LMFDB - Embedded newform 600.2.bp.a.197.1

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			197.1
Root			$0.786335 + 1.54327i$ of defining polynomial
Character	$\chi$	$=$	600.197
Dual form			600.2.bp.a.533.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26007 - 0.642040i) q^{2} +(-1.71073 + 0.270952i) q^{3} +(1.17557 - 1.61803i) q^{4} +(2.18531 + 0.473739i) q^{5} +(-1.98168 + 1.43977i) q^{6} +(1.93871 + 1.93871i) q^{7} +(0.442463 - 2.79360i) q^{8} +(2.85317 - 0.927051i) q^{9} +O(q^{10})$	\(q+(1.26007 - 0.642040i) q^{2} +(-1.71073 + 0.270952i) q^{3} +(1.17557 - 1.61803i) q^{4} +(2.18531 + 0.473739i) q^{5} +(-1.98168 + 1.43977i) q^{6} +(1.93871 + 1.93871i) q^{7} +(0.442463 - 2.79360i) q^{8} +(2.85317 - 0.927051i) q^{9} +(3.05781 - 0.806108i) q^{10} +(-1.74740 + 5.37793i) q^{11} +(-1.57267 + 3.08654i) q^{12} +(3.68764 + 1.19819i) q^{14} +(-3.86682 - 0.218323i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(3.00000 - 3.00000i) q^{18} +(3.33551 - 2.97899i) q^{20} +(-3.84189 - 2.79130i) q^{21} +(1.25100 + 7.89849i) q^{22} +4.89898i q^{24} +(4.55114 + 2.07053i) q^{25} +(-4.62981 + 2.35900i) q^{27} +(5.41598 - 0.857807i) q^{28} +(3.14375 - 4.32700i) q^{29} +(-5.01266 + 2.20755i) q^{30} +(7.96171 - 5.78452i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(1.53215 - 9.67364i) q^{33} +(3.31823 + 5.15511i) q^{35} +(1.85410 - 5.70634i) q^{36} +(2.29036 - 5.89527i) q^{40} +(-6.63319 - 1.05059i) q^{42} +(6.64749 + 9.14949i) q^{44} +(6.67423 - 0.674235i) q^{45} +(3.14534 + 6.17307i) q^{48} +0.517171i q^{49} +(7.06414 - 0.312992i) q^{50} +(-14.3417 + 2.27150i) q^{53} +(-4.31932 + 5.94504i) q^{54} +(-6.36634 + 10.9246i) q^{55} +(6.27379 - 4.55817i) q^{56} +(1.18325 - 7.47075i) q^{58} +(-5.10012 + 1.65713i) q^{59} +(-4.89898 + 6.00000i) q^{60} +(6.31845 - 12.4006i) q^{62} +(7.32874 + 3.73418i) q^{63} +(-7.60845 - 2.47214i) q^{64} +(-4.28023 - 13.1732i) q^{66} +(7.49100 + 4.36539i) q^{70} +(-1.32739 - 8.38081i) q^{72} +(-7.63962 - 14.9936i) q^{73} +(-8.34678 - 2.30897i) q^{75} +(-13.8139 + 7.03855i) q^{77} +(-8.25966 + 11.3684i) q^{79} +(-0.898979 - 8.89898i) q^{80} +(7.28115 - 5.29007i) q^{81} +(0.876698 - 5.53525i) q^{83} +(-9.03284 + 2.93495i) q^{84} +(-4.20569 + 8.25412i) q^{87} +(14.2507 + 7.26108i) q^{88} +(7.97714 - 5.13471i) q^{90} +(-12.0530 + 12.0530i) q^{93} +(7.92672 + 5.75910i) q^{96} +(2.97879 + 18.8074i) q^{97} +(0.332044 + 0.651673i) q^{98} +16.9641i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{17}{20}\right)$

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 $

$2$	1.26007	−	0.642040i	0.891007	−	0.453990i
$2$	1.26007	−	0.642040i	0.891007	−	0.453990i
$3$	−1.71073	+	0.270952i	−0.987688	+	0.156434i
$3$	−1.71073	+	0.270952i	−0.987688	+	0.156434i
$4$	1.17557	−	1.61803i	0.587785	−	0.809017i
$5$	2.18531	+	0.473739i	0.977299	+	0.211862i
$5$	2.18531	+	0.473739i	0.977299	+	0.211862i
$6$	−1.98168	+	1.43977i	−0.809017	+	0.587785i
$7$	1.93871	+	1.93871i	0.732762	+	0.732762i	0.971166	−	0.238404i	$-0.0766241\pi$
$7$	1.93871	+	1.93871i	0.732762	+	0.732762i	−0.238404	+	0.971166i	$0.576624\pi$
$8$	0.442463	−	2.79360i	0.156434	−	0.987688i
$9$	2.85317	−	0.927051i	0.951057	−	0.309017i
$10$	3.05781	−	0.806108i	0.966964	−	0.254914i
$11$	−1.74740	+	5.37793i	−0.526860	+	1.62151i	0.233748	+	0.972297i	$0.424901\pi$
$11$	−1.74740	+	5.37793i	−0.526860	+	1.62151i	−0.760608	+	0.649211i	$0.775099\pi$
$12$	−1.57267	+	3.08654i	−0.453990	+	0.891007i
$13$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$13$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$14$	3.68764	+	1.19819i	0.985563	+	0.320229i
$15$	−3.86682	−	0.218323i	−0.998410	−	0.0563708i
$16$	−1.23607	−	3.80423i	−0.309017	−	0.951057i
$17$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$17$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$18$	3.00000	−	3.00000i	0.707107	−	0.707107i
$19$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$19$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$20$	3.33551	−	2.97899i	0.745843	−	0.666122i
$21$	−3.84189	−	2.79130i	−0.838370	−	0.609112i
$22$	1.25100	+	7.89849i	0.266714	+	1.68396i
$23$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$23$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$24$			4.89898i			1.00000i
$25$	4.55114	+	2.07053i	0.910229	+	0.414106i
$26$		0			0
$27$	−4.62981	+	2.35900i	−0.891007	+	0.453990i
$28$	5.41598	−	0.857807i	1.02352	−	0.162110i
$29$	3.14375	−	4.32700i	0.583780	−	0.803504i	−0.410323	−	0.911940i	$-0.634584\pi$
$29$	3.14375	−	4.32700i	0.583780	−	0.803504i	0.994103	+	0.108436i	$0.0345842\pi$
$30$	−5.01266	+	2.20755i	−0.915182	+	0.403042i
$31$	7.96171	−	5.78452i	1.42996	−	1.03893i	0.439941	−	0.898027i	$-0.354999\pi$
$31$	7.96171	−	5.78452i	1.42996	−	1.03893i	0.990023	−	0.140904i	$-0.0450008\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	1.53215	−	9.67364i	0.266714	−	1.68396i
$34$		0			0
$35$	3.31823	+	5.15511i	0.560883	+	0.871373i
$36$	1.85410	−	5.70634i	0.309017	−	0.951057i
$37$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$37$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$38$		0			0
$39$		0			0
$40$	2.29036	−	5.89527i	0.362137	−	0.932125i
$41$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$41$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$42$	−6.63319	−	1.05059i	−1.02352	−	0.162110i
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$	6.64749	+	9.14949i	1.00215	+	1.37934i
$45$	6.67423	−	0.674235i	0.994936	−	0.100509i
$46$		0			0
$47$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$47$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$48$	3.14534	+	6.17307i	0.453990	+	0.891007i
$49$			0.517171i			0.0738815i
$50$	7.06414	−	0.312992i	0.999020	−	0.0442638i
$51$		0			0
$52$		0			0
$53$	−14.3417	+	2.27150i	−1.96998	+	0.312014i	−0.973433	+	0.228970i	$0.926464\pi$
$53$	−14.3417	+	2.27150i	−1.96998	+	0.312014i	−0.996546	+	0.0830438i	$0.973536\pi$
$54$	−4.31932	+	5.94504i	−0.587785	+	0.809017i
$55$	−6.36634	+	10.9246i	−0.858437	+	1.47308i
$56$	6.27379	−	4.55817i	0.838370	−	0.609112i
$57$		0			0
$58$	1.18325	−	7.47075i	0.155368	−	0.980958i
$59$	−5.10012	+	1.65713i	−0.663979	+	0.215740i	−0.621568	−	0.783360i	$-0.713504\pi$
$59$	−5.10012	+	1.65713i	−0.663979	+	0.215740i	−0.0424110	+	0.999100i	$0.513504\pi$
$60$	−4.89898	+	6.00000i	−0.632456	+	0.774597i
$61$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$61$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$62$	6.31845	−	12.4006i	0.802443	−	1.57488i
$63$	7.32874	+	3.73418i	0.923335	+	0.470462i
$64$	−7.60845	−	2.47214i	−0.951057	−	0.309017i
$65$		0			0
$66$	−4.28023	−	13.1732i	−0.526860	−	1.62151i
$67$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$67$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$68$		0			0
$69$		0			0
$70$	7.49100	+	4.36539i	0.895346	+	0.521763i
$71$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$71$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$72$	−1.32739	−	8.38081i	−0.156434	−	0.987688i
$73$	−7.63962	−	14.9936i	−0.894149	−	1.75487i	−0.602004	−	0.798493i	$-0.705631\pi$
$73$	−7.63962	−	14.9936i	−0.894149	−	1.75487i	−0.292145	−	0.956374i	$-0.594369\pi$
$74$		0			0
$75$	−8.34678	−	2.30897i	−0.963803	−	0.266617i
$76$		0			0
$77$	−13.8139	+	7.03855i	−1.57424	+	0.802117i
$78$		0			0
$79$	−8.25966	+	11.3684i	−0.929284	+	1.27905i	0.0308541	+	0.999524i	$0.490177\pi$
$79$	−8.25966	+	11.3684i	−0.929284	+	1.27905i	−0.960138	+	0.279526i	$0.909823\pi$
$80$	−0.898979	−	8.89898i	−0.100509	−	0.994936i
$81$	7.28115	−	5.29007i	0.809017	−	0.587785i
$82$		0			0
$83$	0.876698	−	5.53525i	0.0962301	−	0.607573i	−0.891695	−	0.452638i	$-0.850483\pi$
$83$	0.876698	−	5.53525i	0.0962301	−	0.607573i	0.987925	−	0.154935i	$-0.0495168\pi$
$84$	−9.03284	+	2.93495i	−0.985563	+	0.320229i
$85$		0			0
$86$		0			0
$87$	−4.20569	+	8.25412i	−0.450897	+	0.884935i
$88$	14.2507	+	7.26108i	1.51913	+	0.774033i
$89$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$89$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$90$	7.97714	−	5.13471i	0.840864	−	0.541246i
$91$		0			0
$92$		0			0
$93$	−12.0530	+	12.0530i	−1.24983	+	1.24983i
$94$		0			0
$95$		0			0
$96$	7.92672	+	5.75910i	0.809017	+	0.587785i
$97$	2.97879	+	18.8074i	0.302451	+	1.90960i	0.403985	+	0.914766i	$0.367625\pi$
$97$	2.97879	+	18.8074i	0.302451	+	1.90960i	−0.101535	+	0.994832i	$0.532375\pi$
$98$	0.332044	+	0.651673i	0.0335415	+	0.0658289i
$99$			16.9641i			1.70495i
$100$	8.70038	−	4.92985i	0.870038	−	0.492985i
$101$	19.2137			1.91183			0.955917	−	0.293636i	$-0.0948654\pi$
$101$	19.2137			1.91183			0.955917	+	0.293636i	$0.0948654\pi$
$102$		0			0
$103$	−12.1742	+	1.92820i	−1.19956	+	0.189991i	−0.724066	−	0.689730i	$-0.757729\pi$
$103$	−12.1742	+	1.92820i	−1.19956	+	0.189991i	−0.475489	+	0.879721i	$0.657729\pi$
$104$		0			0
$105$	−7.07338	−	7.91991i	−0.690291	−	0.772904i
$106$	−16.6132	+	12.0702i	−1.61361	+	1.17236i
$107$	−14.1202	−	14.1202i	−1.36505	−	1.36505i	−0.867353	−	0.497694i	$-0.834180\pi$
$107$	−14.1202	−	14.1202i	−1.36505	−	1.36505i	−0.497694	−	0.867353i	$-0.665820\pi$
$108$	−1.62571	+	10.2644i	−0.156434	+	0.987688i
$109$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$109$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$110$	−1.00801	+	17.8533i	−0.0961096	+	1.70224i
$111$		0			0
$112$	4.97891	−	9.77165i	0.470462	−	0.923335i
$113$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$113$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$114$		0			0
$115$		0			0
$116$	−3.30554	−	10.1734i	−0.306911	−	0.944576i
$117$		0			0
$118$	−5.36258	+	5.36258i	−0.493666	+	0.493666i
$119$		0			0
$120$	−2.32084	+	10.7058i	−0.211862	+	0.977299i
$121$	−16.9696	−	12.3291i	−1.54269	−	1.12083i
$122$		0			0
$123$		0			0
$124$		−	19.6824i		−	1.76753i
$125$	8.96476	+	6.68080i	0.801832	+	0.597549i
$126$	11.6322			1.03628
$127$	−15.4840	+	7.88947i	−1.37398	+	0.700077i	−0.976092	−	0.217357i	$-0.930256\pi$
$127$	−15.4840	+	7.88947i	−1.37398	+	0.700077i	−0.397887	+	0.917434i	$0.630256\pi$
$128$	−11.1744	+	1.76985i	−0.987688	+	0.156434i
$129$		0			0
$130$		0			0
$131$	14.9260	−	10.8443i	1.30409	−	0.947474i	0.304100	−	0.952640i	$-0.401644\pi$
$131$	14.9260	−	10.8443i	1.30409	−	0.947474i	0.999987	+	0.00516600i	$0.00164440\pi$
$132$	−13.8511	−	13.8511i	−1.20559	−	1.20559i
$133$		0			0
$134$		0			0
$135$	−11.2351	+	2.96183i	−0.966964	+	0.254914i
$136$		0			0
$137$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$137$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$138$		0			0
$139$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$139$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$140$	12.2420	+	0.691188i	1.03463	+	0.0584161i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−7.05342	−	9.70820i	−0.587785	−	0.809017i
$145$	8.91993	−	7.96652i	0.740760	−	0.661583i
$146$	−19.2530	−	13.9881i	−1.59339	−	1.15766i
$147$	−0.140129	−	0.884738i	−0.0115576	−	0.0729719i
$148$		0			0
$149$			8.48854i			0.695408i	0.937604	+	0.347704i	$0.113039\pi$
$149$			8.48854i			0.695408i	−0.937604	+	0.347704i	$0.886961\pi$
$150$	−12.0000	+	2.44949i	−0.979796	+	0.200000i
$151$	−16.0158			−1.30335			−0.651673	−	0.758500i	$-0.725932\pi$
$151$	−16.0158			−1.30335			−0.651673	+	0.758500i	$0.725932\pi$
$152$		0			0
$153$		0			0
$154$	−12.8875	+	17.7382i	−1.03851	+	1.42938i
$155$	20.1391	−	8.86918i	1.61761	−	0.712390i
$156$		0			0
$157$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$157$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$158$	−3.10879	+	19.6281i	−0.247322	+	1.56153i
$159$	23.9192	−	7.77182i	1.89692	−	0.616345i
$160$	−6.84628	−	10.6362i	−0.541246	−	0.840864i
$161$		0			0
$162$	5.77836	−	11.3407i	0.453990	−	0.891007i
$163$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$163$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$164$		0			0
$165$	7.93101	−	20.4140i	0.617428	−	1.58923i
$166$	−2.44915	−	7.53770i	−0.190091	−	0.585039i
$167$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$167$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$168$	−9.49769	+	9.49769i	−0.732762	+	0.732762i
$169$	7.64121	+	10.5172i	0.587785	+	0.809017i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.64993	−	5.20079i	−0.201471	−	0.395409i	0.768060	−	0.640378i	$-0.221222\pi$
$173$	−2.64993	−	5.20079i	−0.201471	−	0.395409i	−0.969531	+	0.244969i	$0.921222\pi$
$174$			13.1010i			0.993186i
$175$	4.80918	+	12.8375i	0.363540	+	0.970423i
$176$	22.6188			1.70495
$177$	8.27590	−	4.21678i	0.622055	−	0.316953i
$178$		0			0
$179$	13.0373	−	17.9443i	0.974451	−	1.34122i	0.0346846	−	0.999398i	$-0.488957\pi$
$179$	13.0373	−	17.9443i	0.974451	−	1.34122i	0.939766	−	0.341818i	$-0.111043\pi$
$180$	6.75510	−	11.5917i	0.503495	−	0.863998i
$181$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$181$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	−7.44915	+	22.9261i	−0.546198	+	1.68102i
$187$		0			0
$188$		0			0
$189$	−13.5493	−	4.40242i	−0.985563	−	0.320229i
$190$		0			0
$191$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$191$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$192$	13.6858	+	2.16762i	0.987688	+	0.156434i
$193$	−3.96689	+	3.96689i	−0.285543	+	0.285543i	−0.835315	−	0.549772i	$-0.814715\pi$
$193$	−3.96689	+	3.96689i	−0.285543	+	0.285543i	0.549772	+	0.835315i	$0.314715\pi$
$194$	15.8286	+	21.7861i	1.13642	+	1.56415i
$195$		0			0
$196$	0.836800	+	0.607971i	0.0597714	+	0.0434265i
$197$	4.36924	+	27.5863i	0.311295	+	1.96544i	0.254581	+	0.967051i	$0.418062\pi$
$197$	4.36924	+	27.5863i	0.311295	+	1.96544i	0.0567145	+	0.998390i	$0.481938\pi$
$198$	10.8916	+	21.3760i	0.774033	+	1.51913i
$199$		−	18.9698i		−	1.34473i	−0.740218	−	0.672367i	$-0.765278\pi$
$199$		−	18.9698i		−	1.34473i	0.740218	−	0.672367i	$-0.234722\pi$
$200$	7.79796	−	11.7980i	0.551399	−	0.834242i
$201$		0			0
$202$	24.2107	−	12.3360i	1.70346	−	0.867955i
$203$	14.4836	−	2.29398i	1.01655	−	0.161006i
$204$		0			0
$205$		0			0
$206$	−14.1024	+	10.2460i	−0.982558	+	0.713870i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	−13.9979	−	5.43828i	−0.965945	−	0.375277i
$211$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$211$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$212$	−13.1843	+	25.8756i	−0.905500	+	1.77714i
$213$		0			0
$214$	−26.8581	−	8.72673i	−1.83598	−	0.596547i
$215$		0			0
$216$	4.54160	+	13.9776i	0.309017	+	0.951057i
$217$	26.6499	+	4.22093i	1.80911	+	0.286535i
$218$		0			0
$219$	17.1318	+	23.5800i	1.15766	+	1.59339i
$220$	10.1924	+	23.1436i	0.687168	+	1.56034i
$221$		0			0
$222$		0			0
$223$	0.586245	+	1.15057i	0.0392579	+	0.0770479i	0.909802	−	0.415042i	$-0.136233\pi$
$223$	0.586245	+	1.15057i	0.0392579	+	0.0770479i	−0.870544	+	0.492090i	$0.836233\pi$
$224$		−	15.5097i		−	1.03628i
$225$	14.9047	+	1.68843i	0.993645	+	0.112562i
$226$		0			0
$227$	21.1066	−	10.7544i	1.40090	−	0.713793i	0.419856	−	0.907591i	$-0.362081\pi$
$227$	21.1066	−	10.7544i	1.40090	−	0.713793i	0.981041	+	0.193798i	$0.0620806\pi$
$228$		0			0
$229$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$229$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$230$		0			0
$231$	21.7247	−	15.7840i	1.42938	−	1.03851i
$232$	−10.6969	−	10.6969i	−0.702288	−	0.702288i
$233$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$233$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$234$		0			0
$235$		0			0
$236$	−3.31426	+	10.2002i	−0.215740	+	0.663979i
$237$	11.0497	−	21.6863i	0.717756	−	1.40867i
$238$		0			0
$239$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$239$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$240$	3.94911	+	14.9801i	0.254914	+	0.966964i
$241$	−9.16483	−	28.2064i	−0.590358	−	1.81694i	−0.576594	−	0.817031i	$-0.695619\pi$
$241$	−9.16483	−	28.2064i	−0.590358	−	1.81694i	−0.0137643	−	0.999905i	$-0.504381\pi$
$242$	−29.2987	−	4.64046i	−1.88339	−	0.298300i
$243$	−11.0227	+	11.0227i	−0.707107	+	0.707107i
$244$		0			0
$245$	−0.245004	+	1.13018i	−0.0156527	+	0.0722044i
$246$		0			0
$247$		0			0
$248$	−12.6369	−	24.8013i	−0.802443	−	1.57488i
$249$			9.70684i			0.615146i
$250$	15.5856	+	2.66257i	0.985719	+	0.168396i
$251$	−31.6780			−1.99950			−0.999749	−	0.0224095i	$-0.992866\pi$
$251$	−31.6780			−1.99950			−0.999749	+	0.0224095i	$0.992866\pi$
$252$	14.6575	−	7.46836i	0.923335	−	0.470462i
$253$		0			0
$254$	−14.4456	+	19.8826i	−0.906396	+	1.24755i
$255$		0			0
$256$	−12.9443	+	9.40456i	−0.809017	+	0.587785i
$257$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$257$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	4.95830	−	15.2601i	0.306911	−	0.944576i
$262$	11.8453	−	23.2477i	0.731805	−	1.43625i
$263$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$263$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$264$	−26.3464	−	8.56046i	−1.62151	−	0.526860i
$265$	−32.4171	−	1.83028i	−1.99136	−	0.112434i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−17.1069	−	23.5456i	−1.04302	−	1.43560i	−0.894704	−	0.446660i	$-0.852613\pi$
$269$	−17.1069	−	23.5456i	−1.04302	−	1.43560i	−0.148320	−	0.988939i	$-0.547387\pi$
$270$	−12.2554	+	10.9455i	−0.745843	+	0.666122i
$271$	26.0472	+	18.9244i	1.58225	+	1.14958i	0.914052	+	0.405596i	$0.132936\pi$
$271$	26.0472	+	18.9244i	1.58225	+	1.14958i	0.668202	+	0.743980i	$0.267064\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−19.0878	+	20.8577i	−1.15104	+	1.25777i
$276$		0			0
$277$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$277$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$278$		0			0
$279$	17.3536	−	23.8851i	1.03893	−	1.42996i
$280$	15.8695	−	6.98888i	0.948387	−	0.417665i
$281$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$281$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$282$		0			0
$283$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$283$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−15.1209	−	7.70447i	−0.891007	−	0.453990i
$289$	16.1680	+	5.25329i	0.951057	+	0.309017i
$290$	6.12496	−	15.7653i	0.359670	−	0.925773i
$291$	−10.1918	−	31.3671i	−0.597454	−	1.83877i
$292$	−33.2410	−	5.26486i	−1.94528	−	0.308103i
$293$	2.69816	−	2.69816i	0.157628	−	0.157628i	−0.623887	−	0.781515i	$-0.714447\pi$
$293$	2.69816	−	2.69816i	0.157628	−	0.157628i	0.781515	+	0.623887i	$0.214447\pi$
$294$	−0.744609	−	1.02487i	−0.0434265	−	0.0597714i
$295$	−11.9304	+	1.20521i	−0.694613	+	0.0701702i
$296$		0			0
$297$	−4.59646	−	29.0209i	−0.266714	−	1.68396i
$298$	5.44998	+	10.6962i	0.315709	+	0.619613i
$299$		0			0
$300$	−13.5482	+	10.7910i	−0.782206	+	0.623019i
$301$		0			0
$302$	−20.1811	+	10.2828i	−1.16129	+	0.591706i
$303$	−32.8694	+	5.20600i	−1.88830	+	0.299077i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$307$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$308$	−4.85064	+	30.6257i	−0.276391	+	1.74506i
$309$	20.3042	−	6.59724i	1.15507	−	0.375304i
$310$	19.6824	−	24.1059i	1.11789	−	1.36913i
$311$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$311$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$312$		0			0
$313$	−5.97476	−	3.04429i	−0.337713	−	0.172074i	0.276907	−	0.960897i	$-0.410691\pi$
$313$	−5.97476	−	3.04429i	−0.337713	−	0.172074i	−0.614620	+	0.788823i	$0.710691\pi$
$314$		0			0
$315$	14.2465	+	11.6322i	0.802701	+	0.655403i
$316$	8.68472	+	26.7288i	0.488554	+	1.50361i
$317$	6.77399	+	1.07289i	0.380465	+	0.0602598i	0.343738	−	0.939066i	$-0.388307\pi$
$317$	6.77399	+	1.07289i	0.380465	+	0.0602598i	0.0367271	+	0.999325i	$0.488307\pi$
$318$	25.1501	−	25.1501i	1.41035	−	1.41035i
$319$	17.7770	+	24.4679i	0.995318	+	1.36994i
$320$	−15.4557	−	9.00680i	−0.863998	−	0.503495i
$321$	27.9816	+	20.3298i	1.56178	+	1.13470i
$322$		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
$330$	−3.11297	−	30.8152i	−0.171363	−	1.69632i
$331$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$331$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$332$	−7.92560	−	7.92560i	−0.434974	−	0.434974i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−5.86989	+	18.0657i	−0.320229	+	0.985563i
$337$	−14.7427	+	28.9341i	−0.803085	+	1.57614i	0.0141927	+	0.999899i	$0.495482\pi$
$337$	−14.7427	+	28.9341i	−0.803085	+	1.57614i	−0.817278	+	0.576244i	$0.804518\pi$
$338$	16.3810	+	8.34651i	0.891007	+	0.453990i
$339$		0			0
$340$		0			0
$341$	17.1965	+	52.9254i	0.931243	+	2.86607i
$342$		0			0
$343$	12.5683	−	12.5683i	0.678625	−	0.678625i
$344$		0			0
$345$		0			0
$346$	−6.67822	−	4.85201i	−0.359023	−	0.260846i
$347$	−5.38028	−	33.9698i	−0.288829	−	1.82359i	−0.524093	−	0.851661i	$-0.675596\pi$
$347$	−5.38028	−	33.9698i	−0.288829	−	1.82359i	0.235264	−	0.971931i	$-0.424404\pi$
$348$	8.41137	+	16.5082i	0.450897	+	0.884935i
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	14.3021	+	13.0885i	0.764479	+	0.699609i
$351$		0			0
$352$	28.5013	−	14.5222i	1.51913	−	0.774033i
$353$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$353$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$354$	7.72090	−	10.6269i	0.410361	−	0.564814i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	4.90699	−	30.9815i	0.259342	−	1.63742i
$359$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$359$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$360$	1.06956	−	18.9435i	0.0563708	−	0.998410i
$361$	−5.87132	+	18.0701i	−0.309017	+	0.951057i
$362$		0			0
$363$	32.3710	+	16.4938i	1.69903	+	0.865701i
$364$		0			0
$365$	−9.59187	−	36.3848i	−0.502061	−	1.90447i
$366$		0			0
$367$	1.09223	+	0.172992i	0.0570139	+	0.00903012i	0.184876	−	0.982762i	$-0.440812\pi$
$367$	1.09223	+	0.172992i	0.0570139	+	0.00903012i	−0.127862	+	0.991792i	$0.540812\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−32.2081	−	23.4005i	−1.67216	−	1.21489i
$372$	5.33300	+	33.6712i	0.276503	+	1.74577i
$373$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$373$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$374$		0			0
$375$	−17.1464	−	9.00000i	−0.885438	−	0.464758i
$376$		0			0
$377$		0			0
$378$	−19.8996	+	3.15178i	−1.02352	+	0.162110i
$379$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$379$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$380$		0			0
$381$	24.3511	−	17.6921i	1.24755	−	0.906396i
$382$		0			0
$383$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$383$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$384$	18.6368	−	6.05547i	0.951057	−	0.309017i
$385$	−33.5221	+	8.83720i	−1.70845	+	0.450386i
$386$	−2.45167	+	7.54548i	−0.124787	+	0.384055i
$387$		0			0
$388$	33.9327	+	17.2896i	1.72267	+	0.877746i
$389$	−7.11475	−	2.31172i	−0.360732	−	0.117209i	0.123043	−	0.992401i	$-0.460735\pi$
$389$	−7.11475	−	2.31172i	−0.360732	−	0.117209i	−0.483775	+	0.875192i	$0.660735\pi$
$390$		0			0
$391$		0			0
$392$	1.44477	+	0.228829i	0.0729719	+	0.0115576i
$393$	−22.5959	+	22.5959i	−1.13981	+	1.13981i
$394$	23.2171	+	31.9555i	1.16966	+	1.60990i
$395$	−23.4356	+	20.9306i	−1.17917	+	1.05313i
$396$	27.4485	+	19.9425i	1.37934	+	1.00215i
$397$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$397$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$398$	−12.1794	−	23.9033i	−0.610496	−	1.19817i
$399$		0			0
$400$	2.25125	−	19.8729i	0.112562	−	0.993645i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$		0			0
$404$	22.5871	−	31.0884i	1.12375	−	1.54671i
$405$	18.4177	−	8.11106i	0.915182	−	0.403042i
$406$	16.7776	−	12.1896i	0.832657	−	0.604961i
$407$		0			0
$408$		0			0
$409$	20.5633	−	6.68141i	1.01679	−	0.330375i	0.247234	−	0.968956i	$-0.420478\pi$
$409$	20.5633	−	6.68141i	1.01679	−	0.330375i	0.769554	+	0.638581i	$0.220478\pi$
$410$		0			0
$411$		0			0
$412$	−11.1917	+	21.9649i	−0.551375	+	1.08213i
$413$	−13.1003	−	6.67495i	−0.644625	−	0.328453i
$414$		0			0
$415$	4.53812	−	11.6809i	0.222767	−	0.573393i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	23.9441	+	32.9563i	1.16975	+	1.61002i	0.665300	+	0.746576i	$0.268303\pi$
$419$	23.9441	+	32.9563i	1.16975	+	1.61002i	0.504447	+	0.863443i	$0.331697\pi$
$420$	−21.1299	+	2.13456i	−1.03103	+	0.104156i
$421$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$421$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$422$		0			0
$423$		0			0
$424$			41.0700i			1.99454i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−39.4461	+	6.24765i	−1.90670	+	0.301992i
$429$		0			0
$430$		0			0
$431$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$431$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$432$	14.6969	+	14.6969i	0.707107	+	0.707107i
$433$	6.45700	−	40.7679i	0.310303	−	1.95918i	0.0289266	−	0.999582i	$-0.490791\pi$
$433$	6.45700	−	40.7679i	0.310303	−	1.95918i	0.281377	−	0.959597i	$-0.409209\pi$
$434$	36.2908	−	11.7916i	1.74202	−	0.566015i
$435$	−13.1010	+	16.0454i	−0.628146	+	0.769318i
$436$		0			0
$437$		0			0
$438$	36.7266	+	18.7132i	1.75487	+	0.894149i
$439$	−12.1635	−	3.95216i	−0.580532	−	0.188626i	0.00400696	−	0.999992i	$-0.498725\pi$
$439$	−12.1635	−	3.95216i	−0.580532	−	0.188626i	−0.584539	+	0.811366i	$0.698725\pi$
$440$	27.7022	+	22.6188i	1.32065	+	1.07831i
$441$	0.479444	+	1.47558i	0.0228306	+	0.0702655i
$442$		0			0
$443$	29.5908	−	29.5908i	1.40590	−	1.40590i	0.626401	−	0.779501i	$-0.284527\pi$
$443$	29.5908	−	29.5908i	1.40590	−	1.40590i	0.779501	−	0.626401i	$-0.215473\pi$
$444$		0			0
$445$		0			0
$446$	1.47742	+	1.07341i	0.0699580	+	0.0508275i
$447$	−2.29999	−	14.5216i	−0.108786	−	0.686846i
$448$	−9.95781	−	19.5433i	−0.470462	−	0.923335i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	19.8650	−	7.44184i	0.936446	−	0.350812i
$451$		0			0
$452$		0			0
$453$	27.3986	−	4.33951i	1.28730	−	0.203888i
$454$	19.6912	−	27.1026i	0.924153	−	1.27199i
$455$		0			0
$456$		0			0
$457$	17.6507	+	17.6507i	0.825666	+	0.825666i	0.986914	−	0.161248i	$-0.0515519\pi$
$457$	17.6507	+	17.6507i	0.825666	+	0.825666i	−0.161248	+	0.986914i	$0.551552\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4.20086	+	12.9289i	−0.195654	+	0.602160i	0.804315	+	0.594204i	$0.202533\pi$
$461$	−4.20086	+	12.9289i	−0.195654	+	0.602160i	−0.999968	+	0.00795653i	$0.997467\pi$
$462$	17.2409	−	33.8371i	0.802117	−	1.57424i
$463$	5.22480	+	2.66217i	0.242817	+	0.123722i	0.571165	−	0.820835i	$-0.306492\pi$
$463$	5.22480	+	2.66217i	0.242817	+	0.123722i	−0.328348	+	0.944557i	$0.606492\pi$
$464$	−20.3468	−	6.61107i	−0.944576	−	0.306911i
$465$	−32.0494	+	20.6295i	−1.48626	+	0.956670i
$466$		0			0
$467$	28.3558	+	4.49111i	1.31215	+	0.207824i	0.773010	−	0.634393i	$-0.218750\pi$
$467$	28.3558	+	4.49111i	1.31215	+	0.207824i	0.539138	+	0.842217i	$0.318750\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	2.37275	+	14.9809i	0.109214	+	0.689553i
$473$		0			0
$474$		−	34.4206i		−	1.58099i
$475$		0			0
$476$		0			0
$477$	−38.8134	+	19.7764i	−1.77714	+	0.905500i
$478$		0			0
$479$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$479$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$480$	14.5940	+	16.3406i	0.666122	+	0.745843i
$481$		0			0
$482$	−29.6580	−	29.6580i	−1.35088	−	1.35088i
$483$		0			0
$484$	−39.8979	+	12.9636i	−1.81354	+	0.589255i
$485$	−2.40020	+	42.5110i	−0.108987	+	1.93033i
$486$	−6.81241	+	20.9664i	−0.309017	+	0.951057i
$487$	9.89646	−	19.4229i	0.448451	−	0.880135i	−0.550521	−	0.834821i	$-0.685571\pi$
$487$	9.89646	−	19.4229i	0.448451	−	0.880135i	0.998973	−	0.0453143i	$-0.0144289\pi$
$488$		0			0
$489$		0			0
$490$	0.416896	+	1.58141i	0.0188334	+	0.0714408i
$491$	12.7240	+	39.1604i	0.574226	+	1.76728i	0.638801	+	0.769372i	$0.279431\pi$
$491$	12.7240	+	39.1604i	0.574226	+	1.76728i	−0.0645759	+	0.997913i	$0.520569\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−8.03655	+	37.0718i	−0.361216	+	1.66625i
$496$	−31.8468	−	23.1381i	−1.42996	−	1.03893i
$497$		0			0
$498$	6.23218	+	12.2313i	0.279271	+	0.548099i
$499$		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
$502$	−39.9166	+	20.3385i	−1.78157	+	0.907753i
$503$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$503$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$504$	13.6745	−	18.8214i	0.609112	−	0.838370i
$505$	41.9879	+	9.10228i	1.86843	+	0.405046i
$506$		0			0
$507$	−15.9217	−	15.9217i	−0.707107	−	0.707107i
$508$	−5.43705	+	34.3282i	−0.241230	+	1.52307i
$509$	−39.3824	+	12.7961i	−1.74559	+	0.567177i	−0.995552	−	0.0942147i	$-0.969966\pi$
$509$	−39.3824	+	12.7961i	−1.74559	+	0.567177i	−0.750040	+	0.661392i	$0.769966\pi$
$510$		0			0
$511$	14.2572	−	43.8792i	0.630701	−	1.94110i
$512$	−10.2726	+	20.1612i	−0.453990	+	0.891007i
$513$		0			0
$514$		0			0
$515$	−27.5178	−	1.55367i	−1.21258	−	0.0684628i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	5.94248	+	8.17912i	0.260846	+	0.359023i
$520$		0			0
$521$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$521$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$522$	−3.54975	−	22.4123i	−0.155368	−	0.980958i
$523$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$523$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$524$		−	36.8990i		−	1.61194i
$525$	−11.7055	−	20.6584i	−0.510872	−	0.901605i
$526$		0			0
$527$		0			0
$528$	−38.6945	+	6.12861i	−1.68396	+	0.266714i
$529$	−13.5191	+	18.6074i	−0.587785	+	0.809017i
$530$	−42.0230	+	18.5067i	−1.82536	+	0.803881i
$531$	−13.0153	+	9.45614i	−0.564814	+	0.410361i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−24.1676	−	37.5461i	−1.04486	−	1.62326i
$536$		0			0
$537$	−17.4411	+	34.2302i	−0.752641	+	1.47714i
$538$	−36.6731	−	18.6859i	−1.58109	−	0.805605i
$539$	−2.78131	−	0.903702i	−0.119800	−	0.0389252i
$540$	−8.41531	+	21.6606i	−0.362137	+	0.932125i
$541$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$541$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$542$	44.9716	+	7.12280i	1.93170	+	0.305951i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$547$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$548$		0			0
$549$		0			0
$550$	−10.6606	+	38.5374i	−0.454569	+	1.64324i
$551$		0			0
$552$		0			0
$553$	−38.0531	+	6.02703i	−1.61818	+	0.256295i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	19.8840	+	19.8840i	0.842511	+	0.842511i	0.989185	−	0.146674i	$-0.0468568\pi$
$557$	19.8840	+	19.8840i	0.842511	+	0.842511i	−0.146674	+	0.989185i	$0.546857\pi$
$558$	6.53156	−	41.2387i	0.276503	−	1.74577i
$559$		0			0
$560$	15.5097	−	18.9954i	0.655403	−	0.802701i
$561$		0			0
$562$		0			0
$563$	−12.6546	−	6.44785i	−0.533329	−	0.271744i	0.166517	−	0.986039i	$-0.446748\pi$
$563$	−12.6546	−	6.44785i	−0.533329	−	0.271744i	−0.699846	+	0.714294i	$0.746748\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	24.3719	+	3.86013i	1.02352	+	0.162110i
$568$		0			0
$569$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$569$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$570$		0			0
$571$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$571$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−24.0000			−1.00000
$577$	−29.3444	+	14.9517i	−1.22162	+	0.622447i	−0.941336	−	0.337470i	$-0.890429\pi$
$577$	−29.3444	+	14.9517i	−1.22162	+	0.622447i	−0.280285	+	0.959917i	$0.590429\pi$
$578$	23.7456	−	3.76094i	0.987688	−	0.156434i
$579$	5.71143	−	7.86111i	0.237359	−	0.326696i
$580$	−2.40408	−	23.7980i	−0.0998241	−	0.988156i
$581$	12.4309	−	9.03157i	0.515720	−	0.374693i
$582$	−32.9813	−	32.9813i	−1.36712	−	1.36712i
$583$	12.8446	−	81.0977i	0.531970	−	3.35873i
$584$	−45.2664	+	14.7079i	−1.87314	+	0.608619i
$585$		0			0
$586$	1.66755	−	5.13220i	0.0688860	−	0.212009i
$587$	1.12965	−	2.21706i	0.0466257	−	0.0915080i	−0.866518	−	0.499146i	$-0.833647\pi$
$587$	1.12965	−	2.21706i	0.0466257	−	0.0915080i	0.913144	+	0.407638i	$0.133647\pi$
$588$	−1.59627	−	0.813338i	−0.0658289	−	0.0335415i
$589$		0			0
$590$	−14.2594	+	9.17843i	−0.587048	+	0.377870i
$591$	−14.9491	−	46.0087i	−0.614926	−	1.89255i
$592$		0			0
$593$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$593$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$594$	−24.4244	−	33.6174i	−1.00215	−	1.37934i
$595$		0			0
$596$	13.7347	+	9.97887i	0.562597	+	0.408751i
$597$	5.13991	+	32.4521i	0.210363	+	1.32818i
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	−10.1435	+	22.2960i	−0.414106	+	0.910229i
$601$	47.2101			1.92574			0.962870	−	0.269965i	$-0.0870123\pi$
$601$	47.2101			1.92574			0.962870	+	0.269965i	$0.0870123\pi$
$602$		0			0
$603$		0			0
$604$	−18.8277	+	25.9141i	−0.766087	+	1.05443i
$605$	−31.2430	−	34.9821i	−1.27021	−	1.42223i
$606$	−38.0754	+	27.6634i	−1.54671	+	1.12375i
$607$	34.8413	+	34.8413i	1.41416	+	1.41416i	0.713032	+	0.701131i	$0.247321\pi$
$607$	34.8413	+	34.8413i	1.41416	+	1.41416i	0.701131	+	0.713032i	$0.252679\pi$
$608$		0			0
$609$	−24.1559	+	7.84874i	−0.978847	+	0.318047i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$613$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$614$		0			0
$615$		0			0
$616$	13.5508	+	41.7050i	0.545976	+	1.68034i
$617$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$617$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$618$	21.3491	−	21.3491i	0.858787	−	0.858787i
$619$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$619$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$620$	9.32433	−	43.0122i	0.374474	−	1.72741i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	16.4258	+	18.8466i	0.657032	+	0.753863i
$626$	−9.48320			−0.379025
$627$		0			0
$628$		0			0
$629$		0			0
$630$	25.4200	+	5.51065i	1.01276	+	0.219549i
$631$	−3.96336	+	2.87955i	−0.157779	+	0.114633i	−0.663873	−	0.747845i	$-0.731089\pi$
$631$	−3.96336	+	2.87955i	−0.157779	+	0.114633i	0.506095	+	0.862478i	$0.331089\pi$
$632$	28.1043	+	28.1043i	1.11793	+	1.11793i
$633$		0			0
$634$	9.22457	−	2.99724i	0.366354	−	0.119036i
$635$	−37.5748	+	9.90557i	−1.49111	+	0.393091i
$636$	15.5436	−	47.8384i	0.616345	−	1.89692i
$637$		0			0
$638$	38.1096	+	19.4178i	1.50877	+	0.768759i
$639$		0			0
$640$	−25.2580	−	1.42608i	−0.998410	−	0.0563708i
$641$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$641$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$642$	48.3114	+	7.65178i	1.90670	+	0.301992i
$643$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$643$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$647$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$648$	−11.5567	−	22.6813i	−0.453990	−	0.891007i
$649$		−	30.3238i		−	1.19031i
$650$		0			0
$651$	−46.7344			−1.83166
$652$		0			0
$653$	−28.3659	+	4.49271i	−1.11004	+	0.175813i	−0.684420	−	0.729088i	$-0.739945\pi$
$653$	−28.3659	+	4.49271i	−1.11004	+	0.175813i	−0.425622	+	0.904901i	$0.639945\pi$
$654$		0			0
$655$	37.7552	−	16.6272i	1.47522	−	0.649679i
$656$		0			0
$657$	−35.6969	−	35.6969i	−1.39267	−	1.39267i
$658$		0			0
$659$	−46.1177	+	14.9845i	−1.79649	+	0.583715i	−0.999787	−	0.0206555i	$-0.993425\pi$
$659$	−46.1177	+	14.9845i	−1.79649	+	0.583715i	−0.796703	+	0.604371i	$0.793425\pi$
$660$	−23.7071	−	36.8308i	−0.922799	−	1.43364i
$661$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$661$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$662$		0			0
$663$		0			0
$664$	−15.0754	−	4.89829i	−0.585039	−	0.190091i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−1.31465	−	1.80947i	−0.0508275	−	0.0699580i
$670$		0			0
$671$		0			0
$672$	4.20238	+	26.5328i	0.162110	+	1.02352i
$673$	12.4622	+	24.4585i	0.480384	+	0.942807i	0.996282	+	0.0861567i	$0.0274586\pi$
$673$	12.4622	+	24.4585i	0.480384	+	0.942807i	−0.515897	+	0.856650i	$0.672541\pi$
$674$			45.9245i			1.76895i
$675$	−25.9553	+	1.15001i	−0.999020	+	0.0442638i
$676$	26.0000			1.00000
$677$	25.1745	−	12.8270i	0.967534	−	0.492983i	0.102520	−	0.994731i	$-0.467310\pi$
$677$	25.1745	−	12.8270i	0.967534	−	0.492983i	0.865014	+	0.501748i	$0.167310\pi$
$678$		0			0
$679$	−30.6869	+	42.2370i	−1.17766	+	1.62091i
$680$		0			0
$681$	−33.1938	+	24.1167i	−1.27199	+	0.924153i
$682$	55.6490	+	55.6490i	2.13091	+	2.13091i
$683$	8.00419	−	50.5365i	0.306272	−	1.93372i	−0.0486213	−	0.998817i	$-0.515483\pi$
$683$	8.00419	−	50.5365i	0.306272	−	1.93372i	0.354893	−	0.934907i	$-0.384517\pi$
$684$		0			0
$685$		0			0
$686$	7.76764	−	23.9063i	0.296570	−	0.912748i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$691$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$692$	−11.5302	−	1.82621i	−0.438314	−	0.0694221i
$693$	−32.8884	+	32.8884i	−1.24933	+	1.24933i
$694$	−28.5895	−	39.3500i	−1.08524	−	1.49371i
$695$		0			0
$696$	21.1979	+	15.4012i	0.803504	+	0.583780i
$697$		0			0
$698$		0			0
$699$		0			0
$700$	26.4250	+	7.30995i	0.998772	+	0.276290i
$701$	−52.9444			−1.99968			−0.999841	−	0.0178345i	$-0.994323\pi$
$701$	−52.9444			−1.99968			−0.999841	+	0.0178345i	$0.994323\pi$
$702$		0			0
$703$		0			0
$704$	26.5900	−	36.5980i	1.00215	−	1.37934i
$705$		0			0
$706$		0			0
$707$	37.2497	+	37.2497i	1.40092	+	1.40092i
$708$	2.90601	−	18.3478i	0.109214	−	0.689553i
$709$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$709$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$710$		0			0
$711$	−13.0271	+	40.0932i	−0.488554	+	1.50361i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−13.7082	−	42.1895i	−0.512299	−	1.57669i
$717$		0			0
$718$		0			0
$719$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$719$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$720$	−10.8147	−	24.5569i	−0.403042	−	0.915182i
$721$	−27.3403	−	19.8639i	−1.01821	−	0.739771i
$722$	4.20340	+	26.5392i	0.156434	+	0.987688i
$723$	23.3211	+	45.7703i	0.867321	+	1.70221i
$724$		0			0
$725$	23.2669	−	13.1836i	0.864109	−	0.489626i
$726$	51.3795			1.90687
$727$	−35.2120	+	17.9414i	−1.30594	+	0.665410i	−0.961863	−	0.273532i	$-0.911808\pi$
$727$	−35.2120	+	17.9414i	−1.30594	+	0.665410i	−0.344077	+	0.938941i	$0.611808\pi$
$728$		0			0
$729$	15.8702	−	21.8435i	0.587785	−	0.809017i
$730$	−35.4469	−	39.6892i	−1.31195	−	1.46896i
$731$		0			0
$732$		0			0
$733$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$733$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$734$	1.48736	−	0.483272i	0.0548994	−	0.0178379i
$735$	0.112910	−	1.99981i	0.00416476	−	0.0737640i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$739$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$740$		0			0
$741$		0			0
$742$	−55.6086	−	8.80753i	−2.04146	−	0.323335i
$743$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$743$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$744$	28.3382	+	39.0042i	1.03893	+	1.42996i
$745$	−4.02135	+	18.5501i	−0.147331	+	0.679622i
$746$		0			0
$747$	−2.63009	−	16.6058i	−0.0962301	−	0.607573i
$748$		0			0
$749$		−	54.7497i		−	2.00051i
$750$	−27.3841	−	0.331977i	−0.999927	−	0.0121221i
$751$	−49.4748			−1.80536			−0.902680	−	0.430312i	$-0.858404\pi$
$751$	−49.4748			−1.80536			−0.902680	+	0.430312i	$0.858404\pi$
$752$		0			0
$753$	54.1924	−	8.58323i	1.97488	−	0.312790i
$754$		0			0
$755$	−34.9994	−	7.58729i	−1.27376	−	0.276130i
$756$	−23.0514	+	16.7478i	−0.838370	+	0.609112i
$757$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$757$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$761$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$762$	19.3252	−	37.9278i	0.700077	−	1.37398i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	19.5959	−	19.5959i	0.707107	−	0.707107i
$769$	4.56182	+	6.27881i	0.164504	+	0.226420i	0.883309	−	0.468792i	$-0.155311\pi$
$769$	4.56182	+	6.27881i	0.164504	+	0.226420i	−0.718805	+	0.695212i	$0.755311\pi$
$770$	−36.5665	+	32.6581i	−1.31777	+	1.17691i
$771$		0			0
$772$	1.75521	+	11.0819i	0.0631712	+	0.398847i
$773$	25.2131	+	49.4834i	0.906851	+	1.77980i	0.497859	+	0.867258i	$0.334120\pi$
$773$	25.2131	+	49.4834i	0.906851	+	1.77980i	0.408993	+	0.912538i	$0.365880\pi$
$774$		0			0
$775$	48.2119	−	9.84121i	1.73182	−	0.353507i
$776$	53.8583			1.93340
$777$		0			0
$778$	−10.4493	+	1.65501i	−0.374626	+	0.0593350i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−4.34754	+	27.4493i	−0.155368	+	0.980958i
$784$	1.96743	−	0.639258i	0.0702655	−	0.0228306i
$785$		0			0
$786$	−13.9650	+	42.9800i	−0.498117	+	1.53305i
$787$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$787$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$788$	49.7719	+	25.3601i	1.77305	+	0.903414i
$789$		0			0
$790$	−16.0922	+	41.4207i	−0.572537	+	1.47368i
$791$		0			0
$792$	47.3909	+	7.50599i	1.68396	+	0.266714i
$793$		0			0
$794$		0			0
$795$	55.9526	−	5.65236i	1.98444	−	0.200469i
$796$	−30.6938	−	22.3003i	−1.08791	−	0.790414i
$797$	5.17476	+	32.6721i	0.183299	+	1.15731i	0.892080	+	0.451877i	$0.149246\pi$
$797$	5.17476	+	32.6721i	0.183299	+	1.15731i	−0.708781	+	0.705429i	$0.750754\pi$
$798$		0			0
$799$		0			0
$800$	−9.92245	−	26.4867i	−0.350812	−	0.936446i
$801$		0			0
$802$		0			0
$803$	93.9840	−	14.8856i	3.31662	−	0.525301i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	35.6449	+	35.6449i	1.25476	+	1.25476i
$808$	8.50136	−	53.6755i	0.299077	−	1.88830i
$809$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$809$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$810$	18.0000	−	22.0454i	0.632456	−	0.774597i
$811$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$811$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$812$	13.3148	−	26.1317i	0.467257	−	0.917043i
$813$	−49.6872	−	25.3169i	−1.74261	−	0.887903i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	21.6215	−	21.6215i	0.755978	−	0.755978i
$819$		0			0
$820$		0			0
$821$	42.3669	+	30.7814i	1.47862	+	1.07428i	0.977999	+	0.208609i	$0.0668936\pi$
$821$	42.3669	+	30.7814i	1.47862	+	1.07428i	0.500617	+	0.865669i	$0.333106\pi$
$822$		0			0
$823$	25.6754	+	50.3908i	0.894988	+	1.75651i	0.597687	+	0.801730i	$0.296087\pi$
$823$	25.6754	+	50.3908i	0.894988	+	1.75651i	0.297301	+	0.954784i	$0.403913\pi$
$824$			34.8629i			1.21451i
$825$	27.0026	−	40.8537i	0.940110	−	1.42234i
$826$	−20.7929			−0.723479
$827$	37.1173	−	18.9122i	1.29069	−	0.657642i	0.332323	−	0.943166i	$-0.392168\pi$
$827$	37.1173	−	18.9122i	1.29069	−	0.657642i	0.958372	+	0.285524i	$0.0921676\pi$
$828$		0			0
$829$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$829$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$830$	−1.78124	−	17.6324i	−0.0618277	−	0.612031i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−23.2155	+	45.5629i	−0.802443	+	1.57488i
$838$	51.3306	+	26.1542i	1.77319	+	0.903483i
$839$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$839$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$840$	−25.2548	+	16.2559i	−0.871373	+	0.560883i
$841$	0.121715	+	0.374599i	0.00419706	+	0.0129172i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	11.7160	+	26.6033i	0.403042	+	0.915182i
$846$		0			0
$847$	−8.99650	−	56.8017i	−0.309123	−	1.95173i
$848$	26.3686	+	51.7512i	0.905500	+	1.77714i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$853$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$854$		0			0
$855$		0			0
$856$	−45.6938	+	33.1985i	−1.56178	+	1.13470i
$857$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$857$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$858$		0			0
$859$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$859$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$863$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$864$	27.9552	+	9.08321i	0.951057	+	0.309017i
$865$	−3.32711	−	12.6207i	−0.113125	−	0.429117i
$866$	−18.0383	−	55.5162i	−0.612966	−	1.88652i
$867$	−29.0823	−	4.60619i	−0.987688	−	0.156434i
$868$	38.1584	−	38.1584i	1.29518	−	1.29518i
$869$	−46.7058	−	64.2851i	−1.58439	−	2.18072i
$870$	−6.20646	+	28.6298i	−0.210419	+	0.970640i
$871$		0			0
$872$		0			0
$873$	25.9344	+	50.8991i	0.877746	+	1.72267i
$874$		0			0
$875$	4.42792	+	30.3322i	0.149691	+	1.02541i
$876$	58.2929			1.96953
$877$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$877$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$878$	−17.8643	+	2.82943i	−0.602892	+	0.0954887i
$879$	−3.88474	+	5.34689i	−0.131029	+	0.180346i
$880$	49.4290	+	10.7154i	1.66625	+	0.361216i
$881$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$881$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$882$	1.55151	+	1.55151i	0.0522421	+	0.0522421i
$883$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$883$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$884$		0			0
$885$	20.0830	−	5.29435i	0.675084	−	0.177968i
$886$	18.2881	−	56.2851i	0.614402	−	1.89093i
$887$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$887$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$888$		0			0
$889$	−45.3142	−	14.7235i	−1.51979	−	0.493810i
$890$		0			0
$891$	15.7266	+	48.4014i	0.526860	+	1.62151i
$892$	2.55083	+	0.404012i	0.0854082	+	0.0135273i
$893$		0			0
$894$	−12.2216	−	16.8216i	−0.408751	−	0.562597i
$895$	36.9913	−	33.0375i	1.23648	−	1.10432i
$896$	−25.0952	−	18.2327i	−0.838370	−	0.609112i
$897$		0			0
$898$		0			0
$899$		−	52.6354i		−	1.75549i
$900$	20.2534	−	22.1314i	0.675114	−	0.737713i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	31.7381	−	23.0591i	1.05443	−	0.766087i
$907$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$907$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$908$	7.41141	−	46.7938i	0.245956	−	1.55291i
$909$	54.8199	−	17.8121i	1.81826	−	0.590789i
$910$		0			0
$911$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$911$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$912$		0			0
$913$	28.2363	+	14.3871i	0.934484	+	0.476144i
$914$	33.5737	+	10.9087i	1.11052	+	0.360829i
$915$		0			0
$916$		0			0
$917$	49.9610	+	7.91305i	1.64986	+	0.261312i
$918$		0			0
$919$	−20.1568	−	27.7435i	−0.664913	−	0.915174i	0.334719	−	0.942318i	$-0.391359\pi$
$919$	−20.1568	−	27.7435i	−0.664913	−	0.915174i	−0.999632	+	0.0271443i	$0.991359\pi$
$920$		0			0
$921$		0			0
$922$	3.00749	+	18.9885i	0.0990463	+	0.625354i
$923$		0			0
$924$		−	53.7065i		−	1.76681i
$925$		0			0
$926$	8.29286			0.272520
$927$	−32.9474	+	16.7875i	−1.08213	+	0.551375i
$928$	−29.8830	+	4.73300i	−0.980958	+	0.155368i
$929$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$929$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$930$	−27.1397	+	46.5717i	−0.889945	+	1.52715i
$931$		0			0
$932$		0			0
$933$		0			0
$934$	38.6138	−	12.5464i	1.26348	−	0.410531i
$935$		0			0
$936$		0			0
$937$	27.3990	−	53.7735i	0.895085	−	1.75670i	0.297907	−	0.954595i	$-0.403712\pi$
$937$	27.3990	−	53.7735i	0.895085	−	1.75670i	0.597178	−	0.802108i	$-0.296288\pi$
$938$		0			0
$939$	11.0460	+	3.58908i	0.360474	+	0.117125i
$940$		0			0
$941$	9.30577	+	28.6402i	0.303359	+	0.933644i	0.980284	+	0.197592i	$0.0633122\pi$
$941$	9.30577	+	28.6402i	0.303359	+	0.933644i	−0.676925	+	0.736052i	$0.736688\pi$
$942$		0			0
$943$		0			0
$944$	12.6082	+	17.3537i	0.410361	+	0.564814i
$945$	−27.5237	−	16.0395i	−0.895346	−	0.521763i
$946$		0			0
$947$	−2.13260	−	13.4647i	−0.0693001	−	0.437544i	−0.997805	−	0.0662232i	$-0.978905\pi$
$947$	−2.13260	−	13.4647i	−0.0693001	−	0.437544i	0.928505	−	0.371321i	$-0.121095\pi$
$948$	−22.0994	−	43.3725i	−0.717756	−	1.40867i
$949$		0			0
$950$		0			0
$951$	−11.8791			−0.385208
$952$		0			0
$953$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$953$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$954$	−36.2105	+	49.8395i	−1.17236	+	1.61361i
$955$		0			0
$956$		0			0
$957$	−37.0411	−	37.0411i	−1.19737	−	1.19737i
$958$		0			0
$959$		0			0
$960$	28.8808	+	11.2204i	0.932125	+	0.362137i
$961$	20.3486	−	62.6265i	0.656406	−	2.02021i
$962$		0			0
$963$	−53.3773	−	27.1971i	−1.72006	−	0.876414i
$964$	−56.4129	−	18.3297i	−1.81694	−	0.590358i
$965$	−10.5482	+	6.78961i	−0.339557	+	0.218565i
$966$		0			0
$967$	−14.3586	−	2.27418i	−0.461742	−	0.0731328i	−0.0787703	−	0.996893i	$-0.525099\pi$
$967$	−14.3586	−	2.27418i	−0.461742	−	0.0731328i	−0.382972	+	0.923760i	$0.625099\pi$
$968$	−41.9512	+	41.9512i	−1.34836	+	1.34836i
$969$		0			0
$970$	24.2693	+	55.1080i	0.779242	+	1.76941i
$971$	5.10712	+	3.71054i	0.163895	+	0.119077i	0.666710	−	0.745318i	$-0.267702\pi$
$971$	5.10712	+	3.71054i	0.163895	+	0.119077i	−0.502814	+	0.864394i	$0.667702\pi$
$972$	4.87714	+	30.7931i	0.156434	+	0.987688i
$973$		0			0
$974$		−	30.8282i		−	0.987799i
$975$		0			0
$976$		0			0
$977$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$977$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$978$		0			0
$979$		0			0
$980$	1.54065	+	1.72503i	0.0492141	+	0.0551040i
$981$		0			0
$982$	41.1757	+	41.1757i	1.31397	+	1.31397i
$983$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$983$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$984$		0			0
$985$	−3.52057	+	62.3544i	−0.112175	+	1.98678i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	13.6749	+	51.8729i	0.434617	+	1.64863i
$991$	10.0509	+	30.9333i	0.319276	+	0.982630i	0.973959	+	0.226726i	$0.0728023\pi$
$991$	10.0509	+	30.9333i	0.319276	+	0.982630i	−0.654683	+	0.755904i	$0.727198\pi$
$992$	−54.9849	−	8.70875i	−1.74577	−	0.276503i
$993$		0			0
$994$		0			0
$995$	8.98673	−	41.4548i	0.284898	−	1.31421i
$996$	15.7060	+	11.4111i	0.497664	+	0.361574i
$997$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$997$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.bp.a.197.1	✓	16
3.2	odd	2		600.2.bp.b.197.2	yes	16
8.5	even	2		600.2.bp.b.197.2	yes	16
24.5	odd	2	CM	600.2.bp.a.197.1	✓	16
25.8	odd	20	inner	600.2.bp.a.533.1	yes	16
75.8	even	20		600.2.bp.b.533.2	yes	16
200.133	odd	20		600.2.bp.b.533.2	yes	16
600.533	even	20	inner	600.2.bp.a.533.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.bp.a.197.1	✓	16	1.1	even	1	trivial
600.2.bp.a.197.1	✓	16	24.5	odd	2	CM
600.2.bp.a.533.1	yes	16	25.8	odd	20	inner
600.2.bp.a.533.1	yes	16	600.533	even	20	inner
600.2.bp.b.197.2	yes	16	3.2	odd	2
600.2.bp.b.197.2	yes	16	8.5	even	2
600.2.bp.b.533.2	yes	16	75.8	even	20
600.2.bp.b.533.2	yes	16	200.133	odd	20

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)

\(f(q)\)	\(=\)	\(q+(1.26007 - 0.642040i) q^{2} +(-1.71073 + 0.270952i) q^{3} +(1.17557 - 1.61803i) q^{4} +(2.18531 + 0.473739i) q^{5} +(-1.98168 + 1.43977i) q^{6} +(1.93871 + 1.93871i) q^{7} +(0.442463 - 2.79360i) q^{8} +(2.85317 - 0.927051i) q^{9} +O(q^{10})\)	\(q+(1.26007 - 0.642040i) q^{2} +(-1.71073 + 0.270952i) q^{3} +(1.17557 - 1.61803i) q^{4} +(2.18531 + 0.473739i) q^{5} +(-1.98168 + 1.43977i) q^{6} +(1.93871 + 1.93871i) q^{7} +(0.442463 - 2.79360i) q^{8} +(2.85317 - 0.927051i) q^{9} +(3.05781 - 0.806108i) q^{10} +(-1.74740 + 5.37793i) q^{11} +(-1.57267 + 3.08654i) q^{12} +(3.68764 + 1.19819i) q^{14} +(-3.86682 - 0.218323i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(3.00000 - 3.00000i) q^{18} +(3.33551 - 2.97899i) q^{20} +(-3.84189 - 2.79130i) q^{21} +(1.25100 + 7.89849i) q^{22} +4.89898i q^{24} +(4.55114 + 2.07053i) q^{25} +(-4.62981 + 2.35900i) q^{27} +(5.41598 - 0.857807i) q^{28} +(3.14375 - 4.32700i) q^{29} +(-5.01266 + 2.20755i) q^{30} +(7.96171 - 5.78452i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(1.53215 - 9.67364i) q^{33} +(3.31823 + 5.15511i) q^{35} +(1.85410 - 5.70634i) q^{36} +(2.29036 - 5.89527i) q^{40} +(-6.63319 - 1.05059i) q^{42} +(6.64749 + 9.14949i) q^{44} +(6.67423 - 0.674235i) q^{45} +(3.14534 + 6.17307i) q^{48} +0.517171i q^{49} +(7.06414 - 0.312992i) q^{50} +(-14.3417 + 2.27150i) q^{53} +(-4.31932 + 5.94504i) q^{54} +(-6.36634 + 10.9246i) q^{55} +(6.27379 - 4.55817i) q^{56} +(1.18325 - 7.47075i) q^{58} +(-5.10012 + 1.65713i) q^{59} +(-4.89898 + 6.00000i) q^{60} +(6.31845 - 12.4006i) q^{62} +(7.32874 + 3.73418i) q^{63} +(-7.60845 - 2.47214i) q^{64} +(-4.28023 - 13.1732i) q^{66} +(7.49100 + 4.36539i) q^{70} +(-1.32739 - 8.38081i) q^{72} +(-7.63962 - 14.9936i) q^{73} +(-8.34678 - 2.30897i) q^{75} +(-13.8139 + 7.03855i) q^{77} +(-8.25966 + 11.3684i) q^{79} +(-0.898979 - 8.89898i) q^{80} +(7.28115 - 5.29007i) q^{81} +(0.876698 - 5.53525i) q^{83} +(-9.03284 + 2.93495i) q^{84} +(-4.20569 + 8.25412i) q^{87} +(14.2507 + 7.26108i) q^{88} +(7.97714 - 5.13471i) q^{90} +(-12.0530 + 12.0530i) q^{93} +(7.92672 + 5.75910i) q^{96} +(2.97879 + 18.8074i) q^{97} +(0.332044 + 0.651673i) q^{98} +16.9641i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 4 q^{5} + 4 q^{7} + 8 q^{8}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more