39.1173	+	22.5844i	1.50786	+	0.870565i	0.999958	+	0.00915115i	$0.00291294\pi$
$673$	39.1173	+	22.5844i	1.50786	+	0.870565i	0.507904	+	0.861414i	$0.330420\pi$
$674$	15.0960	+	5.49451i	0.581478	+	0.211641i
$675$		0			0
$676$	−5.70071	+	9.87392i	−0.219258	+	0.379766i
$677$	40.6710	−	23.4814i	1.56311	−	0.902463i	0.566172	−	0.824287i	$-0.308424\pi$
$677$	40.6710	−	23.4814i	1.56311	−	0.902463i	0.996940	−	0.0781759i	$-0.0249096\pi$
$678$		0			0
$679$	−26.1116	−	21.9102i	−1.00207	−	0.840838i
$680$	−4.36550	+	32.6049i	−0.167409	+	1.25034i
$681$		0			0
$682$	−2.06659	−	5.67792i	−0.0791339	−	0.217419i
$683$			19.4215i			0.743142i	0.928405	+	0.371571i	$0.121181\pi$
$683$			19.4215i			0.743142i	−0.928405	+	0.371571i	$0.878819\pi$
$684$		0			0
$685$	3.56165	+	3.90406i	0.136084	+	0.149167i
$686$	−17.5060	+	6.37166i	−0.668382	+	0.243271i
$687$		0			0
$688$	−9.26901	−	11.0464i	−0.353378	−	0.421139i
$689$	−6.39554	−	5.36650i	−0.243651	−	0.204447i
$690$		0			0
$691$	8.93344	+	15.4732i	0.339844	+	0.588627i	0.984403	−	0.175927i	$-0.0562923\pi$
$691$	8.93344	+	15.4732i	0.339844	+	0.588627i	−0.644559	+	0.764555i	$0.722959\pi$
$692$	6.92991	+	4.00099i	0.263436	+	0.152095i
$693$		0			0
$694$	0.0813941	+	0.0296250i	0.00308968	+	0.00112455i
$695$	1.17051	+	5.33536i	0.0444001	+	0.202382i
$696$		0			0
$697$	−25.3346	+	4.46716i	−0.959615	+	0.169206i
$698$	−3.12615	+	3.72561i	−0.118327	+	0.141016i
$699$		0			0
$700$	−3.25462	+	11.9361i	−0.123013	+	0.451143i
$701$	4.04522	−	1.47234i	0.152786	−	0.0556096i	−0.264495	−	0.964387i	$-0.585205\pi$
$701$	4.04522	−	1.47234i	0.152786	−	0.0556096i	0.417281	+	0.908777i	$0.362983\pi$
$702$		0			0
$703$	−0.759235	−	18.8619i	−0.0286351	−	0.711389i
$704$	6.34150			0.239004
$705$		0			0
$706$	−0.726431	+	4.11979i	−0.0273396	+	0.155050i
$707$	−31.2432	−	37.2343i	−1.17502	−	1.40034i
$708$		0			0
$709$	−6.10059	−	34.5982i	−0.229112	−	1.29936i	−0.854665	−	0.519179i	$-0.826238\pi$
$709$	−6.10059	−	34.5982i	−0.229112	−	1.29936i	0.625553	−	0.780182i	$-0.284873\pi$
$710$	−0.480633	+	1.51276i	−0.0180378	+	0.0567729i
$711$		0			0
$712$	−6.12382	+	16.8251i	−0.229500	+	0.630545i
$713$	−8.88632	+	24.4150i	−0.332795	+	0.914347i
$714$		0			0
$715$	−0.344450	+	1.08413i	−0.0128817	+	0.0405443i
$716$	0.856958	+	4.86005i	0.0320260	+	0.181629i
$717$		0			0
$718$	20.3457	+	24.2471i	0.759295	+	0.904893i
$719$	5.10577	−	28.9563i	0.190413	−	1.07989i	−0.728388	−	0.685165i	$-0.759730\pi$
$719$	5.10577	−	28.9563i	0.190413	−	1.07989i	0.918801	−	0.394722i	$-0.129159\pi$
$720$		0			0
$721$	14.3004			0.532574
$722$	−8.28745	−	18.0929i	−0.308427	−	0.673349i
$723$		0			0
$724$	−15.9656	+	5.81100i	−0.593357	+	0.215964i
$725$	19.1757	+	5.22865i	0.712168	+	0.194187i
$726$		0			0
$727$	−14.4993	+	17.2796i	−0.537749	+	0.640864i	−0.964681	−	0.263419i	$-0.915150\pi$
$727$	−14.4993	+	17.2796i	−0.537749	+	0.640864i	0.426933	+	0.904283i	$0.359594\pi$
$728$	5.01220	−	0.883786i	0.185765	−	0.0327553i
$729$		0			0
$730$	−3.51993	−	16.0443i	−0.130278	−	0.593827i
$731$	−47.5506	−	17.3070i	−1.75872	−	0.640123i
$732$		0			0
$733$	32.8225	+	18.9501i	1.21233	+	0.699938i	0.963266	−	0.268550i	$-0.0865443\pi$
$733$	32.8225	+	18.9501i	1.21233	+	0.699938i	0.249062	+	0.968488i	$0.419878\pi$
$734$	9.49990	+	16.4543i	0.350648	+	0.607340i
$735$		0			0
$736$	−13.3238	−	11.1800i	−0.491121	−	0.412099i
$737$	−5.85367	−	6.97613i	−0.215623	−	0.256969i
$738$		0			0
$739$	−24.4523	+	8.89989i	−0.899491	+	0.327388i	−0.750049	−	0.661383i	$-0.769970\pi$
$739$	−24.4523	+	8.89989i	−0.899491	+	0.327388i	−0.149442	+	0.988770i	$0.547748\pi$
$740$	−5.89312	−	6.45968i	−0.216635	−	0.237463i
$741$		0			0
$742$		−	39.2300i		−	1.44018i
$743$	−17.2335	−	47.3487i	−0.632237	−	1.73706i	−0.674841	−	0.737964i	$-0.735788\pi$
$743$	−17.2335	−	47.3487i	−0.632237	−	1.73706i	0.0426041	−	0.999092i	$-0.486435\pi$
$744$		0			0
$745$	−4.23411	+	31.6235i	−0.155126	+	1.15860i
$746$	−20.2315	−	16.9762i	−0.740728	−	0.621544i
$747$		0			0
$748$	3.15105	−	1.81926i	0.115214	−	0.0665187i
$749$	−20.8089	+	36.0420i	−0.760339	+	1.31695i
$750$		0			0
$751$	−25.5462	−	9.29806i	−0.932195	−	0.339291i	−0.169116	−	0.985596i	$-0.554091\pi$
$751$	−25.5462	−	9.29806i	−0.932195	−	0.339291i	−0.763079	+	0.646305i	$0.776313\pi$
$752$	−4.06002	−	2.34405i	−0.148054	−	0.0854789i
$753$		0			0
$754$	−0.441631	−	2.50461i	−0.0160832	−	0.0912126i
$755$	−5.23504	+	0.217030i	−0.190523	+	0.00789854i
$756$		0			0
$757$	32.3985	+	5.71273i	1.17754	+	0.207633i	0.727969	−	0.685610i	$-0.240464\pi$
$757$	32.3985	+	5.71273i	1.17754	+	0.207633i	0.449575	+	0.893243i	$0.351576\pi$
$758$	−9.87411	−	27.1289i	−0.358644	−	0.985366i
$759$		0			0
$760$	−26.7884	−	12.6748i	−0.971719	−	0.459765i
$761$	−3.47213			−0.125865			−0.0629323	−	0.998018i	$-0.520045\pi$
$761$	−3.47213			−0.125865			−0.0629323	+	0.998018i	$0.520045\pi$
$762$		0			0
$763$	10.5858	+	1.86657i	0.383233	+	0.0675743i
$764$	11.9391	−	10.0181i	0.431941	−	0.362442i
$765$		0			0
$766$	−3.33270	−	18.9007i	−0.120415	−	0.682910i
$767$	−5.29909	+	3.05943i	−0.191339	+	0.110470i
$768$		0			0
$769$	−29.7634	−	10.8330i	−1.07330	−	0.390648i	−0.255887	−	0.966707i	$-0.582368\pi$
$769$	−29.7634	−	10.8330i	−1.07330	−	0.390648i	−0.817408	+	0.576059i	$0.804590\pi$
$770$	−4.94277	+	2.03464i	−0.178125	+	0.0733232i
$771$		0			0
$772$	−5.84466	+	3.37442i	−0.210354	+	0.121448i
$773$	34.5358	−	6.08960i	1.24217	−	0.219028i	0.486323	−	0.873779i	$-0.338338\pi$
$773$	34.5358	−	6.08960i	1.24217	−	0.219028i	0.755844	+	0.654752i	$0.227227\pi$
$774$		0			0
$775$	19.7401	+	28.4575i	0.709087	+	1.02222i
$776$	6.56750	−	37.2461i	0.235759	−	1.33706i
$777$		0			0
$778$		−	7.52562i		−	0.269807i
$779$	3.10322	−	22.9672i	0.111184	−	0.822884i
$780$		0			0
$781$	0.530395	−	0.193048i	0.0189790	−	0.00690780i
$782$	18.7201	+	3.30085i	0.669428	+	0.118038i
$783$		0			0
$784$	0.538043	+	0.451472i	0.0192158	+	0.0161240i
$785$	−22.0806	+	28.6454i	−0.788092	+	1.02240i
$786$		0			0
$787$	−36.5314	−	21.0914i	−1.30221	−	0.751829i	−0.321424	−	0.946936i	$-0.604161\pi$
$787$	−36.5314	−	21.0914i	−1.30221	−	0.751829i	−0.980782	+	0.195107i	$0.937495\pi$
$788$	−3.77015	+	10.3584i	−0.134306	+	0.369003i
$789$		0			0
$790$	−7.96005	+	1.74634i	−0.283206	+	0.0621320i
$791$	−5.44425	−	9.42971i	−0.193575	−	0.335282i
$792$		0			0
$793$	3.56216	−	4.24522i	0.126496	−	0.150752i
$794$	9.40703	−	7.89343i	0.333843	−	0.280127i
$795$		0			0
$796$	−6.58251	+	2.39584i	−0.233311	+	0.0849182i
$797$			20.4194i			0.723291i	0.932316	+	0.361646i	$0.117785\pi$
$797$			20.4194i			0.723291i	−0.932316	+	0.361646i	$0.882215\pi$
$798$		0			0
$799$	−16.4514			−0.582008
$800$	−22.4210	+	5.90209i	−0.792702	+	0.208670i
$801$		0			0
$802$	−26.4000	−	31.4623i	−0.932216	−	1.11097i
$803$	−3.75454	+	4.47449i	−0.132495	+	0.157901i
$804$		0			0
$805$	21.9051	+	6.95965i	0.772052	+	0.245296i
$806$	2.21582	−	3.83792i	0.0780491	−	0.135185i
$807$		0			0
$808$	18.4455	−	50.6786i	0.648910	−	1.78287i
$809$	−14.2768	+	24.7282i	−0.501946	+	0.869396i	0.498051	+	0.867148i	$0.334049\pi$
$809$	−14.2768	+	24.7282i	−0.501946	+	0.869396i	−0.999997	+	0.00224865i	$0.999284\pi$
$810$		0			0
$811$	−0.279849	−	1.58710i	−0.00982681	−	0.0557306i	0.979500	−	0.201444i	$-0.0645634\pi$
$811$	−0.279849	−	1.58710i	−0.00982681	−	0.0557306i	−0.989327	+	0.145713i	$0.953452\pi$
$812$	−6.32248	+	7.53483i	−0.221875	+	0.264421i
$813$		0			0
$814$	0.655998	−	3.72035i	0.0229927	−	0.130398i
$815$	31.7493	+	16.6165i	1.11213	+	0.582051i
$816$		0			0
$817$	27.8747	−	36.0723i	0.975213	−	1.26201i
$818$		−	9.29706i		−	0.325064i
$819$		0			0
$820$	−5.74804	−	9.06657i	−0.200730	−	0.316618i
$821$	6.16578	−	5.17371i	0.215187	−	0.180564i	−0.528822	−	0.848733i	$-0.677366\pi$
$821$	6.16578	−	5.17371i	0.215187	−	0.180564i	0.744010	+	0.668169i	$0.232922\pi$
$822$		0			0
$823$	−36.7750	+	6.48442i	−1.28189	+	0.226033i	−0.772784	−	0.634669i	$-0.781137\pi$
$823$	−36.7750	+	6.48442i	−1.28189	+	0.226033i	−0.509110	+	0.860701i	$0.670025\pi$
$824$	7.93356	+	13.7413i	0.276379	+	0.478702i
$825$		0			0
$826$	−27.0179	−	9.83370i	−0.940072	−	0.342158i
$827$	3.73836	−	10.2711i	0.129996	−	0.357160i	−0.857570	−	0.514367i	$-0.828027\pi$
$827$	3.73836	−	10.2711i	0.129996	−	0.357160i	0.987566	+	0.157207i	$0.0502491\pi$
$828$		0			0
$829$	16.8187	+	29.1309i	0.584139	+	1.01176i	0.994982	+	0.100052i	$0.0319010\pi$
$829$	16.8187	+	29.1309i	0.584139	+	1.01176i	−0.410843	+	0.911706i	$0.634766\pi$
$830$	−9.22806	−	7.11324i	−0.320311	−	0.246904i
$831$		0			0
$832$	2.98966	+	3.56293i	0.103648	+	0.123523i
$833$	2.42728	+	0.427995i	0.0841002	+	0.0148291i
$834$		0			0
$835$	11.4180	+	12.5157i	0.395136	+	0.433124i
$836$	0.698579	+	3.20262i	0.0241609	+	0.110765i
$837$		0			0
$838$	2.79492	+	7.67897i	0.0965488	+	0.265266i
$839$	2.40910	−	13.6627i	0.0831714	−	0.471689i	−0.914565	−	0.404439i	$-0.867467\pi$
$839$	2.40910	−	13.6627i	0.0831714	−	0.471689i	0.997736	−	0.0672492i	$-0.0214222\pi$
$840$		0			0
$841$	−10.1104	−	8.48360i	−0.348633	−	0.292538i
$842$	−35.6452	+	6.28522i	−1.22842	+	0.216603i
$843$		0			0
$844$	−4.54052	+	7.86440i	−0.156291	+	0.270704i
$845$	26.1090	−	10.7475i	0.898179	−	0.369725i
$846$		0			0
$847$	−24.4591	−	14.1214i	−0.840423	−	0.485219i
$848$	16.3204	−	9.42259i	0.560445	−	0.323573i
$849$		0			0
$850$	17.9959	−	17.8383i	0.617255	−	0.611847i
$851$	−12.4438	+	10.4416i	−0.426568	+	0.357933i
$852$		0			0
$853$	−10.1059	−	27.7657i	−0.346019	−	0.950680i	−0.983611	−	0.180305i	$-0.942291\pi$
$853$	−10.1059	−	27.7657i	−0.346019	−	0.950680i	0.637591	−	0.770375i	$-0.279931\pi$
$854$	26.0400			0.891071
$855$		0			0
$856$	−46.1773			−1.57831
$857$	1.46586	+	4.02741i	0.0500727	+	0.137574i	0.962208	−	0.272316i	$-0.0877895\pi$
$857$	1.46586	+	4.02741i	0.0500727	+	0.137574i	−0.912135	+	0.409889i	$0.865567\pi$
$858$		0			0
$859$	26.7935	−	22.4824i	0.914181	−	0.767089i	−0.0587290	−	0.998274i	$-0.518705\pi$
$859$	26.7935	−	22.4824i	0.914181	−	0.767089i	0.972910	+	0.231185i	$0.0742603\pi$
$860$	−0.874666	−	21.0981i	−0.0298259	−	0.719438i
$861$		0			0
$862$	−2.57566	+	1.48706i	−0.0877273	+	0.0506494i
$863$	−17.3470	−	10.0153i	−0.590498	−	0.340924i	0.174797	−	0.984605i	$-0.444073\pi$
$863$	−17.3470	−	10.0153i	−0.590498	−	0.340924i	−0.765294	+	0.643681i	$0.777407\pi$
$864$		0			0
$865$	−7.54302	−	18.3244i	−0.256470	−	0.623047i
$866$	11.4443	−	19.8221i	0.388893	−	0.673583i
$867$		0			0
$868$	−16.8790	+	2.97623i	−0.572911	+	0.101020i
$869$	2.21992	+	1.86274i	0.0753058	+	0.0631891i
$870$		0			0
$871$	1.15983	−	6.57770i	0.0392992	−	0.222877i
$872$	4.07921	+	11.2075i	0.138139	+	0.379535i
$873$		0			0
$874$	−7.95907	+	15.1630i	−0.269220	+	0.512898i
$875$	24.4292	−	18.4903i	0.825857	−	0.625087i
$876$		0			0
$877$	44.8994	+	7.91697i	1.51614	+	0.267337i	0.868916	−	0.494959i	$-0.164817\pi$
$877$	44.8994	+	7.91697i	1.51614	+	0.267337i	0.647228	+	0.762297i	$0.275928\pi$
$878$	−21.9320	−	26.1376i	−0.740170	−	0.882100i
$879$		0			0
$880$	−2.03364	−	1.56759i	−0.0685540	−	0.0528433i
$881$	−8.63649	−	14.9588i	−0.290971	−	0.503976i	0.683069	−	0.730354i	$-0.260645\pi$
$881$	−8.63649	−	14.9588i	−0.290971	−	0.503976i	−0.974040	+	0.226378i	$0.927312\pi$
$882$		0			0
$883$	12.0368	−	33.0707i	0.405069	−	1.11292i	−0.554680	−	0.832063i	$-0.687160\pi$
$883$	12.0368	−	33.0707i	0.405069	−	1.11292i	0.959750	−	0.280856i	$-0.0906183\pi$
$884$	2.50768	+	0.912722i	0.0843425	+	0.0306982i
$885$		0			0
$886$	4.06483	+	7.04049i	0.136561	+	0.236530i
$887$	3.11307	−	0.548919i	0.104527	−	0.0184309i	−0.121140	−	0.992635i	$-0.538655\pi$
$887$	3.11307	−	0.548919i	0.104527	−	0.0184309i	0.225667	+	0.974205i	$0.427544\pi$
$888$		0			0
$889$	19.2812	−	16.1789i	0.646671	−	0.542622i
$890$	11.6480	−	7.38465i	0.390443	−	0.247534i
$891$		0			0
$892$		−	25.5727i		−	0.856237i
$893$	4.50482	−	14.1198i	0.150748	−	0.472500i
$894$		0			0
$895$	5.66693	−	10.8278i	0.189424	−	0.361935i
$896$	0.617962	−	3.50464i	0.0206447	−	0.117082i
$897$		0			0
$898$	−15.4729	+	18.4399i	−0.516337	+	0.615346i
$899$	4.78140	+	27.1167i	0.159469	+	0.904391i
$900$		0			0
$901$	33.0655	−	57.2711i	1.10157	−	1.90798i
$902$	1.58629	−	4.35830i	0.0528178	−	0.145116i
$903$		0			0
$904$	6.04071	−	10.4628i	0.200911	−	0.347988i
$905$	40.0995	+	12.7404i	1.33295	+	0.423504i
$906$		0			0
$907$	10.2405	−	12.2041i	0.340029	−	0.405230i	−0.568749	−	0.822511i	$-0.692572\pi$
$907$	10.2405	−	12.2041i	0.340029	−	0.405230i	0.908778	+	0.417281i	$0.137017\pi$
$908$	9.21597	+	10.9832i	0.305843	+	0.364489i
$909$		0			0
$910$	−3.47339	−	1.81785i	−0.115142	−	0.0602612i
$911$	−0.0577380			−0.00191294			−0.000956472	−	1.00000i	$-0.500304\pi$
$911$	−0.0577380			−0.00191294			−0.000956472		1.00000i	$0.500304\pi$
$912$		0			0
$913$			4.14323i			0.137121i
$914$	3.33524	−	1.21393i	0.110320	−	0.0401532i
$915$		0			0
$916$	−7.87599	+	6.60874i	−0.260230	+	0.218359i
$917$	6.58614	−	7.84905i	0.217493	−	0.259199i
$918$		0			0
$919$	25.0245	+	43.3436i	0.825481	+	1.42977i	0.901551	+	0.432672i	$0.142429\pi$
$919$	25.0245	+	43.3436i	0.825481	+	1.42977i	−0.0760708	+	0.997102i	$0.524238\pi$
$920$	5.46490	+	24.9098i	0.180172	+	0.821251i
$921$		0			0
$922$	3.88787	−	10.6818i	0.128040	−	0.351788i
$923$	0.358514	+	0.206988i	0.0118006	+	0.00681310i
$924$		0			0
$925$	1.79231	+	21.5793i	0.0589308	+	0.709521i
$926$	5.86660	+	4.92267i	0.192789	+	0.161769i
$927$		0			0
$928$	−18.1526	−	3.20080i	−0.595889	−	0.105071i
$929$	15.9606	−	5.80920i	0.523652	−	0.190594i	−0.0666498	−	0.997776i	$-0.521231\pi$
$929$	15.9606	−	5.80920i	0.523652	−	0.190594i	0.590302	+	0.807183i	$0.299009\pi$
$930$		0			0
$931$	−1.03199	+	1.96607i	−0.0338220	+	0.0644353i
$932$		−	14.3246i		−	0.469218i
$933$		0			0
$934$	−1.97190	+	11.1832i	−0.0645227	+	0.365926i
$935$	−8.93077	−	1.19575i	−0.292067	−	0.0391052i
$936$		0			0
$937$	33.1807	−	5.85065i	1.08397	−	0.191132i	0.396997	−	0.917820i	$-0.370052\pi$
$937$	33.1807	−	5.85065i	1.08397	−	0.191132i	0.686968	+	0.726687i	$0.258941\pi$
$938$	27.1799	−	15.6923i	0.887456	−	0.512373i
$939$		0			0
$940$	−2.61320	−	6.34830i	−0.0852333	−	0.207059i
$941$	−25.5345	−	9.29380i	−0.832401	−	0.302969i	−0.109557	−	0.993980i	$-0.534943\pi$
$941$	−25.5345	−	9.29380i	−0.832401	−	0.302969i	−0.722844	+	0.691011i	$0.757166\pi$
$942$		0			0
$943$	−17.2715	+	9.97169i	−0.562436	+	0.324723i
$944$	−2.39838	−	13.6019i	−0.0780605	−	0.442703i
$945$		0			0
$946$	6.98867	−	5.86419i	0.227221	−	0.190661i
$947$	32.7904	+	5.78183i	1.06554	+	0.187884i	0.678815	−	0.734309i	$-0.262494\pi$
$947$	32.7904	+	5.78183i	1.06554	+	0.187884i	0.386729	+	0.922193i	$0.373605\pi$
$948$		0			0
$949$	−4.28402			−0.139065
$950$	10.3823	+	20.3300i	0.336847	+	0.659591i
$951$		0			0
$952$	13.7883	+	37.8830i	0.446881	+	1.22780i
$953$	−29.9466	−	5.28039i	−0.970065	−	0.171049i	−0.333906	−	0.942606i	$-0.608367\pi$
$953$	−29.9466	−	5.28039i	−0.970065	−	0.171049i	−0.636159	+	0.771558i	$0.719478\pi$
$954$		0			0
$955$	−38.5627	+	1.59870i	−1.24786	+	0.0517327i
$956$	3.27151	+	18.5536i	0.105808	+	0.600068i
$957$		0			0
$958$	−3.12704	−	1.80540i	−0.101030	−	0.0583297i
$959$	6.08578	+	2.21504i	0.196520	+	0.0715274i
$960$		0			0
$961$	−8.49003	+	14.7052i	−0.273872	+	0.474360i
$962$	2.39952	−	1.38536i	0.0773637	−	0.0446660i
$963$		0			0
$964$	19.6643	+	16.5003i	0.633344	+	0.531438i
$965$	16.5651	+	2.21791i	0.533248	+	0.0713971i
$966$		0			0
$967$	20.1511	+	55.3648i	0.648017	+	1.78041i	0.624934	+	0.780677i	$0.285126\pi$
$967$	20.1511	+	55.3648i	0.648017	+	1.78041i	0.0230823	+	0.999734i	$0.492652\pi$
$968$		−	31.3371i		−	1.00721i
$969$		0			0
$970$	−21.5219	+	19.6342i	−0.691025	+	0.630417i
$971$	−38.4033	+	13.9777i	−1.23242	+	0.448564i	−0.874426	−	0.485159i	$-0.838762\pi$
$971$	−38.4033	+	13.9777i	−1.23242	+	0.448564i	−0.357995	+	0.933724i	$0.616539\pi$
$972$		0			0
$973$	4.30285	+	5.12794i	0.137943	+	0.164394i
$974$	−21.6614	−	18.1761i	−0.694075	−	0.582398i
$975$		0			0
$976$	6.25450	+	10.8331i	0.200202	+	0.346760i
$977$	−31.1276	−	17.9716i	−0.995862	−	0.574961i	−0.0888405	−	0.996046i	$-0.528316\pi$
$977$	−31.1276	−	17.9716i	−0.995862	−	0.574961i	−0.907021	+	0.421085i	$0.861649\pi$
$978$		0			0
$979$	−4.60853	−	1.67737i	−0.147289	−	0.0536089i
$980$	0.220403	+	1.00463i	0.00704052	+	0.0320917i
$981$		0			0
$982$	0.251662	−	0.0443747i	0.00803085	−	0.00141606i
$983$	6.47067	−	7.71144i	0.206382	−	0.245957i	−0.652918	−	0.757429i	$-0.726455\pi$
$983$	6.47067	−	7.71144i	0.206382	−	0.245957i	0.859300	+	0.511472i	$0.170900\pi$
$984$		0			0
$985$	23.0550	−	14.6165i	0.734595	−	0.465720i
$986$	18.9303	−	6.89005i	0.602862	−	0.219424i
$987$		0			0
$988$	−1.47003	+	1.90235i	−0.0467680	+	0.0605217i
$989$	−39.2290			−1.24741
$990$		0			0
$991$	−3.13089	+	17.7562i	−0.0994561	+	0.564043i	0.893834	+	0.448397i	$0.148005\pi$
$991$	−3.13089	+	17.7562i	−0.0994561	+	0.564043i	−0.993290	+	0.115646i	$0.963106\pi$
$992$	−20.6458	−	24.6047i	−0.655504	−	0.781200i
$993$		0			0
$994$	0.337786	+	1.91568i	0.0107139	+	0.0607616i
$995$	16.5328	+	5.25277i	0.524124	+	0.166524i
$996$		0			0
$997$	6.40419	−	17.5954i	0.202823	−	0.557251i	−0.796024	−	0.605265i	$-0.793067\pi$
$997$	6.40419	−	17.5954i	0.202823	−	0.557251i	0.998847	+	0.0480143i	$0.0152893\pi$
$998$	1.16378	−	3.19747i	0.0368390	−	0.101214i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.da.b.784.3		48
3.2	odd	2		95.2.p.a.24.6	yes	48
5.4	even	2	inner	855.2.da.b.784.6		48
15.2	even	4		475.2.l.f.176.3		48
15.8	even	4		475.2.l.f.176.6		48
15.14	odd	2		95.2.p.a.24.3	yes	48
19.4	even	9	inner	855.2.da.b.289.6		48
57.2	even	18		1805.2.b.l.1084.16		24
57.17	odd	18		1805.2.b.k.1084.9		24
57.23	odd	18		95.2.p.a.4.3	✓	48
95.4	even	18	inner	855.2.da.b.289.3		48
285.2	odd	36		9025.2.a.ct.1.9		24
285.17	even	36		9025.2.a.cu.1.16		24
285.23	even	36		475.2.l.f.251.6		48
285.59	even	18		1805.2.b.l.1084.9		24
285.74	odd	18		1805.2.b.k.1084.16		24
285.137	even	36		475.2.l.f.251.3		48
285.173	odd	36		9025.2.a.ct.1.16		24
285.188	even	36		9025.2.a.cu.1.9		24
285.194	odd	18		95.2.p.a.4.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.3	✓	48	57.23	odd	18
95.2.p.a.4.6	yes	48	285.194	odd	18
95.2.p.a.24.3	yes	48	15.14	odd	2
95.2.p.a.24.6	yes	48	3.2	odd	2
475.2.l.f.176.3		48	15.2	even	4
475.2.l.f.176.6		48	15.8	even	4
475.2.l.f.251.3		48	285.137	even	36
475.2.l.f.251.6		48	285.23	even	36
855.2.da.b.289.3		48	95.4	even	18	inner
855.2.da.b.289.6		48	19.4	even	9	inner
855.2.da.b.784.3		48	1.1	even	1	trivial
855.2.da.b.784.6		48	5.4	even	2	inner
1805.2.b.k.1084.9		24	57.17	odd	18
1805.2.b.k.1084.16		24	285.74	odd	18
1805.2.b.l.1084.9		24	285.59	even	18
1805.2.b.l.1084.16		24	57.2	even	18
9025.2.a.ct.1.9		24	285.2	odd	36
9025.2.a.ct.1.16		24	285.173	odd	36
9025.2.a.cu.1.9		24	285.188	even	36
9025.2.a.cu.1.16		24	285.17	even	36

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.da (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.358233 - 0.984236i) q^{2} +(0.691698 - 0.580404i) q^{4} +(-2.23415 + 0.0926215i) q^{5} +(-2.37320 + 1.37016i) q^{7} +(-2.63320 - 1.52028i) q^{8} +O(q^{10})\)	\(q+(-0.358233 - 0.984236i) q^{2} +(0.691698 - 0.580404i) q^{4} +(-2.23415 + 0.0926215i) q^{5} +(-2.37320 + 1.37016i) q^{7} +(-2.63320 - 1.52028i) q^{8} +(0.891507 + 2.16575i) q^{10} +(0.416418 - 0.721257i) q^{11} +(0.601551 - 0.106070i) q^{13} +(2.19872 + 1.84495i) q^{14} +(-0.239424 + 1.35784i) q^{16} +(1.65483 + 4.54662i) q^{17} +(-4.35537 + 0.175314i) q^{19} +(-1.49160 + 1.36077i) q^{20} +(-0.859062 - 0.151476i) q^{22} +(2.41106 + 2.87338i) q^{23} +(4.98284 - 0.413861i) q^{25} +(-0.319893 - 0.554071i) q^{26} +(-0.846286 + 2.32515i) q^{28} +(3.73543 + 1.35958i) q^{29} +(3.46338 + 5.99875i) q^{31} +(-4.56652 + 0.805200i) q^{32} +(3.88213 - 3.25750i) q^{34} +(5.17516 - 3.28096i) q^{35} +4.33071i q^{37} +(1.73279 + 4.22391i) q^{38} +(6.02377 + 3.15264i) q^{40} +(-0.923271 + 5.23613i) q^{41} +(-6.72257 + 8.01164i) q^{43} +(-0.130585 - 0.740582i) q^{44} +(1.96437 - 3.40239i) q^{46} +(-1.16292 + 3.19511i) q^{47} +(0.254704 - 0.441160i) q^{49} +(-2.19235 - 4.75604i) q^{50} +(0.354529 - 0.422511i) q^{52} +(-8.78556 - 10.4702i) q^{53} +(-0.863535 + 1.64996i) q^{55} +8.33212 q^{56} -4.16359i q^{58} +(-9.41315 + 3.42610i) q^{59} +(6.94990 - 5.83166i) q^{61} +(4.66350 - 5.55774i) q^{62} +(3.80717 + 6.59422i) q^{64} +(-1.33413 + 0.292692i) q^{65} +(3.73984 - 10.2751i) q^{67} +(3.78352 + 2.18442i) q^{68} +(-5.08316 - 3.91824i) q^{70} +(0.519169 + 0.435634i) q^{71} +(-6.90688 - 1.21787i) q^{73} +(4.26244 - 1.55140i) q^{74} +(-2.91085 + 2.64914i) q^{76} +2.28224i q^{77} +(-0.604220 + 3.42670i) q^{79} +(0.409144 - 3.05580i) q^{80} +(5.48434 - 0.967036i) q^{82} +(-4.30834 + 2.48742i) q^{83} +(-4.11826 - 10.0046i) q^{85} +(10.2936 + 3.74656i) q^{86} +(-2.19302 + 1.26614i) q^{88} +(-1.02256 - 5.79921i) q^{89} +(-1.28227 + 1.07595i) q^{91} +(3.33544 + 0.588129i) q^{92} +3.56134 q^{94} +(9.71431 - 0.795079i) q^{95} +(4.25430 + 11.6886i) q^{97} +(-0.525449 - 0.0926508i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) \) 48 * q - 18 * q^4 + 6 * q^5	\( 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49} + 18 q^{50} - 36 q^{56} + 36 q^{59} + 48 q^{61} + 18 q^{65} - 123 q^{70} + 24 q^{71} - 84 q^{74} + 66 q^{76} + 48 q^{79} + 39 q^{80} - 84 q^{85} + 42 q^{86} + 12 q^{89} - 30 q^{91} - 72 q^{94} + 63 q^{95}+O(q^{100}) \) 48 * q - 18 * q^4 + 6 * q^5 - 15 * q^10 + 12 * q^11 - 6 * q^14 - 42 * q^16 + 12 * q^19 - 42 * q^20 + 12 * q^25 - 12 * q^26 - 42 * q^31 - 36 * q^34 - 6 * q^35 + 66 * q^40 - 6 * q^41 + 6 * q^44 - 6 * q^46 + 12 * q^49 + 18 * q^50 - 36 * q^56 + 36 * q^59 + 48 * q^61 + 18 * q^65 - 123 * q^70 + 24 * q^71 - 84 * q^74 + 66 * q^76 + 48 * q^79 + 39 * q^80 - 84 * q^85 + 42 * q^86 + 12 * q^89 - 30 * q^91 - 72 * q^94 + 63 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more