LMFDB - Embedded newform 666.2.be.d.125.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(125,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 11]))

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

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

chi := DirichletCharacter("666.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.be (of order $12$, degree $4$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.6040479020157644046336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} - 32x^{8} - 567x^{4} + 6561 $ x^16 - 7x^12 - 32x^8 - 567*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			125.3
Root			$-1.47240 + 0.912166i$ of defining polynomial
Character	$\chi$	$=$	666.125
Dual form			666.2.be.d.341.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.653347 + 2.43832i) q^{5} +(-1.76217 - 3.05217i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.653347 + 2.43832i) q^{5} +(-1.76217 - 3.05217i) q^{7} +(-0.707107 - 0.707107i) q^{8} -2.52434 q^{10} -2.53468 q^{11} +(-2.84445 - 0.762169i) q^{13} +(2.49208 - 2.49208i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.73122 - 0.463878i) q^{17} +(-3.53059 - 0.946020i) q^{19} +(-0.653347 - 2.43832i) q^{20} +(-0.656023 - 2.44831i) q^{22} +(-3.15983 - 3.15983i) q^{23} +(-1.18843 - 0.686141i) q^{25} -2.94479i q^{26} +(3.05217 + 1.76217i) q^{28} +(-0.0393551 + 0.0393551i) q^{29} +(-3.02663 - 3.02663i) q^{31} +(0.965926 + 0.258819i) q^{32} +(0.896143 + 1.55217i) q^{34} +(8.59347 - 2.30261i) q^{35} +(-6.08276 + 0.00578029i) q^{37} -3.65514i q^{38} +(2.18614 - 1.26217i) q^{40} +(4.63342 + 8.02531i) q^{41} +(0.234341 - 0.234341i) q^{43} +(2.19509 - 1.26734i) q^{44} +(2.23434 - 3.86999i) q^{46} -4.39019i q^{47} +(-2.71048 + 4.69469i) q^{49} +(0.355173 - 1.32552i) q^{50} +(2.84445 - 0.762169i) q^{52} +(3.09167 + 1.78498i) q^{53} +(1.65602 - 6.18036i) q^{55} +(-0.912166 + 3.40425i) q^{56} +(-0.0482000 - 0.0278283i) q^{58} +(-9.18421 + 2.46090i) q^{59} +(2.55217 - 9.52481i) q^{61} +(2.14015 - 3.70685i) q^{62} +1.00000i q^{64} +(3.71683 - 6.43773i) q^{65} +(-13.5208 + 7.80626i) q^{67} +(-1.26734 + 1.26734i) q^{68} +(4.44831 + 7.70470i) q^{70} +(-3.56178 + 2.05639i) q^{71} -4.09182i q^{73} +(-1.57992 - 5.87400i) q^{74} +(3.53059 - 0.946020i) q^{76} +(4.46653 + 7.73625i) q^{77} +(2.84445 + 0.762169i) q^{79} +(1.78498 + 1.78498i) q^{80} +(-6.55264 + 6.55264i) q^{82} +(-7.86403 - 4.54030i) q^{83} +4.52434i q^{85} +(0.287007 + 0.165704i) q^{86} +(1.79229 + 1.79229i) q^{88} +(3.78437 + 14.1235i) q^{89} +(2.68614 + 10.0248i) q^{91} +(4.31641 + 1.15658i) q^{92} +(4.24060 - 1.13626i) q^{94} +(4.61340 - 7.99065i) q^{95} +(-0.841688 + 0.841688i) q^{97} +(-5.23624 - 1.40305i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} + 4 q^{13} + 8 q^{16} + 16 q^{19} + 20 q^{22} + 12 q^{28} - 12 q^{31} + 8 q^{34} + 12 q^{37} + 12 q^{40} - 20 q^{43} + 12 q^{46} + 20 q^{49} - 4 q^{52} - 4 q^{55} + 4 q^{61} - 132 q^{67} + 28 q^{70} - 16 q^{76} - 4 q^{79} + 12 q^{82} + 16 q^{88} + 20 q^{91} + 12 q^{94} - 40 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 4 * q^13 + 8 * q^16 + 16 * q^19 + 20 * q^22 + 12 * q^28 - 12 * q^31 + 8 * q^34 + 12 * q^37 + 12 * q^40 - 20 * q^43 + 12 * q^46 + 20 * q^49 - 4 * q^52 - 4 * q^55 + 4 * q^61 - 132 * q^67 + 28 * q^70 - 16 * q^76 - 4 * q^79 + 12 * q^82 + 16 * q^88 + 20 * q^91 + 12 * q^94 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−0.653347	+	2.43832i	−0.292186	+	1.09045i	0.651241	+	0.758871i	$0.274249\pi$
$5$	−0.653347	+	2.43832i	−0.292186	+	1.09045i	−0.943427	+	0.331581i	$0.892418\pi$
$6$		0			0
$7$	−1.76217	−	3.05217i	−0.666037	−	1.15361i	−0.979003	−	0.203846i	$-0.934656\pi$
$7$	−1.76217	−	3.05217i	−0.666037	−	1.15361i	0.312966	−	0.949764i	$-0.398677\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−2.52434			−0.798266
$11$	−2.53468			−0.764234			−0.382117	−	0.924114i	$-0.624805\pi$
$11$	−2.53468			−0.764234			−0.382117	+	0.924114i	$0.624805\pi$
$12$		0			0
$13$	−2.84445	−	0.762169i	−0.788909	−	0.211388i	−0.158200	−	0.987407i	$-0.550569\pi$
$13$	−2.84445	−	0.762169i	−0.788909	−	0.211388i	−0.630709	+	0.776019i	$0.717236\pi$
$14$	2.49208	−	2.49208i	0.666037	−	0.666037i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.73122	−	0.463878i	0.419882	−	0.112507i	−0.0426910	−	0.999088i	$-0.513593\pi$
$17$	1.73122	−	0.463878i	0.419882	−	0.112507i	0.462573	+	0.886581i	$0.346926\pi$
$18$		0			0
$19$	−3.53059	−	0.946020i	−0.809974	−	0.217032i	−0.170015	−	0.985441i	$-0.554382\pi$
$19$	−3.53059	−	0.946020i	−0.809974	−	0.217032i	−0.639958	+	0.768410i	$0.721048\pi$
$20$	−0.653347	−	2.43832i	−0.146093	−	0.545226i
$21$		0			0
$22$	−0.656023	−	2.44831i	−0.139864	−	0.521981i
$23$	−3.15983	−	3.15983i	−0.658871	−	0.658871i	0.296242	−	0.955113i	$-0.404267\pi$
$23$	−3.15983	−	3.15983i	−0.658871	−	0.658871i	−0.955113	+	0.296242i	$0.904267\pi$
$24$		0			0
$25$	−1.18843	−	0.686141i	−0.237686	−	0.137228i
$26$		−	2.94479i		−	0.577522i
$27$		0			0
$28$	3.05217	+	1.76217i	0.576805	+	0.333019i
$29$	−0.0393551	+	0.0393551i	−0.00730806	+	0.00730806i	−0.710751	−	0.703443i	$-0.751645\pi$
$29$	−0.0393551	+	0.0393551i	−0.00730806	+	0.00730806i	0.703443	+	0.710751i	$0.251645\pi$
$30$		0			0
$31$	−3.02663	−	3.02663i	−0.543598	−	0.543598i	0.380983	−	0.924582i	$-0.375585\pi$
$31$	−3.02663	−	3.02663i	−0.543598	−	0.543598i	−0.924582	+	0.380983i	$0.875585\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$		0			0
$34$	0.896143	+	1.55217i	0.153687	+	0.266194i
$35$	8.59347	−	2.30261i	1.45256	−	0.389213i
$36$		0			0
$37$	−6.08276	+	0.00578029i	−1.00000	+	0.000950274i
$37$	−6.08276	+	0.00578029i	−1.00000	+	0.000950274i
$38$		−	3.65514i		−	0.592942i
$39$		0			0
$40$	2.18614	−	1.26217i	0.345659	−	0.199566i
$41$	4.63342	+	8.02531i	0.723618	+	1.25334i	0.959540	+	0.281572i	$0.0908557\pi$
$41$	4.63342	+	8.02531i	0.723618	+	1.25334i	−0.235922	+	0.971772i	$0.575811\pi$
$42$		0			0
$43$	0.234341	−	0.234341i	0.0357366	−	0.0357366i	−0.689013	−	0.724749i	$-0.741956\pi$
$43$	0.234341	−	0.234341i	0.0357366	−	0.0357366i	0.724749	+	0.689013i	$0.241956\pi$
$44$	2.19509	−	1.26734i	0.330923	−	0.191058i
$45$		0			0
$46$	2.23434	−	3.86999i	0.329436	−	0.570599i
$47$		−	4.39019i		−	0.640375i	−0.947354	−	0.320187i	$-0.896254\pi$
$47$		−	4.39019i		−	0.640375i	0.947354	−	0.320187i	$-0.103746\pi$
$48$		0			0
$49$	−2.71048	+	4.69469i	−0.387211	+	0.670669i
$50$	0.355173	−	1.32552i	0.0502290	−	0.187457i
$51$		0			0
$52$	2.84445	−	0.762169i	0.394455	−	0.105694i
$53$	3.09167	+	1.78498i	0.424674	+	0.245185i	0.697075	−	0.716998i	$-0.254485\pi$
$53$	3.09167	+	1.78498i	0.424674	+	0.245185i	−0.272401	+	0.962184i	$0.587818\pi$
$54$		0			0
$55$	1.65602	−	6.18036i	0.223298	−	0.833360i
$56$	−0.912166	+	3.40425i	−0.121893	+	0.454912i
$57$		0			0
$58$	−0.0482000	−	0.0278283i	−0.00632897	−	0.00365403i
$59$	−9.18421	+	2.46090i	−1.19568	+	0.320382i	−0.801130	−	0.598491i	$-0.795767\pi$
$59$	−9.18421	+	2.46090i	−1.19568	+	0.320382i	−0.394553	+	0.918873i	$0.629101\pi$
$60$		0			0
$61$	2.55217	−	9.52481i	0.326771	−	1.21953i	−0.585748	−	0.810493i	$-0.699199\pi$
$61$	2.55217	−	9.52481i	0.326771	−	1.21953i	0.912519	−	0.409034i	$-0.134134\pi$
$62$	2.14015	−	3.70685i	0.271799	−	0.470770i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	3.71683	−	6.43773i	0.461016	−	0.798503i
$66$		0			0
$67$	−13.5208	+	7.80626i	−1.65183	+	0.953687i	−0.675517	+	0.737345i	$0.736079\pi$
$67$	−13.5208	+	7.80626i	−1.65183	+	0.953687i	−0.976318	+	0.216343i	$0.930587\pi$
$68$	−1.26734	+	1.26734i	−0.153687	+	0.153687i
$69$		0			0
$70$	4.44831	+	7.70470i	0.531675	+	0.920888i
$71$	−3.56178	+	2.05639i	−0.422705	+	0.244049i	−0.696234	−	0.717815i	$-0.745142\pi$
$71$	−3.56178	+	2.05639i	−0.422705	+	0.244049i	0.273529	+	0.961864i	$0.411809\pi$
$72$		0			0
$73$		−	4.09182i		−	0.478911i	−0.970907	−	0.239456i	$-0.923031\pi$
$73$		−	4.09182i		−	0.478911i	0.970907	−	0.239456i	$-0.0769690\pi$
$74$	−1.57992	−	5.87400i	−0.183662	−	0.682838i
$75$		0			0
$76$	3.53059	−	0.946020i	0.404987	−	0.108516i
$77$	4.46653	+	7.73625i	0.509008	+	0.881628i
$78$		0			0
$79$	2.84445	+	0.762169i	0.320026	+	0.0857507i	0.415256	−	0.909705i	$-0.363692\pi$
$79$	2.84445	+	0.762169i	0.320026	+	0.0857507i	−0.0952300	+	0.995455i	$0.530359\pi$
$80$	1.78498	+	1.78498i	0.199566	+	0.199566i
$81$		0			0
$82$	−6.55264	+	6.55264i	−0.723618	+	0.723618i
$83$	−7.86403	−	4.54030i	−0.863190	−	0.498363i	0.00188932	−	0.999998i	$-0.499399\pi$
$83$	−7.86403	−	4.54030i	−0.863190	−	0.498363i	−0.865079	+	0.501635i	$0.832732\pi$
$84$		0			0
$85$			4.52434i			0.490733i
$86$	0.287007	+	0.165704i	0.0309488	+	0.0178683i
$87$		0			0
$88$	1.79229	+	1.79229i	0.191058	+	0.191058i
$89$	3.78437	+	14.1235i	0.401143	+	1.49708i	0.811061	+	0.584962i	$0.198891\pi$
$89$	3.78437	+	14.1235i	0.401143	+	1.49708i	−0.409918	+	0.912122i	$0.634443\pi$
$90$		0			0
$91$	2.68614	+	10.0248i	0.281584	+	1.05089i
$92$	4.31641	+	1.15658i	0.450017	+	0.120582i
$93$		0			0
$94$	4.24060	−	1.13626i	0.437384	−	0.117197i
$95$	4.61340	−	7.99065i	0.473325	−	0.819823i
$96$		0			0
$97$	−0.841688	+	0.841688i	−0.0854604	+	0.0854604i	−0.748545	−	0.663084i	$-0.769247\pi$
$97$	−0.841688	+	0.841688i	−0.0854604	+	0.0854604i	0.663084	+	0.748545i	$0.269247\pi$
$98$	−5.23624	−	1.40305i	−0.528940	−	0.141729i
$99$		0			0
$100$	1.37228			0.137228
$101$	−17.0794			−1.69947			−0.849733	−	0.527213i	$-0.823237\pi$
$101$	−17.0794			−1.69947			−0.849733	+	0.527213i	$0.823237\pi$
$102$		0			0
$103$	11.0974	+	11.0974i	1.09345	+	1.09345i	0.995157	+	0.0982974i	$0.0313396\pi$
$103$	11.0974	+	11.0974i	1.09345	+	1.09345i	0.0982974	+	0.995157i	$0.468660\pi$
$104$	1.47240	+	2.55027i	0.144380	+	0.250074i
$105$		0			0
$106$	−0.923972	+	3.44831i	−0.0897441	+	0.334929i
$107$	0.455950	−	0.263243i	0.0440783	−	0.0254486i	−0.477799	−	0.878469i	$-0.658565\pi$
$107$	0.455950	−	0.263243i	0.0440783	−	0.0254486i	0.521877	+	0.853021i	$0.325232\pi$
$108$		0			0
$109$	0.981918	+	3.66457i	0.0940507	+	0.351002i	0.996874	−	0.0790101i	$-0.0251759\pi$
$109$	0.981918	+	3.66457i	0.0940507	+	0.351002i	−0.902823	+	0.430012i	$0.858509\pi$
$110$	6.39838			0.610062
$111$		0			0
$112$	−3.52434			−0.333019
$113$	0.903052	+	3.37024i	0.0849520	+	0.317045i	0.995305	−	0.0967872i	$-0.0308566\pi$
$113$	0.903052	+	3.37024i	0.0849520	+	0.317045i	−0.910353	+	0.413832i	$0.864190\pi$
$114$		0			0
$115$	9.76917	−	5.64023i	0.910979	−	0.525954i
$116$	0.0144050	−	0.0537601i	0.00133747	−	0.00499150i
$117$		0			0
$118$	−4.75410	−	8.23434i	−0.437650	−	0.758032i
$119$	−4.46653	−	4.46653i	−0.409446	−	0.409446i
$120$		0			0
$121$	−4.57541			−0.415947
$122$	9.86081			0.892756
$123$		0			0
$124$	4.13445	+	1.10782i	0.371285	+	0.0994854i
$125$	−6.47539	+	6.47539i	−0.579177	+	0.579177i
$126$		0			0
$127$	8.75686	−	15.1673i	0.777046	−	1.34588i	−0.156591	−	0.987663i	$-0.550051\pi$
$127$	8.75686	−	15.1673i	0.777046	−	1.34588i	0.933637	−	0.358220i	$-0.116616\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$		0			0
$130$	7.18036	+	1.92397i	0.629759	+	0.168743i
$131$	1.32048	+	4.92809i	0.115371	+	0.430569i	0.999314	−	0.0370243i	$-0.0117879\pi$
$131$	1.32048	+	4.92809i	0.115371	+	0.430569i	−0.883944	+	0.467593i	$0.845121\pi$
$132$		0			0
$133$	3.33409	+	12.4430i	0.289103	+	1.07895i
$134$	−11.0397	−	11.0397i	−0.953687	−	0.953687i
$135$		0			0
$136$	−1.55217	−	0.896143i	−0.133097	−	0.0768437i
$137$		−	15.3091i		−	1.30794i	−0.756518	−	0.653972i	$-0.773101\pi$
$137$		−	15.3091i		−	1.30794i	0.756518	−	0.653972i	$-0.226899\pi$
$138$		0			0
$139$	17.9622	+	10.3705i	1.52353	+	0.879612i	0.999612	+	0.0278438i	$0.00886411\pi$
$139$	17.9622	+	10.3705i	1.52353	+	0.879612i	0.523920	+	0.851768i	$0.324469\pi$
$140$	−6.29086	+	6.29086i	−0.531675	+	0.531675i
$141$		0			0
$142$	−2.90818	−	2.90818i	−0.244049	−	0.244049i
$143$	7.20977	+	1.93185i	0.602911	+	0.161550i
$144$		0			0
$145$	−0.0702479	−	0.121673i	−0.00583377	−	0.0101044i
$146$	3.95239	−	1.05904i	0.327103	−	0.0876469i
$147$		0			0
$148$	5.26493	−	3.04639i	0.432775	−	0.250411i
$149$			18.7775i			1.53831i	0.639060	+	0.769157i	$0.279324\pi$
$149$			18.7775i			1.53831i	−0.639060	+	0.769157i	$0.720676\pi$
$150$		0			0
$151$	17.8658	−	10.3148i	1.45390	−	0.839407i	0.455197	−	0.890391i	$-0.349569\pi$
$151$	17.8658	−	10.3148i	1.45390	−	0.839407i	0.998699	+	0.0509835i	$0.0162356\pi$
$152$	1.82757	+	3.16544i	0.148235	+	0.256751i
$153$		0			0
$154$	−6.31662	+	6.31662i	−0.509008	+	0.509008i
$155$	9.35733	−	5.40246i	0.751599	−	0.433936i
$156$		0			0
$157$	8.87651	−	15.3746i	0.708423	−	1.22702i	−0.257019	−	0.966406i	$-0.582740\pi$
$157$	8.87651	−	15.3746i	0.708423	−	1.22702i	0.965442	−	0.260618i	$-0.0839263\pi$
$158$			2.94479i			0.234275i
$159$		0			0
$160$	−1.26217	+	2.18614i	−0.0997832	+	0.172830i
$161$	−4.07618	+	15.2125i	−0.321248	+	1.19891i
$162$		0			0
$163$	−23.3554	+	6.25806i	−1.82934	+	0.490169i	−0.997860	−	0.0653889i	$-0.979171\pi$
$163$	−23.3554	+	6.25806i	−1.82934	+	0.490169i	−0.831478	+	0.555558i	$0.812505\pi$
$164$	−8.02531	−	4.63342i	−0.626672	−	0.361809i
$165$		0			0
$166$	2.35023	−	8.77119i	0.182413	−	0.680776i
$167$	−4.64135	+	17.3217i	−0.359158	+	1.34040i	0.516012	+	0.856581i	$0.327416\pi$
$167$	−4.64135	+	17.3217i	−0.359158	+	1.34040i	−0.875170	+	0.483815i	$0.839251\pi$
$168$		0			0
$169$	−3.74832	−	2.16409i	−0.288332	−	0.166469i
$170$	−4.37017	+	1.17098i	−0.335177	+	0.0898104i
$171$		0			0
$172$	−0.0857746	+	0.320115i	−0.00654025	+	0.0244086i
$173$	−7.39692	+	12.8118i	−0.562377	+	0.974066i	0.434911	+	0.900473i	$0.356780\pi$
$173$	−7.39692	+	12.8118i	−0.562377	+	0.974066i	−0.997288	+	0.0735926i	$0.976554\pi$
$174$		0			0
$175$			4.83638i			0.365596i
$176$	−1.26734	+	2.19509i	−0.0955292	+	0.165461i
$177$		0			0
$178$	−12.6628	+	7.31084i	−0.949114	+	0.547971i
$179$	−3.22506	+	3.22506i	−0.241052	+	0.241052i	−0.817285	−	0.576233i	$-0.804522\pi$
$179$	−3.22506	+	3.22506i	−0.241052	+	0.241052i	0.576233	+	0.817285i	$0.304522\pi$
$180$		0			0
$181$	5.15144	+	8.92256i	0.382904	+	0.663209i	0.991476	−	0.130290i	$-0.0415908\pi$
$181$	5.15144	+	8.92256i	0.382904	+	0.663209i	−0.608572	+	0.793498i	$0.708257\pi$
$182$	−8.98800	+	5.18923i	−0.666235	+	0.384651i
$183$		0			0
$184$			4.46868i			0.329436i
$185$	3.96006	−	14.8355i	0.291149	−	1.09073i
$186$		0			0
$187$	−4.38807	+	1.17578i	−0.320888	+	0.0859816i
$188$	2.19509	+	3.80201i	0.160094	+	0.277290i
$189$		0			0
$190$	8.91241	+	2.38807i	0.646574	+	0.173249i
$191$	0.0134861	+	0.0134861i	0.000975822	+	0.000975822i	0.707595	−	0.706619i	$-0.249780\pi$
$191$	0.0134861	+	0.0134861i	0.000975822	+	0.000975822i	−0.706619	+	0.707595i	$0.749780\pi$
$192$		0			0
$193$	−0.946020	+	0.946020i	−0.0680960	+	0.0680960i	−0.740335	−	0.672239i	$-0.765333\pi$
$193$	−0.946020	+	0.946020i	−0.0680960	+	0.0680960i	0.672239	+	0.740335i	$0.265333\pi$
$194$	−1.03085	−	0.595163i	−0.0740109	−	0.0427302i
$195$		0			0
$196$		−	5.42096i		−	0.387211i
$197$	−10.2579	−	5.92242i	−0.730847	−	0.421955i	0.0878850	−	0.996131i	$-0.471989\pi$
$197$	−10.2579	−	5.92242i	−0.730847	−	0.421955i	−0.818732	+	0.574176i	$0.805323\pi$
$198$		0			0
$199$	−6.15796	−	6.15796i	−0.436527	−	0.436527i	0.454315	−	0.890841i	$-0.349884\pi$
$199$	−6.15796	−	6.15796i	−0.436527	−	0.436527i	−0.890841	+	0.454315i	$0.849884\pi$
$200$	0.355173	+	1.32552i	0.0251145	+	0.0937286i
$201$		0			0
$202$	−4.42048	−	16.4975i	−0.311024	−	1.16076i
$203$	0.189469	+	0.0507680i	0.0132981	+	0.00356321i
$204$		0			0
$205$	−22.5955	+	6.05446i	−1.57814	+	0.422862i
$206$	−7.84701	+	13.5914i	−0.546727	+	0.946959i
$207$		0			0
$208$	−2.08228	+	2.08228i	−0.144380	+	0.144380i
$209$	8.94891	+	2.39785i	0.619009	+	0.165863i
$210$		0			0
$211$	0.148428			0.0102182			0.00510911	−	0.999987i	$-0.498374\pi$
$211$	0.148428			0.0102182			0.00510911	+	0.999987i	$0.498374\pi$
$212$	−3.56995			−0.245185
$213$		0			0
$214$	0.372281	+	0.372281i	0.0254486	+	0.0254486i
$215$	0.418292	+	0.724504i	0.0285273	+	0.0494108i
$216$		0			0
$217$	−3.90434	+	14.5712i	−0.265044	+	0.989157i
$218$	−3.28556	+	1.89692i	−0.222526	+	0.128476i
$219$		0			0
$220$	1.65602	+	6.18036i	0.111649	+	0.416680i
$221$	−5.27792			−0.355031
$222$		0			0
$223$	16.0747			1.07644			0.538219	−	0.842805i	$-0.319097\pi$
$223$	16.0747			1.07644			0.538219	+	0.842805i	$0.319097\pi$
$224$	−0.912166	−	3.40425i	−0.0609466	−	0.227456i
$225$		0			0
$226$	−3.02167	+	1.74456i	−0.200999	+	0.116047i
$227$	3.85296	−	14.3795i	0.255730	−	0.954398i	−0.711953	−	0.702227i	$-0.752189\pi$
$227$	3.85296	−	14.3795i	0.255730	−	0.954398i	0.967683	−	0.252170i	$-0.0811444\pi$
$228$		0			0
$229$	−13.9189	−	24.1083i	−0.919789	−	1.59312i	−0.799734	−	0.600354i	$-0.795026\pi$
$229$	−13.9189	−	24.1083i	−0.919789	−	1.59312i	−0.120054	−	0.992767i	$-0.538307\pi$
$230$	7.97649	+	7.97649i	0.525954	+	0.525954i
$231$		0			0
$232$	0.0556565			0.00365403
$233$	−16.6317			−1.08958			−0.544788	−	0.838574i	$-0.683390\pi$
$233$	−16.6317			−1.08958			−0.544788	+	0.838574i	$0.683390\pi$
$234$		0			0
$235$	10.7047	+	2.86832i	0.698298	+	0.187108i
$236$	6.72331	−	6.72331i	0.437650	−	0.437650i
$237$		0			0
$238$	3.15831	−	5.47036i	0.204723	−	0.354591i
$239$	2.55377	−	0.684281i	0.165190	−	0.0442625i	−0.175276	−	0.984519i	$-0.556082\pi$
$239$	2.55377	−	0.684281i	0.165190	−	0.0442625i	0.340466	+	0.940257i	$0.389415\pi$
$240$		0			0
$241$	−1.80131	−	0.482659i	−0.116032	−	0.0310908i	0.200336	−	0.979727i	$-0.435797\pi$
$241$	−1.80131	−	0.482659i	−0.116032	−	0.0310908i	−0.316368	+	0.948637i	$0.602463\pi$
$242$	−1.18420	−	4.41951i	−0.0761235	−	0.284097i
$243$		0			0
$244$	2.55217	+	9.52481i	0.163386	+	0.609764i
$245$	−9.67628	−	9.67628i	−0.618195	−	0.618195i
$246$		0			0
$247$	9.32158	+	5.38182i	0.593118	+	0.342437i
$248$			4.28030i			0.271799i
$249$		0			0
$250$	−7.93070	−	4.57879i	−0.501582	−	0.289588i
$251$	7.55887	−	7.55887i	0.477112	−	0.477112i	−0.427095	−	0.904207i	$-0.640463\pi$
$251$	7.55887	−	7.55887i	0.477112	−	0.477112i	0.904207	+	0.427095i	$0.140463\pi$
$252$		0			0
$253$	8.00916	+	8.00916i	0.503532	+	0.503532i
$254$	16.9170	+	4.53289i	1.06146	+	0.284419i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	29.2710	−	7.84315i	1.82588	−	0.489242i	0.828394	−	0.560145i	$-0.189255\pi$
$257$	29.2710	−	7.84315i	1.82588	−	0.489242i	0.997483	+	0.0709030i	$0.0225881\pi$
$258$		0			0
$259$	10.7365	+	18.5554i	0.667133	+	1.15298i
$260$			7.43366i			0.461016i
$261$		0			0
$262$	−4.41840	+	2.55097i	−0.272970	+	0.157599i
$263$	−8.57675	−	14.8554i	−0.528865	−	0.916021i	−0.999433	−	0.0336576i	$-0.989284\pi$
$263$	−8.57675	−	14.8554i	−0.528865	−	0.916021i	0.470568	−	0.882364i	$-0.344049\pi$
$264$		0			0
$265$	−6.37228	+	6.37228i	−0.391446	+	0.391446i
$266$	−11.1561	+	6.44097i	−0.684024	+	0.394921i
$267$		0			0
$268$	7.80626	−	13.5208i	0.476844	−	0.825917i
$269$		−	21.7135i		−	1.32389i	−0.749551	−	0.661947i	$-0.769730\pi$
$269$		−	21.7135i		−	1.32389i	0.749551	−	0.661947i	$-0.230270\pi$
$270$		0			0
$271$	4.31058	−	7.46614i	0.261849	−	0.453536i	−0.704884	−	0.709322i	$-0.749001\pi$
$271$	4.31058	−	7.46614i	0.261849	−	0.453536i	0.966733	+	0.255787i	$0.0823344\pi$
$272$	0.463878	−	1.73122i	0.0281267	−	0.104970i
$273$		0			0
$274$	14.7875	−	3.96229i	0.893343	−	0.239371i
$275$	3.01229	+	1.73914i	0.181648	+	0.104874i
$276$		0			0
$277$	2.33652	−	8.72001i	0.140388	−	0.523935i	−0.859530	−	0.511086i	$-0.829243\pi$
$277$	2.33652	−	8.72001i	0.140388	−	0.523935i	0.999917	−	0.0128488i	$-0.00409001\pi$
$278$	−5.36815	+	20.0342i	−0.321960	+	1.20157i
$279$		0			0
$280$	−7.70470	−	4.44831i	−0.460444	−	0.265837i
$281$	−12.8440	+	3.44155i	−0.766211	+	0.205306i	−0.620697	−	0.784050i	$-0.713150\pi$
$281$	−12.8440	+	3.44155i	−0.766211	+	0.205306i	−0.145514	+	0.989356i	$0.546484\pi$
$282$		0			0
$283$	2.87604	−	10.7335i	0.170963	−	0.638041i	−0.826241	−	0.563316i	$-0.809525\pi$
$283$	2.87604	−	10.7335i	0.170963	−	0.638041i	0.997204	−	0.0747253i	$-0.0238080\pi$
$284$	2.05639	−	3.56178i	0.122025	−	0.211353i
$285$		0			0
$286$			7.46410i			0.441362i
$287$	16.3297	−	28.2839i	0.963913	−	1.66955i
$288$		0			0
$289$	−11.9405	+	6.89385i	−0.702383	+	0.405521i
$290$	0.0993456	−	0.0993456i	0.00583377	−	0.00583377i
$291$		0			0
$292$	2.04591	+	3.54362i	0.119728	+	0.207375i
$293$	23.0873	−	13.3295i	1.34878	−	0.778716i	0.360700	−	0.932682i	$-0.382538\pi$
$293$	23.0873	−	13.3295i	1.34878	−	0.778716i	0.988076	+	0.153966i	$0.0492045\pi$
$294$		0			0
$295$		−	24.0019i		−	1.39744i
$296$	4.30525	+	4.29707i	0.250237	+	0.249762i
$297$		0			0
$298$	−18.1377	+	4.85998i	−1.05069	+	0.281531i
$299$	6.57967	+	11.3963i	0.380512	+	0.659067i
$300$		0			0
$301$	−1.12819	−	0.302299i	−0.0650280	−	0.0174242i
$302$	14.5873	+	14.5873i	0.839407	+	0.839407i
$303$		0			0
$304$	−2.58457	+	2.58457i	−0.148235	+	0.148235i
$305$	21.5571	+	12.4460i	1.23436	+	0.712657i
$306$		0			0
$307$		−	10.0904i		−	0.575888i	−0.957647	−	0.287944i	$-0.907028\pi$
$307$		−	10.0904i		−	0.575888i	0.957647	−	0.287944i	$-0.0929717\pi$
$308$	−7.73625	−	4.46653i	−0.440814	−	0.254504i
$309$		0			0
$310$	7.64023	+	7.64023i	0.433936	+	0.433936i
$311$	−4.26071	−	15.9012i	−0.241603	−	0.901674i	−0.975061	−	0.221939i	$-0.928761\pi$
$311$	−4.26071	−	15.9012i	−0.241603	−	0.901674i	0.733458	−	0.679735i	$-0.237905\pi$
$312$		0			0
$313$	5.71141	+	21.3153i	0.322828	+	1.20481i	0.916477	+	0.400087i	$0.131020\pi$
$313$	5.71141	+	21.3153i	0.322828	+	1.20481i	−0.593649	+	0.804724i	$0.702313\pi$
$314$	17.1481	+	4.59482i	0.967724	+	0.259301i
$315$		0			0
$316$	−2.84445	+	0.762169i	−0.160013	+	0.0428754i
$317$	12.7267	−	22.0432i	0.714800	−	1.23807i	−0.248237	−	0.968699i	$-0.579851\pi$
$317$	12.7267	−	22.0432i	0.714800	−	1.23807i	0.963037	−	0.269370i	$-0.0868156\pi$
$318$		0			0
$319$	0.0997525	−	0.0997525i	0.00558507	−	0.00558507i
$320$	−2.43832	−	0.653347i	−0.136306	−	0.0365232i
$321$		0			0
$322$	−15.7491			−0.877665
$323$	−6.55106			−0.364511
$324$		0			0
$325$	2.85748	+	2.85748i	0.158504	+	0.158504i
$326$	−12.0897	−	20.9399i	−0.669584	−	1.15975i
$327$		0			0
$328$	2.39843	−	8.95108i	0.132431	−	0.494240i
$329$	−13.3996	+	7.73625i	−0.738743	+	0.426513i
$330$		0			0
$331$	−3.96000	−	14.7789i	−0.217661	−	0.812322i	−0.985213	−	0.171335i	$-0.945192\pi$
$331$	−3.96000	−	14.7789i	−0.217661	−	0.812322i	0.767552	−	0.640987i	$-0.221475\pi$
$332$	9.08060			0.498363
$333$		0			0
$334$	−17.9328			−0.981238
$335$	−10.2004	−	38.0684i	−0.557307	−	2.07990i
$336$		0			0
$337$	18.4528	−	10.6537i	1.00519	−	0.580346i	0.0954091	−	0.995438i	$-0.469584\pi$
$337$	18.4528	−	10.6537i	1.00519	−	0.580346i	0.909779	+	0.415092i	$0.136251\pi$
$338$	1.12022	−	4.18071i	0.0609318	−	0.227400i
$339$		0			0
$340$	−2.26217	−	3.91819i	−0.122683	−	0.212494i
$341$	7.67152	+	7.67152i	0.415436	+	0.415436i
$342$		0			0
$343$	−5.56508			−0.300486
$344$	−0.331408			−0.0178683
$345$		0			0
$346$	−14.2897	−	3.82893i	−0.768222	−	0.205844i
$347$	9.93850	−	9.93850i	0.533526	−	0.533526i	−0.388094	−	0.921620i	$-0.626866\pi$
$347$	9.93850	−	9.93850i	0.533526	−	0.533526i	0.921620	+	0.388094i	$0.126866\pi$
$348$		0			0
$349$	−2.12590	+	3.68217i	−0.113797	+	0.197102i	−0.917298	−	0.398201i	$-0.869635\pi$
$349$	−2.12590	+	3.68217i	−0.113797	+	0.197102i	0.803501	+	0.595303i	$0.202968\pi$
$350$	−4.67159	+	1.25175i	−0.249707	+	0.0669087i
$351$		0			0
$352$	−2.44831	−	0.656023i	−0.130495	−	0.0349661i
$353$	1.50496	+	5.61658i	0.0801008	+	0.298940i	0.994341	−	0.106231i	$-0.0338784\pi$
$353$	1.50496	+	5.61658i	0.0801008	+	0.298940i	−0.914241	+	0.405172i	$0.867212\pi$
$354$		0			0
$355$	−2.68708	−	10.0283i	−0.142615	−	0.532247i
$356$	−10.3391	−	10.3391i	−0.547971	−	0.547971i
$357$		0			0
$358$	−3.94987	−	2.28046i	−0.208757	−	0.120526i
$359$		−	9.45307i		−	0.498914i	−0.968386	−	0.249457i	$-0.919748\pi$
$359$		−	9.45307i		−	0.498914i	0.968386	−	0.249457i	$-0.0802521\pi$
$360$		0			0
$361$	−4.88434	−	2.81998i	−0.257071	−	0.148420i
$362$	−7.28524	+	7.28524i	−0.382904	+	0.382904i
$363$		0			0
$364$	−7.33867	−	7.33867i	−0.384651	−	0.384651i
$365$	9.97718	+	2.67338i	0.522229	+	0.139931i
$366$		0			0
$367$	6.60386	+	11.4382i	0.344719	+	0.597070i	0.985303	−	0.170818i	$-0.0546410\pi$
$367$	6.60386	+	11.4382i	0.344719	+	0.597070i	−0.640584	+	0.767888i	$0.721308\pi$
$368$	−4.31641	+	1.15658i	−0.225009	+	0.0602909i
$369$		0			0
$370$	15.3549	−	0.0145914i	0.798265	−	0.000758571i
$371$		−	12.5817i		−	0.653210i
$372$		0			0
$373$	−24.8365	+	14.3394i	−1.28599	+	0.742464i	−0.977936	−	0.208906i	$-0.933010\pi$
$373$	−24.8365	+	14.3394i	−1.28599	+	0.742464i	−0.308049	+	0.951370i	$0.599676\pi$
$374$	−2.27143	−	3.93424i	−0.117453	−	0.203435i
$375$		0			0
$376$	−3.10433	+	3.10433i	−0.160094	+	0.160094i
$377$	0.141939	−	0.0819485i	0.00731023	−	0.00422056i
$378$		0			0
$379$	−3.66853	+	6.35409i	−0.188440	+	0.326388i	−0.944730	−	0.327849i	$-0.893676\pi$
$379$	−3.66853	+	6.35409i	−0.188440	+	0.326388i	0.756290	+	0.654236i	$0.227010\pi$
$380$			9.22681i			0.473325i
$381$		0			0
$382$	−0.00953613	+	0.0165171i	−0.000487911	+	0.000845087i
$383$	−4.76950	+	17.8000i	−0.243710	+	0.909539i	0.730317	+	0.683108i	$0.239372\pi$
$383$	−4.76950	+	17.8000i	−0.243710	+	0.909539i	−0.974027	+	0.226430i	$0.927294\pi$
$384$		0			0
$385$	−21.7817	+	5.83638i	−1.11010	+	0.297450i
$386$	−1.15863	−	0.668937i	−0.0589729	−	0.0340480i
$387$		0			0
$388$	0.308079	−	1.14977i	0.0156403	−	0.0583706i
$389$	−5.28310	+	19.7168i	−0.267864	+	0.999681i	0.692610	+	0.721312i	$0.256461\pi$
$389$	−5.28310	+	19.7168i	−0.267864	+	0.999681i	−0.960474	+	0.278369i	$0.910206\pi$
$390$		0			0
$391$	−6.93614	−	4.00458i	−0.350775	−	0.202520i
$392$	5.23624	−	1.40305i	0.264470	−	0.0708646i
$393$		0			0
$394$	3.06567	−	11.4412i	0.154446	−	0.576401i
$395$	−3.71683	+	6.43773i	−0.187014	+	0.323918i
$396$		0			0
$397$		−	38.0722i		−	1.91079i	−0.295329	−	0.955396i	$-0.595429\pi$
$397$		−	38.0722i		−	1.91079i	0.295329	−	0.955396i	$-0.404571\pi$
$398$	4.35434	−	7.54194i	0.218263	−	0.378043i
$399$		0			0
$400$	−1.18843	+	0.686141i	−0.0594215	+	0.0343070i
$401$	4.23616	−	4.23616i	0.211544	−	0.211544i	−0.593379	−	0.804923i	$-0.702207\pi$
$401$	4.23616	−	4.23616i	0.211544	−	0.211544i	0.804923	+	0.593379i	$0.202207\pi$
$402$		0			0
$403$	6.30230	+	10.9159i	0.313940	+	0.543760i
$404$	14.7912	−	8.53971i	0.735891	−	0.424867i
$405$		0			0
$406$			0.196152i			0.00973488i
$407$	15.4178	−	0.0146512i	0.764233	−	0.000726232i
$408$		0			0
$409$	−9.92424	+	2.65919i	−0.490722	+	0.131489i	−0.495691	−	0.868499i	$-0.665085\pi$
$409$	−9.92424	+	2.65919i	−0.490722	+	0.131489i	0.00496879	+	0.999988i	$0.498418\pi$
$410$	−11.6963	−	20.2586i	−0.577640	−	1.00050i
$411$		0			0
$412$	−15.1593	−	4.06191i	−0.746843	−	0.200116i
$413$	23.6952	+	23.6952i	1.16597	+	1.16597i
$414$		0			0
$415$	16.2087	−	16.2087i	0.795652	−	0.795652i
$416$	−2.55027	−	1.47240i	−0.125037	−	0.0721902i
$417$		0			0
$418$			9.26460i			0.453146i
$419$	−17.8075	−	10.2812i	−0.869954	−	0.502268i	−0.00262133	−	0.999997i	$-0.500834\pi$
$419$	−17.8075	−	10.2812i	−0.869954	−	0.502268i	−0.867333	+	0.497728i	$0.834168\pi$
$420$		0			0
$421$	−11.4397	−	11.4397i	−0.557536	−	0.557536i	0.371069	−	0.928605i	$-0.378991\pi$
$421$	−11.4397	−	11.4397i	−0.557536	−	0.557536i	−0.928605	+	0.371069i	$0.878991\pi$
$422$	0.0384160	+	0.143371i	0.00187006	+	0.00697917i
$423$		0			0
$424$	−0.923972	−	3.44831i	−0.0448720	−	0.167465i
$425$	−2.37572	−	0.636571i	−0.115239	−	0.0308782i
$426$		0			0
$427$	−33.5687	+	8.99470i	−1.62450	+	0.435284i
$428$	−0.263243	+	0.455950i	−0.0127243	+	0.0220392i
$429$		0			0
$430$	−0.591555	+	0.591555i	−0.0285273	+	0.0285273i
$431$	5.43828	+	1.45718i	0.261953	+	0.0701900i	0.387405	−	0.921910i	$-0.373372\pi$
$431$	5.43828	+	1.45718i	0.261953	+	0.0701900i	−0.125452	+	0.992100i	$0.540038\pi$
$432$		0			0
$433$	−3.26700			−0.157002			−0.0785010	−	0.996914i	$-0.525013\pi$
$433$	−3.26700			−0.157002			−0.0785010	+	0.996914i	$0.525013\pi$
$434$	−15.0852			−0.724114
$435$		0			0
$436$	−2.68265	−	2.68265i	−0.128476	−	0.128476i
$437$	8.16683	+	14.1454i	0.390672	+	0.676664i
$438$		0			0
$439$	−0.858221	+	3.20292i	−0.0409606	+	0.152867i	−0.983377	−	0.181574i	$-0.941881\pi$
$439$	−0.858221	+	3.20292i	−0.0409606	+	0.152867i	0.942417	+	0.334441i	$0.108548\pi$
$440$	−5.54116	+	3.19919i	−0.264164	+	0.152515i
$441$		0			0
$442$	−1.36603	−	5.09808i	−0.0649752	−	0.242491i
$443$	−7.45001			−0.353960			−0.176980	−	0.984214i	$-0.556633\pi$
$443$	−7.45001			−0.353960			−0.176980	+	0.984214i	$0.556633\pi$
$444$		0			0
$445$	−36.9101			−1.74971
$446$	4.16043	+	15.5269i	0.197002	+	0.735221i
$447$		0			0
$448$	3.05217	−	1.76217i	0.144201	−	0.0832547i
$449$	−7.38745	+	27.5703i	−0.348635	+	1.30112i	0.539672	+	0.841875i	$0.318548\pi$
$449$	−7.38745	+	27.5703i	−0.348635	+	1.30112i	−0.888307	+	0.459249i	$0.848118\pi$
$450$		0			0
$451$	−11.7442	−	20.3416i	−0.553013	−	0.957847i
$452$	−2.46718	−	2.46718i	−0.116047	−	0.116047i
$453$		0			0
$454$	14.8867			0.698668
$455$	−26.1987			−1.22821
$456$		0			0
$457$	25.8888	+	6.93689i	1.21103	+	0.324494i	0.807165	−	0.590326i	$-0.201001\pi$
$457$	25.8888	+	6.93689i	1.21103	+	0.324494i	0.403863	+	0.914820i	$0.367667\pi$
$458$	19.6843	−	19.6843i	0.919789	−	0.919789i
$459$		0			0
$460$	−5.64023	+	9.76917i	−0.262977	+	0.455490i
$461$	16.0558	−	4.30214i	0.747793	−	0.200371i	0.135254	−	0.990811i	$-0.456815\pi$
$461$	16.0558	−	4.30214i	0.747793	−	0.200371i	0.612539	+	0.790440i	$0.290148\pi$
$462$		0			0
$463$	29.5438	+	7.91625i	1.37302	+	0.367899i	0.868580	−	0.495548i	$-0.165033\pi$
$463$	29.5438	+	7.91625i	1.37302	+	0.367899i	0.504439	+	0.863448i	$0.331699\pi$
$464$	0.0144050	+	0.0537601i	0.000668734	+	0.00249575i
$465$		0			0
$466$	−4.30459	−	16.0649i	−0.199406	−	0.744194i
$467$	12.3057	+	12.3057i	0.569438	+	0.569438i	0.931971	−	0.362533i	$-0.118088\pi$
$467$	12.3057	+	12.3057i	0.569438	+	0.569438i	−0.362533	+	0.931971i	$0.618088\pi$
$468$		0			0
$469$	47.6520	+	27.5119i	2.20037	+	1.27038i
$470$			11.0823i			0.511189i
$471$		0			0
$472$	8.23434	+	4.75410i	0.379016	+	0.218825i
$473$	−0.593978	+	0.593978i	−0.0273111	+	0.0273111i
$474$		0			0
$475$	3.54676	+	3.54676i	0.162737	+	0.162737i
$476$	6.10139	+	1.63486i	0.279657	+	0.0749338i
$477$		0			0
$478$	1.32193	+	2.28965i	0.0604636	+	0.104726i
$479$	−14.3266	+	3.83880i	−0.654600	+	0.175399i	−0.570808	−	0.821084i	$-0.693370\pi$
$479$	−14.3266	+	3.83880i	−0.654600	+	0.175399i	−0.0837920	+	0.996483i	$0.526703\pi$
$480$		0			0
$481$	17.3065	+	4.61965i	0.789110	+	0.210638i
$482$		−	1.86485i		−	0.0849417i
$483$		0			0
$484$	3.96243	−	2.28771i	0.180110	−	0.103987i
$485$	−1.50239	−	2.60222i	−0.0682201	−	0.118161i
$486$		0			0
$487$	17.2504	−	17.2504i	0.781688	−	0.781688i	−0.198427	−	0.980116i	$-0.563583\pi$
$487$	17.2504	−	17.2504i	0.781688	−	0.781688i	0.980116	+	0.198427i	$0.0635834\pi$
$488$	−8.53971	+	4.93041i	−0.386575	+	0.223189i
$489$		0			0
$490$	6.84216	−	11.8510i	0.309097	−	0.535372i
$491$		−	11.8443i		−	0.534528i	−0.963623	−	0.267264i	$-0.913880\pi$
$491$		−	11.8443i		−	0.534528i	0.963623	−	0.267264i	$-0.0861195\pi$
$492$		0			0
$493$	−0.0498762	+	0.0863882i	−0.00224631	+	0.00389073i
$494$	−2.78583	+	10.3969i	−0.125341	+	0.467777i
$495$		0			0
$496$	−4.13445	+	1.10782i	−0.185642	+	0.0497427i
$497$	12.5529	+	7.24743i	0.563075	+	0.325091i
$498$		0			0
$499$	−8.14435	+	30.3951i	−0.364591	+	1.36067i	0.503383	+	0.864063i	$0.332089\pi$
$499$	−8.14435	+	30.3951i	−0.364591	+	1.36067i	−0.867974	+	0.496609i	$0.834578\pi$
$500$	2.37016	−	8.84555i	0.105997	−	0.395585i
$501$		0			0
$502$	9.25769	+	5.34493i	0.413191	+	0.238556i
$503$	−22.7619	+	6.09902i	−1.01490	+	0.271942i	−0.727676	−	0.685921i	$-0.759399\pi$
$503$	−22.7619	+	6.09902i	−1.01490	+	0.271942i	−0.287225	+	0.957863i	$0.592733\pi$
$504$		0			0
$505$	11.1588	−	41.6452i	0.496560	−	1.85319i
$506$	−5.66333	+	9.80918i	−0.251766	+	0.436071i
$507$		0			0
$508$			17.5137i			0.777046i
$509$	−5.46574	+	9.46694i	−0.242265	+	0.419615i	−0.961359	−	0.275298i	$-0.911224\pi$
$509$	−5.46574	+	9.46694i	−0.242265	+	0.419615i	0.719094	+	0.694912i	$0.244557\pi$
$510$		0			0
$511$	−12.4889	+	7.21048i	−0.552477	+	0.318973i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	15.1518	+	26.2437i	0.668318	+	1.15756i
$515$	−34.3093	+	19.8085i	−1.51185	+	0.872867i
$516$		0			0
$517$			11.1277i			0.489396i
$518$	−15.1443	+	15.1731i	−0.665404	+	0.666670i
$519$		0			0
$520$	−7.18036	+	1.92397i	−0.314880	+	0.0843717i
$521$	−16.6146	−	28.7774i	−0.727900	−	1.26076i	−0.957769	−	0.287539i	$-0.907163\pi$
$521$	−16.6146	−	28.7774i	−0.727900	−	1.26076i	0.229869	−	0.973222i	$-0.426170\pi$
$522$		0			0
$523$	24.5115	+	6.56785i	1.07181	+	0.287192i	0.751238	−	0.660031i	$-0.229457\pi$
$523$	24.5115	+	6.56785i	1.07181	+	0.287192i	0.320576	+	0.947223i	$0.396123\pi$
$524$	−3.60761	−	3.60761i	−0.157599	−	0.157599i
$525$		0			0
$526$	12.1294	−	12.1294i	0.528865	−	0.528865i
$527$	−6.64373	−	3.83576i	−0.289406	−	0.167088i
$528$		0			0
$529$		−	3.03089i		−	0.131778i
$530$	−7.80442	−	4.50588i	−0.339002	−	0.195723i
$531$		0			0
$532$	−9.10891	−	9.10891i	−0.394921	−	0.394921i
$533$	−7.06289	−	26.3591i	−0.305928	−	1.14174i
$534$		0			0
$535$	0.343977	+	1.28374i	0.0148714	+	0.0555010i
$536$	15.0805	+	4.04082i	0.651380	+	0.174537i
$537$		0			0
$538$	20.9736	−	5.61986i	0.904236	−	0.242289i
$539$	6.87019	−	11.8995i	0.295920	−	0.512548i
$540$		0			0
$541$	−9.44575	+	9.44575i	−0.406105	+	0.406105i	−0.880378	−	0.474273i	$-0.842711\pi$
$541$	−9.44575	+	9.44575i	−0.406105	+	0.406105i	0.474273	+	0.880378i	$0.342711\pi$
$542$	8.32740	+	2.23132i	0.357692	+	0.0958434i
$543$		0			0
$544$	1.79229			0.0768437
$545$	−9.57693			−0.410231
$546$		0			0
$547$	−11.8545	−	11.8545i	−0.506864	−	0.506864i	0.406699	−	0.913562i	$-0.366680\pi$
$547$	−11.8545	−	11.8545i	−0.506864	−	0.506864i	−0.913562	+	0.406699i	$0.866680\pi$
$548$	7.65455	+	13.2581i	0.326986	+	0.566357i
$549$		0			0
$550$	−0.900248	+	3.35977i	−0.0383867	+	0.143261i
$551$	0.176178	−	0.101716i	0.00750542	−	0.00433326i
$552$		0			0
$553$	−2.68614	−	10.0248i	−0.114226	−	0.426298i
$554$	9.02762			0.383547
$555$		0			0
$556$	−20.7409			−0.879612
$557$	−2.77230	−	10.3464i	−0.117466	−	0.438389i	0.881994	−	0.471261i	$-0.156201\pi$
$557$	−2.77230	−	10.3464i	−0.117466	−	0.438389i	−0.999460	+	0.0328724i	$0.989534\pi$
$558$		0			0
$559$	−0.845178	+	0.487964i	−0.0357472	+	0.0206387i
$560$	2.30261	−	8.59347i	0.0973032	−	0.363141i
$561$		0			0
$562$	−6.64857	−	11.5157i	−0.280453	−	0.485759i
$563$	0.836585	+	0.836585i	0.0352579	+	0.0352579i	0.724516	−	0.689258i	$-0.242063\pi$
$563$	0.836585	+	0.836585i	0.0352579	+	0.0352579i	−0.689258	+	0.724516i	$0.742063\pi$
$564$		0			0
$565$	−8.80773			−0.370544
$566$	11.1122			0.467079
$567$		0			0
$568$	3.97265	+	1.06447i	0.166689	+	0.0446641i
$569$	−17.1141	+	17.1141i	−0.717462	+	0.717462i	−0.968085	−	0.250623i	$-0.919365\pi$
$569$	−17.1141	+	17.1141i	−0.717462	+	0.717462i	0.250623	+	0.968085i	$0.419365\pi$
$570$		0			0
$571$	−15.4619	+	26.7808i	−0.647061	+	1.12074i	0.336761	+	0.941590i	$0.390669\pi$
$571$	−15.4619	+	26.7808i	−0.647061	+	1.12074i	−0.983821	+	0.179152i	$0.942665\pi$
$572$	−7.20977	+	1.93185i	−0.301456	+	0.0807748i
$573$		0			0
$574$	31.5466	+	8.45289i	1.31673	+	0.352817i
$575$	1.58715	+	5.92334i	0.0661889	+	0.247020i
$576$		0			0
$577$	−2.77757	−	10.3660i	−0.115632	−	0.431543i	0.883702	−	0.468051i	$-0.155043\pi$
$577$	−2.77757	−	10.3660i	−0.115632	−	0.431543i	−0.999333	+	0.0365072i	$0.988377\pi$
$578$	−9.74938	−	9.74938i	−0.405521	−	0.405521i
$579$		0			0
$580$	0.121673	+	0.0702479i	0.00505220	+	0.00291689i
$581$			32.0031i			1.32771i
$582$		0			0
$583$	−7.83638	−	4.52434i	−0.324550	−	0.187379i
$584$	−2.89335	+	2.89335i	−0.119728	+	0.119728i
$585$		0			0
$586$	18.8507	+	18.8507i	0.778716	+	0.778716i
$587$	16.3756	+	4.38782i	0.675892	+	0.181105i	0.580407	−	0.814326i	$-0.302893\pi$
$587$	16.3756	+	4.38782i	0.675892	+	0.181105i	0.0954843	+	0.995431i	$0.469560\pi$
$588$		0			0
$589$	7.82254	+	13.5490i	0.322322	+	0.558279i
$590$	23.1841	−	6.21215i	0.954473	−	0.255750i
$591$		0			0
$592$	−3.03637	+	5.27071i	−0.124794	+	0.216625i
$593$			6.35970i			0.261161i	0.991438	+	0.130581i	$0.0416842\pi$
$593$			6.35970i			0.261161i	−0.991438	+	0.130581i	$0.958316\pi$
$594$		0			0
$595$	13.8090	−	7.97265i	0.566115	−	0.326847i
$596$	−9.38876	−	16.2618i	−0.384579	−	0.666110i
$597$		0			0
$598$	−9.30506	+	9.30506i	−0.380512	+	0.380512i
$599$	−10.7025	+	6.17908i	−0.437291	+	0.252470i	−0.702448	−	0.711735i	$-0.747910\pi$
$599$	−10.7025	+	6.17908i	−0.437291	+	0.252470i	0.265157	+	0.964205i	$0.414576\pi$
$600$		0			0
$601$	9.18230	−	15.9042i	0.374554	−	0.648746i	−0.615706	−	0.787976i	$-0.711129\pi$
$601$	9.18230	−	15.9042i	0.374554	−	0.648746i	0.990260	+	0.139229i	$0.0444625\pi$
$602$		−	1.16799i		−	0.0476038i
$603$		0			0
$604$	−10.3148	+	17.8658i	−0.419704	+	0.726948i
$605$	2.98933	−	11.1563i	0.121534	−	0.453570i
$606$		0			0
$607$	−33.0032	+	8.84317i	−1.33956	+	0.358933i	−0.856270	−	0.516529i	$-0.827224\pi$
$607$	−33.0032	+	8.84317i	−1.33956	+	0.358933i	−0.483287	+	0.875462i	$0.660557\pi$
$608$	−3.16544	−	1.82757i	−0.128376	−	0.0741177i
$609$		0			0
$610$	−6.44253	+	24.0438i	−0.260850	+	0.973507i
$611$	−3.34607	+	12.4877i	−0.135367	+	0.505198i
$612$		0			0
$613$	15.7888	+	9.11564i	0.637702	+	0.368177i	0.783729	−	0.621103i	$-0.213315\pi$
$613$	15.7888	+	9.11564i	0.637702	+	0.368177i	−0.146027	+	0.989281i	$0.546649\pi$
$614$	9.74655	−	2.61158i	0.393339	−	0.105395i
$615$		0			0
$616$	2.31205	−	8.62867i	0.0931550	−	0.347659i
$617$	−17.4572	+	30.2368i	−0.702800	+	1.21729i	0.264679	+	0.964337i	$0.414734\pi$
$617$	−17.4572	+	30.2368i	−0.702800	+	1.21729i	−0.967479	+	0.252949i	$0.918599\pi$
$618$		0			0
$619$			19.1280i			0.768819i	0.923163	+	0.384409i	$0.125595\pi$
$619$			19.1280i			0.768819i	−0.923163	+	0.384409i	$0.874405\pi$
$620$	−5.40246	+	9.35733i	−0.216968	+	0.375800i
$621$		0			0
$622$	14.2566	−	8.23106i	0.571638	−	0.330035i
$623$	36.4385	−	36.4385i	1.45988	−	1.45988i
$624$		0			0
$625$	−14.9891	−	25.9619i	−0.599565	−	1.03848i
$626$	−19.1108	+	11.0336i	−0.763820	+	0.440992i
$627$		0			0
$628$			17.7530i			0.708423i
$629$	−10.5279	+	2.83167i	−0.419775	+	0.112906i
$630$		0			0
$631$	−33.4000	+	8.94951i	−1.32963	+	0.356274i	−0.852579	−	0.522599i	$-0.824963\pi$
$631$	−33.4000	+	8.94951i	−1.32963	+	0.356274i	−0.477055	+	0.878873i	$0.658296\pi$
$632$	−1.47240	−	2.55027i	−0.0585688	−	0.101444i
$633$		0			0
$634$	24.5860	+	6.58780i	0.976435	+	0.261635i
$635$	31.2616	+	31.2616i	1.24058	+	1.24058i
$636$		0			0
$637$	11.2880	−	11.2880i	0.447246	−	0.447246i
$638$	0.122171	+	0.0705357i	0.00483681	+	0.00279253i
$639$		0			0
$640$		−	2.52434i		−	0.0997832i
$641$	−37.4676	−	21.6319i	−1.47988	−	0.854410i	−0.480140	−	0.877192i	$-0.659414\pi$
$641$	−37.4676	−	21.6319i	−1.47988	−	0.854410i	−0.999740	+	0.0227821i	$0.992748\pi$
$642$		0			0
$643$	−26.5503	−	26.5503i	−1.04704	−	1.04704i	−0.998838	−	0.0482028i	$-0.984651\pi$
$643$	−26.5503	−	26.5503i	−1.04704	−	1.04704i	−0.0482028	−	0.998838i	$-0.515349\pi$
$644$	−4.07618	−	15.2125i	−0.160624	−	0.599457i
$645$		0			0
$646$	−1.69554	−	6.32784i	−0.0667101	−	0.248965i
$647$	−4.43138	−	1.18739i	−0.174216	−	0.0466809i	0.170657	−	0.985331i	$-0.445411\pi$
$647$	−4.43138	−	1.18739i	−0.174216	−	0.0466809i	−0.344872	+	0.938650i	$0.612078\pi$
$648$		0			0
$649$	23.2790	−	6.23759i	0.913781	−	0.244847i
$650$	−2.02054	+	3.49968i	−0.0792522	+	0.137269i
$651$		0			0
$652$	17.0974	−	17.0974i	0.669584	−	0.669584i
$653$	37.5512	+	10.0618i	1.46949	+	0.393750i	0.902757	−	0.430150i	$-0.141539\pi$
$653$	37.5512	+	10.0618i	1.46949	+	0.393750i	0.566736	+	0.823900i	$0.308206\pi$
$654$		0			0
$655$	−12.8790			−0.503224
$656$	9.26683			0.361809
$657$		0			0
$658$	−10.9407	−	10.9407i	−0.426513	−	0.426513i
$659$	23.7957	+	41.2154i	0.926950	+	1.60552i	0.788395	+	0.615170i	$0.210913\pi$
$659$	23.7957	+	41.2154i	0.926950	+	1.60552i	0.138555	+	0.990355i	$0.455754\pi$
$660$		0			0
$661$	−10.1078	+	37.7230i	−0.393150	+	1.46725i	0.431759	+	0.901989i	$0.357893\pi$
$661$	−10.1078	+	37.7230i	−0.393150	+	1.46725i	−0.824909	+	0.565266i	$0.808774\pi$
$662$	13.2504	−	7.65013i	0.514992	−	0.297331i
$663$		0			0
$664$	2.35023	+	8.77119i	0.0912067	+	0.340388i
$665$	−32.5184			−1.26101
$666$		0			0
$667$	0.248711			0.00963014
$668$	−4.64135	−	17.3217i	−0.179579	−	0.670198i
$669$		0			0
$670$	34.1312	−	19.7056i	1.31860	−	0.761296i
$671$	−6.46892	+	24.1423i	−0.249730	+	0.932004i
$672$		0			0
$673$	16.1385	+	27.9527i	0.622094	+	1.07750i	0.989095	+	0.147278i	$0.0470512\pi$
$673$	16.1385	+	27.9527i	0.622094	+	1.07750i	−0.367001	+	0.930221i	$0.619615\pi$
$674$	15.0667	+	15.0667i	0.580346	+	0.580346i
$675$		0			0
$676$	4.32819			0.166469
$677$	2.66637			0.102477			0.0512384	−	0.998686i	$-0.483683\pi$
$677$	2.66637			0.102477			0.0512384	+	0.998686i	$0.483683\pi$
$678$		0			0
$679$	4.05217	+	1.08577i	0.155508	+	0.0416682i
$680$	3.19919	−	3.19919i	0.122683	−	0.122683i
$681$		0			0
$682$	−5.42459	+	9.39566i	−0.207718	+	0.359778i
$683$	32.2749	−	8.64804i	1.23497	−	0.330908i	0.418454	−	0.908238i	$-0.362572\pi$
$683$	32.2749	−	8.64804i	1.23497	−	0.330908i	0.816511	+	0.577330i	$0.195905\pi$
$684$		0			0
$685$	37.3285	+	10.0022i	1.42625	+	0.382163i
$686$	−1.44035	−	5.37546i	−0.0549928	−	0.205236i
$687$		0			0
$688$	−0.0857746	−	0.320115i	−0.00327013	−	0.0122043i
$689$	−7.43366	−	7.43366i	−0.283200	−	0.283200i
$690$		0			0
$691$	25.1394	+	14.5142i	0.956348	+	0.552148i	0.895047	−	0.445971i	$-0.147142\pi$
$691$	25.1394	+	14.5142i	0.956348	+	0.552148i	0.0613009	+	0.998119i	$0.480475\pi$
$692$		−	14.7938i		−	0.562377i
$693$		0			0
$694$	12.1721	+	7.02758i	0.462047	+	0.266763i
$695$	−37.0221	+	37.0221i	−1.40433	+	1.40433i
$696$		0			0
$697$	11.7442	+	11.7442i	0.444844	+	0.444844i
$698$	−4.10693	−	1.10045i	−0.155450	−	0.0416526i
$699$		0			0
$700$	−2.41819	−	4.18843i	−0.0913990	−	0.158308i
$701$	−36.2834	+	9.72211i	−1.37041	+	0.367199i	−0.867627	−	0.497216i	$-0.834356\pi$
$701$	−36.2834	+	9.72211i	−1.37041	+	0.367199i	−0.502779	+	0.864415i	$0.667689\pi$
$702$		0			0
$703$	21.4812	+	5.73400i	0.810180	+	0.216262i
$704$		−	2.53468i		−	0.0955292i
$705$		0			0
$706$	−5.03569	+	2.90736i	−0.189521	+	0.109420i
$707$	30.0968	+	52.1293i	1.13191	+	1.96052i
$708$		0			0
$709$	12.2693	−	12.2693i	0.460782	−	0.460782i	−0.438129	−	0.898912i	$-0.644359\pi$
$709$	12.2693	−	12.2693i	0.460782	−	0.460782i	0.898912	+	0.438129i	$0.144359\pi$
$710$	8.99113	−	5.19103i	0.337431	−	0.194816i
$711$		0			0
$712$	7.31084	−	12.6628i	0.273985	−	0.474557i
$713$			19.1273i			0.716323i
$714$		0			0
$715$	−9.42096	+	16.3176i	−0.352324	+	0.610243i
$716$	1.18045	−	4.40551i	0.0441156	−	0.164642i
$717$		0			0
$718$	9.13096	−	2.44663i	0.340764	−	0.0913075i
$719$	−41.7219	−	24.0881i	−1.55596	−	0.898336i	−0.997636	−	0.0687149i	$-0.978110\pi$
$719$	−41.7219	−	24.0881i	−1.55596	−	0.898336i	−0.558327	−	0.829621i	$-0.688557\pi$
$720$		0			0
$721$	14.3156	−	53.4264i	0.533139	−	1.98970i
$722$	1.45973	−	5.44778i	0.0543254	−	0.202745i
$723$		0			0
$724$	−8.92256	−	5.15144i	−0.331604	−	0.191452i
$725$	0.0737740	−	0.0197677i	0.00273990	−	0.000734153i
$726$		0			0
$727$	6.61434	−	24.6851i	0.245312	−	0.915518i	−0.727914	−	0.685669i	$-0.759510\pi$
$727$	6.61434	−	24.6851i	0.245312	−	0.915518i	0.973226	−	0.229850i	$-0.0738235\pi$
$728$	5.18923	−	8.98800i	0.192325	−	0.333118i
$729$		0			0
$730$			10.3291i			0.382298i
$731$	0.296989	−	0.514400i	0.0109845	−	0.0190258i
$732$		0			0
$733$	22.6612	−	13.0834i	0.837010	−	0.483248i	−0.0192366	−	0.999815i	$-0.506124\pi$
$733$	22.6612	−	13.0834i	0.837010	−	0.483248i	0.856247	+	0.516567i	$0.172790\pi$
$734$	−9.33926	+	9.33926i	−0.344719	+	0.344719i
$735$		0			0
$736$	−2.23434	−	3.86999i	−0.0823589	−	0.142650i
$737$	34.2710	−	19.7864i	1.26239	−	0.728840i
$738$		0			0
$739$			9.69779i			0.356739i	0.983964	+	0.178369i	$0.0570822\pi$
$739$			9.69779i			0.356739i	−0.983964	+	0.178369i	$0.942918\pi$
$740$	3.98825	+	14.8280i	0.146611	+	0.545087i
$741$		0			0
$742$	12.1530	−	3.25639i	0.446151	−	0.119546i
$743$	−10.9128	−	18.9015i	−0.400352	−	0.693430i	0.593416	−	0.804896i	$-0.297779\pi$
$743$	−10.9128	−	18.9015i	−0.400352	−	0.693430i	−0.993768	+	0.111465i	$0.964446\pi$
$744$		0			0
$745$	−45.7857	−	12.2682i	−1.67746	−	0.449473i
$746$	−20.2789	−	20.2789i	−0.742464	−	0.742464i
$747$		0			0
$748$	3.21229	−	3.21229i	0.117453	−	0.117453i
$749$	−1.60692	−	0.927756i	−0.0587156	−	0.0338995i
$750$		0			0
$751$			48.6131i			1.77392i	0.461847	+	0.886959i	$0.347187\pi$
$751$			48.6131i			1.77392i	−0.461847	+	0.886959i	$0.652813\pi$
$752$	−3.80201	−	2.19509i	−0.138645	−	0.0800469i
$753$		0			0
$754$	0.115893	+	0.115893i	0.00422056	+	0.00422056i
$755$	13.4783	+	50.3017i	0.490525	+	1.83067i
$756$		0			0
$757$	5.39990	+	20.1527i	0.196263	+	0.732462i	0.991936	+	0.126737i	$0.0404504\pi$
$757$	5.39990	+	20.1527i	0.196263	+	0.732462i	−0.795674	+	0.605725i	$0.792883\pi$
$758$	−7.08706	−	1.89897i	−0.257414	−	0.0689738i
$759$		0			0
$760$	−8.91241	+	2.38807i	−0.323287	+	0.0866245i
$761$	13.6128	−	23.5781i	0.493465	−	0.854706i	−0.506507	−	0.862236i	$-0.669063\pi$
$761$	13.6128	−	23.5781i	0.493465	−	0.854706i	0.999972	+	0.00752959i	$0.00239677\pi$
$762$		0			0
$763$	9.45457	−	9.45457i	0.342278	−	0.342278i
$764$	−0.0184224	−	0.00493627i	−0.000666499	−	0.000178588i
$765$		0			0
$766$	−18.4279			−0.665828
$767$	27.9997			1.01101
$768$		0			0
$769$	24.6006	+	24.6006i	0.887120	+	0.887120i	0.994246	−	0.107125i	$-0.0341647\pi$
$769$	24.6006	+	24.6006i	0.887120	+	0.887120i	−0.107125	+	0.994246i	$0.534165\pi$
$770$	−11.2750	−	19.5289i	−0.406324	−	0.703773i
$771$		0			0
$772$	0.346267	−	1.29229i	0.0124624	−	0.0465104i
$773$	4.69967	−	2.71335i	0.169035	−	0.0975926i	−0.413096	−	0.910688i	$-0.635552\pi$
$773$	4.69967	−	2.71335i	0.169035	−	0.0975926i	0.582131	+	0.813095i	$0.302219\pi$
$774$		0			0
$775$	1.52024	+	5.67363i	0.0546088	+	0.203803i
$776$	1.19033			0.0427302
$777$		0			0
$778$	−20.4123			−0.731817
$779$	−8.76661	−	32.7174i	−0.314096	−	1.17222i
$780$		0			0
$781$	9.02796	−	5.21229i	0.323046	−	0.186510i
$782$	2.07292	−	7.73625i	0.0741276	−	0.276648i
$783$		0			0
$784$	2.71048	+	4.69469i	0.0968028	+	0.167667i
$785$	31.6887	+	31.6887i	1.13102	+	1.13102i
$786$		0			0
$787$	−35.9351			−1.28095			−0.640474	−	0.767980i	$-0.721262\pi$
$787$	−35.9351			−1.28095			−0.640474	+	0.767980i	$0.721262\pi$
$788$	11.8448			0.421955
$789$		0			0
$790$	−7.18036	−	1.92397i	−0.255466	−	0.0684518i
$791$	8.69519	−	8.69519i	0.309165	−	0.309165i
$792$		0			0
$793$	−14.5190	+	25.1477i	−0.515586	+	0.893021i
$794$	36.7750	−	9.85382i	1.30509	−	0.349699i
$795$		0			0
$796$	8.41194	+	2.25397i	0.298153	+	0.0798899i
$797$	−6.81004	−	25.4154i	−0.241224	−	0.900260i	−0.975244	−	0.221132i	$-0.929025\pi$
$797$	−6.81004	−	25.4154i	−0.241224	−	0.900260i	0.734020	−	0.679128i	$-0.237642\pi$
$798$		0			0
$799$	−2.03651	−	7.60037i	−0.0720466	−	0.268882i
$800$	−0.970349	−	0.970349i	−0.0343070	−	0.0343070i
$801$		0			0
$802$	5.18822	+	2.99542i	0.183202	+	0.105772i
$803$			10.3714i			0.366000i
$804$		0			0
$805$	−34.4298	−	19.8781i	−1.21349	−	0.700610i
$806$	−8.91280	+	8.91280i	−0.313940	+	0.313940i
$807$		0			0
$808$	12.0770	+	12.0770i	0.424867	+	0.424867i
$809$	−47.8579	−	12.8235i	−1.68260	−	0.450850i	−0.714133	−	0.700010i	$-0.753179\pi$
$809$	−47.8579	−	12.8235i	−1.68260	−	0.450850i	−0.968462	+	0.249160i	$0.919846\pi$
$810$		0			0
$811$	15.5448	+	26.9244i	0.545851	+	0.945442i	0.998553	+	0.0537798i	$0.0171269\pi$
$811$	15.5448	+	26.9244i	0.545851	+	0.945442i	−0.452702	+	0.891662i	$0.649540\pi$
$812$	−0.189469	+	0.0507680i	−0.00664905	+	0.00178161i
$813$		0			0
$814$	4.00458	+	14.8887i	0.140360	+	0.521848i
$815$		−	61.0367i		−	2.13802i
$816$		0			0
$817$	−1.04905	+	0.605671i	−0.0367017	+	0.0211897i
$818$	−5.13716	−	8.89783i	−0.179617	−	0.311105i
$819$		0			0
$820$	16.5411	−	16.5411i	0.577640	−	0.577640i
$821$	23.8811	−	13.7877i	0.833455	−	0.481196i	−0.0215790	−	0.999767i	$-0.506869\pi$
$821$	23.8811	−	13.7877i	0.833455	−	0.481196i	0.855034	+	0.518572i	$0.173536\pi$
$822$		0			0
$823$	11.3267	−	19.6185i	0.394826	−	0.683858i	−0.598253	−	0.801307i	$-0.704138\pi$
$823$	11.3267	−	19.6185i	0.394826	−	0.683858i	0.993079	+	0.117449i	$0.0374717\pi$
$824$		−	15.6940i		−	0.546727i
$825$		0			0
$826$	−16.7551	+	29.0206i	−0.582983	+	1.00976i
$827$	−10.8371	+	40.4448i	−0.376844	+	1.40640i	0.473787	+	0.880640i	$0.342887\pi$
$827$	−10.8371	+	40.4448i	−0.376844	+	1.40640i	−0.850631	+	0.525763i	$0.823780\pi$
$828$		0			0
$829$	3.05514	−	0.818623i	0.106109	−	0.0284319i	−0.205374	−	0.978684i	$-0.565841\pi$
$829$	3.05514	−	0.818623i	0.106109	−	0.0284319i	0.311483	+	0.950252i	$0.399174\pi$
$830$	19.8515	+	11.4613i	0.689055	+	0.397826i
$831$		0			0
$832$	0.762169	−	2.84445i	0.0264235	−	0.0986137i
$833$	−2.51466	+	9.38485i	−0.0871279	+	0.325166i
$834$		0			0
$835$	−39.2036	−	22.6342i	−1.35670	−	0.783289i
$836$	−8.94891	+	2.39785i	−0.309505	+	0.0829315i
$837$		0			0
$838$	5.32193	−	19.8617i	0.183843	−	0.686111i
$839$	3.99642	−	6.92200i	0.137972	−	0.238974i	−0.788757	−	0.614705i	$-0.789275\pi$
$839$	3.99642	−	6.92200i	0.137972	−	0.238974i	0.926729	+	0.375731i	$0.122608\pi$
$840$		0			0
$841$			28.9969i			0.999893i
$842$	8.08908	−	14.0107i	0.278768	−	0.482840i
$843$		0			0
$844$	−0.128542	+	0.0742140i	−0.00442461	+	0.00255455i
$845$	7.72571	−	7.72571i	0.265772	−	0.265772i
$846$		0			0
$847$	8.06265	+	13.9649i	0.277036	+	0.479841i
$848$	3.09167	−	1.78498i	0.106168	−	0.0612963i
$849$		0			0
$850$		−	2.45952i		−	0.0843609i
$851$	19.2388	+	19.2023i	0.659497	+	0.658245i
$852$		0			0
$853$	−25.5133	+	6.83626i	−0.873557	+	0.234069i	−0.667625	−	0.744497i	$-0.732689\pi$
$853$	−25.5133	+	6.83626i	−0.873557	+	0.234069i	−0.205932	+	0.978566i	$0.566023\pi$
$854$	−17.3764	−	30.0968i	−0.594609	−	1.02989i
$855$		0			0
$856$	−0.508546	−	0.136264i	−0.0173817	−	0.00465742i
$857$	2.62097	+	2.62097i	0.0895305	+	0.0895305i	0.750454	−	0.660923i	$-0.229835\pi$
$857$	2.62097	+	2.62097i	0.0895305	+	0.0895305i	−0.660923	+	0.750454i	$0.729835\pi$
$858$		0			0
$859$	27.6577	−	27.6577i	0.943669	−	0.943669i	−0.0548273	−	0.998496i	$-0.517461\pi$
$859$	27.6577	−	27.6577i	0.943669	−	0.943669i	0.998496	+	0.0548273i	$0.0174608\pi$
$860$	−0.724504	−	0.418292i	−0.0247054	−	0.0142637i
$861$		0			0
$862$			5.63012i			0.191763i
$863$	−43.7075	−	25.2345i	−1.48782	−	0.858994i	−0.487918	−	0.872890i	$-0.662243\pi$
$863$	−43.7075	−	25.2345i	−1.48782	−	0.858994i	−0.999903	+	0.0138958i	$0.995577\pi$
$864$		0			0
$865$	−26.4066	−	26.4066i	−0.897853	−	0.897853i
$866$	−0.845561	−	3.15568i	−0.0287333	−	0.107234i
$867$		0			0
$868$	−3.90434	−	14.5712i	−0.132522	−	0.494579i
$869$	−7.20977	−	1.93185i	−0.244575	−	0.0655336i
$870$		0			0
$871$	44.4091	−	11.8994i	1.50475	−	0.403195i
$872$	1.89692	−	3.28556i	0.0642378	−	0.111263i
$873$		0			0
$874$	−11.5496	+	11.5496i	−0.390672	+	0.390672i
$875$	31.1747	+	8.35324i	1.05390	+	0.282391i
$876$		0			0
$877$	−1.74526			−0.0589332			−0.0294666	−	0.999566i	$-0.509381\pi$
$877$	−1.74526			−0.0589332			−0.0294666	+	0.999566i	$0.509381\pi$
$878$	−3.31591			−0.111907
$879$		0			0
$880$	−4.52434	−	4.52434i	−0.152515	−	0.152515i
$881$	−20.1615	−	34.9207i	−0.679257	−	1.17651i	−0.975205	−	0.221304i	$-0.928969\pi$
$881$	−20.1615	−	34.9207i	−0.679257	−	1.17651i	0.295948	−	0.955204i	$-0.404365\pi$
$882$		0			0
$883$	−6.10566	+	22.7866i	−0.205472	+	0.766831i	0.783833	+	0.620971i	$0.213262\pi$
$883$	−6.10566	+	22.7866i	−0.205472	+	0.766831i	−0.989305	+	0.145860i	$0.953405\pi$
$884$	4.57081	−	2.63896i	0.153733	−	0.0887578i
$885$		0			0
$886$	−1.92820	−	7.19615i	−0.0647793	−	0.241759i
$887$	−5.10107			−0.171277			−0.0856385	−	0.996326i	$-0.527293\pi$
$887$	−5.10107			−0.171277			−0.0856385	+	0.996326i	$0.527293\pi$
$888$		0			0
$889$	−61.7243			−2.07017
$890$	−9.55303	−	35.6524i	−0.320218	−	1.19507i
$891$		0			0
$892$	−13.9211	+	8.03733i	−0.466111	+	0.269110i
$893$	−4.15321	+	15.5000i	−0.138982	+	0.518687i
$894$		0			0
$895$	−5.75665	−	9.97082i	−0.192424	−	0.333288i
$896$	2.49208	+	2.49208i	0.0832547	+	0.0832547i
$897$		0			0
$898$	−28.5429			−0.952489
$899$	0.238227			0.00794530
$900$		0			0
$901$	6.18036	+	1.65602i	0.205898	+	0.0551701i
$902$	16.6088	−	16.6088i	0.553013	−	0.553013i
$903$		0			0
$904$	1.74456	−	3.02167i	0.0580233	−	0.100499i
$905$	−25.1218	+	6.73136i	−0.835076	+	0.223758i
$906$		0			0
$907$	−22.9072	−	6.13796i	−0.760620	−	0.203808i	−0.142396	−	0.989810i	$-0.545481\pi$
$907$	−22.9072	−	6.13796i	−0.760620	−	0.203808i	−0.618224	+	0.786002i	$0.712147\pi$
$908$	3.85296	+	14.3795i	0.127865	+	0.477199i
$909$		0			0
$910$	−6.78073	−	25.3060i	−0.224779	−	0.838886i
$911$	22.2911	+	22.2911i	0.738537	+	0.738537i	0.972295	−	0.233758i	$-0.0751023\pi$
$911$	22.2911	+	22.2911i	0.738537	+	0.738537i	−0.233758	+	0.972295i	$0.575102\pi$
$912$		0			0
$913$	19.9328	+	11.5082i	0.659679	+	0.380866i
$914$			26.8021i			0.886534i
$915$		0			0
$916$	24.1083	+	13.9189i	0.796561	+	0.459894i
$917$	12.7144	−	12.7144i	0.419868	−	0.419868i
$918$		0			0
$919$	−3.06469	−	3.06469i	−0.101095	−	0.101095i	0.654750	−	0.755845i	$-0.272774\pi$
$919$	−3.06469	−	3.06469i	−0.101095	−	0.101095i	−0.755845	+	0.654750i	$0.772774\pi$
$920$	−10.8961	−	2.91960i	−0.359233	−	0.0962563i
$921$		0			0
$922$	8.31109	+	14.3952i	0.273711	+	0.474082i
$923$	11.6986	−	3.13464i	0.385065	−	0.103178i
$924$		0			0
$925$	7.23290	+	4.16676i	0.237816	+	0.137002i
$926$			30.5860i			1.00512i
$927$		0			0
$928$	−0.0482000	+	0.0278283i	−0.00158224	+	0.000913508i
$929$	7.53562	+	13.0521i	0.247236	+	0.428225i	0.962758	−	0.270365i	$-0.0871445\pi$
$929$	7.53562	+	13.0521i	0.247236	+	0.428225i	−0.715522	+	0.698590i	$0.753811\pi$
$930$		0			0
$931$	14.0109	−	14.0109i	0.459188	−	0.459188i
$932$	14.4034	−	8.31583i	0.471800	−	0.272394i
$933$		0			0
$934$	−8.70142	+	15.0713i	−0.284719	+	0.493148i
$935$		−	11.4677i		−	0.375035i
$936$		0			0
$937$	0.837948	−	1.45137i	0.0273746	−	0.0474141i	−0.852014	−	0.523520i	$-0.824619\pi$
$937$	0.837948	−	1.45137i	0.0273746	−	0.0474141i	0.879388	+	0.476106i	$0.157952\pi$
$938$	−14.2412	+	53.1489i	−0.464992	+	1.73537i
$939$		0			0
$940$	−10.7047	+	2.86832i	−0.349149	+	0.0935541i
$941$	7.70009	+	4.44565i	0.251016	+	0.144924i	0.620229	−	0.784421i	$-0.287040\pi$
$941$	7.70009	+	4.44565i	0.251016	+	0.144924i	−0.369214	+	0.929345i	$0.620373\pi$
$942$		0			0
$943$	10.7178	−	39.9995i	0.349021	−	1.30256i
$944$	−2.46090	+	9.18421i	−0.0800956	+	0.298921i
$945$		0			0
$946$	−0.727471	−	0.420006i	−0.0236521	−	0.0136556i
$947$	−33.2719	+	8.91517i	−1.08119	+	0.289704i	−0.755083	−	0.655629i	$-0.772404\pi$
$947$	−33.2719	+	8.91517i	−1.08119	+	0.289704i	−0.326107	+	0.945333i	$0.605737\pi$
$948$		0			0
$949$	−3.11866	+	11.6390i	−0.101236	+	0.377818i
$950$	−2.50794	+	4.34388i	−0.0813683	+	0.140934i
$951$		0			0
$952$			6.31662i			0.204723i
$953$	5.58405	−	9.67186i	0.180885	−	0.313302i	−0.761297	−	0.648403i	$-0.775437\pi$
$953$	5.58405	−	9.67186i	0.180885	−	0.313302i	0.942182	+	0.335101i	$0.108770\pi$
$954$		0			0
$955$	−0.0416947	+	0.0240724i	−0.00134921	+	0.000778965i
$956$	−1.86949	+	1.86949i	−0.0604636	+	0.0604636i
$957$		0			0
$958$	−7.41600	−	12.8449i	−0.239600	−	0.415000i
$959$	−46.7259	+	26.9772i	−1.50886	+	0.871140i
$960$		0			0
$961$		−	12.6791i		−	0.409002i
$962$	0.0170218	+	17.9125i	0.000548804	+	0.577521i
$963$		0			0
$964$	1.80131	−	0.482659i	0.0580162	−	0.0155454i
$965$	−1.68862	−	2.92478i	−0.0543587	−	0.0941520i
$966$		0			0
$967$	−49.5621	−	13.2801i	−1.59381	−	0.427060i	−0.650644	−	0.759383i	$-0.725501\pi$
$967$	−49.5621	−	13.2801i	−1.59381	−	0.427060i	−0.943166	+	0.332322i	$0.892168\pi$
$968$	3.23531	+	3.23531i	0.103987	+	0.103987i
$969$		0			0
$970$	2.12470	−	2.12470i	0.0682201	−	0.0682201i
$971$	39.6791	+	22.9087i	1.27336	+	0.735176i	0.975619	−	0.219470i	$-0.0704328\pi$
$971$	39.6791	+	22.9087i	1.27336	+	0.735176i	0.297743	+	0.954646i	$0.403766\pi$
$972$		0			0
$973$		−	73.0981i		−	2.34342i
$974$	21.1273	+	12.1978i	0.676962	+	0.390844i
$975$		0			0
$976$	−6.97265	−	6.97265i	−0.223189	−	0.223189i
$977$	−9.60213	−	35.8356i	−0.307199	−	1.14648i	−0.931036	−	0.364929i	$-0.881093\pi$
$977$	−9.60213	−	35.8356i	−0.307199	−	1.14648i	0.623836	−	0.781555i	$-0.285573\pi$
$978$		0			0
$979$	−9.59216	−	35.7984i	−0.306567	−	1.14412i
$980$	13.2180	+	3.54176i	0.422235	+	0.113138i
$981$		0			0
$982$	11.4408	−	3.06554i	0.365089	−	0.0978253i
$983$	−8.94751	+	15.4975i	−0.285381	+	0.494295i	−0.972702	−	0.232060i	$-0.925454\pi$
$983$	−8.94751	+	15.4975i	−0.285381	+	0.494295i	0.687320	+	0.726355i	$0.258787\pi$
$984$		0			0
$985$	21.1427	−	21.1427i	0.673664	−	0.673664i
$986$	−0.0963535	−	0.0258178i	−0.00306852	−	0.000822208i
$987$		0			0
$988$	−10.7636			−0.342437
$989$	−1.48096			−0.0470916
$990$		0			0
$991$	−31.4375	−	31.4375i	−0.998647	−	0.998647i	0.00135241	−	0.999999i	$-0.499570\pi$
$991$	−31.4375	−	31.4375i	−0.998647	−	0.998647i	−0.999999	+	0.00135241i	$0.999570\pi$
$992$	−2.14015	−	3.70685i	−0.0679498	−	0.117692i
$993$		0			0
$994$	−3.75154	+	14.0010i	−0.118992	+	0.444083i
$995$	19.0384	−	10.9918i	0.603558	−	0.348464i
$996$		0			0
$997$	1.82379	+	6.80648i	0.0577600	+	0.215563i	0.988774	−	0.149421i	$-0.0477410\pi$
$997$	1.82379	+	6.80648i	0.0577600	+	0.215563i	−0.931014	+	0.364984i	$0.881074\pi$
$998$	−31.4674			−0.996082
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.be.d.125.3	yes	16
3.2	odd	2	inner	666.2.be.d.125.2	✓	16
37.8	odd	12	inner	666.2.be.d.341.2	yes	16
111.8	even	12	inner	666.2.be.d.341.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.be.d.125.2	✓	16	3.2	odd	2	inner
666.2.be.d.125.3	yes	16	1.1	even	1	trivial
666.2.be.d.341.2	yes	16	37.8	odd	12	inner
666.2.be.d.341.3	yes	16	111.8	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.653347 + 2.43832i) q^{5} +(-1.76217 - 3.05217i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.653347 + 2.43832i) q^{5} +(-1.76217 - 3.05217i) q^{7} +(-0.707107 - 0.707107i) q^{8} -2.52434 q^{10} -2.53468 q^{11} +(-2.84445 - 0.762169i) q^{13} +(2.49208 - 2.49208i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.73122 - 0.463878i) q^{17} +(-3.53059 - 0.946020i) q^{19} +(-0.653347 - 2.43832i) q^{20} +(-0.656023 - 2.44831i) q^{22} +(-3.15983 - 3.15983i) q^{23} +(-1.18843 - 0.686141i) q^{25} -2.94479i q^{26} +(3.05217 + 1.76217i) q^{28} +(-0.0393551 + 0.0393551i) q^{29} +(-3.02663 - 3.02663i) q^{31} +(0.965926 + 0.258819i) q^{32} +(0.896143 + 1.55217i) q^{34} +(8.59347 - 2.30261i) q^{35} +(-6.08276 + 0.00578029i) q^{37} -3.65514i q^{38} +(2.18614 - 1.26217i) q^{40} +(4.63342 + 8.02531i) q^{41} +(0.234341 - 0.234341i) q^{43} +(2.19509 - 1.26734i) q^{44} +(2.23434 - 3.86999i) q^{46} -4.39019i q^{47} +(-2.71048 + 4.69469i) q^{49} +(0.355173 - 1.32552i) q^{50} +(2.84445 - 0.762169i) q^{52} +(3.09167 + 1.78498i) q^{53} +(1.65602 - 6.18036i) q^{55} +(-0.912166 + 3.40425i) q^{56} +(-0.0482000 - 0.0278283i) q^{58} +(-9.18421 + 2.46090i) q^{59} +(2.55217 - 9.52481i) q^{61} +(2.14015 - 3.70685i) q^{62} +1.00000i q^{64} +(3.71683 - 6.43773i) q^{65} +(-13.5208 + 7.80626i) q^{67} +(-1.26734 + 1.26734i) q^{68} +(4.44831 + 7.70470i) q^{70} +(-3.56178 + 2.05639i) q^{71} -4.09182i q^{73} +(-1.57992 - 5.87400i) q^{74} +(3.53059 - 0.946020i) q^{76} +(4.46653 + 7.73625i) q^{77} +(2.84445 + 0.762169i) q^{79} +(1.78498 + 1.78498i) q^{80} +(-6.55264 + 6.55264i) q^{82} +(-7.86403 - 4.54030i) q^{83} +4.52434i q^{85} +(0.287007 + 0.165704i) q^{86} +(1.79229 + 1.79229i) q^{88} +(3.78437 + 14.1235i) q^{89} +(2.68614 + 10.0248i) q^{91} +(4.31641 + 1.15658i) q^{92} +(4.24060 - 1.13626i) q^{94} +(4.61340 - 7.99065i) q^{95} +(-0.841688 + 0.841688i) q^{97} +(-5.23624 - 1.40305i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 4 q^{13} + 8 q^{16} + 16 q^{19} + 20 q^{22} + 12 q^{28} - 12 q^{31} + 8 q^{34} + 12 q^{37} + 12 q^{40} - 20 q^{43} + 12 q^{46} + 20 q^{49} - 4 q^{52} - 4 q^{55} + 4 q^{61} - 132 q^{67} + 28 q^{70} - 16 q^{76} - 4 q^{79} + 12 q^{82} + 16 q^{88} + 20 q^{91} + 12 q^{94} - 40 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 4 * q^13 + 8 * q^16 + 16 * q^19 + 20 * q^22 + 12 * q^28 - 12 * q^31 + 8 * q^34 + 12 * q^37 + 12 * q^40 - 20 * q^43 + 12 * q^46 + 20 * q^49 - 4 * q^52 - 4 * q^55 + 4 * q^61 - 132 * q^67 + 28 * q^70 - 16 * q^76 - 4 * q^79 + 12 * q^82 + 16 * q^88 + 20 * q^91 + 12 * q^94 - 40 * q^97

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