LMFDB - Embedded newform 820.2.cc.a.639.1

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			639.1
Root			$-0.891007 - 0.453990i$ of defining polynomial
Character	$\chi$	$=$	820.639
Dual form			820.2.cc.a.299.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.221232 - 1.39680i) q^{2} +(1.53176 - 0.634475i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(1.99235 + 1.01515i) q^{5} +(-1.22511 - 1.99920i) q^{6} +(2.37484 - 3.87538i) q^{7} +(1.28408 + 2.52015i) q^{8} +(-0.177595 + 0.177595i) q^{9} +(0.977198 - 3.00750i) q^{10} +(-2.52145 + 2.15352i) q^{12} +(-5.93853 - 2.45982i) q^{14} +(3.69589 + 0.290873i) q^{15} +(3.23607 - 2.35114i) q^{16} +(0.287355 + 0.208775i) q^{18} +(-4.41708 - 0.699596i) q^{20} +(1.17884 - 7.44292i) q^{21} +(4.02266 - 5.53671i) q^{23} +(3.56587 + 3.04554i) q^{24} +(2.93893 + 4.04508i) q^{25} +(-2.06278 + 4.97999i) q^{27} +(-2.12209 + 8.83914i) q^{28} +(-0.809475 - 0.947773i) q^{29} +(-0.411356 - 5.22678i) q^{30} +(-4.00000 - 4.00000i) q^{32} +(8.66561 - 5.31029i) q^{35} +(0.228046 - 0.447565i) q^{36} +6.32456i q^{40} +(-1.26993 - 6.27593i) q^{41} -10.6571 q^{42} +(1.99865 + 12.6190i) q^{43} +(-0.534118 + 0.173545i) q^{45} +(-8.62363 - 4.39396i) q^{46} +(-1.82031 - 2.97047i) q^{47} +(3.46513 - 5.65458i) q^{48} +(-6.20079 - 12.1697i) q^{49} +(5.00000 - 5.00000i) q^{50} +(7.41241 + 1.77956i) q^{54} +(12.8160 + 1.00864i) q^{56} +(-1.14477 + 1.34035i) q^{58} +(-7.20977 + 1.73091i) q^{60} +(1.39642 + 0.221172i) q^{61} +(0.266489 + 1.11001i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(0.727135 - 9.23913i) q^{67} +(2.64883 - 11.0332i) q^{69} +(-9.33454 - 10.9293i) q^{70} +(-0.675611 - 0.219519i) q^{72} +(7.06823 + 4.33142i) q^{75} +(8.83415 - 1.39919i) q^{80} +8.18345i q^{81} +(-8.48528 + 3.16228i) q^{82} -17.7266 q^{83} +(2.35769 + 14.8858i) q^{84} +(17.1841 - 5.58345i) q^{86} +(-1.84126 - 0.938168i) q^{87} +(-8.35664 + 13.6368i) q^{89} +(0.360572 + 0.707663i) q^{90} +(-4.22967 + 13.0176i) q^{92} +(-3.74645 + 3.19977i) q^{94} +(-8.66493 - 3.58913i) q^{96} +(-15.6269 + 11.3536i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{13}{40}\right)$	$-1$

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 $

$2$	−0.221232	−	1.39680i	−0.156434	−	0.987688i
$2$	−0.221232	−	1.39680i	−0.156434	−	0.987688i
$3$	1.53176	−	0.634475i	0.884361	−	0.366314i	0.106175	−	0.994348i	$-0.466140\pi$
$3$	1.53176	−	0.634475i	0.884361	−	0.366314i	0.778187	+	0.628033i	$0.216140\pi$
$4$	−1.90211	+	0.618034i	−0.951057	+	0.309017i
$5$	1.99235	+	1.01515i	0.891007	+	0.453990i
$5$	1.99235	+	1.01515i	0.891007	+	0.453990i
$6$	−1.22511	−	1.99920i	−0.500149	−	0.816169i
$7$	2.37484	−	3.87538i	0.897603	−	1.46476i	0.0122035	−	0.999926i	$-0.496115\pi$
$7$	2.37484	−	3.87538i	0.897603	−	1.46476i	0.885400	−	0.464830i	$-0.153885\pi$
$8$	1.28408	+	2.52015i	0.453990	+	0.891007i
$9$	−0.177595	+	0.177595i	−0.0591983	+	0.0591983i
$10$	0.977198	−	3.00750i	0.309017	−	0.951057i
$11$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$11$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$12$	−2.52145	+	2.15352i	−0.727880	+	0.621668i
$13$		0			0		−0.972370	−	0.233445i	$-0.925000\pi$
$13$		0			0		0.972370	+	0.233445i	$0.0750000\pi$
$14$	−5.93853	−	2.45982i	−1.58714	−	0.657414i
$15$	3.69589	+	0.290873i	0.954275	+	0.0751031i
$16$	3.23607	−	2.35114i	0.809017	−	0.587785i
$17$		0			0		0.649448	−	0.760406i	$-0.275000\pi$
$17$		0			0		−0.649448	+	0.760406i	$0.725000\pi$
$18$	0.287355	+	0.208775i	0.0677301	+	0.0492088i
$19$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$19$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$20$	−4.41708	−	0.699596i	−0.987688	−	0.156434i
$21$	1.17884	−	7.44292i	0.257245	−	1.62418i
$22$		0			0
$23$	4.02266	−	5.53671i	0.838782	−	1.15448i	−0.147442	−	0.989071i	$-0.547104\pi$
$23$	4.02266	−	5.53671i	0.838782	−	1.15448i	0.986224	−	0.165414i	$-0.0528960\pi$
$24$	3.56587	+	3.04554i	0.727880	+	0.621668i
$25$	2.93893	+	4.04508i	0.587785	+	0.809017i
$26$		0			0
$27$	−2.06278	+	4.97999i	−0.396982	+	0.958399i
$28$	−2.12209	+	8.83914i	−0.401037	+	1.67044i
$29$	−0.809475	−	0.947773i	−0.150316	−	0.175997i	0.680139	−	0.733083i	$-0.261919\pi$
$29$	−0.809475	−	0.947773i	−0.150316	−	0.175997i	−0.830455	+	0.557086i	$0.811919\pi$
$30$	−0.411356	−	5.22678i	−0.0751031	−	0.954275i
$31$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$31$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$		0			0
$34$		0			0
$35$	8.66561	−	5.31029i	1.46476	−	0.897603i
$36$	0.228046	−	0.447565i	0.0380077	−	0.0745942i
$37$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$37$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$38$		0			0
$39$		0			0
$40$			6.32456i			1.00000i
$41$	−1.26993	−	6.27593i	−0.198330	−	0.980135i
$41$	−1.26993	−	6.27593i	−0.198330	−	0.980135i
$42$	−10.6571			−1.64442
$43$	1.99865	+	12.6190i	0.304792	+	1.92438i	0.375371	+	0.926875i	$0.377515\pi$
$43$	1.99865	+	12.6190i	0.304792	+	1.92438i	−0.0705793	+	0.997506i	$0.522485\pi$
$44$		0			0
$45$	−0.534118	+	0.173545i	−0.0796216	+	0.0258706i
$46$	−8.62363	−	4.39396i	−1.27149	−	0.647854i
$47$	−1.82031	−	2.97047i	−0.265519	−	0.433288i	0.691898	−	0.721995i	$-0.256775\pi$
$47$	−1.82031	−	2.97047i	−0.265519	−	0.433288i	−0.957417	+	0.288707i	$0.906775\pi$
$48$	3.46513	−	5.65458i	0.500149	−	0.816169i
$49$	−6.20079	−	12.1697i	−0.885827	−	1.73853i
$50$	5.00000	−	5.00000i	0.707107	−	0.707107i
$51$		0			0
$52$		0			0
$53$		0			0		0.760406	−	0.649448i	$-0.225000\pi$
$53$		0			0		−0.760406	+	0.649448i	$0.775000\pi$
$54$	7.41241	+	1.77956i	1.00870	+	0.242168i
$55$		0			0
$56$	12.8160	+	1.00864i	1.71261	+	0.134785i
$57$		0			0
$58$	−1.14477	+	1.34035i	−0.150316	+	0.175997i
$59$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$59$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$60$	−7.20977	+	1.73091i	−0.930777	+	0.223460i
$61$	1.39642	+	0.221172i	0.178794	+	0.0283182i	0.245189	−	0.969475i	$-0.421150\pi$
$61$	1.39642	+	0.221172i	0.178794	+	0.0283182i	−0.0663955	+	0.997793i	$0.521150\pi$
$62$		0			0
$63$	0.266489	+	1.11001i	0.0335745	+	0.139848i
$64$	−4.70228	+	6.47214i	−0.587785	+	0.809017i
$65$		0			0
$66$		0			0
$67$	0.727135	−	9.23913i	0.0888337	−	1.12874i	−0.777368	−	0.629046i	$-0.783446\pi$
$67$	0.727135	−	9.23913i	0.0888337	−	1.12874i	0.866202	−	0.499694i	$-0.166554\pi$
$68$		0			0
$69$	2.64883	−	11.0332i	0.318882	−	1.32824i
$70$	−9.33454	−	10.9293i	−1.11569	−	1.30631i
$71$		0			0		−0.0784591	−	0.996917i	$-0.525000\pi$
$71$		0			0		0.0784591	+	0.996917i	$0.475000\pi$
$72$	−0.675611	−	0.219519i	−0.0796216	−	0.0258706i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$		0			0
$75$	7.06823	+	4.33142i	0.816169	+	0.500149i
$76$		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	$0.375000\pi$
$80$	8.83415	−	1.39919i	0.987688	−	0.156434i
$81$			8.18345i			0.909272i
$82$	−8.48528	+	3.16228i	−0.937043	+	0.349215i
$83$	−17.7266			−1.94574			−0.972871	−	0.231347i	$-0.925687\pi$
$83$	−17.7266			−1.94574			−0.972871	+	0.231347i	$0.925687\pi$
$84$	2.35769	+	14.8858i	0.257245	+	1.62418i
$85$		0			0
$86$	17.1841	−	5.58345i	1.85301	−	0.602079i
$87$	−1.84126	−	0.938168i	−0.197404	−	0.100582i
$88$		0			0
$89$	−8.35664	+	13.6368i	−0.885802	+	1.44550i	0.00945916	+	0.999955i	$0.496989\pi$
$89$	−8.35664	+	13.6368i	−0.885802	+	1.44550i	−0.895261	+	0.445542i	$0.853011\pi$
$90$	0.360572	+	0.707663i	0.0380077	+	0.0745942i
$91$		0			0
$92$	−4.22967	+	13.0176i	−0.440974	+	1.35718i
$93$		0			0
$94$	−3.74645	+	3.19977i	−0.386417	+	0.330031i
$95$		0			0
$96$	−8.66493	−	3.58913i	−0.884361	−	0.366314i
$97$		0			0		−0.996917	−	0.0784591i	$-0.975000\pi$
$97$		0			0		0.996917	+	0.0784591i	$0.0250000\pi$
$98$	−15.6269	+	11.3536i	−1.57855	+	1.14689i
$99$		0			0
$100$	−8.09017	−	5.87785i	−0.809017	−	0.587785i
$101$	−19.4677	+	4.67378i	−1.93711	+	0.465059i	−0.947896	+	0.318579i	$0.896794\pi$
$101$	−19.4677	+	4.67378i	−1.93711	+	0.465059i	−0.989214	+	0.146480i	$0.953206\pi$
$102$		0			0
$103$	−1.12930	+	7.13011i	−0.111273	+	0.702550i	0.867475	+	0.497482i	$0.165742\pi$
$103$	−1.12930	+	7.13011i	−0.111273	+	0.702550i	−0.978748	+	0.205069i	$0.934258\pi$
$104$		0			0
$105$	9.90437	−	13.6322i	0.966568	−	1.33037i
$106$		0			0
$107$	7.19805	+	9.90726i	0.695861	+	0.957771i	0.999987	+	0.00513899i	$0.00163580\pi$
$107$	7.19805	+	9.90726i	0.695861	+	0.957771i	−0.304125	+	0.952632i	$0.598364\pi$
$108$	0.845836	−	10.7474i	0.0813906	−	1.03417i
$109$	−6.42175	+	15.5035i	−0.615092	+	1.48496i	0.242249	+	0.970214i	$0.422115\pi$
$109$	−6.42175	+	15.5035i	−0.615092	+	1.48496i	−0.857341	+	0.514749i	$0.827885\pi$
$110$		0			0
$111$		0			0
$112$	−1.42643	−	18.1246i	−0.134785	−	1.71261i
$113$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$113$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$114$		0			0
$115$	13.6352	−	6.94746i	1.27149	−	0.647854i
$116$	2.12547	+	1.30249i	0.197345	+	0.120933i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	4.01277	+	9.68769i	0.366314	+	0.884361i
$121$	10.8646	−	1.72078i	0.987688	−	0.156434i
$122$		−	1.99946i		−	0.181022i
$123$	−5.92715	−	8.80747i	−0.534433	−	0.794142i
$124$		0			0
$125$	1.74899	+	11.0427i	0.156434	+	0.987688i
$126$	1.49150	−	0.617801i	0.132874	−	0.0550381i
$127$	21.4246	−	6.96126i	1.90112	−	0.617712i	0.940585	−	0.339557i	$-0.110277\pi$
$127$	21.4246	−	6.96126i	1.90112	−	0.617712i	0.960536	−	0.278155i	$-0.0897228\pi$
$128$	10.0806	+	5.13632i	0.891007	+	0.453990i
$129$	11.0679	+	18.0612i	0.974475	+	1.59020i
$130$		0			0
$131$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$131$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$132$		0			0
$133$		0			0
$134$	−13.0661	+	1.02832i	−1.12874	+	0.0888337i
$135$	−9.16523	+	7.82785i	−0.788818	+	0.673714i
$136$		0			0
$137$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$137$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$138$	−15.9972	−	1.25901i	−1.36177	−	0.107174i
$139$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$139$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$140$	−13.2010	+	15.4564i	−1.11569	+	1.30631i
$141$	−4.67296	−	3.39510i	−0.393534	−	0.285919i
$142$		0			0
$143$		0			0
$144$	−0.157159	+	0.992260i	−0.0130965	+	0.0826883i
$145$	−0.650623	−	2.71004i	−0.0540313	−	0.225056i
$146$		0			0
$147$	−17.2195	−	14.7068i	−1.42024	−	1.21300i
$148$		0			0
$149$	−1.60541	+	20.3986i	−0.131520	+	1.67112i	0.478008	+	0.878355i	$0.341359\pi$
$149$	−1.60541	+	20.3986i	−0.131520	+	1.67112i	−0.609528	+	0.792765i	$0.708641\pi$
$150$	4.48642	−	10.8312i	0.366314	−	0.884361i
$151$		0			0		0.233445	−	0.972370i	$-0.425000\pi$
$151$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.852640	−	0.522499i	$-0.825000\pi$
$157$		0			0		0.852640	+	0.522499i	$0.175000\pi$
$158$		0			0
$159$		0			0
$160$	−3.90879	−	12.0300i	−0.309017	−	0.951057i
$161$	−11.9037	−	28.7381i	−0.938144	−	2.26488i
$162$	11.4307	−	1.81044i	0.898077	−	0.142241i
$163$		−	24.6525i		−	1.93093i	−0.260531	−	0.965465i	$-0.583898\pi$
$163$		−	24.6525i		−	1.93093i	0.260531	−	0.965465i	$-0.416102\pi$
$164$	6.29429	+	11.1527i	0.491501	+	0.870877i
$165$		0			0
$166$	3.92168	+	24.7605i	0.304381	+	1.92179i
$167$	19.0786	−	7.90263i	1.47635	−	0.611524i	0.508053	−	0.861326i	$-0.330366\pi$
$167$	19.0786	−	7.90263i	1.47635	−	0.611524i	0.968297	+	0.249802i	$0.0803655\pi$
$168$	20.2710	−	6.58644i	1.56394	−	0.508155i
$169$	11.5831	+	5.90188i	0.891007	+	0.453990i
$170$		0			0
$171$		0			0
$172$	−11.6006	−	22.7675i	−0.884541	−	1.73601i
$173$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$173$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$174$	−0.903090	+	2.77943i	−0.0684631	+	0.210708i
$175$	22.6557	−	1.78304i	1.71261	−	0.134785i
$176$		0			0
$177$		0			0
$178$	20.8967	+	8.65568i	1.56627	+	0.648771i
$179$		0			0		−0.996917	−	0.0784591i	$-0.975000\pi$
$179$		0			0		0.996917	+	0.0784591i	$0.0250000\pi$
$180$	0.908695	−	0.660206i	0.0677301	−	0.0492088i
$181$	−5.33115	+	6.24197i	−0.396261	+	0.463962i	−0.922287	−	0.386507i	$-0.873682\pi$
$181$	−5.33115	+	6.24197i	−0.396261	+	0.463962i	0.526026	+	0.850469i	$0.323682\pi$
$182$		0			0
$183$	2.27931	−	0.547215i	0.168492	−	0.0404513i
$184$	19.1187	+	3.02811i	1.40945	+	0.223235i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	5.29828	+	4.52516i	0.386417	+	0.330031i
$189$	14.4006	+	19.8207i	1.04749	+	1.44174i
$190$		0			0
$191$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$191$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$192$	−3.09635	+	12.8972i	−0.223460	+	0.930777i
$193$		0			0		−0.649448	−	0.760406i	$-0.725000\pi$
$193$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$194$		0			0
$195$		0			0
$196$	19.3159	+	19.3159i	1.37971	+	1.37971i
$197$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$197$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$198$		0			0
$199$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$199$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$200$	−6.42040	+	12.6007i	−0.453990	+	0.891007i
$201$	−4.74820	−	14.6135i	−0.334912	−	1.03075i
$202$	10.8352	+	26.1586i	0.762364	+	1.84051i
$203$	−5.59535	+	0.886216i	−0.392717	+	0.0622002i
$204$		0			0
$205$	3.84088	−	13.7930i	0.268259	−	0.963347i
$206$	10.2092			0.711308
$207$	0.268889	+	1.69770i	0.0186891	+	0.117998i
$208$		0			0
$209$		0			0
$210$	−21.2327	−	10.8186i	−1.46519	−	0.746553i
$211$		0			0		−0.522499	−	0.852640i	$-0.675000\pi$
$211$		0			0		0.522499	+	0.852640i	$0.325000\pi$
$212$		0			0
$213$		0			0
$214$	12.2460	−	12.2460i	0.837123	−	0.837123i
$215$	−8.82821	+	27.1704i	−0.602079	+	1.85301i
$216$	−15.1991	+	1.19619i	−1.03417	+	0.0813906i
$217$		0			0
$218$	23.0760	+	5.54005i	1.56290	+	0.375220i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	4.99150	+	3.62654i	0.334255	+	0.242851i	0.742234	−	0.670141i	$-0.233766\pi$
$223$	4.99150	+	3.62654i	0.334255	+	0.242851i	−0.407979	+	0.912991i	$0.633766\pi$
$224$	−25.0009	+	6.00217i	−1.67044	+	0.401037i
$225$	−1.24033	−	0.196448i	−0.0826883	−	0.0130965i
$226$		0			0
$227$	6.07221	+	25.2926i	0.403026	+	1.67873i	0.692403	+	0.721511i	$0.256552\pi$
$227$	6.07221	+	25.2926i	0.403026	+	1.67873i	−0.289377	+	0.957215i	$0.593448\pi$
$228$		0			0
$229$	11.8348	+	10.1079i	0.782064	+	0.667946i	0.948028	−	0.318186i	$-0.103074\pi$
$229$	11.8348	+	10.1079i	0.782064	+	0.667946i	−0.165964	+	0.986132i	$0.553074\pi$
$230$	−12.7208	−	17.5086i	−0.838782	−	1.15448i
$231$		0			0
$232$	1.34910	−	3.25701i	0.0885726	−	0.213833i
$233$		0			0		0.233445	−	0.972370i	$-0.425000\pi$
$233$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$234$		0			0
$235$	−0.611206	−	7.76611i	−0.0398707	−	0.506605i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.852640	−	0.522499i	$-0.825000\pi$
$239$		0			0		0.852640	+	0.522499i	$0.175000\pi$
$240$	12.6440	−	7.74828i	0.816169	−	0.500149i
$241$	−8.56102	+	16.8019i	−0.551464	+	1.08231i	0.432113	+	0.901819i	$0.357768\pi$
$241$	−8.56102	+	16.8019i	−0.551464	+	1.08231i	−0.983577	+	0.180489i	$0.942232\pi$
$242$	−4.80718	−	14.7950i	−0.309017	−	0.951057i
$243$	−0.996141	−	2.40490i	−0.0639024	−	0.154274i
$244$	−2.79285	+	0.442344i	−0.178794	+	0.0283182i
$245$		−	30.5411i		−	1.95120i
$246$	−10.9910	+	10.2275i	−0.700762	+	0.652085i
$247$		0			0
$248$		0			0
$249$	−27.1528	+	11.2471i	−1.72074	+	0.712754i
$250$	15.0375	−	4.88599i	0.951057	−	0.309017i
$251$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$251$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$252$	−1.19291	−	1.94666i	−0.0751465	−	0.122628i
$253$		0			0
$254$	−14.4633	−	28.3858i	−0.907508	−	1.78108i
$255$		0			0
$256$	4.94427	−	15.2169i	0.309017	−	0.951057i
$257$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$257$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$258$	22.7793	−	19.4554i	1.41818	−	1.21124i
$259$		0			0
$260$		0			0
$261$	0.312078	+	0.0245611i	0.0193172	+	0.00152029i
$262$		0			0
$263$	−20.6165	+	24.1388i	−1.27126	+	1.48846i	−0.479623	+	0.877475i	$0.659226\pi$
$263$	−20.6165	+	24.1388i	−1.27126	+	1.48846i	−0.791642	+	0.610985i	$0.790774\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−4.14814	+	26.1904i	−0.253862	+	1.60282i
$268$	4.32700	+	18.0233i	0.264314	+	1.10095i
$269$	18.9249	−	26.0479i	1.15387	−	1.58817i	0.422221	−	0.906493i	$-0.361251\pi$
$269$	18.9249	−	26.0479i	1.15387	−	1.58817i	0.731653	−	0.681677i	$-0.238749\pi$
$270$	12.9616	+	11.0702i	0.788818	+	0.673714i
$271$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$271$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	1.78050	+	22.6234i	0.107174	+	1.36177i
$277$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$277$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$278$		0			0
$279$		0			0
$280$	24.5100	+	15.0198i	1.46476	+	0.897603i
$281$	−25.8068	+	15.8144i	−1.53951	+	0.943410i	−0.545032	+	0.838415i	$0.683483\pi$
$281$	−25.8068	+	15.8144i	−1.53951	+	0.943410i	−0.994473	+	0.104995i	$0.966517\pi$
$282$	−3.70848	+	7.27831i	−0.220837	+	0.433417i
$283$	−8.51987	−	26.2215i	−0.506454	−	1.55870i	−0.798313	−	0.602243i	$-0.794274\pi$
$283$	−8.51987	−	26.2215i	−0.506454	−	1.55870i	0.291859	−	0.956461i	$-0.405726\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−27.3375	−	9.98283i	−1.61368	−	0.589268i
$288$	1.42076			0.0837191
$289$	−2.65939	−	16.7907i	−0.156434	−	0.987688i
$290$	−3.64145	+	1.50834i	−0.213833	+	0.0885726i
$291$		0			0
$292$		0			0
$293$		0			0		−0.522499	−	0.852640i	$-0.675000\pi$
$293$		0			0		0.522499	+	0.852640i	$0.325000\pi$
$294$	−16.7330	+	27.3059i	−0.975891	+	1.59251i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	28.8480	−	2.27039i	1.67112	−	0.131520i
$299$		0			0
$300$	−16.1215	−	3.87044i	−0.930777	−	0.223460i
$301$	53.6499	+	22.2225i	3.09233	+	1.28088i
$302$		0			0
$303$	−26.8544	+	19.5109i	−1.54275	+	1.12087i
$304$		0			0
$305$	2.55764	+	1.85824i	0.146450	+	0.106402i
$306$		0			0
$307$	−28.7097	−	4.54717i	−1.63855	−	0.259521i	−0.731903	−	0.681409i	$-0.761367\pi$
$307$	−28.7097	−	4.54717i	−1.63855	−	0.259521i	−0.906648	+	0.421888i	$0.861367\pi$
$308$		0			0
$309$	2.79406	+	11.6381i	0.158949	+	0.662069i
$310$		0			0
$311$		0			0		−0.760406	−	0.649448i	$-0.775000\pi$
$311$		0			0		0.760406	+	0.649448i	$0.225000\pi$
$312$		0			0
$313$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$313$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$314$		0			0
$315$	−0.595887	+	2.48205i	−0.0335745	+	0.139848i
$316$		0			0
$317$		0			0		−0.0784591	−	0.996917i	$-0.525000\pi$
$317$		0			0		0.0784591	+	0.996917i	$0.475000\pi$
$318$		0			0
$319$		0			0
$320$	−15.9388	+	8.12123i	−0.891007	+	0.453990i
$321$	17.3116	+	10.6085i	0.966238	+	0.592111i
$322$	−37.5080	+	22.9849i	−2.09024	+	1.28090i
$323$		0			0
$324$	−5.05765	−	15.5658i	−0.280981	−	0.864769i
$325$		0			0
$326$	−34.4346	+	5.45391i	−1.90716	+	0.302064i
$327$			27.8220i			1.53856i
$328$	14.1856	−	11.2592i	0.783267	−	0.621685i
$329$	−15.8346			−0.872991
$330$		0			0
$331$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$331$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$332$	33.7179	−	10.9556i	1.85051	−	0.601268i
$333$		0			0
$334$	−15.2592	−	24.9008i	−0.834947	−	1.36251i
$335$	10.8278	−	17.6694i	0.591588	−	0.965384i
$336$	−13.6845	−	26.8574i	−0.746553	−	1.46519i
$337$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$337$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$338$	5.68121	−	17.4850i	0.309017	−	0.951057i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−30.1702	−	2.37444i	−1.62904	−	0.128208i
$344$	−29.2353	+	21.2407i	−1.57626	+	1.14522i
$345$	16.4778	−	19.2930i	0.887134	−	1.03870i
$346$		0			0
$347$	−21.4522	+	5.15021i	−1.15161	+	0.276478i	−0.763920	−	0.645311i	$-0.776728\pi$
$347$	−21.4522	+	5.15021i	−1.15161	+	0.276478i	−0.387692	+	0.921789i	$0.626728\pi$
$348$	4.08210	+	0.646541i	0.218824	+	0.0346583i
$349$	−5.52965	+	34.9128i	−0.295995	+	1.86884i	0.171982	+	0.985100i	$0.444983\pi$
$349$	−5.52965	+	34.9128i	−0.295995	+	1.86884i	−0.467978	+	0.883740i	$0.655017\pi$
$350$	−7.50272	−	31.2511i	−0.401037	−	1.67044i
$351$		0			0
$352$		0			0
$353$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$353$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$354$		0			0
$355$		0			0
$356$	7.46727	−	31.1034i	0.395764	−	1.64848i
$357$		0			0
$358$		0			0
$359$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$359$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$360$	−1.12321	−	1.12321i	−0.0591983	−	0.0591983i
$361$	16.9291	−	8.62582i	0.891007	−	0.453990i
$362$	9.89822	+	6.06564i	0.520239	+	0.318803i
$363$	15.5501	−	9.52912i	0.816169	−	0.500149i
$364$		0			0
$365$		0			0
$366$	−1.26861	−	3.06269i	−0.0663111	−	0.160089i
$367$	24.6944	−	3.91120i	1.28904	−	0.204163i	0.525981	−	0.850497i	$-0.323698\pi$
$367$	24.6944	−	3.91120i	1.28904	−	0.204163i	0.763055	+	0.646333i	$0.223698\pi$
$368$		−	27.3750i		−	1.42702i
$369$	1.34011	+	0.889040i	0.0697632	+	0.0462816i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$373$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$374$		0			0
$375$	9.68534	+	15.8050i	0.500149	+	0.816169i
$376$	5.14861	−	8.40176i	0.265519	−	0.433288i
$377$		0			0
$378$	24.4997	−	24.4997i	1.26013	−	1.26013i
$379$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$379$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$380$		0			0
$381$	28.4005	−	24.2563i	1.45500	−	1.24269i
$382$		0			0
$383$	−18.0006	−	7.45608i	−0.919786	−	0.380988i	−0.127991	−	0.991775i	$-0.540853\pi$
$383$	−18.0006	−	7.45608i	−0.919786	−	0.380988i	−0.791794	+	0.610788i	$0.790853\pi$
$384$	18.6999	+	1.47171i	0.954275	+	0.0751031i
$385$		0			0
$386$		0			0
$387$	−2.59602	−	1.88612i	−0.131963	−	0.0958769i
$388$		0			0
$389$	32.0990	+	5.08398i	1.62748	+	0.257768i	0.902402	−	0.430895i	$-0.141802\pi$
$389$	32.0990	+	5.08398i	1.62748	+	0.257768i	0.725082	+	0.688663i	$0.241802\pi$
$390$		0			0
$391$		0			0
$392$	22.7072	−	31.2538i	1.14689	−	1.57855i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.233445	−	0.972370i	$-0.425000\pi$
$397$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$398$		0			0
$399$		0			0
$400$	19.0211	+	6.18034i	0.951057	+	0.309017i
$401$	−28.3192	−	28.3192i	−1.41420	−	1.41420i	−0.710705	−	0.703490i	$-0.751624\pi$
$401$	−28.3192	−	28.3192i	−1.41420	−	1.41420i	−0.703490	−	0.710705i	$-0.748376\pi$
$402$	−19.3617	+	9.86526i	−0.965672	+	0.492035i
$403$		0			0
$404$	34.1412	−	20.9218i	1.69859	−	1.04090i
$405$	−8.30746	+	16.3043i	−0.412801	+	0.810167i
$406$	2.47574	+	7.61954i	0.122869	+	0.378151i
$407$		0			0
$408$		0			0
$409$		−	39.1280i		−	1.93475i	−0.253344	−	0.967376i	$-0.581530\pi$
$409$		−	39.1280i		−	1.93475i	0.253344	−	0.967376i	$-0.418470\pi$
$410$	−20.1159	−	2.31350i	−0.993451	−	0.114255i
$411$		0			0
$412$	−2.25860	−	14.2602i	−0.111273	−	0.702550i
$413$		0			0
$414$	2.31186	−	0.751169i	0.113622	−	0.0369179i
$415$	−35.3175	−	17.9952i	−1.73367	−	0.883349i
$416$		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	$0.750000\pi$
$420$	−10.4141	+	32.0512i	−0.508155	+	1.56394i
$421$	−40.6272	+	3.19743i	−1.98005	+	0.155833i	−0.999235	−	0.0391149i	$-0.987546\pi$
$421$	−40.6272	+	3.19743i	−1.98005	+	0.155833i	−0.980814	+	0.194948i	$0.937546\pi$
$422$		0			0
$423$	0.850818	+	0.204263i	0.0413682	+	0.00993162i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	4.17340	−	4.88643i	0.201965	−	0.236471i
$428$	−19.8145	−	14.3961i	−0.957771	−	0.695861i
$429$		0			0
$430$	39.9048	+	6.32030i	1.92438	+	0.304792i
$431$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$431$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$432$	5.03336	+	20.9655i	0.242168	+	1.00870i
$433$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$433$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$434$		0			0
$435$	−2.71605	−	3.73832i	−0.130225	−	0.179239i
$436$	2.63322	−	33.4582i	0.126108	−	1.60236i
$437$		0			0
$438$		0			0
$439$		0			0		−0.649448	−	0.760406i	$-0.725000\pi$
$439$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$440$		0			0
$441$	3.26251	+	1.06005i	0.155358	+	0.0504788i
$442$		0			0
$443$	−24.1213	+	12.2904i	−1.14604	+	0.583935i	−0.920671	−	0.390339i	$-0.872358\pi$
$443$	−24.1213	+	12.2904i	−1.14604	+	0.583935i	−0.225367	+	0.974274i	$0.572358\pi$
$444$		0			0
$445$	−30.4928	+	18.6860i	−1.44550	+	0.885802i
$446$	3.96128	−	7.77444i	0.187572	−	0.368130i
$447$	10.4833	+	32.2643i	0.495844	+	1.52605i
$448$	13.9148	+	33.5934i	0.657414	+	1.58714i
$449$	−31.9921	+	5.06705i	−1.50980	+	0.239129i	−0.855777	−	0.517345i	$-0.826920\pi$
$449$	−31.9921	+	5.06705i	−1.50980	+	0.239129i	−0.654024	+	0.756474i	$0.726920\pi$
$450$			1.77595i			0.0837191i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	33.9853	−	14.0772i	1.59501	−	0.660675i
$455$		0			0
$456$		0			0
$457$		0			0		−0.522499	−	0.852640i	$-0.675000\pi$
$457$		0			0		0.522499	+	0.852640i	$0.325000\pi$
$458$	11.5004	−	18.7670i	0.537380	−	0.876925i
$459$		0			0
$460$	−21.6419	+	21.6419i	−1.00906	+	1.00906i
$461$	13.1976	−	40.6180i	0.614673	−	1.89177i	0.208288	−	0.978068i	$-0.433211\pi$
$461$	13.1976	−	40.6180i	0.614673	−	1.89177i	0.406385	−	0.913702i	$-0.366789\pi$
$462$		0			0
$463$	−16.7085	+	14.2704i	−0.776509	+	0.663201i	−0.946666	−	0.322216i	$-0.895572\pi$
$463$	−16.7085	+	14.2704i	−0.776509	+	0.663201i	0.170158	+	0.985417i	$0.445572\pi$
$464$	−4.84786	−	1.16387i	−0.225056	−	0.0540313i
$465$		0			0
$466$		0			0
$467$	29.5928	−	21.5004i	1.36939	−	0.994920i	0.371605	−	0.928391i	$-0.378808\pi$
$467$	29.5928	−	21.5004i	1.36939	−	0.994920i	0.997785	−	0.0665285i	$-0.0211923\pi$
$468$		0			0
$469$	−34.0783	−	24.7593i	−1.57359	−	1.14328i
$470$	−10.7125	+	2.57184i	−0.494131	+	0.118630i
$471$		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		0.233445	−	0.972370i	$-0.425000\pi$
$479$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$480$	−13.6201	−	15.9471i	−0.621668	−	0.727880i
$481$		0			0
$482$	25.3630	+	8.24093i	1.15525	+	0.375364i
$483$	−36.4672	−	36.4672i	−1.65932	−	1.65932i
$484$	−19.6021	+	9.98779i	−0.891007	+	0.453990i
$485$		0			0
$486$	−3.13879	+	1.92345i	−0.142378	+	0.0872495i
$487$	18.6937	−	36.6885i	0.847094	−	1.66252i	0.102762	−	0.994706i	$-0.467232\pi$
$487$	18.6937	−	36.6885i	0.847094	−	1.66252i	0.744332	−	0.667809i	$-0.232768\pi$
$488$	1.23573	+	3.80320i	0.0559390	+	0.172163i
$489$	−15.6414	−	37.7616i	−0.707328	−	1.70764i
$490$	−42.6599	+	6.75667i	−1.92718	+	0.305235i
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$	16.7174	+	13.0896i	0.753680	+	0.590126i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	21.7170	+	35.4389i	0.973161	+	1.58805i
$499$		0			0		0.522499	−	0.852640i	$-0.325000\pi$
$499$		0			0		−0.522499	+	0.852640i	$0.675000\pi$
$500$	−10.1515	−	19.9235i	−0.453990	−	0.891007i
$501$	24.2098	−	24.2098i	1.08162	−	1.08162i
$502$		0			0
$503$	−35.5760	+	2.79990i	−1.58626	+	0.124841i	−0.840663	−	0.541559i	$-0.817834\pi$
$503$	−35.5760	+	2.79990i	−1.58626	+	0.124841i	−0.745594	+	0.666400i	$0.767834\pi$
$504$	−2.45519	+	2.09693i	−0.109363	+	0.0934046i
$505$	−43.5311	−	10.4509i	−1.93711	−	0.465059i
$506$		0			0
$507$	21.4871	+	1.69107i	0.954275	+	0.0751031i
$508$	−36.4496	+	26.4822i	−1.61719	+	1.17496i
$509$	−14.7148	+	17.2288i	−0.652222	+	0.763654i	−0.983702	−	0.179808i	$-0.942452\pi$
$509$	−14.7148	+	17.2288i	−0.652222	+	0.763654i	0.331479	+	0.943462i	$0.392452\pi$
$510$		0			0
$511$		0			0
$512$	−22.3488	−	3.53971i	−0.987688	−	0.156434i
$513$		0			0
$514$		0			0
$515$	−9.48811	+	13.0593i	−0.418096	+	0.575460i
$516$	−32.2148	−	27.5141i	−1.41818	−	1.21124i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−9.44175	−	11.0549i	−0.413651	−	0.484323i	0.513990	−	0.857796i	$-0.328167\pi$
$521$	−9.44175	−	11.0549i	−0.413651	−	0.484323i	−0.927641	+	0.373473i	$0.878167\pi$
$522$	−0.0347346	−	0.441345i	−0.00152029	−	0.0193172i
$523$	3.42071	+	1.11146i	0.149577	+	0.0486006i	0.382849	−	0.923811i	$-0.374943\pi$
$523$	3.42071	+	1.11146i	0.149577	+	0.0486006i	−0.233271	+	0.972412i	$0.574943\pi$
$524$		0			0
$525$	33.5718	−	17.1057i	1.46519	−	0.746553i
$526$	38.2781	+	23.4568i	1.66900	+	1.02277i
$527$		0			0
$528$		0			0
$529$	−7.36603	−	22.6703i	−0.320262	−	0.985666i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	37.5004			1.62280
$535$	4.28364	+	27.0459i	0.185198	+	1.16929i
$536$	24.2177	−	10.0313i	1.04604	−	0.433286i
$537$		0			0
$538$	−40.5706	−	20.6718i	−1.74912	−	0.891223i
$539$		0			0
$540$	12.5954	−	20.5539i	0.542021	−	0.884498i
$541$	12.6429	+	24.8131i	0.543560	+	1.06680i	0.985488	+	0.169746i	$0.0542948\pi$
$541$	12.6429	+	24.8131i	0.543560	+	1.06680i	−0.441928	+	0.897051i	$0.645705\pi$
$542$		0			0
$543$	−4.20565	+	12.9437i	−0.180482	+	0.555466i
$544$		0			0
$545$	−28.5328	+	24.3693i	−1.22221	+	1.04387i
$546$		0			0
$547$	25.0194	+	10.3634i	1.06975	+	0.443106i	0.846903	−	0.531747i	$-0.178464\pi$
$547$	25.0194	+	10.3634i	1.06975	+	0.443106i	0.222849	+	0.974853i	$0.428464\pi$
$548$		0			0
$549$	−0.287277	+	0.208719i	−0.0122607	+	0.00890790i
$550$		0			0
$551$		0			0
$552$	31.2066	−	7.49203i	1.32824	−	0.318882i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.760406	−	0.649448i	$-0.775000\pi$
$557$		0			0		0.760406	+	0.649448i	$0.225000\pi$
$558$		0			0
$559$		0			0
$560$	15.5573	−	37.5585i	0.657414	−	1.58714i
$561$		0			0
$562$	27.7989	+	32.5484i	1.17263	+	1.37297i
$563$	−3.59291	−	45.6522i	−0.151423	−	1.92401i	−0.337222	−	0.941425i	$-0.609487\pi$
$563$	−3.59291	−	45.6522i	−0.151423	−	1.92401i	0.185799	−	0.982588i	$-0.440513\pi$
$564$	10.9868	+	3.56982i	0.462627	+	0.150317i
$565$		0			0
$566$	−34.7413	+	17.7016i	−1.46029	+	0.744054i
$567$	31.7140	+	19.4343i	1.33186	+	0.816166i
$568$		0			0
$569$	21.5760	−	42.3453i	0.904513	−	1.77521i	0.374451	−	0.927247i	$-0.377831\pi$
$569$	21.5760	−	42.3453i	0.904513	−	1.77521i	0.530062	−	0.847959i	$-0.322169\pi$
$570$		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
$574$	−7.89612	+	40.3936i	−0.329578	+	1.68600i
$575$	34.2188			1.42702
$576$	−0.314317	−	1.98452i	−0.0130965	−	0.0826883i
$577$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$577$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$578$	−22.8649	+	7.42927i	−0.951057	+	0.309017i
$579$		0			0
$580$	2.91245	+	4.75269i	0.120933	+	0.197345i
$581$	−42.0977	+	68.6971i	−1.74651	+	2.85004i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	45.2261	+	10.8578i	1.86668	+	0.448151i	0.998816	−	0.0486476i	$-0.0154911\pi$
$587$	45.2261	+	10.8578i	1.86668	+	0.448151i	0.867866	+	0.496798i	$0.165491\pi$
$588$	41.8428	+	17.3318i	1.72557	+	0.714753i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$593$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$594$		0			0
$595$		0			0
$596$	−9.55338	−	39.7927i	−0.391322	−	1.62997i
$597$		0			0
$598$		0			0
$599$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$599$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$600$	−1.83964	+	23.3749i	−0.0751031	+	0.954275i
$601$	−10.1297	+	24.4554i	−0.413201	+	0.997555i	0.571072	+	0.820900i	$0.306528\pi$
$601$	−10.1297	+	24.4554i	−0.413201	+	0.997555i	−0.984273	+	0.176655i	$0.943472\pi$
$602$	19.1714	−	79.8546i	0.781368	−	3.25463i
$603$	1.51169	+	1.76996i	0.0615607	+	0.0720783i
$604$		0			0
$605$	23.3929	+	7.60081i	0.951057	+	0.309017i
$606$	33.1939	+	33.1939i	1.34841	+	1.34841i
$607$	−7.40968	+	3.77542i	−0.300750	+	0.153240i	−0.597853	−	0.801606i	$-0.703979\pi$
$607$	−7.40968	+	3.77542i	−0.300750	+	0.153240i	0.297103	+	0.954845i	$0.403979\pi$
$608$		0			0
$609$	−8.00844	+	4.90758i	−0.324518	+	0.198865i
$610$	2.02976	−	3.98362i	0.0821825	−	0.161292i
$611$		0			0
$612$		0			0
$613$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$613$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$614$			41.1078i			1.65898i
$615$	−2.86803	−	23.5645i	−0.115650	−	0.950214i
$616$		0			0
$617$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$617$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$618$	15.6380	−	6.47748i	0.629053	−	0.260562i
$619$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$619$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$620$		0			0
$621$	19.2749	+	31.4538i	0.773476	+	1.26220i
$622$		0			0
$623$	33.0021	+	64.7703i	1.32220	+	2.59497i
$624$		0			0
$625$	−7.72542	+	23.7764i	−0.309017	+	0.951057i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	3.59876	+	0.283229i	0.143378	+	0.0112841i
$631$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$631$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	49.7520	+	7.87994i	1.97435	+	0.312706i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	14.8699	+	20.4667i	0.587785	+	0.809017i
$641$	2.79898	−	35.5644i	0.110553	−	1.40471i	−0.652214	−	0.758035i	$-0.726159\pi$
$641$	2.79898	−	35.5644i	0.110553	−	1.40471i	0.762767	−	0.646674i	$-0.223841\pi$
$642$	10.9882	−	26.5278i	0.433669	−	1.04697i
$643$	10.9502	−	45.6107i	0.431832	−	1.79871i	−0.153765	−	0.988107i	$-0.549140\pi$
$643$	10.9502	−	45.6107i	0.431832	−	1.79871i	0.585597	−	0.810602i	$-0.300860\pi$
$644$	40.4033	+	47.3062i	1.59211	+	1.86413i
$645$	3.71628	+	47.2198i	0.146328	+	1.85928i
$646$		0			0
$647$	−35.9166	−	35.9166i	−1.41203	−	1.41203i	−0.745308	−	0.666720i	$-0.767698\pi$
$647$	−35.9166	−	35.9166i	−1.41203	−	1.41203i	−0.666720	−	0.745308i	$-0.732302\pi$
$648$	−20.6235	+	10.5082i	−0.810167	+	0.412801i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	15.2361	+	46.8918i	0.596690	+	1.83642i
$653$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$653$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$654$	38.8619	−	6.15511i	1.51962	−	0.240684i
$655$		0			0
$656$	−18.8652	−	17.3235i	−0.736561	−	0.676371i
$657$		0			0
$658$	3.50312	+	22.1178i	0.136566	+	0.862243i
$659$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$659$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$660$		0			0
$661$	42.9179	+	21.8677i	1.66931	+	0.850556i	0.993545	+	0.113440i	$0.0361871\pi$
$661$	42.9179	+	21.8677i	1.66931	+	0.850556i	0.675766	+	0.737116i	$0.263813\pi$
$662$		0			0
$663$		0			0
$664$	−22.7623	−	44.6735i	−0.883349	−	1.73367i
$665$		0			0
$666$		0			0
$667$	−8.50379	+	0.669263i	−0.329268	+	0.0259140i
$668$	−31.4056	+	26.8229i	−1.21512	+	1.03781i
$669$	9.94672	+	2.38800i	0.384562	+	0.0923252i
$670$	−27.0762	−	11.2153i	−1.04604	−	0.433286i
$671$		0			0
$672$	−34.4870	+	25.0563i	−1.33037	+	0.966568i
$673$		0			0		0.649448	−	0.760406i	$-0.275000\pi$
$673$		0			0		−0.649448	+	0.760406i	$0.725000\pi$
$674$		0			0
$675$	−26.2068	+	6.29170i	−1.00870	+	0.242168i
$676$	−25.6799	−	4.06730i	−0.987688	−	0.156434i
$677$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$677$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	25.3487	+	34.8894i	0.971362	+	1.33697i
$682$		0			0
$683$	0.520412	−	1.25639i	0.0199130	−	0.0480743i	−0.913610	−	0.406591i	$-0.866717\pi$
$683$	0.520412	−	1.25639i	0.0199130	−	0.0480743i	0.933523	+	0.358517i	$0.116717\pi$
$684$		0			0
$685$		0			0
$686$	3.35797	+	42.6671i	0.128208	+	1.62904i
$687$	24.5412	+	7.97392i	0.936305	+	0.304224i
$688$	36.1368	+	36.1368i	1.37770	+	1.37770i
$689$		0			0
$690$	−30.5939	−	18.7480i	−1.16469	−	0.713723i
$691$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$691$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$692$		0			0
$693$		0			0
$694$	11.9397	+	28.8250i	0.453226	+	1.09418i
$695$		0			0
$696$		−	5.84492i		−	0.221551i
$697$		0			0
$698$	49.9896			1.89214
$699$		0			0
$700$	−41.9917	+	17.3935i	−1.58714	+	0.657414i
$701$	47.3175	−	15.3744i	1.78716	−	0.580682i	0.787778	−	0.615959i	$-0.211231\pi$
$701$	47.3175	−	15.3744i	1.78716	−	0.580682i	0.999378	+	0.0352773i	$0.0112314\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−5.86363	−	11.5080i	−0.220837	−	0.433417i
$706$		0			0
$707$	−28.1199	+	86.5442i	−1.05756	+	3.25483i
$708$		0			0
$709$	5.46492	−	4.66749i	0.205240	−	0.175291i	−0.540887	−	0.841095i	$-0.681911\pi$
$709$	5.46492	−	4.66749i	0.205240	−	0.175291i	0.746127	+	0.665804i	$0.231911\pi$
$710$		0			0
$711$		0			0
$712$	−45.0973	−	3.54924i	−1.69009	−	0.133013i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.233445	−	0.972370i	$-0.575000\pi$
$719$		0			0		0.233445	+	0.972370i	$0.425000\pi$
$720$	−1.32041	+	1.81739i	−0.0492088	+	0.0677301i
$721$	24.9500	+	21.3093i	0.929186	+	0.793599i
$722$	−15.7938	−	21.7383i	−0.587785	−	0.809017i
$723$	−2.45300	+	31.1683i	−0.0912279	+	1.15916i
$724$	6.28269	−	15.1678i	0.233495	−	0.563706i
$725$	1.45484	−	6.05983i	0.0540313	−	0.225056i
$726$	−16.7505	−	19.6123i	−0.621668	−	0.727880i
$727$	−4.23098	−	53.7596i	−0.156918	−	1.99383i	−0.0786754	−	0.996900i	$-0.525069\pi$
$727$	−4.23098	−	53.7596i	−0.156918	−	1.99383i	−0.0782428	−	0.996934i	$-0.524931\pi$
$728$		0			0
$729$	−20.4114	−	20.4114i	−0.755978	−	0.755978i
$730$		0			0
$731$		0			0
$732$	−3.99731	+	2.44956i	−0.147745	+	0.0905382i
$733$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$733$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$734$	−10.9264	−	33.6279i	−0.403299	−	1.24123i
$735$	−19.3776	−	46.7816i	−0.714753	−	1.72557i
$736$	−38.2375	+	6.05622i	−1.40945	+	0.223235i
$737$		0			0
$738$	0.945339	−	2.06855i	0.0347984	−	0.0761443i
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−26.7885	−	13.6494i	−0.982774	−	0.500748i	−0.112678	−	0.993632i	$-0.535943\pi$
$743$	−26.7885	−	13.6494i	−0.982774	−	0.500748i	−0.870095	+	0.492883i	$0.835943\pi$
$744$		0			0
$745$	−23.9063	+	39.0115i	−0.875858	+	1.42927i
$746$		0			0
$747$	3.14815	−	3.14815i	0.115185	−	0.115185i
$748$		0			0
$749$	55.4886	−	4.36704i	2.02751	−	0.159568i
$750$	19.9338	−	17.0251i	0.727880	−	0.621668i
$751$		0			0		−0.972370	−	0.233445i	$-0.925000\pi$
$751$		0			0		0.972370	+	0.233445i	$0.0750000\pi$
$752$	−12.8746	−	5.33285i	−0.469490	−	0.194469i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−39.6414	−	28.8012i	−1.44174	−	1.04749i
$757$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$757$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−24.6322	+	33.9034i	−0.892918	+	1.22900i	0.0797547	+	0.996815i	$0.474586\pi$
$761$	−24.6322	+	33.9034i	−0.892918	+	1.22900i	−0.972673	+	0.232181i	$0.925414\pi$
$762$	−40.1644	−	34.3036i	−1.45500	−	1.24269i
$763$	44.8312	+	61.7049i	1.62300	+	2.23387i
$764$		0			0
$765$		0			0
$766$	−6.43237	+	26.7927i	−0.232411	+	0.968061i
$767$		0			0
$768$	−2.08132	−	26.4456i	−0.0751031	−	0.954275i
$769$	39.4313	+	12.8120i	1.42193	+	0.462013i	0.916215	−	0.400687i	$-0.131229\pi$
$769$	39.4313	+	12.8120i	1.42193	+	0.462013i	0.505715	+	0.862700i	$0.331229\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$773$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$774$	−2.06022	+	4.04340i	−0.0740529	+	0.145337i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		−	45.9607i		−	1.64777i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	6.38967	−	2.07613i	0.228348	−	0.0741948i
$784$	−48.6789	−	24.8031i	−1.73853	−	0.885827i
$785$		0			0
$786$		0			0
$787$	−12.3931	−	24.3228i	−0.441766	−	0.867015i	−0.999320	−	0.0368739i	$-0.988260\pi$
$787$	−12.3931	−	24.3228i	−0.441766	−	0.867015i	0.557554	−	0.830141i	$-0.311740\pi$
$788$		0			0
$789$	−16.2640	+	50.0554i	−0.579013	+	1.78202i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$797$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$798$		0			0
$799$		0			0
$800$	4.42463	−	27.9360i	0.156434	−	0.987688i
$801$	−0.937729	−	3.90592i	−0.0331330	−	0.138009i
$802$	−33.2913	+	45.8215i	−1.17556	+	1.61801i
$803$		0			0
$804$	18.0632	+	24.8619i	0.637041	+	0.876812i
$805$	5.45722	−	69.3405i	0.192342	−	2.44393i
$806$		0			0
$807$	12.4617	−	51.9065i	0.438671	−	1.82720i
$808$	−36.7767	−	43.0600i	−1.29380	−	1.51485i
$809$	−1.68433	−	21.4015i	−0.0592179	−	0.752435i	−0.952812	−	0.303560i	$-0.901825\pi$
$809$	−1.68433	−	21.4015i	−0.0592179	−	0.752435i	0.893594	−	0.448875i	$-0.148175\pi$
$810$	24.6118	+	7.99685i	0.864769	+	0.280981i
$811$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$811$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$812$	10.0953	−	5.14380i	0.354275	−	0.180512i
$813$		0			0
$814$		0			0
$815$	25.0261	−	49.1164i	0.876624	−	1.72047i
$816$		0			0
$817$		0			0
$818$	−54.6540	+	8.65634i	−1.91093	+	0.302662i
$819$		0			0
$820$	1.21877	+	28.6097i	0.0425613	+	0.999094i
$821$	14.9400			0.521408			0.260704	−	0.965419i	$-0.416045\pi$
$821$	14.9400			0.521408			0.260704	+	0.965419i	$0.416045\pi$
$822$		0			0
$823$	35.8145	−	14.8349i	1.24842	−	0.517111i	0.342081	−	0.939670i	$-0.388868\pi$
$823$	35.8145	−	14.8349i	1.24842	−	0.517111i	0.906335	+	0.422560i	$0.138868\pi$
$824$	−19.4190	+	6.30962i	−0.676494	+	0.219806i
$825$		0			0
$826$		0			0
$827$	−22.3115	+	36.4090i	−0.775845	+	1.26606i	0.183274	+	0.983062i	$0.441331\pi$
$827$	−22.3115	+	36.4090i	−0.775845	+	1.26606i	−0.959119	+	0.283003i	$0.908669\pi$
$828$	−1.56069	−	3.06303i	−0.0542377	−	0.106448i
$829$	3.17555	−	3.17555i	0.110291	−	0.110291i	−0.649808	−	0.760099i	$-0.725151\pi$
$829$	3.17555	−	3.17555i	0.110291	−	0.110291i	0.760099	+	0.649808i	$0.225151\pi$
$830$	−17.3224	+	53.3127i	−0.601268	+	1.85051i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	46.0337	+	3.62293i	1.59306	+	0.125377i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$839$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$840$	47.0732	+	7.45565i	1.62418	+	0.257245i
$841$	4.29357	−	27.1086i	0.148054	−	0.934778i
$842$	13.4542	+	56.0408i	0.463662	+	1.93129i
$843$	−29.4959	+	40.5977i	−1.01589	+	1.39826i
$844$		0			0
$845$	17.0863	+	23.5172i	0.587785	+	0.809017i
$846$	0.0970875	−	1.23361i	0.00333794	−	0.0424125i
$847$	19.1329	−	46.1909i	0.657414	−	1.58714i
$848$		0			0
$849$	−29.6873	−	34.7593i	−1.01886	−	1.19294i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$853$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$854$	−7.74866	−	4.74838i	−0.265154	−	0.162486i
$855$		0			0
$856$	−15.7249	+	30.8618i	−0.537466	+	1.05484i
$857$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$857$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$858$		0			0
$859$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$859$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$860$		−	57.1374i		−	1.94837i
$861$	−48.2083	+	2.05367i	−1.64293	+	0.0699887i
$862$		0			0
$863$	1.48407	+	9.37003i	0.0505183	+	0.318960i	0.999987	+	0.00509811i	$0.00162279\pi$
$863$	1.48407	+	9.37003i	0.0505183	+	0.318960i	−0.949469	+	0.313862i	$0.898377\pi$
$864$	28.1711	−	11.6688i	0.958399	−	0.396982i
$865$		0			0
$866$		0			0
$867$	−14.7268	−	24.0320i	−0.500149	−	0.816169i
$868$		0			0
$869$		0			0
$870$	−4.62082	+	4.62082i	−0.156660	+	0.156660i
$871$		0			0
$872$	−47.3171	+	3.72393i	−1.60236	+	0.126108i
$873$		0			0
$874$		0			0
$875$	46.9482	+	19.4466i	1.58714	+	0.657414i
$876$		0			0
$877$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$877$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	15.5086	+	2.45632i	0.522498	+	0.0827556i	0.412112	−	0.911133i	$-0.364791\pi$
$881$	15.5086	+	2.45632i	0.522498	+	0.0827556i	0.110386	+	0.993889i	$0.464791\pi$
$882$	0.758915	−	4.79160i	0.0255540	−	0.161342i
$883$	−13.8730	−	57.7850i	−0.466862	−	1.94462i	−0.244159	−	0.969735i	$-0.578512\pi$
$883$	−13.8730	−	57.7850i	−0.466862	−	1.94462i	−0.222703	−	0.974886i	$-0.571488\pi$
$884$		0			0
$885$		0			0
$886$	22.5037	+	30.9737i	0.756026	+	1.04058i
$887$	1.90399	−	24.1925i	0.0639298	−	0.812305i	−0.878466	−	0.477805i	$-0.841433\pi$
$887$	1.90399	−	24.1925i	0.0639298	−	0.812305i	0.942396	−	0.334500i	$-0.108567\pi$
$888$		0			0
$889$	23.9023	−	99.5601i	0.801656	−	3.33914i
$890$	32.8466	+	38.4585i	1.10102	+	1.28913i
$891$		0			0
$892$	−11.7357	−	3.81317i	−0.392941	−	0.127674i
$893$		0			0
$894$	42.7477	−	21.7810i	1.42970	−	0.728467i
$895$		0			0
$896$	43.8449	−	26.8682i	1.46476	−	0.897603i
$897$		0			0
$898$	14.1553	+	43.5656i	0.472370	+	1.45380i
$899$		0			0
$900$	2.48065	−	0.392896i	0.0826883	−	0.0130965i
$901$		0			0
$902$		0			0
$903$	96.2784			3.20394
$904$		0			0
$905$	−16.9581	+	7.02427i	−0.563706	+	0.233495i
$906$		0			0
$907$	12.1083	+	6.16950i	0.402051	+	0.204855i	0.643310	−	0.765606i	$-0.277561\pi$
$907$	12.1083	+	6.16950i	0.402051	+	0.204855i	−0.241260	+	0.970461i	$0.577561\pi$
$908$	−27.1817	−	44.3565i	−0.902056	−	1.47202i
$909$	2.62733	−	4.28741i	0.0871429	−	0.142204i
$910$		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
$915$	5.09670	+	1.22361i	0.168492	+	0.0404513i
$916$	−28.7581	−	11.9120i	−0.950193	−	0.393583i
$917$		0			0
$918$		0			0
$919$		0			0		0.649448	−	0.760406i	$-0.275000\pi$
$919$		0			0		−0.649448	+	0.760406i	$0.725000\pi$
$920$	35.0173	+	25.4415i	1.15448	+	0.838782i
$921$	−46.8614	+	11.2504i	−1.54414	+	0.370714i
$922$	−59.6551	−	9.44843i	−1.96463	−	0.311168i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	23.6293	+	20.1814i	0.776509	+	0.663201i
$927$	−1.06571	−	1.46683i	−0.0350026	−	0.0481770i
$928$	−0.553194	+	7.02899i	−0.0181595	+	0.230738i
$929$	−23.2622	+	56.1600i	−0.763209	+	1.84255i	−0.312282	+	0.949989i	$0.601093\pi$
$929$	−23.2622	+	56.1600i	−0.763209	+	1.84255i	−0.450927	+	0.892561i	$0.648907\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−36.5787	−	36.5787i	−1.19689	−	1.19689i
$935$		0			0
$936$		0			0
$937$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$937$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$938$	−27.0447	+	53.0782i	−0.883041	+	1.73306i
$939$		0			0
$940$	5.96230	+	14.3943i	0.194469	+	0.469490i
$941$	−47.8820	+	7.58377i	−1.56091	+	0.247224i	−0.876329	−	0.481714i	$-0.840015\pi$
$941$	−47.8820	+	7.58377i	−1.56091	+	0.247224i	−0.684580	+	0.728937i	$0.740015\pi$
$942$		0			0
$943$	−39.8565	−	18.2147i	−1.29791	−	0.593151i
$944$		0			0
$945$	8.56996	+	54.1086i	0.278781	+	1.76015i
$946$		0			0
$947$	−34.5155	+	11.2148i	−1.12160	+	0.364431i	−0.810380	−	0.585905i	$-0.800739\pi$
$947$	−34.5155	+	11.2148i	−1.12160	+	0.364431i	−0.311225	+	0.950336i	$0.600739\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$953$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−19.2617	+	22.5525i	−0.621668	+	0.727880i
$961$	25.0795	+	18.2213i	0.809017	+	0.587785i
$962$		0			0
$963$	−3.03782	−	0.481143i	−0.0978922	−	0.0155046i
$964$	5.89985	−	37.2502i	0.190021	−	1.19975i
$965$		0			0
$966$	−42.8698	+	59.0052i	−1.37931	+	1.89846i
$967$	−20.8234	−	17.7849i	−0.669636	−	0.571923i	0.248285	−	0.968687i	$-0.420133\pi$
$967$	−20.8234	−	17.7849i	−0.669636	−	0.571923i	−0.917921	+	0.396764i	$0.870133\pi$
$968$	18.2876	+	25.1707i	0.587785	+	0.809017i
$969$		0			0
$970$		0			0
$971$		0			0		0.233445	−	0.972370i	$-0.425000\pi$
$971$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$972$	3.38108	+	3.95874i	0.108448	+	0.126976i
$973$		0			0
$974$	−55.3822	−	17.9948i	−1.77456	−	0.576590i
$975$		0			0
$976$	5.03893	−	2.56746i	0.161292	−	0.0821825i
$977$		0			0		−0.852640	−	0.522499i	$-0.825000\pi$
$977$		0			0		0.852640	+	0.522499i	$0.175000\pi$
$978$	−49.2852	+	30.2020i	−1.57597	+	0.965753i
$979$		0			0
$980$	18.8755	+	58.0927i	0.602954	+	1.85570i
$981$	−1.61287	−	3.89381i	−0.0514949	−	0.124320i
$982$		0			0
$983$		−	15.0075i		−	0.478664i	−0.970938	−	0.239332i	$-0.923072\pi$
$983$		−	15.0075i		−	0.478664i	0.970938	−	0.239332i	$-0.0769284\pi$
$984$	14.5852	−	26.2468i	0.464959	−	0.836716i
$985$		0			0
$986$		0			0
$987$	−24.2548	+	10.0467i	−0.772040	+	0.319789i
$988$		0			0
$989$	77.9077	+	39.6960i	2.47732	+	1.26226i
$990$		0			0
$991$		0			0		0.522499	−	0.852640i	$-0.325000\pi$
$991$		0			0		−0.522499	+	0.852640i	$0.675000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	44.6966	−	38.1745i	1.41627	−	1.20961i
$997$		0			0		−0.972370	−	0.233445i	$-0.925000\pi$
$997$		0			0		0.972370	+	0.233445i	$0.0750000\pi$
$998$		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.639.1	yes	16
4.3	odd	2		820.2.cc.f.639.1	yes	16
5.4	even	2		820.2.cc.f.639.1	yes	16
20.19	odd	2	CM	820.2.cc.a.639.1	yes	16
41.12	odd	40	inner	820.2.cc.a.299.1	✓	16
164.135	even	40		820.2.cc.f.299.1	yes	16
205.94	odd	40		820.2.cc.f.299.1	yes	16
820.299	even	40	inner	820.2.cc.a.299.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.cc.a.299.1	✓	16	41.12	odd	40	inner
820.2.cc.a.299.1	✓	16	820.299	even	40	inner
820.2.cc.a.639.1	yes	16	1.1	even	1	trivial
820.2.cc.a.639.1	yes	16	20.19	odd	2	CM
820.2.cc.f.299.1	yes	16	164.135	even	40
820.2.cc.f.299.1	yes	16	205.94	odd	40
820.2.cc.f.639.1	yes	16	4.3	odd	2
820.2.cc.f.639.1	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)

\(f(q)\)	\(=\)	\(q+(-0.221232 - 1.39680i) q^{2} +(1.53176 - 0.634475i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(1.99235 + 1.01515i) q^{5} +(-1.22511 - 1.99920i) q^{6} +(2.37484 - 3.87538i) q^{7} +(1.28408 + 2.52015i) q^{8} +(-0.177595 + 0.177595i) q^{9} +(0.977198 - 3.00750i) q^{10} +(-2.52145 + 2.15352i) q^{12} +(-5.93853 - 2.45982i) q^{14} +(3.69589 + 0.290873i) q^{15} +(3.23607 - 2.35114i) q^{16} +(0.287355 + 0.208775i) q^{18} +(-4.41708 - 0.699596i) q^{20} +(1.17884 - 7.44292i) q^{21} +(4.02266 - 5.53671i) q^{23} +(3.56587 + 3.04554i) q^{24} +(2.93893 + 4.04508i) q^{25} +(-2.06278 + 4.97999i) q^{27} +(-2.12209 + 8.83914i) q^{28} +(-0.809475 - 0.947773i) q^{29} +(-0.411356 - 5.22678i) q^{30} +(-4.00000 - 4.00000i) q^{32} +(8.66561 - 5.31029i) q^{35} +(0.228046 - 0.447565i) q^{36} +6.32456i q^{40} +(-1.26993 - 6.27593i) q^{41} -10.6571 q^{42} +(1.99865 + 12.6190i) q^{43} +(-0.534118 + 0.173545i) q^{45} +(-8.62363 - 4.39396i) q^{46} +(-1.82031 - 2.97047i) q^{47} +(3.46513 - 5.65458i) q^{48} +(-6.20079 - 12.1697i) q^{49} +(5.00000 - 5.00000i) q^{50} +(7.41241 + 1.77956i) q^{54} +(12.8160 + 1.00864i) q^{56} +(-1.14477 + 1.34035i) q^{58} +(-7.20977 + 1.73091i) q^{60} +(1.39642 + 0.221172i) q^{61} +(0.266489 + 1.11001i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(0.727135 - 9.23913i) q^{67} +(2.64883 - 11.0332i) q^{69} +(-9.33454 - 10.9293i) q^{70} +(-0.675611 - 0.219519i) q^{72} +(7.06823 + 4.33142i) q^{75} +(8.83415 - 1.39919i) q^{80} +8.18345i q^{81} +(-8.48528 + 3.16228i) q^{82} -17.7266 q^{83} +(2.35769 + 14.8858i) q^{84} +(17.1841 - 5.58345i) q^{86} +(-1.84126 - 0.938168i) q^{87} +(-8.35664 + 13.6368i) q^{89} +(0.360572 + 0.707663i) q^{90} +(-4.22967 + 13.0176i) q^{92} +(-3.74645 + 3.19977i) q^{94} +(-8.66493 - 3.58913i) q^{96} +(-15.6269 + 11.3536i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 12 q^{3} + 20 q^{6} + 16 q^{7} + 8 q^{8} + 12 q^{9} - 16 q^{12} + 20 q^{15} + 16 q^{16} + 4 q^{18} + 4 q^{21} + 8 q^{24} - 48 q^{27} + 8 q^{28} - 80 q^{30} - 64 q^{32} - 20 q^{35} + 24 q^{36}+ \cdots - 104 q^{98}+O(q^{100}) \) 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

Properties

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