LMFDB - Embedded newform 1638.2.m.k.289.3

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 15x^{8} + 14x^{7} + 110x^{6} + 36x^{5} + 233x^{4} + 164x^{3} + 345x^{2} + 76x + 16 $ x^10 - 2x^9 + 15x^8 + 14x^7 + 110x^6 + 36x^5 + 233x^4 + 164x^3 + 345x^2 + 76*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.3
Root			$-0.114009 - 0.197470i$ of defining polynomial
Character	$\chi$	$=$	1638.289
Dual form			1638.2.m.k.1621.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-0.114009 + 0.197470i) q^{5} +(-2.59452 + 0.518144i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.114009 + 0.197470i) q^{5} +(-2.59452 + 0.518144i) q^{7} +1.00000 q^{8} +(-0.114009 + 0.197470i) q^{10} +(1.70561 - 2.95420i) q^{11} +(-1.62906 - 3.21655i) q^{13} +(-2.59452 + 0.518144i) q^{14} +1.00000 q^{16} +5.41122 q^{17} +(-3.17107 - 5.49246i) q^{19} +(-0.114009 + 0.197470i) q^{20} +(1.70561 - 2.95420i) q^{22} +1.91925 q^{23} +(2.47400 + 4.28510i) q^{25} +(-1.62906 - 3.21655i) q^{26} +(-2.59452 + 0.518144i) q^{28} +(-0.851453 - 1.47476i) q^{29} +(-1.78052 - 3.08395i) q^{31} +1.00000 q^{32} +5.41122 q^{34} +(0.193482 - 0.571413i) q^{35} -4.18320 q^{37} +(-3.17107 - 5.49246i) q^{38} +(-0.114009 + 0.197470i) q^{40} +(-1.59160 - 2.75673i) q^{41} +(5.17961 - 8.97135i) q^{43} +(1.70561 - 2.95420i) q^{44} +1.91925 q^{46} +(5.57211 - 9.65117i) q^{47} +(6.46305 - 2.68867i) q^{49} +(2.47400 + 4.28510i) q^{50} +(-1.62906 - 3.21655i) q^{52} +(3.31400 + 5.74001i) q^{53} +(0.388911 + 0.673613i) q^{55} +(-2.59452 + 0.518144i) q^{56} +(-0.851453 - 1.47476i) q^{58} +14.7704 q^{59} +(3.35999 + 5.81968i) q^{61} +(-1.78052 - 3.08395i) q^{62} +1.00000 q^{64} +(0.820899 + 0.0450268i) q^{65} +(-5.58065 + 9.66597i) q^{67} +5.41122 q^{68} +(0.193482 - 0.571413i) q^{70} +(0.0390952 - 0.0677149i) q^{71} +(-6.31721 - 10.9417i) q^{73} -4.18320 q^{74} +(-3.17107 - 5.49246i) q^{76} +(-2.89453 + 8.54848i) q^{77} +(0.811077 - 1.40483i) q^{79} +(-0.114009 + 0.197470i) q^{80} +(-1.59160 - 2.75673i) q^{82} +1.70291 q^{83} +(-0.616929 + 1.06855i) q^{85} +(5.17961 - 8.97135i) q^{86} +(1.70561 - 2.95420i) q^{88} -17.5457 q^{89} +(5.89325 + 7.50131i) q^{91} +1.91925 q^{92} +(5.57211 - 9.65117i) q^{94} +1.44613 q^{95} +(6.82663 - 11.8241i) q^{97} +(6.46305 - 2.68867i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 10 q^{8}+O(q^{10}) $ 10 * q + 10 * q^2 + 10 * q^4 + 2 * q^5 - 2 * q^7 + 10 * q^8	$ 10 q + 10 q^{2} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 10 q^{8} + 2 q^{10} - 6 q^{11} - 4 q^{13} - 2 q^{14} + 10 q^{16} + 8 q^{17} + 3 q^{19} + 2 q^{20} - 6 q^{22} + 12 q^{23} - q^{25} - 4 q^{26} - 2 q^{28} - 10 q^{31} + 10 q^{32} + 8 q^{34} - 16 q^{35} - 2 q^{37} + 3 q^{38} + 2 q^{40} + 4 q^{41} + 3 q^{43} - 6 q^{44} + 12 q^{46} + 15 q^{47} + 4 q^{49} - q^{50} - 4 q^{52} + 17 q^{53} + 3 q^{55} - 2 q^{56} + 4 q^{59} + 11 q^{61} - 10 q^{62} + 10 q^{64} + 4 q^{65} - q^{67} + 8 q^{68} - 16 q^{70} - 18 q^{71} + 12 q^{73} - 2 q^{74} + 3 q^{76} - 18 q^{77} - 4 q^{79} + 2 q^{80} + 4 q^{82} + q^{85} + 3 q^{86} - 6 q^{88} + 14 q^{89} + 26 q^{91} + 12 q^{92} + 15 q^{94} + 48 q^{95} - 6 q^{97} + 4 q^{98}+O(q^{100}) $ 10 * q + 10 * q^2 + 10 * q^4 + 2 * q^5 - 2 * q^7 + 10 * q^8 + 2 * q^10 - 6 * q^11 - 4 * q^13 - 2 * q^14 + 10 * q^16 + 8 * q^17 + 3 * q^19 + 2 * q^20 - 6 * q^22 + 12 * q^23 - q^25 - 4 * q^26 - 2 * q^28 - 10 * q^31 + 10 * q^32 + 8 * q^34 - 16 * q^35 - 2 * q^37 + 3 * q^38 + 2 * q^40 + 4 * q^41 + 3 * q^43 - 6 * q^44 + 12 * q^46 + 15 * q^47 + 4 * q^49 - q^50 - 4 * q^52 + 17 * q^53 + 3 * q^55 - 2 * q^56 + 4 * q^59 + 11 * q^61 - 10 * q^62 + 10 * q^64 + 4 * q^65 - q^67 + 8 * q^68 - 16 * q^70 - 18 * q^71 + 12 * q^73 - 2 * q^74 + 3 * q^76 - 18 * q^77 - 4 * q^79 + 2 * q^80 + 4 * q^82 + q^85 + 3 * q^86 - 6 * q^88 + 14 * q^89 + 26 * q^91 + 12 * q^92 + 15 * q^94 + 48 * q^95 - 6 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.114009	+	0.197470i	−0.0509865	+	0.0883113i	−0.890392	−	0.455194i	$-0.849570\pi$
$5$	−0.114009	+	0.197470i	−0.0509865	+	0.0883113i	0.839406	+	0.543505i	$0.182903\pi$
$6$		0			0
$7$	−2.59452	+	0.518144i	−0.980636	+	0.195840i
$7$	−2.59452	+	0.518144i	−0.980636	+	0.195840i
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.114009	+	0.197470i	−0.0360529	+	0.0624455i
$11$	1.70561	−	2.95420i	0.514260	−	0.890725i	−0.485603	−	0.874180i	$-0.661400\pi$
$11$	1.70561	−	2.95420i	0.514260	−	0.890725i	0.999863	−	0.0165453i	$-0.00526677\pi$
$12$		0			0
$13$	−1.62906	−	3.21655i	−0.451819	−	0.892110i
$13$	−1.62906	−	3.21655i	−0.451819	−	0.892110i
$14$	−2.59452	+	0.518144i	−0.693414	+	0.138480i
$15$		0			0
$16$	1.00000			0.250000
$17$	5.41122			1.31241			0.656206	−	0.754581i	$-0.272160\pi$
$17$	5.41122			1.31241			0.656206	+	0.754581i	$0.272160\pi$
$18$		0			0
$19$	−3.17107	−	5.49246i	−0.727494	−	1.26006i	−0.957939	−	0.286971i	$-0.907352\pi$
$19$	−3.17107	−	5.49246i	−0.727494	−	1.26006i	0.230446	−	0.973085i	$-0.425982\pi$
$20$	−0.114009	+	0.197470i	−0.0254933	+	0.0441556i
$21$		0			0
$22$	1.70561	−	2.95420i	0.363637	−	0.629838i
$23$	1.91925			0.400190			0.200095	−	0.979776i	$-0.435875\pi$
$23$	1.91925			0.400190			0.200095	+	0.979776i	$0.435875\pi$
$24$		0			0
$25$	2.47400	+	4.28510i	0.494801	+	0.857020i
$26$	−1.62906	−	3.21655i	−0.319484	−	0.630817i
$27$		0			0
$28$	−2.59452	+	0.518144i	−0.490318	+	0.0979200i
$29$	−0.851453	−	1.47476i	−0.158111	−	0.273856i	0.776077	−	0.630639i	$-0.217207\pi$
$29$	−0.851453	−	1.47476i	−0.158111	−	0.273856i	−0.934187	+	0.356783i	$0.883874\pi$
$30$		0			0
$31$	−1.78052	−	3.08395i	−0.319791	−	0.553895i	0.660653	−	0.750691i	$-0.270279\pi$
$31$	−1.78052	−	3.08395i	−0.319791	−	0.553895i	−0.980444	+	0.196797i	$0.936946\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	5.41122			0.928016
$35$	0.193482	−	0.571413i	0.0327043	−	0.0965864i
$36$		0			0
$37$	−4.18320			−0.687713			−0.343857	−	0.939022i	$-0.611733\pi$
$37$	−4.18320			−0.687713			−0.343857	+	0.939022i	$0.611733\pi$
$38$	−3.17107	−	5.49246i	−0.514416	−	0.890994i
$39$		0			0
$40$	−0.114009	+	0.197470i	−0.0180265	+	0.0312227i
$41$	−1.59160	−	2.75673i	−0.248566	−	0.430529i	0.714562	−	0.699572i	$-0.246626\pi$
$41$	−1.59160	−	2.75673i	−0.248566	−	0.430529i	−0.963128	+	0.269043i	$0.913293\pi$
$42$		0			0
$43$	5.17961	−	8.97135i	0.789883	−	1.36812i	−0.136154	−	0.990688i	$-0.543474\pi$
$43$	5.17961	−	8.97135i	0.789883	−	1.36812i	0.926038	−	0.377431i	$-0.123192\pi$
$44$	1.70561	−	2.95420i	0.257130	−	0.445362i
$45$		0			0
$46$	1.91925			0.282977
$47$	5.57211	−	9.65117i	0.812775	−	1.40777i	−0.0981388	−	0.995173i	$-0.531289\pi$
$47$	5.57211	−	9.65117i	0.812775	−	1.40777i	0.910914	−	0.412596i	$-0.135378\pi$
$48$		0			0
$49$	6.46305	−	2.68867i	0.923293	−	0.384095i
$50$	2.47400	+	4.28510i	0.349877	+	0.606005i
$51$		0			0
$52$	−1.62906	−	3.21655i	−0.225909	−	0.446055i
$53$	3.31400	+	5.74001i	0.455212	+	0.788451i	0.998700	−	0.0509659i	$-0.0162300\pi$
$53$	3.31400	+	5.74001i	0.455212	+	0.788451i	−0.543488	+	0.839417i	$0.682897\pi$
$54$		0			0
$55$	0.388911	+	0.673613i	0.0524407	+	0.0908299i
$56$	−2.59452	+	0.518144i	−0.346707	+	0.0692399i
$57$		0			0
$58$	−0.851453	−	1.47476i	−0.111801	−	0.193646i
$59$	14.7704			1.92295			0.961474	−	0.274897i	$-0.0886437\pi$
$59$	14.7704			1.92295			0.961474	+	0.274897i	$0.0886437\pi$
$60$		0			0
$61$	3.35999	+	5.81968i	0.430203	+	0.745134i	0.996891	−	0.0787991i	$-0.0251086\pi$
$61$	3.35999	+	5.81968i	0.430203	+	0.745134i	−0.566687	+	0.823933i	$0.691775\pi$
$62$	−1.78052	−	3.08395i	−0.226127	−	0.391663i
$63$		0			0
$64$	1.00000			0.125000
$65$	0.820899	+	0.0450268i	0.101820	+	0.00558489i
$66$		0			0
$67$	−5.58065	+	9.66597i	−0.681785	+	1.18089i	0.292651	+	0.956219i	$0.405463\pi$
$67$	−5.58065	+	9.66597i	−0.681785	+	1.18089i	−0.974436	+	0.224667i	$0.927871\pi$
$68$	5.41122			0.656206
$69$		0			0
$70$	0.193482	−	0.571413i	0.0231255	−	0.0682969i
$71$	0.0390952	−	0.0677149i	0.00463975	−	0.00803628i	−0.863696	−	0.504013i	$-0.831856\pi$
$71$	0.0390952	−	0.0677149i	0.00463975	−	0.00803628i	0.868336	+	0.495976i	$0.165190\pi$
$72$		0			0
$73$	−6.31721	−	10.9417i	−0.739373	−	1.28063i	−0.952778	−	0.303668i	$-0.901789\pi$
$73$	−6.31721	−	10.9417i	−0.739373	−	1.28063i	0.213404	−	0.976964i	$-0.431545\pi$
$74$	−4.18320			−0.486287
$75$		0			0
$76$	−3.17107	−	5.49246i	−0.363747	−	0.630028i
$77$	−2.89453	+	8.54848i	−0.329862	+	0.974189i
$78$		0			0
$79$	0.811077	−	1.40483i	0.0912532	−	0.158055i	−0.816785	−	0.576941i	$-0.804246\pi$
$79$	0.811077	−	1.40483i	0.0912532	−	0.158055i	0.908039	+	0.418886i	$0.137579\pi$
$80$	−0.114009	+	0.197470i	−0.0127466	+	0.0220778i
$81$		0			0
$82$	−1.59160	−	2.75673i	−0.175763	−	0.304430i
$83$	1.70291			0.186918			0.0934592	−	0.995623i	$-0.470208\pi$
$83$	1.70291			0.186918			0.0934592	+	0.995623i	$0.470208\pi$
$84$		0			0
$85$	−0.616929	+	1.06855i	−0.0669154	+	0.115901i
$86$	5.17961	−	8.97135i	0.558532	−	0.967406i
$87$		0			0
$88$	1.70561	−	2.95420i	0.181818	−	0.314919i
$89$	−17.5457			−1.85984			−0.929920	−	0.367762i	$-0.880124\pi$
$89$	−17.5457			−1.85984			−0.929920	+	0.367762i	$0.880124\pi$
$90$		0			0
$91$	5.89325	+	7.50131i	0.617780	+	0.786351i
$92$	1.91925			0.200095
$93$		0			0
$94$	5.57211	−	9.65117i	0.574719	−	0.995443i
$95$	1.44613			0.148369
$96$		0			0
$97$	6.82663	−	11.8241i	0.693140	−	1.20055i	−0.277664	−	0.960678i	$-0.589560\pi$
$97$	6.82663	−	11.8241i	0.693140	−	1.20055i	0.970804	−	0.239875i	$-0.0771064\pi$
$98$	6.46305	−	2.68867i	0.652867	−	0.271596i
$99$		0			0
$100$	2.47400	+	4.28510i	0.247400	+	0.428510i
$101$	−8.25823	+	14.3037i	−0.821724	+	1.42327i	0.0826732	+	0.996577i	$0.473654\pi$
$101$	−8.25823	+	14.3037i	−0.821724	+	1.42327i	−0.904397	+	0.426691i	$0.859679\pi$
$102$		0			0
$103$	−3.17961	+	5.50725i	−0.313296	+	0.542645i	−0.979074	−	0.203505i	$-0.934767\pi$
$103$	−3.17961	+	5.50725i	−0.313296	+	0.542645i	0.665777	+	0.746150i	$0.268100\pi$
$104$	−1.62906	−	3.21655i	−0.159742	−	0.315408i
$105$		0			0
$106$	3.31400	+	5.74001i	0.321884	+	0.557519i
$107$	−6.54724			−0.632945			−0.316473	−	0.948602i	$-0.602499\pi$
$107$	−6.54724			−0.632945			−0.316473	+	0.948602i	$0.602499\pi$
$108$		0			0
$109$	0.797093	+	1.38061i	0.0763477	+	0.132238i	0.901672	−	0.432422i	$-0.142341\pi$
$109$	0.797093	+	1.38061i	0.0763477	+	0.132238i	−0.825324	+	0.564660i	$0.809007\pi$
$110$	0.388911	+	0.673613i	0.0370812	+	0.0642265i
$111$		0			0
$112$	−2.59452	+	0.518144i	−0.245159	+	0.0489600i
$113$	4.12255	−	7.14047i	0.387817	−	0.671719i	−0.604339	−	0.796728i	$-0.706563\pi$
$113$	4.12255	−	7.14047i	0.387817	−	0.671719i	0.992156	+	0.125009i	$0.0398960\pi$
$114$		0			0
$115$	−0.218812	+	0.378993i	−0.0204043	+	0.0353413i
$116$	−0.851453	−	1.47476i	−0.0790555	−	0.136928i
$117$		0			0
$118$	14.7704			1.35973
$119$	−14.0395	+	2.80379i	−1.28700	+	0.257023i
$120$		0			0
$121$	−0.318198	−	0.551135i	−0.0289271	−	0.0501032i
$122$	3.35999	+	5.81968i	0.304200	+	0.526889i
$123$		0			0
$124$	−1.78052	−	3.08395i	−0.159896	−	0.276947i
$125$	−2.26833			−0.202886
$126$		0			0
$127$	−6.40560	−	11.0948i	−0.568405	−	0.984506i	−0.996724	−	0.0808783i	$-0.974227\pi$
$127$	−6.40560	−	11.0948i	−0.568405	−	0.984506i	0.428319	−	0.903627i	$-0.359106\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	0.820899	+	0.0450268i	0.0719976	+	0.00394912i
$131$	1.75964	−	3.04778i	0.153740	−	0.266286i	−0.778859	−	0.627199i	$-0.784201\pi$
$131$	1.75964	−	3.04778i	0.153740	−	0.266286i	0.932600	+	0.360913i	$0.117535\pi$
$132$		0			0
$133$	11.0733	+	12.6072i	0.960176	+	1.09318i
$134$	−5.58065	+	9.66597i	−0.482095	+	0.835012i
$135$		0			0
$136$	5.41122			0.464008
$137$	−17.6955			−1.51183			−0.755915	−	0.654669i	$-0.772808\pi$
$137$	−17.6955			−1.51183			−0.755915	+	0.654669i	$0.772808\pi$
$138$		0			0
$139$	3.98321	−	6.89912i	0.337851	−	0.585176i	−0.646177	−	0.763188i	$-0.723633\pi$
$139$	3.98321	−	6.89912i	0.337851	−	0.585176i	0.984028	+	0.178012i	$0.0569665\pi$
$140$	0.193482	−	0.571413i	0.0163522	−	0.0482932i
$141$		0			0
$142$	0.0390952	−	0.0677149i	0.00328080	−	0.00568251i
$143$	−12.2809	−	0.673613i	−1.02698	−	0.0563303i
$144$		0			0
$145$	0.388295			0.0322461
$146$	−6.31721	−	10.9417i	−0.522816	−	0.905544i
$147$		0			0
$148$	−4.18320			−0.343857
$149$	1.34679	+	2.33271i	0.110333	+	0.191103i	0.915905	−	0.401396i	$-0.131475\pi$
$149$	1.34679	+	2.33271i	0.110333	+	0.191103i	−0.805571	+	0.592499i	$0.798141\pi$
$150$		0			0
$151$	6.56432	+	11.3697i	0.534197	+	0.925256i	0.999202	+	0.0399480i	$0.0127192\pi$
$151$	6.56432	+	11.3697i	0.534197	+	0.925256i	−0.465005	+	0.885308i	$0.653947\pi$
$152$	−3.17107	−	5.49246i	−0.257208	−	0.445497i
$153$		0			0
$154$	−2.89453	+	8.54848i	−0.233248	+	0.688856i
$155$	0.811985			0.0652202
$156$		0			0
$157$	−1.59071	−	2.75520i	−0.126953	−	0.219889i	0.795542	−	0.605899i	$-0.207186\pi$
$157$	−1.59071	−	2.75520i	−0.126953	−	0.219889i	−0.922495	+	0.386010i	$0.873853\pi$
$158$	0.811077	−	1.40483i	0.0645258	−	0.111762i
$159$		0			0
$160$	−0.114009	+	0.197470i	−0.00901323	+	0.0156114i
$161$	−4.97952	+	0.994446i	−0.392441	+	0.0783733i
$162$		0			0
$163$	8.14702	+	14.1111i	0.638124	+	1.10526i	0.985844	+	0.167665i	$0.0536226\pi$
$163$	8.14702	+	14.1111i	0.638124	+	1.10526i	−0.347720	+	0.937598i	$0.613044\pi$
$164$	−1.59160	−	2.75673i	−0.124283	−	0.215264i
$165$		0			0
$166$	1.70291			0.132171
$167$	−0.826739	−	1.43195i	−0.0639750	−	0.110808i	0.832264	−	0.554380i	$-0.187044\pi$
$167$	−0.826739	−	1.43195i	−0.0639750	−	0.110808i	−0.896239	+	0.443572i	$0.853711\pi$
$168$		0			0
$169$	−7.69235	+	10.4799i	−0.591720	+	0.806144i
$170$	−0.616929	+	1.06855i	−0.0473163	+	0.0819543i
$171$		0			0
$172$	5.17961	−	8.97135i	0.394942	−	0.684059i
$173$	7.02100	+	12.1607i	0.533797	+	0.924563i	0.999221	+	0.0394751i	$0.0125686\pi$
$173$	7.02100	+	12.1607i	0.533797	+	0.924563i	−0.465424	+	0.885088i	$0.654098\pi$
$174$		0			0
$175$	−8.63915	−	9.83588i	−0.653058	−	0.743523i
$176$	1.70561	−	2.95420i	0.128565	−	0.222681i
$177$		0			0
$178$	−17.5457			−1.31511
$179$	−4.66663	+	8.08283i	−0.348800	+	0.604139i	−0.986037	−	0.166529i	$-0.946744\pi$
$179$	−4.66663	+	8.08283i	−0.348800	+	0.604139i	0.637237	+	0.770668i	$0.280077\pi$
$180$		0			0
$181$	1.13838			0.0846148			0.0423074	−	0.999105i	$-0.486529\pi$
$181$	1.13838			0.0846148			0.0423074	+	0.999105i	$0.486529\pi$
$182$	5.89325	+	7.50131i	0.436837	+	0.556034i
$183$		0			0
$184$	1.91925			0.141489
$185$	0.476924	−	0.826056i	0.0350641	−	0.0607328i
$186$		0			0
$187$	9.22941	−	15.9858i	0.674922	−	1.16900i
$188$	5.57211	−	9.65117i	0.406388	−	0.703884i
$189$		0			0
$190$	1.44613			0.104913
$191$	9.04253	+	15.6621i	0.654294	+	1.13327i	0.982070	+	0.188515i	$0.0603675\pi$
$191$	9.04253	+	15.6621i	0.654294	+	1.13327i	−0.327776	+	0.944755i	$0.606299\pi$
$192$		0			0
$193$	2.91296	−	5.04539i	0.209679	−	0.363175i	−0.741934	−	0.670473i	$-0.766091\pi$
$193$	2.91296	−	5.04539i	0.209679	−	0.363175i	0.951614	+	0.307297i	$0.0994246\pi$
$194$	6.82663	−	11.8241i	0.490124	−	0.848919i
$195$		0			0
$196$	6.46305	−	2.68867i	0.461647	−	0.192048i
$197$	10.3527	+	17.9315i	0.737602	+	1.27756i	0.953572	+	0.301165i	$0.0973755\pi$
$197$	10.3527	+	17.9315i	0.737602	+	1.27756i	−0.215970	+	0.976400i	$0.569291\pi$
$198$		0			0
$199$	−16.3984			−1.16245			−0.581227	−	0.813741i	$-0.697427\pi$
$199$	−16.3984			−1.16245			−0.581227	+	0.813741i	$0.697427\pi$
$200$	2.47400	+	4.28510i	0.174938	+	0.303002i
$201$		0			0
$202$	−8.25823	+	14.3037i	−0.581047	+	1.00640i
$203$	2.97325	+	3.38512i	0.208681	+	0.237589i
$204$		0			0
$205$	0.725829			0.0506941
$206$	−3.17961	+	5.50725i	−0.221534	+	0.383708i
$207$		0			0
$208$	−1.62906	−	3.21655i	−0.112955	−	0.223027i
$209$	−21.6344			−1.49648
$210$		0			0
$211$	3.74446	+	6.48560i	0.257779	+	0.446487i	0.965647	−	0.259858i	$-0.0836759\pi$
$211$	3.74446	+	6.48560i	0.257779	+	0.446487i	−0.707867	+	0.706345i	$0.750343\pi$
$212$	3.31400	+	5.74001i	0.227606	+	0.394226i
$213$		0			0
$214$	−6.54724			−0.447560
$215$	1.18105	+	2.04564i	0.0805468	+	0.139511i
$216$		0			0
$217$	6.21753	+	7.07881i	0.422073	+	0.480541i
$218$	0.797093	+	1.38061i	0.0539860	+	0.0935064i
$219$		0			0
$220$	0.388911	+	0.673613i	0.0262203	+	0.0454150i
$221$	−8.81517	−	17.4054i	−0.592973	−	1.17082i
$222$		0			0
$223$	−8.41325	−	14.5722i	−0.563393	−	0.975825i	−0.997197	−	0.0748181i	$-0.976162\pi$
$223$	−8.41325	−	14.5722i	−0.563393	−	0.975825i	0.433804	−	0.901007i	$-0.357171\pi$
$224$	−2.59452	+	0.518144i	−0.173354	+	0.0346199i
$225$		0			0
$226$	4.12255	−	7.14047i	0.274228	−	0.474977i
$227$	4.23214			0.280897			0.140449	−	0.990088i	$-0.455146\pi$
$227$	4.23214			0.280897			0.140449	+	0.990088i	$0.455146\pi$
$228$		0			0
$229$	−6.86498	+	11.8905i	−0.453650	+	0.785745i	−0.998609	−	0.0527171i	$-0.983212\pi$
$229$	−6.86498	+	11.8905i	−0.453650	+	0.785745i	0.544959	+	0.838463i	$0.316545\pi$
$230$	−0.218812	+	0.378993i	−0.0144280	+	0.0249901i
$231$		0			0
$232$	−0.851453	−	1.47476i	−0.0559007	−	0.0968228i
$233$	3.85349	−	6.67444i	0.252450	−	0.437257i	−0.711749	−	0.702433i	$-0.752097\pi$
$233$	3.85349	−	6.67444i	0.252450	−	0.437257i	0.964200	+	0.265176i	$0.0854302\pi$
$234$		0			0
$235$	1.27054	+	2.20065i	0.0828812	+	0.143554i
$236$	14.7704			0.961474
$237$		0			0
$238$	−14.0395	+	2.80379i	−0.910046	+	0.181743i
$239$	25.2189			1.63128			0.815638	−	0.578562i	$-0.196386\pi$
$239$	25.2189			1.63128			0.815638	+	0.578562i	$0.196386\pi$
$240$		0			0
$241$	27.8367			1.79312			0.896560	−	0.442923i	$-0.146059\pi$
$241$	27.8367			1.79312			0.896560	+	0.442923i	$0.146059\pi$
$242$	−0.318198	−	0.551135i	−0.0204545	−	0.0354283i
$243$		0			0
$244$	3.35999	+	5.81968i	0.215102	+	0.372567i
$245$	−0.205917	+	1.58279i	−0.0131556	+	0.101121i
$246$		0			0
$247$	−12.5009	+	19.1474i	−0.795413	+	1.21832i
$248$	−1.78052	−	3.08395i	−0.113063	−	0.195831i
$249$		0			0
$250$	−2.26833			−0.143462
$251$	−2.12395	+	3.67878i	−0.134062	+	0.232203i	−0.925239	−	0.379385i	$-0.876136\pi$
$251$	−2.12395	+	3.67878i	−0.134062	+	0.232203i	0.791177	+	0.611588i	$0.209469\pi$
$252$		0			0
$253$	3.27348	−	5.66984i	0.205802	−	0.356460i
$254$	−6.40560	−	11.0948i	−0.401923	−	0.696151i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−14.7167			−0.918003			−0.459002	−	0.888435i	$-0.651793\pi$
$257$	−14.7167			−0.918003			−0.459002	+	0.888435i	$0.651793\pi$
$258$		0			0
$259$	10.8534	−	2.16750i	0.674396	−	0.134682i
$260$	0.820899	+	0.0450268i	0.0509100	+	0.00279245i
$261$		0			0
$262$	1.75964	−	3.04778i	0.108711	−	0.188292i
$263$	11.7053	−	20.2741i	0.721777	−	1.25015i	−0.238510	−	0.971140i	$-0.576659\pi$
$263$	11.7053	−	20.2741i	0.721777	−	1.25015i	0.960287	−	0.279015i	$-0.0900078\pi$
$264$		0			0
$265$	−1.51131			−0.0928388
$266$	11.0733	+	12.6072i	0.678947	+	0.772998i
$267$		0			0
$268$	−5.58065	+	9.66597i	−0.340892	+	0.590443i
$269$	9.35772			0.570550			0.285275	−	0.958446i	$-0.407915\pi$
$269$	9.35772			0.570550			0.285275	+	0.958446i	$0.407915\pi$
$270$		0			0
$271$	−15.1475			−0.920145			−0.460072	−	0.887881i	$-0.652177\pi$
$271$	−15.1475			−0.920145			−0.460072	+	0.887881i	$0.652177\pi$
$272$	5.41122			0.328103
$273$		0			0
$274$	−17.6955			−1.06903
$275$	16.8787			1.01783
$276$		0			0
$277$	−32.8782			−1.97546			−0.987731	−	0.156165i	$-0.950087\pi$
$277$	−32.8782			−1.97546			−0.987731	+	0.156165i	$0.950087\pi$
$278$	3.98321	−	6.89912i	0.238897	−	0.413782i
$279$		0			0
$280$	0.193482	−	0.571413i	0.0115627	−	0.0341484i
$281$	16.8072			1.00263			0.501316	−	0.865264i	$-0.332850\pi$
$281$	16.8072			1.00263			0.501316	+	0.865264i	$0.332850\pi$
$282$		0			0
$283$	6.07998	−	10.5308i	0.361417	−	0.625993i	−0.626777	−	0.779199i	$-0.715626\pi$
$283$	6.07998	−	10.5308i	0.361417	−	0.625993i	0.988194	+	0.153205i	$0.0489596\pi$
$284$	0.0390952	−	0.0677149i	0.00231988	−	0.00401814i
$285$		0			0
$286$	−12.2809	−	0.673613i	−0.726182	−	0.0398316i
$287$	5.55782	+	6.32771i	0.328067	+	0.373513i
$288$		0			0
$289$	12.2813			0.722427
$290$	0.388295			0.0228014
$291$		0			0
$292$	−6.31721	−	10.9417i	−0.369687	−	0.640316i
$293$	−13.8954	+	24.0675i	−0.811778	+	1.40604i	0.0998407	+	0.995003i	$0.468167\pi$
$293$	−13.8954	+	24.0675i	−0.811778	+	1.40604i	−0.911619	+	0.411037i	$0.865167\pi$
$294$		0			0
$295$	−1.68397	+	2.91672i	−0.0980444	+	0.169818i
$296$	−4.18320			−0.243143
$297$		0			0
$298$	1.34679	+	2.33271i	0.0780175	+	0.135130i
$299$	−3.12656	−	6.17335i	−0.180814	−	0.357014i
$300$		0			0
$301$	−8.79015	+	25.9601i	−0.506656	+	1.49632i
$302$	6.56432	+	11.3697i	0.377734	+	0.654255i
$303$		0			0
$304$	−3.17107	−	5.49246i	−0.181873	−	0.315014i
$305$	−1.53228			−0.0877383
$306$		0			0
$307$	−14.6849			−0.838110			−0.419055	−	0.907961i	$-0.637639\pi$
$307$	−14.6849			−0.838110			−0.419055	+	0.907961i	$0.637639\pi$
$308$	−2.89453	+	8.54848i	−0.164931	+	0.487095i
$309$		0			0
$310$	0.811985			0.0461176
$311$	−3.86348	−	6.69174i	−0.219078	−	0.379453i	0.735449	−	0.677580i	$-0.236971\pi$
$311$	−3.86348	−	6.69174i	−0.219078	−	0.379453i	−0.954526	+	0.298127i	$0.903638\pi$
$312$		0			0
$313$	−10.0982	+	17.4906i	−0.570784	+	0.988626i	0.425702	+	0.904863i	$0.360027\pi$
$313$	−10.0982	+	17.4906i	−0.570784	+	0.988626i	−0.996486	+	0.0837628i	$0.973306\pi$
$314$	−1.59071	−	2.75520i	−0.0897692	−	0.155485i
$315$		0			0
$316$	0.811077	−	1.40483i	0.0456266	−	0.0790276i
$317$	−7.36088	+	12.7494i	−0.413428	+	0.716079i	−0.995262	−	0.0972291i	$-0.969002\pi$
$317$	−7.36088	+	12.7494i	−0.413428	+	0.716079i	0.581834	+	0.813308i	$0.302335\pi$
$318$		0			0
$319$	−5.80898			−0.325241
$320$	−0.114009	+	0.197470i	−0.00637332	+	0.0110389i
$321$		0			0
$322$	−4.97952	+	0.994446i	−0.277498	+	0.0554183i
$323$	−17.1594	−	29.7209i	−0.954772	−	1.65371i
$324$		0			0
$325$	9.75294	−	14.9384i	0.540996	−	0.828634i
$326$	8.14702	+	14.1111i	0.451222	+	0.781539i
$327$		0			0
$328$	−1.59160	−	2.75673i	−0.0878813	−	0.152215i
$329$	−9.45624	+	27.9273i	−0.521339	+	1.53968i
$330$		0			0
$331$	−2.05436	−	3.55826i	−0.112918	−	0.195579i	0.804028	−	0.594592i	$-0.202686\pi$
$331$	−2.05436	−	3.55826i	−0.112918	−	0.195579i	−0.916946	+	0.399012i	$0.869353\pi$
$332$	1.70291			0.0934592
$333$		0			0
$334$	−0.826739	−	1.43195i	−0.0452371	−	0.0783530i
$335$	−1.27249	−	2.20402i	−0.0695237	−	0.120419i
$336$		0			0
$337$	−7.44592			−0.405605			−0.202802	−	0.979220i	$-0.565005\pi$
$337$	−7.44592			−0.405605			−0.202802	+	0.979220i	$0.565005\pi$
$338$	−7.69235	+	10.4799i	−0.418409	+	0.570030i
$339$		0			0
$340$	−0.616929	+	1.06855i	−0.0334577	+	0.0579504i
$341$	−12.1475			−0.657824
$342$		0			0
$343$	−15.3754	+	10.3246i	−0.830193	+	0.557475i
$344$	5.17961	−	8.97135i	0.279266	−	0.483703i
$345$		0			0
$346$	7.02100	+	12.1607i	0.377451	+	0.653765i
$347$	10.5281			0.565180			0.282590	−	0.959241i	$-0.408806\pi$
$347$	10.5281			0.565180			0.282590	+	0.959241i	$0.408806\pi$
$348$		0			0
$349$	−4.74127	−	8.21212i	−0.253794	−	0.439585i	0.710773	−	0.703422i	$-0.248345\pi$
$349$	−4.74127	−	8.21212i	−0.253794	−	0.439585i	−0.964567	+	0.263837i	$0.915012\pi$
$350$	−8.63915	−	9.83588i	−0.461782	−	0.525750i
$351$		0			0
$352$	1.70561	−	2.95420i	0.0909092	−	0.157459i
$353$	2.72112	−	4.71311i	0.144830	−	0.250854i	−0.784479	−	0.620155i	$-0.787070\pi$
$353$	2.72112	−	4.71311i	0.144830	−	0.250854i	0.929310	+	0.369301i	$0.120403\pi$
$354$		0			0
$355$	0.00891445	+	0.0154403i	0.000473130	+	0.000819485i
$356$	−17.5457			−0.929920
$357$		0			0
$358$	−4.66663	+	8.08283i	−0.246639	+	0.427191i
$359$	5.29579	−	9.17257i	0.279501	−	0.484110i	−0.691760	−	0.722128i	$-0.743164\pi$
$359$	5.29579	−	9.17257i	0.279501	−	0.484110i	0.971261	+	0.238018i	$0.0764976\pi$
$360$		0			0
$361$	−10.6114	+	18.3795i	−0.558494	+	0.967340i
$362$	1.13838			0.0598317
$363$		0			0
$364$	5.89325	+	7.50131i	0.308890	+	0.393175i
$365$	2.88088			0.150792
$366$		0			0
$367$	3.59896	−	6.23359i	0.187864	−	0.325391i	−0.756674	−	0.653793i	$-0.773177\pi$
$367$	3.59896	−	6.23359i	0.187864	−	0.325391i	0.944538	+	0.328402i	$0.106510\pi$
$368$	1.91925			0.100048
$369$		0			0
$370$	0.476924	−	0.826056i	0.0247941	−	0.0429446i
$371$	−11.5724	−	13.1754i	−0.600808	−	0.684035i
$372$		0			0
$373$	14.2762	+	24.7271i	0.739192	+	1.28032i	0.952859	+	0.303412i	$0.0981259\pi$
$373$	14.2762	+	24.7271i	0.739192	+	1.28032i	−0.213667	+	0.976907i	$0.568541\pi$
$374$	9.22941	−	15.9858i	0.477242	−	0.826607i
$375$		0			0
$376$	5.57211	−	9.65117i	0.287360	−	0.497721i
$377$	−3.35657	+	5.14121i	−0.172872	+	0.264786i
$378$		0			0
$379$	15.5638	+	26.9572i	0.799457	+	1.38470i	0.919970	+	0.391989i	$0.128213\pi$
$379$	15.5638	+	26.9572i	0.799457	+	1.38470i	−0.120513	+	0.992712i	$0.538454\pi$
$380$	1.44613			0.0741847
$381$		0			0
$382$	9.04253	+	15.6621i	0.462656	+	0.801343i
$383$	10.9760	+	19.0111i	0.560849	+	0.971420i	0.997423	+	0.0717509i	$0.0228587\pi$
$383$	10.9760	+	19.0111i	0.560849	+	0.971420i	−0.436573	+	0.899669i	$0.643808\pi$
$384$		0			0
$385$	−1.35806	−	1.54619i	−0.0692133	−	0.0788011i
$386$	2.91296	−	5.04539i	0.148266	−	0.256804i
$387$		0			0
$388$	6.82663	−	11.8241i	0.346570	−	0.600277i
$389$	−1.87365	−	3.24525i	−0.0949976	−	0.164541i	0.814610	−	0.580009i	$-0.196951\pi$
$389$	−1.87365	−	3.24525i	−0.0949976	−	0.164541i	−0.909608	+	0.415468i	$0.863618\pi$
$390$		0			0
$391$	10.3855			0.525215
$392$	6.46305	−	2.68867i	0.326434	−	0.135798i
$393$		0			0
$394$	10.3527	+	17.9315i	0.521564	+	0.903375i
$395$	0.184941	+	0.320327i	0.00930537	+	0.0161174i
$396$		0			0
$397$	1.95502	+	3.38620i	0.0981198	+	0.169949i	0.910906	−	0.412613i	$-0.135384\pi$
$397$	1.95502	+	3.38620i	0.0981198	+	0.169949i	−0.812787	+	0.582562i	$0.802050\pi$
$398$	−16.3984			−0.821979
$399$		0			0
$400$	2.47400	+	4.28510i	0.123700	+	0.214255i
$401$	26.2260			1.30967			0.654833	−	0.755774i	$-0.272739\pi$
$401$	26.2260			1.30967			0.654833	+	0.755774i	$0.272739\pi$
$402$		0			0
$403$	−7.01912	+	10.7511i	−0.349647	+	0.535549i
$404$	−8.25823	+	14.3037i	−0.410862	+	0.711634i
$405$		0			0
$406$	2.97325	+	3.38512i	0.147560	+	0.168001i
$407$	−7.13490	+	12.3580i	−0.353664	+	0.612563i
$408$		0			0
$409$	4.03519			0.199527			0.0997635	−	0.995011i	$-0.468191\pi$
$409$	4.03519			0.199527			0.0997635	+	0.995011i	$0.468191\pi$
$410$	0.725829			0.0358461
$411$		0			0
$412$	−3.17961	+	5.50725i	−0.156648	+	0.271323i
$413$	−38.3222	+	7.65321i	−1.88571	+	0.376590i
$414$		0			0
$415$	−0.194147	+	0.336273i	−0.00953032	+	0.0165070i
$416$	−1.62906	−	3.21655i	−0.0798710	−	0.157704i
$417$		0			0
$418$	−21.6344			−1.05817
$419$	−1.74139	−	3.01617i	−0.0850723	−	0.147350i	0.820350	−	0.571862i	$-0.193779\pi$
$419$	−1.74139	−	3.01617i	−0.0850723	−	0.147350i	−0.905422	+	0.424513i	$0.860445\pi$
$420$		0			0
$421$	18.6028			0.906647			0.453323	−	0.891346i	$-0.350238\pi$
$421$	18.6028			0.906647			0.453323	+	0.891346i	$0.350238\pi$
$422$	3.74446	+	6.48560i	0.182277	+	0.315714i
$423$		0			0
$424$	3.31400	+	5.74001i	0.160942	+	0.278760i
$425$	13.3874	+	23.1876i	0.649383	+	1.12476i
$426$		0			0
$427$	−11.7330	−	13.3583i	−0.567800	−	0.646454i
$428$	−6.54724			−0.316473
$429$		0			0
$430$	1.18105	+	2.04564i	0.0569552	+	0.0986493i
$431$	−9.52662	+	16.5006i	−0.458881	+	0.794806i	−0.998902	−	0.0468461i	$-0.985083\pi$
$431$	−9.52662	+	16.5006i	−0.458881	+	0.794806i	0.540021	+	0.841652i	$0.318416\pi$
$432$		0			0
$433$	−16.7336	+	28.9834i	−0.804164	+	1.39285i	0.112689	+	0.993630i	$0.464053\pi$
$433$	−16.7336	+	28.9834i	−0.804164	+	1.39285i	−0.916854	+	0.399223i	$0.869280\pi$
$434$	6.21753	+	7.07881i	0.298451	+	0.339794i
$435$		0			0
$436$	0.797093	+	1.38061i	0.0381738	+	0.0661190i
$437$	−6.08607	−	10.5414i	−0.291136	−	0.504262i
$438$		0			0
$439$	38.0459			1.81583			0.907915	−	0.419154i	$-0.137673\pi$
$439$	38.0459			1.81583			0.907915	+	0.419154i	$0.137673\pi$
$440$	0.388911	+	0.673613i	0.0185406	+	0.0321132i
$441$		0			0
$442$	−8.81517	−	17.4054i	−0.419295	−	0.827892i
$443$	−4.35467	+	7.54250i	−0.206896	+	0.358355i	−0.950735	−	0.310004i	$-0.899670\pi$
$443$	−4.35467	+	7.54250i	−0.206896	+	0.358355i	0.743839	+	0.668359i	$0.233003\pi$
$444$		0			0
$445$	2.00037	−	3.46475i	0.0948268	−	0.164245i
$446$	−8.41325	−	14.5722i	−0.398379	−	0.690013i
$447$		0			0
$448$	−2.59452	+	0.518144i	−0.122579	+	0.0244800i
$449$	11.4930	−	19.9065i	0.542389	−	0.939445i	−0.456377	−	0.889786i	$-0.650853\pi$
$449$	11.4930	−	19.9065i	0.542389	−	0.939445i	0.998766	−	0.0496589i	$-0.0158134\pi$
$450$		0			0
$451$	−10.8586			−0.511310
$452$	4.12255	−	7.14047i	0.193908	−	0.335859i
$453$		0			0
$454$	4.23214			0.198624
$455$	−2.15317	+	0.308521i	−0.100942	+	0.0144637i
$456$		0			0
$457$	11.5899			0.542150			0.271075	−	0.962558i	$-0.412621\pi$
$457$	11.5899			0.542150			0.271075	+	0.962558i	$0.412621\pi$
$458$	−6.86498	+	11.8905i	−0.320779	+	0.555606i
$459$		0			0
$460$	−0.218812	+	0.378993i	−0.0102022	+	0.0176707i
$461$	17.4236	−	30.1785i	0.811496	−	1.40555i	−0.100321	−	0.994955i	$-0.531987\pi$
$461$	17.4236	−	30.1785i	0.811496	−	1.40555i	0.911817	−	0.410597i	$-0.134680\pi$
$462$		0			0
$463$	−39.5334			−1.83727			−0.918635	−	0.395106i	$-0.870708\pi$
$463$	−39.5334			−1.83727			−0.918635	+	0.395106i	$0.870708\pi$
$464$	−0.851453	−	1.47476i	−0.0395277	−	0.0684640i
$465$		0			0
$466$	3.85349	−	6.67444i	0.178509	−	0.309187i
$467$	0.425191	−	0.736452i	0.0196755	−	0.0340789i	−0.856020	−	0.516943i	$-0.827070\pi$
$467$	0.425191	−	0.736452i	0.0196755	−	0.0340789i	0.875695	+	0.482864i	$0.160403\pi$
$468$		0			0
$469$	9.47074	−	27.9701i	0.437318	−	1.29154i
$470$	1.27054	+	2.20065i	0.0586059	+	0.101508i
$471$		0			0
$472$	14.7704			0.679865
$473$	−17.6688	−	30.6032i	−0.812411	−	1.40714i
$474$		0			0
$475$	15.6905	−	27.1767i	0.719929	−	1.24695i
$476$	−14.0395	+	2.80379i	−0.643499	+	0.128511i
$477$		0			0
$478$	25.2189			1.15349
$479$	5.78732	−	10.0239i	0.264429	−	0.458005i	−0.702985	−	0.711205i	$-0.748150\pi$
$479$	5.78732	−	10.0239i	0.264429	−	0.458005i	0.967414	+	0.253200i	$0.0814831\pi$
$480$		0			0
$481$	6.81466	+	13.4555i	0.310722	+	0.613516i
$482$	27.8367			1.26793
$483$		0			0
$484$	−0.318198	−	0.551135i	−0.0144635	−	0.0250516i
$485$	1.55660	+	2.69611i	0.0706816	+	0.122424i
$486$		0			0
$487$	−13.9320			−0.631321			−0.315661	−	0.948872i	$-0.602226\pi$
$487$	−13.9320			−0.631321			−0.315661	+	0.948872i	$0.602226\pi$
$488$	3.35999	+	5.81968i	0.152100	+	0.263445i
$489$		0			0
$490$	−0.205917	+	1.58279i	−0.00930240	+	0.0715033i
$491$	−4.76716	−	8.25697i	−0.215139	−	0.372632i	0.738177	−	0.674608i	$-0.235687\pi$
$491$	−4.76716	−	8.25697i	−0.215139	−	0.372632i	−0.953316	+	0.301976i	$0.902354\pi$
$492$		0			0
$493$	−4.60740	−	7.98025i	−0.207507	−	0.359412i
$494$	−12.5009	+	19.1474i	−0.562442	+	0.861483i
$495$		0			0
$496$	−1.78052	−	3.08395i	−0.0799478	−	0.138474i
$497$	−0.0663472	+	0.195945i	−0.00297608	+	0.00878932i
$498$		0			0
$499$	21.9135	−	37.9553i	0.980982	−	1.69911i	0.322397	−	0.946605i	$-0.395511\pi$
$499$	21.9135	−	37.9553i	0.980982	−	1.69911i	0.658585	−	0.752506i	$-0.271155\pi$
$500$	−2.26833			−0.101443
$501$		0			0
$502$	−2.12395	+	3.67878i	−0.0947963	+	0.164192i
$503$	7.35181	−	12.7337i	0.327801	−	0.567768i	−0.654274	−	0.756257i	$-0.727026\pi$
$503$	7.35181	−	12.7337i	0.327801	−	0.567768i	0.982075	+	0.188489i	$0.0603591\pi$
$504$		0			0
$505$	−1.88303	−	3.26150i	−0.0837937	−	0.145135i
$506$	3.27348	−	5.66984i	0.145524	−	0.252055i
$507$		0			0
$508$	−6.40560	−	11.0948i	−0.284202	−	0.492253i
$509$	14.4795			0.641792			0.320896	−	0.947114i	$-0.396016\pi$
$509$	14.4795			0.641792			0.320896	+	0.947114i	$0.396016\pi$
$510$		0			0
$511$	22.0595	+	25.1153i	0.975855	+	1.11104i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−14.7167			−0.649126
$515$	−0.725011	−	1.25576i	−0.0319478	−	0.0553352i
$516$		0			0
$517$	−19.0077	−	32.9222i	−0.835956	−	1.44792i
$518$	10.8534	−	2.16750i	0.476870	−	0.0952344i
$519$		0			0
$520$	0.820899	+	0.0450268i	0.0359988	+	0.00197456i
$521$	−7.18959	−	12.4527i	−0.314982	−	0.545564i	0.664452	−	0.747331i	$-0.268665\pi$
$521$	−7.18959	−	12.4527i	−0.314982	−	0.545564i	−0.979434	+	0.201767i	$0.935332\pi$
$522$		0			0
$523$	−1.02354			−0.0447563			−0.0223781	−	0.999750i	$-0.507124\pi$
$523$	−1.02354			−0.0447563			−0.0223781	+	0.999750i	$0.507124\pi$
$524$	1.75964	−	3.04778i	0.0768701	−	0.133143i
$525$		0			0
$526$	11.7053	−	20.2741i	0.510374	−	0.883993i
$527$	−9.63479	−	16.6879i	−0.419698	−	0.726938i
$528$		0			0
$529$	−19.3165			−0.839848
$530$	−1.51131			−0.0656470
$531$		0			0
$532$	11.0733	+	12.6072i	0.480088	+	0.546592i
$533$	−6.27435	+	9.61032i	−0.271772	+	0.416269i
$534$		0			0
$535$	0.746446	−	1.29288i	0.0322717	−	0.0558962i
$536$	−5.58065	+	9.66597i	−0.241047	+	0.417506i
$537$		0			0
$538$	9.35772			0.403440
$539$	3.08058	−	23.6790i	0.132690	−	1.01993i
$540$		0			0
$541$	0.804352	−	1.39318i	0.0345818	−	0.0598974i	−0.848217	−	0.529650i	$-0.822323\pi$
$541$	0.804352	−	1.39318i	0.0345818	−	0.0598974i	0.882798	+	0.469752i	$0.155657\pi$
$542$	−15.1475			−0.650641
$543$		0			0
$544$	5.41122			0.232004
$545$	−0.363504			−0.0155708
$546$		0			0
$547$	26.9289			1.15140			0.575699	−	0.817661i	$-0.304730\pi$
$547$	26.9289			1.15140			0.575699	+	0.817661i	$0.304730\pi$
$548$	−17.6955			−0.755915
$549$		0			0
$550$	16.8787			0.719711
$551$	−5.40004	+	9.35314i	−0.230049	+	0.398457i
$552$		0			0
$553$	−1.37645	+	4.06510i	−0.0585327	+	0.172866i
$554$	−32.8782			−1.39686
$555$		0			0
$556$	3.98321	−	6.89912i	0.168926	−	0.292588i
$557$	−18.1841	+	31.4957i	−0.770484	+	1.33452i	0.166815	+	0.985988i	$0.446652\pi$
$557$	−18.1841	+	31.4957i	−0.770484	+	1.33452i	−0.937298	+	0.348528i	$0.886681\pi$
$558$		0			0
$559$	−37.2947	−	2.04564i	−1.57740	−	0.0865212i
$560$	0.193482	−	0.571413i	0.00817609	−	0.0241466i
$561$		0			0
$562$	16.8072			0.708968
$563$	3.73021			0.157210			0.0786048	−	0.996906i	$-0.474953\pi$
$563$	3.73021			0.157210			0.0786048	+	0.996906i	$0.474953\pi$
$564$		0			0
$565$	0.940019	+	1.62816i	0.0395469	+	0.0684972i
$566$	6.07998	−	10.5308i	0.255561	−	0.442644i
$567$		0			0
$568$	0.0390952	−	0.0677149i	0.00164040	−	0.00284126i
$569$	15.3919			0.645263			0.322632	−	0.946525i	$-0.395433\pi$
$569$	15.3919			0.645263			0.322632	+	0.946525i	$0.395433\pi$
$570$		0			0
$571$	−10.1994	−	17.6659i	−0.426832	−	0.739296i	0.569757	−	0.821813i	$-0.307037\pi$
$571$	−10.1994	−	17.6659i	−0.426832	−	0.739296i	−0.996590	+	0.0825176i	$0.973704\pi$
$572$	−12.2809	−	0.673613i	−0.513488	−	0.0281652i
$573$		0			0
$574$	5.55782	+	6.32771i	0.231979	+	0.264114i
$575$	4.74822	+	8.22416i	0.198015	+	0.342971i
$576$		0			0
$577$	−5.90380	−	10.2257i	−0.245779	−	0.425701i	0.716572	−	0.697513i	$-0.245710\pi$
$577$	−5.90380	−	10.2257i	−0.245779	−	0.425701i	−0.962350	+	0.271813i	$0.912377\pi$
$578$	12.2813			0.510833
$579$		0			0
$580$	0.388295			0.0161231
$581$	−4.41822	+	0.882351i	−0.183299	+	0.0366061i
$582$		0			0
$583$	22.6095			0.936391
$584$	−6.31721	−	10.9417i	−0.261408	−	0.452772i
$585$		0			0
$586$	−13.8954	+	24.0675i	−0.574014	+	0.994221i
$587$	21.9241	+	37.9736i	0.904903	+	1.56734i	0.821047	+	0.570861i	$0.193390\pi$
$587$	21.9241	+	37.9736i	0.904903	+	1.56734i	0.0838564	+	0.996478i	$0.473276\pi$
$588$		0			0
$589$	−11.2923	+	19.5589i	−0.465292	+	0.805910i
$590$	−1.68397	+	2.91672i	−0.0693279	+	0.120079i
$591$		0			0
$592$	−4.18320			−0.171928
$593$	5.18125	−	8.97419i	0.212768	−	0.368526i	−0.739812	−	0.672814i	$-0.765085\pi$
$593$	5.18125	−	8.97419i	0.212768	−	0.368526i	0.952580	+	0.304288i	$0.0984187\pi$
$594$		0			0
$595$	1.04697	−	3.09204i	0.0429216	−	0.126761i
$596$	1.34679	+	2.33271i	0.0551667	+	0.0955515i
$597$		0			0
$598$	−3.12656	−	6.17335i	−0.127855	−	0.252447i
$599$	19.7135	+	34.1448i	0.805471	+	1.39512i	0.915973	+	0.401241i	$0.131421\pi$
$599$	19.7135	+	34.1448i	0.805471	+	1.39512i	−0.110501	+	0.993876i	$0.535246\pi$
$600$		0			0
$601$	−1.03443	−	1.79169i	−0.0421954	−	0.0730845i	0.844156	−	0.536097i	$-0.180102\pi$
$601$	−1.03443	−	1.79169i	−0.0421954	−	0.0730845i	−0.886352	+	0.463012i	$0.846769\pi$
$602$	−8.79015	+	25.9601i	−0.358260	+	1.05806i
$603$		0			0
$604$	6.56432	+	11.3697i	0.267098	+	0.462628i
$605$	0.145110			0.00589957
$606$		0			0
$607$	−2.88978	−	5.00524i	−0.117292	−	0.203157i	0.801401	−	0.598127i	$-0.204088\pi$
$607$	−2.88978	−	5.00524i	−0.117292	−	0.203157i	−0.918694	+	0.394970i	$0.870755\pi$
$608$	−3.17107	−	5.49246i	−0.128604	−	0.222749i
$609$		0			0
$610$	−1.53228			−0.0620403
$611$	−40.1207	−	2.20065i	−1.62311	−	0.0890287i
$612$		0			0
$613$	−7.45451	+	12.9116i	−0.301085	+	0.521494i	−0.976382	−	0.216051i	$-0.930682\pi$
$613$	−7.45451	+	12.9116i	−0.301085	+	0.521494i	0.675297	+	0.737546i	$0.264015\pi$
$614$	−14.6849			−0.592633
$615$		0			0
$616$	−2.89453	+	8.54848i	−0.116624	+	0.344428i
$617$	1.29988	−	2.25147i	0.0523314	−	0.0906406i	−0.838673	−	0.544635i	$-0.816668\pi$
$617$	1.29988	−	2.25147i	0.0523314	−	0.0906406i	0.891004	+	0.453995i	$0.150001\pi$
$618$		0			0
$619$	24.4693	+	42.3821i	0.983505	+	1.70348i	0.648399	+	0.761300i	$0.275439\pi$
$619$	24.4693	+	42.3821i	0.983505	+	1.70348i	0.335106	+	0.942180i	$0.391228\pi$
$620$	0.811985			0.0326101
$621$		0			0
$622$	−3.86348	−	6.69174i	−0.154911	−	0.268314i
$623$	45.5226	−	9.09119i	1.82383	−	0.364231i
$624$		0			0
$625$	−12.1114	+	20.9776i	−0.484456	+	0.839103i
$626$	−10.0982	+	17.4906i	−0.403605	+	0.699064i
$627$		0			0
$628$	−1.59071	−	2.75520i	−0.0634764	−	0.109944i
$629$	−22.6362			−0.902564
$630$		0			0
$631$	14.0099	−	24.2659i	0.557726	−	0.966010i	−0.439960	−	0.898017i	$-0.645007\pi$
$631$	14.0099	−	24.2659i	0.557726	−	0.966010i	0.997686	−	0.0679924i	$-0.0216594\pi$
$632$	0.811077	−	1.40483i	0.0322629	−	0.0558810i
$633$		0			0
$634$	−7.36088	+	12.7494i	−0.292338	+	0.506344i
$635$	2.92119			0.115924
$636$		0			0
$637$	−19.1769	−	16.4087i	−0.759817	−	0.650138i
$638$	−5.80898			−0.229980
$639$		0			0
$640$	−0.114009	+	0.197470i	−0.00450662	+	0.00780569i
$641$	35.9312			1.41920			0.709598	−	0.704607i	$-0.248877\pi$
$641$	35.9312			1.41920			0.709598	+	0.704607i	$0.248877\pi$
$642$		0			0
$643$	10.6007	−	18.3609i	0.418050	−	0.724084i	−0.577693	−	0.816254i	$-0.696047\pi$
$643$	10.6007	−	18.3609i	0.418050	−	0.724084i	0.995743	+	0.0921702i	$0.0293804\pi$
$644$	−4.97952	+	0.994446i	−0.196221	+	0.0391866i
$645$		0			0
$646$	−17.1594	−	29.7209i	−0.675126	−	1.16935i
$647$	2.06144	−	3.57052i	0.0810436	−	0.140372i	−0.822655	−	0.568541i	$-0.807508\pi$
$647$	2.06144	−	3.57052i	0.0810436	−	0.140372i	0.903698	+	0.428169i	$0.140841\pi$
$648$		0			0
$649$	25.1926	−	43.6348i	0.988895	−	1.71282i
$650$	9.75294	−	14.9384i	0.382542	−	0.585933i
$651$		0			0
$652$	8.14702	+	14.1111i	0.319062	+	0.552632i
$653$	47.4371			1.85636			0.928179	−	0.372134i	$-0.121374\pi$
$653$	47.4371			1.85636			0.928179	+	0.372134i	$0.121374\pi$
$654$		0			0
$655$	0.401230	+	0.694951i	0.0156773	+	0.0271540i
$656$	−1.59160	−	2.75673i	−0.0621415	−	0.107632i
$657$		0			0
$658$	−9.45624	+	27.9273i	−0.368643	+	1.08872i
$659$	12.4744	−	21.6062i	0.485932	−	0.841659i	−0.513937	−	0.857828i	$-0.671814\pi$
$659$	12.4744	−	21.6062i	0.485932	−	0.841659i	0.999869	+	0.0161688i	$0.00514690\pi$
$660$		0			0
$661$	4.30765	−	7.46106i	0.167548	−	0.290202i	−0.770009	−	0.638033i	$-0.779748\pi$
$661$	4.30765	−	7.46106i	0.167548	−	0.290202i	0.937557	+	0.347831i	$0.113082\pi$
$662$	−2.05436	−	3.55826i	−0.0798450	−	0.138296i
$663$		0			0
$664$	1.70291			0.0660856
$665$	−3.75200	+	0.749302i	−0.145496	+	0.0290567i
$666$		0			0
$667$	−1.63415	−	2.83043i	−0.0632745	−	0.109595i
$668$	−0.826739	−	1.43195i	−0.0319875	−	0.0554040i
$669$		0			0
$670$	−1.27249	−	2.20402i	−0.0491607	−	0.0851488i
$671$	22.9233			0.884946
$672$		0			0
$673$	3.15527	+	5.46509i	0.121627	+	0.210664i	0.920409	−	0.390956i	$-0.127856\pi$
$673$	3.15527	+	5.46509i	0.121627	+	0.210664i	−0.798783	+	0.601620i	$0.794522\pi$
$674$	−7.44592			−0.286806
$675$		0			0
$676$	−7.69235	+	10.4799i	−0.295860	+	0.403072i
$677$	3.67011	−	6.35682i	0.141054	−	0.244313i	−0.786840	−	0.617157i	$-0.788284\pi$
$677$	3.67011	−	6.35682i	0.141054	−	0.244313i	0.927894	+	0.372845i	$0.121618\pi$
$678$		0			0
$679$	−11.5853	+	34.2150i	−0.444601	+	1.31305i
$680$	−0.616929	+	1.06855i	−0.0236582	+	0.0409771i
$681$		0			0
$682$	−12.1475			−0.465152
$683$	−19.9112			−0.761880			−0.380940	−	0.924600i	$-0.624400\pi$
$683$	−19.9112			−0.761880			−0.380940	+	0.924600i	$0.624400\pi$
$684$		0			0
$685$	2.01746	−	3.49434i	0.0770830	−	0.133512i
$686$	−15.3754	+	10.3246i	−0.587035	+	0.394195i
$687$		0			0
$688$	5.17961	−	8.97135i	0.197471	−	0.342030i
$689$	13.0643	−	20.0104i	0.497711	−	0.762336i
$690$		0			0
$691$	−19.0691			−0.725422			−0.362711	−	0.931902i	$-0.618149\pi$
$691$	−19.0691			−0.725422			−0.362711	+	0.931902i	$0.618149\pi$
$692$	7.02100	+	12.1607i	0.266898	+	0.462282i
$693$		0			0
$694$	10.5281			0.399642
$695$	0.908246	+	1.57313i	0.0344518	+	0.0596722i
$696$		0			0
$697$	−8.61248	−	14.9173i	−0.326221	−	0.565032i
$698$	−4.74127	−	8.21212i	−0.179460	−	0.310833i
$699$		0			0
$700$	−8.63915	−	9.83588i	−0.326529	−	0.371761i
$701$	−21.2816			−0.803796			−0.401898	−	0.915685i	$-0.631649\pi$
$701$	−21.2816			−0.803796			−0.401898	+	0.915685i	$0.631649\pi$
$702$		0			0
$703$	13.2652	+	22.9760i	0.500307	+	0.866557i
$704$	1.70561	−	2.95420i	0.0642825	−	0.111341i
$705$		0			0
$706$	2.72112	−	4.71311i	0.102411	−	0.177380i
$707$	14.0148	−	41.3901i	0.527079	−	1.55663i
$708$		0			0
$709$	13.4109	+	23.2283i	0.503655	+	0.872357i	0.999991	+	0.00422606i	$0.00134520\pi$
$709$	13.4109	+	23.2283i	0.503655	+	0.872357i	−0.496336	+	0.868131i	$0.665321\pi$
$710$	0.00891445	+	0.0154403i	0.000334553	+	0.000579463i
$711$		0			0
$712$	−17.5457			−0.657553
$713$	−3.41726	−	5.91887i	−0.127977	−	0.221663i
$714$		0			0
$715$	1.53315	−	2.34830i	0.0573366	−	0.0878215i
$716$	−4.66663	+	8.08283i	−0.174400	+	0.302070i
$717$		0			0
$718$	5.29579	−	9.17257i	0.197637	−	0.342317i
$719$	−21.5853	−	37.3869i	−0.804997	−	1.39430i	−0.916293	−	0.400508i	$-0.868834\pi$
$719$	−21.5853	−	37.3869i	−0.804997	−	1.39430i	0.111297	−	0.993787i	$-0.464500\pi$
$720$		0			0
$721$	5.39601	−	15.9362i	0.200958	−	0.593494i
$722$	−10.6114	+	18.3795i	−0.394915	+	0.684012i
$723$		0			0
$724$	1.13838			0.0423074
$725$	4.21300	−	7.29713i	0.156467	−	0.271008i
$726$		0			0
$727$	−16.1609			−0.599373			−0.299687	−	0.954038i	$-0.596882\pi$
$727$	−16.1609			−0.599373			−0.299687	+	0.954038i	$0.596882\pi$
$728$	5.89325	+	7.50131i	0.218418	+	0.278017i
$729$		0			0
$730$	2.88088			0.106626
$731$	28.0280	−	48.5459i	1.03665	−	1.79554i
$732$		0			0
$733$	6.79983	−	11.7777i	0.251158	−	0.435018i	−0.712687	−	0.701482i	$-0.752522\pi$
$733$	6.79983	−	11.7777i	0.251158	−	0.435018i	0.963845	+	0.266464i	$0.0858554\pi$
$734$	3.59896	−	6.23359i	0.132840	−	0.230086i
$735$		0			0
$736$	1.91925			0.0707444
$737$	19.0368	+	32.9727i	0.701230	+	1.21457i
$738$		0			0
$739$	−0.191803	+	0.332212i	−0.00705557	+	0.0122206i	−0.869532	−	0.493877i	$-0.835579\pi$
$739$	−0.191803	+	0.332212i	−0.00705557	+	0.0122206i	0.862476	+	0.506098i	$0.168913\pi$
$740$	0.476924	−	0.826056i	0.0175321	−	0.0303664i
$741$		0			0
$742$	−11.5724	−	13.1754i	−0.424835	−	0.483685i
$743$	−10.4715	−	18.1372i	−0.384162	−	0.665388i	0.607491	−	0.794327i	$-0.292176\pi$
$743$	−10.4715	−	18.1372i	−0.384162	−	0.665388i	−0.991653	+	0.128939i	$0.958843\pi$
$744$		0			0
$745$	−0.614187			−0.0225021
$746$	14.2762	+	24.7271i	0.522688	+	0.905322i
$747$		0			0
$748$	9.22941	−	15.9858i	0.337461	−	0.584499i
$749$	16.9869	−	3.39241i	0.620689	−	0.123956i
$750$		0			0
$751$	15.8139			0.577057			0.288529	−	0.957471i	$-0.406834\pi$
$751$	15.8139			0.577057			0.288529	+	0.957471i	$0.406834\pi$
$752$	5.57211	−	9.65117i	0.203194	−	0.351942i
$753$		0			0
$754$	−3.35657	+	5.14121i	−0.122239	+	0.187232i
$755$	−2.99358			−0.108947
$756$		0			0
$757$	−4.41633	−	7.64930i	−0.160514	−	0.278019i	0.774539	−	0.632526i	$-0.217982\pi$
$757$	−4.41633	−	7.64930i	−0.160514	−	0.278019i	−0.935053	+	0.354507i	$0.884649\pi$
$758$	15.5638	+	26.9572i	0.565302	+	0.979131i
$759$		0			0
$760$	1.44613			0.0524565
$761$	19.3703	+	33.5503i	0.702172	+	1.21620i	0.967702	+	0.252096i	$0.0811197\pi$
$761$	19.3703	+	33.5503i	0.702172	+	1.21620i	−0.265530	+	0.964103i	$0.585547\pi$
$762$		0			0
$763$	−2.78343	−	3.16900i	−0.100767	−	0.114725i
$764$	9.04253	+	15.6621i	0.327147	+	0.566635i
$765$		0			0
$766$	10.9760	+	19.0111i	0.396580	+	0.686897i
$767$	−24.0619	−	47.5098i	−0.868824	−	1.71548i
$768$		0			0
$769$	−9.17950	−	15.8994i	−0.331021	−	0.573345i	0.651691	−	0.758484i	$-0.274060\pi$
$769$	−9.17950	−	15.8994i	−0.331021	−	0.573345i	−0.982712	+	0.185139i	$0.940726\pi$
$770$	−1.35806	−	1.54619i	−0.0489412	−	0.0557208i
$771$		0			0
$772$	2.91296	−	5.04539i	0.104840	−	0.181588i
$773$	−12.8481			−0.462116			−0.231058	−	0.972940i	$-0.574219\pi$
$773$	−12.8481			−0.462116			−0.231058	+	0.972940i	$0.574219\pi$
$774$		0			0
$775$	8.81004	−	15.2594i	0.316466	−	0.548135i
$776$	6.82663	−	11.8241i	0.245062	−	0.424460i
$777$		0			0
$778$	−1.87365	−	3.24525i	−0.0671734	−	0.116348i
$779$	−10.0941	+	17.4836i	−0.361660	+	0.626414i
$780$		0			0
$781$	−0.133362	−	0.230990i	−0.00477208	−	0.00826548i
$782$	10.3855			0.371383
$783$		0			0
$784$	6.46305	−	2.68867i	0.230823	−	0.0960238i
$785$	0.725425			0.0258915
$786$		0			0
$787$	−3.39457			−0.121003			−0.0605017	−	0.998168i	$-0.519270\pi$
$787$	−3.39457			−0.121003			−0.0605017	+	0.998168i	$0.519270\pi$
$788$	10.3527	+	17.9315i	0.368801	+	0.638782i
$789$		0			0
$790$	0.184941	+	0.320327i	0.00657989	+	0.0113967i
$791$	−6.99624	+	20.6621i	−0.248758	+	0.734661i
$792$		0			0
$793$	13.2457	−	20.2882i	0.470367	−	0.720454i
$794$	1.95502	+	3.38620i	0.0693812	+	0.120172i
$795$		0			0
$796$	−16.3984			−0.581227
$797$	−1.71983	+	2.97884i	−0.0609197	+	0.105516i	−0.894877	−	0.446313i	$-0.852737\pi$
$797$	−1.71983	+	2.97884i	−0.0609197	+	0.105516i	0.833957	+	0.551829i	$0.186070\pi$
$798$		0			0
$799$	30.1519	−	52.2246i	1.06670	−	1.84757i
$800$	2.47400	+	4.28510i	0.0874692	+	0.151501i
$801$		0			0
$802$	26.2260			0.926074
$803$	−43.0987			−1.52092
$804$		0			0
$805$	0.371339	−	1.09668i	0.0130880	−	0.0386530i
$806$	−7.01912	+	10.7511i	−0.247238	+	0.378690i
$807$		0			0
$808$	−8.25823	+	14.3037i	−0.290523	+	0.503201i
$809$	−13.9913	+	24.2336i	−0.491908	+	0.852009i	−0.999957	−	0.00931928i	$-0.997034\pi$
$809$	−13.9913	+	24.2336i	−0.491908	+	0.852009i	0.508049	+	0.861328i	$0.330367\pi$
$810$		0			0
$811$	26.2105			0.920377			0.460188	−	0.887821i	$-0.347782\pi$
$811$	26.2105			0.920377			0.460188	+	0.887821i	$0.347782\pi$
$812$	2.97325	+	3.38512i	0.104341	+	0.118794i
$813$		0			0
$814$	−7.13490	+	12.3580i	−0.250078	+	0.433148i
$815$	−3.71535			−0.130143
$816$		0			0
$817$	−65.6997			−2.29854
$818$	4.03519			0.141087
$819$		0			0
$820$	0.725829			0.0253470
$821$	15.5463			0.542571			0.271285	−	0.962499i	$-0.412551\pi$
$821$	15.5463			0.542571			0.271285	+	0.962499i	$0.412551\pi$
$822$		0			0
$823$	−47.8212			−1.66694			−0.833471	−	0.552563i	$-0.813650\pi$
$823$	−47.8212			−1.66694			−0.833471	+	0.552563i	$0.813650\pi$
$824$	−3.17961	+	5.50725i	−0.110767	+	0.191854i
$825$		0			0
$826$	−38.3222	+	7.65321i	−1.33340	+	0.266289i
$827$	−28.2671			−0.982944			−0.491472	−	0.870893i	$-0.663541\pi$
$827$	−28.2671			−0.982944			−0.491472	+	0.870893i	$0.663541\pi$
$828$		0			0
$829$	−19.8413	+	34.3661i	−0.689116	+	1.19358i	0.283009	+	0.959117i	$0.408667\pi$
$829$	−19.8413	+	34.3661i	−0.689116	+	1.19358i	−0.972124	+	0.234466i	$0.924666\pi$
$830$	−0.194147	+	0.336273i	−0.00673895	+	0.0116722i
$831$		0			0
$832$	−1.62906	−	3.21655i	−0.0564773	−	0.111514i
$833$	34.9730	−	14.5490i	1.21174	−	0.504092i
$834$		0			0
$835$	0.377024			0.0130474
$836$	−21.6344			−0.748242
$837$		0			0
$838$	−1.74139	−	3.01617i	−0.0601552	−	0.104192i
$839$	−2.60142	+	4.50579i	−0.0898110	+	0.155557i	−0.907431	−	0.420201i	$-0.861960\pi$
$839$	−2.60142	+	4.50579i	−0.0898110	+	0.155557i	0.817620	+	0.575758i	$0.195293\pi$
$840$		0			0
$841$	13.0501	−	22.6034i	0.450002	−	0.779426i
$842$	18.6028			0.641096
$843$		0			0
$844$	3.74446	+	6.48560i	0.128890	+	0.223243i
$845$	−1.19246	−	2.71381i	−0.0410219	−	0.0933580i
$846$		0			0
$847$	1.11114	+	1.26506i	0.0381792	+	0.0434679i
$848$	3.31400	+	5.74001i	0.113803	+	0.197113i
$849$		0			0
$850$	13.3874	+	23.1876i	0.459183	+	0.795328i
$851$	−8.02859			−0.275216
$852$		0			0
$853$	21.5926			0.739318			0.369659	−	0.929167i	$-0.379474\pi$
$853$	21.5926			0.739318			0.369659	+	0.929167i	$0.379474\pi$
$854$	−11.7330	−	13.3583i	−0.401495	−	0.457112i
$855$		0			0
$856$	−6.54724			−0.223780
$857$	6.31723	+	10.9418i	0.215792	+	0.373763i	0.953517	−	0.301338i	$-0.0974333\pi$
$857$	6.31723	+	10.9418i	0.215792	+	0.373763i	−0.737725	+	0.675101i	$0.764100\pi$
$858$		0			0
$859$	4.17670	−	7.23426i	0.142507	−	0.246830i	−0.785933	−	0.618312i	$-0.787817\pi$
$859$	4.17670	−	7.23426i	0.142507	−	0.246830i	0.928440	+	0.371482i	$0.121150\pi$
$860$	1.18105	+	2.04564i	0.0402734	+	0.0697556i
$861$		0			0
$862$	−9.52662	+	16.5006i	−0.324478	+	0.562012i
$863$	6.28858	−	10.8921i	0.214066	−	0.370772i	−0.738918	−	0.673796i	$-0.764663\pi$
$863$	6.28858	−	10.8921i	0.214066	−	0.370772i	0.952983	+	0.303023i	$0.0979960\pi$
$864$		0			0
$865$	−3.20184			−0.108866
$866$	−16.7336	+	28.9834i	−0.568630	+	0.984896i
$867$		0			0
$868$	6.21753	+	7.07881i	0.211037	+	0.240271i
$869$	−2.76676	−	4.79216i	−0.0938558	−	0.162563i
$870$		0			0
$871$	40.1822	+	2.20402i	1.36152	+	0.0746804i
$872$	0.797093	+	1.38061i	0.0269930	+	0.0467532i
$873$		0			0
$874$	−6.08607	−	10.5414i	−0.205864	−	0.356567i
$875$	5.88523	−	1.17532i	0.198957	−	0.0397331i
$876$		0			0
$877$	−3.24950	−	5.62831i	−0.109728	−	0.190054i	0.805932	−	0.592008i	$-0.201665\pi$
$877$	−3.24950	−	5.62831i	−0.109728	−	0.190054i	−0.915660	+	0.401954i	$0.868331\pi$
$878$	38.0459			1.28399
$879$		0			0
$880$	0.388911	+	0.673613i	0.0131102	+	0.0227075i
$881$	−6.17234	−	10.6908i	−0.207951	−	0.360182i	0.743118	−	0.669161i	$-0.233346\pi$
$881$	−6.17234	−	10.6908i	−0.207951	−	0.360182i	−0.951069	+	0.308979i	$0.900013\pi$
$882$		0			0
$883$	42.2001			1.42015			0.710073	−	0.704128i	$-0.248662\pi$
$883$	42.2001			1.42015			0.710073	+	0.704128i	$0.248662\pi$
$884$	−8.81517	−	17.4054i	−0.296486	−	0.585408i
$885$		0			0
$886$	−4.35467	+	7.54250i	−0.146298	+	0.253395i
$887$	34.3380			1.15296			0.576478	−	0.817112i	$-0.304426\pi$
$887$	34.3380			1.15296			0.576478	+	0.817112i	$0.304426\pi$
$888$		0			0
$889$	22.3681	+	25.4667i	0.750204	+	0.854125i
$890$	2.00037	−	3.46475i	0.0670527	−	0.116139i
$891$		0			0
$892$	−8.41325	−	14.5722i	−0.281696	−	0.487913i
$893$	−70.6782			−2.36516
$894$		0			0
$895$	−1.06408	−	1.84304i	−0.0355682	−	0.0616059i
$896$	−2.59452	+	0.518144i	−0.0866768	+	0.0173100i
$897$		0			0
$898$	11.4930	−	19.9065i	0.383527	−	0.664288i
$899$	−3.03206	+	5.25169i	−0.101125	+	0.175154i
$900$		0			0
$901$	17.9328	+	31.0604i	0.597427	+	1.03477i
$902$	−10.8586			−0.361551
$903$		0			0
$904$	4.12255	−	7.14047i	0.137114	−	0.237488i
$905$	−0.129786	+	0.224795i	−0.00431422	+	0.00747244i
$906$		0			0
$907$	9.36040	−	16.2127i	0.310807	−	0.538334i	−0.667730	−	0.744403i	$-0.732734\pi$
$907$	9.36040	−	16.2127i	0.310807	−	0.538334i	0.978537	+	0.206070i	$0.0660674\pi$
$908$	4.23214			0.140449
$909$		0			0
$910$	−2.15317	+	0.308521i	−0.0713768	+	0.0102274i
$911$	30.3513			1.00558			0.502791	−	0.864408i	$-0.332306\pi$
$911$	30.3513			1.00558			0.502791	+	0.864408i	$0.332306\pi$
$912$		0			0
$913$	2.90449	−	5.03073i	0.0961247	−	0.166493i
$914$	11.5899			0.383358
$915$		0			0
$916$	−6.86498	+	11.8905i	−0.226825	+	0.392873i
$917$	−2.98622	+	8.81926i	−0.0986137	+	0.291238i
$918$		0			0
$919$	−20.3758	−	35.2919i	−0.672135	−	1.16417i	−0.977297	−	0.211872i	$-0.932044\pi$
$919$	−20.3758	−	35.2919i	−0.672135	−	1.16417i	0.305162	−	0.952300i	$-0.401289\pi$
$920$	−0.218812	+	0.378993i	−0.00721402	+	0.0124950i
$921$		0			0
$922$	17.4236	−	30.1785i	0.573814	−	0.993876i
$923$	−0.281497	−	0.0154403i	−0.00926557	−	0.000508223i
$924$		0			0
$925$	−10.3492	−	17.9254i	−0.340281	−	0.589384i
$926$	−39.5334			−1.29915
$927$		0			0
$928$	−0.851453	−	1.47476i	−0.0279503	−	0.0484114i
$929$	2.60978	+	4.52027i	0.0856242	+	0.148305i	0.905657	−	0.424011i	$-0.139378\pi$
$929$	2.60978	+	4.52027i	0.0856242	+	0.148305i	−0.820033	+	0.572316i	$0.806045\pi$
$930$		0			0
$931$	−35.2622	−	26.9721i	−1.15567	−	0.883974i
$932$	3.85349	−	6.67444i	0.126225	−	0.218629i
$933$		0			0
$934$	0.425191	−	0.736452i	0.0139127	−	0.0240974i
$935$	2.10448	+	3.64506i	0.0688238	+	0.119206i
$936$		0			0
$937$	−31.2199			−1.01991			−0.509956	−	0.860201i	$-0.670338\pi$
$937$	−31.2199			−1.01991			−0.509956	+	0.860201i	$0.670338\pi$
$938$	9.47074	−	27.9701i	0.309231	−	0.913257i
$939$		0			0
$940$	1.27054	+	2.20065i	0.0414406	+	0.0717772i
$941$	25.3480	+	43.9041i	0.826322	+	1.43123i	0.900904	+	0.434018i	$0.142904\pi$
$941$	25.3480	+	43.9041i	0.826322	+	1.43123i	−0.0745820	+	0.997215i	$0.523762\pi$
$942$		0			0
$943$	−3.05467	−	5.29084i	−0.0994737	−	0.172294i
$944$	14.7704			0.480737
$945$		0			0
$946$	−17.6688	−	30.6032i	−0.574461	−	0.994996i
$947$	−48.3407			−1.57086			−0.785431	−	0.618949i	$-0.787559\pi$
$947$	−48.3407			−1.57086			−0.785431	+	0.618949i	$0.787559\pi$
$948$		0			0
$949$	−24.9035	+	38.1443i	−0.808402	+	1.23822i
$950$	15.6905	−	27.1767i	0.509066	−	0.881729i
$951$		0			0
$952$	−14.0395	+	2.80379i	−0.455023	+	0.0908713i
$953$	−0.444682	+	0.770211i	−0.0144046	+	0.0249496i	−0.873138	−	0.487473i	$-0.837919\pi$
$953$	−0.444682	+	0.770211i	−0.0144046	+	0.0249496i	0.858733	+	0.512423i	$0.171252\pi$
$954$		0			0
$955$	−4.12373			−0.133441
$956$	25.2189			0.815638
$957$		0			0
$958$	5.78732	−	10.0239i	0.186980	−	0.323859i
$959$	45.9114	−	9.16883i	1.48256	−	0.296077i
$960$		0			0
$961$	9.15948	−	15.8647i	0.295467	−	0.511764i
$962$	6.81466	+	13.4555i	0.219714	+	0.433821i
$963$		0			0
$964$	27.8367			0.896560
$965$	0.664209	+	1.15044i	0.0213817	+	0.0370341i
$966$		0			0
$967$	4.75544			0.152925			0.0764623	−	0.997072i	$-0.475638\pi$
$967$	4.75544			0.152925			0.0764623	+	0.997072i	$0.475638\pi$
$968$	−0.318198	−	0.551135i	−0.0102273	−	0.0177142i
$969$		0			0
$970$	1.55660	+	2.69611i	0.0499794	+	0.0865669i
$971$	0.775940	+	1.34397i	0.0249011	+	0.0431300i	0.878207	−	0.478280i	$-0.158740\pi$
$971$	0.775940	+	1.34397i	0.0249011	+	0.0431300i	−0.853306	+	0.521410i	$0.825406\pi$
$972$		0			0
$973$	−6.75978	+	19.9638i	−0.216708	+	0.640009i
$974$	−13.9320			−0.446412
$975$		0			0
$976$	3.35999	+	5.81968i	0.107551	+	0.186283i
$977$	−15.7709	+	27.3161i	−0.504557	+	0.873919i	0.495429	+	0.868648i	$0.335011\pi$
$977$	−15.7709	+	27.3161i	−0.504557	+	0.873919i	−0.999986	+	0.00527014i	$0.998322\pi$
$978$		0			0
$979$	−29.9261	+	51.8335i	−0.956442	+	1.65661i
$980$	−0.205917	+	1.58279i	−0.00657779	+	0.0505604i
$981$		0			0
$982$	−4.76716	−	8.25697i	−0.152126	−	0.263490i
$983$	15.7150	+	27.2192i	0.501230	+	0.868157i	0.999999	+	0.00142135i	$0.000452430\pi$
$983$	15.7150	+	27.2192i	0.501230	+	0.868157i	−0.498769	+	0.866735i	$0.666214\pi$
$984$		0			0
$985$	−4.72124			−0.150431
$986$	−4.60740	−	7.98025i	−0.146729	−	0.254143i
$987$		0			0
$988$	−12.5009	+	19.1474i	−0.397706	+	0.609160i
$989$	9.94095	−	17.2182i	0.316104	−	0.547508i
$990$		0			0
$991$	−0.302804	+	0.524472i	−0.00961888	+	0.0166604i	−0.870795	−	0.491647i	$-0.836395\pi$
$991$	−0.302804	+	0.524472i	−0.00961888	+	0.0166604i	0.861176	+	0.508307i	$0.169729\pi$
$992$	−1.78052	−	3.08395i	−0.0565316	−	0.0979157i
$993$		0			0
$994$	−0.0663472	+	0.195945i	−0.00210441	+	0.00621499i
$995$	1.86957	−	3.23820i	0.0592695	−	0.102658i
$996$		0			0
$997$	0.368340			0.0116654			0.00583272	−	0.999983i	$-0.498143\pi$
$997$	0.368340			0.0116654			0.00583272	+	0.999983i	$0.498143\pi$
$998$	21.9135	−	37.9553i	0.693659	−	1.20145i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.m.k.289.3		10
3.2	odd	2		546.2.j.e.289.3	✓	10
7.4	even	3		1638.2.p.j.991.3		10
13.9	even	3		1638.2.p.j.919.3		10
21.11	odd	6		546.2.k.e.445.3	yes	10
39.35	odd	6		546.2.k.e.373.3	yes	10
91.74	even	3	inner	1638.2.m.k.1621.3		10
273.74	odd	6		546.2.j.e.529.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.e.289.3	✓	10	3.2	odd	2
546.2.j.e.529.3	yes	10	273.74	odd	6
546.2.k.e.373.3	yes	10	39.35	odd	6
546.2.k.e.445.3	yes	10	21.11	odd	6
1638.2.m.k.289.3		10	1.1	even	1	trivial
1638.2.m.k.1621.3		10	91.74	even	3	inner
1638.2.p.j.919.3		10	13.9	even	3
1638.2.p.j.991.3		10	7.4	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.114009 + 0.197470i) q^{5} +(-2.59452 + 0.518144i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.114009 + 0.197470i) q^{5} +(-2.59452 + 0.518144i) q^{7} +1.00000 q^{8} +(-0.114009 + 0.197470i) q^{10} +(1.70561 - 2.95420i) q^{11} +(-1.62906 - 3.21655i) q^{13} +(-2.59452 + 0.518144i) q^{14} +1.00000 q^{16} +5.41122 q^{17} +(-3.17107 - 5.49246i) q^{19} +(-0.114009 + 0.197470i) q^{20} +(1.70561 - 2.95420i) q^{22} +1.91925 q^{23} +(2.47400 + 4.28510i) q^{25} +(-1.62906 - 3.21655i) q^{26} +(-2.59452 + 0.518144i) q^{28} +(-0.851453 - 1.47476i) q^{29} +(-1.78052 - 3.08395i) q^{31} +1.00000 q^{32} +5.41122 q^{34} +(0.193482 - 0.571413i) q^{35} -4.18320 q^{37} +(-3.17107 - 5.49246i) q^{38} +(-0.114009 + 0.197470i) q^{40} +(-1.59160 - 2.75673i) q^{41} +(5.17961 - 8.97135i) q^{43} +(1.70561 - 2.95420i) q^{44} +1.91925 q^{46} +(5.57211 - 9.65117i) q^{47} +(6.46305 - 2.68867i) q^{49} +(2.47400 + 4.28510i) q^{50} +(-1.62906 - 3.21655i) q^{52} +(3.31400 + 5.74001i) q^{53} +(0.388911 + 0.673613i) q^{55} +(-2.59452 + 0.518144i) q^{56} +(-0.851453 - 1.47476i) q^{58} +14.7704 q^{59} +(3.35999 + 5.81968i) q^{61} +(-1.78052 - 3.08395i) q^{62} +1.00000 q^{64} +(0.820899 + 0.0450268i) q^{65} +(-5.58065 + 9.66597i) q^{67} +5.41122 q^{68} +(0.193482 - 0.571413i) q^{70} +(0.0390952 - 0.0677149i) q^{71} +(-6.31721 - 10.9417i) q^{73} -4.18320 q^{74} +(-3.17107 - 5.49246i) q^{76} +(-2.89453 + 8.54848i) q^{77} +(0.811077 - 1.40483i) q^{79} +(-0.114009 + 0.197470i) q^{80} +(-1.59160 - 2.75673i) q^{82} +1.70291 q^{83} +(-0.616929 + 1.06855i) q^{85} +(5.17961 - 8.97135i) q^{86} +(1.70561 - 2.95420i) q^{88} -17.5457 q^{89} +(5.89325 + 7.50131i) q^{91} +1.91925 q^{92} +(5.57211 - 9.65117i) q^{94} +1.44613 q^{95} +(6.82663 - 11.8241i) q^{97} +(6.46305 - 2.68867i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 10 q^{8}+O(q^{10}) \) 10 * q + 10 * q^2 + 10 * q^4 + 2 * q^5 - 2 * q^7 + 10 * q^8	\( 10 q + 10 q^{2} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 10 q^{8} + 2 q^{10} - 6 q^{11} - 4 q^{13} - 2 q^{14} + 10 q^{16} + 8 q^{17} + 3 q^{19} + 2 q^{20} - 6 q^{22} + 12 q^{23} - q^{25} - 4 q^{26} - 2 q^{28} - 10 q^{31} + 10 q^{32} + 8 q^{34} - 16 q^{35} - 2 q^{37} + 3 q^{38} + 2 q^{40} + 4 q^{41} + 3 q^{43} - 6 q^{44} + 12 q^{46} + 15 q^{47} + 4 q^{49} - q^{50} - 4 q^{52} + 17 q^{53} + 3 q^{55} - 2 q^{56} + 4 q^{59} + 11 q^{61} - 10 q^{62} + 10 q^{64} + 4 q^{65} - q^{67} + 8 q^{68} - 16 q^{70} - 18 q^{71} + 12 q^{73} - 2 q^{74} + 3 q^{76} - 18 q^{77} - 4 q^{79} + 2 q^{80} + 4 q^{82} + q^{85} + 3 q^{86} - 6 q^{88} + 14 q^{89} + 26 q^{91} + 12 q^{92} + 15 q^{94} + 48 q^{95} - 6 q^{97} + 4 q^{98}+O(q^{100}) \) 10 * q + 10 * q^2 + 10 * q^4 + 2 * q^5 - 2 * q^7 + 10 * q^8 + 2 * q^10 - 6 * q^11 - 4 * q^13 - 2 * q^14 + 10 * q^16 + 8 * q^17 + 3 * q^19 + 2 * q^20 - 6 * q^22 + 12 * q^23 - q^25 - 4 * q^26 - 2 * q^28 - 10 * q^31 + 10 * q^32 + 8 * q^34 - 16 * q^35 - 2 * q^37 + 3 * q^38 + 2 * q^40 + 4 * q^41 + 3 * q^43 - 6 * q^44 + 12 * q^46 + 15 * q^47 + 4 * q^49 - q^50 - 4 * q^52 + 17 * q^53 + 3 * q^55 - 2 * q^56 + 4 * q^59 + 11 * q^61 - 10 * q^62 + 10 * q^64 + 4 * q^65 - q^67 + 8 * q^68 - 16 * q^70 - 18 * q^71 + 12 * q^73 - 2 * q^74 + 3 * q^76 - 18 * q^77 - 4 * q^79 + 2 * q^80 + 4 * q^82 + q^85 + 3 * q^86 - 6 * q^88 + 14 * q^89 + 26 * q^91 + 12 * q^92 + 15 * q^94 + 48 * q^95 - 6 * q^97 + 4 * q^98

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