LMFDB - Embedded newform 1638.2.p.i.919.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(919,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, 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("1638.919");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.p (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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			919.2
Root			$-1.38232 + 0.298668i$ of defining polynomial
Character	$\chi$	$=$	1638.919
Dual form			1638.2.p.i.991.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.14553 + 1.98411i) q^{5} +(-1.12588 + 2.39424i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.14553 + 1.98411i) q^{5} +(-1.12588 + 2.39424i) q^{7} -1.00000 q^{8} -2.29105 q^{10} -0.878558 q^{11} +(-0.786978 - 3.51862i) q^{13} +(-2.63641 + 0.222079i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.20391 + 5.54934i) q^{17} +1.50820 q^{19} +(-1.14553 - 1.98411i) q^{20} +(-0.439279 - 0.760853i) q^{22} +(0.658760 + 1.14101i) q^{23} +(-0.124459 - 0.215569i) q^{25} +(2.65372 - 2.44085i) q^{26} +(-1.51053 - 2.17216i) q^{28} +(0.669294 - 1.15925i) q^{29} +(-1.94748 - 3.37313i) q^{31} +(0.500000 - 0.866025i) q^{32} -6.40782 q^{34} +(-3.46071 - 4.97654i) q^{35} +(-4.69338 - 8.12917i) q^{37} +(0.754098 + 1.30614i) q^{38} +(1.14553 - 1.98411i) q^{40} +(-1.80195 + 3.12107i) q^{41} +(-4.95801 - 8.58752i) q^{43} +(0.439279 - 0.760853i) q^{44} +(-0.658760 + 1.14101i) q^{46} +(0.188939 - 0.327251i) q^{47} +(-4.46478 - 5.39126i) q^{49} +(0.124459 - 0.215569i) q^{50} +(3.44070 + 1.07777i) q^{52} +(1.22356 + 2.11926i) q^{53} +(1.00641 - 1.74315i) q^{55} +(1.12588 - 2.39424i) q^{56} +1.33859 q^{58} +(-2.98411 + 5.16864i) q^{59} +4.81564 q^{61} +(1.94748 - 3.37313i) q^{62} +1.00000 q^{64} +(7.88282 + 2.46922i) q^{65} +9.75996 q^{67} +(-3.20391 - 5.54934i) q^{68} +(2.57945 - 5.48533i) q^{70} +(-1.02408 - 1.77376i) q^{71} +(0.432504 + 0.749119i) q^{73} +(4.69338 - 8.12917i) q^{74} +(-0.754098 + 1.30614i) q^{76} +(0.989151 - 2.10348i) q^{77} +(-4.18014 + 7.24022i) q^{79} +2.29105 q^{80} -3.60390 q^{82} -8.66710 q^{83} +(-7.34033 - 12.7138i) q^{85} +(4.95801 - 8.58752i) q^{86} +0.878558 q^{88} +(-6.41693 - 11.1145i) q^{89} +(9.31046 + 2.07733i) q^{91} -1.31752 q^{92} +0.377877 q^{94} +(-1.72768 + 2.99243i) q^{95} +(4.40338 + 7.62688i) q^{97} +(2.43658 - 6.56225i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8	$ 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8} - 4 q^{10} - 12 q^{11} - 11 q^{13} + 3 q^{14} - 4 q^{16} - 4 q^{17} - 12 q^{19} - 2 q^{20} - 6 q^{22} + 10 q^{23} - 18 q^{25} - 10 q^{26} - 2 q^{29} + 6 q^{31} + 4 q^{32} - 8 q^{34} - 18 q^{35} - 28 q^{37} - 6 q^{38} + 2 q^{40} - 6 q^{43} + 6 q^{44} - 10 q^{46} - q^{47} - 7 q^{49} + 18 q^{50} + q^{52} - 7 q^{53} + q^{55} - 3 q^{56} - 4 q^{58} - 2 q^{59} - 48 q^{61} - 6 q^{62} + 8 q^{64} - 19 q^{65} + 30 q^{67} - 4 q^{68} - 18 q^{70} - 6 q^{71} + q^{73} + 28 q^{74} + 6 q^{76} + 22 q^{77} - 12 q^{79} + 4 q^{80} + 32 q^{83} - 13 q^{85} + 6 q^{86} + 12 q^{88} - 25 q^{89} + 34 q^{91} - 20 q^{92} - 2 q^{94} + 8 q^{95} - q^{97} - 2 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8 - 4 * q^10 - 12 * q^11 - 11 * q^13 + 3 * q^14 - 4 * q^16 - 4 * q^17 - 12 * q^19 - 2 * q^20 - 6 * q^22 + 10 * q^23 - 18 * q^25 - 10 * q^26 - 2 * q^29 + 6 * q^31 + 4 * q^32 - 8 * q^34 - 18 * q^35 - 28 * q^37 - 6 * q^38 + 2 * q^40 - 6 * q^43 + 6 * q^44 - 10 * q^46 - q^47 - 7 * q^49 + 18 * q^50 + q^52 - 7 * q^53 + q^55 - 3 * q^56 - 4 * q^58 - 2 * q^59 - 48 * q^61 - 6 * q^62 + 8 * q^64 - 19 * q^65 + 30 * q^67 - 4 * q^68 - 18 * q^70 - 6 * q^71 + q^73 + 28 * q^74 + 6 * q^76 + 22 * q^77 - 12 * q^79 + 4 * q^80 + 32 * q^83 - 13 * q^85 + 6 * q^86 + 12 * q^88 - 25 * q^89 + 34 * q^91 - 20 * q^92 - 2 * q^94 + 8 * q^95 - q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.14553	+	1.98411i	−0.512295	+	0.887321i	0.487604	+	0.873065i	$0.337871\pi$
$5$	−1.14553	+	1.98411i	−0.512295	+	0.887321i	−0.999898	+	0.0142554i	$0.995462\pi$
$6$		0			0
$7$	−1.12588	+	2.39424i	−0.425543	+	0.904938i
$7$	−1.12588	+	2.39424i	−0.425543	+	0.904938i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−2.29105			−0.724494
$11$	−0.878558			−0.264895			−0.132448	−	0.991190i	$-0.542284\pi$
$11$	−0.878558			−0.264895			−0.132448	+	0.991190i	$0.542284\pi$
$12$		0			0
$13$	−0.786978	−	3.51862i	−0.218268	−	0.975889i
$13$	−0.786978	−	3.51862i	−0.218268	−	0.975889i
$14$	−2.63641	+	0.222079i	−0.704611	+	0.0593532i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.20391	+	5.54934i	−0.777062	+	1.34591i	0.156565	+	0.987668i	$0.449958\pi$
$17$	−3.20391	+	5.54934i	−0.777062	+	1.34591i	−0.933628	+	0.358244i	$0.883376\pi$
$18$		0			0
$19$	1.50820			0.346004			0.173002	−	0.984921i	$-0.444653\pi$
$19$	1.50820			0.346004			0.173002	+	0.984921i	$0.444653\pi$
$20$	−1.14553	−	1.98411i	−0.256147	−	0.443660i
$21$		0			0
$22$	−0.439279	−	0.760853i	−0.0936545	−	0.162214i
$23$	0.658760	+	1.14101i	0.137361	+	0.237916i	0.926497	−	0.376302i	$-0.122805\pi$
$23$	0.658760	+	1.14101i	0.137361	+	0.237916i	−0.789136	+	0.614219i	$0.789471\pi$
$24$		0			0
$25$	−0.124459	−	0.215569i	−0.0248918	−	0.0431139i
$26$	2.65372	−	2.44085i	0.520438	−	0.478690i
$27$		0			0
$28$	−1.51053	−	2.17216i	−0.285464	−	0.410500i
$29$	0.669294	−	1.15925i	0.124285	−	0.215267i	−0.797168	−	0.603757i	$-0.793670\pi$
$29$	0.669294	−	1.15925i	0.124285	−	0.215267i	0.921453	+	0.388490i	$0.127003\pi$
$30$		0			0
$31$	−1.94748	−	3.37313i	−0.349777	−	0.605831i	0.636433	−	0.771332i	$-0.280409\pi$
$31$	−1.94748	−	3.37313i	−0.349777	−	0.605831i	−0.986210	+	0.165501i	$0.947076\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−6.40782			−1.09893
$35$	−3.46071	−	4.97654i	−0.584967	−	0.841188i
$36$		0			0
$37$	−4.69338	−	8.12917i	−0.771586	−	1.33643i	−0.936693	−	0.350151i	$-0.886130\pi$
$37$	−4.69338	−	8.12917i	−0.771586	−	1.33643i	0.165107	−	0.986276i	$-0.447203\pi$
$38$	0.754098	+	1.30614i	0.122331	+	0.211883i
$39$		0			0
$40$	1.14553	−	1.98411i	0.181124	−	0.313715i
$41$	−1.80195	+	3.12107i	−0.281417	+	0.487429i	−0.971734	−	0.236078i	$-0.924138\pi$
$41$	−1.80195	+	3.12107i	−0.281417	+	0.487429i	0.690317	+	0.723507i	$0.257471\pi$
$42$		0			0
$43$	−4.95801	−	8.58752i	−0.756089	−	1.30959i	−0.944831	−	0.327558i	$-0.893774\pi$
$43$	−4.95801	−	8.58752i	−0.756089	−	1.30959i	0.188742	−	0.982027i	$-0.439559\pi$
$44$	0.439279	−	0.760853i	0.0662238	−	0.114703i
$45$		0			0
$46$	−0.658760	+	1.14101i	−0.0971289	+	0.168232i
$47$	0.188939	−	0.327251i	0.0275595	−	0.0477345i	−0.851917	−	0.523677i	$-0.824560\pi$
$47$	0.188939	−	0.327251i	0.0275595	−	0.0477345i	0.879476	+	0.475943i	$0.157893\pi$
$48$		0			0
$49$	−4.46478	−	5.39126i	−0.637826	−	0.770180i
$50$	0.124459	−	0.215569i	0.0176012	−	0.0304861i
$51$		0			0
$52$	3.44070	+	1.07777i	0.477139	+	0.149459i
$53$	1.22356	+	2.11926i	0.168068	+	0.291103i	0.937741	−	0.347336i	$-0.112914\pi$
$53$	1.22356	+	2.11926i	0.168068	+	0.291103i	−0.769672	+	0.638439i	$0.779580\pi$
$54$		0			0
$55$	1.00641	−	1.74315i	0.135704	−	0.235047i
$56$	1.12588	−	2.39424i	0.150452	−	0.319944i
$57$		0			0
$58$	1.33859			0.175765
$59$	−2.98411	+	5.16864i	−0.388498	+	0.672899i	−0.992248	−	0.124275i	$-0.960339\pi$
$59$	−2.98411	+	5.16864i	−0.388498	+	0.672899i	0.603749	+	0.797174i	$0.293673\pi$
$60$		0			0
$61$	4.81564			0.616580			0.308290	−	0.951292i	$-0.400243\pi$
$61$	4.81564			0.616580			0.308290	+	0.951292i	$0.400243\pi$
$62$	1.94748	−	3.37313i	0.247330	−	0.428388i
$63$		0			0
$64$	1.00000			0.125000
$65$	7.88282	+	2.46922i	0.977744	+	0.306269i
$66$		0			0
$67$	9.75996			1.19237			0.596184	−	0.802848i	$-0.296683\pi$
$67$	9.75996			1.19237			0.596184	+	0.802848i	$0.296683\pi$
$68$	−3.20391	−	5.54934i	−0.388531	−	0.672956i
$69$		0			0
$70$	2.57945	−	5.48533i	0.308303	−	0.655622i
$71$	−1.02408	−	1.77376i	−0.121536	−	0.210507i	0.798837	−	0.601547i	$-0.205449\pi$
$71$	−1.02408	−	1.77376i	−0.121536	−	0.210507i	−0.920374	+	0.391040i	$0.872115\pi$
$72$		0			0
$73$	0.432504	+	0.749119i	0.0506207	+	0.0876777i	0.890225	−	0.455520i	$-0.150547\pi$
$73$	0.432504	+	0.749119i	0.0506207	+	0.0876777i	−0.839605	+	0.543198i	$0.817213\pi$
$74$	4.69338	−	8.12917i	0.545594	−	0.944997i
$75$		0			0
$76$	−0.754098	+	1.30614i	−0.0865010	+	0.149824i
$77$	0.989151	−	2.10348i	0.112724	−	0.239714i
$78$		0			0
$79$	−4.18014	+	7.24022i	−0.470303	+	0.814588i	−0.999423	−	0.0339584i	$-0.989189\pi$
$79$	−4.18014	+	7.24022i	−0.470303	+	0.814588i	0.529120	+	0.848547i	$0.322522\pi$
$80$	2.29105			0.256147
$81$		0			0
$82$	−3.60390			−0.397984
$83$	−8.66710			−0.951338			−0.475669	−	0.879624i	$-0.657794\pi$
$83$	−8.66710			−0.951338			−0.475669	+	0.879624i	$0.657794\pi$
$84$		0			0
$85$	−7.34033	−	12.7138i	−0.796170	−	1.37901i
$86$	4.95801	−	8.58752i	0.534636	−	0.926016i
$87$		0			0
$88$	0.878558			0.0936545
$89$	−6.41693	−	11.1145i	−0.680194	−	1.17813i	−0.974922	−	0.222549i	$-0.928562\pi$
$89$	−6.41693	−	11.1145i	−0.680194	−	1.17813i	0.294728	−	0.955581i	$-0.404771\pi$
$90$		0			0
$91$	9.31046	+	2.07733i	0.976002	+	0.217763i
$92$	−1.31752			−0.137361
$93$		0			0
$94$	0.377877			0.0389751
$95$	−1.72768	+	2.99243i	−0.177256	+	0.307017i
$96$		0			0
$97$	4.40338	+	7.62688i	0.447096	+	0.774393i	0.998196	−	0.0600467i	$-0.0191250\pi$
$97$	4.40338	+	7.62688i	0.447096	+	0.774393i	−0.551100	+	0.834439i	$0.685792\pi$
$98$	2.43658	−	6.56225i	0.246132	−	0.662887i
$99$		0			0
$100$	0.248918			0.0248918
$101$	10.0539			1.00040			0.500198	−	0.865911i	$-0.333261\pi$
$101$	10.0539			1.00040			0.500198	+	0.865911i	$0.333261\pi$
$102$		0			0
$103$	−6.17983	+	10.7038i	−0.608916	+	1.05467i	0.382503	+	0.923954i	$0.375062\pi$
$103$	−6.17983	+	10.7038i	−0.608916	+	1.05467i	−0.991419	+	0.130720i	$0.958271\pi$
$104$	0.786978	+	3.51862i	0.0771695	+	0.345029i
$105$		0			0
$106$	−1.22356	+	2.11926i	−0.118842	+	0.205841i
$107$	−3.40406	−	5.89601i	−0.329083	−	0.569989i	0.653247	−	0.757145i	$-0.273406\pi$
$107$	−3.40406	−	5.89601i	−0.329083	−	0.569989i	−0.982330	+	0.187156i	$0.940073\pi$
$108$		0			0
$109$	−0.460710	−	0.797973i	−0.0441280	−	0.0764320i	0.843118	−	0.537729i	$-0.180718\pi$
$109$	−0.460710	−	0.797973i	−0.0441280	−	0.0764320i	−0.887246	+	0.461297i	$0.847384\pi$
$110$	2.01282			0.191915
$111$		0			0
$112$	2.63641	−	0.222079i	0.249118	−	0.0209845i
$113$	−5.68802	−	9.85195i	−0.535084	−	0.926793i	−0.999159	−	0.0409973i	$-0.986947\pi$
$113$	−5.68802	−	9.85195i	−0.535084	−	0.926793i	0.464075	−	0.885796i	$-0.346387\pi$
$114$		0			0
$115$	−3.01851			−0.281477
$116$	0.669294	+	1.15925i	0.0621424	+	0.107634i
$117$		0			0
$118$	−5.96823			−0.549420
$119$	−9.67923	−	13.9188i	−0.887293	−	1.27594i
$120$		0			0
$121$	−10.2281			−0.929831
$122$	2.40782	+	4.17047i	0.217994	+	0.377576i
$123$		0			0
$124$	3.89495			0.349777
$125$	−10.8850			−0.973582
$126$		0			0
$127$	4.26019	−	7.37887i	0.378031	−	0.654769i	−0.612745	−	0.790281i	$-0.709935\pi$
$127$	4.26019	−	7.37887i	0.378031	−	0.654769i	0.990776	+	0.135512i	$0.0432679\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	1.80301	+	8.06133i	0.158134	+	0.707026i
$131$	−2.51964	+	4.36415i	−0.220142	+	0.381298i	−0.954851	−	0.297085i	$-0.903986\pi$
$131$	−2.51964	+	4.36415i	−0.220142	+	0.381298i	0.734709	+	0.678383i	$0.237319\pi$
$132$		0			0
$133$	−1.69805	+	3.61099i	−0.147240	+	0.313112i
$134$	4.87998	+	8.45237i	0.421566	+	0.730174i
$135$		0			0
$136$	3.20391	−	5.54934i	0.274733	−	0.475852i
$137$	−9.47262	+	16.4071i	−0.809300	+	1.40175i	0.104049	+	0.994572i	$0.466820\pi$
$137$	−9.47262	+	16.4071i	−0.809300	+	1.40175i	−0.913349	+	0.407177i	$0.866513\pi$
$138$		0			0
$139$	0.565160	+	0.978885i	0.0479362	+	0.0830280i	0.888998	−	0.457911i	$-0.151402\pi$
$139$	0.565160	+	0.978885i	0.0479362	+	0.0830280i	−0.841062	+	0.540939i	$0.818069\pi$
$140$	6.04016	−	0.508795i	0.510487	−	0.0430010i
$141$		0			0
$142$	1.02408	−	1.77376i	0.0859392	−	0.148851i
$143$	0.691405	+	3.09131i	0.0578182	+	0.258508i
$144$		0			0
$145$	1.53339	+	2.65590i	0.127341	+	0.220561i
$146$	−0.432504	+	0.749119i	−0.0357943	+	0.0619975i
$147$		0			0
$148$	9.38675			0.771586
$149$	−1.60500			−0.131487			−0.0657433	−	0.997837i	$-0.520942\pi$
$149$	−1.60500			−0.131487			−0.0657433	+	0.997837i	$0.520942\pi$
$150$		0			0
$151$	10.2417	+	17.7391i	0.833457	+	1.44359i	0.895281	+	0.445502i	$0.146975\pi$
$151$	10.2417	+	17.7391i	0.833457	+	1.44359i	−0.0618242	+	0.998087i	$0.519692\pi$
$152$	−1.50820			−0.122331
$153$		0			0
$154$	2.31624	−	0.195109i	0.186648	−	0.0157224i
$155$	8.92354			0.716756
$156$		0			0
$157$	−5.16462	−	8.94539i	−0.412182	−	0.713919i	0.582946	−	0.812511i	$-0.301900\pi$
$157$	−5.16462	−	8.94539i	−0.412182	−	0.713919i	−0.995128	+	0.0985911i	$0.968566\pi$
$158$	−8.36029			−0.665109
$159$		0			0
$160$	1.14553	+	1.98411i	0.0905618	+	0.156858i
$161$	−3.47353	+	0.292594i	−0.273753	+	0.0230596i
$162$		0			0
$163$	−6.89780			−0.540277			−0.270139	−	0.962821i	$-0.587069\pi$
$163$	−6.89780			−0.540277			−0.270139	+	0.962821i	$0.587069\pi$
$164$	−1.80195	−	3.12107i	−0.140709	−	0.243715i
$165$		0			0
$166$	−4.33355	−	7.50593i	−0.336349	−	0.582573i
$167$	−9.73115	+	16.8549i	−0.753019	+	1.30427i	0.193334	+	0.981133i	$0.438070\pi$
$167$	−9.73115	+	16.8549i	−0.753019	+	1.30427i	−0.946353	+	0.323135i	$0.895263\pi$
$168$		0			0
$169$	−11.7613	+	5.53815i	−0.904718	+	0.426011i
$170$	7.34033	−	12.7138i	0.562977	−	0.975105i
$171$		0			0
$172$	9.91602			0.756089
$173$	−22.0138			−1.67368			−0.836840	−	0.547447i	$-0.815600\pi$
$173$	−22.0138			−1.67368			−0.836840	+	0.547447i	$0.815600\pi$
$174$		0			0
$175$	0.656251	−	0.0552795i	0.0496079	−	0.00417874i
$176$	0.439279	+	0.760853i	0.0331119	+	0.0573515i
$177$		0			0
$178$	6.41693	−	11.1145i	0.480969	−	0.833064i
$179$	9.81637			0.733710			0.366855	−	0.930278i	$-0.380435\pi$
$179$	9.81637			0.733710			0.366855	+	0.930278i	$0.380435\pi$
$180$		0			0
$181$	22.9753			1.70774			0.853869	−	0.520487i	$-0.174250\pi$
$181$	22.9753			1.70774			0.853869	+	0.520487i	$0.174250\pi$
$182$	2.85621	+	9.10176i	0.211716	+	0.674667i
$183$		0			0
$184$	−0.658760	−	1.14101i	−0.0485645	−	0.0841161i
$185$	21.5055			1.58112
$186$		0			0
$187$	2.81482	−	4.87541i	0.205840	−	0.356525i
$188$	0.188939	+	0.327251i	0.0137798	+	0.0238673i
$189$		0			0
$190$	−3.45536			−0.250678
$191$	9.69073			0.701196			0.350598	−	0.936526i	$-0.385978\pi$
$191$	9.69073			0.701196			0.350598	+	0.936526i	$0.385978\pi$
$192$		0			0
$193$	−21.1067			−1.51929			−0.759647	−	0.650336i	$-0.774628\pi$
$193$	−21.1067			−1.51929			−0.759647	+	0.650336i	$0.774628\pi$
$194$	−4.40338	+	7.62688i	−0.316144	+	0.547578i
$195$		0			0
$196$	6.90136	−	1.17099i	0.492954	−	0.0836418i
$197$	6.76019	−	11.7090i	0.481644	−	0.834232i	−0.518134	−	0.855299i	$-0.673373\pi$
$197$	6.76019	−	11.7090i	0.481644	−	0.834232i	0.999778	+	0.0210677i	$0.00670656\pi$
$198$		0			0
$199$	3.79449	−	6.57226i	0.268985	−	0.465895i	−0.699615	−	0.714520i	$-0.746645\pi$
$199$	3.79449	−	6.57226i	0.268985	−	0.465895i	0.968600	+	0.248625i	$0.0799786\pi$
$200$	0.124459	+	0.215569i	0.00880058	+	0.0152431i
$201$		0			0
$202$	5.02693	+	8.70689i	0.353693	+	0.612615i
$203$	2.02198	+	2.90763i	0.141915	+	0.204076i
$204$		0			0
$205$	−4.12836	−	7.15053i	−0.288337	−	0.499415i
$206$	−12.3597			−0.861138
$207$		0			0
$208$	−2.65372	+	2.44085i	−0.184003	+	0.169243i
$209$	−1.32504			−0.0916548
$210$		0			0
$211$	−6.06832	+	10.5106i	−0.417760	+	0.723582i	−0.995714	−	0.0924876i	$-0.970518\pi$
$211$	−6.06832	+	10.5106i	−0.417760	+	0.723582i	0.577954	+	0.816070i	$0.303851\pi$
$212$	−2.44711			−0.168068
$213$		0			0
$214$	3.40406	−	5.89601i	0.232697	−	0.403043i
$215$	22.7181			1.54936
$216$		0			0
$217$	10.2687	−	0.864988i	0.697085	−	0.0587192i
$218$	0.460710	−	0.797973i	0.0312032	−	0.0540456i
$219$		0			0
$220$	1.00641	+	1.74315i	0.0678522	+	0.117523i
$221$	22.0474	+	6.90613i	1.48307	+	0.464557i
$222$		0			0
$223$	−11.0968	+	19.2202i	−0.743094	+	1.28708i	0.207986	+	0.978132i	$0.433309\pi$
$223$	−11.0968	+	19.2202i	−0.743094	+	1.28708i	−0.951080	+	0.308945i	$0.900024\pi$
$224$	1.51053	+	2.17216i	0.100927	+	0.145134i
$225$		0			0
$226$	5.68802	−	9.85195i	0.378362	−	0.655342i
$227$	−12.2142	+	21.1556i	−0.810686	+	1.40415i	0.101699	+	0.994815i	$0.467572\pi$
$227$	−12.2142	+	21.1556i	−0.810686	+	1.40415i	−0.912385	+	0.409333i	$0.865761\pi$
$228$		0			0
$229$	−14.9717	+	25.9317i	−0.989358	+	1.71362i	−0.368670	+	0.929560i	$0.620187\pi$
$229$	−14.9717	+	25.9317i	−0.989358	+	1.71362i	−0.620688	+	0.784058i	$0.713147\pi$
$230$	−1.50925	−	2.61410i	−0.0995173	−	0.172369i
$231$		0			0
$232$	−0.669294	+	1.15925i	−0.0439413	+	0.0761086i
$233$	11.4574	−	19.8448i	0.750600	−	1.30008i	−0.196932	−	0.980417i	$-0.563098\pi$
$233$	11.4574	−	19.8448i	0.750600	−	1.30008i	0.947532	−	0.319660i	$-0.103569\pi$
$234$		0			0
$235$	0.432868	+	0.749750i	0.0282372	+	0.0489083i
$236$	−2.98411	−	5.16864i	−0.194249	−	0.336450i
$237$		0			0
$238$	7.21444	−	15.3419i	0.467643	−	0.994466i
$239$	1.03992			0.0672669			0.0336334	−	0.999434i	$-0.489292\pi$
$239$	1.03992			0.0672669			0.0336334	+	0.999434i	$0.489292\pi$
$240$		0			0
$241$	−3.23944	+	5.61088i	−0.208671	+	0.361428i	−0.951296	−	0.308279i	$-0.900247\pi$
$241$	−3.23944	+	5.61088i	−0.208671	+	0.361428i	0.742625	+	0.669707i	$0.233580\pi$
$242$	−5.11407	−	8.85783i	−0.328745	−	0.569403i
$243$		0			0
$244$	−2.40782	+	4.17047i	−0.154145	+	0.266987i
$245$	15.8114	−	2.68279i	1.01015	−	0.171397i
$246$		0			0
$247$	−1.18692	−	5.30677i	−0.0755218	−	0.337662i
$248$	1.94748	+	3.37313i	0.123665	+	0.214194i
$249$		0			0
$250$	−5.44249	−	9.42666i	−0.344213	−	0.596195i
$251$	−5.33039	−	9.23251i	−0.336451	−	0.582751i	0.647311	−	0.762226i	$-0.275893\pi$
$251$	−5.33039	−	9.23251i	−0.336451	−	0.582751i	−0.983763	+	0.179475i	$0.942560\pi$
$252$		0			0
$253$	−0.578759	−	1.00244i	−0.0363863	−	0.0630229i
$254$	8.52039			0.534617
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.0419	+	24.3213i	0.875910	+	1.51712i	0.855791	+	0.517322i	$0.173071\pi$
$257$	14.0419	+	24.3213i	0.875910	+	1.51712i	0.0201190	+	0.999798i	$0.493595\pi$
$258$		0			0
$259$	24.7474	−	2.08460i	1.53773	−	0.129531i
$260$	−6.07982	+	5.59212i	−0.377054	+	0.346808i
$261$		0			0
$262$	−5.03929			−0.311328
$263$	24.1769			1.49081			0.745407	−	0.666610i	$-0.232255\pi$
$263$	24.1769			1.49081			0.745407	+	0.666610i	$0.232255\pi$
$264$		0			0
$265$	−5.60646			−0.344402
$266$	−3.97623	+	0.334939i	−0.243798	+	0.0205364i
$267$		0			0
$268$	−4.87998	+	8.45237i	−0.298092	+	0.516311i
$269$	−3.96946	+	6.87530i	−0.242022	+	0.419195i	−0.961290	−	0.275538i	$-0.911144\pi$
$269$	−3.96946	+	6.87530i	−0.242022	+	0.419195i	0.719268	+	0.694733i	$0.244477\pi$
$270$		0			0
$271$	14.3347	+	24.8284i	0.870770	+	1.50822i	0.861201	+	0.508264i	$0.169713\pi$
$271$	14.3347	+	24.8284i	0.870770	+	1.50822i	0.00956909	+	0.999954i	$0.496954\pi$
$272$	6.40782			0.388531
$273$		0			0
$274$	−18.9452			−1.14452
$275$	0.109344	+	0.189390i	0.00659372	+	0.0114207i
$276$		0			0
$277$	−6.24357	+	10.8142i	−0.375139	+	0.649761i	−0.990348	−	0.138604i	$-0.955739\pi$
$277$	−6.24357	+	10.8142i	−0.375139	+	0.649761i	0.615208	+	0.788364i	$0.289072\pi$
$278$	−0.565160	+	0.978885i	−0.0338960	+	0.0587096i
$279$		0			0
$280$	3.46071	+	4.97654i	0.206817	+	0.297405i
$281$	−23.4616			−1.39960			−0.699800	−	0.714339i	$-0.746728\pi$
$281$	−23.4616			−1.39960			−0.699800	+	0.714339i	$0.746728\pi$
$282$		0			0
$283$	−15.7899			−0.938612			−0.469306	−	0.883036i	$-0.655496\pi$
$283$	−15.7899			−0.938612			−0.469306	+	0.883036i	$0.655496\pi$
$284$	2.04817			0.121536
$285$		0			0
$286$	−2.33145	+	2.14443i	−0.137861	+	0.126803i
$287$	−5.44381	−	7.82825i	−0.321338	−	0.462087i
$288$		0			0
$289$	−12.0301	−	20.8367i	−0.707652	−	1.22569i
$290$	−1.53339	+	2.65590i	−0.0900436	+	0.155960i
$291$		0			0
$292$	−0.865008			−0.0506207
$293$	−3.38969	−	5.87112i	−0.198028	−	0.342994i	0.749861	−	0.661595i	$-0.230120\pi$
$293$	−3.38969	−	5.87112i	−0.198028	−	0.342994i	−0.947889	+	0.318601i	$0.896787\pi$
$294$		0			0
$295$	−6.83676	−	11.8416i	−0.398051	−	0.689445i
$296$	4.69338	+	8.12917i	0.272797	+	0.472498i
$297$		0			0
$298$	−0.802500	−	1.38997i	−0.0464876	−	0.0805188i
$299$	3.49634	−	3.21587i	0.202198	−	0.185979i
$300$		0			0
$301$	26.1427	−	2.20214i	1.50684	−	0.126929i
$302$	−10.2417	+	17.7391i	−0.589343	+	1.02077i
$303$		0			0
$304$	−0.754098	−	1.30614i	−0.0432505	−	0.0749121i
$305$	−5.51644	+	9.55476i	−0.315871	+	0.547104i
$306$		0			0
$307$	−1.27687			−0.0728749			−0.0364374	−	0.999336i	$-0.511601\pi$
$307$	−1.27687			−0.0728749			−0.0364374	+	0.999336i	$0.511601\pi$
$308$	1.32709	+	1.90837i	0.0756180	+	0.108739i
$309$		0			0
$310$	4.46177	+	7.72801i	0.253411	+	0.438921i
$311$	12.4336	+	21.5357i	0.705047	+	1.22118i	0.966675	+	0.256009i	$0.0824075\pi$
$311$	12.4336	+	21.5357i	0.705047	+	1.22118i	−0.261627	+	0.965169i	$0.584259\pi$
$312$		0			0
$313$	13.1601	−	22.7940i	0.743855	−	1.28839i	−0.206873	−	0.978368i	$-0.566329\pi$
$313$	13.1601	−	22.7940i	0.743855	−	1.28839i	0.950728	−	0.310026i	$-0.100338\pi$
$314$	5.16462	−	8.94539i	0.291456	−	0.504817i
$315$		0			0
$316$	−4.18014	−	7.24022i	−0.235151	−	0.407294i
$317$	−9.33620	+	16.1708i	−0.524373	+	0.908241i	0.475224	+	0.879865i	$0.342367\pi$
$317$	−9.33620	+	16.1708i	−0.524373	+	0.908241i	−0.999597	+	0.0283764i	$0.990966\pi$
$318$		0			0
$319$	−0.588013	+	1.01847i	−0.0329224	+	0.0570233i
$320$	−1.14553	+	1.98411i	−0.0640368	+	0.110915i
$321$		0			0
$322$	−1.99016	−	2.86187i	−0.110907	−	0.159486i
$323$	−4.83213	+	8.36949i	−0.268867	+	0.465691i
$324$		0			0
$325$	−0.660560	+	0.607572i	−0.0366413	+	0.0337020i
$326$	−3.44890	−	5.97367i	−0.191017	−	0.330851i
$327$		0			0
$328$	1.80195	−	3.12107i	0.0994960	−	0.172332i
$329$	0.570797	+	0.820811i	0.0314690	+	0.0452528i
$330$		0			0
$331$	36.0485			1.98140			0.990701	−	0.136057i	$-0.0434429\pi$
$331$	36.0485			1.98140			0.990701	+	0.136057i	$0.0434429\pi$
$332$	4.33355	−	7.50593i	0.237834	−	0.411941i
$333$		0			0
$334$	−19.4623			−1.06493
$335$	−11.1803	+	19.3648i	−0.610844	+	1.05801i
$336$		0			0
$337$	16.9888			0.925440			0.462720	−	0.886504i	$-0.346873\pi$
$337$	16.9888			0.925440			0.462720	+	0.886504i	$0.346873\pi$
$338$	−10.6768	−	7.41654i	−0.580744	−	0.403406i
$339$		0			0
$340$	14.6807			0.796170
$341$	1.71097	+	2.96349i	0.0926542	+	0.160482i
$342$		0			0
$343$	17.9348	−	4.61985i	0.968388	−	0.249449i
$344$	4.95801	+	8.58752i	0.267318	+	0.463008i
$345$		0			0
$346$	−11.0069	−	19.0645i	−0.591736	−	1.02492i
$347$	6.01805	−	10.4236i	0.323066	−	0.559566i	−0.658053	−	0.752971i	$-0.728620\pi$
$347$	6.01805	−	10.4236i	0.323066	−	0.559566i	0.981119	+	0.193405i	$0.0619531\pi$
$348$		0			0
$349$	−11.4544	+	19.8396i	−0.613140	+	1.06199i	0.377568	+	0.925982i	$0.376760\pi$
$349$	−11.4544	+	19.8396i	−0.613140	+	1.06199i	−0.990708	+	0.136007i	$0.956573\pi$
$350$	0.375999	+	0.540690i	0.0200980	+	0.0289011i
$351$		0			0
$352$	−0.439279	+	0.760853i	−0.0234136	+	0.0405536i
$353$	−24.3166			−1.29424			−0.647121	−	0.762387i	$-0.724027\pi$
$353$	−24.3166			−1.29424			−0.647121	+	0.762387i	$0.724027\pi$
$354$		0			0
$355$	4.69246			0.249050
$356$	12.8339			0.680194
$357$		0			0
$358$	4.90819	+	8.50123i	0.259406	+	0.449304i
$359$	14.4734	−	25.0686i	0.763875	−	1.32307i	−0.176965	−	0.984217i	$-0.556628\pi$
$359$	14.4734	−	25.0686i	0.763875	−	1.32307i	0.940840	−	0.338853i	$-0.110039\pi$
$360$		0			0
$361$	−16.7253			−0.880281
$362$	11.4876	+	19.8972i	0.603777	+	1.04577i
$363$		0			0
$364$	−6.45425	+	7.02443i	−0.338295	+	0.368180i
$365$	−1.98178			−0.103731
$366$		0			0
$367$	−27.0045			−1.40962			−0.704811	−	0.709395i	$-0.748968\pi$
$367$	−27.0045			−1.40962			−0.704811	+	0.709395i	$0.748968\pi$
$368$	0.658760	−	1.14101i	0.0343403	−	0.0594791i
$369$		0			0
$370$	10.7528	+	18.6243i	0.559010	+	0.968234i
$371$	−6.45160	+	0.543452i	−0.334950	+	0.0282146i
$372$		0			0
$373$	19.2350			0.995952			0.497976	−	0.867191i	$-0.334077\pi$
$373$	19.2350			0.995952			0.497976	+	0.867191i	$0.334077\pi$
$374$	5.62964			0.291102
$375$		0			0
$376$	−0.188939	+	0.327251i	−0.00974377	+	0.0168767i
$377$	−4.60568	−	1.44268i	−0.237205	−	0.0743020i
$378$		0			0
$379$	−16.1551	+	27.9815i	−0.829834	+	1.43731i	0.0683340	+	0.997662i	$0.478232\pi$
$379$	−16.1551	+	27.9815i	−0.829834	+	1.43731i	−0.898168	+	0.439652i	$0.855102\pi$
$380$	−1.72768	−	2.99243i	−0.0886280	−	0.153508i
$381$		0			0
$382$	4.84536	+	8.39241i	0.247910	+	0.429393i
$383$	31.4223			1.60560			0.802802	−	0.596246i	$-0.203342\pi$
$383$	31.4223			1.60560			0.802802	+	0.596246i	$0.203342\pi$
$384$		0			0
$385$	3.04043	+	4.37217i	0.154955	+	0.222827i
$386$	−10.5533	−	18.2789i	−0.537151	−	0.930373i
$387$		0			0
$388$	−8.80677			−0.447096
$389$	−2.89119	−	5.00769i	−0.146589	−	0.253900i	0.783375	−	0.621549i	$-0.213496\pi$
$389$	−2.89119	−	5.00769i	−0.146589	−	0.253900i	−0.929965	+	0.367649i	$0.880163\pi$
$390$		0			0
$391$	−8.44244			−0.426952
$392$	4.46478	+	5.39126i	0.225506	+	0.272300i
$393$		0			0
$394$	13.5204			0.681147
$395$	−9.57692	−	16.5877i	−0.481867	−	0.834619i
$396$		0			0
$397$	6.98708			0.350672			0.175336	−	0.984509i	$-0.443899\pi$
$397$	6.98708			0.350672			0.175336	+	0.984509i	$0.443899\pi$
$398$	7.58899			0.380402
$399$		0			0
$400$	−0.124459	+	0.215569i	−0.00622295	+	0.0107785i
$401$	−2.96749	−	5.13984i	−0.148189	−	0.256671i	0.782369	−	0.622815i	$-0.214011\pi$
$401$	−2.96749	−	5.13984i	−0.148189	−	0.256671i	−0.930558	+	0.366144i	$0.880678\pi$
$402$		0			0
$403$	−10.3361	+	9.50700i	−0.514879	+	0.473577i
$404$	−5.02693	+	8.70689i	−0.250099	+	0.433184i
$405$		0			0
$406$	−1.50709	+	3.20490i	−0.0747956	+	0.159057i
$407$	4.12340	+	7.14194i	0.204389	+	0.354013i
$408$		0			0
$409$	7.38923	−	12.7985i	0.365374	−	0.632846i	−0.623462	−	0.781854i	$-0.714274\pi$
$409$	7.38923	−	12.7985i	0.365374	−	0.632846i	0.988836	+	0.149007i	$0.0476077\pi$
$410$	4.12836	−	7.15053i	0.203885	−	0.353139i
$411$		0			0
$412$	−6.17983	−	10.7038i	−0.304458	−	0.527337i
$413$	−9.01521	−	12.9640i	−0.443609	−	0.637915i
$414$		0			0
$415$	9.92839	−	17.1965i	0.487365	−	0.844142i
$416$	−3.44070	−	1.07777i	−0.168694	−	0.0528418i
$417$		0			0
$418$	−0.662519	−	1.14752i	−0.0324049	−	0.0561269i
$419$	5.07336	−	8.78731i	0.247850	−	0.429288i	−0.715079	−	0.699043i	$-0.753609\pi$
$419$	5.07336	−	8.78731i	0.247850	−	0.429288i	0.962929	+	0.269755i	$0.0869428\pi$
$420$		0			0
$421$	7.70885			0.375706			0.187853	−	0.982197i	$-0.439847\pi$
$421$	7.70885			0.375706			0.187853	+	0.982197i	$0.439847\pi$
$422$	−12.1366			−0.590802
$423$		0			0
$424$	−1.22356	−	2.11926i	−0.0594211	−	0.102920i
$425$	1.59502			0.0773700
$426$		0			0
$427$	−5.42184	+	11.5298i	−0.262381	+	0.557967i
$428$	6.80813			0.329083
$429$		0			0
$430$	11.3591	+	19.6745i	0.547782	+	0.948787i
$431$	−35.7786			−1.72339			−0.861696	−	0.507424i	$-0.830598\pi$
$431$	−35.7786			−1.72339			−0.861696	+	0.507424i	$0.830598\pi$
$432$		0			0
$433$	−6.32535	−	10.9558i	−0.303977	−	0.526504i	0.673056	−	0.739592i	$-0.264981\pi$
$433$	−6.32535	−	10.9558i	−0.303977	−	0.526504i	−0.977033	+	0.213088i	$0.931648\pi$
$434$	5.88345	+	8.46047i	0.282415	+	0.406115i
$435$		0			0
$436$	0.921420			0.0441280
$437$	0.993540	+	1.72086i	0.0475275	+	0.0823200i
$438$		0			0
$439$	13.6023	+	23.5598i	0.649200	+	1.12445i	0.983314	+	0.181915i	$0.0582296\pi$
$439$	13.6023	+	23.5598i	0.649200	+	1.12445i	−0.334114	+	0.942533i	$0.608437\pi$
$440$	−1.00641	+	1.74315i	−0.0479787	+	0.0831016i
$441$		0			0
$442$	5.04281	+	22.5467i	0.239862	+	1.07244i
$443$	1.74860	−	3.02867i	0.0830786	−	0.143896i	−0.821492	−	0.570220i	$-0.806858\pi$
$443$	1.74860	−	3.02867i	0.0830786	−	0.143896i	0.904571	+	0.426323i	$0.140191\pi$
$444$		0			0
$445$	29.4030			1.39384
$446$	−22.1935			−1.05089
$447$		0			0
$448$	−1.12588	+	2.39424i	−0.0531929	+	0.113117i
$449$	−8.08366	−	14.0013i	−0.381491	−	0.660762i	0.609784	−	0.792567i	$-0.291256\pi$
$449$	−8.08366	−	14.0013i	−0.381491	−	0.660762i	−0.991276	+	0.131805i	$0.957923\pi$
$450$		0			0
$451$	1.58312	−	2.74204i	0.0745460	−	0.129118i
$452$	11.3760			0.535084
$453$		0			0
$454$	−24.4284			−1.14648
$455$	−14.7870	+	16.0933i	−0.693226	+	0.754467i
$456$		0			0
$457$	−13.1305	−	22.7426i	−0.614217	−	1.06386i	−0.990521	−	0.137359i	$-0.956139\pi$
$457$	−13.1305	−	22.7426i	−0.614217	−	1.06386i	0.376304	−	0.926496i	$-0.377195\pi$
$458$	−29.9434			−1.39916
$459$		0			0
$460$	1.50925	−	2.61410i	0.0703693	−	0.121883i
$461$	4.94386	+	8.56302i	0.230259	+	0.398819i	0.957884	−	0.287155i	$-0.0927095\pi$
$461$	4.94386	+	8.56302i	0.230259	+	0.398819i	−0.727626	+	0.685974i	$0.759376\pi$
$462$		0			0
$463$	−14.2082			−0.660310			−0.330155	−	0.943927i	$-0.607101\pi$
$463$	−14.2082			−0.660310			−0.330155	+	0.943927i	$0.607101\pi$
$464$	−1.33859			−0.0621424
$465$		0			0
$466$	22.9148			1.06151
$467$	1.47500	−	2.55478i	0.0682550	−	0.118221i	−0.829878	−	0.557944i	$-0.811590\pi$
$467$	1.47500	−	2.55478i	0.0682550	−	0.118221i	0.898133	+	0.439723i	$0.144924\pi$
$468$		0			0
$469$	−10.9886	+	23.3677i	−0.507404	+	1.07902i
$470$	−0.432868	+	0.749750i	−0.0199667	+	0.0345834i
$471$		0			0
$472$	2.98411	−	5.16864i	0.137355	−	0.237906i
$473$	4.35590	+	7.54463i	0.200284	+	0.346903i
$474$		0			0
$475$	−0.187709	−	0.325121i	−0.00861267	−	0.0149176i
$476$	16.8937	−	1.42304i	0.774320	−	0.0652251i
$477$		0			0
$478$	0.519960	+	0.900598i	0.0237824	+	0.0411924i
$479$	−19.8096			−0.905124			−0.452562	−	0.891733i	$-0.649490\pi$
$479$	−19.8096			−0.905124			−0.452562	+	0.891733i	$0.649490\pi$
$480$		0			0
$481$	−24.9098	+	22.9117i	−1.13579	+	1.04468i
$482$	−6.47888			−0.295105
$483$		0			0
$484$	5.11407	−	8.85783i	0.232458	−	0.402628i
$485$	−20.1768			−0.916179
$486$		0			0
$487$	6.29728	−	10.9072i	0.285357	−	0.494253i	−0.687339	−	0.726337i	$-0.741221\pi$
$487$	6.29728	−	10.9072i	0.285357	−	0.494253i	0.972696	+	0.232084i	$0.0745546\pi$
$488$	−4.81564			−0.217994
$489$		0			0
$490$	10.2291	+	12.3517i	0.462101	+	0.557991i
$491$	−5.81280	+	10.0681i	−0.262328	+	0.454365i	−0.966860	−	0.255307i	$-0.917824\pi$
$491$	−5.81280	+	10.0681i	−0.262328	+	0.454365i	0.704532	+	0.709672i	$0.251157\pi$
$492$		0			0
$493$	4.28872	+	7.42827i	0.193154	+	0.334553i
$494$	4.00234	−	3.68128i	0.180074	−	0.165629i
$495$		0			0
$496$	−1.94748	+	3.37313i	−0.0874442	+	0.151458i
$497$	5.39982	−	0.454855i	0.242215	−	0.0204030i
$498$		0			0
$499$	6.22713	−	10.7857i	0.278765	−	0.482834i	−0.692313	−	0.721597i	$-0.743408\pi$
$499$	6.22713	−	10.7857i	0.278765	−	0.482834i	0.971078	+	0.238763i	$0.0767418\pi$
$500$	5.44249	−	9.42666i	0.243395	−	0.421573i
$501$		0			0
$502$	5.33039	−	9.23251i	0.237907	−	0.412067i
$503$	15.7073	+	27.2058i	0.700354	+	1.21305i	0.968342	+	0.249627i	$0.0803079\pi$
$503$	15.7073	+	27.2058i	0.700354	+	1.21305i	−0.267988	+	0.963422i	$0.586359\pi$
$504$		0			0
$505$	−11.5170	+	19.9479i	−0.512498	+	0.887672i
$506$	0.578759	−	1.00244i	0.0257290	−	0.0445639i
$507$		0			0
$508$	4.26019	+	7.37887i	0.189016	+	0.327384i
$509$	3.59886	+	6.23341i	0.159517	+	0.276291i	0.934695	−	0.355452i	$-0.115673\pi$
$509$	3.59886	+	6.23341i	0.159517	+	0.276291i	−0.775178	+	0.631743i	$0.782340\pi$
$510$		0			0
$511$	−2.28052	+	0.192100i	−0.100884	+	0.00849801i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−14.0419	+	24.3213i	−0.619362	+	1.07277i
$515$	−14.1583	−	24.5229i	−0.623889	−	1.08061i
$516$		0			0
$517$	−0.165994	+	0.287509i	−0.00730039	+	0.0126446i
$518$	14.1790	+	20.3896i	0.622990	+	0.895866i
$519$		0			0
$520$	−7.88282	−	2.46922i	−0.345685	−	0.108282i
$521$	−11.2983	−	19.5692i	−0.494987	−	0.857342i	0.504996	−	0.863121i	$-0.331494\pi$
$521$	−11.2983	−	19.5692i	−0.494987	−	0.857342i	−0.999983	+	0.00577905i	$0.998160\pi$
$522$		0			0
$523$	3.03635	+	5.25912i	0.132770	+	0.229965i	0.924744	−	0.380591i	$-0.124279\pi$
$523$	3.03635	+	5.25912i	0.132770	+	0.229965i	−0.791973	+	0.610556i	$0.790946\pi$
$524$	−2.51964	−	4.36415i	−0.110071	−	0.190649i
$525$		0			0
$526$	12.0885	+	20.9378i	0.527082	+	0.912933i
$527$	24.9582			1.08719
$528$		0			0
$529$	10.6321	−	18.4153i	0.462264	−	0.800665i
$530$	−2.80323	−	4.85534i	−0.121764	−	0.210902i
$531$		0			0
$532$	−2.27818	−	3.27605i	−0.0987717	−	0.142035i
$533$	12.3999	+	3.88416i	0.537101	+	0.168242i
$534$		0			0
$535$	15.5978			0.674350
$536$	−9.75996			−0.421566
$537$		0			0
$538$	−7.93891			−0.342271
$539$	3.92257	+	4.73653i	0.168957	+	0.204017i
$540$		0			0
$541$	3.16494	−	5.48183i	0.136071	−	0.235682i	−0.789935	−	0.613191i	$-0.789886\pi$
$541$	3.16494	−	5.48183i	0.136071	−	0.235682i	0.926006	+	0.377508i	$0.123219\pi$
$542$	−14.3347	+	24.8284i	−0.615728	+	1.06647i
$543$		0			0
$544$	3.20391	+	5.54934i	0.137367	+	0.237926i
$545$	2.11102			0.0904262
$546$		0			0
$547$	17.3685			0.742625			0.371312	−	0.928508i	$-0.378908\pi$
$547$	17.3685			0.742625			0.371312	+	0.928508i	$0.378908\pi$
$548$	−9.47262	−	16.4071i	−0.404650	−	0.700875i
$549$		0			0
$550$	−0.109344	+	0.189390i	−0.00466246	+	0.00807562i
$551$	1.00943	−	1.74838i	0.0430030	−	0.0744834i
$552$		0			0
$553$	−12.6285	−	18.1599i	−0.537018	−	0.772237i
$554$	−12.4871			−0.530527
$555$		0			0
$556$	−1.13032			−0.0479362
$557$	−39.8232			−1.68736			−0.843681	−	0.536845i	$-0.819616\pi$
$557$	−39.8232			−1.68736			−0.843681	+	0.536845i	$0.819616\pi$
$558$		0			0
$559$	−26.3144	+	24.2035i	−1.11298	+	1.02370i
$560$	−2.57945	+	5.48533i	−0.109002	+	0.231798i
$561$		0			0
$562$	−11.7308	−	20.3183i	−0.494833	−	0.857077i
$563$	−2.29585	+	3.97654i	−0.0967587	+	0.167591i	−0.910341	−	0.413858i	$-0.864181\pi$
$563$	−2.29585	+	3.97654i	−0.0967587	+	0.167591i	0.813583	+	0.581449i	$0.197514\pi$
$564$		0			0
$565$	26.0631			1.09648
$566$	−7.89495	−	13.6745i	−0.331850	−	0.574780i
$567$		0			0
$568$	1.02408	+	1.77376i	0.0429696	+	0.0744255i
$569$	−8.74146	−	15.1407i	−0.366461	−	0.634729i	0.622548	−	0.782581i	$-0.286097\pi$
$569$	−8.74146	−	15.1407i	−0.366461	−	0.634729i	−0.989010	+	0.147852i	$0.952764\pi$
$570$		0			0
$571$	8.05500	+	13.9517i	0.337091	+	0.583859i	0.983884	−	0.178806i	$-0.0572235\pi$
$571$	8.05500	+	13.9517i	0.337091	+	0.583859i	−0.646793	+	0.762666i	$0.723890\pi$
$572$	−3.02285	−	0.946879i	−0.126392	−	0.0395910i
$573$		0			0
$574$	4.05756	−	8.62861i	0.169359	−	0.360151i
$575$	0.163977	−	0.284017i	0.00683833	−	0.0118443i
$576$		0			0
$577$	3.99841	+	6.92544i	0.166456	+	0.288310i	0.937171	−	0.348870i	$-0.113434\pi$
$577$	3.99841	+	6.92544i	0.166456	+	0.288310i	−0.770716	+	0.637179i	$0.780101\pi$
$578$	12.0301	−	20.8367i	0.500386	−	0.866693i
$579$		0			0
$580$	−3.06677			−0.127341
$581$	9.75812	−	20.7511i	0.404835	−	0.860902i
$582$		0			0
$583$	−1.07496	−	1.86189i	−0.0445205	−	0.0771117i
$584$	−0.432504	−	0.749119i	−0.0178971	−	0.0309987i
$585$		0			0
$586$	3.38969	−	5.87112i	0.140027	−	0.242534i
$587$	−10.4049	+	18.0219i	−0.429458	+	0.743842i	−0.996825	−	0.0796223i	$-0.974629\pi$
$587$	−10.4049	+	18.0219i	−0.429458	+	0.743842i	0.567367	+	0.823465i	$0.307962\pi$
$588$		0			0
$589$	−2.93718	−	5.08734i	−0.121024	−	0.209620i
$590$	6.83676	−	11.8416i	0.281465	−	0.487511i
$591$		0			0
$592$	−4.69338	+	8.12917i	−0.192897	+	0.334107i
$593$	12.2317	−	21.1859i	0.502296	−	0.870002i	−0.497701	−	0.867349i	$-0.665822\pi$
$593$	12.2317	−	21.1859i	0.502296	−	0.870002i	0.999996	−	0.00265305i	$-0.000844492\pi$
$594$		0			0
$595$	38.7043	−	3.26027i	1.58672	−	0.133658i
$596$	0.802500	−	1.38997i	0.0328717	−	0.0569354i
$597$		0			0
$598$	4.53319	+	1.41998i	0.185376	+	0.0580672i
$599$	22.4292	+	38.8484i	0.916431	+	1.58730i	0.804793	+	0.593555i	$0.202276\pi$
$599$	22.4292	+	38.8484i	0.916431	+	1.58730i	0.111638	+	0.993749i	$0.464390\pi$
$600$		0			0
$601$	12.2159	−	21.1585i	0.498296	−	0.863073i	−0.501702	−	0.865040i	$-0.667293\pi$
$601$	12.2159	−	21.1585i	0.498296	−	0.863073i	0.999998	+	0.00196699i	$0.000626114\pi$
$602$	14.9785	+	21.5392i	0.610477	+	0.877872i
$603$		0			0
$604$	−20.4834			−0.833457
$605$	11.7166	−	20.2937i	0.476347	−	0.825058i
$606$		0			0
$607$	−36.1822			−1.46859			−0.734296	−	0.678829i	$-0.762488\pi$
$607$	−36.1822			−1.46859			−0.734296	+	0.678829i	$0.762488\pi$
$608$	0.754098	−	1.30614i	0.0305827	−	0.0529708i
$609$		0			0
$610$	−11.0329			−0.446709
$611$	−1.30016	−	0.407263i	−0.0525990	−	0.0164761i
$612$		0			0
$613$	6.21294			0.250938			0.125469	−	0.992098i	$-0.459956\pi$
$613$	6.21294			0.250938			0.125469	+	0.992098i	$0.459956\pi$
$614$	−0.638435	−	1.10580i	−0.0257652	−	0.0446266i
$615$		0			0
$616$	−0.989151	+	2.10348i	−0.0398540	+	0.0847516i
$617$	−21.8788	−	37.8953i	−0.880809	−	1.52561i	−0.850443	−	0.526067i	$-0.823666\pi$
$617$	−21.8788	−	37.8953i	−0.880809	−	1.52561i	−0.0303660	−	0.999539i	$-0.509667\pi$
$618$		0			0
$619$	9.54369	+	16.5301i	0.383593	+	0.664403i	0.991573	−	0.129550i	$-0.0413532\pi$
$619$	9.54369	+	16.5301i	0.383593	+	0.664403i	−0.607980	+	0.793952i	$0.708020\pi$
$620$	−4.46177	+	7.72801i	−0.179189	+	0.310364i
$621$		0			0
$622$	−12.4336	+	21.5357i	−0.498544	+	0.863503i
$623$	33.8354	−	2.85013i	1.35559	−	0.114188i
$624$		0			0
$625$	13.0913	−	22.6748i	0.523653	−	0.906993i
$626$	26.3203			1.05197
$627$		0			0
$628$	10.3292			0.412182
$629$	60.1486			2.39828
$630$		0			0
$631$	−11.2873	−	19.5502i	−0.449340	−	0.778280i	0.549003	−	0.835820i	$-0.315008\pi$
$631$	−11.2873	−	19.5502i	−0.449340	−	0.778280i	−0.998343	+	0.0575405i	$0.981674\pi$
$632$	4.18014	−	7.24022i	0.166277	−	0.288000i
$633$		0			0
$634$	−18.6724			−0.741576
$635$	9.76032	+	16.9054i	0.387327	+	0.670869i
$636$		0			0
$637$	−15.4561	+	19.9527i	−0.612393	+	0.790554i
$638$	−1.17603			−0.0465593
$639$		0			0
$640$	−2.29105			−0.0905618
$641$	10.9122	−	18.9004i	0.431005	−	0.746523i	−0.565955	−	0.824436i	$-0.691492\pi$
$641$	10.9122	−	18.9004i	0.431005	−	0.746523i	0.996960	+	0.0779133i	$0.0248257\pi$
$642$		0			0
$643$	7.72503	+	13.3801i	0.304645	+	0.527661i	0.977182	−	0.212402i	$-0.0681287\pi$
$643$	7.72503	+	13.3801i	0.304645	+	0.527661i	−0.672537	+	0.740064i	$0.734795\pi$
$644$	1.48337	−	3.15446i	0.0584530	−	0.124303i
$645$		0			0
$646$	−9.66426			−0.380235
$647$	−10.7846			−0.423986			−0.211993	−	0.977271i	$-0.567995\pi$
$647$	−10.7846			−0.423986			−0.211993	+	0.977271i	$0.567995\pi$
$648$		0			0
$649$	2.62172	−	4.54094i	0.102911	−	0.178248i
$650$	−0.856453	−	0.268275i	−0.0335928	−	0.0105226i
$651$		0			0
$652$	3.44890	−	5.97367i	0.135069	−	0.233947i
$653$	−10.1666	−	17.6091i	−0.397850	−	0.689096i	0.595611	−	0.803273i	$-0.296910\pi$
$653$	−10.1666	−	17.6091i	−0.397850	−	0.689096i	−0.993460	+	0.114178i	$0.963577\pi$
$654$		0			0
$655$	−5.77264	−	9.99850i	−0.225556	−	0.390674i
$656$	3.60390			0.140709
$657$		0			0
$658$	−0.425445	+	0.904730i	−0.0165856	+	0.0352700i
$659$	−15.1395	−	26.2224i	−0.589752	−	1.02148i	−0.994265	−	0.106948i	$-0.965892\pi$
$659$	−15.1395	−	26.2224i	−0.589752	−	1.02148i	0.404512	−	0.914532i	$-0.367441\pi$
$660$		0			0
$661$	9.88743			0.384577			0.192288	−	0.981338i	$-0.438409\pi$
$661$	9.88743			0.384577			0.192288	+	0.981338i	$0.438409\pi$
$662$	18.0242	+	31.2189i	0.700531	+	1.21336i
$663$		0			0
$664$	8.66710			0.336349
$665$	−5.21943	−	7.50560i	−0.202401	−	0.291055i
$666$		0			0
$667$	1.76362			0.0682875
$668$	−9.73115	−	16.8549i	−0.376510	−	0.652134i
$669$		0			0
$670$	−22.3606			−0.863864
$671$	−4.23082			−0.163329
$672$		0			0
$673$	−7.13518	+	12.3585i	−0.275041	+	0.476385i	−0.970146	−	0.242524i	$-0.922025\pi$
$673$	−7.13518	+	12.3585i	−0.275041	+	0.476385i	0.695104	+	0.718909i	$0.255358\pi$
$674$	8.49441	+	14.7128i	0.327193	+	0.566714i
$675$		0			0
$676$	1.08449	−	12.9547i	0.0417111	−	0.498257i
$677$	−16.7860	+	29.0742i	−0.645139	+	1.11741i	0.339130	+	0.940739i	$0.389867\pi$
$677$	−16.7860	+	29.0742i	−0.645139	+	1.11741i	−0.984269	+	0.176674i	$0.943466\pi$
$678$		0			0
$679$	−23.2183	+	1.95580i	−0.891036	+	0.0750567i
$680$	7.34033	+	12.7138i	0.281489	+	0.487553i
$681$		0			0
$682$	−1.71097	+	2.96349i	−0.0655164	+	0.113478i
$683$	−8.84505	+	15.3201i	−0.338446	+	0.586206i	−0.984141	−	0.177390i	$-0.943235\pi$
$683$	−8.84505	+	15.3201i	−0.338446	+	0.586206i	0.645694	+	0.763596i	$0.276568\pi$
$684$		0			0
$685$	−21.7023	−	37.5894i	−0.829201	−	1.43622i
$686$	12.9683	+	13.2221i	0.495132	+	0.504821i
$687$		0			0
$688$	−4.95801	+	8.58752i	−0.189022	+	0.327396i
$689$	6.49395	−	5.97303i	0.247400	−	0.227554i
$690$		0			0
$691$	−19.1359	−	33.1443i	−0.727963	−	1.26087i	−0.957743	−	0.287626i	$-0.907134\pi$
$691$	−19.1359	−	33.1443i	−0.727963	−	1.26087i	0.229780	−	0.973243i	$-0.426199\pi$
$692$	11.0069	−	19.0645i	0.418420	−	0.724725i
$693$		0			0
$694$	12.0361			0.456884
$695$	−2.58962			−0.0982299
$696$		0			0
$697$	−11.5466	−	19.9992i	−0.437358	−	0.757526i
$698$	−22.9088			−0.867110
$699$		0			0
$700$	−0.280252	+	0.595970i	−0.0105925	+	0.0225255i
$701$	29.3574			1.10882			0.554408	−	0.832245i	$-0.312945\pi$
$701$	29.3574			1.10882			0.554408	+	0.832245i	$0.312945\pi$
$702$		0			0
$703$	−7.07854	−	12.2604i	−0.266972	−	0.462409i
$704$	−0.878558			−0.0331119
$705$		0			0
$706$	−12.1583	−	21.0588i	−0.457584	−	0.792558i
$707$	−11.3194	+	24.0714i	−0.425711	+	0.905296i
$708$		0			0
$709$	−1.32163			−0.0496347			−0.0248174	−	0.999692i	$-0.507900\pi$
$709$	−1.32163			−0.0496347			−0.0248174	+	0.999692i	$0.507900\pi$
$710$	2.34623	+	4.06379i	0.0880524	+	0.152511i
$711$		0			0
$712$	6.41693	+	11.1145i	0.240485	+	0.416532i
$713$	2.56584	−	4.44416i	0.0960915	−	0.166435i
$714$		0			0
$715$	−6.92551	−	2.16935i	−0.259000	−	0.0811291i
$716$	−4.90819	+	8.50123i	−0.183428	+	0.317706i
$717$		0			0
$718$	28.9467			1.08028
$719$	−24.7181			−0.921830			−0.460915	−	0.887444i	$-0.652479\pi$
$719$	−24.7181			−0.921830			−0.460915	+	0.887444i	$0.652479\pi$
$720$		0			0
$721$	−18.6697	−	26.8472i	−0.695295	−	0.999841i
$722$	−8.36267	−	14.4846i	−0.311226	−	0.539060i
$723$		0			0
$724$	−11.4876	+	19.8972i	−0.426935	+	0.739473i
$725$	−0.333199			−0.0123747
$726$		0			0
$727$	8.76033			0.324903			0.162451	−	0.986717i	$-0.448060\pi$
$727$	8.76033			0.324903			0.162451	+	0.986717i	$0.448060\pi$
$728$	−9.31046	−	2.07733i	−0.345069	−	0.0769909i
$729$		0			0
$730$	−0.990889	−	1.71627i	−0.0366744	−	0.0635220i
$731$	63.5401			2.35011
$732$		0			0
$733$	−6.38026	+	11.0509i	−0.235660	+	0.408176i	−0.959464	−	0.281830i	$-0.909059\pi$
$733$	−6.38026	+	11.0509i	−0.235660	+	0.408176i	0.723804	+	0.690006i	$0.242392\pi$
$734$	−13.5022	−	23.3866i	−0.498377	−	0.863214i
$735$		0			0
$736$	1.31752			0.0485645
$737$	−8.57469			−0.315853
$738$		0			0
$739$	21.6648			0.796953			0.398476	−	0.917179i	$-0.369539\pi$
$739$	21.6648			0.796953			0.398476	+	0.917179i	$0.369539\pi$
$740$	−10.7528	+	18.6243i	−0.395280	+	0.684645i
$741$		0			0
$742$	−3.69644	−	5.31552i	−0.135701	−	0.195139i
$743$	−6.46703	+	11.2012i	−0.237252	+	0.410933i	−0.959925	−	0.280258i	$-0.909580\pi$
$743$	−6.46703	+	11.2012i	−0.237252	+	0.410933i	0.722673	+	0.691191i	$0.242913\pi$
$744$		0			0
$745$	1.83857	−	3.18449i	0.0673599	−	0.116671i
$746$	9.61751	+	16.6580i	0.352122	+	0.609893i
$747$		0			0
$748$	2.81482	+	4.87541i	0.102920	+	0.178263i
$749$	17.9490	−	1.51194i	0.655844	−	0.0552452i
$750$		0			0
$751$	−4.30364	−	7.45412i	−0.157042	−	0.272005i	0.776759	−	0.629798i	$-0.216862\pi$
$751$	−4.30364	−	7.45412i	−0.157042	−	0.272005i	−0.933801	+	0.357794i	$0.883529\pi$
$752$	−0.377877			−0.0137798
$753$		0			0
$754$	−1.05344	−	4.70998i	−0.0383640	−	0.171527i
$755$	−46.9285			−1.70790
$756$		0			0
$757$	7.93369	−	13.7416i	0.288355	−	0.499445i	−0.685062	−	0.728484i	$-0.740225\pi$
$757$	7.93369	−	13.7416i	0.288355	−	0.499445i	0.973417	+	0.229039i	$0.0735584\pi$
$758$	−32.3103			−1.17356
$759$		0			0
$760$	1.72768	−	2.99243i	0.0626695	−	0.108547i
$761$	−26.0348			−0.943761			−0.471880	−	0.881663i	$-0.656425\pi$
$761$	−26.0348			−0.943761			−0.471880	+	0.881663i	$0.656425\pi$
$762$		0			0
$763$	2.42925	−	0.204628i	0.0879446	−	0.00740804i
$764$	−4.84536	+	8.39241i	−0.175299	+	0.303627i
$765$		0			0
$766$	15.7111	+	27.2125i	0.567667	+	0.983228i
$767$	20.5349	+	6.43235i	0.741472	+	0.232259i
$768$		0			0
$769$	18.9239	−	32.7772i	0.682415	−	1.18198i	−0.291827	−	0.956471i	$-0.594263\pi$
$769$	18.9239	−	32.7772i	0.682415	−	1.18198i	0.974242	−	0.225506i	$-0.0724036\pi$
$770$	−2.26620	+	4.81918i	−0.0816681	+	0.173671i
$771$		0			0
$772$	10.5533	−	18.2789i	0.379823	−	0.657873i
$773$	21.3629	−	37.0016i	0.768370	−	1.33086i	−0.170076	−	0.985431i	$-0.554401\pi$
$773$	21.3629	−	37.0016i	0.768370	−	1.33086i	0.938446	−	0.345425i	$-0.112265\pi$
$774$		0			0
$775$	−0.484762	+	0.839632i	−0.0174132	+	0.0301605i
$776$	−4.40338	−	7.62688i	−0.158072	−	0.273789i
$777$		0			0
$778$	2.89119	−	5.00769i	0.103654	−	0.179534i
$779$	−2.71770	+	4.70719i	−0.0973715	+	0.168652i
$780$		0			0
$781$	0.899716	+	1.55835i	0.0321944	+	0.0557623i
$782$	−4.22122	−	7.31137i	−0.150950	−	0.261454i
$783$		0			0
$784$	−2.43658	+	6.56225i	−0.0870206	+	0.234366i
$785$	23.6648			0.844634
$786$		0			0
$787$	−3.51846	+	6.09415i	−0.125419	+	0.217233i	−0.921897	−	0.387435i	$-0.873361\pi$
$787$	−3.51846	+	6.09415i	−0.125419	+	0.217233i	0.796477	+	0.604668i	$0.206694\pi$
$788$	6.76019	+	11.7090i	0.240822	+	0.417116i
$789$		0			0
$790$	9.57692	−	16.5877i	0.340732	−	0.590165i
$791$	29.9920	−	2.52638i	1.06639	−	0.0898279i
$792$		0			0
$793$	−3.78980	−	16.9444i	−0.134580	−	0.601713i
$794$	3.49354	+	6.05099i	0.123981	+	0.214742i
$795$		0			0
$796$	3.79449	+	6.57226i	0.134492	+	0.232947i
$797$	−6.48013	−	11.2239i	−0.229538	−	0.397572i	0.728133	−	0.685436i	$-0.240388\pi$
$797$	−6.48013	−	11.2239i	−0.229538	−	0.397572i	−0.957671	+	0.287864i	$0.907055\pi$
$798$		0			0
$799$	1.21069	+	2.09697i	0.0428310	+	0.0741854i
$800$	−0.248918			−0.00880058
$801$		0			0
$802$	2.96749	−	5.13984i	0.104786	−	0.181494i
$803$	−0.379979	−	0.658144i	−0.0134092	−	0.0232254i
$804$		0			0
$805$	3.39848	−	7.22704i	0.119781	−	0.254720i
$806$	−13.4014	−	4.19784i	−0.472043	−	0.147863i
$807$		0			0
$808$	−10.0539			−0.353693
$809$	−24.0929			−0.847060			−0.423530	−	0.905882i	$-0.639209\pi$
$809$	−24.0929			−0.847060			−0.423530	+	0.905882i	$0.639209\pi$
$810$		0			0
$811$	−0.569121			−0.0199845			−0.00999227	−	0.999950i	$-0.503181\pi$
$811$	−0.569121			−0.0199845			−0.00999227	+	0.999950i	$0.503181\pi$
$812$	−3.52907	+	0.297272i	−0.123846	+	0.0104322i
$813$		0			0
$814$	−4.12340	+	7.14194i	−0.144525	+	0.250325i
$815$	7.90160	−	13.6860i	0.276781	−	0.479399i
$816$		0			0
$817$	−7.47765	−	12.9517i	−0.261610	−	0.453122i
$818$	14.7785			0.516717
$819$		0			0
$820$	8.25672			0.288337
$821$	25.7343	+	44.5731i	0.898134	+	1.55561i	0.829878	+	0.557945i	$0.188410\pi$
$821$	25.7343	+	44.5731i	0.898134	+	1.55561i	0.0682560	+	0.997668i	$0.478257\pi$
$822$		0			0
$823$	−19.4326	+	33.6583i	−0.677379	+	1.17326i	0.298388	+	0.954445i	$0.403551\pi$
$823$	−19.4326	+	33.6583i	−0.677379	+	1.17326i	−0.975767	+	0.218811i	$0.929782\pi$
$824$	6.17983	−	10.7038i	0.215284	−	0.372884i
$825$		0			0
$826$	6.71951	−	14.2894i	0.233802	−	0.497191i
$827$	−28.2170			−0.981203			−0.490601	−	0.871384i	$-0.663223\pi$
$827$	−28.2170			−0.981203			−0.490601	+	0.871384i	$0.663223\pi$
$828$		0			0
$829$	−11.5781			−0.402124			−0.201062	−	0.979579i	$-0.564439\pi$
$829$	−11.5781			−0.402124			−0.201062	+	0.979579i	$0.564439\pi$
$830$	19.8568			0.689239
$831$		0			0
$832$	−0.786978	−	3.51862i	−0.0272835	−	0.121986i
$833$	44.2227	−	7.50347i	1.53223	−	0.259980i
$834$		0			0
$835$	−22.2946	−	38.6153i	−0.771536	−	1.33634i
$836$	0.662519	−	1.14752i	0.0229137	−	0.0396877i
$837$		0			0
$838$	10.1467			0.350512
$839$	15.9568	+	27.6379i	0.550889	+	0.954167i	0.998211	+	0.0597941i	$0.0190444\pi$
$839$	15.9568	+	27.6379i	0.550889	+	0.954167i	−0.447322	+	0.894373i	$0.647622\pi$
$840$		0			0
$841$	13.6041	+	23.5630i	0.469107	+	0.812516i
$842$	3.85442	+	6.67606i	0.132832	+	0.230072i
$843$		0			0
$844$	−6.06832	−	10.5106i	−0.208880	−	0.361791i
$845$	2.48462	−	29.6799i	0.0854736	−	1.02102i
$846$		0			0
$847$	11.5157	−	24.4886i	0.395683	−	0.841439i
$848$	1.22356	−	2.11926i	0.0420171	−	0.0727757i
$849$		0			0
$850$	0.797511	+	1.38133i	0.0273544	+	0.0473792i
$851$	6.18362	−	10.7103i	0.211972	−	0.367146i
$852$		0			0
$853$	6.06219			0.207565			0.103783	−	0.994600i	$-0.466905\pi$
$853$	6.06219			0.207565			0.103783	+	0.994600i	$0.466905\pi$
$854$	−12.6960	+	1.06945i	−0.434449	+	0.0365960i
$855$		0			0
$856$	3.40406	+	5.89601i	0.116348	+	0.201521i
$857$	−27.2702	−	47.2333i	−0.931531	−	1.61346i	−0.780706	−	0.624899i	$-0.785140\pi$
$857$	−27.2702	−	47.2333i	−0.931531	−	1.61346i	−0.150825	−	0.988560i	$-0.548193\pi$
$858$		0			0
$859$	27.3472	−	47.3667i	0.933074	−	1.61613i	0.155042	−	0.987908i	$-0.450449\pi$
$859$	27.3472	−	47.3667i	0.933074	−	1.61613i	0.778033	−	0.628224i	$-0.216218\pi$
$860$	−11.3591	+	19.6745i	−0.387341	+	0.670894i
$861$		0			0
$862$	−17.8893	−	30.9851i	−0.609311	−	1.05536i
$863$	2.28666	−	3.96062i	0.0778389	−	0.134821i	−0.824478	−	0.565893i	$-0.808531\pi$
$863$	2.28666	−	3.96062i	0.0778389	−	0.134821i	0.902317	+	0.431073i	$0.141865\pi$
$864$		0			0
$865$	25.2174	−	43.6778i	0.857418	−	1.48509i
$866$	6.32535	−	10.9558i	0.214944	−	0.372294i
$867$		0			0
$868$	−4.38525	+	9.32545i	−0.148845	+	0.316527i
$869$	3.67250	−	6.36095i	0.124581	−	0.215780i
$870$		0			0
$871$	−7.68087	−	34.3416i	−0.260256	−	1.16362i
$872$	0.460710	+	0.797973i	0.0156016	+	0.0270228i
$873$		0			0
$874$	−0.993540	+	1.72086i	−0.0336070	+	0.0582090i
$875$	12.2552	−	26.0613i	0.414301	−	0.881031i
$876$		0			0
$877$	58.7214			1.98288			0.991440	−	0.130560i	$-0.0416775\pi$
$877$	58.7214			1.98288			0.991440	+	0.130560i	$0.0416775\pi$
$878$	−13.6023	+	23.5598i	−0.459054	+	0.795105i
$879$		0			0
$880$	−2.01282			−0.0678522
$881$	−6.95948	+	12.0542i	−0.234471	+	0.406115i	−0.959119	−	0.283004i	$-0.908669\pi$
$881$	−6.95948	+	12.0542i	−0.234471	+	0.406115i	0.724648	+	0.689119i	$0.242002\pi$
$882$		0			0
$883$	40.5135			1.36339			0.681695	−	0.731637i	$-0.261243\pi$
$883$	40.5135			1.36339			0.681695	+	0.731637i	$0.261243\pi$
$884$	−17.0046	+	15.6405i	−0.571926	+	0.526048i
$885$		0			0
$886$	3.49721			0.117491
$887$	23.9892	+	41.5506i	0.805480	+	1.39513i	0.915967	+	0.401255i	$0.131426\pi$
$887$	23.9892	+	41.5506i	0.805480	+	1.39513i	−0.110487	+	0.993878i	$0.535241\pi$
$888$		0			0
$889$	12.8703	+	18.5077i	0.431657	+	0.620727i
$890$	14.7015	+	25.4638i	0.492796	+	0.853548i
$891$		0			0
$892$	−11.0968	−	19.2202i	−0.371547	−	0.643538i
$893$	0.284957	−	0.493560i	0.00953572	−	0.0165163i
$894$		0			0
$895$	−11.2449	+	19.4768i	−0.375876	+	0.651036i
$896$	−2.63641	+	0.222079i	−0.0880764	+	0.00741914i
$897$		0			0
$898$	8.08366	−	14.0013i	0.269755	−	0.467230i
$899$	−5.21373			−0.173888
$900$		0			0
$901$	−15.6807			−0.522398
$902$	3.16623			0.105424
$903$		0			0
$904$	5.68802	+	9.85195i	0.189181	+	0.327671i
$905$	−26.3188	+	45.5854i	−0.874866	+	1.51531i
$906$		0			0
$907$	−25.3615			−0.842114			−0.421057	−	0.907034i	$-0.638341\pi$
$907$	−25.3615			−0.842114			−0.421057	+	0.907034i	$0.638341\pi$
$908$	−12.2142	−	21.1556i	−0.405343	−	0.702074i
$909$		0			0
$910$	−21.3308	−	4.75927i	−0.707107	−	0.157768i
$911$	50.6581			1.67838			0.839189	−	0.543840i	$-0.183030\pi$
$911$	50.6581			1.67838			0.839189	+	0.543840i	$0.183030\pi$
$912$		0			0
$913$	7.61455			0.252005
$914$	13.1305	−	22.7426i	0.434317	−	0.752259i
$915$		0			0
$916$	−14.9717	−	25.9317i	−0.494679	−	0.856809i
$917$	−7.61202	−	10.9462i	−0.251371	−	0.361474i
$918$		0			0
$919$	−25.1562			−0.829825			−0.414913	−	0.909861i	$-0.636188\pi$
$919$	−25.1562			−0.829825			−0.414913	+	0.909861i	$0.636188\pi$
$920$	3.01851			0.0995173
$921$		0			0
$922$	−4.94386	+	8.56302i	−0.162817	+	0.282008i
$923$	−5.43527	+	4.99927i	−0.178904	+	0.164553i
$924$		0			0
$925$	−1.16827	+	2.02350i	−0.0384124	+	0.0665322i
$926$	−7.10408	−	12.3046i	−0.233455	−	0.404355i
$927$		0			0
$928$	−0.669294	−	1.15925i	−0.0219706	−	0.0380543i
$929$	−30.2210			−0.991519			−0.495759	−	0.868460i	$-0.665110\pi$
$929$	−30.2210			−0.991519			−0.495759	+	0.868460i	$0.665110\pi$
$930$		0			0
$931$	−6.73377	−	8.13108i	−0.220691	−	0.266486i
$932$	11.4574	+	19.8448i	0.375300	+	0.650039i
$933$		0			0
$934$	2.95000			0.0965271
$935$	6.44890	+	11.1698i	0.210902	+	0.365292i
$936$		0			0
$937$	−33.2013			−1.08464			−0.542320	−	0.840172i	$-0.682454\pi$
$937$	−33.2013			−1.08464			−0.542320	+	0.840172i	$0.682454\pi$
$938$	−25.7313	+	2.16748i	−0.840157	+	0.0707709i
$939$		0			0
$940$	−0.865737			−0.0282372
$941$	−10.3309	−	17.8937i	−0.336779	−	0.583318i	0.647046	−	0.762451i	$-0.276004\pi$
$941$	−10.3309	−	17.8937i	−0.336779	−	0.583318i	−0.983825	+	0.179133i	$0.942671\pi$
$942$		0			0
$943$	−4.74821			−0.154623
$944$	5.96823			0.194249
$945$		0			0
$946$	−4.35590	+	7.54463i	−0.141622	+	0.245297i
$947$	2.50723	+	4.34266i	0.0814741	+	0.141117i	0.903883	−	0.427779i	$-0.140704\pi$
$947$	2.50723	+	4.34266i	0.0814741	+	0.141117i	−0.822409	+	0.568896i	$0.807371\pi$
$948$		0			0
$949$	2.29549	−	2.11135i	0.0745148	−	0.0685375i
$950$	0.187709	−	0.325121i	0.00609008	−	0.0105483i
$951$		0			0
$952$	9.67923	+	13.9188i	0.313706	+	0.451112i
$953$	−20.4600	−	35.4378i	−0.662765	−	1.14794i	−0.979886	−	0.199558i	$-0.936049\pi$
$953$	−20.4600	−	35.4378i	−0.662765	−	1.14794i	0.317121	−	0.948385i	$-0.397284\pi$
$954$		0			0
$955$	−11.1010	+	19.2275i	−0.359219	+	0.622186i
$956$	−0.519960	+	0.900598i	−0.0168167	+	0.0291274i
$957$		0			0
$958$	−9.90480	−	17.1556i	−0.320010	−	0.554273i
$959$	−28.6174	−	41.1521i	−0.924104	−	1.32887i
$960$		0			0
$961$	7.91468	−	13.7086i	0.255312	−	0.442214i
$962$	−32.2970	−	10.1167i	−1.04130	−	0.326176i
$963$		0			0
$964$	−3.23944	−	5.61088i	−0.104335	−	0.180714i
$965$	24.1783	−	41.8780i	0.778326	−	1.34810i
$966$		0			0
$967$	48.1932			1.54979			0.774894	−	0.632091i	$-0.217803\pi$
$967$	48.1932			1.54979			0.774894	+	0.632091i	$0.217803\pi$
$968$	10.2281			0.328745
$969$		0			0
$970$	−10.0884	−	17.4736i	−0.323918	−	0.561043i
$971$	32.1224			1.03086			0.515428	−	0.856933i	$-0.327633\pi$
$971$	32.1224			1.03086			0.515428	+	0.856933i	$0.327633\pi$
$972$		0			0
$973$	−2.97999	+	0.251020i	−0.0955341	+	0.00804735i
$974$	12.5946			0.403556
$975$		0			0
$976$	−2.40782	−	4.17047i	−0.0770725	−	0.133493i
$977$	−19.9484			−0.638205			−0.319102	−	0.947720i	$-0.603381\pi$
$977$	−19.9484			−0.638205			−0.319102	+	0.947720i	$0.603381\pi$
$978$		0			0
$979$	5.63764	+	9.76469i	0.180180	+	0.312081i
$980$	−5.58233	+	15.0344i	−0.178321	+	0.480258i
$981$		0			0
$982$	−11.6256			−0.370988
$983$	−4.74110	−	8.21182i	−0.151218	−	0.261916i	0.780458	−	0.625208i	$-0.214986\pi$
$983$	−4.74110	−	8.21182i	−0.151218	−	0.261916i	−0.931675	+	0.363292i	$0.881653\pi$
$984$		0			0
$985$	15.4880	+	26.8259i	0.493487	+	0.854745i
$986$	−4.28872	+	7.42827i	−0.136581	+	0.236564i
$987$		0			0
$988$	5.18925	+	1.62548i	0.165092	+	0.0517135i
$989$	6.53228	−	11.3142i	0.207714	−	0.359772i
$990$		0			0
$991$	25.5305			0.811002			0.405501	−	0.914095i	$-0.367097\pi$
$991$	25.5305			0.811002			0.405501	+	0.914095i	$0.367097\pi$
$992$	−3.89495			−0.123665
$993$		0			0
$994$	3.09382	+	4.44895i	0.0981301	+	0.141112i
$995$	8.69338	+	15.0574i	0.275599	+	0.477351i
$996$		0			0
$997$	−26.0704	+	45.1552i	−0.825657	+	1.43008i	0.0757592	+	0.997126i	$0.475862\pi$
$997$	−26.0704	+	45.1552i	−0.825657	+	1.43008i	−0.901416	+	0.432954i	$0.857471\pi$
$998$	12.4543			0.394233
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.p.i.919.2		8
3.2	odd	2		546.2.k.b.373.3	yes	8
7.4	even	3		1638.2.m.g.1621.2		8
13.3	even	3		1638.2.m.g.289.2		8
21.11	odd	6		546.2.j.d.529.3	yes	8
39.29	odd	6		546.2.j.d.289.3	✓	8
91.81	even	3	inner	1638.2.p.i.991.2		8
273.263	odd	6		546.2.k.b.445.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.d.289.3	✓	8	39.29	odd	6
546.2.j.d.529.3	yes	8	21.11	odd	6
546.2.k.b.373.3	yes	8	3.2	odd	2
546.2.k.b.445.3	yes	8	273.263	odd	6
1638.2.m.g.289.2		8	13.3	even	3
1638.2.m.g.1621.2		8	7.4	even	3
1638.2.p.i.919.2		8	1.1	even	1	trivial
1638.2.p.i.991.2		8	91.81	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.p (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.14553 + 1.98411i) q^{5} +(-1.12588 + 2.39424i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.14553 + 1.98411i) q^{5} +(-1.12588 + 2.39424i) q^{7} -1.00000 q^{8} -2.29105 q^{10} -0.878558 q^{11} +(-0.786978 - 3.51862i) q^{13} +(-2.63641 + 0.222079i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.20391 + 5.54934i) q^{17} +1.50820 q^{19} +(-1.14553 - 1.98411i) q^{20} +(-0.439279 - 0.760853i) q^{22} +(0.658760 + 1.14101i) q^{23} +(-0.124459 - 0.215569i) q^{25} +(2.65372 - 2.44085i) q^{26} +(-1.51053 - 2.17216i) q^{28} +(0.669294 - 1.15925i) q^{29} +(-1.94748 - 3.37313i) q^{31} +(0.500000 - 0.866025i) q^{32} -6.40782 q^{34} +(-3.46071 - 4.97654i) q^{35} +(-4.69338 - 8.12917i) q^{37} +(0.754098 + 1.30614i) q^{38} +(1.14553 - 1.98411i) q^{40} +(-1.80195 + 3.12107i) q^{41} +(-4.95801 - 8.58752i) q^{43} +(0.439279 - 0.760853i) q^{44} +(-0.658760 + 1.14101i) q^{46} +(0.188939 - 0.327251i) q^{47} +(-4.46478 - 5.39126i) q^{49} +(0.124459 - 0.215569i) q^{50} +(3.44070 + 1.07777i) q^{52} +(1.22356 + 2.11926i) q^{53} +(1.00641 - 1.74315i) q^{55} +(1.12588 - 2.39424i) q^{56} +1.33859 q^{58} +(-2.98411 + 5.16864i) q^{59} +4.81564 q^{61} +(1.94748 - 3.37313i) q^{62} +1.00000 q^{64} +(7.88282 + 2.46922i) q^{65} +9.75996 q^{67} +(-3.20391 - 5.54934i) q^{68} +(2.57945 - 5.48533i) q^{70} +(-1.02408 - 1.77376i) q^{71} +(0.432504 + 0.749119i) q^{73} +(4.69338 - 8.12917i) q^{74} +(-0.754098 + 1.30614i) q^{76} +(0.989151 - 2.10348i) q^{77} +(-4.18014 + 7.24022i) q^{79} +2.29105 q^{80} -3.60390 q^{82} -8.66710 q^{83} +(-7.34033 - 12.7138i) q^{85} +(4.95801 - 8.58752i) q^{86} +0.878558 q^{88} +(-6.41693 - 11.1145i) q^{89} +(9.31046 + 2.07733i) q^{91} -1.31752 q^{92} +0.377877 q^{94} +(-1.72768 + 2.99243i) q^{95} +(4.40338 + 7.62688i) q^{97} +(2.43658 - 6.56225i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8	\( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8} - 4 q^{10} - 12 q^{11} - 11 q^{13} + 3 q^{14} - 4 q^{16} - 4 q^{17} - 12 q^{19} - 2 q^{20} - 6 q^{22} + 10 q^{23} - 18 q^{25} - 10 q^{26} - 2 q^{29} + 6 q^{31} + 4 q^{32} - 8 q^{34} - 18 q^{35} - 28 q^{37} - 6 q^{38} + 2 q^{40} - 6 q^{43} + 6 q^{44} - 10 q^{46} - q^{47} - 7 q^{49} + 18 q^{50} + q^{52} - 7 q^{53} + q^{55} - 3 q^{56} - 4 q^{58} - 2 q^{59} - 48 q^{61} - 6 q^{62} + 8 q^{64} - 19 q^{65} + 30 q^{67} - 4 q^{68} - 18 q^{70} - 6 q^{71} + q^{73} + 28 q^{74} + 6 q^{76} + 22 q^{77} - 12 q^{79} + 4 q^{80} + 32 q^{83} - 13 q^{85} + 6 q^{86} + 12 q^{88} - 25 q^{89} + 34 q^{91} - 20 q^{92} - 2 q^{94} + 8 q^{95} - q^{97} - 2 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8 - 4 * q^10 - 12 * q^11 - 11 * q^13 + 3 * q^14 - 4 * q^16 - 4 * q^17 - 12 * q^19 - 2 * q^20 - 6 * q^22 + 10 * q^23 - 18 * q^25 - 10 * q^26 - 2 * q^29 + 6 * q^31 + 4 * q^32 - 8 * q^34 - 18 * q^35 - 28 * q^37 - 6 * q^38 + 2 * q^40 - 6 * q^43 + 6 * q^44 - 10 * q^46 - q^47 - 7 * q^49 + 18 * q^50 + q^52 - 7 * q^53 + q^55 - 3 * q^56 - 4 * q^58 - 2 * q^59 - 48 * q^61 - 6 * q^62 + 8 * q^64 - 19 * q^65 + 30 * q^67 - 4 * q^68 - 18 * q^70 - 6 * q^71 + q^73 + 28 * q^74 + 6 * q^76 + 22 * q^77 - 12 * q^79 + 4 * q^80 + 32 * q^83 - 13 * q^85 + 6 * q^86 + 12 * q^88 - 25 * q^89 + 34 * q^91 - 20 * q^92 - 2 * q^94 + 8 * q^95 - q^97 - 2 * q^98

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