LMFDB - Embedded newform 820.2.cc.a.719.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(19,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([20, 20, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.cc (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-4,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\Q(\zeta_{40})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{40}]$

Embedding invariants

Embedding label			719.1
Root			$0.987688 - 0.156434i$ of defining polynomial
Character	$\chi$	$=$	820.719
Dual form			820.2.cc.a.479.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26007 - 0.642040i) q^{2} +(-2.64054 + 1.09375i) q^{3} +(1.17557 - 1.61803i) q^{4} +(2.20854 - 0.349798i) q^{5} +(-2.62505 + 3.07353i) q^{6} +(0.842968 + 0.986988i) q^{7} +(0.442463 - 2.79360i) q^{8} +(3.65485 - 3.65485i) q^{9} +(2.55834 - 1.85874i) q^{10} +(-1.33442 + 5.55826i) q^{12} +(1.69589 + 0.702459i) q^{14} +(-5.44914 + 3.33924i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(2.25882 - 6.95194i) q^{18} +(2.03031 - 3.98470i) q^{20} +(-3.30541 - 1.68419i) q^{21} +(1.50894 + 0.490285i) q^{23} +(1.88716 + 7.86057i) q^{24} +(4.75528 - 1.54508i) q^{25} +(-2.37206 + 5.72665i) q^{27} +(2.58795 - 0.203676i) q^{28} +(9.81881 + 2.35729i) q^{29} +(-4.72240 + 7.70625i) q^{30} +(-4.00000 - 4.00000i) q^{32} +(2.20697 + 1.88493i) q^{35} +(-1.61714 - 10.2102i) q^{36} -6.32456i q^{40} +(-4.33089 - 4.71629i) q^{41} -5.24637 q^{42} +(11.6418 - 5.93180i) q^{43} +(6.79342 - 9.35034i) q^{45} +(2.21616 - 0.351005i) q^{46} +(0.887425 - 1.03904i) q^{47} +(7.42475 + 8.69327i) q^{48} +(0.831490 - 5.24982i) q^{49} +(5.00000 - 5.00000i) q^{50} +(0.687770 + 8.73895i) q^{54} +(3.13024 - 1.91821i) q^{56} +(13.8859 - 3.33371i) q^{58} +(-1.00285 + 12.7424i) q^{60} +(-4.67048 + 9.16634i) q^{61} +(6.68822 + 0.526374i) q^{63} +(-7.60845 - 2.47214i) q^{64} +(4.08412 + 6.66467i) q^{67} +(-4.52067 + 0.355785i) q^{69} +(3.99115 + 0.958190i) q^{70} +(-8.59307 - 11.8273i) q^{72} +(-10.8666 + 9.28094i) q^{75} +(-4.06061 - 7.96940i) q^{80} -2.20966i q^{81} +(-8.48528 - 3.16228i) q^{82} +1.46878 q^{83} +(-6.61081 + 3.36838i) q^{84} +(10.8611 - 14.9490i) q^{86} +(-28.5052 + 4.51479i) q^{87} +(-4.79619 - 5.61562i) q^{89} +(2.55692 - 16.1438i) q^{90} +(2.56717 - 1.86515i) q^{92} +(0.451115 - 1.87903i) q^{94} +(14.9372 + 6.18717i) q^{96} +(-2.32285 - 7.14901i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 12 q^{3} + 20 q^{6} + 16 q^{7} + 8 q^{8} + 12 q^{9} - 16 q^{12} + 20 q^{15} + 16 q^{16} + 4 q^{18} + 4 q^{21} + 8 q^{24} - 48 q^{27} + 8 q^{28} - 80 q^{30} - 64 q^{32} - 20 q^{35} + 24 q^{36}+ \cdots - 104 q^{98}+O(q^{100}) $ 16 * q - 4 * q^2 - 12 * q^3 + 20 * q^6 + 16 * q^7 + 8 * q^8 + 12 * q^9 - 16 * q^12 + 20 * q^15 + 16 * q^16 + 4 * q^18 + 4 * q^21 + 8 * q^24 - 48 * q^27 + 8 * q^28 - 80 * q^30 - 64 * q^32 - 20 * q^35 + 24 * q^36 + 8 * q^42 + 44 * q^47 + 48 * q^48 + 68 * q^49 + 80 * q^50 + 52 * q^54 - 24 * q^56 + 52 * q^58 + 36 * q^63 + 24 * q^67 + 20 * q^69 + 20 * q^70 - 80 * q^72 + 40 * q^75 + 8 * q^84 - 128 * q^87 - 80 * q^89 + 60 * q^90 + 28 * q^94 + 80 * q^96 - 104 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{29}{40}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.26007	−	0.642040i	0.891007	−	0.453990i
$2$	1.26007	−	0.642040i	0.891007	−	0.453990i
$3$	−2.64054	+	1.09375i	−1.52452	+	0.631476i	−0.978490	−	0.206292i	$-0.933860\pi$
$3$	−2.64054	+	1.09375i	−1.52452	+	0.631476i	−0.546027	+	0.837768i	$0.683860\pi$
$4$	1.17557	−	1.61803i	0.587785	−	0.809017i
$5$	2.20854	−	0.349798i	0.987688	−	0.156434i
$5$	2.20854	−	0.349798i	0.987688	−	0.156434i
$6$	−2.62505	+	3.07353i	−1.07167	+	1.25477i
$7$	0.842968	+	0.986988i	0.318612	+	0.373046i	0.896480	−	0.443083i	$-0.146115\pi$
$7$	0.842968	+	0.986988i	0.318612	+	0.373046i	−0.577869	+	0.816130i	$0.696115\pi$
$8$	0.442463	−	2.79360i	0.156434	−	0.987688i
$9$	3.65485	−	3.65485i	1.21828	−	1.21828i
$10$	2.55834	−	1.85874i	0.809017	−	0.587785i
$11$		0			0		−0.852640	−	0.522499i	$-0.825000\pi$
$11$		0			0		0.852640	+	0.522499i	$0.175000\pi$
$12$	−1.33442	+	5.55826i	−0.385214	+	1.60453i
$13$		0			0		−0.0784591	−	0.996917i	$-0.525000\pi$
$13$		0			0		0.0784591	+	0.996917i	$0.475000\pi$
$14$	1.69589	+	0.702459i	0.453245	+	0.187740i
$15$	−5.44914	+	3.33924i	−1.40696	+	0.862188i
$16$	−1.23607	−	3.80423i	−0.309017	−	0.951057i
$17$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$17$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$18$	2.25882	−	6.95194i	0.532410	−	1.63859i
$19$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$19$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$20$	2.03031	−	3.98470i	0.453990	−	0.891007i
$21$	−3.30541	−	1.68419i	−0.721299	−	0.367520i
$22$		0			0
$23$	1.50894	+	0.490285i	0.314636	+	0.102231i	0.462078	−	0.886839i	$-0.347104\pi$
$23$	1.50894	+	0.490285i	0.314636	+	0.102231i	−0.147442	+	0.989071i	$0.547104\pi$
$24$	1.88716	+	7.86057i	0.385214	+	1.60453i
$25$	4.75528	−	1.54508i	0.951057	−	0.309017i
$26$		0			0
$27$	−2.37206	+	5.72665i	−0.456502	+	1.10209i
$28$	2.58795	−	0.203676i	0.489076	−	0.0384911i
$29$	9.81881	+	2.35729i	1.82331	+	0.437737i	0.992852	−	0.119349i	$-0.0380806\pi$
$29$	9.81881	+	2.35729i	1.82331	+	0.437737i	0.830455	+	0.557086i	$0.188081\pi$
$30$	−4.72240	+	7.70625i	−0.862188	+	1.40696i
$31$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$31$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$		0			0
$34$		0			0
$35$	2.20697	+	1.88493i	0.373046	+	0.318612i
$36$	−1.61714	−	10.2102i	−0.269523	−	1.70170i
$37$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$37$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$38$		0			0
$39$		0			0
$40$		−	6.32456i		−	1.00000i
$41$	−4.33089	−	4.71629i	−0.676371	−	0.736561i
$41$	−4.33089	−	4.71629i	−0.676371	−	0.736561i
$42$	−5.24637			−0.809533
$43$	11.6418	−	5.93180i	1.77536	−	0.904591i	0.848485	−	0.529220i	$-0.177515\pi$
$43$	11.6418	−	5.93180i	1.77536	−	0.904591i	0.926875	−	0.375371i	$-0.122485\pi$
$44$		0			0
$45$	6.79342	−	9.35034i	1.01270	−	1.39387i
$46$	2.21616	−	0.351005i	0.326755	−	0.0517529i
$47$	0.887425	−	1.03904i	0.129444	−	0.151560i	−0.691898	−	0.721995i	$-0.743225\pi$
$47$	0.887425	−	1.03904i	0.129444	−	0.151560i	0.821343	+	0.570435i	$0.193225\pi$
$48$	7.42475	+	8.69327i	1.07167	+	1.25477i
$49$	0.831490	−	5.24982i	0.118784	−	0.749974i
$50$	5.00000	−	5.00000i	0.707107	−	0.707107i
$51$		0			0
$52$		0			0
$53$		0			0		0.233445	−	0.972370i	$-0.425000\pi$
$53$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$54$	0.687770	+	8.73895i	0.0935937	+	1.18922i
$55$		0			0
$56$	3.13024	−	1.91821i	0.418296	−	0.256332i
$57$		0			0
$58$	13.8859	−	3.33371i	1.82331	−	0.437737i
$59$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$59$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$60$	−1.00285	+	12.7424i	−0.129467	+	1.64504i
$61$	−4.67048	+	9.16634i	−0.597994	+	1.17363i	0.371481	+	0.928441i	$0.378850\pi$
$61$	−4.67048	+	9.16634i	−0.597994	+	1.17363i	−0.969475	+	0.245189i	$0.921150\pi$
$62$		0			0
$63$	6.68822	+	0.526374i	0.842636	+	0.0663169i
$64$	−7.60845	−	2.47214i	−0.951057	−	0.309017i
$65$		0			0
$66$		0			0
$67$	4.08412	+	6.66467i	0.498954	+	0.814219i	0.998648	−	0.0519829i	$-0.0165541\pi$
$67$	4.08412	+	6.66467i	0.498954	+	0.814219i	−0.499694	+	0.866202i	$0.666554\pi$
$68$		0			0
$69$	−4.52067	+	0.355785i	−0.544225	+	0.0428314i
$70$	3.99115	+	0.958190i	0.477034	+	0.114526i
$71$		0			0		0.522499	−	0.852640i	$-0.325000\pi$
$71$		0			0		−0.522499	+	0.852640i	$0.675000\pi$
$72$	−8.59307	−	11.8273i	−1.01270	−	1.39387i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$		0			0
$75$	−10.8666	+	9.28094i	−1.25477	+	1.07167i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$79$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$80$	−4.06061	−	7.96940i	−0.453990	−	0.891007i
$81$		−	2.20966i		−	0.245517i
$82$	−8.48528	−	3.16228i	−0.937043	−	0.349215i
$83$	1.46878			0.161220			0.0806100	−	0.996746i	$-0.474313\pi$
$83$	1.46878			0.161220			0.0806100	+	0.996746i	$0.474313\pi$
$84$	−6.61081	+	3.36838i	−0.721299	+	0.367520i
$85$		0			0
$86$	10.8611	−	14.9490i	1.17118	−	1.61199i
$87$	−28.5052	+	4.51479i	−3.05608	+	0.484036i
$88$		0			0
$89$	−4.79619	−	5.61562i	−0.508395	−	0.595254i	0.445542	−	0.895261i	$-0.353011\pi$
$89$	−4.79619	−	5.61562i	−0.508395	−	0.595254i	−0.953937	+	0.300007i	$0.903011\pi$
$90$	2.55692	−	16.1438i	0.269523	−	1.70170i
$91$		0			0
$92$	2.56717	−	1.86515i	0.267646	−	0.194456i
$93$		0			0
$94$	0.451115	−	1.87903i	0.0465290	−	0.193807i
$95$		0			0
$96$	14.9372	+	6.18717i	1.52452	+	0.631476i
$97$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$97$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$98$	−2.32285	−	7.14901i	−0.234644	−	0.722159i
$99$		0			0
$100$	3.09017	−	9.51057i	0.309017	−	0.951057i
$101$	−1.52965	+	19.4360i	−0.152206	+	1.93396i	0.166374	+	0.986063i	$0.446794\pi$
$101$	−1.52965	+	19.4360i	−0.152206	+	1.93396i	−0.318579	+	0.947896i	$0.603206\pi$
$102$		0			0
$103$	−18.0633	−	9.20373i	−1.77983	−	0.906871i	−0.912360	−	0.409389i	$-0.865742\pi$
$103$	−18.0633	−	9.20373i	−1.77983	−	0.906871i	−0.867475	−	0.497482i	$-0.834258\pi$
$104$		0			0
$105$	−7.88924	−	2.56337i	−0.769911	−	0.250159i
$106$		0			0
$107$	−19.6754	+	6.39291i	−1.90209	+	0.618026i	−0.949456	+	0.313900i	$0.898364\pi$
$107$	−19.6754	+	6.39291i	−1.90209	+	0.618026i	−0.952632	+	0.304125i	$0.901636\pi$
$108$	6.47739	+	10.5701i	0.623287	+	1.01711i
$109$	−5.70123	+	13.7640i	−0.546079	+	1.31835i	0.374294	+	0.927310i	$0.377885\pi$
$109$	−5.70123	+	13.7640i	−0.546079	+	1.31835i	−0.920373	+	0.391041i	$0.872115\pi$
$110$		0			0
$111$		0			0
$112$	2.71276	−	4.42682i	0.256332	−	0.418296i
$113$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$113$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$114$		0			0
$115$	3.50406	+	0.554988i	0.326755	+	0.0517529i
$116$	15.3569	−	13.1160i	1.42585	−	1.21779i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	6.91747	+	16.7002i	0.631476	+	1.52452i
$121$	4.99390	+	9.80107i	0.453990	+	0.891007i
$122$			14.5489i			1.31720i
$123$	16.5943	+	7.71667i	1.49626	+	0.695789i
$124$		0			0
$125$	9.96176	−	5.07577i	0.891007	−	0.453990i
$126$	8.76560	−	3.63083i	0.780901	−	0.323460i
$127$	8.12891	−	11.1885i	0.721324	−	0.992818i	−0.278155	−	0.960536i	$-0.589723\pi$
$127$	8.12891	−	11.1885i	0.721324	−	0.992818i	0.999479	−	0.0322812i	$-0.0102772\pi$
$128$	−11.1744	+	1.76985i	−0.987688	+	0.156434i
$129$	−24.2528	+	28.3964i	−2.13534	+	2.50016i
$130$		0			0
$131$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$131$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$132$		0			0
$133$		0			0
$134$	9.42527	+	5.77581i	0.814219	+	0.498954i
$135$	−3.23560	+	13.4773i	−0.278476	+	1.15994i
$136$		0			0
$137$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$137$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$138$	−5.46795	+	3.35076i	−0.465463	+	0.285236i
$139$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$139$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$140$	5.64434	−	1.35509i	0.477034	−	0.114526i
$141$	−1.20683	+	3.71425i	−0.101634	+	0.312796i
$142$		0			0
$143$		0			0
$144$	−18.4215	−	9.38624i	−1.53513	−	0.782186i
$145$	22.5098	+	1.77156i	1.86934	+	0.147120i
$146$		0			0
$147$	3.54640	+	14.7718i	0.292502	+	1.21836i
$148$		0			0
$149$	−12.4796	−	20.3649i	−1.02237	−	1.66836i	−0.687653	−	0.726039i	$-0.741359\pi$
$149$	−12.4796	−	20.3649i	−1.02237	−	1.66836i	−0.334718	−	0.942318i	$-0.608641\pi$
$150$	−7.73397	+	18.6714i	−0.631476	+	1.52452i
$151$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$151$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.760406	−	0.649448i	$-0.225000\pi$
$157$		0			0		−0.760406	+	0.649448i	$0.775000\pi$
$158$		0			0
$159$		0			0
$160$	−10.2333	−	7.43496i	−0.809017	−	0.587785i
$161$	0.788084	+	1.90260i	0.0621097	+	0.149946i
$162$	−1.41869	−	2.78433i	−0.111463	−	0.218757i
$163$			6.65248i			0.521062i	0.965465	+	0.260531i	$0.0838976\pi$
$163$			6.65248i			0.521062i	−0.965465	+	0.260531i	$0.916102\pi$
$164$	−12.7224	+	1.46318i	−0.993451	+	0.114255i
$165$		0			0
$166$	1.85078	−	0.943017i	0.143648	−	0.0731923i
$167$	−21.0900	+	8.73576i	−1.63199	+	0.675993i	−0.995453	−	0.0952515i	$-0.969634\pi$
$167$	−21.0900	+	8.73576i	−1.63199	+	0.675993i	−0.636539	+	0.771245i	$0.719634\pi$
$168$	−6.16748	+	8.48881i	−0.475831	+	0.654926i
$169$	−12.8399	+	2.03365i	−0.987688	+	0.156434i
$170$		0			0
$171$		0			0
$172$	4.08792	−	25.8101i	0.311701	−	1.96800i
$173$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$173$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$174$	−33.0200	+	23.9905i	−2.50324	+	1.81871i
$175$	5.53353	+	3.39095i	0.418296	+	0.256332i
$176$		0			0
$177$		0			0
$178$	−9.64900	−	3.99675i	−0.723223	−	0.299569i
$179$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$179$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$180$	−7.14302	−	21.9840i	−0.532410	−	1.63859i
$181$	−25.8584	+	6.20805i	−1.92204	+	0.461441i	−0.925457	+	0.378854i	$0.876318\pi$
$181$	−25.8584	+	6.20805i	−1.92204	+	0.461441i	−0.996584	+	0.0825874i	$0.973682\pi$
$182$		0			0
$183$	2.30694	−	29.3124i	0.170534	−	2.16684i
$184$	2.03731	−	3.99845i	0.150193	−	0.294770i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−0.637973	−	2.65735i	−0.0465290	−	0.193807i
$189$	−7.65170	+	2.48619i	−0.556579	+	0.180844i
$190$		0			0
$191$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$191$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$192$	22.7943	−	1.79395i	1.64504	−	0.129467i
$193$		0			0		−0.972370	−	0.233445i	$-0.925000\pi$
$193$		0			0		0.972370	+	0.233445i	$0.0750000\pi$
$194$		0			0
$195$		0			0
$196$	−7.51691	−	7.51691i	−0.536922	−	0.536922i
$197$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$197$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$198$		0			0
$199$		0			0		−0.760406	−	0.649448i	$-0.775000\pi$
$199$		0			0		0.760406	+	0.649448i	$0.225000\pi$
$200$	−2.21232	−	13.9680i	−0.156434	−	0.987688i
$201$	−18.0737	−	13.1313i	−1.27482	−	0.926214i
$202$	10.5512	+	25.4729i	0.742383	+	1.79227i
$203$	5.95032	+	11.6782i	0.417631	+	0.819647i
$204$		0			0
$205$	−11.2147	−	8.90118i	−0.783267	−	0.621685i
$206$	−28.6703			−1.99755
$207$	7.30688	−	3.72304i	0.507863	−	0.258769i
$208$		0			0
$209$		0			0
$210$	−11.5868	+	1.83517i	−0.799566	+	0.126639i
$211$		0			0		0.649448	−	0.760406i	$-0.275000\pi$
$211$		0			0		−0.649448	+	0.760406i	$0.725000\pi$
$212$		0			0
$213$		0			0
$214$	−20.6879	+	20.6879i	−1.41419	+	1.41419i
$215$	23.6365	−	17.1729i	1.61199	−	1.17118i
$216$	14.9484	+	9.16042i	1.01711	+	0.623287i
$217$		0			0
$218$	1.65306	+	21.0041i	0.111959	+	1.42257i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	7.99900	−	24.6184i	0.535653	−	1.64857i	−0.206581	−	0.978429i	$-0.566234\pi$
$223$	7.99900	−	24.6184i	0.535653	−	1.64857i	0.742234	−	0.670141i	$-0.233766\pi$
$224$	0.576083	−	7.31982i	0.0384911	−	0.489076i
$225$	11.7328	−	23.0269i	0.782186	−	1.53513i
$226$		0			0
$227$	25.2850	+	1.98997i	1.67822	+	0.132079i	0.881474	−	0.472233i	$-0.156552\pi$
$227$	25.2850	+	1.98997i	1.67822	+	0.132079i	0.796748	+	0.604312i	$0.206552\pi$
$228$		0			0
$229$	2.64063	+	10.9990i	0.174498	+	0.726836i	0.989153	+	0.146890i	$0.0469263\pi$
$229$	2.64063	+	10.9990i	0.174498	+	0.726836i	−0.814655	+	0.579946i	$0.803074\pi$
$230$	4.77169	−	1.55042i	0.314636	−	0.102231i
$231$		0			0
$232$	10.9298	−	26.3869i	0.717576	−	1.73238i
$233$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$233$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$234$		0			0
$235$	1.59646	−	2.60518i	0.104141	−	0.169943i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.760406	−	0.649448i	$-0.225000\pi$
$239$		0			0		−0.760406	+	0.649448i	$0.775000\pi$
$240$	19.4387	+	16.6023i	1.25477	+	1.07167i
$241$	3.99792	+	25.2418i	0.257528	+	1.62597i	0.689642	+	0.724151i	$0.257768\pi$
$241$	3.99792	+	25.2418i	0.257528	+	1.62597i	−0.432113	+	0.901819i	$0.642232\pi$
$242$	12.5854	+	9.14379i	0.809017	+	0.587785i
$243$	−4.69936	−	11.3453i	−0.301464	−	0.727799i
$244$	9.34097	+	18.3327i	0.597994	+	1.17363i
$245$		−	11.8853i		−	0.759323i
$246$	25.8645	−	0.930635i	1.64906	−	0.0593351i
$247$		0			0
$248$		0			0
$249$	−3.87838	+	1.60648i	−0.245783	+	0.101806i
$250$	9.29370	−	12.7917i	0.587785	−	0.809017i
$251$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$251$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$252$	8.71416	−	10.2030i	0.548941	−	0.642727i
$253$		0			0
$254$	3.05957	−	19.3174i	0.191975	−	1.21208i
$255$		0			0
$256$	−12.9443	+	9.40456i	−0.809017	+	0.587785i
$257$		0			0		−0.852640	−	0.522499i	$-0.825000\pi$
$257$		0			0		0.852640	+	0.522499i	$0.175000\pi$
$258$	−12.3287	+	51.3527i	−0.767552	+	3.19708i
$259$		0			0
$260$		0			0
$261$	44.5018	−	27.2708i	2.75459	−	1.68802i
$262$		0			0
$263$	−8.24818	+	1.98021i	−0.508605	+	0.122105i	−0.479623	−	0.877475i	$-0.659226\pi$
$263$	−8.24818	+	1.98021i	−0.508605	+	0.122105i	−0.0289818	+	0.999580i	$0.509226\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	18.8066	+	9.58244i	1.15095	+	0.586436i
$268$	15.5848	+	1.22655i	0.951995	+	0.0749236i
$269$	28.2798	+	9.18868i	1.72425	+	0.560244i	0.992600	−	0.121434i	$-0.0387492\pi$
$269$	28.2798	+	9.18868i	1.72425	+	0.560244i	0.731653	+	0.681677i	$0.238749\pi$
$270$	4.57583	+	19.0597i	0.278476	+	1.15994i
$271$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$271$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−4.73870	+	7.73285i	−0.285236	+	0.465463i
$277$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$277$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$278$		0			0
$279$		0			0
$280$	6.24226	−	5.33139i	0.373046	−	0.318612i
$281$	−15.5289	−	13.2629i	−0.926377	−	0.791201i	0.0518675	−	0.998654i	$-0.483483\pi$
$281$	−15.5289	−	13.2629i	−0.926377	−	0.791201i	−0.978245	+	0.207453i	$0.933483\pi$
$282$	0.863997	+	5.45506i	0.0514503	+	0.324844i
$283$	16.3928	+	11.9101i	0.974450	+	0.707979i	0.956461	−	0.291859i	$-0.0942738\pi$
$283$	16.3928	+	11.9101i	0.974450	+	0.707979i	0.0179883	+	0.999838i	$0.494274\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.00413	−	8.25022i	0.0592720	−	0.486995i
$288$	−29.2388			−1.72291
$289$	15.1471	−	7.71784i	0.891007	−	0.453990i
$290$	29.5014	−	12.2199i	1.73238	−	0.717576i
$291$		0			0
$292$		0			0
$293$		0			0		0.649448	−	0.760406i	$-0.275000\pi$
$293$		0			0		−0.649448	+	0.760406i	$0.725000\pi$
$294$	13.9528	+	16.3366i	0.813744	+	0.952772i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−28.8003	−	17.6489i	−1.66836	−	1.02237i
$299$		0			0
$300$	2.24244	+	28.4929i	0.129467	+	1.64504i
$301$	15.6683	+	6.49002i	0.903105	+	0.374078i
$302$		0			0
$303$	−17.2190	−	52.9947i	−0.989207	−	3.04447i
$304$		0			0
$305$	−7.10857	+	21.8779i	−0.407036	+	1.25273i
$306$		0			0
$307$	−15.2963	+	30.0208i	−0.873009	+	1.71338i	−0.191599	+	0.981473i	$0.561367\pi$
$307$	−15.2963	+	30.0208i	−0.873009	+	1.71338i	−0.681409	+	0.731903i	$0.738633\pi$
$308$		0			0
$309$	57.7636	+	4.54609i	3.28605	+	0.258618i
$310$		0			0
$311$		0			0		−0.233445	−	0.972370i	$-0.575000\pi$
$311$		0			0		0.233445	+	0.972370i	$0.425000\pi$
$312$		0			0
$313$		0			0		−0.522499	−	0.852640i	$-0.675000\pi$
$313$		0			0		0.522499	+	0.852640i	$0.325000\pi$
$314$		0			0
$315$	14.9553	−	1.17701i	0.842636	−	0.0663169i
$316$		0			0
$317$		0			0		0.522499	−	0.852640i	$-0.325000\pi$
$317$		0			0		−0.522499	+	0.852640i	$0.675000\pi$
$318$		0			0
$319$		0			0
$320$	−17.6683	−	2.79838i	−0.987688	−	0.156434i
$321$	44.9613	−	38.4006i	2.50950	−	2.14331i
$322$	2.21459	+	1.89144i	0.123414	+	0.105406i
$323$		0			0
$324$	−3.57530	−	2.59761i	−0.198628	−	0.144311i
$325$		0			0
$326$	4.27115	+	8.38261i	0.236557	+	0.464270i
$327$		−	42.5801i		−	2.35468i
$328$	−15.0917	+	10.0120i	−0.833301	+	0.552820i
$329$	1.77359			0.0977813
$330$		0			0
$331$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$331$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$332$	1.72666	−	2.37654i	0.0947627	−	0.130430i
$333$		0			0
$334$	−20.9662	+	24.5483i	−1.14722	+	1.34322i
$335$	11.3512	+	13.2906i	0.620183	+	0.726141i
$336$	−2.32133	+	14.6563i	−0.126639	+	0.799566i
$337$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$337$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$338$	−14.8736	+	10.8063i	−0.809017	+	0.587785i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	13.6294	−	8.35209i	0.735917	−	0.450970i
$344$	−11.4200	−	35.1472i	−0.615726	−	1.89501i
$345$	−9.85962	+	2.36709i	−0.530824	+	0.127440i
$346$		0			0
$347$	2.05567	−	26.1197i	0.110354	−	1.40218i	−0.653566	−	0.756870i	$-0.726728\pi$
$347$	2.05567	−	26.1197i	0.110354	−	1.40218i	0.763920	−	0.645311i	$-0.223272\pi$
$348$	−26.2048	+	51.4299i	−1.40473	+	2.75693i
$349$	−26.6210	−	13.5641i	−1.42499	−	0.726069i	−0.439891	−	0.898051i	$-0.644983\pi$
$349$	−26.6210	−	13.5641i	−1.42499	−	0.726069i	−0.985100	+	0.171982i	$0.944983\pi$
$350$	9.14978	+	0.720103i	0.489076	+	0.0384911i
$351$		0			0
$352$		0			0
$353$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$353$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$354$		0			0
$355$		0			0
$356$	−14.7245	+	1.15884i	−0.780398	+	0.0614186i
$357$		0			0
$358$		0			0
$359$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$359$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$360$	−23.1153	−	23.1153i	−1.21828	−	1.21828i
$361$	−18.7661	−	2.97225i	−0.987688	−	0.156434i
$362$	−28.5977	+	24.4247i	−1.50306	+	1.28374i
$363$	−23.9065	−	20.4181i	−1.25477	−	1.07167i
$364$		0			0
$365$		0			0
$366$	−15.9128	−	38.4170i	−0.831777	−	2.00809i
$367$	16.9303	+	33.2275i	0.883753	+	1.73446i	0.646333	+	0.763055i	$0.276302\pi$
$367$	16.9303	+	33.2275i	0.883753	+	1.73446i	0.237419	+	0.971407i	$0.423698\pi$
$368$		−	6.34638i		−	0.330828i
$369$	−33.0661	−	1.40861i	−1.72135	−	0.0733294i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$373$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$374$		0			0
$375$	−20.7528	+	24.2984i	−1.07167	+	1.25477i
$376$	−2.51002	−	2.93885i	−0.129444	−	0.151560i
$377$		0			0
$378$	−8.04547	+	8.04547i	−0.413814	+	0.413814i
$379$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$379$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$380$		0			0
$381$	−9.22734	+	38.4346i	−0.472731	+	1.96907i
$382$		0			0
$383$	−28.1607	−	11.6646i	−1.43895	−	0.596031i	−0.479404	−	0.877594i	$-0.659147\pi$
$383$	−28.1607	−	11.6646i	−1.43895	−	0.596031i	−0.959543	+	0.281563i	$0.909147\pi$
$384$	27.5707	−	16.8954i	1.40696	−	0.862188i
$385$		0			0
$386$		0			0
$387$	20.8692	−	64.2289i	1.06084	−	3.26494i
$388$		0			0
$389$	5.09350	−	9.99655i	0.258251	−	0.506845i	−0.725082	−	0.688663i	$-0.758198\pi$
$389$	5.09350	−	9.99655i	0.258251	−	0.506845i	0.983332	+	0.181818i	$0.0581980\pi$
$390$		0			0
$391$		0			0
$392$	−14.2980	−	4.64571i	−0.722159	−	0.234644i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$397$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$398$		0			0
$399$		0			0
$400$	−11.7557	−	16.1803i	−0.587785	−	0.809017i
$401$	−26.9778	−	26.9778i	−1.34721	−	1.34721i	−0.888679	−	0.458531i	$-0.848376\pi$
$401$	−26.9778	−	26.9778i	−1.34721	−	1.34721i	−0.458531	−	0.888679i	$-0.651624\pi$
$402$	−31.2051	−	4.94240i	−1.55637	−	0.246505i
$403$		0			0
$404$	29.6500	+	25.3235i	1.47514	+	1.25989i
$405$	−0.772933	−	4.88011i	−0.0384074	−	0.242495i
$406$	14.9957	+	10.8950i	0.744224	+	0.540710i
$407$		0			0
$408$		0			0
$409$			14.7087i			0.727300i	0.931536	+	0.363650i	$0.118470\pi$
$409$			14.7087i			0.727300i	−0.931536	+	0.363650i	$0.881530\pi$
$410$	−19.8462	−	4.01588i	−0.980135	−	0.198330i
$411$		0			0
$412$	−36.1267	+	18.4075i	−1.77983	+	0.906871i
$413$		0			0
$414$	6.81686	−	9.38261i	0.335031	−	0.461130i
$415$	3.24386	−	0.513778i	0.159235	−	0.0252204i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$419$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$420$	−13.4220	+	9.75164i	−0.654926	+	0.475831i
$421$	32.8250	+	20.1152i	1.59979	+	0.980355i	0.980814	+	0.194948i	$0.0624538\pi$
$421$	32.8250	+	20.1152i	1.59979	+	0.980355i	0.618980	+	0.785407i	$0.287546\pi$
$422$		0			0
$423$	−0.554135	−	7.04095i	−0.0269430	−	0.342343i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−12.9841	+	3.11722i	−0.628346	+	0.150853i
$428$	−12.7858	+	39.3507i	−0.618026	+	1.90209i
$429$		0			0
$430$	18.7580	−	36.8146i	0.904591	−	1.77536i
$431$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$431$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$432$	24.7175	+	1.94531i	1.18922	+	0.0935937i
$433$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$433$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$434$		0			0
$435$	−61.3757	+	19.9422i	−2.94274	+	0.956153i
$436$	15.5684	+	25.4053i	0.745591	+	1.21669i
$437$		0			0
$438$		0			0
$439$		0			0		−0.972370	−	0.233445i	$-0.925000\pi$
$439$		0			0		0.972370	+	0.233445i	$0.0750000\pi$
$440$		0			0
$441$	−16.1483	−	22.2263i	−0.768969	−	1.05839i
$442$		0			0
$443$	15.5914	+	2.46944i	0.740770	+	0.117326i	0.515404	−	0.856948i	$-0.327642\pi$
$443$	15.5914	+	2.46944i	0.740770	+	0.117326i	0.225367	+	0.974274i	$0.427642\pi$
$444$		0			0
$445$	−12.5569	−	10.7246i	−0.595254	−	0.508395i
$446$	−5.72665	−	36.1567i	−0.271165	−	1.71207i
$447$	55.2270	+	40.1248i	2.61215	+	1.89784i
$448$	−3.97371	−	9.59338i	−0.187740	−	0.453245i
$449$	7.25537	+	14.2395i	0.342402	+	0.672002i	0.996426	−	0.0844719i	$-0.0269203\pi$
$449$	7.25537	+	14.2395i	0.342402	+	0.672002i	−0.654024	+	0.756474i	$0.726920\pi$
$450$		−	36.5485i		−	1.72291i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	33.1385	−	13.7264i	1.55527	−	0.644213i
$455$		0			0
$456$		0			0
$457$		0			0		0.649448	−	0.760406i	$-0.275000\pi$
$457$		0			0		−0.649448	+	0.760406i	$0.725000\pi$
$458$	10.3892	+	12.1642i	0.485455	+	0.568395i
$459$		0			0
$460$	5.01726	−	5.01726i	0.233931	−	0.233931i
$461$	14.1181	−	10.2574i	0.657545	−	0.477734i	−0.208288	−	0.978068i	$-0.566789\pi$
$461$	14.1181	−	10.2574i	0.657545	−	0.477734i	0.865833	+	0.500333i	$0.166789\pi$
$462$		0			0
$463$	−9.33414	+	38.8795i	−0.433794	+	1.80688i	0.142681	+	0.989769i	$0.454428\pi$
$463$	−9.33414	+	38.8795i	−0.433794	+	1.80688i	−0.576475	+	0.817115i	$0.695572\pi$
$464$	−3.16906	−	40.2667i	−0.147120	−	1.86934i
$465$		0			0
$466$		0			0
$467$	−12.3994	−	38.1615i	−0.573777	−	1.76590i	−0.640306	−	0.768120i	$-0.721192\pi$
$467$	−12.3994	−	38.1615i	−0.573777	−	1.76590i	0.0665285	−	0.997785i	$-0.478808\pi$
$468$		0			0
$469$	−3.13517	+	9.64908i	−0.144769	+	0.445553i
$470$	0.339024	−	4.30771i	0.0156380	−	0.198700i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$479$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$480$	35.1535	+	8.43962i	1.60453	+	0.385214i
$481$		0			0
$482$	21.2439	+	29.2398i	0.967634	+	1.33183i
$483$	−4.16193	−	4.16193i	−0.189375	−	0.189375i
$484$	21.7291	+	3.44156i	0.987688	+	0.156434i
$485$		0			0
$486$	−13.2056	−	11.2787i	−0.599020	−	0.511611i
$487$	5.79720	+	36.6021i	0.262696	+	1.65860i	0.667809	+	0.744332i	$0.267232\pi$
$487$	5.79720	+	36.6021i	0.262696	+	1.65860i	−0.405113	+	0.914267i	$0.632768\pi$
$488$	23.5406	+	17.1033i	1.06563	+	0.774228i
$489$	−7.27613	−	17.5661i	−0.329038	−	0.794368i
$490$	−7.63082	−	14.9763i	−0.344725	−	0.676562i
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$	31.9936	−	17.7787i	1.44238	−	0.801525i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−3.85562	+	4.51436i	−0.172775	+	0.202293i
$499$		0			0		−0.649448	−	0.760406i	$-0.725000\pi$
$499$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$500$	3.49798	−	22.0854i	0.156434	−	0.987688i
$501$	46.1342	−	46.1342i	2.06113	−	2.06113i
$502$		0			0
$503$	−34.4591	−	21.1166i	−1.53646	−	0.941542i	−0.994899	−	0.100879i	$-0.967834\pi$
$503$	−34.4591	−	21.1166i	−1.53646	−	0.941542i	−0.541559	−	0.840663i	$-0.682166\pi$
$504$	4.42977	−	18.4513i	0.197318	−	0.821888i
$505$	3.42040	+	43.4603i	0.152206	+	1.93396i
$506$		0			0
$507$	31.6801	−	19.4136i	1.40696	−	0.862188i
$508$	−8.54724	−	26.3057i	−0.379223	−	1.16713i
$509$	−11.2511	+	2.70116i	−0.498698	+	0.119727i	−0.474988	−	0.879992i	$-0.657548\pi$
$509$	−11.2511	+	2.70116i	−0.498698	+	0.119727i	−0.0237097	+	0.999719i	$0.507548\pi$
$510$		0			0
$511$		0			0
$512$	−10.2726	+	20.1612i	−0.453990	+	0.891007i
$513$		0			0
$514$		0			0
$515$	−43.1130	−	14.0083i	−1.89979	−	0.617278i
$516$	17.4354	+	72.6238i	0.767552	+	3.19708i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.50754	−	1.56232i	−0.285100	−	0.0684465i	0.0883730	−	0.996087i	$-0.471833\pi$
$521$	−6.50754	−	1.56232i	−0.285100	−	0.0684465i	−0.373473	+	0.927641i	$0.621833\pi$
$522$	38.5667	−	62.9351i	1.68802	−	2.75459i
$523$	26.8011	+	36.8885i	1.17193	+	1.61302i	0.649584	+	0.760290i	$0.274943\pi$
$523$	26.8011	+	36.8885i	1.17193	+	1.61302i	0.522346	+	0.852734i	$0.325057\pi$
$524$		0			0
$525$	−18.3204	−	2.90166i	−0.799566	−	0.126639i
$526$	−9.12194	+	7.79087i	−0.397735	+	0.339698i
$527$		0			0
$528$		0			0
$529$	−16.5709	−	12.0394i	−0.720472	−	0.523454i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	29.8500			1.29174
$535$	−41.2175	+	21.0014i	−1.78199	+	0.907969i
$536$	20.4255	−	8.46053i	0.882248	−	0.365439i
$537$		0			0
$538$	41.5342	−	6.57837i	1.79067	−	0.283614i
$539$		0			0
$540$	18.0030	+	21.0788i	0.774725	+	0.907087i
$541$	−6.89001	+	43.5018i	−0.296225	+	1.87029i	0.169746	+	0.985488i	$0.445705\pi$
$541$	−6.89001	+	43.5018i	−0.296225	+	1.87029i	−0.465971	+	0.884800i	$0.654295\pi$
$542$		0			0
$543$	61.4901	−	44.6752i	2.63879	−	1.91720i
$544$		0			0
$545$	−7.77677	+	32.3926i	−0.333120	+	1.38755i
$546$		0			0
$547$	−30.2236	−	12.5190i	−1.29227	−	0.535274i	−0.372606	−	0.927990i	$-0.621536\pi$
$547$	−30.2236	−	12.5190i	−1.29227	−	0.535274i	−0.919660	+	0.392716i	$0.871536\pi$
$548$		0			0
$549$	16.4317	+	50.5715i	0.701287	+	2.15834i
$550$		0			0
$551$		0			0
$552$	−1.00631	+	12.7864i	−0.0428314	+	0.544225i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.233445	−	0.972370i	$-0.575000\pi$
$557$		0			0		0.233445	+	0.972370i	$0.425000\pi$
$558$		0			0
$559$		0			0
$560$	4.44274	−	10.7257i	0.187740	−	0.453245i
$561$		0			0
$562$	−28.0829	−	6.74211i	−1.18461	−	0.284399i
$563$	2.68120	−	4.37532i	0.112999	−	0.184398i	−0.791141	−	0.611634i	$-0.790513\pi$
$563$	2.68120	−	4.37532i	0.112999	−	0.184398i	0.904140	+	0.427236i	$0.140513\pi$
$564$	4.59107	+	6.31906i	0.193319	+	0.266080i
$565$		0			0
$566$	28.3028	+	4.48273i	1.18966	+	0.188423i
$567$	2.18090	−	1.86267i	0.0915894	−	0.0782247i
$568$		0			0
$569$	−6.39776	−	40.3939i	−0.268208	−	1.69340i	−0.642659	−	0.766153i	$-0.722169\pi$
$569$	−6.39776	−	40.3939i	−0.268208	−	1.69340i	0.374451	−	0.927247i	$-0.377831\pi$
$570$		0			0
$571$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$571$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$572$		0			0
$573$		0			0
$574$	−4.03169	−	11.0406i	−0.168279	−	0.460824i
$575$	7.93298			0.330828
$576$	−36.8431	+	18.7725i	−1.53513	+	0.782186i
$577$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$577$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$578$	14.1313	−	19.4501i	0.587785	−	0.809017i
$579$		0			0
$580$	29.3283	−	34.3390i	1.21779	−	1.42585i
$581$	1.23814	+	1.44967i	0.0513666	+	0.0601425i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.76739	+	35.1631i	0.114223	+	1.45134i	0.740669	+	0.671871i	$0.234509\pi$
$587$	2.76739	+	35.1631i	0.114223	+	1.45134i	−0.626446	+	0.779465i	$0.715491\pi$
$588$	28.0703	+	11.6271i	1.15760	+	0.479494i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$593$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$594$		0			0
$595$		0			0
$596$	−47.6218	−	3.74792i	−1.95066	−	0.153521i
$597$		0			0
$598$		0			0
$599$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$599$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$600$	21.1192	+	34.4634i	0.862188	+	1.40696i
$601$	18.3308	−	44.2544i	0.747727	−	1.80517i	0.176655	−	0.984273i	$-0.443472\pi$
$601$	18.3308	−	44.2544i	0.747727	−	1.80517i	0.571072	−	0.820900i	$-0.306528\pi$
$602$	23.9100	−	1.88176i	0.974500	−	0.0766948i
$603$	39.2852	+	9.43155i	1.59982	+	0.384082i
$604$		0			0
$605$	14.4576	+	19.8992i	0.587785	+	0.809017i
$606$	−55.7220	−	55.7220i	−2.26355	−	2.26355i
$607$	33.9806	+	5.38200i	1.37923	+	0.218449i	0.801606	−	0.597853i	$-0.203979\pi$
$607$	33.9806	+	5.38200i	1.37923	+	0.218449i	0.577626	+	0.816302i	$0.303979\pi$
$608$		0			0
$609$	−28.4850	−	24.3285i	−1.15427	−	0.985841i
$610$	5.08918	+	32.1318i	0.206055	+	1.30098i
$611$		0			0
$612$		0			0
$613$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$613$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$614$			47.6492i			1.92297i
$615$	39.3485	+	11.2379i	1.58668	+	0.453156i
$616$		0			0
$617$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$617$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$618$	75.7051	−	31.3581i	3.04531	−	1.26141i
$619$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$619$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$620$		0			0
$621$	−6.38698	+	7.47820i	−0.256301	+	0.300090i
$622$		0			0
$623$	1.49951	−	9.46756i	0.0600768	−	0.379310i
$624$		0			0
$625$	20.2254	−	14.6946i	0.809017	−	0.587785i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	18.0891	−	11.0850i	0.720687	−	0.441638i
$631$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$631$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	14.0393	−	27.5537i	0.557133	−	1.09343i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−24.0600	+	7.81758i	−0.951057	+	0.309017i
$641$	−15.4731	−	25.2498i	−0.611150	−	0.997307i	−0.997197	−	0.0748272i	$-0.976159\pi$
$641$	−15.4731	−	25.2498i	−0.611150	−	0.997307i	0.386046	−	0.922479i	$-0.373841\pi$
$642$	31.9999	−	77.2545i	1.26293	−	3.04899i
$643$	26.3002	−	2.06987i	1.03718	−	0.0816277i	0.451581	−	0.892230i	$-0.350860\pi$
$643$	26.3002	−	2.06987i	1.03718	−	0.0816277i	0.585597	+	0.810602i	$0.300860\pi$
$644$	4.00492	+	0.961497i	0.157816	+	0.0378883i
$645$	−43.6302	+	71.1980i	−1.71794	+	2.80342i
$646$		0			0
$647$	−9.19770	−	9.19770i	−0.361599	−	0.361599i	0.502803	−	0.864401i	$-0.332302\pi$
$647$	−9.19770	−	9.19770i	−0.361599	−	0.361599i	−0.864401	+	0.502803i	$0.832302\pi$
$648$	−6.17290	−	0.977692i	−0.242495	−	0.0384074i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	10.7639	+	7.82045i	0.421548	+	0.306273i
$653$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$653$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$654$	−27.3381	−	53.6540i	−1.06900	−	2.09804i
$655$		0			0
$656$	−12.5886	+	22.3053i	−0.491501	+	0.870877i
$657$		0			0
$658$	2.23486	−	1.13872i	0.0871238	−	0.0443918i
$659$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$659$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$660$		0			0
$661$	2.20318	−	0.348950i	0.0856938	−	0.0135726i	−0.113440	−	0.993545i	$-0.536187\pi$
$661$	2.20318	−	0.348950i	0.0856938	−	0.0135726i	0.199134	+	0.979972i	$0.436187\pi$
$662$		0			0
$663$		0			0
$664$	0.649883	−	4.10320i	0.0252204	−	0.159235i
$665$		0			0
$666$		0			0
$667$	13.6603	+	8.37103i	0.528928	+	0.324127i
$668$	−10.6580	+	44.3938i	−0.412371	+	1.71765i
$669$	5.80463	+	73.7548i	0.224420	+	2.85152i
$670$	22.8364	+	9.45916i	0.882248	+	0.365439i
$671$		0			0
$672$	6.48487	+	19.9584i	0.250159	+	0.769911i
$673$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$673$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$674$		0			0
$675$	−2.43164	+	30.8969i	−0.0935937	+	1.18922i
$676$	−11.8038	+	23.1662i	−0.453990	+	0.891007i
$677$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$677$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−68.9425	+	22.4008i	−2.64188	+	0.858399i
$682$		0			0
$683$	2.61399	−	6.31072i	0.100021	−	0.241473i	−0.865946	−	0.500138i	$-0.833283\pi$
$683$	2.61399	−	6.31072i	0.100021	−	0.241473i	0.965967	+	0.258665i	$0.0832826\pi$
$684$		0			0
$685$		0			0
$686$	11.8116	−	19.2748i	0.450970	−	0.735917i
$687$	−19.0029	−	26.1552i	−0.725004	−	0.997882i
$688$	−36.9560	−	36.9560i	−1.40893	−	1.40893i
$689$		0			0
$690$	−10.9041	+	9.31297i	−0.415111	+	0.354539i
$691$		0			0		−0.760406	−	0.649448i	$-0.775000\pi$
$691$		0			0		0.760406	+	0.649448i	$0.225000\pi$
$692$		0			0
$693$		0			0
$694$	−14.1796	−	34.2326i	−0.538251	−	1.29945i
$695$		0			0
$696$			81.6300i			3.09418i
$697$		0			0
$698$	−42.2531			−1.59930
$699$		0			0
$700$	11.9917	−	4.96714i	0.453245	−	0.187740i
$701$	−10.6564	+	14.6673i	−0.402486	+	0.553975i	−0.961366	−	0.275274i	$-0.911231\pi$
$701$	−10.6564	+	14.6673i	−0.402486	+	0.553975i	0.558879	+	0.829249i	$0.311231\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−1.36610	+	8.62521i	−0.0514503	+	0.324844i
$706$		0			0
$707$	−20.4726	+	14.8742i	−0.769951	+	0.559402i
$708$		0			0
$709$	9.89662	−	41.2224i	0.371675	−	1.54814i	−0.402652	−	0.915353i	$-0.631911\pi$
$709$	9.89662	−	41.2224i	0.371675	−	1.54814i	0.774327	−	0.632786i	$-0.218089\pi$
$710$		0			0
$711$		0			0
$712$	−17.8099	+	10.9139i	−0.667456	+	0.409018i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.996917	−	0.0784591i	$-0.975000\pi$
$719$		0			0		0.996917	+	0.0784591i	$0.0250000\pi$
$720$	−43.9679	−	14.2860i	−1.63859	−	0.532410i
$721$	−6.14284	−	25.5868i	−0.228771	−	0.952901i
$722$	−25.5549	+	8.30330i	−0.951057	+	0.309017i
$723$	−38.1649	−	62.2794i	−1.41937	−	2.31620i
$724$	−20.3535	+	49.1378i	−0.756433	+	1.82619i
$725$	50.3334	−	3.96133i	1.86934	−	0.147120i
$726$	−43.2331	−	10.3794i	−1.60453	−	0.385214i
$727$	−25.1079	+	40.9724i	−0.931202	+	1.51958i	−0.0786754	+	0.996900i	$0.525069\pi$
$727$	−25.1079	+	40.9724i	−0.931202	+	1.51958i	−0.852527	+	0.522684i	$0.824931\pi$
$728$		0			0
$729$	29.5051	+	29.5051i	1.09278	+	1.09278i
$730$		0			0
$731$		0			0
$732$	−44.7165	−	38.1915i	−1.65277	−	1.41160i
$733$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$733$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$734$	42.6668	+	30.9992i	1.57486	+	1.14420i
$735$	12.9995	+	31.3836i	0.479494	+	1.15760i
$736$	−4.07463	−	7.99691i	−0.150193	−	0.294770i
$737$		0			0
$738$	−42.5701	+	19.4548i	−1.56703	+	0.716141i
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	42.1217	−	6.67142i	1.54530	−	0.244751i	0.675201	−	0.737634i	$-0.264057\pi$
$743$	42.1217	−	6.67142i	1.54530	−	0.244751i	0.870095	+	0.492883i	$0.164057\pi$
$744$		0			0
$745$	−34.6853	−	40.6113i	−1.27077	−	1.48788i
$746$		0			0
$747$	5.36819	−	5.36819i	0.196412	−	0.196412i
$748$		0			0
$749$	−22.8954	−	14.0303i	−0.836580	−	0.512657i
$750$	−10.5495	+	43.9419i	−0.385214	+	1.60453i
$751$		0			0		−0.0784591	−	0.996917i	$-0.525000\pi$
$751$		0			0		0.0784591	+	0.996917i	$0.475000\pi$
$752$	−5.04967	−	2.09164i	−0.184142	−	0.0762743i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−4.97238	+	15.3034i	−0.180844	+	0.556579i
$757$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$757$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	51.0382	+	16.5833i	1.85013	+	0.601145i	0.996815	+	0.0797547i	$0.0254137\pi$
$761$	51.0382	+	16.5833i	1.85013	+	0.601145i	0.853319	+	0.521390i	$0.174586\pi$
$762$	13.0494	+	54.3548i	0.472731	+	1.96907i
$763$	−18.3909	+	5.97555i	−0.665794	+	0.216329i
$764$		0			0
$765$		0			0
$766$	−42.9737	+	3.38210i	−1.55270	+	0.122200i
$767$		0			0
$768$	23.8937	−	38.9909i	0.862188	−	1.40696i
$769$	−29.8682	−	41.1101i	−1.07708	−	1.48247i	−0.862700	−	0.505715i	$-0.831229\pi$
$769$	−29.8682	−	41.1101i	−1.07708	−	1.48247i	−0.214375	−	0.976751i	$-0.568771\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.760406	−	0.649448i	$-0.775000\pi$
$773$		0			0		0.760406	+	0.649448i	$0.225000\pi$
$774$	−14.9407	−	94.3321i	−0.537033	−	3.39070i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		−	15.8666i		−	0.568846i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−36.7901	+	50.6372i	−1.31477	+	1.80963i
$784$	−20.9993	+	3.32596i	−0.749974	+	0.118784i
$785$		0			0
$786$		0			0
$787$	−8.61249	+	54.3771i	−0.307002	+	1.93834i	0.0368739	+	0.999320i	$0.488260\pi$
$787$	−8.61249	+	54.3771i	−0.307002	+	1.93834i	−0.343876	+	0.939015i	$0.611740\pi$
$788$		0			0
$789$	19.6138	−	14.2503i	0.698270	−	0.507323i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$797$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$798$		0			0
$799$		0			0
$800$	−25.2015	−	12.8408i	−0.891007	−	0.453990i
$801$	−38.0536	−	2.99488i	−1.34456	−	0.105819i
$802$	−51.3149	−	16.6732i	−1.81199	−	0.588752i
$803$		0			0
$804$	−42.4939	+	13.8071i	−1.49865	+	0.486939i
$805$	2.40604	+	3.92630i	0.0848018	+	0.138384i
$806$		0			0
$807$	−84.7242	+	6.66794i	−2.98243	+	0.234723i
$808$	53.6198	+	12.8730i	1.88634	+	0.452870i
$809$	29.6173	−	48.3310i	1.04129	−	1.69923i	0.448875	−	0.893594i	$-0.351825\pi$
$809$	29.6173	−	48.3310i	1.04129	−	1.69923i	0.592413	−	0.805634i	$-0.298175\pi$
$810$	−4.10718	−	5.65304i	−0.144311	−	0.198628i
$811$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$811$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$812$	25.8907	+	4.10068i	0.908585	+	0.143906i
$813$		0			0
$814$		0			0
$815$	2.32702	+	14.6922i	0.0815121	+	0.514647i
$816$		0			0
$817$		0			0
$818$	9.44359	+	18.5341i	0.330187	+	0.648029i
$819$		0			0
$820$	−27.5861	+	7.68176i	−0.963347	+	0.268259i
$821$	57.2334			1.99746			0.998730	−	0.0503864i	$-0.0160453\pi$
$821$	57.2334			1.99746			0.998730	+	0.0503864i	$0.0160453\pi$
$822$		0			0
$823$	29.2602	−	12.1200i	1.01995	−	0.422476i	0.190872	−	0.981615i	$-0.438868\pi$
$823$	29.2602	−	12.1200i	1.01995	−	0.422476i	0.829074	+	0.559139i	$0.188868\pi$
$824$	−33.7040	+	46.3895i	−1.17413	+	1.61606i
$825$		0			0
$826$		0			0
$827$	−29.0536	−	34.0175i	−1.01029	−	1.18290i	−0.983062	−	0.183274i	$-0.941331\pi$
$827$	−29.0536	−	34.0175i	−1.01029	−	1.18290i	−0.0272324	−	0.999629i	$-0.508669\pi$
$828$	2.56574	−	16.1995i	0.0891658	−	0.562971i
$829$	30.9751	−	30.9751i	1.07581	−	1.07581i	0.0789305	−	0.996880i	$-0.474849\pi$
$829$	30.9751	−	30.9751i	1.07581	−	1.07581i	0.996880	−	0.0789305i	$-0.0251505\pi$
$830$	3.75764	−	2.73009i	0.130430	−	0.0947627i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−43.5223	+	26.6705i	−1.50615	+	0.922970i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$839$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$840$	−10.6517	+	20.9052i	−0.367520	+	0.721299i
$841$	65.0130	+	33.1258i	2.24183	+	1.14227i
$842$	54.2767	+	4.27167i	1.87050	+	0.147211i
$843$	55.5111	+	18.0366i	1.91190	+	0.621215i
$844$		0			0
$845$	−27.6462	+	8.98278i	−0.951057	+	0.309017i
$846$	−5.21882	−	8.51634i	−0.179427	−	0.292798i
$847$	−5.46385	+	13.1909i	−0.187740	+	0.453245i
$848$		0			0
$849$	−56.3124	−	13.5194i	−1.93264	−	0.463985i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$853$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$854$	−14.3596	+	12.2643i	−0.491375	+	0.419674i
$855$		0			0
$856$	9.15363	+	57.7938i	0.312865	+	1.97535i
$857$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$857$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$858$		0			0
$859$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$859$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$860$		−	58.4325i		−	1.99253i
$861$	6.37221	+	22.8833i	0.217164	+	0.779861i
$862$		0			0
$863$	8.45283	−	4.30693i	0.287738	−	0.146610i	−0.304164	−	0.952620i	$-0.598377\pi$
$863$	8.45283	−	4.30693i	0.287738	−	0.146610i	0.591902	+	0.806010i	$0.298377\pi$
$864$	32.3948	−	13.4184i	1.10209	−	0.456502i
$865$		0			0
$866$		0			0
$867$	−31.5552	+	36.9464i	−1.07167	+	1.25477i
$868$		0			0
$869$		0			0
$870$	−64.5342	+	64.5342i	−2.18791	+	2.18791i
$871$		0			0
$872$	35.9286	+	22.0171i	1.21669	+	0.745591i
$873$		0			0
$874$		0			0
$875$	13.4072	+	5.55343i	0.453245	+	0.187740i
$876$		0			0
$877$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$877$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.25188	−	2.45696i	0.0421770	−	0.0827771i	−0.868956	−	0.494889i	$-0.835209\pi$
$881$	1.25188	−	2.45696i	0.0421770	−	0.0827771i	0.911133	+	0.412112i	$0.135209\pi$
$882$	−34.6183	−	17.6389i	−1.16566	−	0.593932i
$883$	−42.3539	−	3.33333i	−1.42532	−	0.112175i	−0.657798	−	0.753194i	$-0.728512\pi$
$883$	−42.3539	−	3.33333i	−1.42532	−	0.112175i	−0.767525	+	0.641019i	$0.778512\pi$
$884$		0			0
$885$		0			0
$886$	21.2318	−	6.89863i	0.713296	−	0.231764i
$887$	−1.60597	−	2.62071i	−0.0539234	−	0.0879949i	0.824543	−	0.565800i	$-0.191433\pi$
$887$	−1.60597	−	2.62071i	−0.0539234	−	0.0879949i	−0.878466	+	0.477805i	$0.841433\pi$
$888$		0			0
$889$	17.8953	−	1.40839i	0.600189	−	0.0472359i
$890$	−22.7082	−	5.45176i	−0.761182	−	0.182744i
$891$		0			0
$892$	−30.4300	−	41.8833i	−1.01887	−	1.40236i
$893$		0			0
$894$	95.3518	+	15.1022i	3.18904	+	0.505095i
$895$		0			0
$896$	−11.1665	−	9.53709i	−0.373046	−	0.318612i
$897$		0			0
$898$	18.2846	+	13.2845i	0.610165	+	0.443311i
$899$		0			0
$900$	−23.4656	−	46.0538i	−0.782186	−	1.53513i
$901$		0			0
$902$		0			0
$903$	−48.4712			−1.61302
$904$		0			0
$905$	−54.9377	+	22.7559i	−1.82619	+	0.756433i
$906$		0			0
$907$	−54.7779	+	8.67597i	−1.81887	+	0.288081i	−0.970461	−	0.241260i	$-0.922439\pi$
$907$	−54.7779	+	8.67597i	−1.81887	+	0.288081i	−0.848410	+	0.529340i	$0.822439\pi$
$908$	32.9441	−	38.5726i	1.09329	−	1.28008i
$909$	65.4452	+	76.6265i	2.17068	+	2.54154i
$910$		0			0
$911$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$911$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−5.15847	−	65.5446i	−0.170534	−	2.16684i
$916$	20.9010	+	8.65749i	0.690590	+	0.286052i
$917$		0			0
$918$		0			0
$919$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$919$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$920$	3.10083	−	9.54339i	0.102231	−	0.314636i
$921$	7.55548	−	96.0014i	0.248961	−	3.16335i
$922$	11.2042	−	21.9894i	0.368990	−	0.724183i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	13.2005	+	54.9839i	0.433794	+	1.80688i
$927$	−99.6571	+	32.3806i	−3.27317	+	1.06352i
$928$	−29.8461	−	48.7044i	−0.979746	−	1.59880i
$929$	9.00122	−	21.7309i	0.295320	−	0.712967i	−0.704674	−	0.709532i	$-0.748907\pi$
$929$	9.00122	−	21.7309i	0.295320	−	0.712967i	0.999994	−	0.00343511i	$-0.00109343\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−40.1254	−	40.1254i	−1.31294	−	1.31294i
$935$		0			0
$936$		0			0
$937$		0			0		−0.760406	−	0.649448i	$-0.775000\pi$
$937$		0			0		0.760406	+	0.649448i	$0.225000\pi$
$938$	2.24454	+	14.1715i	0.0732867	+	0.462714i
$939$		0			0
$940$	−2.33852	−	5.64570i	−0.0762743	−	0.184142i
$941$	−26.7467	−	52.4933i	−0.871917	−	1.71123i	−0.684580	−	0.728937i	$-0.740015\pi$
$941$	−26.7467	−	52.4933i	−0.871917	−	1.71123i	−0.187336	−	0.982296i	$-0.559985\pi$
$942$		0			0
$943$	−4.22273	−	9.23998i	−0.137511	−	0.300895i
$944$		0			0
$945$	−16.0294	+	8.16739i	−0.521437	+	0.265685i
$946$		0			0
$947$	29.2177	−	40.2148i	0.949449	−	1.30680i	−0.00232231	−	0.999997i	$-0.500739\pi$
$947$	29.2177	−	40.2148i	0.949449	−	1.30680i	0.951772	−	0.306808i	$-0.0992608\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$953$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	49.7146	−	11.9354i	1.60453	−	0.385214i
$961$	−9.57953	+	29.4828i	−0.309017	+	0.951057i
$962$		0			0
$963$	−48.5453	+	95.2756i	−1.56435	+	3.07021i
$964$	45.5420	+	23.2048i	1.46681	+	0.747376i
$965$		0			0
$966$	−7.91647	−	2.57222i	−0.254708	−	0.0827597i
$967$	13.7379	+	57.2226i	0.441782	+	1.84015i	0.535473	+	0.844552i	$0.320133\pi$
$967$	13.7379	+	57.2226i	0.441782	+	1.84015i	−0.0936918	+	0.995601i	$0.529867\pi$
$968$	29.5899	−	9.61435i	0.951057	−	0.309017i
$969$		0			0
$970$		0			0
$971$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$971$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$972$	−23.8814	−	5.73343i	−0.765998	−	0.183900i
$973$		0			0
$974$	30.8049	+	42.3993i	0.987052	+	1.35856i
$975$		0			0
$976$	40.6439	+	6.43736i	1.30098	+	0.206055i
$977$		0			0		0.760406	−	0.649448i	$-0.225000\pi$
$977$		0			0		−0.760406	+	0.649448i	$0.775000\pi$
$978$	−20.4466	−	17.4631i	−0.653811	−	0.558407i
$979$		0			0
$980$	−19.2308	−	13.9720i	−0.614305	−	0.446319i
$981$	29.4682	+	71.1425i	0.940847	+	2.27141i
$982$		0			0
$983$			33.0869i			1.05531i	0.849459	+	0.527655i	$0.176928\pi$
$983$			33.0869i			1.05531i	−0.849459	+	0.527655i	$0.823072\pi$
$984$	28.8997	−	42.9436i	0.921289	−	1.36899i
$985$		0			0
$986$		0			0
$987$	−4.68324	+	1.93986i	−0.149069	+	0.0617465i
$988$		0			0
$989$	20.4751	−	3.24294i	0.651070	−	0.103119i
$990$		0			0
$991$		0			0		−0.649448	−	0.760406i	$-0.725000\pi$
$991$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−1.95998	+	8.16388i	−0.0621042	+	0.258683i
$997$		0			0		−0.0784591	−	0.996917i	$-0.525000\pi$
$997$		0			0		0.0784591	+	0.996917i	$0.475000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.cc.a.719.1	yes	16
4.3	odd	2		820.2.cc.f.719.1	yes	16
5.4	even	2		820.2.cc.f.719.1	yes	16
20.19	odd	2	CM	820.2.cc.a.719.1	yes	16
41.28	odd	40	inner	820.2.cc.a.479.1	✓	16
164.151	even	40		820.2.cc.f.479.1	yes	16
205.69	odd	40		820.2.cc.f.479.1	yes	16
820.479	even	40	inner	820.2.cc.a.479.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.cc.a.479.1	✓	16	41.28	odd	40	inner
820.2.cc.a.479.1	✓	16	820.479	even	40	inner
820.2.cc.a.719.1	yes	16	1.1	even	1	trivial
820.2.cc.a.719.1	yes	16	20.19	odd	2	CM
820.2.cc.f.479.1	yes	16	164.151	even	40
820.2.cc.f.479.1	yes	16	205.69	odd	40
820.2.cc.f.719.1	yes	16	4.3	odd	2
820.2.cc.f.719.1	yes	16	5.4	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.cc (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26007 - 0.642040i) q^{2} +(-2.64054 + 1.09375i) q^{3} +(1.17557 - 1.61803i) q^{4} +(2.20854 - 0.349798i) q^{5} +(-2.62505 + 3.07353i) q^{6} +(0.842968 + 0.986988i) q^{7} +(0.442463 - 2.79360i) q^{8} +(3.65485 - 3.65485i) q^{9} +(2.55834 - 1.85874i) q^{10} +(-1.33442 + 5.55826i) q^{12} +(1.69589 + 0.702459i) q^{14} +(-5.44914 + 3.33924i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(2.25882 - 6.95194i) q^{18} +(2.03031 - 3.98470i) q^{20} +(-3.30541 - 1.68419i) q^{21} +(1.50894 + 0.490285i) q^{23} +(1.88716 + 7.86057i) q^{24} +(4.75528 - 1.54508i) q^{25} +(-2.37206 + 5.72665i) q^{27} +(2.58795 - 0.203676i) q^{28} +(9.81881 + 2.35729i) q^{29} +(-4.72240 + 7.70625i) q^{30} +(-4.00000 - 4.00000i) q^{32} +(2.20697 + 1.88493i) q^{35} +(-1.61714 - 10.2102i) q^{36} -6.32456i q^{40} +(-4.33089 - 4.71629i) q^{41} -5.24637 q^{42} +(11.6418 - 5.93180i) q^{43} +(6.79342 - 9.35034i) q^{45} +(2.21616 - 0.351005i) q^{46} +(0.887425 - 1.03904i) q^{47} +(7.42475 + 8.69327i) q^{48} +(0.831490 - 5.24982i) q^{49} +(5.00000 - 5.00000i) q^{50} +(0.687770 + 8.73895i) q^{54} +(3.13024 - 1.91821i) q^{56} +(13.8859 - 3.33371i) q^{58} +(-1.00285 + 12.7424i) q^{60} +(-4.67048 + 9.16634i) q^{61} +(6.68822 + 0.526374i) q^{63} +(-7.60845 - 2.47214i) q^{64} +(4.08412 + 6.66467i) q^{67} +(-4.52067 + 0.355785i) q^{69} +(3.99115 + 0.958190i) q^{70} +(-8.59307 - 11.8273i) q^{72} +(-10.8666 + 9.28094i) q^{75} +(-4.06061 - 7.96940i) q^{80} -2.20966i q^{81} +(-8.48528 - 3.16228i) q^{82} +1.46878 q^{83} +(-6.61081 + 3.36838i) q^{84} +(10.8611 - 14.9490i) q^{86} +(-28.5052 + 4.51479i) q^{87} +(-4.79619 - 5.61562i) q^{89} +(2.55692 - 16.1438i) q^{90} +(2.56717 - 1.86515i) q^{92} +(0.451115 - 1.87903i) q^{94} +(14.9372 + 6.18717i) q^{96} +(-2.32285 - 7.14901i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 12 q^{3} + 20 q^{6} + 16 q^{7} + 8 q^{8} + 12 q^{9} - 16 q^{12} + 20 q^{15} + 16 q^{16} + 4 q^{18} + 4 q^{21} + 8 q^{24} - 48 q^{27} + 8 q^{28} - 80 q^{30} - 64 q^{32} - 20 q^{35} + 24 q^{36}+ \cdots - 104 q^{98}+O(q^{100}) \) 16 * q - 4 * q^2 - 12 * q^3 + 20 * q^6 + 16 * q^7 + 8 * q^8 + 12 * q^9 - 16 * q^12 + 20 * q^15 + 16 * q^16 + 4 * q^18 + 4 * q^21 + 8 * q^24 - 48 * q^27 + 8 * q^28 - 80 * q^30 - 64 * q^32 - 20 * q^35 + 24 * q^36 + 8 * q^42 + 44 * q^47 + 48 * q^48 + 68 * q^49 + 80 * q^50 + 52 * q^54 - 24 * q^56 + 52 * q^58 + 36 * q^63 + 24 * q^67 + 20 * q^69 + 20 * q^70 - 80 * q^72 + 40 * q^75 + 8 * q^84 - 128 * q^87 - 80 * q^89 + 60 * q^90 + 28 * q^94 + 80 * q^96 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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