LMFDB - Embedded newform 600.2.bp.b.173.2

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			173.2
Root			$-1.71073 - 0.270952i$ of defining polynomial
Character	$\chi$	$=$	600.173
Dual form			600.2.bp.b.437.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.221232 - 1.39680i) q^{2} +(1.54327 - 0.786335i) q^{3} +(-1.90211 - 0.618034i) q^{4} +(-1.66775 + 1.48949i) q^{5} +(-0.756934 - 2.32960i) q^{6} +(-2.83274 + 2.83274i) q^{7} +(-1.28408 + 2.52015i) q^{8} +(1.76336 - 2.42705i) q^{9} +(1.71157 + 2.65905i) q^{10} +(-4.95856 + 3.60260i) q^{11} +(-3.42145 + 0.541905i) q^{12} +(3.33009 + 4.58347i) q^{14} +(-1.40255 + 3.61010i) q^{15} +(3.23607 + 2.35114i) q^{16} +(-3.00000 - 3.00000i) q^{18} +(4.09282 - 1.80246i) q^{20} +(-2.14420 + 6.59917i) q^{21} +(3.93513 + 7.72313i) q^{22} +4.89898i q^{24} +(0.562811 - 4.96822i) q^{25} +(0.812857 - 5.13218i) q^{27} +(7.13893 - 3.63747i) q^{28} +(-8.89092 - 2.88884i) q^{29} +(4.73231 + 2.75776i) q^{30} +(2.47112 + 7.60531i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-4.81953 + 9.45887i) q^{33} +(0.504965 - 8.94368i) q^{35} +(-4.85410 + 3.52671i) q^{36} +(-1.61222 - 6.11562i) q^{40} +(8.74337 + 4.45497i) q^{42} +(11.6583 - 3.78800i) q^{44} +(0.674235 + 6.67423i) q^{45} +(6.84291 + 1.08381i) q^{48} -9.04886i q^{49} +(-6.81511 - 1.88526i) q^{50} +(-9.90359 + 5.04613i) q^{53} +(-6.98881 - 2.27080i) q^{54} +(2.90360 - 13.3940i) q^{55} +(-3.50146 - 10.7764i) q^{56} +(-6.00209 + 11.7798i) q^{58} +(4.99294 - 6.87220i) q^{59} +(4.89898 - 6.00000i) q^{60} +(11.1698 - 1.76912i) q^{62} +(1.88008 + 11.8703i) q^{63} +(-4.70228 - 6.47214i) q^{64} +(12.1459 + 8.82454i) q^{66} +(-12.3808 - 2.68396i) q^{70} +(3.85224 + 7.56044i) q^{72} +(-2.93471 - 0.464812i) q^{73} +(-3.03812 - 8.10986i) q^{75} +(3.84107 - 24.2516i) q^{77} +(16.8983 + 5.49059i) q^{79} +(-8.89898 + 0.898979i) q^{80} +(-2.78115 - 8.55951i) q^{81} +(-8.27209 + 16.2349i) q^{83} +(8.15702 - 11.2272i) q^{84} +(-15.9927 + 2.53299i) q^{87} +(-2.71191 - 17.1223i) q^{88} +(9.47175 + 0.534780i) q^{90} +(9.79391 + 9.79391i) q^{93} +(3.02774 - 9.31841i) q^{96} +(7.51450 + 14.7480i) q^{97} +(-12.6395 - 2.00190i) q^{98} +18.3873i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

Character values

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

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	0.221232	−	1.39680i	0.156434	−	0.987688i
$2$	0.221232	−	1.39680i	0.156434	−	0.987688i
$3$	1.54327	−	0.786335i	0.891007	−	0.453990i
$3$	1.54327	−	0.786335i	0.891007	−	0.453990i
$4$	−1.90211	−	0.618034i	−0.951057	−	0.309017i
$5$	−1.66775	+	1.48949i	−0.745843	+	0.666122i
$5$	−1.66775	+	1.48949i	−0.745843	+	0.666122i
$6$	−0.756934	−	2.32960i	−0.309017	−	0.951057i
$7$	−2.83274	+	2.83274i	−1.07068	+	1.07068i	−0.0733714	+	0.997305i	$0.523376\pi$
$7$	−2.83274	+	2.83274i	−1.07068	+	1.07068i	−0.997305	+	0.0733714i	$0.976624\pi$
$8$	−1.28408	+	2.52015i	−0.453990	+	0.891007i
$9$	1.76336	−	2.42705i	0.587785	−	0.809017i
$10$	1.71157	+	2.65905i	0.541246	+	0.840864i
$11$	−4.95856	+	3.60260i	−1.49506	+	1.08623i	−0.522764	+	0.852477i	$0.675099\pi$
$11$	−4.95856	+	3.60260i	−1.49506	+	1.08623i	−0.972297	+	0.233748i	$0.924901\pi$
$12$	−3.42145	+	0.541905i	−0.987688	+	0.156434i
$13$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$13$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$14$	3.33009	+	4.58347i	0.890004	+	1.22498i
$15$	−1.40255	+	3.61010i	−0.362137	+	0.932125i
$16$	3.23607	+	2.35114i	0.809017	+	0.587785i
$17$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$17$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$18$	−3.00000	−	3.00000i	−0.707107	−	0.707107i
$19$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$19$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$20$	4.09282	−	1.80246i	0.915182	−	0.403042i
$21$	−2.14420	+	6.59917i	−0.467903	+	1.44006i
$22$	3.93513	+	7.72313i	0.838973	+	1.64658i
$23$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$23$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$24$			4.89898i			1.00000i
$25$	0.562811	−	4.96822i	0.112562	−	0.993645i
$26$		0			0
$27$	0.812857	−	5.13218i	0.156434	−	0.987688i
$28$	7.13893	−	3.63747i	1.34913	−	0.687416i
$29$	−8.89092	−	2.88884i	−1.65100	−	0.536443i	−0.672046	−	0.740510i	$-0.734584\pi$
$29$	−8.89092	−	2.88884i	−1.65100	−	0.536443i	−0.978957	+	0.204066i	$0.934584\pi$
$30$	4.73231	+	2.75776i	0.863998	+	0.503495i
$31$	2.47112	+	7.60531i	0.443825	+	1.36595i	0.883767	+	0.467928i	$0.154999\pi$
$31$	2.47112	+	7.60531i	0.443825	+	1.36595i	−0.439941	+	0.898027i	$0.645001\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$	−4.81953	+	9.45887i	−0.838973	+	1.64658i
$34$		0			0
$35$	0.504965	−	8.94368i	0.0853546	−	1.51176i
$36$	−4.85410	+	3.52671i	−0.809017	+	0.587785i
$37$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$37$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$38$		0			0
$39$		0			0
$40$	−1.61222	−	6.11562i	−0.254914	−	0.966964i
$41$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$41$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$42$	8.74337	+	4.45497i	1.34913	+	0.687416i
$43$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$43$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$44$	11.6583	−	3.78800i	1.75755	−	0.571063i
$45$	0.674235	+	6.67423i	0.100509	+	0.994936i
$46$		0			0
$47$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$47$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$48$	6.84291	+	1.08381i	0.987688	+	0.156434i
$49$		−	9.04886i		−	1.29269i
$50$	−6.81511	−	1.88526i	−0.963803	−	0.266617i
$51$		0			0
$52$		0			0
$53$	−9.90359	+	5.04613i	−1.36036	+	0.693139i	−0.973433	−	0.228970i	$-0.926464\pi$
$53$	−9.90359	+	5.04613i	−1.36036	+	0.693139i	−0.386929	+	0.922110i	$0.626464\pi$
$54$	−6.98881	−	2.27080i	−0.951057	−	0.309017i
$55$	2.90360	−	13.3940i	0.391521	−	1.80605i
$56$	−3.50146	−	10.7764i	−0.467903	−	1.44006i
$57$		0			0
$58$	−6.00209	+	11.7798i	−0.788113	+	1.54676i
$59$	4.99294	−	6.87220i	0.650026	−	0.894684i	−0.349074	−	0.937095i	$-0.613504\pi$
$59$	4.99294	−	6.87220i	0.650026	−	0.894684i	0.999100	+	0.0424110i	$0.0135039\pi$
$60$	4.89898	−	6.00000i	0.632456	−	0.774597i
$61$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$61$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$62$	11.1698	−	1.76912i	1.41857	−	0.224679i
$63$	1.88008	+	11.8703i	0.236868	+	1.49552i
$64$	−4.70228	−	6.47214i	−0.587785	−	0.809017i
$65$		0			0
$66$	12.1459	+	8.82454i	1.49506	+	1.08623i
$67$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$67$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$68$		0			0
$69$		0			0
$70$	−12.3808	−	2.68396i	−1.47979	−	0.320795i
$71$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$71$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$72$	3.85224	+	7.56044i	0.453990	+	0.891007i
$73$	−2.93471	−	0.464812i	−0.343482	−	0.0544022i	−0.0176895	−	0.999844i	$-0.505631\pi$
$73$	−2.93471	−	0.464812i	−0.343482	−	0.0544022i	−0.325792	+	0.945441i	$0.605631\pi$
$74$		0			0
$75$	−3.03812	−	8.10986i	−0.350812	−	0.936446i
$76$		0			0
$77$	3.84107	−	24.2516i	0.437731	−	2.76372i
$78$		0			0
$79$	16.8983	+	5.49059i	1.90121	+	0.617740i	0.960138	+	0.279526i	$0.0901773\pi$
$79$	16.8983	+	5.49059i	1.90121	+	0.617740i	0.941069	+	0.338214i	$0.109823\pi$
$80$	−8.89898	+	0.898979i	−0.994936	+	0.100509i
$81$	−2.78115	−	8.55951i	−0.309017	−	0.951057i
$82$		0			0
$83$	−8.27209	+	16.2349i	−0.907980	+	1.78201i	−0.452638	+	0.891695i	$0.649517\pi$
$83$	−8.27209	+	16.2349i	−0.907980	+	1.78201i	−0.455342	+	0.890316i	$0.650483\pi$
$84$	8.15702	−	11.2272i	0.890004	−	1.22498i
$85$		0			0
$86$		0			0
$87$	−15.9927	+	2.53299i	−1.71459	+	0.271565i
$88$	−2.71191	−	17.1223i	−0.289090	−	1.82525i
$89$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$89$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$90$	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
$97$	7.51450	+	14.7480i	0.762982	+	1.49744i	0.864517	+	0.502604i	$0.167625\pi$
$97$	7.51450	+	14.7480i	0.762982	+	1.49744i	−0.101535	+	0.994832i	$0.532375\pi$
$98$	−12.6395	−	2.00190i	−1.27678	−	0.202222i
$99$			18.3873i			1.84800i
$100$	−4.14106	+	9.10229i	−0.414106	+	0.910229i
$101$	6.51870			0.648635			0.324317	−	0.945948i	$-0.394865\pi$
$101$	6.51870			0.648635			0.324317	+	0.945948i	$0.394865\pi$
$102$		0			0
$103$	6.00467	−	3.05953i	0.591658	−	0.301465i	−0.132408	−	0.991195i	$-0.542271\pi$
$103$	6.00467	−	3.05953i	0.591658	−	0.301465i	0.724066	+	0.689730i	$0.242271\pi$
$104$		0			0
$105$	−6.25342	−	14.1996i	−0.610272	−	1.38574i
$106$	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	$0.865820\pi$
$108$	−4.71801	+	9.25961i	−0.453990	+	0.891007i
$109$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$109$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$110$	−18.0664	−	7.01893i	−1.72256	−	0.669229i
$111$		0			0
$112$	−15.8271	+	2.50677i	−1.49552	+	0.236868i
$113$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$113$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$114$		0			0
$115$		0			0
$116$	15.1261	+	10.9898i	1.40443	+	1.02038i
$117$		0			0
$118$	−8.49450	−	8.49450i	−0.781983	−	0.781983i
$119$		0			0
$120$	−7.29700	−	8.17030i	−0.666122	−	0.745843i
$121$	8.20936	−	25.2658i	0.746305	−	2.29689i
$122$		0			0
$123$		0			0
$124$		−	15.9934i		−	1.43625i
$125$	6.46151	+	9.12408i	0.577935	+	0.816083i
$126$	16.9965			1.51416
$127$	0.218556	−	1.37991i	0.0193937	−	0.122447i	−0.976092	−	0.217357i	$-0.930256\pi$
$127$	0.218556	−	1.37991i	0.0193937	−	0.122447i	0.995486	+	0.0949102i	$0.0302564\pi$
$128$	−10.0806	+	5.13632i	−0.891007	+	0.453990i
$129$		0			0
$130$		0			0
$131$	4.18734	+	12.8873i	0.365849	+	1.12597i	0.949447	+	0.313926i	$0.101644\pi$
$131$	4.18734	+	12.8873i	0.365849	+	1.12597i	−0.583598	+	0.812043i	$0.698356\pi$
$132$	15.0132	−	15.0132i	1.30673	−	1.30673i
$133$		0			0
$134$		0			0
$135$	6.28871	+	9.76996i	0.541246	+	0.840864i
$136$		0			0
$137$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$137$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$138$		0			0
$139$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$139$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$140$	−6.48800	+	16.6998i	−0.548336	+	1.41139i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	11.4127	−	3.70820i	0.951057	−	0.309017i
$145$	19.1308	−	8.42511i	1.58873	−	0.699667i
$146$	−1.29850	+	3.99638i	−0.107465	+	0.330743i
$147$	−7.11543	−	13.9648i	−0.586871	−	1.15180i
$148$		0			0
$149$		−	23.5077i		−	1.92583i	−0.269812	−	0.962913i	$-0.586961\pi$
$149$		−	23.5077i		−	1.92583i	0.269812	−	0.962913i	$-0.413039\pi$
$150$	−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
$154$	−33.0249	−	10.7304i	−2.66122	−	0.864683i
$155$	−15.4493	−	9.00308i	−1.24092	−	0.723145i
$156$		0			0
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$	11.4077	−	22.3889i	0.907549	−	1.78116i
$159$	−11.3159	+	15.5751i	−0.897413	+	1.23518i
$160$	−0.713040	+	12.6290i	−0.0563708	+	0.998410i
$161$		0			0
$162$	−12.5712	+	1.99109i	−0.987688	+	0.156434i
$163$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$163$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$164$		0			0
$165$	−6.05113	−	22.9537i	−0.471080	−	1.78695i
$166$	20.8469	+	15.1461i	1.61803	+	1.17557i
$167$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$167$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$168$	−13.8775	−	13.8775i	−1.07068	−	1.07068i
$169$	−12.3637	+	4.01722i	−0.951057	+	0.309017i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−22.3129	−	3.53401i	−1.69642	−	0.268686i	−0.768060	−	0.640378i	$-0.778778\pi$
$173$	−22.3129	−	3.53401i	−1.69642	−	0.268686i	−0.928356	+	0.371692i	$0.878778\pi$
$174$			22.8990i			1.73597i
$175$	12.4794	+	15.6680i	0.943354	+	1.18439i
$176$	−24.5165			−1.84800
$177$	2.30161	−	14.5318i	0.172999	−	1.09227i
$178$		0			0
$179$	15.6634	+	5.08934i	1.17074	+	0.380395i	0.828917	−	0.559371i	$-0.188957\pi$
$179$	15.6634	+	5.08934i	1.17074	+	0.380395i	0.341818	+	0.939766i	$0.388957\pi$
$180$	2.84243	−	13.1118i	0.211862	−	0.977299i
$181$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$181$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$182$		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
$189$	12.2355	+	16.8408i	0.890004	+	1.22498i
$190$		0			0
$191$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$191$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$192$	−12.3461	−	6.29068i	−0.891007	−	0.453990i
$193$	2.17344	+	2.17344i	0.156448	+	0.156448i	0.780991	−	0.624543i	$-0.214715\pi$
$193$	2.17344	+	2.17344i	0.156448	+	0.156448i	−0.624543	+	0.780991i	$0.714715\pi$
$194$	22.2625	−	7.23354i	1.59836	−	0.519338i
$195$		0			0
$196$	−5.59250	+	17.2120i	−0.399465	+	1.22943i
$197$	2.70429	+	5.30746i	0.192673	+	0.378141i	0.967051	−	0.254581i	$-0.0819375\pi$
$197$	2.70429	+	5.30746i	0.192673	+	0.378141i	−0.774379	+	0.632722i	$0.781938\pi$
$198$	25.6835	+	4.06786i	1.82525	+	0.289090i
$199$		−	3.07150i		−	0.217733i	−0.994056	−	0.108866i	$-0.965278\pi$
$199$		−	3.07150i		−	0.217733i	0.994056	−	0.108866i	$-0.0347221\pi$
$200$	11.7980	+	7.79796i	0.834242	+	0.551399i
$201$		0			0
$202$	1.44214	−	9.10533i	0.101469	−	0.640649i
$203$	33.3690	−	17.0024i	2.34205	−	1.19333i
$204$		0			0
$205$		0			0
$206$	−2.94514	−	9.06421i	−0.205198	−	0.631533i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	−21.2174	+	5.59340i	−1.46414	+	0.385982i
$211$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$211$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$212$	21.9564	−	3.47756i	1.50797	−	0.238840i
$213$		0			0
$214$	16.0712	+	22.1202i	1.09861	+	1.51210i
$215$		0			0
$216$	11.8901	+	8.63864i	0.809017	+	0.587785i
$217$	−28.5439	−	14.5439i	−1.93769	−	0.987301i
$218$		0			0
$219$	−4.89454	+	1.59033i	−0.330743	+	0.107465i
$220$	−13.8009	+	23.6824i	−0.930458	+	1.59667i
$221$		0			0
$222$		0			0
$223$	−23.0929	−	3.65756i	−1.54642	−	0.244928i	−0.675873	−	0.737018i	$-0.736233\pi$
$223$	−23.0929	−	3.65756i	−1.54642	−	0.244928i	−0.870544	+	0.492090i	$0.836233\pi$
$224$			22.6619i			1.51416i
$225$	−11.0657	−	10.1267i	−0.737713	−	0.675114i
$226$		0			0
$227$	1.28550	−	8.11635i	0.0853219	−	0.538701i	−0.907591	−	0.419856i	$-0.862081\pi$
$227$	1.28550	−	8.11635i	0.0853219	−	0.538701i	0.992913	−	0.118846i	$-0.0379194\pi$
$228$		0			0
$229$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$229$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$230$		0			0
$231$	−13.1420	−	40.4470i	−0.864683	−	2.66122i
$232$	18.6969	−	18.6969i	1.22751	−	1.22751i
$233$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$233$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$234$		0			0
$235$		0			0
$236$	−13.7444	+	9.98589i	−0.894684	+	0.650026i
$237$	30.3961	−	4.81426i	1.97444	−	0.312720i
$238$		0			0
$239$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$239$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$240$	−13.0266	+	8.38494i	−0.840864	+	0.541246i
$241$	−0.345740	−	0.251195i	−0.0222710	−	0.0161809i	0.576594	−	0.817031i	$-0.304381\pi$
$241$	−0.345740	−	0.251195i	−0.0222710	−	0.0161809i	−0.598865	+	0.800850i	$0.704381\pi$
$242$	−33.4752	−	17.0564i	−2.15186	−	1.09643i
$243$	−11.0227	−	11.0227i	−0.707107	−	0.707107i
$244$		0			0
$245$	13.4782	+	15.0913i	0.861093	+	0.964147i
$246$		0			0
$247$		0			0
$248$	−22.3396	−	3.53825i	−1.41857	−	0.224679i
$249$			31.5594i			2.00000i
$250$	14.1740	−	7.00692i	0.896444	−	0.443156i
$251$	30.3470			1.91549			0.957743	−	0.287627i	$-0.0928663\pi$
$251$	30.3470			1.91549			0.957743	+	0.287627i	$0.0928663\pi$
$252$	3.76016	−	23.7407i	0.236868	−	1.49552i
$253$		0			0
$254$	−1.87910	−	0.610558i	−0.117905	−	0.0383098i
$255$		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
$261$	−22.6892	+	16.4847i	−1.40443	+	1.02038i
$262$	18.9274	−	2.99780i	1.16934	−	0.185205i
$263$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$263$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$264$	−17.6491	−	24.2919i	−1.08623	−	1.49506i
$265$	9.00057	−	23.1670i	0.552901	−	1.42314i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	21.8777	−	7.10851i	1.33391	−	0.433413i	0.446660	−	0.894704i	$-0.352613\pi$
$269$	21.8777	−	7.10851i	1.33391	−	0.433413i	0.887249	+	0.461291i	$0.152613\pi$
$270$	15.0380	−	6.62265i	0.915182	−	0.403042i
$271$	−5.09806	+	15.6902i	−0.309685	+	0.953112i	0.668202	+	0.743980i	$0.267064\pi$
$271$	−5.09806	+	15.6902i	−0.309685	+	0.953112i	−0.977887	+	0.209133i	$0.932936\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	15.1078	+	26.6628i	0.911035	+	1.60783i
$276$		0			0
$277$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$277$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$278$		0			0
$279$	22.8159	+	7.41335i	1.36595	+	0.443825i
$280$	21.8910	+	12.7570i	1.30824	+	0.762375i
$281$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$281$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$282$		0			0
$283$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$283$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.65478	−	16.7616i	−0.156434	−	0.987688i
$289$	9.99235	+	13.7533i	0.587785	+	0.809017i
$290$	−7.53588	−	28.5858i	−0.442522	−	1.67862i
$291$	23.1938	+	16.8513i	1.35964	+	0.987839i
$292$	5.29488	+	2.69788i	0.309859	+	0.157881i
$293$	11.9573	+	11.9573i	0.698550	+	0.698550i	0.964098	−	0.265547i	$-0.0855527\pi$
$293$	11.9573	+	11.9573i	0.698550	+	0.698550i	−0.265547	+	0.964098i	$0.585553\pi$
$294$	−21.0803	+	6.84939i	−1.22943	+	0.399465i
$295$	1.90910	+	18.8981i	0.111152	+	1.10029i
$296$		0			0
$297$	14.4586	+	28.3766i	0.838973	+	1.64658i
$298$	−32.8356	−	5.20065i	−1.90212	−	0.301266i
$299$		0			0
$300$	0.766672	+	17.3035i	0.0442638	+	0.999020i
$301$		0			0
$302$	−5.01709	+	31.6767i	−0.288701	+	1.82279i
$303$	10.0601	−	5.12588i	0.577938	−	0.294474i
$304$		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	$0.750000\pi$
$308$	−22.2944	+	43.7553i	−1.27034	+	2.49319i
$309$	6.86100	−	9.44336i	0.390309	−	0.537214i
$310$	−15.9934	+	19.5878i	−0.908364	+	1.11251i
$311$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$311$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$312$		0			0
$313$	5.01352	+	31.6541i	0.283381	+	1.78920i	0.560287	+	0.828298i	$0.310691\pi$
$313$	5.01352	+	31.6541i	0.283381	+	1.78920i	−0.276907	+	0.960897i	$0.589309\pi$
$314$		0			0
$315$	−20.8163	−	16.9965i	−1.17287	−	0.957642i
$316$	−28.7491	−	20.8874i	−1.61726	−	1.17501i
$317$	13.3562	+	6.80530i	0.750156	+	0.382224i	0.786884	−	0.617102i	$-0.211693\pi$
$317$	13.3562	+	6.80530i	0.750156	+	0.382224i	−0.0367271	+	0.999325i	$0.511693\pi$
$318$	19.2518	+	19.2518i	1.07959	+	1.07959i
$319$	54.4935	−	17.7060i	3.05105	−	0.991346i
$320$	17.4825	+	3.78991i	0.977299	+	0.211862i
$321$	−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
$330$	−33.4005	+	3.37414i	−1.83864	+	0.185740i
$331$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$331$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$332$	25.7682	−	25.7682i	1.41421	−	1.41421i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−22.4543	+	16.3140i	−1.22498	+	0.890004i
$337$	−35.7325	+	5.65947i	−1.94647	+	0.308291i	−0.999899	−	0.0141927i	$-0.995482\pi$
$337$	−35.7325	+	5.65947i	−1.94647	+	0.308291i	−0.946575	+	0.322484i	$0.895482\pi$
$338$	2.87601	+	18.1584i	0.156434	+	0.987688i
$339$		0			0
$340$		0			0
$341$	−39.6521	−	28.8089i	−2.14728	−	1.56009i
$342$		0			0
$343$	5.80390	+	5.80390i	0.313381	+	0.313381i
$344$		0			0
$345$		0			0
$346$	−9.87263	+	30.3848i	−0.530756	+	1.63350i
$347$	16.4538	+	32.2925i	0.883288	+	1.73355i	0.648024	+	0.761620i	$0.275596\pi$
$347$	16.4538	+	32.2925i	0.883288	+	1.73355i	0.235264	+	0.971931i	$0.424404\pi$
$348$	31.9853	+	5.06598i	1.71459	+	0.271565i
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	24.6459	−	13.9650i	1.31738	−	0.746460i
$351$		0			0
$352$	−5.42382	+	34.2446i	−0.289090	+	1.82525i
$353$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$353$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$354$	−19.7888	−	6.42978i	−1.05176	−	0.341739i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	10.5740	−	20.7527i	0.558855	−	1.09681i
$359$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$359$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$360$	−17.6858	−	6.87107i	−0.932125	−	0.362137i
$361$	15.3713	−	11.1679i	0.809017	−	0.587785i
$362$		0			0
$363$	−7.19813	−	45.4472i	−0.377804	−	2.38536i
$364$		0			0
$365$	5.58671	−	3.59604i	0.292422	−	0.188225i
$366$		0			0
$367$	−11.4821	−	5.85040i	−0.599359	−	0.305388i	0.127862	−	0.991792i	$-0.459188\pi$
$367$	−11.4821	−	5.85040i	−0.599359	−	0.305388i	−0.727221	+	0.686403i	$0.759188\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	13.7599	−	42.3487i	0.714380	−	2.19864i
$372$	−12.5762	−	24.6821i	−0.652044	−	1.27971i
$373$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$373$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$374$		0			0
$375$	17.1464	+	9.00000i	0.885438	+	0.464758i
$376$		0			0
$377$		0			0
$378$	26.2301	−	13.3649i	1.34913	−	0.687416i
$379$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$379$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$380$		0			0
$381$	−0.747778	−	2.30142i	−0.0383098	−	0.117905i
$382$		0			0
$383$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$383$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$384$	−11.5182	+	15.8534i	−0.587785	+	0.809017i
$385$	29.7166	+	46.1669i	1.51450	+	2.35288i
$386$	3.51670	−	2.55503i	0.178995	−	0.130048i
$387$		0			0
$388$	−5.17864	−	32.6967i	−0.262906	−	1.65992i
$389$	−15.8328	−	21.7919i	−0.802753	−	1.10490i	−0.992401	−	0.123043i	$-0.960735\pi$
$389$	−15.8328	−	21.7919i	−0.802753	−	1.10490i	0.189648	−	0.981852i	$-0.439265\pi$
$390$		0			0
$391$		0			0
$392$	22.8045	+	11.6195i	1.15180	+	0.586871i
$393$	16.5959	+	16.5959i	0.837153	+	0.837153i
$394$	8.01175	−	2.60318i	0.403626	−	0.131146i
$395$	−36.3604	+	16.0130i	−1.82949	+	0.805700i
$396$	11.3640	−	34.9748i	0.571063	−	1.75755i
$397$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$397$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$398$	−4.29028	−	0.679514i	−0.215052	−	0.0340609i
$399$		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
$404$	−12.3993	−	4.02878i	−0.616888	−	0.200439i
$405$	17.3876	+	10.1326i	0.863998	+	0.503495i
$406$	−16.3667	−	50.3714i	−0.812264	−	2.49989i
$407$		0			0
$408$		0			0
$409$	22.0917	−	30.4067i	1.09237	−	1.50351i	0.247234	−	0.968956i	$-0.420478\pi$
$409$	22.0917	−	30.4067i	1.09237	−	1.50351i	0.845132	−	0.534557i	$-0.179522\pi$
$410$		0			0
$411$		0			0
$412$	−13.3125	+	2.10849i	−0.655858	+	0.103878i
$413$	5.32344	+	33.6109i	0.261950	+	1.65388i
$414$		0			0
$415$	−10.3860	−	39.3971i	−0.509827	−	1.93393i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−38.0423	+	12.3607i	−1.85849	+	0.603860i	−0.863443	+	0.504447i	$0.831697\pi$
$419$	−38.0423	+	12.3607i	−1.85849	+	0.603860i	−0.995046	+	0.0994131i	$0.968303\pi$
$420$	3.11891	+	30.8740i	0.152187	+	1.50650i
$421$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$421$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$422$		0			0
$423$		0			0
$424$		−	31.4381i		−	1.52677i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	34.4529	−	17.5547i	1.66535	−	0.848536i
$429$		0			0
$430$		0			0
$431$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$431$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$432$	14.6969	−	14.6969i	0.707107	−	0.707107i
$433$	9.06101	−	17.7832i	0.435444	−	0.854608i	−0.564137	−	0.825681i	$-0.690791\pi$
$433$	9.06101	−	17.7832i	0.435444	−	0.854608i	0.999582	−	0.0289266i	$-0.00920891\pi$
$434$	−26.6297	+	36.6527i	−1.27827	+	1.75938i
$435$	22.8990	−	28.0454i	1.09792	−	1.34467i
$436$		0			0
$437$		0			0
$438$	1.13855	+	7.18854i	0.0544022	+	0.343482i
$439$	−7.70518	−	10.6053i	−0.367748	−	0.506162i	0.584539	−	0.811366i	$-0.301275\pi$
$439$	−7.70518	−	10.6053i	−0.367748	−	0.506162i	−0.952287	+	0.305204i	$0.901275\pi$
$440$	30.0264	+	24.5165i	1.43145	+	1.16878i
$441$	−21.9621	−	15.9564i	−1.04581	−	0.759827i
$442$		0			0
$443$	12.2087	+	12.2087i	0.580054	+	0.580054i	0.934918	−	0.354864i	$-0.115473\pi$
$443$	12.2087	+	12.2087i	0.580054	+	0.580054i	−0.354864	+	0.934918i	$0.615473\pi$
$444$		0			0
$445$		0			0
$446$	−10.2178	+	31.4471i	−0.483826	+	1.48906i
$447$	−18.4849	−	36.2787i	−0.874307	−	1.71592i
$448$	31.6543	+	5.01354i	1.49552	+	0.236868i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	−16.5931	+	13.2162i	−0.782206	+	0.623019i
$451$		0			0
$452$		0			0
$453$	−34.9982	+	17.8325i	−1.64436	+	0.837844i
$454$	−11.0525	−	3.59119i	−0.518722	−	0.168543i
$455$		0			0
$456$		0			0
$457$	9.48241	−	9.48241i	0.443568	−	0.443568i	−0.449641	−	0.893209i	$-0.648448\pi$
$457$	9.48241	−	9.48241i	0.443568	−	0.443568i	0.893209	+	0.449641i	$0.148448\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.276415	−	0.200827i	0.0128739	−	0.00935346i	−0.581330	−	0.813668i	$-0.697467\pi$
$461$	0.276415	−	0.200827i	0.0128739	−	0.00935346i	0.594204	+	0.804315i	$0.297467\pi$
$462$	−59.4040	+	9.40866i	−2.76372	+	0.437731i
$463$	6.66935	+	42.1086i	0.309951	+	1.95695i	0.289558	+	0.957160i	$0.406492\pi$
$463$	6.66935	+	42.1086i	0.309951	+	1.95695i	0.0203929	+	0.999792i	$0.493508\pi$
$464$	−21.9796	−	30.2523i	−1.02038	−	1.40443i
$465$	−30.9218	−	1.74586i	−1.43397	−	0.0809625i
$466$		0			0
$467$	−37.6149	−	19.1657i	−1.74061	−	0.886885i	−0.967599	−	0.252492i	$-0.918750\pi$
$467$	−37.6149	−	19.1657i	−1.74061	−	0.886885i	−0.773010	−	0.634393i	$-0.781250\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	10.9076	+	21.4074i	0.502064	+	0.985355i
$473$		0			0
$474$		−	43.5224i		−	1.99905i
$475$		0			0
$476$		0			0
$477$	−5.21633	+	32.9346i	−0.238840	+	1.50797i
$478$		0			0
$479$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$479$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$480$	8.83021	+	20.0506i	0.403042	+	0.915182i
$481$		0			0
$482$	−0.427358	+	0.427358i	−0.0194656	+	0.0194656i
$483$		0			0
$484$	−31.2302	+	42.9848i	−1.41956	+	1.95385i
$485$	−34.4995	−	13.4033i	−1.56654	−	0.608613i
$486$	−17.8351	+	12.9580i	−0.809017	+	0.587785i
$487$	−43.3209	+	6.86135i	−1.96306	+	0.310917i	−0.964082	+	0.265603i	$0.914429\pi$
$487$	−43.3209	+	6.86135i	−1.96306	+	0.310917i	−0.998973	+	0.0453143i	$0.985571\pi$
$488$		0			0
$489$		0			0
$490$	24.0614	−	15.4878i	1.08698	−	0.699665i
$491$	35.7784	+	25.9945i	1.61466	+	1.17312i	0.845285	+	0.534315i	$0.179431\pi$
$491$	35.7784	+	25.9945i	1.61466	+	1.17312i	0.769372	+	0.638801i	$0.220569\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−27.3878	−	30.6656i	−1.23099	−	1.37832i
$496$	−9.88446	+	30.4212i	−0.443825	+	1.36595i
$497$		0			0
$498$	44.0823	+	6.98195i	1.97537	+	0.312869i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	−6.65153	−	21.3485i	−0.297465	−	0.954733i
$501$		0			0
$502$	6.71372	−	42.3887i	0.299648	−	1.89190i
$503$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$503$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$504$	−32.3292	−	10.5044i	−1.44006	−	0.467903i
$505$	−10.8716	+	9.70956i	−0.483779	+	0.432070i
$506$		0			0
$507$	−15.9217	+	15.9217i	−0.707107	+	0.707107i
$508$	−1.26855	+	2.48966i	−0.0562826	+	0.110461i
$509$	5.78285	−	7.95941i	0.256320	−	0.352795i	−0.661392	−	0.750040i	$-0.730034\pi$
$509$	5.78285	−	7.95941i	0.256320	−	0.352795i	0.917712	+	0.397246i	$0.130034\pi$
$510$		0			0
$511$	9.62997	−	6.99658i	0.426005	−	0.309511i
$512$	22.3488	−	3.53971i	0.987688	−	0.156434i
$513$		0			0
$514$		0			0
$515$	−5.45716	+	14.0465i	−0.240471	+	0.618962i
$516$		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	$-0.400000\pi$
$521$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$522$	18.0063	+	35.3393i	0.788113	+	1.54676i
$523$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$523$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$524$		−	27.1010i		−	1.18391i
$525$	31.5794	+	14.3669i	1.37824	+	0.627025i
$526$		0			0
$527$		0			0
$528$	−37.8355	+	19.2781i	−1.64658	+	0.838973i
$529$	21.8743	+	7.10739i	0.951057	+	0.309017i
$530$	−30.3686	−	17.6973i	−1.31913	−	0.768722i
$531$	−7.87484	−	24.2363i	−0.341739	−	1.05176i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	2.43699	−	43.1628i	0.105360	−	1.86609i
$536$		0			0
$537$	28.1747	−	4.46244i	1.21583	−	0.192568i
$538$	−5.08913	−	32.1315i	−0.219408	−	1.38529i
$539$	32.5995	+	44.8693i	1.40416	+	1.93266i
$540$	−5.92366	−	22.4702i	−0.254914	−	0.966964i
$541$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$541$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$542$	20.7883	+	10.5921i	0.892932	+	0.454972i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$547$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$548$		0			0
$549$		0			0
$550$	40.5850	−	15.2040i	1.73055	−	0.648299i
$551$		0			0
$552$		0			0
$553$	−63.4220	+	32.3151i	−2.69698	+	1.37418i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−19.3507	+	19.3507i	−0.819916	+	0.819916i	−0.986095	−	0.166180i	$-0.946857\pi$
$557$	−19.3507	+	19.3507i	−0.819916	+	0.819916i	0.166180	+	0.986095i	$0.446857\pi$
$558$	15.4026	−	30.2293i	0.652044	−	1.27971i
$559$		0			0
$560$	22.6619	−	27.7551i	0.957642	−	1.17287i
$561$		0			0
$562$		0			0
$563$	−6.05011	−	38.1989i	−0.254982	−	1.60989i	−0.699846	−	0.714294i	$-0.746748\pi$
$563$	−6.05011	−	38.1989i	−0.254982	−	1.60989i	0.444864	−	0.895598i	$-0.353252\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	32.1252	+	16.3686i	1.34913	+	0.687416i
$568$		0			0
$569$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$569$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$570$		0			0
$571$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$571$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−24.0000			−1.00000
$577$	−3.20905	+	20.2611i	−0.133595	+	0.843483i	0.826322	+	0.563198i	$0.190429\pi$
$577$	−3.20905	+	20.2611i	−0.133595	+	0.843483i	−0.959917	+	0.280285i	$0.909571\pi$
$578$	21.4212	−	10.9147i	0.891007	−	0.453990i
$579$	5.06325	+	1.64515i	0.210422	+	0.0683701i
$580$	−41.5959	+	4.20204i	−1.72718	+	0.174480i
$581$	−22.5566	−	69.4220i	−0.935804	−	2.88011i
$582$	28.6691	−	28.6691i	1.18837	−	1.18837i
$583$	30.9283	−	60.7002i	1.28092	−	2.51395i
$584$	4.93980	−	6.79905i	0.204410	−	0.281346i
$585$		0			0
$586$	19.3472	−	14.0566i	0.799227	−	0.580673i
$587$	−26.1058	+	4.13475i	−1.07750	+	0.170659i	−0.669863	−	0.742484i	$-0.733647\pi$
$587$	−26.1058	+	4.13475i	−1.07750	+	0.170659i	−0.407638	+	0.913144i	$0.633647\pi$
$588$	4.90362	+	30.9603i	0.202222	+	1.27678i
$589$		0			0
$590$	26.8193	+	1.51423i	1.10413	+	0.0623399i
$591$	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	$0.250000\pi$
$594$	42.8352	−	13.9180i	1.75755	−	0.571063i
$595$		0			0
$596$	−14.5286	+	44.7143i	−0.595113	+	1.83157i
$597$	−2.41523	−	4.74015i	−0.0988487	−	0.194001i
$598$		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
$605$	23.9421	+	54.3650i	0.973384	+	2.21025i
$606$	−4.93422	−	15.1860i	−0.200439	−	0.616888i
$607$	20.2420	−	20.2420i	0.821596	−	0.821596i	−0.164741	−	0.986337i	$-0.552679\pi$
$607$	20.2420	−	20.2420i	0.821596	−	0.821596i	0.986337	+	0.164741i	$0.0526787\pi$
$608$		0			0
$609$	38.1278	−	52.4784i	1.54502	−	2.12653i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$613$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$614$		0			0
$615$		0			0
$616$	56.1853	+	40.8210i	2.26377	+	1.64472i
$617$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$617$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$618$	−11.6726	−	11.6726i	−0.469542	−	0.469542i
$619$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$619$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$620$	23.8221	+	26.6731i	0.956718	+	1.07122i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−24.3665	−	5.59235i	−0.974659	−	0.223694i
$626$	45.3237			1.81150
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−28.3459	+	25.3161i	−1.12933	+	1.00862i
$631$	−1.51387	−	4.65921i	−0.0602661	−	0.185480i	0.916391	−	0.400284i	$-0.131089\pi$
$631$	−1.51387	−	4.65921i	−0.0602661	−	0.185480i	−0.976657	+	0.214804i	$0.931089\pi$
$632$	−35.5359	+	35.5359i	−1.41354	+	1.41354i
$633$		0			0
$634$	12.4605	−	17.1504i	0.494868	−	0.681128i
$635$	1.69087	+	2.62688i	0.0670999	+	0.104245i
$636$	31.1501	−	22.6319i	1.23518	−	0.897413i
$637$		0			0
$638$	−12.6761	−	80.0337i	−0.501852	−	3.16857i
$639$		0			0
$640$	9.16143	−	23.5811i	0.362137	−	0.932125i
$641$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$641$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$642$	42.1961	+	21.5000i	1.66535	+	0.848536i
$643$		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		−0.453990	−	0.891007i	$-0.650000\pi$
$647$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$648$	25.1424	+	3.98217i	0.987688	+	0.156434i
$649$			52.0638i			2.04368i
$650$		0			0
$651$	−55.4873			−2.17472
$652$		0			0
$653$	27.9164	−	14.2241i	1.09245	−	0.556633i	0.187553	−	0.982255i	$-0.439945\pi$
$653$	27.9164	−	14.2241i	1.09245	−	0.556633i	0.904901	+	0.425622i	$0.139945\pi$
$654$		0			0
$655$	−26.1790	−	15.2558i	−1.02290	−	0.596095i
$656$		0			0
$657$	−6.30306	+	6.30306i	−0.245906	+	0.245906i
$658$		0			0
$659$	−30.1716	+	41.5277i	−1.17532	+	1.61769i	−0.570949	+	0.820985i	$0.693425\pi$
$659$	−30.1716	+	41.5277i	−1.17532	+	1.61769i	−0.604371	+	0.796703i	$0.706575\pi$
$660$	−2.67625	+	47.4004i	−0.104173	+	1.84506i
$661$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$661$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$662$		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
$669$	−38.5147	+	12.5142i	−1.48906	+	0.483826i
$670$		0			0
$671$		0			0
$672$	17.8199	+	34.9735i	0.687416	+	1.34913i
$673$	−12.3476	−	1.95567i	−0.475964	−	0.0753854i	−0.0861567	−	0.996282i	$-0.527459\pi$
$673$	−12.3476	−	1.95567i	−0.475964	−	0.0753854i	−0.389808	+	0.920896i	$0.627459\pi$
$674$			51.1633i			1.97074i
$675$	−25.0403	−	6.92691i	−0.963803	−	0.266617i
$676$	26.0000			1.00000
$677$	7.86746	−	49.6732i	0.302371	−	1.90910i	−0.102520	−	0.994731i	$-0.532690\pi$
$677$	7.86746	−	49.6732i	0.302371	−	1.90910i	0.404891	−	0.914365i	$-0.367310\pi$
$678$		0			0
$679$	−63.0640	−	20.4907i	−2.42018	−	0.786363i
$680$		0			0
$681$	−4.39829	−	13.5366i	−0.168543	−	0.518722i
$682$	−49.0127	+	49.0127i	−1.87679	+	1.87679i
$683$	15.9436	−	31.2910i	0.610063	−	1.19732i	−0.354893	−	0.934907i	$-0.615483\pi$
$683$	15.9436	−	31.2910i	0.610063	−	1.19732i	0.964956	−	0.262410i	$-0.0845173\pi$
$684$		0			0
$685$		0			0
$686$	9.39091	−	6.82290i	0.358547	−	0.260499i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$691$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$692$	40.2575	+	20.5122i	1.53036	+	0.779757i
$693$	−52.0866	−	52.0866i	−1.97861	−	1.97861i
$694$	48.7463	−	15.8386i	1.85038	−	0.601227i
$695$		0			0
$696$	14.1523	−	43.5564i	0.536443	−	1.65100i
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−14.0539	−	37.5150i	−0.531186	−	1.41793i
$701$	−0.944387			−0.0356690			−0.0178345	−	0.999841i	$-0.505677\pi$
$701$	−0.944387			−0.0356690			−0.0178345	+	0.999841i	$0.505677\pi$
$702$		0			0
$703$		0			0
$704$	46.6331	+	15.1520i	1.75755	+	0.571063i
$705$		0			0
$706$		0			0
$707$	−18.4658	+	18.4658i	−0.694478	+	0.694478i
$708$	−13.3590	+	26.2186i	−0.502064	+	0.985355i
$709$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$709$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$710$		0			0
$711$	43.1237	−	31.3312i	1.61726	−	1.17501i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−26.6481	−	19.3610i	−0.995887	−	0.723554i
$717$		0			0
$718$		0			0
$719$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$719$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$720$	−13.5102	+	23.1835i	−0.503495	+	0.863998i
$721$	−8.34282	+	25.6766i	−0.310703	+	0.956245i
$722$	−12.1988	−	23.9414i	−0.453990	−	0.891007i
$723$	−0.731092	−	0.115794i	−0.0271896	−	0.00430641i
$724$		0			0
$725$	−19.3563	+	42.5462i	−0.718875	+	1.58013i
$726$	−65.0732			−2.41509
$727$	−5.73972	+	36.2392i	−0.212875	+	1.34404i	0.617386	+	0.786661i	$0.288192\pi$
$727$	−5.73972	+	36.2392i	−0.212875	+	1.34404i	−0.830260	+	0.557376i	$0.811808\pi$
$728$		0			0
$729$	−25.6785	−	8.34346i	−0.951057	−	0.309017i
$730$	−3.78700	−	8.59909i	−0.140163	−	0.318267i
$731$		0			0
$732$		0			0
$733$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$733$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$734$	−10.7120	+	14.7439i	−0.395389	+	0.544206i
$735$	32.6673	+	12.6915i	1.20495	+	0.468133i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$739$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$740$		0			0
$741$		0			0
$742$	−56.1086	−	28.5888i	−2.05981	−	1.04953i
$743$		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
$745$	35.0146	+	39.2051i	1.28284	+	1.43636i
$746$		0			0
$747$	24.8163	+	48.7047i	0.907980	+	1.78201i
$748$		0			0
$749$		−	77.4529i		−	2.83007i
$750$	16.3646	−	21.9591i	0.597549	−	0.801832i
$751$	−7.14198			−0.260615			−0.130307	−	0.991474i	$-0.541596\pi$
$751$	−7.14198			−0.260615			−0.130307	+	0.991474i	$0.541596\pi$
$752$		0			0
$753$	46.8336	−	23.8629i	1.70671	−	0.869612i
$754$		0			0
$755$	37.8213	−	33.7788i	1.37646	−	1.22933i
$756$	−12.8652	−	39.5950i	−0.467903	−	1.44006i
$757$		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	$-0.200000\pi$
$761$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$762$	−3.38007	+	0.535350i	−0.122447	+	0.0193937i
$763$		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	−0.883309	+	0.468792i	$0.844689\pi$
$769$	−51.9529	+	16.8805i	−1.87347	+	0.608727i	−0.990161	+	0.139935i	$0.955311\pi$
$770$	71.0603	−	31.2946i	2.56084	−	1.12778i
$771$		0			0
$772$	−2.79087	−	5.47739i	−0.100446	−	0.197135i
$773$	45.9867	+	7.28358i	1.65403	+	0.261972i	0.912538	−	0.408993i	$-0.134120\pi$
$773$	45.9867	+	7.28358i	1.65403	+	0.261972i	0.741489	+	0.670965i	$0.234120\pi$
$774$		0			0
$775$	39.1757	−	7.99670i	1.40723	−	0.287250i
$776$	−46.8164			−1.68061
$777$		0			0
$778$	−33.9417	+	17.2942i	−1.21687	+	0.620026i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−22.0531	+	43.2816i	−0.788113	+	1.54676i
$784$	21.2752	−	29.2827i	0.759827	−	1.04581i
$785$		0			0
$786$	26.8528	−	19.5097i	0.957806	−	0.695887i
$787$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$787$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$788$	−1.86367	−	11.7667i	−0.0663904	−	0.419173i
$789$		0			0
$790$	14.3229	+	54.3309i	0.509585	+	1.93301i
$791$		0			0
$792$	−46.3388	−	23.6108i	−1.64658	−	0.838973i
$793$		0			0
$794$		0			0
$795$	−4.32675	−	42.8304i	−0.153454	−	1.51904i
$796$	−1.89829	+	5.84234i	−0.0672832	+	0.207076i
$797$	24.3600	+	47.8091i	0.862874	+	1.69349i	0.708781	+	0.705429i	$0.249246\pi$
$797$	24.3600	+	47.8091i	0.862874	+	1.69349i	0.154093	+	0.988056i	$0.450754\pi$
$798$		0			0
$799$		0			0
$800$	−17.6216	−	22.1241i	−0.623019	−	0.782206i
$801$		0			0
$802$		0			0
$803$	16.2265	−	8.26780i	0.572619	−	0.291764i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	28.1736	−	28.1736i	0.991756	−	0.991756i
$808$	−8.37052	+	16.4281i	−0.294474	+	0.577938i
$809$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$809$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$810$	18.0000	−	22.0454i	0.632456	−	0.774597i
$811$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$811$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$812$	−73.9797	+	11.7172i	−2.59618	+	0.411194i
$813$	4.47008	+	28.2230i	0.156773	+	0.989823i
$814$		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
$821$	−17.6129	+	54.2069i	−0.614694	+	1.89183i	−0.208609	+	0.977999i	$0.566894\pi$
$821$	−17.6129	+	54.2069i	−0.614694	+	1.89183i	−0.406085	+	0.913835i	$0.633106\pi$
$822$		0			0
$823$	−40.5610	−	6.42424i	−1.41387	−	0.223935i	−0.597687	−	0.801730i	$-0.703913\pi$
$823$	−40.5610	−	6.42424i	−1.41387	−	0.223935i	−0.816182	+	0.577795i	$0.803913\pi$
$824$			19.0613i			0.664033i
$825$	44.2813	+	29.2681i	1.54168	+	1.01898i
$826$	48.1255			1.67450
$827$	−7.91378	+	49.9657i	−0.275189	+	1.73748i	0.332323	+	0.943166i	$0.392168\pi$
$827$	−7.91378	+	49.9657i	−0.275189	+	1.73748i	−0.607512	+	0.794310i	$0.707832\pi$
$828$		0			0
$829$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$829$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$830$	−57.3276	+	5.79126i	−1.98987	+	0.201018i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	41.0405	−	6.50017i	1.41857	−	0.224679i
$838$	8.84928	+	55.8722i	0.305693	+	1.93007i
$839$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$839$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$840$	43.8149	+	2.47381i	1.51176	+	0.0853546i
$841$	47.2416	+	34.3231i	1.62902	+	1.18355i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	14.6360	−	25.1155i	0.503495	−	0.863998i
$846$		0			0
$847$	48.3165	+	94.8265i	1.66018	+	3.25828i
$848$	−43.9128	−	6.95511i	−1.50797	−	0.238840i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$853$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$854$		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	$-0.300000\pi$
$859$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$863$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$864$	−17.2773	−	23.7801i	−0.587785	−	0.809017i
$865$	42.4763	−	27.3410i	1.44424	−	0.929623i
$866$	−22.8351	−	16.5907i	−0.775968	−	0.563773i
$867$	26.2356	+	13.3677i	0.891007	+	0.453990i
$868$	45.3052	+	45.3052i	1.53776	+	1.53776i
$869$	−103.572	+	33.6525i	−3.51343	+	1.14158i
$870$	−34.1079	−	38.1899i	−1.15637	−	1.29476i
$871$		0			0
$872$		0			0
$873$	49.0450	+	7.76796i	1.65992	+	0.262906i
$874$		0			0
$875$	−44.1500	−	7.54238i	−1.49254	−	0.254979i
$876$	10.2929			0.347763
$877$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$877$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$878$	−16.5181	+	8.41639i	−0.557459	+	0.284039i
$879$	27.8557	+	9.05085i	0.939548	+	0.305278i
$880$	40.8874	−	36.5171i	1.37832	−	1.23099i
$881$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$881$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$882$	−27.1466	+	27.1466i	−0.914073	+	0.914073i
$883$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$883$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$884$		0			0
$885$	17.8065	+	27.6637i	0.598558	+	0.929904i
$886$	19.7541	−	14.3522i	0.663653	−	0.482172i
$887$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$887$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$888$		0			0
$889$	3.28981	+	4.52803i	0.110337	+	0.151865i
$890$		0			0
$891$	44.6270	+	32.4234i	1.49506	+	1.08623i
$892$	41.6649	+	21.2293i	1.39504	+	0.710810i
$893$		0			0
$894$	−54.7636	+	17.7938i	−1.83157	+	0.595113i
$895$	−33.7032	+	14.8427i	−1.12657	+	0.496138i
$896$	14.0059	−	43.1056i	0.467903	−	1.44006i
$897$		0			0
$898$		0			0
$899$		−	74.7569i		−	2.49328i
$900$	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	$0.750000\pi$
$908$	−7.46136	+	14.6437i	−0.247614	+	0.485970i
$909$	11.4948	−	15.8212i	0.381258	−	0.524756i
$910$		0			0
$911$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$911$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$912$		0			0
$913$	−17.4702	−	110.303i	−0.578180	−	3.65049i
$914$	−11.1472	−	15.3429i	−0.368718	−	0.507497i
$915$		0			0
$916$		0			0
$917$	−48.3681	−	24.6448i	−1.59725	−	0.813842i
$918$		0			0
$919$	−32.6144	+	10.5971i	−1.07585	+	0.349565i	−0.792764	−	0.609529i	$-0.791359\pi$
$919$	−32.6144	+	10.5971i	−1.07585	+	0.349565i	−0.283087	+	0.959094i	$0.591359\pi$
$920$		0			0
$921$		0			0
$922$	−0.219364	−	0.430526i	−0.00722437	−	0.0141786i
$923$		0			0
$924$			85.0571i			2.79817i
$925$		0			0
$926$	60.2929			1.98135
$927$	3.16273	−	19.9687i	0.103878	−	0.655858i
$928$	−47.1190	+	24.0083i	−1.54676	+	0.788113i
$929$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$929$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$930$	−9.27952	+	42.8054i	−0.304287	+	1.40365i
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−35.0924	+	48.3005i	−1.14826	+	1.58044i
$935$		0			0
$936$		0			0
$937$	−59.8290	+	9.47598i	−1.95453	+	0.309567i	−0.954595	+	0.297907i	$0.903712\pi$
$937$	−59.8290	+	9.47598i	−1.95453	+	0.309567i	−0.999932	+	0.0116601i	$0.996288\pi$
$938$		0			0
$939$	32.6279	+	44.9085i	1.06477	+	1.46553i
$940$		0			0
$941$	9.80736	+	7.12546i	0.319711	+	0.232284i	0.736052	−	0.676925i	$-0.236688\pi$
$941$	9.80736	+	7.12546i	0.319711	+	0.232284i	−0.416341	+	0.909208i	$0.636688\pi$
$942$		0			0
$943$		0			0
$944$	32.3150	−	10.4998i	1.05176	−	0.341739i
$945$	−45.4901	−	9.86150i	−1.47979	−	0.320795i
$946$		0			0
$947$	−27.8265	−	54.6126i	−0.904240	−	1.77467i	−0.532919	−	0.846166i	$-0.678905\pi$
$947$	−27.8265	−	54.6126i	−0.904240	−	1.77467i	−0.371321	−	0.928505i	$-0.621095\pi$
$948$	−60.7921	−	9.62853i	−1.97444	−	0.312720i
$949$		0			0
$950$		0			0
$951$	25.9634			0.841920
$952$		0			0
$953$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$953$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$954$	44.8492	+	14.5724i	1.45204	+	0.471798i
$955$		0			0
$956$		0			0
$957$	70.1752	−	70.1752i	2.26844	−	2.26844i
$958$		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
$963$	9.07338	+	57.2871i	0.292386	+	1.84605i
$964$	0.502389	+	0.691479i	0.0161809	+	0.0222710i
$965$	−6.86209	−	0.387437i	−0.220899	−	0.0124721i
$966$		0			0
$967$	28.9688	+	14.7603i	0.931574	+	0.474660i	0.852803	−	0.522232i	$-0.174901\pi$
$967$	28.9688	+	14.7603i	0.931574	+	0.474660i	0.0787703	+	0.996893i	$0.474901\pi$
$968$	53.1321	+	53.1321i	1.70773	+	1.70773i
$969$		0			0
$970$	−26.3541	+	45.2237i	−0.846180	+	1.45205i
$971$	7.77586	−	23.9316i	0.249539	−	0.768002i	−0.745318	−	0.666710i	$-0.767702\pi$
$971$	7.77586	−	23.9316i	0.249539	−	0.768002i	0.994857	−	0.101293i	$-0.0322979\pi$
$972$	14.1540	+	27.7788i	0.453990	+	0.891007i
$973$		0			0
$974$			62.0286i			1.98752i
$975$		0			0
$976$		0			0
$977$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$977$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$978$		0			0
$979$		0			0
$980$	−16.3102	−	37.0353i	−0.521010	−	1.18305i
$981$		0			0
$982$	44.2245	−	44.2245i	1.41126	−	1.41126i
$983$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$983$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$984$		0			0
$985$	−12.4155	−	4.82353i	−0.395592	−	0.153690i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−48.8928	+	31.4712i	−1.55392	+	1.00022i
$991$	33.3469	+	24.2279i	1.05930	+	0.769626i	0.973959	−	0.226726i	$-0.0728023\pi$
$991$	33.3469	+	24.2279i	1.05930	+	0.769626i	0.0853402	+	0.996352i	$0.472802\pi$
$992$	40.3057	+	20.5368i	1.27971	+	0.652044i
$993$		0			0
$994$		0			0
$995$	4.57499	+	5.12251i	0.145037	+	0.162395i
$996$	19.5048	−	60.0296i	0.618033	−	1.90211i
$997$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$997$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$998$		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.173.2	yes	16
3.2	odd	2		600.2.bp.a.173.1	✓	16
8.5	even	2		600.2.bp.a.173.1	✓	16
24.5	odd	2	CM	600.2.bp.b.173.2	yes	16
25.12	odd	20	inner	600.2.bp.b.437.2	yes	16
75.62	even	20		600.2.bp.a.437.1	yes	16
200.37	odd	20		600.2.bp.a.437.1	yes	16
600.437	even	20	inner	600.2.bp.b.437.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.bp.a.173.1	✓	16	3.2	odd	2
600.2.bp.a.173.1	✓	16	8.5	even	2
600.2.bp.a.437.1	yes	16	75.62	even	20
600.2.bp.a.437.1	yes	16	200.37	odd	20
600.2.bp.b.173.2	yes	16	1.1	even	1	trivial
600.2.bp.b.173.2	yes	16	24.5	odd	2	CM
600.2.bp.b.437.2	yes	16	25.12	odd	20	inner
600.2.bp.b.437.2	yes	16	600.437	even	20	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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bp (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.221232 - 1.39680i) q^{2} +(1.54327 - 0.786335i) q^{3} +(-1.90211 - 0.618034i) q^{4} +(-1.66775 + 1.48949i) q^{5} +(-0.756934 - 2.32960i) q^{6} +(-2.83274 + 2.83274i) q^{7} +(-1.28408 + 2.52015i) q^{8} +(1.76336 - 2.42705i) q^{9} +(1.71157 + 2.65905i) q^{10} +(-4.95856 + 3.60260i) q^{11} +(-3.42145 + 0.541905i) q^{12} +(3.33009 + 4.58347i) q^{14} +(-1.40255 + 3.61010i) q^{15} +(3.23607 + 2.35114i) q^{16} +(-3.00000 - 3.00000i) q^{18} +(4.09282 - 1.80246i) q^{20} +(-2.14420 + 6.59917i) q^{21} +(3.93513 + 7.72313i) q^{22} +4.89898i q^{24} +(0.562811 - 4.96822i) q^{25} +(0.812857 - 5.13218i) q^{27} +(7.13893 - 3.63747i) q^{28} +(-8.89092 - 2.88884i) q^{29} +(4.73231 + 2.75776i) q^{30} +(2.47112 + 7.60531i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-4.81953 + 9.45887i) q^{33} +(0.504965 - 8.94368i) q^{35} +(-4.85410 + 3.52671i) q^{36} +(-1.61222 - 6.11562i) q^{40} +(8.74337 + 4.45497i) q^{42} +(11.6583 - 3.78800i) q^{44} +(0.674235 + 6.67423i) q^{45} +(6.84291 + 1.08381i) q^{48} -9.04886i q^{49} +(-6.81511 - 1.88526i) q^{50} +(-9.90359 + 5.04613i) q^{53} +(-6.98881 - 2.27080i) q^{54} +(2.90360 - 13.3940i) q^{55} +(-3.50146 - 10.7764i) q^{56} +(-6.00209 + 11.7798i) q^{58} +(4.99294 - 6.87220i) q^{59} +(4.89898 - 6.00000i) q^{60} +(11.1698 - 1.76912i) q^{62} +(1.88008 + 11.8703i) q^{63} +(-4.70228 - 6.47214i) q^{64} +(12.1459 + 8.82454i) q^{66} +(-12.3808 - 2.68396i) q^{70} +(3.85224 + 7.56044i) q^{72} +(-2.93471 - 0.464812i) q^{73} +(-3.03812 - 8.10986i) q^{75} +(3.84107 - 24.2516i) q^{77} +(16.8983 + 5.49059i) q^{79} +(-8.89898 + 0.898979i) q^{80} +(-2.78115 - 8.55951i) q^{81} +(-8.27209 + 16.2349i) q^{83} +(8.15702 - 11.2272i) q^{84} +(-15.9927 + 2.53299i) q^{87} +(-2.71191 - 17.1223i) q^{88} +(9.47175 + 0.534780i) q^{90} +(9.79391 + 9.79391i) q^{93} +(3.02774 - 9.31841i) q^{96} +(7.51450 + 14.7480i) q^{97} +(-12.6395 - 2.00190i) q^{98} +18.3873i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 4 q^{5} + 4 q^{7} - 8 q^{8} + 8 q^{10} - 24 q^{11} - 12 q^{15} + 16 q^{16} - 48 q^{18} - 8 q^{20} + 36 q^{21} - 16 q^{22} + 32 q^{28} + 12 q^{30} + 64 q^{32} + 12 q^{33} + 8 q^{35} - 24 q^{36}+ \cdots + 72 q^{98}+O(q^{100}) \) 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

Introduction

L-functions

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