LMFDB - Embedded newform 820.2.cc.a.19.1

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			19.1
Root			$-0.987688 + 0.156434i$ of defining polynomial
Character	$\chi$	$=$	820.19
Dual form			820.2.cc.a.259.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26007 - 0.642040i) q^{2} +(0.749049 + 1.80837i) q^{3} +(1.17557 - 1.61803i) q^{4} +(-2.20854 + 0.349798i) q^{5} +(2.10490 + 1.79775i) q^{6} +(3.90076 - 3.33156i) q^{7} +(0.442463 - 2.79360i) q^{8} +(-0.587789 + 0.587789i) q^{9} +(-2.55834 + 1.85874i) q^{10} +(3.80656 + 0.913873i) q^{12} +(2.77625 - 6.70246i) q^{14} +(-2.28687 - 3.73183i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(-0.363274 + 1.11804i) q^{18} +(-2.03031 + 3.98470i) q^{20} +(8.94655 + 4.55849i) q^{21} +(-1.50894 - 0.490285i) q^{23} +(5.38328 - 1.29241i) q^{24} +(4.75528 - 1.54508i) q^{25} +(3.92187 + 1.62449i) q^{27} +(-0.804965 - 10.2281i) q^{28} +(-0.874538 + 3.64271i) q^{29} +(-5.27760 - 3.23412i) q^{30} +(-4.00000 - 4.00000i) q^{32} +(-7.44961 + 8.72237i) q^{35} +(0.260075 + 1.64205i) q^{36} +6.32456i q^{40} +(4.33089 + 4.71629i) q^{41} +14.2000 q^{42} +(-11.6418 + 5.93180i) q^{43} +(1.09255 - 1.50376i) q^{45} +(-2.21616 + 0.351005i) q^{46} +(10.3743 + 8.86045i) q^{47} +(5.95355 - 5.08482i) q^{48} +(3.02157 - 19.0775i) q^{49} +(5.00000 - 5.00000i) q^{50} +(5.98484 - 0.471017i) q^{54} +(-7.58113 - 12.3713i) q^{56} +(1.23678 + 5.15157i) q^{58} +(-8.72660 - 0.686798i) q^{60} +(4.67048 - 9.16634i) q^{61} +(-0.334568 + 4.25108i) q^{63} +(-7.60845 - 2.47214i) q^{64} +(-12.2645 + 7.51567i) q^{67} +(-0.243658 - 3.09597i) q^{69} +(-3.78695 + 15.7738i) q^{70} +(1.38198 + 1.90213i) q^{72} +(6.35602 + 7.44194i) q^{75} +(4.06061 + 7.96940i) q^{80} +10.8028i q^{81} +(8.48528 + 3.16228i) q^{82} -1.46878 q^{83} +(17.8931 - 9.11699i) q^{84} +(-10.8611 + 14.9490i) q^{86} +(-7.24243 + 1.14709i) q^{87} +(-13.2027 + 11.2761i) q^{89} +(0.411215 - 2.59631i) q^{90} +(-2.56717 + 1.86515i) q^{92} +(18.7611 + 4.50414i) q^{94} +(4.23726 - 10.2297i) q^{96} +(-8.44108 - 25.9790i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{9}{40}\right)$	$-1$

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
$3$	0.749049	+	1.80837i	0.432464	+	1.04406i	0.978490	+	0.206292i	$0.0661398\pi$
$3$	0.749049	+	1.80837i	0.432464	+	1.04406i	−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
$6$	2.10490	+	1.79775i	0.859322	+	0.733930i
$7$	3.90076	−	3.33156i	1.47435	−	1.25921i	0.577869	−	0.816130i	$-0.303885\pi$
$7$	3.90076	−	3.33156i	1.47435	−	1.25921i	0.896480	−	0.443083i	$-0.146115\pi$
$8$	0.442463	−	2.79360i	0.156434	−	0.987688i
$9$	−0.587789	+	0.587789i	−0.195930	+	0.195930i
$10$	−2.55834	+	1.85874i	−0.809017	+	0.587785i
$11$		0			0		0.522499	−	0.852640i	$-0.325000\pi$
$11$		0			0		−0.522499	+	0.852640i	$0.675000\pi$
$12$	3.80656	+	0.913873i	1.09886	+	0.263813i
$13$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$13$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$14$	2.77625	−	6.70246i	0.741984	−	1.79131i
$15$	−2.28687	−	3.73183i	−0.590467	−	0.963554i
$16$	−1.23607	−	3.80423i	−0.309017	−	0.951057i
$17$		0			0		−0.233445	−	0.972370i	$-0.575000\pi$
$17$		0			0		0.233445	+	0.972370i	$0.425000\pi$
$18$	−0.363274	+	1.11804i	−0.0856245	+	0.263525i
$19$		0			0		−0.996917	−	0.0784591i	$-0.975000\pi$
$19$		0			0		0.996917	+	0.0784591i	$0.0250000\pi$
$20$	−2.03031	+	3.98470i	−0.453990	+	0.891007i
$21$	8.94655	+	4.55849i	1.95230	+	0.994745i
$22$		0			0
$23$	−1.50894	−	0.490285i	−0.314636	−	0.102231i	0.147442	−	0.989071i	$-0.452896\pi$
$23$	−1.50894	−	0.490285i	−0.314636	−	0.102231i	−0.462078	+	0.886839i	$0.652896\pi$
$24$	5.38328	−	1.29241i	1.09886	−	0.263813i
$25$	4.75528	−	1.54508i	0.951057	−	0.309017i
$26$		0			0
$27$	3.92187	+	1.62449i	0.754765	+	0.312634i
$28$	−0.804965	−	10.2281i	−0.152124	−	1.93292i
$29$	−0.874538	+	3.64271i	−0.162398	+	0.676435i	0.830455	+	0.557086i	$0.188081\pi$
$29$	−0.874538	+	3.64271i	−0.162398	+	0.676435i	−0.992852	+	0.119349i	$0.961919\pi$
$30$	−5.27760	−	3.23412i	−0.963554	−	0.590467i
$31$		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
$35$	−7.44961	+	8.72237i	−1.25921	+	1.47435i
$36$	0.260075	+	1.64205i	0.0433459	+	0.273675i
$37$		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
$42$	14.2000			2.19111
$43$	−11.6418	+	5.93180i	−1.77536	+	0.904591i	−0.848485	+	0.529220i	$0.822485\pi$
$43$	−11.6418	+	5.93180i	−1.77536	+	0.904591i	−0.926875	+	0.375371i	$0.877515\pi$
$44$		0			0
$45$	1.09255	−	1.50376i	0.162867	−	0.224168i
$46$	−2.21616	+	0.351005i	−0.326755	+	0.0517529i
$47$	10.3743	+	8.86045i	1.51324	+	1.29243i	0.821343	+	0.570435i	$0.193225\pi$
$47$	10.3743	+	8.86045i	1.51324	+	1.29243i	0.691898	+	0.721995i	$0.256775\pi$
$48$	5.95355	−	5.08482i	0.859322	−	0.733930i
$49$	3.02157	−	19.0775i	0.431653	−	2.72535i
$50$	5.00000	−	5.00000i	0.707107	−	0.707107i
$51$		0			0
$52$		0			0
$53$		0			0		−0.972370	−	0.233445i	$-0.925000\pi$
$53$		0			0		0.972370	+	0.233445i	$0.0750000\pi$
$54$	5.98484	−	0.471017i	0.814433	−	0.0640973i
$55$		0			0
$56$	−7.58113	−	12.3713i	−1.01307	−	1.65318i
$57$		0			0
$58$	1.23678	+	5.15157i	0.162398	+	0.676435i
$59$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$59$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$60$	−8.72660	−	0.686798i	−1.12660	−	0.0886653i
$61$	4.67048	−	9.16634i	0.597994	−	1.17363i	−0.371481	−	0.928441i	$-0.621150\pi$
$61$	4.67048	−	9.16634i	0.597994	−	1.17363i	0.969475	−	0.245189i	$-0.0788501\pi$
$62$		0			0
$63$	−0.334568	+	4.25108i	−0.0421516	+	0.535586i
$64$	−7.60845	−	2.47214i	−0.951057	−	0.309017i
$65$		0			0
$66$		0			0
$67$	−12.2645	+	7.51567i	−1.49834	+	0.918185i	−0.499694	+	0.866202i	$0.666554\pi$
$67$	−12.2645	+	7.51567i	−1.49834	+	0.918185i	−0.998648	+	0.0519829i	$0.983446\pi$
$68$		0			0
$69$	−0.243658	−	3.09597i	−0.0293330	−	0.372711i
$70$	−3.78695	+	15.7738i	−0.452627	+	1.88533i
$71$		0			0		−0.852640	−	0.522499i	$-0.825000\pi$
$71$		0			0		0.852640	+	0.522499i	$0.175000\pi$
$72$	1.38198	+	1.90213i	0.162867	+	0.224168i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$		0			0
$75$	6.35602	+	7.44194i	0.733930	+	0.859322i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$79$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$80$	4.06061	+	7.96940i	0.453990	+	0.891007i
$81$			10.8028i			1.20031i
$82$	8.48528	+	3.16228i	0.937043	+	0.349215i
$83$	−1.46878			−0.161220			−0.0806100	−	0.996746i	$-0.525687\pi$
$83$	−1.46878			−0.161220			−0.0806100	+	0.996746i	$0.525687\pi$
$84$	17.8931	−	9.11699i	1.95230	−	0.994745i
$85$		0			0
$86$	−10.8611	+	14.9490i	−1.17118	+	1.61199i
$87$	−7.24243	+	1.14709i	−0.776470	+	0.122981i
$88$		0			0
$89$	−13.2027	+	11.2761i	−1.39948	+	1.19527i	−0.445542	+	0.895261i	$0.646989\pi$
$89$	−13.2027	+	11.2761i	−1.39948	+	1.19527i	−0.953937	+	0.300007i	$0.903011\pi$
$90$	0.411215	−	2.59631i	0.0433459	−	0.273675i
$91$		0			0
$92$	−2.56717	+	1.86515i	−0.267646	+	0.194456i
$93$		0			0
$94$	18.7611	+	4.50414i	1.93506	+	0.464566i
$95$		0			0
$96$	4.23726	−	10.2297i	0.432464	−	1.04406i
$97$		0			0		−0.522499	−	0.852640i	$-0.675000\pi$
$97$		0			0		0.522499	+	0.852640i	$0.325000\pi$
$98$	−8.44108	−	25.9790i	−0.852678	−	2.62427i
$99$		0			0
$100$	3.09017	−	9.51057i	0.309017	−	0.951057i
$101$	4.87372	+	0.383570i	0.484953	+	0.0381666i	0.318579	−	0.947896i	$-0.396794\pi$
$101$	4.87372	+	0.383570i	0.484953	+	0.0381666i	0.166374	+	0.986063i	$0.446794\pi$
$102$		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
$105$	−21.3533	−	6.93812i	−2.08387	−	0.677091i
$106$		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	$0.901636\pi$
$108$	7.23893	−	4.43602i	0.696566	−	0.426856i
$109$	13.5167	+	5.59881i	1.29467	+	0.536269i	0.920373	−	0.391041i	$-0.127885\pi$
$109$	13.5167	+	5.59881i	1.29467	+	0.536269i	0.374294	+	0.927310i	$0.377885\pi$
$110$		0			0
$111$		0			0
$112$	−17.4956	−	10.7213i	−1.65318	−	1.01307i
$113$		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
$116$	4.86595	+	5.69730i	0.451792	+	0.528981i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−11.4371	+	4.73740i	−1.04406	+	0.432464i
$121$	−4.99390	−	9.80107i	−0.453990	−	0.891007i
$122$		−	14.5489i		−	1.31720i
$123$	−5.28474	+	11.3646i	−0.476509	+	1.02471i
$124$		0			0
$125$	−9.96176	+	5.07577i	−0.891007	+	0.453990i
$126$	2.30778	+	5.57148i	0.205594	+	0.496347i
$127$	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
$129$	−19.4471	−	16.6094i	−1.71223	−	1.46238i
$130$		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
$134$	−10.6288	+	17.3446i	−0.918185	+	1.49834i
$135$	−9.22985	−	2.21589i	−0.794379	−	0.190714i
$136$		0			0
$137$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$137$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$138$	−2.29476	−	3.74471i	−0.195343	−	0.318771i
$139$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$139$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$140$	5.35555	+	22.3075i	0.452627	+	1.88533i
$141$	−8.25210	+	25.3974i	−0.694953	+	2.13884i
$142$		0			0
$143$		0			0
$144$	2.96263	+	1.50954i	0.246886	+	0.125795i
$145$	0.657236	−	8.35098i	0.0545805	−	0.693511i
$146$		0			0
$147$	36.7623	−	8.82585i	3.03210	−	0.727944i
$148$		0			0
$149$	−4.30812	+	2.64002i	−0.352935	+	0.216279i	−0.687653	−	0.726039i	$-0.741359\pi$
$149$	−4.30812	+	2.64002i	−0.352935	+	0.216279i	0.334718	+	0.942318i	$0.391359\pi$
$150$	12.7871	+	5.29658i	1.04406	+	0.432464i
$151$		0			0		−0.0784591	−	0.996917i	$-0.525000\pi$
$151$		0			0		0.0784591	+	0.996917i	$0.475000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.649448	−	0.760406i	$-0.725000\pi$
$157$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$158$		0			0
$159$		0			0
$160$	10.2333	+	7.43496i	0.809017	+	0.587785i
$161$	−7.51944	+	3.11465i	−0.592615	+	0.245469i
$162$	6.93582	+	13.6123i	0.544929	+	1.06948i
$163$			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
$167$	−4.63820	−	11.1976i	−0.358914	−	0.866496i	−0.995453	−	0.0952515i	$-0.969634\pi$
$167$	−4.63820	−	11.1976i	−0.358914	−	0.866496i	0.636539	−	0.771245i	$-0.280366\pi$
$168$	16.6932	−	22.9762i	1.28790	−	1.77265i
$169$	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	$0.750000\pi$
$174$	−8.38951	+	6.09534i	−0.636007	+	0.462086i
$175$	13.4017	−	21.8695i	1.01307	−	1.65318i
$176$		0			0
$177$		0			0
$178$	−9.39660	+	22.6854i	−0.704305	+	1.70034i
$179$		0			0		−0.522499	−	0.852640i	$-0.675000\pi$
$179$		0			0		0.522499	+	0.852640i	$0.325000\pi$
$180$	−1.14877	−	3.53556i	−0.0856245	−	0.263525i
$181$	0.956919	+	3.98585i	0.0711272	+	0.296266i	0.996584	−	0.0825874i	$-0.0263184\pi$
$181$	0.956919	+	3.98585i	0.0711272	+	0.296266i	−0.925457	+	0.378854i	$0.876318\pi$
$182$		0			0
$183$	20.0745	+	1.57990i	1.48395	+	0.116789i
$184$	−2.03731	+	3.99845i	−0.150193	+	0.294770i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	26.5322	−	6.36981i	1.93506	−	0.464566i
$189$	20.7104	−	6.72922i	1.50646	−	0.489479i
$190$		0			0
$191$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$191$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$192$	−1.22858	−	15.6106i	−0.0886653	−	1.12660i
$193$		0			0		0.233445	−	0.972370i	$-0.425000\pi$
$193$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$194$		0			0
$195$		0			0
$196$	−27.3159	−	27.3159i	−1.95114	−	1.95114i
$197$		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		0.649448	−	0.760406i	$-0.275000\pi$
$199$		0			0		−0.649448	+	0.760406i	$0.725000\pi$
$200$	−2.21232	−	13.9680i	−0.156434	−	0.987688i
$201$	−22.7778	−	16.5490i	−1.60662	−	1.16728i
$202$	6.38751	−	2.64579i	0.449424	−	0.186157i
$203$	8.72457	+	17.1229i	0.612345	+	1.20179i
$204$		0			0
$205$	−11.2147	−	8.90118i	−0.783267	−	0.621685i
$206$	−28.6703			−1.99755
$207$	1.17512	−	0.598756i	0.0816768	−	0.0416164i
$208$		0			0
$209$		0			0
$210$	−31.3613	+	4.96715i	−2.16414	+	0.342766i
$211$		0			0		−0.760406	−	0.649448i	$-0.775000\pi$
$211$		0			0		0.760406	+	0.649448i	$0.225000\pi$
$212$		0			0
$213$		0			0
$214$	−20.6879	+	20.6879i	−1.41419	+	1.41419i
$215$	23.6365	−	17.1729i	1.61199	−	1.17118i
$216$	6.27348	−	10.2374i	0.426856	−	0.696566i
$217$		0			0
$218$	20.6267	−	1.62336i	1.39702	−	0.109948i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−7.99900	+	24.6184i	−0.535653	+	1.64857i	0.206581	+	0.978429i	$0.433766\pi$
$223$	−7.99900	+	24.6184i	−0.535653	+	1.64857i	−0.742234	+	0.670141i	$0.766234\pi$
$224$	−28.9293	−	2.27679i	−1.93292	−	0.152124i
$225$	−1.88692	+	3.70329i	−0.125795	+	0.246886i
$226$		0			0
$227$	1.27652	−	16.2198i	0.0847259	−	1.07655i	−0.796748	−	0.604312i	$-0.793448\pi$
$227$	1.27652	−	16.2198i	0.0847259	−	1.07655i	0.881474	−	0.472233i	$-0.156552\pi$
$228$		0			0
$229$	27.2966	−	6.55333i	1.80381	−	0.433056i	0.814655	−	0.579946i	$-0.196926\pi$
$229$	27.2966	−	6.55333i	1.80381	−	0.433056i	0.989153	+	0.146890i	$0.0469263\pi$
$230$	4.77169	−	1.55042i	0.314636	−	0.102231i
$231$		0			0
$232$	9.78935	+	4.05488i	0.642702	+	0.266216i
$233$		0			0		−0.0784591	−	0.996917i	$-0.525000\pi$
$233$		0			0		0.0784591	+	0.996917i	$0.475000\pi$
$234$		0			0
$235$	−26.0113	−	15.9398i	−1.69679	−	1.03979i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.649448	−	0.760406i	$-0.725000\pi$
$239$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$240$	−11.3700	+	13.3126i	−0.733930	+	0.859322i
$241$	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
$243$	−7.76976	+	3.21834i	−0.498430	+	0.206457i
$244$	−9.34097	−	18.3327i	−0.597994	−	1.17363i
$245$			43.1902i			2.75932i
$246$	0.637342	+	17.7132i	0.0406354	+	1.12935i
$247$		0			0
$248$		0			0
$249$	−1.10019	−	2.65610i	−0.0697218	−	0.168323i
$250$	−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	$0.950000\pi$
$252$	6.48509	+	5.53879i	0.408522	+	0.348911i
$253$		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		0.522499	−	0.852640i	$-0.325000\pi$
$257$		0			0		−0.522499	+	0.852640i	$0.675000\pi$
$258$	−35.1688	−	8.44327i	−2.18951	−	0.525655i
$259$		0			0
$260$		0			0
$261$	−1.62710	−	2.65519i	−0.100715	−	0.164352i
$262$		0			0
$263$	7.30817	+	30.4407i	0.450641	+	1.87705i	0.479623	+	0.877475i	$0.340774\pi$
$263$	7.30817	+	30.4407i	0.450641	+	1.87705i	−0.0289818	+	0.999580i	$0.509226\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−30.2808	−	15.4288i	−1.85316	−	0.944230i
$268$	−2.25713	+	28.6795i	−0.137876	+	1.75188i
$269$	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	$0.238749\pi$
$270$	−13.0530	+	3.13374i	−0.794379	+	0.190714i
$271$		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
$276$	−5.29582	−	3.24528i	−0.318771	−	0.195343i
$277$		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
$280$	21.0707	+	24.6706i	1.25921	+	1.47435i
$281$	17.2678	−	20.2180i	1.03011	−	1.20611i	0.0518675	−	0.998654i	$-0.483483\pi$
$281$	17.2678	−	20.2180i	1.03011	−	1.20611i	0.978245	−	0.207453i	$-0.0665174\pi$
$282$	5.90785	+	37.3007i	0.351808	+	2.22123i
$283$	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
$287$	32.6064	+	3.96851i	1.92469	+	0.234254i
$288$	4.70231			0.277087
$289$	−15.1471	+	7.71784i	−0.891007	+	0.453990i
$290$	−4.53349	−	10.9448i	−0.266216	−	0.642702i
$291$		0			0
$292$		0			0
$293$		0			0		−0.760406	−	0.649448i	$-0.775000\pi$
$293$		0			0		0.760406	+	0.649448i	$0.225000\pi$
$294$	40.6567	−	34.7241i	2.37115	−	2.02515i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−3.73355	+	6.09261i	−0.216279	+	0.352935i
$299$		0			0
$300$	19.5133	−	1.53573i	1.12660	−	0.0886653i
$301$	−25.6498	+	61.9240i	−1.47843	+	3.56924i
$302$		0			0
$303$	2.95702	+	9.10077i	0.169876	+	0.522826i
$304$		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	$-0.438633\pi$
$307$	15.2963	−	30.0208i	0.873009	−	1.71338i	0.681409	−	0.731903i	$-0.261367\pi$
$308$		0			0
$309$	3.11337	−	39.5592i	0.177114	−	2.25044i
$310$		0			0
$311$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$311$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$312$		0			0
$313$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$313$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$314$		0			0
$315$	−0.748116	−	9.50571i	−0.0421516	−	0.535586i
$316$		0			0
$317$		0			0		−0.852640	−	0.522499i	$-0.825000\pi$
$317$		0			0		0.852640	+	0.522499i	$0.175000\pi$
$318$		0			0
$319$		0			0
$320$	17.6683	+	2.79838i	0.987688	+	0.156434i
$321$	−26.2985	−	30.7916i	−1.46784	−	1.71862i
$322$	−7.47531	+	8.75247i	−0.416583	+	0.487756i
$323$		0			0
$324$	17.4793	+	12.6994i	0.971071	+	0.705524i
$325$		0			0
$326$	4.27115	+	8.38261i	0.236557	+	0.464270i
$327$			28.6370i			1.58363i
$328$	15.0917	−	10.0120i	0.833301	−	0.552820i
$329$	69.9867			3.85849
$330$		0			0
$331$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$331$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$332$	−1.72666	+	2.37654i	−0.0947627	+	0.130430i
$333$		0			0
$334$	−13.0338	−	11.1319i	−0.713176	−	0.609110i
$335$	24.4576	−	20.8887i	1.33626	−	1.14127i
$336$	6.28300	−	39.6693i	0.342766	−	2.16414i
$337$		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
$343$	−33.0090	−	53.8658i	−1.78232	−	2.90848i
$344$	11.4200	+	35.1472i	0.615726	+	1.89501i
$345$	1.62109	+	6.75233i	0.0872766	+	0.363533i
$346$		0			0
$347$	−26.4048	−	2.07811i	−1.41749	−	0.111559i	−0.653566	−	0.756870i	$-0.726728\pi$
$347$	−26.4048	−	2.07811i	−1.41749	−	0.111559i	−0.763920	+	0.645311i	$0.776728\pi$
$348$	−6.65796	+	13.0670i	−0.356904	+	0.700463i
$349$	−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	$0.944983\pi$
$350$	2.84598	−	36.1616i	0.152124	−	1.93292i
$351$		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
$356$	2.72451	+	34.6182i	0.144399	+	1.83476i
$357$		0			0
$358$		0			0
$359$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$359$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$360$	−3.71751	−	3.71751i	−0.195930	−	0.195930i
$361$	18.7661	+	2.97225i	0.987688	+	0.156434i
$362$	3.76486	+	4.40809i	0.197877	+	0.231684i
$363$	13.9832	−	16.3723i	0.733930	−	0.859322i
$364$		0			0
$365$		0			0
$366$	26.3097	−	10.8978i	1.37523	−	0.569639i
$367$	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
$369$	−5.31784	−	0.226539i	−0.276835	−	0.0117932i
$370$		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
$375$	−16.6407	−	14.2125i	−0.859322	−	0.733930i
$376$	29.3428	−	25.0611i	1.51324	−	1.29243i
$377$		0			0
$378$	21.7762	−	21.7762i	1.12005	−	1.12005i
$379$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$379$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$380$		0			0
$381$	26.3218	+	6.31931i	1.34851	+	0.323748i
$382$		0			0
$383$	−9.39650	+	22.6852i	−0.480139	+	1.15916i	0.479404	+	0.877594i	$0.340853\pi$
$383$	−9.39650	+	22.6852i	−0.480139	+	1.15916i	−0.959543	+	0.281563i	$0.909147\pi$
$384$	−11.5707	−	18.8817i	−0.590467	−	0.963554i
$385$		0			0
$386$		0			0
$387$	3.35628	−	10.3296i	0.170610	−	0.525082i
$388$		0			0
$389$	−5.09350	+	9.99655i	−0.258251	+	0.506845i	−0.983332	−	0.181818i	$-0.941802\pi$
$389$	−5.09350	+	9.99655i	−0.258251	+	0.506845i	0.725082	+	0.688663i	$0.241802\pi$
$390$		0			0
$391$		0			0
$392$	−51.9579	−	16.8822i	−2.62427	−	0.852678i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.0784591	−	0.996917i	$-0.525000\pi$
$397$		0			0		0.0784591	+	0.996917i	$0.475000\pi$
$398$		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	$-0.651624\pi$
$402$	−39.3268	−	6.22875i	−1.96144	−	0.310662i
$403$		0			0
$404$	6.35003	−	7.43493i	0.315926	−	0.369901i
$405$	−3.77879	−	23.8584i	−0.187770	−	1.18553i
$406$	21.9872	+	15.9746i	1.09121	+	0.792808i
$407$		0			0
$408$		0			0
$409$		−	14.7087i		−	0.727300i	−0.931536	−	0.363650i	$-0.881530\pi$
$409$		−	14.7087i		−	0.727300i	0.931536	−	0.363650i	$-0.118470\pi$
$410$	−19.8462	−	4.01588i	−0.980135	−	0.198330i
$411$		0			0
$412$	−36.1267	+	18.4075i	−1.77983	+	0.906871i
$413$		0			0
$414$	1.09632	−	1.50895i	0.0538811	−	0.0741610i
$415$	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	$0.750000\pi$
$420$	−36.3285	+	26.3942i	−1.77265	+	1.28790i
$421$	7.42420	−	12.1152i	0.361834	−	0.590459i	−0.618980	−	0.785407i	$-0.712454\pi$
$421$	7.42420	−	12.1152i	0.361834	−	0.590459i	0.980814	+	0.194948i	$0.0624538\pi$
$422$		0			0
$423$	−11.3060	+	0.889798i	−0.549715	+	0.0432635i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−12.3198	−	51.3157i	−0.596198	−	2.48334i
$428$	−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	$0.150000\pi$
$432$	1.33224	−	16.9277i	0.0640973	−	0.814433i
$433$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$433$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$434$		0			0
$435$	15.5939	−	5.06677i	0.747672	−	0.242933i
$436$	24.9489	−	15.2887i	1.19484	−	0.732197i
$437$		0			0
$438$		0			0
$439$		0			0		0.233445	−	0.972370i	$-0.425000\pi$
$439$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$440$		0			0
$441$	9.43748	+	12.9896i	0.449404	+	0.618551i
$442$		0			0
$443$	−15.5914	−	2.46944i	−0.740770	−	0.117326i	−0.225367	−	0.974274i	$-0.572358\pi$
$443$	−15.5914	−	2.46944i	−0.740770	−	0.117326i	−0.515404	+	0.856948i	$0.672358\pi$
$444$		0			0
$445$	25.2142	−	29.5220i	1.19527	−	1.39948i
$446$	5.72665	+	36.1567i	0.271165	+	1.71207i
$447$	−8.00112	−	5.81316i	−0.378440	−	0.274953i
$448$	−37.9148	+	15.7048i	−1.79131	+	0.741984i
$449$	−7.25537	−	14.2395i	−0.342402	−	0.672002i	0.654024	−	0.756474i	$-0.273080\pi$
$449$	−7.25537	−	14.2395i	−0.342402	−	0.672002i	−0.996426	+	0.0844719i	$0.973080\pi$
$450$			5.87789i			0.277087i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−8.80523	−	21.2577i	−0.413250	−	0.997674i
$455$		0			0
$456$		0			0
$457$		0			0		−0.760406	−	0.649448i	$-0.775000\pi$
$457$		0			0		0.760406	+	0.649448i	$0.225000\pi$
$458$	30.1882	−	25.7831i	1.41060	−	1.20477i
$459$		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
$463$	15.4744	+	3.71507i	0.719156	+	0.172654i	0.576475	−	0.817115i	$-0.304428\pi$
$463$	15.4744	+	3.71507i	0.719156	+	0.172654i	0.142681	+	0.989769i	$0.454428\pi$
$464$	14.9387	−	1.17570i	0.693511	−	0.0545805i
$465$		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
$469$	−22.8018	+	70.1767i	−1.05289	+	3.24046i
$470$	−43.0101	−	3.38497i	−1.98391	−	0.156137i
$471$		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		−0.0784591	−	0.996917i	$-0.525000\pi$
$479$		0			0		0.0784591	+	0.996917i	$0.475000\pi$
$480$	−5.77984	+	24.0748i	−0.263813	+	1.09886i
$481$		0			0
$482$	21.2439	+	29.2398i	0.967634	+	1.33183i
$483$	−11.2649	−	11.2649i	−0.512569	−	0.512569i
$484$	−21.7291	−	3.44156i	−0.987688	−	0.156434i
$485$		0			0
$486$	−7.72417	+	9.04384i	−0.350375	+	0.410237i
$487$	−5.79720	−	36.6021i	−0.262696	−	1.65860i	−0.667809	−	0.744332i	$-0.732768\pi$
$487$	−5.79720	−	36.6021i	−0.262696	−	1.65860i	0.405113	−	0.914267i	$-0.367232\pi$
$488$	−23.5406	−	17.1033i	−1.06563	−	0.774228i
$489$	−12.0301	+	4.98303i	−0.544020	+	0.225341i
$490$	27.7298	+	54.4229i	1.25271	+	2.45857i
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$	12.1757	+	21.9107i	0.548921	+	0.987812i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−3.09164	−	2.64051i	−0.138540	−	0.118324i
$499$		0			0		0.760406	−	0.649448i	$-0.225000\pi$
$499$		0			0		−0.760406	+	0.649448i	$0.775000\pi$
$500$	−3.49798	+	22.0854i	−0.156434	+	0.987688i
$501$	16.7751	−	16.7751i	0.749457	−	0.749457i
$502$		0			0
$503$	10.1674	−	16.5916i	0.453340	−	0.739783i	−0.541559	−	0.840663i	$-0.682166\pi$
$503$	10.1674	−	16.5916i	0.453340	−	0.739783i	0.994899	+	0.100879i	$0.0321657\pi$
$504$	11.7278	+	2.81560i	0.522398	+	0.125417i
$505$	−10.8980	+	0.857688i	−0.484953	+	0.0381666i
$506$		0			0
$507$	13.2953	+	21.6960i	0.590467	+	0.963554i
$508$	−8.54724	−	26.3057i	−0.379223	−	1.16713i
$509$	−10.1813	−	42.4082i	−0.451279	−	1.87971i	−0.474988	−	0.879992i	$-0.657548\pi$
$509$	−10.1813	−	42.4082i	−0.451279	−	1.87971i	0.0237097	−	0.999719i	$-0.492452\pi$
$510$		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
$516$	−49.7361	+	11.9406i	−2.18951	+	0.525655i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	10.5418	−	43.9099i	0.461846	−	1.92373i	0.0883730	−	0.996087i	$-0.471833\pi$
$521$	10.5418	−	43.9099i	0.461846	−	1.92373i	0.373473	−	0.927641i	$-0.378167\pi$
$522$	−3.75501	−	2.30107i	−0.164352	−	0.100715i
$523$	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
$525$	49.5866	+	7.85375i	2.16414	+	0.342766i
$526$	28.7530	+	33.6654i	1.25369	+	1.46788i
$527$		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
$534$	−48.0620			−2.07985
$535$	41.2175	−	21.0014i	1.78199	−	0.907969i
$536$	15.5692	+	37.5874i	0.672488	+	1.62353i
$537$		0			0
$538$	41.5342	−	6.57837i	1.79067	−	0.283614i
$539$		0			0
$540$	−14.4357	+	12.3293i	−0.621215	+	0.530568i
$541$	6.89001	−	43.5018i	0.296225	−	1.87029i	−0.169746	−	0.985488i	$-0.554295\pi$
$541$	6.89001	−	43.5018i	0.296225	−	1.87029i	0.465971	−	0.884800i	$-0.345705\pi$
$542$		0			0
$543$	−6.49110	+	4.71606i	−0.278560	+	0.202386i
$544$		0			0
$545$	−31.8107	−	7.63706i	−1.36262	−	0.327136i
$546$		0			0
$547$	−12.7945	+	30.8887i	−0.547054	+	1.32071i	0.372606	+	0.927990i	$0.378464\pi$
$547$	−12.7945	+	30.8887i	−0.547054	+	1.32071i	−0.919660	+	0.392716i	$0.871536\pi$
$548$		0			0
$549$	2.64262	+	8.13314i	0.112784	+	0.347114i
$550$		0			0
$551$		0			0
$552$	−8.75671	−	0.689168i	−0.372711	−	0.0293330i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$557$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$558$		0			0
$559$		0			0
$560$	42.3901	+	17.5585i	1.79131	+	0.741984i
$561$		0			0
$562$	8.77796	−	36.5628i	0.370276	−	1.54231i
$563$	40.2250	+	24.6499i	1.69528	+	1.03887i	0.904140	+	0.427236i	$0.140513\pi$
$563$	40.2250	+	24.6499i	1.69528	+	1.03887i	0.791141	+	0.611634i	$0.209487\pi$
$564$	31.3929	+	43.2086i	1.32188	+	1.81941i
$565$		0			0
$566$	28.3028	+	4.48273i	1.18966	+	0.188423i
$567$	35.9902	+	42.1391i	1.51145	+	1.76968i
$568$		0			0
$569$	6.39776	+	40.3939i	0.268208	+	1.69340i	0.642659	+	0.766153i	$0.277831\pi$
$569$	6.39776	+	40.3939i	0.268208	+	1.69340i	−0.374451	+	0.927247i	$0.622169\pi$
$570$		0			0
$571$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$571$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$572$		0			0
$573$		0			0
$574$	43.6344	−	15.9340i	1.82126	−	0.665071i
$575$	−7.93298			−0.330828
$576$	5.92526	−	3.01907i	0.246886	−	0.125795i
$577$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$577$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$578$	−14.1313	+	19.4501i	−0.587785	+	0.809017i
$579$		0			0
$580$	−12.7395	−	10.8806i	−0.528981	−	0.451792i
$581$	−5.72937	+	4.89335i	−0.237694	+	0.203010i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−33.1226	+	2.60680i	−1.36711	+	0.107594i	−0.740669	−	0.671871i	$-0.765491\pi$
$587$	−33.1226	+	2.60680i	−1.36711	+	0.107594i	−0.626446	+	0.779465i	$0.715491\pi$
$588$	28.9362	−	69.8581i	1.19331	−	2.88090i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.996917	−	0.0784591i	$-0.975000\pi$
$593$		0			0		0.996917	+	0.0784591i	$0.0250000\pi$
$594$		0			0
$595$		0			0
$596$	−0.792859	+	10.0742i	−0.0324768	+	0.412656i
$597$		0			0
$598$		0			0
$599$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$599$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$600$	23.6022	−	14.4634i	0.963554	−	0.590467i
$601$	9.66925	+	4.00513i	0.394417	+	0.163373i	0.571072	−	0.820900i	$-0.306528\pi$
$601$	9.66925	+	4.00513i	0.394417	+	0.163373i	−0.176655	+	0.984273i	$0.556528\pi$
$602$	7.43707	+	94.4969i	0.303112	+	3.85141i
$603$	2.79129	−	11.6265i	0.113670	−	0.473470i
$604$		0			0
$605$	14.4576	+	19.8992i	0.587785	+	0.809017i
$606$	9.56912	+	9.56912i	0.388719	+	0.388719i
$607$	−33.9806	−	5.38200i	−1.37923	−	0.218449i	−0.577626	−	0.816302i	$-0.696021\pi$
$607$	−33.9806	−	5.38200i	−1.37923	−	0.218449i	−0.801606	+	0.597853i	$0.796021\pi$
$608$		0			0
$609$	−24.4294	+	28.6031i	−0.989928	+	1.15906i
$610$	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
$615$	7.69624	−	26.9477i	0.310342	−	1.08663i
$616$		0			0
$617$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$617$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$618$	−21.4755	−	51.8464i	−0.863870	−	2.08557i
$619$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$619$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$620$		0			0
$621$	−5.12142	−	4.37410i	−0.205515	−	0.175527i
$622$		0			0
$623$	−13.9332	+	87.9710i	−0.558224	+	3.52448i
$624$		0			0
$625$	20.2254	−	14.6946i	0.809017	−	0.587785i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−7.04572	−	11.4976i	−0.280708	−	0.458074i
$631$		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
$641$	−35.0209	+	21.4608i	−1.38324	+	0.847652i	−0.997197	−	0.0748272i	$-0.976159\pi$
$641$	−35.0209	+	21.4608i	−1.38324	+	0.847652i	−0.386046	+	0.922479i	$0.626159\pi$
$642$	−52.9075	−	21.9150i	−2.08809	−	0.864916i
$643$	−3.39830	−	43.1795i	−0.134016	−	1.70283i	−0.585597	−	0.810602i	$-0.699140\pi$
$643$	−3.39830	−	43.1795i	−0.134016	−	1.70283i	0.451581	−	0.892230i	$-0.350860\pi$
$644$	−3.80002	+	15.8282i	−0.149742	+	0.623719i
$645$	48.7597	+	29.8800i	1.91991	+	1.17652i
$646$		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	$0.832302\pi$
$648$	30.1787	+	4.77984i	1.18553	+	0.187770i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	10.7639	+	7.82045i	0.421548	+	0.306273i
$653$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$653$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$654$	18.3861	+	36.0847i	0.718952	+	1.41102i
$655$		0			0
$656$	12.5886	−	22.3053i	0.491501	−	0.870877i
$657$		0			0
$658$	88.1884	−	44.9342i	3.43794	−	1.75172i
$659$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$659$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$660$		0			0
$661$	−2.20318	+	0.348950i	−0.0856938	+	0.0135726i	−0.199134	−	0.979972i	$-0.563813\pi$
$661$	−2.20318	+	0.348950i	−0.0856938	+	0.0135726i	0.113440	+	0.993545i	$0.463813\pi$
$662$		0			0
$663$		0			0
$664$	−0.649883	+	4.10320i	−0.0252204	+	0.159235i
$665$		0			0
$666$		0			0
$667$	3.10559	−	5.06787i	0.120249	−	0.196229i
$668$	−23.5706	−	5.65881i	−0.911975	−	0.218946i
$669$	−50.5107	+	3.97528i	−1.95286	+	0.153693i
$670$	17.4069	−	42.0240i	0.672488	−	1.62353i
$671$		0			0
$672$	−17.5522	−	54.0202i	−0.677091	−	2.08387i
$673$		0			0		−0.233445	−	0.972370i	$-0.575000\pi$
$673$		0			0		0.233445	+	0.972370i	$0.425000\pi$
$674$		0			0
$675$	21.1596	+	1.66530i	0.814433	+	0.0640973i
$676$	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
$681$	30.2875	−	9.84100i	1.16062	−	0.377108i
$682$		0			0
$683$	−47.8757	−	19.8308i	−1.83191	−	0.758803i	−0.965967	−	0.258665i	$-0.916717\pi$
$683$	−47.8757	−	19.8308i	−1.83191	−	0.758803i	−0.865946	−	0.500138i	$-0.833283\pi$
$684$		0			0
$685$		0			0
$686$	−76.1778	−	46.6818i	−2.90848	−	1.78232i
$687$	32.2973	+	44.4534i	1.23222	+	1.69600i
$688$	36.9560	+	36.9560i	1.40893	+	1.40893i
$689$		0			0
$690$	6.37796	+	7.46763i	0.242805	+	0.284288i
$691$		0			0		0.649448	−	0.760406i	$-0.275000\pi$
$691$		0			0		−0.649448	+	0.760406i	$0.725000\pi$
$692$		0			0
$693$		0			0
$694$	−34.6063	+	14.3344i	−1.31364	+	0.544126i
$695$		0			0
$696$			20.7400i			0.786148i
$697$		0			0
$698$	−42.2531			−1.59930
$699$		0			0
$700$	−19.6310	−	47.3935i	−0.741984	−	1.79131i
$701$	10.6564	−	14.6673i	0.402486	−	0.553975i	−0.558879	−	0.829249i	$-0.688769\pi$
$701$	10.6564	−	14.6673i	0.402486	−	0.553975i	0.961366	+	0.275274i	$0.0887686\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	9.34114	−	58.9776i	0.351808	−	2.22123i
$706$		0			0
$707$	20.2891	−	14.7409i	0.763050	−	0.554388i
$708$		0			0
$709$	−31.3395	−	7.52394i	−1.17698	−	0.282568i	−0.402652	−	0.915353i	$-0.631911\pi$
$709$	−31.3395	−	7.52394i	−1.17698	−	0.282568i	−0.774327	+	0.632786i	$0.781911\pi$
$710$		0			0
$711$		0			0
$712$	25.6594	+	41.8723i	0.961626	+	1.56923i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$719$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$720$	−7.07112	−	2.29755i	−0.263525	−	0.0856245i
$721$	−101.124	+	24.2776i	−3.76604	+	0.904146i
$722$	25.5549	−	8.30330i	0.951057	−	0.309017i
$723$	−42.6518	+	26.1371i	−1.58624	+	0.972048i
$724$	7.57417	+	3.13733i	0.281492	+	0.116598i
$725$	1.46963	+	18.6734i	0.0545805	+	0.693511i
$726$	7.10827	−	29.6081i	0.263813	−	1.09886i
$727$	−20.8653	−	12.7863i	−0.773851	−	0.474217i	0.0786754	−	0.996900i	$-0.474931\pi$
$727$	−20.8653	−	12.7863i	−0.773851	−	0.474217i	−0.852527	+	0.522684i	$0.824931\pi$
$728$		0			0
$729$	11.2763	+	11.2763i	0.417641	+	0.417641i
$730$		0			0
$731$		0			0
$732$	26.1553	−	30.6240i	0.966729	−	1.13189i
$733$		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
$735$	−78.1037	+	32.3516i	−2.88090	+	1.19331i
$736$	4.07463	+	7.99691i	0.150193	+	0.294770i
$737$		0			0
$738$	−6.84631	+	3.12880i	−0.252016	+	0.115173i
$739$		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	−0.870095	−	0.492883i	$-0.835943\pi$
$743$	−42.1217	+	6.67142i	−1.54530	+	0.244751i	−0.675201	+	0.737634i	$0.735943\pi$
$744$		0			0
$745$	8.59118	−	7.33756i	0.314757	−	0.268828i
$746$		0			0
$747$	0.863335	−	0.863335i	0.0315878	−	0.0315878i
$748$		0			0
$749$	−55.4505	+	90.4869i	−2.02612	+	3.30632i
$750$	−30.0935	−	7.22480i	−1.09886	−	0.263813i
$751$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$751$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$752$	20.8839	−	50.4181i	0.761557	−	1.83856i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	13.4584	−	41.4208i	0.489479	−	1.50646i
$757$		0			0		−0.996917	−	0.0784591i	$-0.975000\pi$
$757$		0			0		0.996917	+	0.0784591i	$0.0250000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−51.0382	−	16.5833i	−1.85013	−	0.601145i	−0.996815	−	0.0797547i	$-0.974586\pi$
$761$	−51.0382	−	16.5833i	−1.85013	−	0.601145i	−0.853319	−	0.521390i	$-0.825414\pi$
$762$	37.2247	−	8.93685i	1.34851	−	0.323748i
$763$	71.3783	−	23.1922i	2.58407	−	0.839615i
$764$		0			0
$765$		0			0
$766$	2.72449	+	34.6179i	0.0984397	+	1.25080i
$767$		0			0
$768$	−26.7028	−	16.3635i	−0.963554	−	0.590467i
$769$	29.8682	+	41.1101i	1.07708	+	1.48247i	0.862700	+	0.505715i	$0.168771\pi$
$769$	29.8682	+	41.1101i	1.07708	+	1.48247i	0.214375	+	0.976751i	$0.431229\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.649448	−	0.760406i	$-0.275000\pi$
$773$		0			0		−0.649448	+	0.760406i	$0.725000\pi$
$774$	−2.40283	−	15.1709i	−0.0863681	−	0.545307i
$775$		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
$783$	−9.34739	+	12.8656i	−0.334048	+	0.459778i
$784$	−76.3098	+	12.0863i	−2.72535	+	0.431653i
$785$		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
$789$	−49.5737	+	36.0174i	−1.76487	+	1.28225i
$790$		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
$801$	1.13239	−	14.3884i	0.0400110	−	0.508388i
$802$	−51.3149	−	16.6732i	−1.81199	−	0.588752i
$803$		0			0
$804$	−53.5537	+	17.4007i	−1.88869	+	0.613674i
$805$	15.5175	−	9.50912i	0.546919	−	0.335152i
$806$		0			0
$807$	4.56651	+	58.0231i	0.160749	+	2.04251i
$808$	3.22798	−	13.4455i	0.113560	−	0.473012i
$809$	4.08264	+	2.50184i	0.143538	+	0.0879602i	0.592413	−	0.805634i	$-0.298175\pi$
$809$	4.08264	+	2.50184i	0.143538	+	0.0879602i	−0.448875	+	0.893594i	$0.648175\pi$
$810$	−20.0796	−	27.6372i	−0.705524	−	0.971071i
$811$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$811$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$812$	37.9618	+	6.01256i	1.33220	+	0.211000i
$813$		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
$823$	−18.3087	−	44.2011i	−0.638201	−	1.54075i	−0.829074	−	0.559139i	$-0.811132\pi$
$823$	−18.3087	−	44.2011i	−0.638201	−	1.54075i	0.190872	−	0.981615i	$-0.438868\pi$
$824$	−33.7040	+	46.3895i	−1.17413	+	1.61606i
$825$		0			0
$826$		0			0
$827$	−27.4874	+	23.4764i	−0.955830	+	0.816356i	−0.983062	−	0.183274i	$-0.941331\pi$
$827$	−27.4874	+	23.4764i	−0.955830	+	0.816356i	0.0272324	+	0.999629i	$0.491331\pi$
$828$	0.412634	−	2.60527i	0.0143400	−	0.0905394i
$829$	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
$835$	14.1605	+	23.1079i	0.490046	+	0.799682i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.996917	−	0.0784591i	$-0.975000\pi$
$839$		0			0		0.996917	+	0.0784591i	$0.0250000\pi$
$840$	−28.8304	+	56.5829i	−0.994745	+	1.95230i
$841$	13.3347	+	6.79434i	0.459816	+	0.234288i
$842$	1.57661	−	20.0327i	0.0543334	−	0.690371i
$843$	49.4960	+	16.0822i	1.70473	+	0.553902i
$844$		0			0
$845$	−27.6462	+	8.98278i	−0.951057	+	0.309017i
$846$	−13.6751	+	8.38008i	−0.470158	+	0.288113i
$847$	−52.1329	−	21.5942i	−1.79131	−	0.741984i
$848$		0			0
$849$	−9.25872	+	38.5654i	−0.317758	+	1.32356i
$850$		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	$0.0500000\pi$
$854$	−48.4706	−	56.7518i	−1.65863	−	1.94201i
$855$		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
$861$	17.2473	+	61.9369i	0.587786	+	2.11080i
$862$		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	$0.298377\pi$
$864$	−9.18952	−	22.1855i	−0.312634	−	0.754765i
$865$		0			0
$866$		0			0
$867$	−25.3026	−	21.6105i	−0.859322	−	0.733930i
$868$		0			0
$869$		0			0
$870$	16.3964	−	16.3964i	0.555891	−	0.555891i
$871$		0			0
$872$	21.6215	−	35.2831i	0.732197	−	1.19484i
$873$		0			0
$874$		0			0
$875$	−21.9482	+	52.9876i	−0.741984	+	1.79131i
$876$		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	$0.135209\pi$
$882$	20.2317	+	10.3086i	0.681238	+	0.347108i
$883$	3.26057	−	41.4295i	0.109727	−	1.39421i	−0.657798	−	0.753194i	$-0.728512\pi$
$883$	3.26057	−	41.4295i	0.109727	−	1.39421i	0.767525	−	0.641019i	$-0.221488\pi$
$884$		0			0
$885$		0			0
$886$	−21.2318	+	6.89863i	−0.713296	+	0.231764i
$887$	50.7199	−	31.0812i	1.70301	−	1.04360i	0.824543	−	0.565800i	$-0.191433\pi$
$887$	50.7199	−	31.0812i	1.70301	−	1.04360i	0.878466	−	0.477805i	$-0.158567\pi$
$888$		0			0
$889$	−5.56623	−	70.7256i	−0.186685	−	2.37206i
$890$	12.8174	−	53.3885i	0.429641	−	1.78959i
$891$		0			0
$892$	30.4300	+	41.8833i	1.01887	+	1.40236i
$893$		0			0
$894$	−13.8143	−	2.18797i	−0.462019	−	0.0731765i
$895$		0			0
$896$	−37.6924	+	44.1321i	−1.25921	+	1.47435i
$897$		0			0
$898$	−18.2846	−	13.2845i	−0.610165	−	0.443311i
$899$		0			0
$900$	3.77384	+	7.40658i	0.125795	+	0.246886i
$901$		0			0
$902$		0			0
$903$	−131.194			−4.36587
$904$		0			0
$905$	−3.50764	−	8.46818i	−0.116598	−	0.281492i
$906$		0			0
$907$	54.7779	−	8.67597i	1.81887	−	0.288081i	0.848410	−	0.529340i	$-0.177561\pi$
$907$	54.7779	−	8.67597i	1.81887	−	0.288081i	0.970461	+	0.241260i	$0.0775605\pi$
$908$	−24.7435	−	21.1330i	−0.821143	−	0.701322i
$909$	−3.09018	+	2.63926i	−0.102495	+	0.0875387i
$910$		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
$915$	−44.8880	+	3.53276i	−1.48395	+	0.116789i
$916$	21.4855	−	51.8707i	0.709902	−	1.71386i
$917$		0			0
$918$		0			0
$919$		0			0		−0.233445	−	0.972370i	$-0.575000\pi$
$919$		0			0		0.233445	+	0.972370i	$0.425000\pi$
$920$	3.10083	−	9.54339i	0.102231	−	0.314636i
$921$	65.7462	+	5.17434i	2.16641	+	0.170500i
$922$	11.2042	−	21.9894i	0.368990	−	0.724183i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	21.8841	−	5.25391i	0.719156	−	0.172654i
$927$	16.0273	−	5.20759i	0.526406	−	0.171040i
$928$	18.0690	−	11.0727i	0.593144	−	0.363479i
$929$	51.9574	+	21.5215i	1.70467	+	0.706096i	0.999994	−	0.00343511i	$-0.00109343\pi$
$929$	51.9574	+	21.5215i	1.70467	+	0.706096i	0.704674	+	0.709532i	$0.251093\pi$
$930$		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		0.649448	−	0.760406i	$-0.275000\pi$
$937$		0			0		−0.649448	+	0.760406i	$0.725000\pi$
$938$	16.3243	+	103.067i	0.533006	+	3.36527i
$939$		0			0
$940$	−56.3692	+	23.3489i	−1.83856	+	0.761557i
$941$	−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
$945$	−43.3858	+	22.1062i	−1.41134	+	0.719114i
$946$		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
$960$	8.17393	+	34.0469i	0.263813	+	1.09886i
$961$	−9.57953	+	29.4828i	−0.309017	+	0.951057i
$962$		0			0
$963$	7.80728	−	15.3226i	0.251586	−	0.493765i
$964$	45.5420	+	23.2048i	1.46681	+	0.747376i
$965$		0			0
$966$	−21.4270	−	6.96207i	−0.689404	−	0.224001i
$967$	19.5649	−	4.69712i	0.629165	−	0.151049i	0.0936918	−	0.995601i	$-0.470133\pi$
$967$	19.5649	−	4.69712i	0.629165	−	0.151049i	0.535473	+	0.844552i	$0.320133\pi$
$968$	−29.5899	+	9.61435i	−0.951057	+	0.309017i
$969$		0			0
$970$		0			0
$971$		0			0		−0.0784591	−	0.996917i	$-0.525000\pi$
$971$		0			0		0.0784591	+	0.996917i	$0.475000\pi$
$972$	−3.92652	+	16.3551i	−0.125943	+	0.524591i
$973$		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		−0.649448	−	0.760406i	$-0.725000\pi$
$977$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$978$	−11.9595	+	14.0028i	−0.382423	+	0.447760i
$979$		0			0
$980$	69.8833	+	50.7732i	2.23234	+	1.62189i
$981$	−11.2359	+	4.65406i	−0.358735	+	0.148593i
$982$		0			0
$983$			33.0869i			1.05531i	0.849459	+	0.527655i	$0.176928\pi$
$983$			33.0869i			1.05531i	−0.849459	+	0.527655i	$0.823072\pi$
$984$	29.4098	+	19.7919i	0.937550	+	0.630942i
$985$		0			0
$986$		0			0
$987$	52.4235	+	126.561i	1.66866	+	4.02850i
$988$		0			0
$989$	20.4751	−	3.24294i	0.651070	−	0.103119i
$990$		0			0
$991$		0			0		0.760406	−	0.649448i	$-0.225000\pi$
$991$		0			0		−0.760406	+	0.649448i	$0.775000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−5.59101	−	1.34228i	−0.177158	−	0.0425318i
$997$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$997$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$998$		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.19.1	✓	16
4.3	odd	2		820.2.cc.f.19.1	yes	16
5.4	even	2		820.2.cc.f.19.1	yes	16
20.19	odd	2	CM	820.2.cc.a.19.1	✓	16
41.13	odd	40	inner	820.2.cc.a.259.1	yes	16
164.95	even	40		820.2.cc.f.259.1	yes	16
205.54	odd	40		820.2.cc.f.259.1	yes	16
820.259	even	40	inner	820.2.cc.a.259.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.cc.a.19.1	✓	16	1.1	even	1	trivial
820.2.cc.a.19.1	✓	16	20.19	odd	2	CM
820.2.cc.a.259.1	yes	16	41.13	odd	40	inner
820.2.cc.a.259.1	yes	16	820.259	even	40	inner
820.2.cc.f.19.1	yes	16	4.3	odd	2
820.2.cc.f.19.1	yes	16	5.4	even	2
820.2.cc.f.259.1	yes	16	164.95	even	40
820.2.cc.f.259.1	yes	16	205.54	odd	40

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)

\(f(q)\)	\(=\)	\(q+(1.26007 - 0.642040i) q^{2} +(0.749049 + 1.80837i) q^{3} +(1.17557 - 1.61803i) q^{4} +(-2.20854 + 0.349798i) q^{5} +(2.10490 + 1.79775i) q^{6} +(3.90076 - 3.33156i) q^{7} +(0.442463 - 2.79360i) q^{8} +(-0.587789 + 0.587789i) q^{9} +(-2.55834 + 1.85874i) q^{10} +(3.80656 + 0.913873i) q^{12} +(2.77625 - 6.70246i) q^{14} +(-2.28687 - 3.73183i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(-0.363274 + 1.11804i) q^{18} +(-2.03031 + 3.98470i) q^{20} +(8.94655 + 4.55849i) q^{21} +(-1.50894 - 0.490285i) q^{23} +(5.38328 - 1.29241i) q^{24} +(4.75528 - 1.54508i) q^{25} +(3.92187 + 1.62449i) q^{27} +(-0.804965 - 10.2281i) q^{28} +(-0.874538 + 3.64271i) q^{29} +(-5.27760 - 3.23412i) q^{30} +(-4.00000 - 4.00000i) q^{32} +(-7.44961 + 8.72237i) q^{35} +(0.260075 + 1.64205i) q^{36} +6.32456i q^{40} +(4.33089 + 4.71629i) q^{41} +14.2000 q^{42} +(-11.6418 + 5.93180i) q^{43} +(1.09255 - 1.50376i) q^{45} +(-2.21616 + 0.351005i) q^{46} +(10.3743 + 8.86045i) q^{47} +(5.95355 - 5.08482i) q^{48} +(3.02157 - 19.0775i) q^{49} +(5.00000 - 5.00000i) q^{50} +(5.98484 - 0.471017i) q^{54} +(-7.58113 - 12.3713i) q^{56} +(1.23678 + 5.15157i) q^{58} +(-8.72660 - 0.686798i) q^{60} +(4.67048 - 9.16634i) q^{61} +(-0.334568 + 4.25108i) q^{63} +(-7.60845 - 2.47214i) q^{64} +(-12.2645 + 7.51567i) q^{67} +(-0.243658 - 3.09597i) q^{69} +(-3.78695 + 15.7738i) q^{70} +(1.38198 + 1.90213i) q^{72} +(6.35602 + 7.44194i) q^{75} +(4.06061 + 7.96940i) q^{80} +10.8028i q^{81} +(8.48528 + 3.16228i) q^{82} -1.46878 q^{83} +(17.8931 - 9.11699i) q^{84} +(-10.8611 + 14.9490i) q^{86} +(-7.24243 + 1.14709i) q^{87} +(-13.2027 + 11.2761i) q^{89} +(0.411215 - 2.59631i) q^{90} +(-2.56717 + 1.86515i) q^{92} +(18.7611 + 4.50414i) q^{94} +(4.23726 - 10.2297i) q^{96} +(-8.44108 - 25.9790i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 12 q^{3} + 20 q^{6} + 16 q^{7} + 8 q^{8} + 12 q^{9} - 16 q^{12} + 20 q^{15} + 16 q^{16} + 4 q^{18} + 4 q^{21} + 8 q^{24} - 48 q^{27} + 8 q^{28} - 80 q^{30} - 64 q^{32} - 20 q^{35} + 24 q^{36}+ \cdots - 104 q^{98}+O(q^{100}) \) 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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