LMFDB - Embedded newform 1638.2.m.g.1621.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(289,1638)]

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, 2]))

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

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

chi := DirichletCharacter("1638.289");

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.m (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			1621.2
Root			$-1.38232 - 0.298668i$ of defining polynomial
Character	$\chi$	$=$	1638.1621
Dual form			1638.2.m.g.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(-1.14553 - 1.98411i) q^{5} +(2.63641 + 0.222079i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.14553 - 1.98411i) q^{5} +(2.63641 + 0.222079i) q^{7} -1.00000 q^{8} +(1.14553 + 1.98411i) q^{10} +(0.439279 + 0.760853i) q^{11} +(-0.786978 - 3.51862i) q^{13} +(-2.63641 - 0.222079i) q^{14} +1.00000 q^{16} +6.40782 q^{17} +(-0.754098 + 1.30614i) q^{19} +(-1.14553 - 1.98411i) q^{20} +(-0.439279 - 0.760853i) q^{22} -1.31752 q^{23} +(-0.124459 + 0.215569i) q^{25} +(0.786978 + 3.51862i) q^{26} +(2.63641 + 0.222079i) q^{28} +(0.669294 - 1.15925i) q^{29} +(-1.94748 + 3.37313i) q^{31} -1.00000 q^{32} -6.40782 q^{34} +(-2.57945 - 5.48533i) q^{35} +9.38675 q^{37} +(0.754098 - 1.30614i) q^{38} +(1.14553 + 1.98411i) q^{40} +(-1.80195 + 3.12107i) q^{41} +(-4.95801 - 8.58752i) q^{43} +(0.439279 + 0.760853i) q^{44} +1.31752 q^{46} +(0.188939 + 0.327251i) q^{47} +(6.90136 + 1.17099i) q^{49} +(0.124459 - 0.215569i) q^{50} +(-0.786978 - 3.51862i) q^{52} +(1.22356 - 2.11926i) q^{53} +(1.00641 - 1.74315i) q^{55} +(-2.63641 - 0.222079i) q^{56} +(-0.669294 + 1.15925i) q^{58} +5.96823 q^{59} +(-2.40782 + 4.17047i) q^{61} +(1.94748 - 3.37313i) q^{62} +1.00000 q^{64} +(-6.07982 + 5.59212i) q^{65} +(-4.87998 - 8.45237i) q^{67} +6.40782 q^{68} +(2.57945 + 5.48533i) q^{70} +(-1.02408 - 1.77376i) q^{71} +(0.432504 - 0.749119i) q^{73} -9.38675 q^{74} +(-0.754098 + 1.30614i) q^{76} +(0.989151 + 2.10348i) q^{77} +(-4.18014 - 7.24022i) q^{79} +(-1.14553 - 1.98411i) q^{80} +(1.80195 - 3.12107i) q^{82} -8.66710 q^{83} +(-7.34033 - 12.7138i) q^{85} +(4.95801 + 8.58752i) q^{86} +(-0.439279 - 0.760853i) q^{88} +12.8339 q^{89} +(-1.29339 - 9.45130i) q^{91} -1.31752 q^{92} +(-0.188939 - 0.327251i) q^{94} +3.45536 q^{95} +(4.40338 + 7.62688i) q^{97} +(-6.90136 - 1.17099i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8	$ 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8} + 2 q^{10} + 6 q^{11} - 11 q^{13} + 3 q^{14} + 8 q^{16} + 8 q^{17} + 6 q^{19} - 2 q^{20} - 6 q^{22} - 20 q^{23} - 18 q^{25} + 11 q^{26} - 3 q^{28} - 2 q^{29} + 6 q^{31} - 8 q^{32} - 8 q^{34} + 18 q^{35} + 56 q^{37} - 6 q^{38} + 2 q^{40} - 6 q^{43} + 6 q^{44} + 20 q^{46} - q^{47} + 5 q^{49} + 18 q^{50} - 11 q^{52} - 7 q^{53} + q^{55} + 3 q^{56} + 2 q^{58} + 4 q^{59} + 24 q^{61} - 6 q^{62} + 8 q^{64} - 22 q^{65} - 15 q^{67} + 8 q^{68} - 18 q^{70} - 6 q^{71} + q^{73} - 56 q^{74} + 6 q^{76} + 22 q^{77} - 12 q^{79} - 2 q^{80} + 32 q^{83} - 13 q^{85} + 6 q^{86} - 6 q^{88} + 50 q^{89} - 8 q^{91} - 20 q^{92} + q^{94} - 16 q^{95} - q^{97} - 5 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8 + 2 * q^10 + 6 * q^11 - 11 * q^13 + 3 * q^14 + 8 * q^16 + 8 * q^17 + 6 * q^19 - 2 * q^20 - 6 * q^22 - 20 * q^23 - 18 * q^25 + 11 * q^26 - 3 * q^28 - 2 * q^29 + 6 * q^31 - 8 * q^32 - 8 * q^34 + 18 * q^35 + 56 * q^37 - 6 * q^38 + 2 * q^40 - 6 * q^43 + 6 * q^44 + 20 * q^46 - q^47 + 5 * q^49 + 18 * q^50 - 11 * q^52 - 7 * q^53 + q^55 + 3 * q^56 + 2 * q^58 + 4 * q^59 + 24 * q^61 - 6 * q^62 + 8 * q^64 - 22 * q^65 - 15 * q^67 + 8 * q^68 - 18 * q^70 - 6 * q^71 + q^73 - 56 * q^74 + 6 * q^76 + 22 * q^77 - 12 * q^79 - 2 * q^80 + 32 * q^83 - 13 * q^85 + 6 * q^86 - 6 * q^88 + 50 * q^89 - 8 * q^91 - 20 * q^92 + q^94 - 16 * q^95 - q^97 - 5 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.14553	−	1.98411i	−0.512295	−	0.887321i	−0.999898	−	0.0142554i	$-0.995462\pi$
$5$	−1.14553	−	1.98411i	−0.512295	−	0.887321i	0.487604	−	0.873065i	$-0.337871\pi$
$6$		0			0
$7$	2.63641	+	0.222079i	0.996471	+	0.0839380i
$7$	2.63641	+	0.222079i	0.996471	+	0.0839380i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.14553	+	1.98411i	0.362247	+	0.627430i
$11$	0.439279	+	0.760853i	0.132448	+	0.229406i	0.924619	−	0.380892i	$-0.124383\pi$
$11$	0.439279	+	0.760853i	0.132448	+	0.229406i	−0.792172	+	0.610298i	$0.791050\pi$
$12$		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
$16$	1.00000			0.250000
$17$	6.40782			1.55412			0.777062	−	0.629423i	$-0.216709\pi$
$17$	6.40782			1.55412			0.777062	+	0.629423i	$0.216709\pi$
$18$		0			0
$19$	−0.754098	+	1.30614i	−0.173002	+	0.299648i	−0.939468	−	0.342637i	$-0.888680\pi$
$19$	−0.754098	+	1.30614i	−0.173002	+	0.299648i	0.766466	+	0.642285i	$0.222013\pi$
$20$	−1.14553	−	1.98411i	−0.256147	−	0.443660i
$21$		0			0
$22$	−0.439279	−	0.760853i	−0.0936545	−	0.162214i
$23$	−1.31752			−0.274722			−0.137361	−	0.990521i	$-0.543862\pi$
$23$	−1.31752			−0.274722			−0.137361	+	0.990521i	$0.543862\pi$
$24$		0			0
$25$	−0.124459	+	0.215569i	−0.0248918	+	0.0431139i
$26$	0.786978	+	3.51862i	0.154339	+	0.690058i
$27$		0			0
$28$	2.63641	+	0.222079i	0.498235	+	0.0419690i
$29$	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	−0.986210	−	0.165501i	$-0.947076\pi$
$31$	−1.94748	+	3.37313i	−0.349777	+	0.605831i	0.636433	+	0.771332i	$0.280409\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−6.40782			−1.09893
$35$	−2.57945	−	5.48533i	−0.436007	−	0.927190i
$36$		0			0
$37$	9.38675			1.54317			0.771586	−	0.636124i	$-0.219464\pi$
$37$	9.38675			1.54317			0.771586	+	0.636124i	$0.219464\pi$
$38$	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
$46$	1.31752			0.194258
$47$	0.188939	+	0.327251i	0.0275595	+	0.0477345i	0.879476	−	0.475943i	$-0.157893\pi$
$47$	0.188939	+	0.327251i	0.0275595	+	0.0477345i	−0.851917	+	0.523677i	$0.824560\pi$
$48$		0			0
$49$	6.90136	+	1.17099i	0.985909	+	0.167284i
$50$	0.124459	−	0.215569i	0.0176012	−	0.0304861i
$51$		0			0
$52$	−0.786978	−	3.51862i	−0.109134	−	0.487944i
$53$	1.22356	−	2.11926i	0.168068	−	0.291103i	−0.769672	−	0.638439i	$-0.779580\pi$
$53$	1.22356	−	2.11926i	0.168068	−	0.291103i	0.937741	+	0.347336i	$0.112914\pi$
$54$		0			0
$55$	1.00641	−	1.74315i	0.135704	−	0.235047i
$56$	−2.63641	−	0.222079i	−0.352306	−	0.0296766i
$57$		0			0
$58$	−0.669294	+	1.15925i	−0.0878826	+	0.152217i
$59$	5.96823			0.776997			0.388498	−	0.921449i	$-0.372994\pi$
$59$	5.96823			0.776997			0.388498	+	0.921449i	$0.372994\pi$
$60$		0			0
$61$	−2.40782	+	4.17047i	−0.308290	+	0.533974i	−0.977988	−	0.208659i	$-0.933090\pi$
$61$	−2.40782	+	4.17047i	−0.308290	+	0.533974i	0.669698	+	0.742633i	$0.266423\pi$
$62$	1.94748	−	3.37313i	0.247330	−	0.428388i
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.07982	+	5.59212i	−0.754108	+	0.693617i
$66$		0			0
$67$	−4.87998	−	8.45237i	−0.596184	−	1.03262i	−0.993379	−	0.114887i	$-0.963349\pi$
$67$	−4.87998	−	8.45237i	−0.596184	−	1.03262i	0.397194	−	0.917735i	$-0.369984\pi$
$68$	6.40782			0.777062
$69$		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	−0.839605	−	0.543198i	$-0.817213\pi$
$73$	0.432504	−	0.749119i	0.0506207	−	0.0876777i	0.890225	+	0.455520i	$0.150547\pi$
$74$	−9.38675			−1.09119
$75$		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	0.529120	−	0.848547i	$-0.322522\pi$
$79$	−4.18014	−	7.24022i	−0.470303	−	0.814588i	−0.999423	+	0.0339584i	$0.989189\pi$
$80$	−1.14553	−	1.98411i	−0.128074	−	0.221830i
$81$		0			0
$82$	1.80195	−	3.12107i	0.198992	−	0.344664i
$83$	−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
$88$	−0.439279	−	0.760853i	−0.0468273	−	0.0811072i
$89$	12.8339			1.36039			0.680194	−	0.733033i	$-0.261896\pi$
$89$	12.8339			1.36039			0.680194	+	0.733033i	$0.261896\pi$
$90$		0			0
$91$	−1.29339	−	9.45130i	−0.135584	−	0.990766i
$92$	−1.31752			−0.137361
$93$		0			0
$94$	−0.188939	−	0.327251i	−0.0194875	−	0.0337534i
$95$	3.45536			0.354512
$96$		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	$0.685792\pi$
$98$	−6.90136	−	1.17099i	−0.697143	−	0.118287i
$99$		0			0
$100$	−0.124459	+	0.215569i	−0.0124459	+	0.0215569i
$101$	−5.02693	−	8.70689i	−0.500198	−	0.866368i	−1.00000		0.000228594i	$-0.999927\pi$
$101$	−5.02693	−	8.70689i	−0.500198	−	0.866368i	0.499802	−	0.866140i	$-0.333406\pi$
$102$		0			0
$103$	−6.17983	−	10.7038i	−0.608916	−	1.05467i	−0.991419	−	0.130720i	$-0.958271\pi$
$103$	−6.17983	−	10.7038i	−0.608916	−	1.05467i	0.382503	−	0.923954i	$-0.375062\pi$
$104$	0.786978	+	3.51862i	0.0771695	+	0.345029i
$105$		0			0
$106$	−1.22356	+	2.11926i	−0.118842	+	0.205841i
$107$	6.80813			0.658166			0.329083	−	0.944301i	$-0.393260\pi$
$107$	6.80813			0.658166			0.329083	+	0.944301i	$0.393260\pi$
$108$		0			0
$109$	−0.460710	+	0.797973i	−0.0441280	+	0.0764320i	−0.887246	−	0.461297i	$-0.847384\pi$
$109$	−0.460710	+	0.797973i	−0.0441280	+	0.0764320i	0.843118	+	0.537729i	$0.180718\pi$
$110$	−1.00641	+	1.74315i	−0.0959575	+	0.166203i
$111$		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
$115$	1.50925	+	2.61410i	0.140739	+	0.243767i
$116$	0.669294	−	1.15925i	0.0621424	−	0.107634i
$117$		0			0
$118$	−5.96823			−0.549420
$119$	16.8937	+	1.42304i	1.54864	+	0.130450i
$120$		0			0
$121$	5.11407	−	8.85783i	0.464915	−	0.805257i
$122$	2.40782	−	4.17047i	0.217994	−	0.377576i
$123$		0			0
$124$	−1.94748	+	3.37313i	−0.174888	+	0.302916i
$125$	−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	$0.0432679\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	6.07982	−	5.59212i	0.533235	−	0.490461i
$131$	−2.51964	−	4.36415i	−0.220142	−	0.381298i	0.734709	−	0.678383i	$-0.237319\pi$
$131$	−2.51964	−	4.36415i	−0.220142	−	0.381298i	−0.954851	+	0.297085i	$0.903986\pi$
$132$		0			0
$133$	−2.27818	+	3.27605i	−0.197543	+	0.284069i
$134$	4.87998	+	8.45237i	0.421566	+	0.730174i
$135$		0			0
$136$	−6.40782			−0.549466
$137$	18.9452			1.61860			0.809300	−	0.587395i	$-0.199847\pi$
$137$	18.9452			1.61860			0.809300	+	0.587395i	$0.199847\pi$
$138$		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	$0.818069\pi$
$140$	−2.57945	−	5.48533i	−0.218003	−	0.463595i
$141$		0			0
$142$	1.02408	+	1.77376i	0.0859392	+	0.148851i
$143$	2.33145	−	2.14443i	0.194965	−	0.179326i
$144$		0			0
$145$	−3.06677			−0.254682
$146$	−0.432504	+	0.749119i	−0.0357943	+	0.0619975i
$147$		0			0
$148$	9.38675			0.771586
$149$	0.802500	−	1.38997i	0.0657433	−	0.113871i	−0.831280	−	0.555854i	$-0.812391\pi$
$149$	0.802500	−	1.38997i	0.0657433	−	0.113871i	0.897023	+	0.441983i	$0.145725\pi$
$150$		0			0
$151$	10.2417	−	17.7391i	0.833457	−	1.44359i	−0.0618242	−	0.998087i	$-0.519692\pi$
$151$	10.2417	−	17.7391i	0.833457	−	1.44359i	0.895281	−	0.445502i	$-0.146975\pi$
$152$	0.754098	−	1.30614i	0.0611655	−	0.105942i
$153$		0			0
$154$	−0.989151	−	2.10348i	−0.0797081	−	0.169503i
$155$	8.92354			0.716756
$156$		0			0
$157$	−5.16462	+	8.94539i	−0.412182	+	0.713919i	−0.995128	−	0.0985911i	$-0.968566\pi$
$157$	−5.16462	+	8.94539i	−0.412182	+	0.713919i	0.582946	+	0.812511i	$0.301900\pi$
$158$	4.18014	+	7.24022i	0.332554	+	0.576001i
$159$		0			0
$160$	1.14553	+	1.98411i	0.0905618	+	0.156858i
$161$	−3.47353	−	0.292594i	−0.273753	−	0.0230596i
$162$		0			0
$163$	3.44890	−	5.97367i	0.270139	−	0.467894i	−0.698759	−	0.715358i	$-0.746264\pi$
$163$	3.44890	−	5.97367i	0.270139	−	0.467894i	0.968897	+	0.247464i	$0.0795972\pi$
$164$	−1.80195	+	3.12107i	−0.140709	+	0.243715i
$165$		0			0
$166$	8.66710			0.672697
$167$	−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
$172$	−4.95801	−	8.58752i	−0.378045	−	0.654793i
$173$	11.0069	−	19.0645i	0.836840	−	1.44945i	−0.0556826	−	0.998449i	$-0.517734\pi$
$173$	11.0069	−	19.0645i	0.836840	−	1.44945i	0.892523	−	0.451002i	$-0.148933\pi$
$174$		0			0
$175$	−0.375999	+	0.540690i	−0.0284229	+	0.0408724i
$176$	0.439279	+	0.760853i	0.0331119	+	0.0573515i
$177$		0			0
$178$	−12.8339			−0.961939
$179$	−4.90819	−	8.50123i	−0.366855	−	0.635412i	0.622217	−	0.782845i	$-0.286232\pi$
$179$	−4.90819	−	8.50123i	−0.366855	−	0.635412i	−0.989072	+	0.147433i	$0.952899\pi$
$180$		0			0
$181$	22.9753			1.70774			0.853869	−	0.520487i	$-0.174250\pi$
$181$	22.9753			1.70774			0.853869	+	0.520487i	$0.174250\pi$
$182$	1.29339	+	9.45130i	0.0958723	+	0.700577i
$183$		0			0
$184$	1.31752			0.0971289
$185$	−10.7528	−	18.6243i	−0.790559	−	1.36929i
$186$		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
$191$	−4.84536	+	8.39241i	−0.350598	+	0.607254i	−0.986354	−	0.164636i	$-0.947355\pi$
$191$	−4.84536	+	8.39241i	−0.350598	+	0.607254i	0.635756	+	0.771890i	$0.280688\pi$
$192$		0			0
$193$	10.5533	+	18.2789i	0.759647	+	1.31575i	0.943031	+	0.332705i	$0.107961\pi$
$193$	10.5533	+	18.2789i	0.759647	+	1.31575i	−0.183384	+	0.983041i	$0.558705\pi$
$194$	−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
$199$	−7.58899			−0.537969			−0.268985	−	0.963144i	$-0.586688\pi$
$199$	−7.58899			−0.537969			−0.268985	+	0.963144i	$0.586688\pi$
$200$	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
$205$	8.25672			0.576674
$206$	6.17983	+	10.7038i	0.430569	+	0.745767i
$207$		0			0
$208$	−0.786978	−	3.51862i	−0.0545671	−	0.243972i
$209$	−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	$0.303851\pi$
$212$	1.22356	−	2.11926i	0.0840341	−	0.145551i
$213$		0			0
$214$	−6.80813			−0.465394
$215$	−11.3591	+	19.6745i	−0.774681	+	1.34179i
$216$		0			0
$217$	−5.88345	+	8.46047i	−0.399395	+	0.574334i
$218$	0.460710	−	0.797973i	0.0312032	−	0.0540456i
$219$		0			0
$220$	1.00641	−	1.74315i	0.0678522	−	0.117523i
$221$	−5.04281	−	22.5467i	−0.339216	−	1.51665i
$222$		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	$0.900024\pi$
$224$	−2.63641	−	0.222079i	−0.176153	−	0.0148383i
$225$		0			0
$226$	5.68802	+	9.85195i	0.378362	+	0.655342i
$227$	24.4284			1.62137			0.810686	−	0.585482i	$-0.199095\pi$
$227$	24.4284			1.62137			0.810686	+	0.585482i	$0.199095\pi$
$228$		0			0
$229$	−14.9717	−	25.9317i	−0.989358	−	1.71362i	−0.620688	−	0.784058i	$-0.713147\pi$
$229$	−14.9717	−	25.9317i	−0.989358	−	1.71362i	−0.368670	−	0.929560i	$-0.620187\pi$
$230$	−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	0.947532	+	0.319660i	$0.103569\pi$
$233$	11.4574	+	19.8448i	0.750600	+	1.30008i	−0.196932	+	0.980417i	$0.563098\pi$
$234$		0			0
$235$	0.432868	−	0.749750i	0.0282372	−	0.0489083i
$236$	5.96823			0.388498
$237$		0			0
$238$	−16.8937	−	1.42304i	−1.09505	−	0.0922422i
$239$	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
$241$	6.47888			0.417342			0.208671	−	0.977986i	$-0.433086\pi$
$241$	6.47888			0.417342			0.208671	+	0.977986i	$0.433086\pi$
$242$	−5.11407	+	8.85783i	−0.328745	+	0.569403i
$243$		0			0
$244$	−2.40782	+	4.17047i	−0.154145	+	0.266987i
$245$	−5.58233	−	15.0344i	−0.356642	−	0.960516i
$246$		0			0
$247$	5.18925	+	1.62548i	0.330184	+	0.103427i
$248$	1.94748	−	3.37313i	0.123665	−	0.214194i
$249$		0			0
$250$	10.8850			0.688426
$251$	−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
$254$	−4.26019	+	7.37887i	−0.267308	+	0.462992i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−28.0838			−1.75182			−0.875910	−	0.482475i	$-0.839738\pi$
$257$	−28.0838			−1.75182			−0.875910	+	0.482475i	$0.839738\pi$
$258$		0			0
$259$	24.7474	+	2.08460i	1.53773	+	0.129531i
$260$	−6.07982	+	5.59212i	−0.377054	+	0.346808i
$261$		0			0
$262$	2.51964	+	4.36415i	0.155664	+	0.269618i
$263$	−12.0885	−	20.9378i	−0.745407	−	1.29108i	−0.950004	−	0.312237i	$-0.898922\pi$
$263$	−12.0885	−	20.9378i	−0.745407	−	1.29108i	0.204597	−	0.978846i	$-0.434412\pi$
$264$		0			0
$265$	−5.60646			−0.344402
$266$	2.27818	−	3.27605i	0.139684	−	0.200867i
$267$		0			0
$268$	−4.87998	−	8.45237i	−0.298092	−	0.516311i
$269$	7.93891			0.484044			0.242022	−	0.970271i	$-0.422189\pi$
$269$	7.93891			0.484044			0.242022	+	0.970271i	$0.422189\pi$
$270$		0			0
$271$	−28.6694			−1.74154			−0.870770	−	0.491690i	$-0.836379\pi$
$271$	−28.6694			−1.74154			−0.870770	+	0.491690i	$0.836379\pi$
$272$	6.40782			0.388531
$273$		0			0
$274$	−18.9452			−1.14452
$275$	−0.218689			−0.0131874
$276$		0			0
$277$	12.4871			0.750279			0.375139	−	0.926968i	$-0.377595\pi$
$277$	12.4871			0.750279			0.375139	+	0.926968i	$0.377595\pi$
$278$	−0.565160	−	0.978885i	−0.0338960	−	0.0587096i
$279$		0			0
$280$	2.57945	+	5.48533i	0.154152	+	0.327811i
$281$	−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
$283$	7.89495	+	13.6745i	0.469306	+	0.812862i	0.999384	−	0.0350867i	$-0.0111707\pi$
$283$	7.89495	+	13.6745i	0.469306	+	0.812862i	−0.530078	+	0.847949i	$0.677837\pi$
$284$	−1.02408	−	1.77376i	−0.0607682	−	0.105254i
$285$		0			0
$286$	−2.33145	+	2.14443i	−0.137861	+	0.126803i
$287$	−5.44381	+	7.82825i	−0.321338	+	0.462087i
$288$		0			0
$289$	24.0602			1.41530
$290$	3.06677			0.180087
$291$		0			0
$292$	0.432504	−	0.749119i	0.0253104	−	0.0438388i
$293$	−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
$296$	−9.38675			−0.545594
$297$		0			0
$298$	−0.802500	+	1.38997i	−0.0464876	+	0.0805188i
$299$	1.03686	+	4.63585i	0.0599631	+	0.268098i
$300$		0			0
$301$	−11.1643	−	23.7413i	−0.643497	−	1.36843i
$302$	−10.2417	+	17.7391i	−0.589343	+	1.02077i
$303$		0			0
$304$	−0.754098	+	1.30614i	−0.0432505	+	0.0749121i
$305$	11.0329			0.631741
$306$		0			0
$307$	−1.27687			−0.0728749			−0.0364374	−	0.999336i	$-0.511601\pi$
$307$	−1.27687			−0.0728749			−0.0364374	+	0.999336i	$0.511601\pi$
$308$	0.989151	+	2.10348i	0.0563621	+	0.119857i
$309$		0			0
$310$	−8.92354			−0.506823
$311$	12.4336	−	21.5357i	0.705047	−	1.22118i	−0.261627	−	0.965169i	$-0.584259\pi$
$311$	12.4336	−	21.5357i	0.705047	−	1.22118i	0.966675	−	0.256009i	$-0.0824075\pi$
$312$		0			0
$313$	13.1601	+	22.7940i	0.743855	+	1.28839i	0.950728	+	0.310026i	$0.100338\pi$
$313$	13.1601	+	22.7940i	0.743855	+	1.28839i	−0.206873	+	0.978368i	$0.566329\pi$
$314$	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	−0.999597	−	0.0283764i	$-0.990966\pi$
$317$	−9.33620	−	16.1708i	−0.524373	−	0.908241i	0.475224	−	0.879865i	$-0.342367\pi$
$318$		0			0
$319$	1.17603			0.0658448
$320$	−1.14553	−	1.98411i	−0.0640368	−	0.110915i
$321$		0			0
$322$	3.47353	+	0.292594i	0.193572	+	0.0163056i
$323$	−4.83213	+	8.36949i	−0.268867	+	0.465691i
$324$		0			0
$325$	0.856453	+	0.268275i	0.0475074	+	0.0148812i
$326$	−3.44890	+	5.97367i	−0.191017	+	0.330851i
$327$		0			0
$328$	1.80195	−	3.12107i	0.0994960	−	0.172332i
$329$	0.425445	+	0.904730i	0.0234555	+	0.0498794i
$330$		0			0
$331$	−18.0242	+	31.2189i	−0.990701	+	1.71594i	−0.377522	+	0.926001i	$0.623224\pi$
$331$	−18.0242	+	31.2189i	−0.990701	+	1.71594i	−0.613179	+	0.789944i	$0.710110\pi$
$332$	−8.66710			−0.475669
$333$		0			0
$334$	9.73115	−	16.8549i	0.532465	−	0.922256i
$335$	−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	$0.346873\pi$
$338$	11.7613	−	5.53815i	0.639732	−	0.301236i
$339$		0			0
$340$	−7.34033	−	12.7138i	−0.398085	−	0.689503i
$341$	−3.42194			−0.185308
$342$		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
$347$	−12.0361			−0.646132			−0.323066	−	0.946376i	$-0.604714\pi$
$347$	−12.0361			−0.646132			−0.323066	+	0.946376i	$0.604714\pi$
$348$		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
$353$	12.1583	+	21.0588i	0.647121	+	1.12085i	0.983807	+	0.179230i	$0.0573606\pi$
$353$	12.1583	+	21.0588i	0.647121	+	1.12085i	−0.336686	+	0.941617i	$0.609306\pi$
$354$		0			0
$355$	−2.34623	+	4.06379i	−0.124525	+	0.215683i
$356$	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	0.940840	+	0.338853i	$0.110039\pi$
$359$	14.4734	+	25.0686i	0.763875	+	1.32307i	−0.176965	+	0.984217i	$0.556628\pi$
$360$		0			0
$361$	8.36267	+	14.4846i	0.440141	+	0.762346i
$362$	−22.9753			−1.20755
$363$		0			0
$364$	−1.29339	−	9.45130i	−0.0677920	−	0.495383i
$365$	−1.98178			−0.103731
$366$		0			0
$367$	13.5022	+	23.3866i	0.704811	+	1.22077i	0.966760	+	0.255687i	$0.0823017\pi$
$367$	13.5022	+	23.3866i	0.704811	+	1.22077i	−0.261948	+	0.965082i	$0.584365\pi$
$368$	−1.31752			−0.0686805
$369$		0			0
$370$	10.7528	+	18.6243i	0.559010	+	0.968234i
$371$	3.69644	−	5.31552i	0.191910	−	0.275968i
$372$		0			0
$373$	−9.61751	+	16.6580i	−0.497976	+	0.862519i	−0.999997	−	0.00233570i	$-0.999257\pi$
$373$	−9.61751	+	16.6580i	−0.497976	+	0.862519i	0.502021	+	0.864855i	$0.332590\pi$
$374$	−2.81482	−	4.87541i	−0.145551	−	0.252101i
$375$		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	$0.855102\pi$
$380$	3.45536			0.177256
$381$		0			0
$382$	4.84536	−	8.39241i	0.247910	−	0.429393i
$383$	−15.7111	+	27.2125i	−0.802802	+	1.39049i	0.114963	+	0.993370i	$0.463325\pi$
$383$	−15.7111	+	27.2125i	−0.802802	+	1.39049i	−0.917765	+	0.397124i	$0.870008\pi$
$384$		0			0
$385$	3.04043	−	4.37217i	0.154955	−	0.222827i
$386$	−10.5533	−	18.2789i	−0.537151	−	0.930373i
$387$		0			0
$388$	4.40338	+	7.62688i	0.223548	+	0.387196i
$389$	−2.89119	+	5.00769i	−0.146589	+	0.253900i	−0.929965	−	0.367649i	$-0.880163\pi$
$389$	−2.89119	+	5.00769i	−0.146589	+	0.253900i	0.783375	+	0.621549i	$0.213496\pi$
$390$		0			0
$391$	−8.44244			−0.426952
$392$	−6.90136	−	1.17099i	−0.348571	−	0.0591437i
$393$		0			0
$394$	−6.76019	+	11.7090i	−0.340574	+	0.589891i
$395$	−9.57692	+	16.5877i	−0.481867	+	0.834619i
$396$		0			0
$397$	−3.49354	+	6.05099i	−0.175336	+	0.303690i	−0.940277	−	0.340409i	$-0.889434\pi$
$397$	−3.49354	+	6.05099i	−0.175336	+	0.303690i	0.764942	+	0.644100i	$0.222768\pi$
$398$	7.58899			0.380402
$399$		0			0
$400$	−0.124459	+	0.215569i	−0.00622295	+	0.0107785i
$401$	5.93497			0.296378			0.148189	−	0.988959i	$-0.452656\pi$
$401$	5.93497			0.296378			0.148189	+	0.988959i	$0.452656\pi$
$402$		0			0
$403$	13.4014	+	4.19784i	0.667569	+	0.209110i
$404$	−5.02693	−	8.70689i	−0.250099	−	0.433184i
$405$		0			0
$406$	−2.02198	+	2.90763i	−0.100349	+	0.144303i
$407$	4.12340	+	7.14194i	0.204389	+	0.354013i
$408$		0			0
$409$	−14.7785			−0.730748			−0.365374	−	0.930861i	$-0.619059\pi$
$409$	−14.7785			−0.730748			−0.365374	+	0.930861i	$0.619059\pi$
$410$	−8.25672			−0.407770
$411$		0			0
$412$	−6.17983	−	10.7038i	−0.304458	−	0.527337i
$413$	15.7347	+	1.32542i	0.774255	+	0.0652196i
$414$		0			0
$415$	9.92839	+	17.1965i	0.487365	+	0.844142i
$416$	0.786978	+	3.51862i	0.0385848	+	0.172514i
$417$		0			0
$418$	1.32504			0.0648097
$419$	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	$0.439847\pi$
$422$	6.06832	−	10.5106i	0.295401	−	0.511650i
$423$		0			0
$424$	−1.22356	+	2.11926i	−0.0594211	+	0.102920i
$425$	−0.797511	+	1.38133i	−0.0386850	+	0.0670044i
$426$		0			0
$427$	−7.27419	+	10.4604i	−0.352023	+	0.506212i
$428$	6.80813			0.329083
$429$		0			0
$430$	11.3591	−	19.6745i	0.547782	−	0.948787i
$431$	17.8893	+	30.9851i	0.861696	+	1.49250i	0.870290	+	0.492539i	$0.163931\pi$
$431$	17.8893	+	30.9851i	0.861696	+	1.49250i	−0.00859398	+	0.999963i	$0.502736\pi$
$432$		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
$436$	−0.460710	+	0.797973i	−0.0220640	+	0.0382160i
$437$	0.993540	−	1.72086i	0.0475275	−	0.0823200i
$438$		0			0
$439$	−27.2045			−1.29840			−0.649200	−	0.760618i	$-0.724896\pi$
$439$	−27.2045			−1.29840			−0.649200	+	0.760618i	$0.724896\pi$
$440$	−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	0.904571	−	0.426323i	$-0.140191\pi$
$443$	1.74860	+	3.02867i	0.0830786	+	0.143896i	−0.821492	+	0.570220i	$0.806858\pi$
$444$		0			0
$445$	−14.7015	−	25.4638i	−0.696919	−	1.20710i
$446$	11.0968	−	19.2202i	0.525447	−	0.910101i
$447$		0			0
$448$	2.63641	+	0.222079i	0.124559	+	0.0104923i
$449$	−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
$451$	−3.16623			−0.149092
$452$	−5.68802	−	9.85195i	−0.267542	−	0.463397i
$453$		0			0
$454$	−24.4284			−1.14648
$455$	−17.2708	+	13.3929i	−0.809668	+	0.627871i
$456$		0			0
$457$	26.2609			1.22843			0.614217	−	0.789137i	$-0.289472\pi$
$457$	26.2609			1.22843			0.614217	+	0.789137i	$0.289472\pi$
$458$	14.9717	+	25.9317i	0.699582	+	1.21171i
$459$		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	$0.607101\pi$
$464$	0.669294	−	1.15925i	0.0310712	−	0.0538169i
$465$		0			0
$466$	−11.4574	−	19.8448i	−0.530754	−	0.919293i
$467$	1.47500	+	2.55478i	0.0682550	+	0.118221i	0.898133	−	0.439723i	$-0.144924\pi$
$467$	1.47500	+	2.55478i	0.0682550	+	0.118221i	−0.829878	+	0.557944i	$0.811590\pi$
$468$		0			0
$469$	−10.9886	−	23.3677i	−0.507404	−	1.07902i
$470$	−0.432868	+	0.749750i	−0.0199667	+	0.0345834i
$471$		0			0
$472$	−5.96823			−0.274710
$473$	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
$478$	−1.03992			−0.0475649
$479$	9.90480	+	17.1556i	0.452562	+	0.783861i	0.998544	−	0.0539362i	$-0.0171768\pi$
$479$	9.90480	+	17.1556i	0.452562	+	0.783861i	−0.545982	+	0.837797i	$0.683843\pi$
$480$		0			0
$481$	−7.38717	−	33.0284i	−0.336826	−	1.50597i
$482$	−6.47888			−0.295105
$483$		0			0
$484$	5.11407	−	8.85783i	0.232458	−	0.402628i
$485$	10.0884	−	17.4736i	0.458090	−	0.793435i
$486$		0			0
$487$	−12.5946			−0.570714			−0.285357	−	0.958421i	$-0.592112\pi$
$487$	−12.5946			−0.570714			−0.285357	+	0.958421i	$0.592112\pi$
$488$	2.40782	−	4.17047i	0.108997	−	0.188788i
$489$		0			0
$490$	5.58233	+	15.0344i	0.252184	+	0.679187i
$491$	−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
$494$	−5.18925	−	1.62548i	−0.233476	−	0.0731339i
$495$		0			0
$496$	−1.94748	+	3.37313i	−0.0874442	+	0.151458i
$497$	−2.30599	−	4.90381i	−0.103438	−	0.219966i
$498$		0			0
$499$	6.22713	+	10.7857i	0.278765	+	0.482834i	0.971078	−	0.238763i	$-0.0767418\pi$
$499$	6.22713	+	10.7857i	0.278765	+	0.482834i	−0.692313	+	0.721597i	$0.743408\pi$
$500$	−10.8850			−0.486791
$501$		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
$509$	−7.19772			−0.319034			−0.159517	−	0.987195i	$-0.550994\pi$
$509$	−7.19772			−0.319034			−0.159517	+	0.987195i	$0.550994\pi$
$510$		0			0
$511$	1.30662	−	1.87894i	0.0578016	−	0.0831193i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	28.0838			1.23872
$515$	−14.1583	+	24.5229i	−0.623889	+	1.08061i
$516$		0			0
$517$	−0.165994	+	0.287509i	−0.00730039	+	0.0126446i
$518$	−24.7474	−	2.08460i	−1.08734	−	0.0915922i
$519$		0			0
$520$	6.07982	−	5.59212i	0.266618	−	0.245231i
$521$	−11.2983	+	19.5692i	−0.494987	+	0.857342i	−0.999983	−	0.00577905i	$-0.998160\pi$
$521$	−11.2983	+	19.5692i	−0.494987	+	0.857342i	0.504996	+	0.863121i	$0.331494\pi$
$522$		0			0
$523$	−6.07271			−0.265541			−0.132770	−	0.991147i	$-0.542387\pi$
$523$	−6.07271			−0.265541			−0.132770	+	0.991147i	$0.542387\pi$
$524$	−2.51964	−	4.36415i	−0.110071	−	0.190649i
$525$		0			0
$526$	12.0885	+	20.9378i	0.527082	+	0.912933i
$527$	−12.4791	+	21.6144i	−0.543597	+	0.941538i
$528$		0			0
$529$	−21.2641			−0.924528
$530$	5.60646			0.243529
$531$		0			0
$532$	−2.27818	+	3.27605i	−0.0987717	+	0.142035i
$533$	12.3999	+	3.88416i	0.537101	+	0.168242i
$534$		0			0
$535$	−7.79888	−	13.5081i	−0.337175	−	0.584005i
$536$	4.87998	+	8.45237i	0.210783	+	0.365087i
$537$		0			0
$538$	−7.93891			−0.342271
$539$	2.14067	+	5.76531i	0.0922053	+	0.248330i
$540$		0			0
$541$	3.16494	+	5.48183i	0.136071	+	0.235682i	0.926006	−	0.377508i	$-0.123219\pi$
$541$	3.16494	+	5.48183i	0.136071	+	0.235682i	−0.789935	+	0.613191i	$0.789886\pi$
$542$	28.6694			1.23146
$543$		0			0
$544$	−6.40782			−0.274733
$545$	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	$0.378908\pi$
$548$	18.9452			0.809300
$549$		0			0
$550$	0.218689			0.00932492
$551$	1.00943	+	1.74838i	0.0430030	+	0.0744834i
$552$		0			0
$553$	−9.41269	−	20.0165i	−0.400268	−	0.851190i
$554$	−12.4871			−0.530527
$555$		0			0
$556$	0.565160	+	0.978885i	0.0239681	+	0.0415140i
$557$	19.9116	+	34.4879i	0.843681	+	1.46130i	0.886762	+	0.462226i	$0.152949\pi$
$557$	19.9116	+	34.4879i	0.843681	+	1.46130i	−0.0430813	+	0.999072i	$0.513717\pi$
$558$		0			0
$559$	−26.3144	+	24.2035i	−1.11298	+	1.02370i
$560$	−2.57945	−	5.48533i	−0.109002	−	0.231798i
$561$		0			0
$562$	23.4616			0.989667
$563$	4.59171			0.193517			0.0967587	−	0.995308i	$-0.469152\pi$
$563$	4.59171			0.193517			0.0967587	+	0.995308i	$0.469152\pi$
$564$		0			0
$565$	−13.0316	+	22.5713i	−0.548242	+	0.949583i
$566$	−7.89495	−	13.6745i	−0.331850	−	0.574780i
$567$		0			0
$568$	1.02408	+	1.77376i	0.0429696	+	0.0744255i
$569$	17.4829			0.732922			0.366461	−	0.930433i	$-0.380569\pi$
$569$	17.4829			0.732922			0.366461	+	0.930433i	$0.380569\pi$
$570$		0			0
$571$	8.05500	−	13.9517i	0.337091	−	0.583859i	−0.646793	−	0.762666i	$-0.723890\pi$
$571$	8.05500	−	13.9517i	0.337091	−	0.583859i	0.983884	+	0.178806i	$0.0572235\pi$
$572$	2.33145	−	2.14443i	0.0974827	−	0.0896631i
$573$		0			0
$574$	5.44381	−	7.82825i	0.227220	−	0.326745i
$575$	0.163977	−	0.284017i	0.00683833	−	0.0118443i
$576$		0			0
$577$	3.99841	−	6.92544i	0.166456	−	0.288310i	−0.770716	−	0.637179i	$-0.780101\pi$
$577$	3.99841	−	6.92544i	0.166456	−	0.288310i	0.937171	+	0.348870i	$0.113434\pi$
$578$	−24.0602			−1.00077
$579$		0			0
$580$	−3.06677			−0.127341
$581$	−22.8501	−	1.92478i	−0.947981	−	0.0798534i
$582$		0			0
$583$	2.14993			0.0890409
$584$	−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
$592$	9.38675			0.385793
$593$	12.2317	+	21.1859i	0.502296	+	0.870002i	0.999996	+	0.00265305i	$0.000844492\pi$
$593$	12.2317	+	21.1859i	0.502296	+	0.870002i	−0.497701	+	0.867349i	$0.665822\pi$
$594$		0			0
$595$	−16.5287	−	35.1490i	−0.677609	−	1.44097i
$596$	0.802500	−	1.38997i	0.0328717	−	0.0569354i
$597$		0			0
$598$	−1.03686	−	4.63585i	−0.0424003	−	0.189574i
$599$	22.4292	−	38.8484i	0.916431	−	1.58730i	0.111638	−	0.993749i	$-0.464390\pi$
$599$	22.4292	−	38.8484i	0.916431	−	1.58730i	0.804793	−	0.593555i	$-0.202276\pi$
$600$		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	$0.000626114\pi$
$602$	11.1643	+	23.7413i	0.455021	+	0.967625i
$603$		0			0
$604$	10.2417	−	17.7391i	0.416728	−	0.721795i
$605$	−23.4332			−0.952695
$606$		0			0
$607$	18.0911	−	31.3347i	0.734296	−	1.27184i	−0.220735	−	0.975334i	$-0.570846\pi$
$607$	18.0911	−	31.3347i	0.734296	−	1.27184i	0.955032	−	0.296504i	$-0.0958209\pi$
$608$	0.754098	−	1.30614i	0.0305827	−	0.0529708i
$609$		0			0
$610$	−11.0329			−0.446709
$611$	1.00278	−	0.922343i	0.0405682	−	0.0373140i
$612$		0			0
$613$	−3.10647	−	5.38056i	−0.125469	−	0.217319i	0.796447	−	0.604708i	$-0.206710\pi$
$613$	−3.10647	−	5.38056i	−0.125469	−	0.217319i	−0.921916	+	0.387389i	$0.873377\pi$
$614$	1.27687			0.0515303
$615$		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	−0.607980	−	0.793952i	$-0.708020\pi$
$619$	9.54369	−	16.5301i	0.383593	−	0.664403i	0.991573	+	0.129550i	$0.0413532\pi$
$620$	8.92354			0.358378
$621$		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
$626$	−13.1601	−	22.7940i	−0.525985	−	0.911032i
$627$		0			0
$628$	−5.16462	+	8.94539i	−0.206091	+	0.356960i
$629$	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
$634$	9.33620	+	16.1708i	0.370788	+	0.642224i
$635$	−19.5206			−0.774653
$636$		0			0
$637$	−1.31097	−	25.2048i	−0.0519425	−	0.998650i
$638$	−1.17603			−0.0465593
$639$		0			0
$640$	1.14553	+	1.98411i	0.0452809	+	0.0784288i
$641$	−21.8244			−0.862010			−0.431005	−	0.902349i	$-0.641841\pi$
$641$	−21.8244			−0.862010			−0.431005	+	0.902349i	$0.641841\pi$
$642$		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	$0.734795\pi$
$644$	−3.47353	−	0.292594i	−0.136876	−	0.0115298i
$645$		0			0
$646$	4.83213	−	8.36949i	0.190118	−	0.329293i
$647$	5.39230	+	9.33974i	0.211993	+	0.367183i	0.952338	−	0.305044i	$-0.0986712\pi$
$647$	5.39230	+	9.33974i	0.211993	+	0.367183i	−0.740345	+	0.672227i	$0.765338\pi$
$648$		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
$653$	20.3332			0.795699			0.397850	−	0.917451i	$-0.369757\pi$
$653$	20.3332			0.795699			0.397850	+	0.917451i	$0.369757\pi$
$654$		0			0
$655$	−5.77264	+	9.99850i	−0.225556	+	0.390674i
$656$	−1.80195	+	3.12107i	−0.0703543	+	0.121857i
$657$		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
$661$	−4.94372	−	8.56277i	−0.192288	−	0.333053i	0.753720	−	0.657196i	$-0.228258\pi$
$661$	−4.94372	−	8.56277i	−0.192288	−	0.333053i	−0.946008	+	0.324143i	$0.894924\pi$
$662$	18.0242	−	31.2189i	0.700531	−	1.21336i
$663$		0			0
$664$	8.66710			0.336349
$665$	9.10975	+	0.767363i	0.353261	+	0.0297571i
$666$		0			0
$667$	−0.881809	+	1.52734i	−0.0341438	+	0.0591387i
$668$	−9.73115	+	16.8549i	−0.376510	+	0.652134i
$669$		0			0
$670$	11.1803	−	19.3648i	0.431932	−	0.748128i
$671$	−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	$0.255358\pi$
$674$	−16.9888			−0.654385
$675$		0			0
$676$	−11.7613	+	5.53815i	−0.452359	+	0.213006i
$677$	−16.7860	−	29.0742i	−0.645139	−	1.11741i	−0.984269	−	0.176674i	$-0.943466\pi$
$677$	−16.7860	−	29.0742i	−0.645139	−	1.11741i	0.339130	−	0.940739i	$-0.389867\pi$
$678$		0			0
$679$	9.91537	+	21.0855i	0.380517	+	0.809188i
$680$	7.34033	+	12.7138i	0.281489	+	0.487553i
$681$		0			0
$682$	3.42194			0.131033
$683$	17.6901			0.676893			0.338446	−	0.940986i	$-0.390099\pi$
$683$	17.6901			0.676893			0.338446	+	0.940986i	$0.390099\pi$
$684$		0			0
$685$	−21.7023	−	37.5894i	−0.829201	−	1.43622i
$686$	−17.9348	−	4.61985i	−0.684754	−	0.176387i
$687$		0			0
$688$	−4.95801	−	8.58752i	−0.189022	−	0.327396i
$689$	−8.41978	−	2.63741i	−0.320768	−	0.100477i
$690$		0			0
$691$	38.2717			1.45593			0.727963	−	0.685617i	$-0.240467\pi$
$691$	38.2717			1.45593			0.727963	+	0.685617i	$0.240467\pi$
$692$	11.0069	−	19.0645i	0.418420	−	0.724725i
$693$		0			0
$694$	12.0361			0.456884
$695$	1.29481	−	2.24268i	0.0491149	−	0.0850696i
$696$		0			0
$697$	−11.5466	+	19.9992i	−0.437358	+	0.757526i
$698$	11.4544	−	19.8396i	0.433555	−	0.750940i
$699$		0			0
$700$	−0.375999	+	0.540690i	−0.0142114	+	0.0204362i
$701$	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
$704$	0.439279	+	0.760853i	0.0165559	+	0.0286757i
$705$		0			0
$706$	−12.1583	−	21.0588i	−0.457584	−	0.792558i
$707$	−11.3194	−	24.0714i	−0.425711	−	0.905296i
$708$		0			0
$709$	0.660813	−	1.14456i	0.0248174	−	0.0429849i	−0.853350	−	0.521338i	$-0.825433\pi$
$709$	0.660813	−	1.14456i	0.0248174	−	0.0429849i	0.878167	+	0.478354i	$0.158766\pi$
$710$	2.34623	−	4.06379i	0.0880524	−	0.152511i
$711$		0			0
$712$	−12.8339			−0.480969
$713$	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
$718$	−14.4734	−	25.0686i	−0.540141	−	0.935552i
$719$	12.3591	−	21.4065i	0.460915	−	0.798328i	−0.538092	−	0.842886i	$-0.680855\pi$
$719$	12.3591	−	21.4065i	0.460915	−	0.798328i	0.999007	+	0.0445581i	$0.0141880\pi$
$720$		0			0
$721$	−13.9155	−	29.5920i	−0.518240	−	1.10206i
$722$	−8.36267	−	14.4846i	−0.311226	−	0.539060i
$723$		0			0
$724$	22.9753			0.853869
$725$	0.166599	+	0.288559i	0.00618734	+	0.0107168i
$726$		0			0
$727$	8.76033			0.324903			0.162451	−	0.986717i	$-0.448060\pi$
$727$	8.76033			0.324903			0.162451	+	0.986717i	$0.448060\pi$
$728$	1.29339	+	9.45130i	0.0479362	+	0.350289i
$729$		0			0
$730$	1.98178			0.0733489
$731$	−31.7700	−	55.0273i	−1.17506	−	2.03526i
$732$		0			0
$733$	−6.38026	−	11.0509i	−0.235660	−	0.408176i	0.723804	−	0.690006i	$-0.242392\pi$
$733$	−6.38026	−	11.0509i	−0.235660	−	0.408176i	−0.959464	+	0.281830i	$0.909059\pi$
$734$	−13.5022	−	23.3866i	−0.498377	−	0.863214i
$735$		0			0
$736$	1.31752			0.0485645
$737$	4.28734	−	7.42590i	0.157926	−	0.273536i
$738$		0			0
$739$	−10.8324	−	18.7623i	−0.398476	−	0.690181i	0.595062	−	0.803680i	$-0.297128\pi$
$739$	−10.8324	−	18.7623i	−0.398476	−	0.690181i	−0.993538	+	0.113499i	$0.963794\pi$
$740$	−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
$745$	−3.67714			−0.134720
$746$	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
$751$	8.60728			0.314084			0.157042	−	0.987592i	$-0.449804\pi$
$751$	8.60728			0.314084			0.157042	+	0.987592i	$0.449804\pi$
$752$	0.188939	+	0.327251i	0.00688989	+	0.0119336i
$753$		0			0
$754$	4.60568	+	1.44268i	0.167729	+	0.0525394i
$755$	−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	$0.0735584\pi$
$758$	16.1551	−	27.9815i	0.586781	−	1.01633i
$759$		0			0
$760$	−3.45536			−0.125339
$761$	13.0174	−	22.5468i	0.471880	−	0.817321i	−0.527602	−	0.849492i	$-0.676909\pi$
$761$	13.0174	−	22.5468i	0.471880	−	0.817321i	0.999482	+	0.0321708i	$0.0102421\pi$
$762$		0			0
$763$	−1.39184	+	2.00147i	−0.0503879	+	0.0724582i
$764$	−4.84536	+	8.39241i	−0.175299	+	0.303627i
$765$		0			0
$766$	15.7111	−	27.2125i	0.567667	−	0.983228i
$767$	−4.69686	−	20.9999i	−0.169594	−	0.758263i
$768$		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	$-0.0724036\pi$
$770$	−3.04043	+	4.37217i	−0.109570	+	0.157562i
$771$		0			0
$772$	10.5533	+	18.2789i	0.379823	+	0.657873i
$773$	−42.7258			−1.53674			−0.768370	−	0.640006i	$-0.778932\pi$
$773$	−42.7258			−1.53674			−0.768370	+	0.640006i	$0.778932\pi$
$774$		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
$782$	8.44244			0.301901
$783$		0			0
$784$	6.90136	+	1.17099i	0.246477	+	0.0418209i
$785$	23.6648			0.844634
$786$		0			0
$787$	7.03691			0.250839			0.125419	−	0.992104i	$-0.459972\pi$
$787$	7.03691			0.250839			0.125419	+	0.992104i	$0.459972\pi$
$788$	6.76019	−	11.7090i	0.240822	−	0.417116i
$789$		0			0
$790$	9.57692	−	16.5877i	0.340732	−	0.590165i
$791$	−12.8081	−	27.2370i	−0.455403	−	0.968436i
$792$		0			0
$793$	16.5692	+	5.19013i	0.588389	+	0.184307i
$794$	3.49354	−	6.05099i	0.123981	−	0.214742i
$795$		0			0
$796$	−7.58899			−0.268985
$797$	−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
$800$	0.124459	−	0.215569i	0.00440029	−	0.00762153i
$801$		0			0
$802$	−5.93497			−0.209571
$803$	0.759959			0.0268184
$804$		0			0
$805$	3.39848	+	7.22704i	0.119781	+	0.254720i
$806$	−13.4014	−	4.19784i	−0.472043	−	0.147863i
$807$		0			0
$808$	5.02693	+	8.70689i	0.176847	+	0.306307i
$809$	12.0464	+	20.8650i	0.423530	+	0.733575i	0.996282	−	0.0861534i	$-0.0274575\pi$
$809$	12.0464	+	20.8650i	0.423530	+	0.733575i	−0.572752	+	0.819729i	$0.694124\pi$
$810$		0			0
$811$	−0.569121			−0.0199845			−0.00999227	−	0.999950i	$-0.503181\pi$
$811$	−0.569121			−0.0199845			−0.00999227	+	0.999950i	$0.503181\pi$
$812$	2.02198	−	2.90763i	0.0709576	−	0.102038i
$813$		0			0
$814$	−4.12340	−	7.14194i	−0.144525	−	0.250325i
$815$	−15.8032			−0.553562
$816$		0			0
$817$	14.9553			0.523220
$818$	14.7785			0.516717
$819$		0			0
$820$	8.25672			0.288337
$821$	−51.4686			−1.79627			−0.898134	−	0.439722i	$-0.855077\pi$
$821$	−51.4686			−1.79627			−0.898134	+	0.439722i	$0.855077\pi$
$822$		0			0
$823$	38.8653			1.35476			0.677379	−	0.735634i	$-0.263116\pi$
$823$	38.8653			1.35476			0.677379	+	0.735634i	$0.263116\pi$
$824$	6.17983	+	10.7038i	0.215284	+	0.372884i
$825$		0			0
$826$	−15.7347	−	1.32542i	−0.547481	−	0.0461172i
$827$	−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
$829$	5.78905	+	10.0269i	0.201062	+	0.348250i	0.948871	−	0.315665i	$-0.102227\pi$
$829$	5.78905	+	10.0269i	0.201062	+	0.348250i	−0.747809	+	0.663914i	$0.768894\pi$
$830$	−9.92839	−	17.1965i	−0.344619	−	0.596898i
$831$		0			0
$832$	−0.786978	−	3.51862i	−0.0272835	−	0.121986i
$833$	44.2227	+	7.50347i	1.53223	+	0.259980i
$834$		0			0
$835$	44.5892			1.54307
$836$	−1.32504			−0.0458274
$837$		0			0
$838$	−5.07336	+	8.78731i	−0.175256	+	0.303553i
$839$	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
$842$	−7.70885			−0.265665
$843$		0			0
$844$	−6.06832	+	10.5106i	−0.208880	+	0.361791i
$845$	24.4612	+	16.9917i	0.841491	+	0.584531i
$846$		0			0
$847$	15.4499	−	22.2172i	0.530866	−	0.763391i
$848$	1.22356	−	2.11926i	0.0420171	−	0.0727757i
$849$		0			0
$850$	0.797511	−	1.38133i	0.0273544	−	0.0473792i
$851$	−12.3672			−0.423944
$852$		0			0
$853$	6.06219			0.207565			0.103783	−	0.994600i	$-0.466905\pi$
$853$	6.06219			0.207565			0.103783	+	0.994600i	$0.466905\pi$
$854$	7.27419	−	10.4604i	0.248918	−	0.357946i
$855$		0			0
$856$	−6.80813			−0.232697
$857$	−27.2702	+	47.2333i	−0.931531	+	1.61346i	−0.150825	+	0.988560i	$0.548193\pi$
$857$	−27.2702	+	47.2333i	−0.931531	+	1.61346i	−0.780706	+	0.624899i	$0.785140\pi$
$858$		0			0
$859$	27.3472	+	47.3667i	0.933074	+	1.61613i	0.778033	+	0.628224i	$0.216218\pi$
$859$	27.3472	+	47.3667i	0.933074	+	1.61613i	0.155042	+	0.987908i	$0.450449\pi$
$860$	−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	0.902317	−	0.431073i	$-0.141865\pi$
$863$	2.28666	+	3.96062i	0.0778389	+	0.134821i	−0.824478	+	0.565893i	$0.808531\pi$
$864$		0			0
$865$	−50.4348			−1.71484
$866$	6.32535	+	10.9558i	0.214944	+	0.372294i
$867$		0			0
$868$	−5.88345	+	8.46047i	−0.199697	+	0.287167i
$869$	3.67250	−	6.36095i	0.124581	−	0.215780i
$870$		0			0
$871$	−25.9002	+	23.8226i	−0.877596	+	0.807198i
$872$	0.460710	−	0.797973i	0.0156016	−	0.0270228i
$873$		0			0
$874$	−0.993540	+	1.72086i	−0.0336070	+	0.0582090i
$875$	−28.6973	−	2.41733i	−0.970146	−	0.0817205i
$876$		0			0
$877$	−29.3607	+	50.8542i	−0.991440	+	1.71723i	−0.382652	+	0.923893i	$0.624989\pi$
$877$	−29.3607	+	50.8542i	−0.991440	+	1.71723i	−0.608788	+	0.793333i	$0.708344\pi$
$878$	27.2045			0.918108
$879$		0			0
$880$	1.00641	−	1.74315i	0.0339261	−	0.0587617i
$881$	−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	$0.261243\pi$
$884$	−5.04281	−	22.5467i	−0.169608	−	0.758327i
$885$		0			0
$886$	−1.74860	−	3.02867i	−0.0587455	−	0.101750i
$887$	−47.9785			−1.61096			−0.805480	−	0.592623i	$-0.798092\pi$
$887$	−47.9785			−1.61096			−0.805480	+	0.592623i	$0.798092\pi$
$888$		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
$893$	−0.569914			−0.0190714
$894$		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
$899$	2.60687	+	4.51523i	0.0869439	+	0.150591i
$900$		0			0
$901$	7.84033	−	13.5798i	0.261199	−	0.452410i
$902$	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
$907$	12.6807	+	21.9637i	0.421057	+	0.729292i	0.996043	−	0.0888709i	$-0.0283259\pi$
$907$	12.6807	+	21.9637i	0.421057	+	0.729292i	−0.574986	+	0.818163i	$0.694993\pi$
$908$	24.4284			0.810686
$909$		0			0
$910$	17.2708	−	13.3929i	0.572522	−	0.443972i
$911$	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
$913$	−3.80727	−	6.59439i	−0.126002	−	0.218242i
$914$	−26.2609			−0.868634
$915$		0			0
$916$	−14.9717	−	25.9317i	−0.494679	−	0.856809i
$917$	−5.67364	−	12.0653i	−0.187360	−	0.398431i
$918$		0			0
$919$	12.5781	−	21.7859i	0.414913	−	0.718650i	−0.580507	−	0.814255i	$-0.697145\pi$
$919$	12.5781	−	21.7859i	0.414913	−	0.718650i	0.995419	+	0.0956058i	$0.0304788\pi$
$920$	−1.50925	−	2.61410i	−0.0497586	−	0.0861845i
$921$		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
$926$	14.2082			0.466909
$927$		0			0
$928$	−0.669294	+	1.15925i	−0.0219706	+	0.0380543i
$929$	15.1105	−	26.1722i	0.495759	−	0.858681i	−0.504229	−	0.863570i	$-0.668223\pi$
$929$	15.1105	−	26.1722i	0.495759	−	0.858681i	0.999988	+	0.00488962i	$0.00155642\pi$
$930$		0			0
$931$	−6.73377	+	8.13108i	−0.220691	+	0.266486i
$932$	11.4574	+	19.8448i	0.375300	+	0.650039i
$933$		0			0
$934$	−1.47500	−	2.55478i	−0.0482635	−	0.0835949i
$935$	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	$0.682454\pi$
$938$	10.9886	+	23.3677i	0.358789	+	0.762982i
$939$		0			0
$940$	0.432868	−	0.749750i	0.0141186	−	0.0244542i
$941$	−10.3309	+	17.8937i	−0.336779	+	0.583318i	−0.983825	−	0.179133i	$-0.942671\pi$
$941$	−10.3309	+	17.8937i	−0.336779	+	0.583318i	0.647046	+	0.762451i	$0.276004\pi$
$942$		0			0
$943$	2.37411	−	4.11207i	0.0773115	−	0.133908i
$944$	5.96823			0.194249
$945$		0			0
$946$	−4.35590	+	7.54463i	−0.141622	+	0.245297i
$947$	−5.01447			−0.162948			−0.0814741	−	0.996675i	$-0.525963\pi$
$947$	−5.01447			−0.162948			−0.0814741	+	0.996675i	$0.525963\pi$
$948$		0			0
$949$	−2.97623	−	0.932275i	−0.0966126	−	0.0302629i
$950$	0.187709	+	0.325121i	0.00609008	+	0.0105483i
$951$		0			0
$952$	−16.8937	−	1.42304i	−0.547527	−	0.0461211i
$953$	−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
$955$	22.2020			0.718438
$956$	1.03992			0.0336334
$957$		0			0
$958$	−9.90480	−	17.1556i	−0.320010	−	0.554273i
$959$	49.9475	+	4.20734i	1.61289	+	0.135862i
$960$		0			0
$961$	7.91468	+	13.7086i	0.255312	+	0.442214i
$962$	7.38717	+	33.0284i	0.238172	+	1.06488i
$963$		0			0
$964$	6.47888			0.208671
$965$	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	$0.217803\pi$
$968$	−5.11407	+	8.85783i	−0.164372	+	0.284701i
$969$		0			0
$970$	−10.0884	+	17.4736i	−0.323918	+	0.561043i
$971$	−16.0612	+	27.8188i	−0.515428	+	0.892747i	0.484412	+	0.874840i	$0.339034\pi$
$971$	−16.0612	+	27.8188i	−0.515428	+	0.892747i	−0.999840	+	0.0179070i	$0.994300\pi$
$972$		0			0
$973$	1.27261	+	2.70626i	0.0407978	+	0.0867586i
$974$	12.5946			0.403556
$975$		0			0
$976$	−2.40782	+	4.17047i	−0.0770725	+	0.133493i
$977$	9.97418	+	17.2758i	0.319102	+	0.552701i	0.980301	−	0.197509i	$-0.0632853\pi$
$977$	9.97418	+	17.2758i	0.319102	+	0.552701i	−0.661199	+	0.750211i	$0.729952\pi$
$978$		0			0
$979$	5.63764	+	9.76469i	0.180180	+	0.312081i
$980$	−5.58233	−	15.0344i	−0.178321	−	0.480258i
$981$		0			0
$982$	5.81280	−	10.0681i	0.185494	−	0.321285i
$983$	−4.74110	+	8.21182i	−0.151218	+	0.261916i	−0.931675	−	0.363292i	$-0.881653\pi$
$983$	−4.74110	+	8.21182i	−0.151218	+	0.261916i	0.780458	+	0.625208i	$0.214986\pi$
$984$		0			0
$985$	−30.9759			−0.986974
$986$	−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
$991$	−12.7652	−	22.1100i	−0.405501	−	0.702348i	0.588879	−	0.808221i	$-0.299570\pi$
$991$	−12.7652	−	22.1100i	−0.405501	−	0.702348i	−0.994380	+	0.105873i	$0.966236\pi$
$992$	1.94748	−	3.37313i	0.0618324	−	0.107097i
$993$		0			0
$994$	2.30599	+	4.90381i	0.0731416	+	0.155539i
$995$	8.69338	+	15.0574i	0.275599	+	0.477351i
$996$		0			0
$997$	52.1407			1.65131			0.825657	−	0.564172i	$-0.190805\pi$
$997$	52.1407			1.65131			0.825657	+	0.564172i	$0.190805\pi$
$998$	−6.22713	−	10.7857i	−0.197116	−	0.341415i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.d.289.3	✓	8	273.107	odd	6
546.2.j.d.529.3	yes	8	3.2	odd	2
546.2.k.b.373.3	yes	8	21.2	odd	6
546.2.k.b.445.3	yes	8	39.29	odd	6
1638.2.m.g.289.2		8	91.16	even	3	inner
1638.2.m.g.1621.2		8	1.1	even	1	trivial
1638.2.p.i.919.2		8	7.2	even	3
1638.2.p.i.991.2		8	13.3	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.14553 - 1.98411i) q^{5} +(2.63641 + 0.222079i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.14553 - 1.98411i) q^{5} +(2.63641 + 0.222079i) q^{7} -1.00000 q^{8} +(1.14553 + 1.98411i) q^{10} +(0.439279 + 0.760853i) q^{11} +(-0.786978 - 3.51862i) q^{13} +(-2.63641 - 0.222079i) q^{14} +1.00000 q^{16} +6.40782 q^{17} +(-0.754098 + 1.30614i) q^{19} +(-1.14553 - 1.98411i) q^{20} +(-0.439279 - 0.760853i) q^{22} -1.31752 q^{23} +(-0.124459 + 0.215569i) q^{25} +(0.786978 + 3.51862i) q^{26} +(2.63641 + 0.222079i) q^{28} +(0.669294 - 1.15925i) q^{29} +(-1.94748 + 3.37313i) q^{31} -1.00000 q^{32} -6.40782 q^{34} +(-2.57945 - 5.48533i) q^{35} +9.38675 q^{37} +(0.754098 - 1.30614i) q^{38} +(1.14553 + 1.98411i) q^{40} +(-1.80195 + 3.12107i) q^{41} +(-4.95801 - 8.58752i) q^{43} +(0.439279 + 0.760853i) q^{44} +1.31752 q^{46} +(0.188939 + 0.327251i) q^{47} +(6.90136 + 1.17099i) q^{49} +(0.124459 - 0.215569i) q^{50} +(-0.786978 - 3.51862i) q^{52} +(1.22356 - 2.11926i) q^{53} +(1.00641 - 1.74315i) q^{55} +(-2.63641 - 0.222079i) q^{56} +(-0.669294 + 1.15925i) q^{58} +5.96823 q^{59} +(-2.40782 + 4.17047i) q^{61} +(1.94748 - 3.37313i) q^{62} +1.00000 q^{64} +(-6.07982 + 5.59212i) q^{65} +(-4.87998 - 8.45237i) q^{67} +6.40782 q^{68} +(2.57945 + 5.48533i) q^{70} +(-1.02408 - 1.77376i) q^{71} +(0.432504 - 0.749119i) q^{73} -9.38675 q^{74} +(-0.754098 + 1.30614i) q^{76} +(0.989151 + 2.10348i) q^{77} +(-4.18014 - 7.24022i) q^{79} +(-1.14553 - 1.98411i) q^{80} +(1.80195 - 3.12107i) q^{82} -8.66710 q^{83} +(-7.34033 - 12.7138i) q^{85} +(4.95801 + 8.58752i) q^{86} +(-0.439279 - 0.760853i) q^{88} +12.8339 q^{89} +(-1.29339 - 9.45130i) q^{91} -1.31752 q^{92} +(-0.188939 - 0.327251i) q^{94} +3.45536 q^{95} +(4.40338 + 7.62688i) q^{97} +(-6.90136 - 1.17099i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8	\( 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8} + 2 q^{10} + 6 q^{11} - 11 q^{13} + 3 q^{14} + 8 q^{16} + 8 q^{17} + 6 q^{19} - 2 q^{20} - 6 q^{22} - 20 q^{23} - 18 q^{25} + 11 q^{26} - 3 q^{28} - 2 q^{29} + 6 q^{31} - 8 q^{32} - 8 q^{34} + 18 q^{35} + 56 q^{37} - 6 q^{38} + 2 q^{40} - 6 q^{43} + 6 q^{44} + 20 q^{46} - q^{47} + 5 q^{49} + 18 q^{50} - 11 q^{52} - 7 q^{53} + q^{55} + 3 q^{56} + 2 q^{58} + 4 q^{59} + 24 q^{61} - 6 q^{62} + 8 q^{64} - 22 q^{65} - 15 q^{67} + 8 q^{68} - 18 q^{70} - 6 q^{71} + q^{73} - 56 q^{74} + 6 q^{76} + 22 q^{77} - 12 q^{79} - 2 q^{80} + 32 q^{83} - 13 q^{85} + 6 q^{86} - 6 q^{88} + 50 q^{89} - 8 q^{91} - 20 q^{92} + q^{94} - 16 q^{95} - q^{97} - 5 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8 + 2 * q^10 + 6 * q^11 - 11 * q^13 + 3 * q^14 + 8 * q^16 + 8 * q^17 + 6 * q^19 - 2 * q^20 - 6 * q^22 - 20 * q^23 - 18 * q^25 + 11 * q^26 - 3 * q^28 - 2 * q^29 + 6 * q^31 - 8 * q^32 - 8 * q^34 + 18 * q^35 + 56 * q^37 - 6 * q^38 + 2 * q^40 - 6 * q^43 + 6 * q^44 + 20 * q^46 - q^47 + 5 * q^49 + 18 * q^50 - 11 * q^52 - 7 * q^53 + q^55 + 3 * q^56 + 2 * q^58 + 4 * q^59 + 24 * q^61 - 6 * q^62 + 8 * q^64 - 22 * q^65 - 15 * q^67 + 8 * q^68 - 18 * q^70 - 6 * q^71 + q^73 - 56 * q^74 + 6 * q^76 + 22 * q^77 - 12 * q^79 - 2 * q^80 + 32 * q^83 - 13 * q^85 + 6 * q^86 - 6 * q^88 + 50 * q^89 - 8 * q^91 - 20 * q^92 + q^94 - 16 * q^95 - q^97 - 5 * q^98

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