LMFDB - Embedded newform 600.2.bp.b.413.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(53,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 10, 10, 7]))

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

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

chi := DirichletCharacter("600.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.bp (of order $20$, degree $8$, 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	16.0.6879707136000000000000.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 9x^{12} + 81x^{8} - 729x^{4} + 6561 $ x^16 - 9x^12 + 81x^8 - 729*x^4 + 6561
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{20}]$

Embedding invariants

Embedding label			413.2
Root			$0.270952 + 1.71073i$ of defining polynomial
Character	$\chi$	$=$	600.413
Dual form			600.2.bp.b.77.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39680 - 0.221232i) q^{2} +(0.786335 - 1.54327i) q^{3} +(1.90211 - 0.618034i) q^{4} +(1.48949 - 1.66775i) q^{5} +(0.756934 - 2.32960i) q^{6} +(-2.44450 + 2.44450i) q^{7} +(2.52015 - 1.28408i) q^{8} +(-1.76336 - 2.42705i) q^{9} +O(q^{10})$	\(q+(1.39680 - 0.221232i) q^{2} +(0.786335 - 1.54327i) q^{3} +(1.90211 - 0.618034i) q^{4} +(1.48949 - 1.66775i) q^{5} +(0.756934 - 2.32960i) q^{6} +(-2.44450 + 2.44450i) q^{7} +(2.52015 - 1.28408i) q^{8} +(-1.76336 - 2.42705i) q^{9} +(1.71157 - 2.65905i) q^{10} +(2.05209 + 1.49093i) q^{11} +(0.541905 - 3.42145i) q^{12} +(-2.87368 + 3.95528i) q^{14} +(-1.40255 - 3.61010i) q^{15} +(3.23607 - 2.35114i) q^{16} +(-3.00000 - 3.00000i) q^{18} +(1.80246 - 4.09282i) q^{20} +(1.85032 + 5.69471i) q^{21} +(3.19621 + 1.62855i) q^{22} -4.89898i q^{24} +(-0.562811 - 4.96822i) q^{25} +(-5.13218 + 0.812857i) q^{27} +(-3.13893 + 6.16049i) q^{28} +(-5.08670 + 1.65277i) q^{29} +(-2.75776 - 4.73231i) q^{30} +(-2.47112 + 7.60531i) q^{31} +(4.00000 - 4.00000i) q^{32} +(3.91454 - 1.99456i) q^{33} +(0.435756 + 7.71789i) q^{35} +(-4.85410 - 3.52671i) q^{36} +(1.61222 - 6.11562i) q^{40} +(3.84439 + 7.54503i) q^{42} +(4.82476 + 1.56766i) q^{44} +(-6.67423 - 0.674235i) q^{45} +(-1.08381 - 6.84291i) q^{48} -4.95114i q^{49} +(-1.88526 - 6.81511i) q^{50} +(-5.04613 + 9.90359i) q^{53} +(-6.98881 + 2.27080i) q^{54} +(5.54309 - 1.20165i) q^{55} +(-3.02157 + 9.29942i) q^{56} +(-6.73946 + 3.43393i) q^{58} +(7.52373 + 10.3555i) q^{59} +(-4.89898 - 6.00000i) q^{60} +(-1.76912 + 11.1698i) q^{62} +(10.2434 + 1.62240i) q^{63} +(4.70228 - 6.47214i) q^{64} +(5.02658 - 3.65202i) q^{66} +(2.31611 + 10.6840i) q^{70} +(-7.56044 - 3.85224i) q^{72} +(-2.63243 - 16.6205i) q^{73} +(-8.10986 - 3.03812i) q^{75} +(-8.66092 + 1.37175i) q^{77} +(16.8983 - 5.49059i) q^{79} +(0.898979 - 8.89898i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(16.2349 - 8.27209i) q^{83} +(7.03905 + 9.68842i) q^{84} +(-1.44918 + 9.14977i) q^{87} +(7.08605 + 1.12232i) q^{88} +(-9.47175 + 0.534780i) q^{90} +(9.79391 + 9.79391i) q^{93} +(-3.02774 - 9.31841i) q^{96} +(-9.51450 - 4.84788i) q^{97} +(-1.09535 - 6.91576i) q^{98} -7.60958i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 4 q^{5} + 4 q^{7} - 8 q^{8}+O(q^{10}) $ 16 * q + 4 * q^2 - 4 * q^5 + 4 * q^7 - 8 * q^8	$ 16 q + 4 q^{2} - 4 q^{5} + 4 q^{7} - 8 q^{8} + 8 q^{10} - 24 q^{11} - 12 q^{15} + 16 q^{16} - 48 q^{18} - 8 q^{20} + 36 q^{21} - 16 q^{22} + 32 q^{28} + 12 q^{30} + 64 q^{32} + 12 q^{33} + 8 q^{35} - 24 q^{36} + 24 q^{42} - 48 q^{45} - 4 q^{50} + 28 q^{55} - 24 q^{56} - 8 q^{58} + 80 q^{59} + 12 q^{63} + 36 q^{66} - 32 q^{70} + 24 q^{72} - 28 q^{73} - 24 q^{75} - 12 q^{77} - 64 q^{80} + 36 q^{81} + 24 q^{83} - 36 q^{87} + 32 q^{88} + 24 q^{93} - 16 q^{97} + 72 q^{98}+O(q^{100}) $ 16 * q + 4 * q^2 - 4 * q^5 + 4 * q^7 - 8 * q^8 + 8 * q^10 - 24 * q^11 - 12 * q^15 + 16 * q^16 - 48 * q^18 - 8 * q^20 + 36 * q^21 - 16 * q^22 + 32 * q^28 + 12 * q^30 + 64 * q^32 + 12 * q^33 + 8 * q^35 - 24 * q^36 + 24 * q^42 - 48 * q^45 - 4 * q^50 + 28 * q^55 - 24 * q^56 - 8 * q^58 + 80 * q^59 + 12 * q^63 + 36 * q^66 - 32 * q^70 + 24 * q^72 - 28 * q^73 - 24 * q^75 - 12 * q^77 - 64 * q^80 + 36 * q^81 + 24 * q^83 - 36 * q^87 + 32 * q^88 + 24 * q^93 - 16 * q^97 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	1.39680	−	0.221232i	0.987688	−	0.156434i
$2$	1.39680	−	0.221232i	0.987688	−	0.156434i
$3$	0.786335	−	1.54327i	0.453990	−	0.891007i
$3$	0.786335	−	1.54327i	0.453990	−	0.891007i
$4$	1.90211	−	0.618034i	0.951057	−	0.309017i
$5$	1.48949	−	1.66775i	0.666122	−	0.745843i
$5$	1.48949	−	1.66775i	0.666122	−	0.745843i
$6$	0.756934	−	2.32960i	0.309017	−	0.951057i
$7$	−2.44450	+	2.44450i	−0.923933	+	0.923933i	−0.997305	−	0.0733714i	$-0.976624\pi$
$7$	−2.44450	+	2.44450i	−0.923933	+	0.923933i	0.0733714	+	0.997305i	$0.476624\pi$
$8$	2.52015	−	1.28408i	0.891007	−	0.453990i
$9$	−1.76336	−	2.42705i	−0.587785	−	0.809017i
$10$	1.71157	−	2.65905i	0.541246	−	0.840864i
$11$	2.05209	+	1.49093i	0.618729	+	0.449533i	0.852477	−	0.522764i	$-0.175099\pi$
$11$	2.05209	+	1.49093i	0.618729	+	0.449533i	−0.233748	+	0.972297i	$0.575099\pi$
$12$	0.541905	−	3.42145i	0.156434	−	0.987688i
$13$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$13$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$14$	−2.87368	+	3.95528i	−0.768023	+	1.05709i
$15$	−1.40255	−	3.61010i	−0.362137	−	0.932125i
$16$	3.23607	−	2.35114i	0.809017	−	0.587785i
$17$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$17$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$18$	−3.00000	−	3.00000i	−0.707107	−	0.707107i
$19$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$19$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$20$	1.80246	−	4.09282i	0.403042	−	0.915182i
$21$	1.85032	+	5.69471i	0.403774	+	1.24269i
$22$	3.19621	+	1.62855i	0.681434	+	0.347208i
$23$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$23$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$24$		−	4.89898i		−	1.00000i
$25$	−0.562811	−	4.96822i	−0.112562	−	0.993645i
$26$		0			0
$27$	−5.13218	+	0.812857i	−0.987688	+	0.156434i
$28$	−3.13893	+	6.16049i	−0.593202	+	1.16422i
$29$	−5.08670	+	1.65277i	−0.944576	+	0.306911i	−0.740510	−	0.672046i	$-0.765416\pi$
$29$	−5.08670	+	1.65277i	−0.944576	+	0.306911i	−0.204066	+	0.978957i	$0.565416\pi$
$30$	−2.75776	−	4.73231i	−0.503495	−	0.863998i
$31$	−2.47112	+	7.60531i	−0.443825	+	1.36595i	0.439941	+	0.898027i	$0.354999\pi$
$31$	−2.47112	+	7.60531i	−0.443825	+	1.36595i	−0.883767	+	0.467928i	$0.845001\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$	3.91454	−	1.99456i	0.681434	−	0.347208i
$34$		0			0
$35$	0.435756	+	7.71789i	0.0736562	+	1.30456i
$36$	−4.85410	−	3.52671i	−0.809017	−	0.587785i
$37$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$37$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$38$		0			0
$39$		0			0
$40$	1.61222	−	6.11562i	0.254914	−	0.966964i
$41$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$41$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$42$	3.84439	+	7.54503i	0.593202	+	1.16422i
$43$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$43$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$44$	4.82476	+	1.56766i	0.727360	+	0.236334i
$45$	−6.67423	−	0.674235i	−0.994936	−	0.100509i
$46$		0			0
$47$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$47$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$48$	−1.08381	−	6.84291i	−0.156434	−	0.987688i
$49$		−	4.95114i		−	0.707305i
$50$	−1.88526	−	6.81511i	−0.266617	−	0.963803i
$51$		0			0
$52$		0			0
$53$	−5.04613	+	9.90359i	−0.693139	+	1.36036i	0.228970	+	0.973433i	$0.426464\pi$
$53$	−5.04613	+	9.90359i	−0.693139	+	1.36036i	−0.922110	+	0.386929i	$0.873536\pi$
$54$	−6.98881	+	2.27080i	−0.951057	+	0.309017i
$55$	5.54309	−	1.20165i	0.747430	−	0.162031i
$56$	−3.02157	+	9.29942i	−0.403774	+	1.24269i
$57$		0			0
$58$	−6.73946	+	3.43393i	−0.884935	+	0.450897i
$59$	7.52373	+	10.3555i	0.979506	+	1.34817i	0.937095	+	0.349074i	$0.113504\pi$
$59$	7.52373	+	10.3555i	0.979506	+	1.34817i	0.0424110	+	0.999100i	$0.486496\pi$
$60$	−4.89898	−	6.00000i	−0.632456	−	0.774597i
$61$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$61$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$62$	−1.76912	+	11.1698i	−0.224679	+	1.41857i
$63$	10.2434	+	1.62240i	1.29055	+	0.204403i
$64$	4.70228	−	6.47214i	0.587785	−	0.809017i
$65$		0			0
$66$	5.02658	−	3.65202i	0.618729	−	0.449533i
$67$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$67$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$68$		0			0
$69$		0			0
$70$	2.31611	+	10.6840i	0.276828	+	1.27698i
$71$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$71$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$72$	−7.56044	−	3.85224i	−0.891007	−	0.453990i
$73$	−2.63243	−	16.6205i	−0.308103	−	1.94528i	−0.325792	−	0.945441i	$-0.605631\pi$
$73$	−2.63243	−	16.6205i	−0.308103	−	1.94528i	0.0176895	−	0.999844i	$-0.494369\pi$
$74$		0			0
$75$	−8.10986	−	3.03812i	−0.936446	−	0.350812i
$76$		0			0
$77$	−8.66092	+	1.37175i	−0.987003	+	0.156326i
$78$		0			0
$79$	16.8983	−	5.49059i	1.90121	−	0.617740i	0.941069	−	0.338214i	$-0.109823\pi$
$79$	16.8983	−	5.49059i	1.90121	−	0.617740i	0.960138	−	0.279526i	$-0.0901773\pi$
$80$	0.898979	−	8.89898i	0.100509	−	0.994936i
$81$	−2.78115	+	8.55951i	−0.309017	+	0.951057i
$82$		0			0
$83$	16.2349	−	8.27209i	1.78201	−	0.907980i	0.890316	−	0.455342i	$-0.150483\pi$
$83$	16.2349	−	8.27209i	1.78201	−	0.907980i	0.891695	−	0.452638i	$-0.149517\pi$
$84$	7.03905	+	9.68842i	0.768023	+	1.05709i
$85$		0			0
$86$		0			0
$87$	−1.44918	+	9.14977i	−0.155368	+	0.980958i
$88$	7.08605	+	1.12232i	0.755375	+	0.119640i
$89$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$89$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$90$	−9.47175	+	0.534780i	−0.998410	+	0.0563708i
$91$		0			0
$92$		0			0
$93$	9.79391	+	9.79391i	1.01558	+	1.01558i
$94$		0			0
$95$		0			0
$96$	−3.02774	−	9.31841i	−0.309017	−	0.951057i
$97$	−9.51450	−	4.84788i	−0.966051	−	0.492228i	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−9.51450	−	4.84788i	−0.966051	−	0.492228i	−0.864517	+	0.502604i	$0.832375\pi$
$98$	−1.09535	−	6.91576i	−0.110647	−	0.698597i
$99$		−	7.60958i		−	0.764791i
$100$	−4.14106	−	9.10229i	−0.414106	−	0.910229i
$101$	19.0133			1.89190			0.945948	−	0.324317i	$-0.105135\pi$
$101$	19.0133			1.89190			0.945948	+	0.324317i	$0.105135\pi$
$102$		0			0
$103$	−8.69227	+	17.0595i	−0.856474	+	1.68093i	−0.132408	+	0.991195i	$0.542271\pi$
$103$	−8.69227	+	17.0595i	−0.856474	+	1.68093i	−0.724066	+	0.689730i	$0.757729\pi$
$104$		0			0
$105$	12.2534	+	5.39635i	1.19581	+	0.526630i
$106$	−4.85746	+	14.9497i	−0.471798	+	1.45204i
$107$	−13.6710	+	13.6710i	−1.32163	+	1.32163i	−0.409166	+	0.912460i	$0.634180\pi$
$107$	−13.6710	+	13.6710i	−1.32163	+	1.32163i	−0.912460	+	0.409166i	$0.865820\pi$
$108$	−9.25961	+	4.71801i	−0.891007	+	0.453990i
$109$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$109$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$110$	7.47676	−	2.90478i	0.712881	−	0.276960i
$111$		0			0
$112$	−2.16320	+	13.6579i	−0.204403	+	1.29055i
$113$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$113$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$114$		0			0
$115$		0			0
$116$	−8.65400	+	6.28750i	−0.803504	+	0.583780i
$117$		0			0
$118$	12.8001	+	12.8001i	1.17835	+	1.17835i
$119$		0			0
$120$	−8.17030	−	7.29700i	−0.745843	−	0.666122i
$121$	−1.41098	−	4.34256i	−0.128271	−	0.394778i
$122$		0			0
$123$		0			0
$124$			15.9934i			1.43625i
$125$	−9.12408	−	6.46151i	−0.816083	−	0.577935i
$126$	14.6670			1.30664
$127$	−22.2186	+	3.51907i	−1.97158	+	0.312267i	−0.976092	+	0.217357i	$0.930256\pi$
$127$	−22.2186	+	3.51907i	−1.97158	+	0.312267i	−0.995486	+	0.0949102i	$0.969744\pi$
$128$	5.13632	−	10.0806i	0.453990	−	0.891007i
$129$		0			0
$130$		0			0
$131$	5.70121	−	17.5465i	0.498117	−	1.53305i	−0.313926	−	0.949447i	$-0.601644\pi$
$131$	5.70121	−	17.5465i	0.498117	−	1.53305i	0.812043	−	0.583598i	$-0.198356\pi$
$132$	6.21319	−	6.21319i	0.540789	−	0.540789i
$133$		0			0
$134$		0			0
$135$	−6.28871	+	9.76996i	−0.541246	+	0.840864i
$136$		0			0
$137$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$137$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$138$		0			0
$139$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$139$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$140$	5.59878	+	14.4110i	0.473183	+	1.21795i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−11.4127	−	3.70820i	−0.951057	−	0.309017i
$145$	−4.82020	+	10.9452i	−0.400295	+	0.908945i
$146$	−7.35397	−	22.6332i	−0.608619	−	1.87314i
$147$	−7.64093	−	3.89325i	−0.630214	−	0.321110i
$148$		0			0
$149$			6.58694i			0.539623i	0.962913	+	0.269812i	$0.0869614\pi$
$149$			6.58694i			0.539623i	−0.962913	+	0.269812i	$0.913039\pi$
$150$	−12.0000	−	2.44949i	−0.979796	−	0.200000i
$151$	−22.6780			−1.84551			−0.922755	−	0.385388i	$-0.874068\pi$
$151$	−22.6780			−1.84551			−0.922755	+	0.385388i	$0.874068\pi$
$152$		0			0
$153$		0			0
$154$	−11.7941	+	3.83214i	−0.950397	+	0.308803i
$155$	9.00308	+	15.4493i	0.723145	+	1.24092i
$156$		0			0
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$	22.3889	−	11.4077i	1.78116	−	0.907549i
$159$	11.3159	+	15.5751i	0.897413	+	1.23518i
$160$	−0.713040	−	12.6290i	−0.0563708	−	0.998410i
$161$		0			0
$162$	−1.99109	+	12.5712i	−0.156434	+	0.987688i
$163$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$163$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$164$		0			0
$165$	2.50425	−	9.49938i	0.194956	−	0.739525i
$166$	20.8469	−	15.1461i	1.61803	−	1.17557i
$167$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$167$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$168$	11.9755	+	11.9755i	0.923933	+	0.923933i
$169$	12.3637	+	4.01722i	0.951057	+	0.309017i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.53401	−	22.3129i	−0.268686	−	1.69642i	−0.640378	−	0.768060i	$-0.721222\pi$
$173$	−3.53401	−	22.3129i	−0.268686	−	1.69642i	0.371692	−	0.928356i	$-0.378778\pi$
$174$			13.1010i			0.993186i
$175$	13.5206	+	10.7690i	1.02206	+	0.814061i
$176$	10.1461			0.764791
$177$	21.8975	−	3.46823i	1.64592	−	0.260688i
$178$		0			0
$179$	−20.0571	+	6.51694i	−1.49914	+	0.487099i	−0.939766	−	0.341818i	$-0.888957\pi$
$179$	−20.0571	+	6.51694i	−1.49914	+	0.487099i	−0.559371	+	0.828917i	$0.688957\pi$
$180$	−13.1118	+	2.84243i	−0.977299	+	0.211862i
$181$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$181$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	15.8469	+	11.5134i	1.16195	+	0.844206i
$187$		0			0
$188$		0			0
$189$	10.5586	−	14.5326i	0.768023	−	1.05709i
$190$		0			0
$191$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$191$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$192$	−6.29068	−	12.3461i	−0.453990	−	0.891007i
$193$	−19.5263	−	19.5263i	−1.40553	−	1.40553i	−0.780991	−	0.624543i	$-0.785285\pi$
$193$	−19.5263	−	19.5263i	−1.40553	−	1.40553i	−0.624543	−	0.780991i	$-0.714715\pi$
$194$	−14.3624	−	4.66662i	−1.03116	−	0.335044i
$195$		0			0
$196$	−3.05997	−	9.41762i	−0.218569	−	0.672687i
$197$	5.30746	+	2.70429i	0.378141	+	0.192673i	0.632722	−	0.774379i	$-0.281938\pi$
$197$	5.30746	+	2.70429i	0.378141	+	0.192673i	−0.254581	+	0.967051i	$0.581938\pi$
$198$	−1.68348	−	10.6291i	−0.119640	−	0.755375i
$199$		−	3.07150i		−	0.217733i	−0.994056	−	0.108866i	$-0.965278\pi$
$199$		−	3.07150i		−	0.217733i	0.994056	−	0.108866i	$-0.0347221\pi$
$200$	−7.79796	−	11.7980i	−0.551399	−	0.834242i
$201$		0			0
$202$	26.5579	−	4.20635i	1.86860	−	0.295958i
$203$	8.39423	−	16.4746i	0.589159	−	1.15629i
$204$		0			0
$205$		0			0
$206$	−8.36727	+	25.7518i	−0.582975	+	1.79421i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	18.3095	+	4.82679i	1.26347	+	0.333080i
$211$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$211$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$212$	−3.47756	+	21.9564i	−0.238840	+	1.50797i
$213$		0			0
$214$	−16.0712	+	22.1202i	−1.09861	+	1.51210i
$215$		0			0
$216$	−11.8901	+	8.63864i	−0.809017	+	0.587785i
$217$	−12.5505	−	24.6318i	−0.851985	−	1.67212i
$218$		0			0
$219$	−27.7199	−	9.00674i	−1.87314	−	0.608619i
$220$	9.80092	−	5.71149i	0.660778	−	0.385069i
$221$		0			0
$222$		0			0
$223$	−2.90707	−	18.3545i	−0.194672	−	1.22911i	−0.870544	−	0.492090i	$-0.836233\pi$
$223$	−2.90707	−	18.3545i	−0.194672	−	1.22911i	0.675873	−	0.737018i	$-0.263767\pi$
$224$			19.5560i			1.30664i
$225$	−11.0657	+	10.1267i	−0.737713	+	0.675114i
$226$		0			0
$227$	−8.11635	+	1.28550i	−0.538701	+	0.0853219i	−0.419856	−	0.907591i	$-0.637919\pi$
$227$	−8.11635	+	1.28550i	−0.538701	+	0.0853219i	−0.118846	+	0.992913i	$0.537919\pi$
$228$		0			0
$229$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$229$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$230$		0			0
$231$	−4.69339	+	14.4448i	−0.308803	+	0.950397i
$232$	−10.6969	+	10.6969i	−0.702288	+	0.702288i
$233$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$233$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$234$		0			0
$235$		0			0
$236$	20.7110	+	15.0475i	1.34817	+	0.979506i
$237$	4.81426	−	30.3961i	0.312720	−	1.97444i
$238$		0			0
$239$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$239$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$240$	−13.0266	−	8.38494i	−0.840864	−	0.541246i
$241$	0.345740	−	0.251195i	0.0222710	−	0.0161809i	−0.576594	−	0.817031i	$-0.695619\pi$
$241$	0.345740	−	0.251195i	0.0222710	−	0.0161809i	0.598865	+	0.800850i	$0.295619\pi$
$242$	−2.93158	−	5.75354i	−0.188449	−	0.369852i
$243$	11.0227	+	11.0227i	0.707107	+	0.707107i
$244$		0			0
$245$	−8.25728	−	7.37469i	−0.527538	−	0.471152i
$246$		0			0
$247$		0			0
$248$	3.53825	+	22.3396i	0.224679	+	1.41857i
$249$		−	31.5594i		−	2.00000i
$250$	−14.1740	−	7.00692i	−0.896444	−	0.443156i
$251$	9.11373			0.575253			0.287627	−	0.957743i	$-0.407134\pi$
$251$	9.11373			0.575253			0.287627	+	0.957743i	$0.407134\pi$
$252$	20.4869	−	3.24480i	1.29055	−	0.204403i
$253$		0			0
$254$	−30.2564	+	9.83090i	−1.89846	+	0.616845i
$255$		0			0
$256$	4.94427	−	15.2169i	0.309017	−	0.951057i
$257$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$257$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	12.9810	+	9.43125i	0.803504	+	0.583780i
$262$	4.08161	−	25.7703i	0.252163	−	1.59209i
$263$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$263$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$264$	7.30405	−	10.0532i	0.449533	−	0.618729i
$265$	9.00057	+	23.1670i	0.552901	+	1.42314i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	22.2400	+	7.22620i	1.35599	+	0.440589i	0.894704	−	0.446660i	$-0.147387\pi$
$269$	22.2400	+	7.22620i	1.35599	+	0.440589i	0.461291	+	0.887249i	$0.347387\pi$
$270$	−6.62265	+	15.0380i	−0.403042	+	0.915182i
$271$	−5.09806	−	15.6902i	−0.309685	−	0.953112i	−0.977887	−	0.209133i	$-0.932936\pi$
$271$	−5.09806	−	15.6902i	−0.309685	−	0.953112i	0.668202	−	0.743980i	$-0.267064\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.25234	−	11.0344i	0.377031	−	0.665397i
$276$		0			0
$277$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$277$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$278$		0			0
$279$	22.8159	−	7.41335i	1.36595	−	0.443825i
$280$	11.0085	+	18.8907i	0.657887	+	1.12893i
$281$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$281$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$282$		0			0
$283$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$283$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−16.7616	−	2.65478i	−0.987688	−	0.156434i
$289$	−9.99235	+	13.7533i	−0.587785	+	0.809017i
$290$	−4.31145	+	16.3546i	−0.253177	+	0.960375i
$291$	−14.9632	+	10.8714i	−0.877156	+	0.637291i
$292$	−15.2792	−	29.9872i	−0.894149	−	1.75487i
$293$	−11.9573	−	11.9573i	−0.698550	−	0.698550i	0.265547	−	0.964098i	$-0.414447\pi$
$293$	−11.9573	−	11.9573i	−0.698550	−	0.698550i	−0.964098	+	0.265547i	$0.914447\pi$
$294$	−11.5342	−	3.74768i	−0.672687	−	0.218569i
$295$	28.4770	+	2.87676i	1.65800	+	0.167492i
$296$		0			0
$297$	−11.7436	−	5.98367i	−0.681434	−	0.347208i
$298$	1.45724	+	9.20065i	0.0844156	+	0.532979i
$299$		0			0
$300$	−17.3035	−	0.766672i	−0.999020	−	0.0442638i
$301$		0			0
$302$	−31.6767	+	5.01709i	−1.82279	+	0.288701i
$303$	14.9508	−	29.3427i	0.858903	−	1.68569i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$	−15.6263	+	7.96197i	−0.890388	+	0.453675i
$309$	19.4924	+	26.8290i	1.10888	+	1.52625i
$310$	15.9934	+	19.5878i	0.908364	+	1.11251i
$311$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$311$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$312$		0			0
$313$	14.8115	+	2.34591i	0.837194	+	0.132599i	0.560287	−	0.828298i	$-0.310691\pi$
$313$	14.8115	+	2.34591i	0.837194	+	0.132599i	0.276907	+	0.960897i	$0.410691\pi$
$314$		0			0
$315$	17.9633	−	14.6670i	1.01212	−	0.826391i
$316$	28.7491	−	20.8874i	1.61726	−	1.17501i
$317$	−6.80530	−	13.3562i	−0.382224	−	0.750156i	0.617102	−	0.786884i	$-0.288307\pi$
$317$	−6.80530	−	13.3562i	−0.382224	−	0.750156i	−0.999325	+	0.0367271i	$0.988307\pi$
$318$	19.2518	+	19.2518i	1.07959	+	1.07959i
$319$	−12.9025	−	4.19229i	−0.722403	−	0.234723i
$320$	−3.78991	−	17.4825i	−0.211862	−	0.977299i
$321$	10.3480	+	31.8480i	0.577572	+	1.77758i
$322$		0			0
$323$		0			0
$324$			18.0000i			1.00000i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	1.39638	−	13.8228i	0.0768684	−	0.760919i
$331$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$331$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$332$	25.7682	−	25.7682i	1.41421	−	1.41421i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	19.3768	+	14.0781i	1.05709	+	0.768023i
$337$	0.978905	−	6.18056i	0.0533243	−	0.336677i	−0.946575	−	0.322484i	$-0.895482\pi$
$337$	0.978905	−	6.18056i	0.0533243	−	0.336677i	0.999899	−	0.0141927i	$-0.00451783\pi$
$338$	18.1584	+	2.87601i	0.987688	+	0.156434i
$339$		0			0
$340$		0			0
$341$	−16.4100	+	11.9225i	−0.888649	+	0.645641i
$342$		0			0
$343$	−5.00844	−	5.00844i	−0.270430	−	0.270430i
$344$		0			0
$345$		0			0
$346$	−9.87263	−	30.3848i	−0.530756	−	1.63350i
$347$	32.2925	+	16.4538i	1.73355	+	0.883288i	0.971931	+	0.235264i	$0.0755955\pi$
$347$	32.2925	+	16.4538i	1.73355	+	0.883288i	0.761620	+	0.648024i	$0.224404\pi$
$348$	2.89836	+	18.2995i	0.155368	+	0.980958i
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	21.2681	+	12.0510i	1.13683	+	0.644153i
$351$		0			0
$352$	14.1721	−	2.24464i	0.755375	−	0.119640i
$353$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$353$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$354$	29.8192	−	9.68886i	1.58487	−	0.514957i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−26.5740	+	13.5401i	−1.40448	+	0.715619i
$359$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$359$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$360$	−17.6858	+	6.87107i	−0.932125	+	0.362137i
$361$	15.3713	+	11.1679i	0.809017	+	0.587785i
$362$		0			0
$363$	−7.81124	−	1.23718i	−0.409984	−	0.0649350i
$364$		0			0
$365$	−31.6399	−	20.3659i	−1.65611	−	1.06600i
$366$		0			0
$367$	−16.3810	−	32.1496i	−0.855083	−	1.67820i	−0.727221	−	0.686403i	$-0.759188\pi$
$367$	−16.3810	−	32.1496i	−0.855083	−	1.67820i	−0.127862	−	0.991792i	$-0.540812\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−11.8740	−	36.5445i	−0.616470	−	1.89730i
$372$	24.6821	+	12.5762i	1.27971	+	0.652044i
$373$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$373$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$374$		0			0
$375$	−17.1464	+	9.00000i	−0.885438	+	0.464758i
$376$		0			0
$377$		0			0
$378$	11.5332	−	22.6351i	0.593202	−	1.16422i
$379$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$379$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$380$		0			0
$381$	−12.0403	+	37.0564i	−0.616845	+	1.89846i
$382$		0			0
$383$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$383$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$384$	−11.5182	−	15.8534i	−0.587785	−	0.809017i
$385$	−10.6126	+	16.4875i	−0.540870	+	0.840281i
$386$	−31.5942	−	22.9545i	−1.60810	−	1.16836i
$387$		0			0
$388$	−21.0938	−	3.34093i	−1.07088	−	0.169610i
$389$	16.9384	−	23.3137i	0.858809	−	1.18205i	−0.123043	−	0.992401i	$-0.539265\pi$
$389$	16.9384	−	23.3137i	0.858809	−	1.18205i	0.981852	−	0.189648i	$-0.0607347\pi$
$390$		0			0
$391$		0			0
$392$	−6.35765	−	12.4776i	−0.321110	−	0.630214i
$393$	−22.5959	−	22.5959i	−1.13981	−	1.13981i
$394$	8.01175	+	2.60318i	0.403626	+	0.131146i
$395$	16.0130	−	36.3604i	0.805700	−	1.82949i
$396$	−4.70298	−	14.4743i	−0.236334	−	0.727360i
$397$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$397$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$398$	−0.679514	−	4.29028i	−0.0340609	−	0.215052i
$399$		0			0
$400$	−13.5023	−	14.7543i	−0.675114	−	0.737713i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$		0			0
$404$	36.1655	−	11.7509i	1.79930	−	0.584628i
$405$	10.1326	+	17.3876i	0.503495	+	0.863998i
$406$	8.08037	−	24.8688i	0.401022	−	1.23422i
$407$		0			0
$408$		0			0
$409$	22.0917	+	30.4067i	1.09237	+	1.50351i	0.845132	+	0.534557i	$0.179522\pi$
$409$	22.0917	+	30.4067i	1.09237	+	1.50351i	0.247234	+	0.968956i	$0.420478\pi$
$410$		0			0
$411$		0			0
$412$	−5.99030	+	37.8213i	−0.295121	+	1.86332i
$413$	−43.7058	−	6.92232i	−2.15062	−	0.340625i
$414$		0			0
$415$	10.3860	−	39.3971i	0.509827	−	1.93393i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−8.29083	−	2.69385i	−0.405034	−	0.131603i	0.0994131	−	0.995046i	$-0.468303\pi$
$419$	−8.29083	−	2.69385i	−0.405034	−	0.131603i	−0.504447	+	0.863443i	$0.668303\pi$
$420$	26.6425	+	2.69144i	1.30002	+	0.131329i
$421$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$421$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$422$		0			0
$423$		0			0
$424$			31.4381i			1.52677i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−17.5547	+	34.4529i	−0.848536	+	1.66535i
$429$		0			0
$430$		0			0
$431$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$431$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$432$	−14.6969	+	14.6969i	−0.707107	+	0.707107i
$433$	32.5389	−	16.5794i	1.56372	−	0.796754i	0.564137	−	0.825681i	$-0.309209\pi$
$433$	32.5389	−	16.5794i	1.56372	−	0.796754i	0.999582	+	0.0289266i	$0.00920891\pi$
$434$	−22.9799	−	31.6292i	−1.10307	−	1.51825i
$435$	13.1010	+	16.0454i	0.628146	+	0.769318i
$436$		0			0
$437$		0			0
$438$	−40.7118	−	6.44812i	−1.94528	−	0.308103i
$439$	7.70518	−	10.6053i	0.367748	−	0.506162i	−0.584539	−	0.811366i	$-0.698725\pi$
$439$	7.70518	−	10.6053i	0.367748	−	0.506162i	0.952287	+	0.305204i	$0.0987245\pi$
$440$	12.4264	−	10.1461i	0.592405	−	0.483696i
$441$	−12.0167	+	8.73062i	−0.572222	+	0.415744i
$442$		0			0
$443$	−12.2087	−	12.2087i	−0.580054	−	0.580054i	0.354864	−	0.934918i	$-0.384527\pi$
$443$	−12.2087	−	12.2087i	−0.580054	−	0.580054i	−0.934918	+	0.354864i	$0.884527\pi$
$444$		0			0
$445$		0			0
$446$	−8.12120	−	24.9945i	−0.384550	−	1.18352i
$447$	10.1654	+	5.17954i	0.480808	+	0.244984i
$448$	4.32640	+	27.3158i	0.204403	+	1.29055i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	−13.2162	+	16.5931i	−0.623019	+	0.782206i
$451$		0			0
$452$		0			0
$453$	−17.8325	+	34.9982i	−0.837844	+	1.64436i
$454$	−11.0525	+	3.59119i	−0.518722	+	0.168543i
$455$		0			0
$456$		0			0
$457$	−28.7069	+	28.7069i	−1.34285	+	1.34285i	−0.449641	+	0.893209i	$0.648448\pi$
$457$	−28.7069	+	28.7069i	−1.34285	+	1.34285i	−0.893209	+	0.449641i	$0.851552\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−34.7396	−	25.2398i	−1.61798	−	1.17553i	−0.813668	−	0.581330i	$-0.802533\pi$
$461$	−34.7396	−	25.2398i	−1.61798	−	1.17553i	−0.804315	−	0.594204i	$-0.797467\pi$
$462$	−3.36010	+	21.2148i	−0.156326	+	0.987003i
$463$	−5.79174	−	0.917322i	−0.269165	−	0.0426315i	0.0203929	−	0.999792i	$-0.493508\pi$
$463$	−5.79174	−	0.917322i	−0.269165	−	0.0426315i	−0.289558	+	0.957160i	$0.593508\pi$
$464$	−12.5750	+	17.3080i	−0.583780	+	0.803504i
$465$	30.9218	−	1.74586i	1.43397	−	0.0809625i
$466$		0			0
$467$	19.1657	+	37.6149i	0.886885	+	1.74061i	0.634393	+	0.773010i	$0.281250\pi$
$467$	19.1657	+	37.6149i	0.886885	+	1.74061i	0.252492	+	0.967599i	$0.418750\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	32.2582	+	16.4364i	1.48480	+	0.756546i
$473$		0			0
$474$		−	43.5224i		−	1.99905i
$475$		0			0
$476$		0			0
$477$	32.9346	−	5.21633i	1.50797	−	0.238840i
$478$		0			0
$479$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$479$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$480$	−20.0506	−	8.83021i	−0.915182	−	0.403042i
$481$		0			0
$482$	0.427358	−	0.427358i	0.0194656	−	0.0194656i
$483$		0			0
$484$	−5.36770	−	7.38800i	−0.243986	−	0.335818i
$485$	−22.2569	+	8.64696i	−1.01063	+	0.392638i
$486$	17.8351	+	12.9580i	0.809017	+	0.587785i
$487$	0.769962	−	4.86135i	0.0348903	−	0.220289i	−0.964082	−	0.265603i	$-0.914429\pi$
$487$	0.769962	−	4.86135i	0.0348903	−	0.220289i	0.998973	+	0.0453143i	$0.0144289\pi$
$488$		0			0
$489$		0			0
$490$	−13.1653	−	8.47421i	−0.594748	−	0.382826i
$491$	−2.31526	+	1.68213i	−0.104486	+	0.0759136i	−0.638801	−	0.769372i	$-0.720569\pi$
$491$	−2.31526	+	1.68213i	−0.104486	+	0.0759136i	0.534315	+	0.845285i	$0.320569\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−12.6909	−	11.3344i	−0.570414	−	0.509445i
$496$	9.88446	+	30.4212i	0.443825	+	1.36595i
$497$		0			0
$498$	−6.98195	−	44.0823i	−0.312869	−	1.97537i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	−21.3485	−	6.65153i	−0.954733	−	0.297465i
$501$		0			0
$502$	12.7301	−	2.01625i	0.568171	−	0.0899895i
$503$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$503$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$504$	27.8983	−	9.06470i	1.24269	−	0.403774i
$505$	28.3202	−	31.7096i	1.26023	−	1.41106i
$506$		0			0
$507$	15.9217	−	15.9217i	0.707107	−	0.707107i
$508$	−40.0873	+	20.4255i	−1.77859	+	0.906235i
$509$	25.8840	+	35.6262i	1.14729	+	1.57910i	0.750040	+	0.661392i	$0.230034\pi$
$509$	25.8840	+	35.6262i	1.14729	+	1.57910i	0.397246	+	0.917712i	$0.369966\pi$
$510$		0			0
$511$	47.0638	+	34.1939i	2.08198	+	1.51265i
$512$	3.53971	−	22.3488i	0.156434	−	0.987688i
$513$		0			0
$514$		0			0
$515$	15.5040	+	39.9067i	0.683189	+	1.75850i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−37.2137	−	12.0915i	−1.63350	−	0.530756i
$520$		0			0
$521$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$521$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$522$	20.2184	+	10.3018i	0.884935	+	0.450897i
$523$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$523$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$524$		−	36.8990i		−	1.61194i
$525$	27.2512	−	12.3979i	1.18934	−	0.541087i
$526$		0			0
$527$		0			0
$528$	7.97823	−	15.6582i	0.347208	−	0.681434i
$529$	−21.8743	+	7.10739i	−0.951057	+	0.309017i
$530$	17.6973	+	30.3686i	0.768722	+	1.31913i
$531$	11.8664	−	36.5209i	0.514957	−	1.58487i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	2.43699	+	43.1628i	0.105360	+	1.86609i
$536$		0			0
$537$	−5.71419	+	36.0780i	−0.246585	+	1.55688i
$538$	32.6635	+	5.17339i	1.40822	+	0.223041i
$539$	7.38181	−	10.1602i	0.317957	−	0.437630i
$540$	−5.92366	+	22.4702i	−0.254914	+	0.966964i
$541$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$541$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$542$	−10.5921	−	20.7883i	−0.454972	−	0.892932i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$547$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$548$		0			0
$549$		0			0
$550$	6.29214	−	16.7960i	0.268298	−	0.716186i
$551$		0			0
$552$		0			0
$553$	−27.8861	+	54.7296i	−1.18584	+	2.32734i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	19.3507	−	19.3507i	0.819916	−	0.819916i	−0.166180	−	0.986095i	$-0.553143\pi$
$557$	19.3507	−	19.3507i	0.819916	−	0.819916i	0.986095	+	0.166180i	$0.0531432\pi$
$558$	30.2293	−	15.4026i	1.27971	−	0.652044i
$559$		0			0
$560$	19.5560	+	23.9511i	0.826391	+	1.01212i
$561$		0			0
$562$		0			0
$563$	38.1989	+	6.05011i	1.60989	+	0.254982i	0.895598	−	0.444864i	$-0.146748\pi$
$563$	38.1989	+	6.05011i	1.60989	+	0.254982i	0.714294	+	0.699846i	$0.246748\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−14.1252	−	27.7222i	−0.593202	−	1.16422i
$568$		0			0
$569$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$569$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$570$		0			0
$571$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$571$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−24.0000			−1.00000
$577$	42.9069	−	6.79579i	1.78624	−	0.282912i	0.826322	−	0.563198i	$-0.190429\pi$
$577$	42.9069	−	6.79579i	1.78624	−	0.282912i	0.959917	+	0.280285i	$0.0904290\pi$
$578$	−10.9147	+	21.4212i	−0.453990	+	0.891007i
$579$	−45.4885	+	14.7801i	−1.89044	+	0.614241i
$580$	−2.40408	+	23.7980i	−0.0998241	+	0.988156i
$581$	−19.4650	+	59.9073i	−0.807546	+	2.48537i
$582$	−18.4955	+	18.4955i	−0.766663	+	0.766663i
$583$	−25.1207	+	12.7996i	−1.04039	+	0.530107i
$584$	−27.9762	−	38.5059i	−1.15766	−	1.59339i
$585$		0			0
$586$	−19.3472	−	14.0566i	−0.799227	−	0.580673i
$587$	−4.13475	+	26.1058i	−0.170659	+	1.07750i	0.742484	+	0.669863i	$0.233647\pi$
$587$	−4.13475	+	26.1058i	−0.170659	+	1.07750i	−0.913144	+	0.407638i	$0.866353\pi$
$588$	−16.9401	−	2.68305i	−0.698597	−	0.110647i
$589$		0			0
$590$	40.4132	−	2.28175i	1.66379	−	0.0939383i
$591$	8.34689	−	6.06437i	0.343345	−	0.249455i
$592$		0			0
$593$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$593$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$594$	−17.7273	−	5.75995i	−0.727360	−	0.236334i
$595$		0			0
$596$	4.07095	+	12.5291i	0.166753	+	0.513212i
$597$	−4.74015	−	2.41523i	−0.194001	−	0.0988487i
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	−24.3392	+	2.75720i	−0.993645	+	0.112562i
$601$	−30.4135			−1.24059			−0.620297	−	0.784367i	$-0.712988\pi$
$601$	−30.4135			−1.24059			−0.620297	+	0.784367i	$0.712988\pi$
$602$		0			0
$603$		0			0
$604$	−43.1361	+	14.0158i	−1.75518	+	0.570294i
$605$	−9.34397	−	4.11505i	−0.379887	−	0.167300i
$606$	14.3918	−	44.2935i	0.584628	−	1.79930i
$607$	−28.3595	+	28.3595i	−1.15108	+	1.15108i	−0.164741	+	0.986337i	$0.552679\pi$
$607$	−28.3595	+	28.3595i	−1.15108	+	1.15108i	−0.986337	+	0.164741i	$0.947321\pi$
$608$		0			0
$609$	−18.8241	−	25.9091i	−0.762790	−	1.04989i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$613$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$614$		0			0
$615$		0			0
$616$	−20.0653	+	14.5783i	−0.808456	+	0.587377i
$617$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$617$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$618$	33.1625	+	33.1625i	1.33399	+	1.33399i
$619$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$619$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$620$	26.6731	+	23.8221i	1.07122	+	0.956718i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−24.3665	+	5.59235i	−0.974659	+	0.223694i
$626$	21.2077			0.847630
$627$		0			0
$628$		0			0
$629$		0			0
$630$	21.8464	−	24.4609i	0.870381	−	0.974547i
$631$	1.51387	−	4.65921i	0.0602661	−	0.185480i	−0.916391	−	0.400284i	$-0.868911\pi$
$631$	1.51387	−	4.65921i	0.0602661	−	0.185480i	0.976657	+	0.214804i	$0.0689114\pi$
$632$	35.5359	−	35.5359i	1.41354	−	1.41354i
$633$		0			0
$634$	−12.4605	−	17.1504i	−0.494868	−	0.681128i
$635$	−27.2255	+	42.2967i	−1.08041	+	1.67849i
$636$	31.1501	+	22.6319i	1.23518	+	0.897413i
$637$		0			0
$638$	−18.9498	−	3.00135i	−0.750228	−	0.118824i
$639$		0			0
$640$	−9.16143	−	23.5811i	−0.362137	−	0.932125i
$641$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$641$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$642$	21.5000	+	42.1961i	0.848536	+	1.66535i
$643$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$643$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$647$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$648$	3.98217	+	25.1424i	0.156434	+	0.987688i
$649$			32.4679i			1.27448i
$650$		0			0
$651$	−47.8824			−1.87666
$652$		0			0
$653$	−14.2241	+	27.9164i	−0.556633	+	1.09245i	0.425622	+	0.904901i	$0.360055\pi$
$653$	−14.2241	+	27.9164i	−0.556633	+	1.09245i	−0.982255	+	0.187553i	$0.939945\pi$
$654$		0			0
$655$	−20.7714	−	35.6436i	−0.811604	−	1.39271i
$656$		0			0
$657$	−35.6969	+	35.6969i	−1.39267	+	1.39267i
$658$		0			0
$659$	0.623343	+	0.857959i	0.0242820	+	0.0334213i	0.820985	−	0.570949i	$-0.193425\pi$
$659$	0.623343	+	0.857959i	0.0242820	+	0.0334213i	−0.796703	+	0.604371i	$0.793425\pi$
$660$	−1.10756	−	19.6166i	−0.0431119	−	0.763575i
$661$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$661$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$662$		0			0
$663$		0			0
$664$	30.2923	−	41.6938i	1.17557	−	1.61803i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−30.6119	−	9.94639i	−1.18352	−	0.384550i
$670$		0			0
$671$		0			0
$672$	30.1801	+	15.3775i	1.16422	+	0.593202i
$673$	7.87739	+	49.7359i	0.303651	+	1.91718i	0.389808	+	0.920896i	$0.372541\pi$
$673$	7.87739	+	49.7359i	0.303651	+	1.91718i	−0.0861567	+	0.996282i	$0.527459\pi$
$674$		−	8.84959i		−	0.340873i
$675$	6.92691	+	25.0403i	0.266617	+	0.963803i
$676$	26.0000			1.00000
$677$	49.6732	−	7.86746i	1.90910	−	0.302371i	0.914365	−	0.404891i	$-0.132690\pi$
$677$	49.6732	−	7.86746i	1.90910	−	0.302371i	0.994731	+	0.102520i	$0.0326905\pi$
$678$		0			0
$679$	35.1088	−	11.4075i	1.34735	−	0.437781i
$680$		0			0
$681$	−4.39829	+	13.5366i	−0.168543	+	0.518722i
$682$	−20.2838	+	20.2838i	−0.776708	+	0.776708i
$683$	−31.2910	+	15.9436i	−1.19732	+	0.610063i	−0.934907	−	0.354893i	$-0.884517\pi$
$683$	−31.2910	+	15.9436i	−1.19732	+	0.610063i	−0.262410	+	0.964956i	$0.584517\pi$
$684$		0			0
$685$		0			0
$686$	−8.10383	−	5.88777i	−0.309406	−	0.224796i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$691$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$692$	−20.5122	−	40.2575i	−0.779757	−	1.53036i
$693$	18.6016	+	18.6016i	0.706616	+	0.706616i
$694$	48.7463	+	15.8386i	1.85038	+	0.601227i
$695$		0			0
$696$	8.09688	+	24.9196i	0.306911	+	0.944576i
$697$		0			0
$698$		0			0
$699$		0			0
$700$	32.3733	+	12.1277i	1.22360	+	0.458384i
$701$	52.9444			1.99968			0.999841	−	0.0178345i	$-0.00567720\pi$
$701$	52.9444			1.99968			0.999841	+	0.0178345i	$0.00567720\pi$
$702$		0			0
$703$		0			0
$704$	19.2990	−	6.27064i	0.727360	−	0.236334i
$705$		0			0
$706$		0			0
$707$	−46.4780	+	46.4780i	−1.74799	+	1.74799i
$708$	39.5081	−	20.1304i	1.48480	−	0.756546i
$709$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$709$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$710$		0			0
$711$	−43.1237	−	31.3312i	−1.61726	−	1.17501i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−34.1232	+	24.7919i	−1.27524	+	0.926518i
$717$		0			0
$718$		0			0
$719$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$719$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$720$	−23.1835	+	13.5102i	−0.863998	+	0.503495i
$721$	−20.4538	−	62.9502i	−0.761738	−	2.34439i
$722$	23.9414	+	12.1988i	0.891007	+	0.453990i
$723$	−0.115794	−	0.731092i	−0.00430641	−	0.0271896i
$724$		0			0
$725$	11.0742	+	24.3416i	0.411284	+	0.904026i
$726$	−11.1845			−0.415094
$727$	39.0328	−	6.18219i	1.44765	−	0.229285i	0.617386	−	0.786661i	$-0.288192\pi$
$727$	39.0328	−	6.18219i	1.44765	−	0.229285i	0.830260	+	0.557376i	$0.188192\pi$
$728$		0			0
$729$	25.6785	−	8.34346i	0.951057	−	0.309017i
$730$	−48.7003	−	21.4474i	−1.80248	−	0.793804i
$731$		0			0
$732$		0			0
$733$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$733$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$734$	−29.9936	−	41.2826i	−1.10708	−	1.52377i
$735$	−17.8741	+	6.94423i	−0.659297	+	0.256142i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$739$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$740$		0			0
$741$		0			0
$742$	−24.6705	−	48.4186i	−0.905683	−	1.77750i
$743$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$743$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$744$	37.2583	+	12.1059i	1.36595	+	0.443825i
$745$	10.9854	+	9.81121i	0.402474	+	0.359455i
$746$		0			0
$747$	−48.7047	−	24.8163i	−1.78201	−	0.907980i
$748$		0			0
$749$		−	66.8375i		−	2.44219i
$750$	−21.9591	+	16.3646i	−0.801832	+	0.597549i
$751$	7.14198			0.260615			0.130307	−	0.991474i	$-0.458404\pi$
$751$	7.14198			0.260615			0.130307	+	0.991474i	$0.458404\pi$
$752$		0			0
$753$	7.16644	−	14.0649i	0.261160	−	0.512555i
$754$		0			0
$755$	−33.7788	+	37.8213i	−1.22933	+	1.37646i
$756$	11.1019	−	34.1683i	0.403774	−	1.24269i
$757$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$757$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$761$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$762$	−8.61993	+	54.4241i	−0.312267	+	1.97158i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−19.5959	−	19.5959i	−0.707107	−	0.707107i
$769$	51.9529	+	16.8805i	1.87347	+	0.608727i	0.990161	+	0.139935i	$0.0446894\pi$
$769$	51.9529	+	16.8805i	1.87347	+	0.608727i	0.883309	+	0.468792i	$0.155311\pi$
$770$	−11.1762	+	25.3776i	−0.402762	+	0.914546i
$771$		0			0
$772$	−49.2091	−	25.0733i	−1.77108	−	0.902408i
$773$	7.28358	+	45.9867i	0.261972	+	1.65403i	0.670965	+	0.741489i	$0.265880\pi$
$773$	7.28358	+	45.9867i	0.261972	+	1.65403i	−0.408993	+	0.912538i	$0.634120\pi$
$774$		0			0
$775$	39.1757	+	7.99670i	1.40723	+	0.287250i
$776$	−30.2030			−1.08422
$777$		0			0
$778$	18.5018	−	36.3119i	0.663323	−	1.30184i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	24.7624	−	12.6171i	0.884935	−	0.450897i
$784$	−11.6408	−	16.0222i	−0.415744	−	0.572222i
$785$		0			0
$786$	−36.5610	−	26.5631i	−1.30409	−	0.947474i
$787$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$787$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$788$	11.7667	+	1.86367i	0.419173	+	0.0663904i
$789$		0			0
$790$	14.3229	−	54.3309i	0.509585	−	1.93301i
$791$		0			0
$792$	−9.77130	−	19.1773i	−0.347208	−	0.681434i
$793$		0			0
$794$		0			0
$795$	42.8304	+	4.32675i	1.51904	+	0.153454i
$796$	−1.89829	−	5.84234i	−0.0672832	−	0.207076i
$797$	−47.8091	−	24.3600i	−1.69349	−	0.862874i	−0.988056	−	0.154093i	$-0.950754\pi$
$797$	−47.8091	−	24.3600i	−1.69349	−	0.862874i	−0.705429	−	0.708781i	$-0.749246\pi$
$798$		0			0
$799$		0			0
$800$	−22.1241	−	17.6216i	−0.782206	−	0.623019i
$801$		0			0
$802$		0			0
$803$	19.3781	−	38.0316i	0.683838	−	1.34211i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	28.6400	−	28.6400i	1.00818	−	1.00818i
$808$	47.9164	−	24.4146i	1.68569	−	0.858903i
$809$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$809$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$810$	18.0000	+	22.0454i	0.632456	+	0.774597i
$811$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$811$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$812$	5.78491	−	36.5245i	0.203011	−	1.28176i
$813$	−28.2230	−	4.47008i	−0.989823	−	0.156773i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	37.5847	+	37.5847i	1.31412	+	1.31412i
$819$		0			0
$820$		0			0
$821$	−1.83849	−	5.65830i	−0.0641639	−	0.197476i	0.913835	−	0.406085i	$-0.133106\pi$
$821$	−1.83849	−	5.65830i	−0.0641639	−	0.197476i	−0.977999	+	0.208609i	$0.933106\pi$
$822$		0			0
$823$	−6.26818	−	39.5758i	−0.218495	−	1.37952i	−0.816182	−	0.577795i	$-0.803913\pi$
$823$	−6.26818	−	39.5758i	−0.218495	−	1.37952i	0.597687	−	0.801730i	$-0.296087\pi$
$824$			54.1541i			1.88655i
$825$	−12.1126	−	18.3258i	−0.421705	−	0.638021i
$826$	−62.5798			−2.17743
$827$	49.9657	−	7.91378i	1.73748	−	0.275189i	0.794310	−	0.607512i	$-0.207832\pi$
$827$	49.9657	−	7.91378i	1.73748	−	0.275189i	0.943166	+	0.332323i	$0.107832\pi$
$828$		0			0
$829$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$829$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$830$	5.79126	−	57.3276i	0.201018	−	1.98987i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	6.50017	−	41.0405i	0.224679	−	1.41857i
$838$	−12.1766	−	1.92859i	−0.420634	−	0.0666219i
$839$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$839$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$840$	37.8098	−	2.13476i	1.30456	−	0.0736562i
$841$	−0.318653	+	0.231515i	−0.0109880	+	0.00798328i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	25.1155	−	14.6360i	0.863998	−	0.503495i
$846$		0			0
$847$	14.0645	+	7.16623i	0.483263	+	0.246235i
$848$	6.95511	+	43.9128i	0.238840	+	1.50797i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$853$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$854$		0			0
$855$		0			0
$856$	−16.8983	+	52.0076i	−0.577572	+	1.77758i
$857$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$857$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$858$		0			0
$859$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$859$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$863$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$864$	−17.2773	+	23.7801i	−0.587785	+	0.809017i
$865$	−42.4763	−	27.3410i	−1.44424	−	0.929623i
$866$	41.7825	−	30.3568i	1.41983	−	1.03156i
$867$	13.3677	+	26.2356i	0.453990	+	0.891007i
$868$	−39.0958	−	39.0958i	−1.32700	−	1.32700i
$869$	42.8630	+	13.9270i	1.45403	+	0.472442i
$870$	21.8493	+	19.5139i	0.740760	+	0.661583i
$871$		0			0
$872$		0			0
$873$	5.01140	+	31.6407i	0.169610	+	1.07088i
$874$		0			0
$875$	38.0989	−	6.50865i	1.28798	−	0.220033i
$876$	−58.2929			−1.96953
$877$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$877$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$878$	8.41639	−	16.5181i	0.284039	−	0.557459i
$879$	−27.8557	+	9.05085i	−0.939548	+	0.305278i
$880$	15.1126	−	16.9212i	0.509445	−	0.570414i
$881$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$881$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$882$	−14.8534	+	14.8534i	−0.500140	+	0.500140i
$883$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$883$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$884$		0			0
$885$	26.8321	−	41.6856i	0.901951	−	1.40125i
$886$	−19.7541	−	14.3522i	−0.663653	−	0.482172i
$887$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$887$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$888$		0			0
$889$	45.7108	−	62.9156i	1.53309	−	2.11012i
$890$		0			0
$891$	−18.4688	+	13.4184i	−0.618729	+	0.449533i
$892$	−16.8733	−	33.1157i	−0.564959	−	1.10879i
$893$		0			0
$894$	15.3450	+	4.98588i	0.513212	+	0.166753i
$895$	−19.0063	+	43.1573i	−0.635309	+	1.44259i
$896$	12.0863	+	37.1977i	0.403774	+	1.24269i
$897$		0			0
$898$		0			0
$899$		−	42.7701i		−	1.42646i
$900$	−14.7895	+	26.1011i	−0.492985	+	0.870038i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−17.1657	+	52.8307i	−0.570294	+	1.75518i
$907$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$907$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$908$	−14.6437	+	7.46136i	−0.485970	+	0.247614i
$909$	−33.5273	−	46.1463i	−1.11203	−	1.53058i
$910$		0			0
$911$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$911$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$912$		0			0
$913$	45.6486	+	7.23003i	1.51075	+	0.239279i
$914$	−33.7469	+	46.4487i	−1.11625	+	1.53639i
$915$		0			0
$916$		0			0
$917$	28.9558	+	56.8290i	0.956205	+	1.87666i
$918$		0			0
$919$	−32.6144	−	10.5971i	−1.07585	−	0.349565i	−0.283087	−	0.959094i	$-0.591359\pi$
$919$	−32.6144	−	10.5971i	−1.07585	−	0.349565i	−0.792764	+	0.609529i	$0.791359\pi$
$920$		0			0
$921$		0			0
$922$	−54.1081	−	27.5695i	−1.78196	−	0.907952i
$923$		0			0
$924$			30.3763i			0.999306i
$925$		0			0
$926$	−8.29286			−0.272520
$927$	56.7319	−	8.98545i	1.86332	−	0.295121i
$928$	−13.7357	+	26.9579i	−0.450897	+	0.884935i
$929$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$929$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$930$	42.8054	−	9.27952i	1.40365	−	0.304287i
$931$		0			0
$932$		0			0
$933$		0			0
$934$	35.0924	+	48.3005i	1.14826	+	1.58044i
$935$		0			0
$936$		0			0
$937$	1.38779	−	8.76214i	0.0453370	−	0.286247i	−0.954595	−	0.297907i	$-0.903712\pi$
$937$	1.38779	−	8.76214i	0.0453370	−	0.286247i	0.999932	+	0.0116601i	$0.00371160\pi$
$938$		0			0
$939$	15.2671	−	21.0134i	0.498224	−	0.685747i
$940$		0			0
$941$	48.6558	−	35.3505i	1.58613	−	1.15239i	0.676925	−	0.736052i	$-0.263312\pi$
$941$	48.6558	−	35.3505i	1.58613	−	1.15239i	0.909208	−	0.416341i	$-0.136688\pi$
$942$		0			0
$943$		0			0
$944$	48.6946	+	15.8218i	1.58487	+	0.514957i
$945$	−8.50992	−	39.2554i	−0.276828	−	1.27698i
$946$		0			0
$947$	−54.6126	−	27.8265i	−1.77467	−	0.904240i	−0.928505	−	0.371321i	$-0.878905\pi$
$947$	−54.6126	−	27.8265i	−1.77467	−	0.904240i	−0.846166	−	0.532919i	$-0.821095\pi$
$948$	−9.62853	−	60.7921i	−0.312720	−	1.97444i
$949$		0			0
$950$		0			0
$951$	−25.9634			−0.841920
$952$		0			0
$953$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$953$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$954$	44.8492	−	14.5724i	1.45204	−	0.471798i
$955$		0			0
$956$		0			0
$957$	−16.6155	+	16.6155i	−0.537104	+	0.537104i
$958$		0			0
$959$		0			0
$960$	−29.9603	−	7.89822i	−0.966964	−	0.254914i
$961$	−26.6548	−	19.3659i	−0.859833	−	0.624705i
$962$		0			0
$963$	57.2871	+	9.07338i	1.84605	+	0.292386i
$964$	0.502389	−	0.691479i	0.0161809	−	0.0222710i
$965$	−61.6494	+	3.48076i	−1.98456	+	0.112050i
$966$		0			0
$967$	24.0698	+	47.2397i	0.774033	+	1.51913i	0.852803	+	0.522232i	$0.174901\pi$
$967$	24.0698	+	47.2397i	0.774033	+	1.51913i	−0.0787703	+	0.996893i	$0.525099\pi$
$968$	−9.13207	−	9.13207i	−0.293516	−	0.293516i
$969$		0			0
$970$	−29.1755	+	17.0020i	−0.936768	+	0.545902i
$971$	−17.6189	−	54.2253i	−0.565417	−	1.74017i	−0.666710	−	0.745318i	$-0.732298\pi$
$971$	−17.6189	−	54.2253i	−0.565417	−	1.74017i	0.101293	−	0.994857i	$-0.467702\pi$
$972$	27.7788	+	14.1540i	0.891007	+	0.453990i
$973$		0			0
$974$		−	6.96068i		−	0.223035i
$975$		0			0
$976$		0			0
$977$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$977$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$978$		0			0
$979$		0			0
$980$	−20.2641	−	8.92422i	−0.647313	−	0.285074i
$981$		0			0
$982$	−2.86181	+	2.86181i	−0.0913242	+	0.0913242i
$983$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$983$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$984$		0			0
$985$	12.4155	−	4.82353i	0.395592	−	0.153690i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−20.2342	−	13.0243i	−0.643086	−	0.413940i
$991$	33.3469	−	24.2279i	1.05930	−	0.769626i	0.0853402	−	0.996352i	$-0.472802\pi$
$991$	33.3469	−	24.2279i	1.05930	−	0.769626i	0.973959	+	0.226726i	$0.0728023\pi$
$992$	20.5368	+	40.3057i	0.652044	+	1.27971i
$993$		0			0
$994$		0			0
$995$	−5.12251	−	4.57499i	−0.162395	−	0.145037i
$996$	−19.5048	−	60.0296i	−0.618033	−	1.90211i
$997$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$997$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.bp.b.413.2	yes	16
3.2	odd	2		600.2.bp.a.413.1	yes	16
8.5	even	2		600.2.bp.a.413.1	yes	16
24.5	odd	2	CM	600.2.bp.b.413.2	yes	16
25.2	odd	20	inner	600.2.bp.b.77.2	yes	16
75.2	even	20		600.2.bp.a.77.1	✓	16
200.77	odd	20		600.2.bp.a.77.1	✓	16
600.77	even	20	inner	600.2.bp.b.77.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.bp.a.77.1	✓	16	75.2	even	20
600.2.bp.a.77.1	✓	16	200.77	odd	20
600.2.bp.a.413.1	yes	16	3.2	odd	2
600.2.bp.a.413.1	yes	16	8.5	even	2
600.2.bp.b.77.2	yes	16	25.2	odd	20	inner
600.2.bp.b.77.2	yes	16	600.77	even	20	inner
600.2.bp.b.413.2	yes	16	1.1	even	1	trivial
600.2.bp.b.413.2	yes	16	24.5	odd	2	CM

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bp (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39680 - 0.221232i) q^{2} +(0.786335 - 1.54327i) q^{3} +(1.90211 - 0.618034i) q^{4} +(1.48949 - 1.66775i) q^{5} +(0.756934 - 2.32960i) q^{6} +(-2.44450 + 2.44450i) q^{7} +(2.52015 - 1.28408i) q^{8} +(-1.76336 - 2.42705i) q^{9} +O(q^{10})\)	\(q+(1.39680 - 0.221232i) q^{2} +(0.786335 - 1.54327i) q^{3} +(1.90211 - 0.618034i) q^{4} +(1.48949 - 1.66775i) q^{5} +(0.756934 - 2.32960i) q^{6} +(-2.44450 + 2.44450i) q^{7} +(2.52015 - 1.28408i) q^{8} +(-1.76336 - 2.42705i) q^{9} +(1.71157 - 2.65905i) q^{10} +(2.05209 + 1.49093i) q^{11} +(0.541905 - 3.42145i) q^{12} +(-2.87368 + 3.95528i) q^{14} +(-1.40255 - 3.61010i) q^{15} +(3.23607 - 2.35114i) q^{16} +(-3.00000 - 3.00000i) q^{18} +(1.80246 - 4.09282i) q^{20} +(1.85032 + 5.69471i) q^{21} +(3.19621 + 1.62855i) q^{22} -4.89898i q^{24} +(-0.562811 - 4.96822i) q^{25} +(-5.13218 + 0.812857i) q^{27} +(-3.13893 + 6.16049i) q^{28} +(-5.08670 + 1.65277i) q^{29} +(-2.75776 - 4.73231i) q^{30} +(-2.47112 + 7.60531i) q^{31} +(4.00000 - 4.00000i) q^{32} +(3.91454 - 1.99456i) q^{33} +(0.435756 + 7.71789i) q^{35} +(-4.85410 - 3.52671i) q^{36} +(1.61222 - 6.11562i) q^{40} +(3.84439 + 7.54503i) q^{42} +(4.82476 + 1.56766i) q^{44} +(-6.67423 - 0.674235i) q^{45} +(-1.08381 - 6.84291i) q^{48} -4.95114i q^{49} +(-1.88526 - 6.81511i) q^{50} +(-5.04613 + 9.90359i) q^{53} +(-6.98881 + 2.27080i) q^{54} +(5.54309 - 1.20165i) q^{55} +(-3.02157 + 9.29942i) q^{56} +(-6.73946 + 3.43393i) q^{58} +(7.52373 + 10.3555i) q^{59} +(-4.89898 - 6.00000i) q^{60} +(-1.76912 + 11.1698i) q^{62} +(10.2434 + 1.62240i) q^{63} +(4.70228 - 6.47214i) q^{64} +(5.02658 - 3.65202i) q^{66} +(2.31611 + 10.6840i) q^{70} +(-7.56044 - 3.85224i) q^{72} +(-2.63243 - 16.6205i) q^{73} +(-8.10986 - 3.03812i) q^{75} +(-8.66092 + 1.37175i) q^{77} +(16.8983 - 5.49059i) q^{79} +(0.898979 - 8.89898i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(16.2349 - 8.27209i) q^{83} +(7.03905 + 9.68842i) q^{84} +(-1.44918 + 9.14977i) q^{87} +(7.08605 + 1.12232i) q^{88} +(-9.47175 + 0.534780i) q^{90} +(9.79391 + 9.79391i) q^{93} +(-3.02774 - 9.31841i) q^{96} +(-9.51450 - 4.84788i) q^{97} +(-1.09535 - 6.91576i) q^{98} -7.60958i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 4 q^{5} + 4 q^{7} - 8 q^{8}+O(q^{10}) \) 16 * q + 4 * q^2 - 4 * q^5 + 4 * q^7 - 8 * q^8	\( 16 q + 4 q^{2} - 4 q^{5} + 4 q^{7} - 8 q^{8} + 8 q^{10} - 24 q^{11} - 12 q^{15} + 16 q^{16} - 48 q^{18} - 8 q^{20} + 36 q^{21} - 16 q^{22} + 32 q^{28} + 12 q^{30} + 64 q^{32} + 12 q^{33} + 8 q^{35} - 24 q^{36} + 24 q^{42} - 48 q^{45} - 4 q^{50} + 28 q^{55} - 24 q^{56} - 8 q^{58} + 80 q^{59} + 12 q^{63} + 36 q^{66} - 32 q^{70} + 24 q^{72} - 28 q^{73} - 24 q^{75} - 12 q^{77} - 64 q^{80} + 36 q^{81} + 24 q^{83} - 36 q^{87} + 32 q^{88} + 24 q^{93} - 16 q^{97} + 72 q^{98}+O(q^{100}) \) 16 * q + 4 * q^2 - 4 * q^5 + 4 * q^7 - 8 * q^8 + 8 * q^10 - 24 * q^11 - 12 * q^15 + 16 * q^16 - 48 * q^18 - 8 * q^20 + 36 * q^21 - 16 * q^22 + 32 * q^28 + 12 * q^30 + 64 * q^32 + 12 * q^33 + 8 * q^35 - 24 * q^36 + 24 * q^42 - 48 * q^45 - 4 * q^50 + 28 * q^55 - 24 * q^56 - 8 * q^58 + 80 * q^59 + 12 * q^63 + 36 * q^66 - 32 * q^70 + 24 * q^72 - 28 * q^73 - 24 * q^75 - 12 * q^77 - 64 * q^80 + 36 * q^81 + 24 * q^83 - 36 * q^87 + 32 * q^88 + 24 * q^93 - 16 * q^97 + 72 * q^98

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