LMFDB - Embedded newform 820.2.cc.a.539.1

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			539.1
Root			$-0.156434 + 0.987688i$ of defining polynomial
Character	$\chi$	$=$	820.539
Dual form			820.2.cc.a.499.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.642040 + 1.26007i) q^{2} +(-0.808747 - 1.95249i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-0.349798 + 2.20854i) q^{5} +(2.97953 + 0.234494i) q^{6} +(-5.11403 + 0.402483i) q^{7} +(2.79360 - 0.442463i) q^{8} +(-1.03682 + 1.03682i) q^{9} +(-2.55834 - 1.85874i) q^{10} +(-2.20845 + 3.60387i) q^{12} +(2.77625 - 6.70246i) q^{14} +(4.59504 - 1.10317i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-0.640788 - 1.97214i) q^{18} +(3.98470 - 2.03031i) q^{20} +(4.92180 + 9.65957i) q^{21} +(4.06728 - 1.32154i) q^{23} +(-3.12322 - 5.09664i) q^{24} +(-4.75528 - 1.54508i) q^{25} +(-2.99457 - 1.24039i) q^{27} +(6.66313 + 7.80152i) q^{28} +(9.17546 + 5.62273i) q^{29} +(-1.56012 + 6.49837i) q^{30} +(-4.00000 - 4.00000i) q^{32} +(0.899978 - 11.4353i) q^{35} +(2.89646 + 0.458754i) q^{36} +6.32456i q^{40} +(-0.731592 - 6.36119i) q^{41} -15.3318 q^{42} +(2.32190 - 4.55699i) q^{43} +(-1.92717 - 2.65253i) q^{45} +(-0.946117 + 5.97355i) q^{46} +(10.2027 + 0.802973i) q^{47} +(8.42737 - 0.663249i) q^{48} +(19.0775 - 3.02157i) q^{49} +(5.00000 - 5.00000i) q^{50} +(3.48561 - 2.97700i) q^{54} +(-14.1085 + 3.38715i) q^{56} +(-12.9761 + 7.95174i) q^{58} +(-7.18677 - 6.13808i) q^{60} +(13.5717 - 6.91514i) q^{61} +(4.88501 - 5.71961i) q^{63} +(7.60845 - 2.47214i) q^{64} +(2.77307 + 11.5507i) q^{67} +(-5.86969 - 6.87252i) q^{69} +(13.8315 + 8.47596i) q^{70} +(-2.43770 + 3.35521i) q^{72} +(0.829061 + 10.5342i) q^{75} +(-7.96940 - 4.06061i) q^{80} +11.2489i q^{81} +(8.48528 + 3.16228i) q^{82} +16.8188 q^{83} +(9.84359 - 19.3191i) q^{84} +(4.25139 + 5.85154i) q^{86} +(3.55769 - 22.4623i) q^{87} +(-9.67595 + 0.761514i) q^{89} +(4.57970 - 0.725353i) q^{90} +(-6.91967 - 5.02743i) q^{92} +(-7.56237 + 12.3407i) q^{94} +(-4.57496 + 11.0449i) q^{96} +(-8.44108 + 25.9790i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.642040	+	1.26007i	−0.453990	+	0.891007i
$2$	−0.642040	+	1.26007i	−0.453990	+	0.891007i
$3$	−0.808747	−	1.95249i	−0.466930	−	1.12727i	−0.965496	−	0.260418i	$-0.916140\pi$
$3$	−0.808747	−	1.95249i	−0.466930	−	1.12727i	0.498566	−	0.866852i	$-0.333860\pi$
$4$	−1.17557	−	1.61803i	−0.587785	−	0.809017i
$5$	−0.349798	+	2.20854i	−0.156434	+	0.987688i
$5$	−0.349798	+	2.20854i	−0.156434	+	0.987688i
$6$	2.97953	+	0.234494i	1.21639	+	0.0957317i
$7$	−5.11403	+	0.402483i	−1.93292	+	0.152124i	−0.985706	−	0.168476i	$-0.946115\pi$
$7$	−5.11403	+	0.402483i	−1.93292	+	0.152124i	−0.947215	+	0.320600i	$0.896115\pi$
$8$	2.79360	−	0.442463i	0.987688	−	0.156434i
$9$	−1.03682	+	1.03682i	−0.345606	+	0.345606i
$10$	−2.55834	−	1.85874i	−0.809017	−	0.587785i
$11$		0			0		−0.972370	−	0.233445i	$-0.925000\pi$
$11$		0			0		0.972370	+	0.233445i	$0.0750000\pi$
$12$	−2.20845	+	3.60387i	−0.637525	+	1.04035i
$13$		0			0		0.760406	−	0.649448i	$-0.225000\pi$
$13$		0			0		−0.760406	+	0.649448i	$0.775000\pi$
$14$	2.77625	−	6.70246i	0.741984	−	1.79131i
$15$	4.59504	−	1.10317i	1.18643	−	0.284838i
$16$	−1.23607	+	3.80423i	−0.309017	+	0.951057i
$17$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$17$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$18$	−0.640788	−	1.97214i	−0.151035	−	0.464839i
$19$		0			0		−0.760406	−	0.649448i	$-0.775000\pi$
$19$		0			0		0.760406	+	0.649448i	$0.225000\pi$
$20$	3.98470	−	2.03031i	0.891007	−	0.453990i
$21$	4.92180	+	9.65957i	1.07402	+	2.10789i
$22$		0			0
$23$	4.06728	−	1.32154i	0.848086	−	0.275560i	0.147442	−	0.989071i	$-0.452896\pi$
$23$	4.06728	−	1.32154i	0.848086	−	0.275560i	0.700644	+	0.713511i	$0.252896\pi$
$24$	−3.12322	−	5.09664i	−0.637525	−	1.04035i
$25$	−4.75528	−	1.54508i	−0.951057	−	0.309017i
$26$		0			0
$27$	−2.99457	−	1.24039i	−0.576305	−	0.238713i
$28$	6.66313	+	7.80152i	1.25921	+	1.47435i
$29$	9.17546	+	5.62273i	1.70384	+	1.04411i	0.873386	+	0.487029i	$0.161919\pi$
$29$	9.17546	+	5.62273i	1.70384	+	1.04411i	0.830455	+	0.557086i	$0.188081\pi$
$30$	−1.56012	+	6.49837i	−0.284838	+	1.18643i
$31$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$31$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$		0			0
$34$		0			0
$35$	0.899978	−	11.4353i	0.152124	−	1.93292i
$36$	2.89646	+	0.458754i	0.482743	+	0.0764590i
$37$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$37$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$38$		0			0
$39$		0			0
$40$			6.32456i			1.00000i
$41$	−0.731592	−	6.36119i	−0.114255	−	0.993451i
$41$	−0.731592	−	6.36119i	−0.114255	−	0.993451i
$42$	−15.3318			−2.36574
$43$	2.32190	−	4.55699i	0.354087	−	0.694935i	−0.643419	−	0.765514i	$-0.722485\pi$
$43$	2.32190	−	4.55699i	0.354087	−	0.694935i	0.997506	+	0.0705793i	$0.0224848\pi$
$44$		0			0
$45$	−1.92717	−	2.65253i	−0.287286	−	0.395415i
$46$	−0.946117	+	5.97355i	−0.139497	+	0.880752i
$47$	10.2027	+	0.802973i	1.48822	+	0.117126i	0.796325	−	0.604869i	$-0.206775\pi$
$47$	10.2027	+	0.802973i	1.48822	+	0.117126i	0.691898	+	0.721995i	$0.256775\pi$
$48$	8.42737	−	0.663249i	1.21639	−	0.0957317i
$49$	19.0775	−	3.02157i	2.72535	−	0.431653i
$50$	5.00000	−	5.00000i	0.707107	−	0.707107i
$51$		0			0
$52$		0			0
$53$		0			0		0.522499	−	0.852640i	$-0.325000\pi$
$53$		0			0		−0.522499	+	0.852640i	$0.675000\pi$
$54$	3.48561	−	2.97700i	0.474332	−	0.405118i
$55$		0			0
$56$	−14.1085	+	3.38715i	−1.88533	+	0.452627i
$57$		0			0
$58$	−12.9761	+	7.95174i	−1.70384	+	1.04411i
$59$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$59$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$60$	−7.18677	−	6.13808i	−0.927808	−	0.792423i
$61$	13.5717	−	6.91514i	1.73768	−	0.885393i	0.768206	−	0.640203i	$-0.221150\pi$
$61$	13.5717	−	6.91514i	1.73768	−	0.885393i	0.969475	−	0.245189i	$-0.0788501\pi$
$62$		0			0
$63$	4.88501	−	5.71961i	0.615453	−	0.720603i
$64$	7.60845	−	2.47214i	0.951057	−	0.309017i
$65$		0			0
$66$		0			0
$67$	2.77307	+	11.5507i	0.338784	+	1.41114i	0.838478	+	0.544936i	$0.183446\pi$
$67$	2.77307	+	11.5507i	0.338784	+	1.41114i	−0.499694	+	0.866202i	$0.666554\pi$
$68$		0			0
$69$	−5.86969	−	6.87252i	−0.706627	−	0.827354i
$70$	13.8315	+	8.47596i	1.65318	+	1.01307i
$71$		0			0		0.233445	−	0.972370i	$-0.425000\pi$
$71$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$72$	−2.43770	+	3.35521i	−0.287286	+	0.395415i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$		0			0
$75$	0.829061	+	10.5342i	0.0957317	+	1.21639i
$76$		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	$0.875000\pi$
$80$	−7.96940	−	4.06061i	−0.891007	−	0.453990i
$81$			11.2489i			1.24987i
$82$	8.48528	+	3.16228i	0.937043	+	0.349215i
$83$	16.8188			1.84610			0.923052	−	0.384676i	$-0.125687\pi$
$83$	16.8188			1.84610			0.923052	+	0.384676i	$0.125687\pi$
$84$	9.84359	−	19.3191i	1.07402	−	2.10789i
$85$		0			0
$86$	4.25139	+	5.85154i	0.458439	+	0.630987i
$87$	3.55769	−	22.4623i	0.381424	−	2.40822i
$88$		0			0
$89$	−9.67595	+	0.761514i	−1.02565	+	0.0807203i	−0.580106	−	0.814541i	$-0.696989\pi$
$89$	−9.67595	+	0.761514i	−1.02565	+	0.0807203i	−0.445542	+	0.895261i	$0.646989\pi$
$90$	4.57970	−	0.725353i	0.482743	−	0.0764590i
$91$		0			0
$92$	−6.91967	−	5.02743i	−0.721425	−	0.524146i
$93$		0			0
$94$	−7.56237	+	12.3407i	−0.779999	+	1.27284i
$95$		0			0
$96$	−4.57496	+	11.0449i	−0.466930	+	1.12727i
$97$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$97$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$98$	−8.44108	+	25.9790i	−0.852678	+	2.62427i
$99$		0			0
$100$	3.09017	+	9.51057i	0.309017	+	0.951057i
$101$	−5.70642	−	4.87374i	−0.567810	−	0.484955i	0.318579	−	0.947896i	$-0.396794\pi$
$101$	−5.70642	−	4.87374i	−0.567810	−	0.484955i	−0.886389	+	0.462941i	$0.846794\pi$
$102$		0			0
$103$	2.41087	+	4.73160i	0.237550	+	0.466218i	0.978748	−	0.205069i	$-0.0657418\pi$
$103$	2.41087	+	4.73160i	0.237550	+	0.466218i	−0.741198	+	0.671287i	$0.765742\pi$
$104$		0			0
$105$	−23.0552	+	7.49108i	−2.24995	+	0.731054i
$106$		0			0
$107$	−15.9771	−	5.19128i	−1.54457	−	0.501860i	−0.591935	−	0.805986i	$-0.701636\pi$
$107$	−15.9771	−	5.19128i	−1.54457	−	0.501860i	−0.952632	+	0.304125i	$0.901636\pi$
$108$	1.51333	+	6.30348i	0.145620	+	0.606553i
$109$	−19.0255	−	7.88063i	−1.82232	−	0.754828i	−0.974446	−	0.224623i	$-0.927885\pi$
$109$	−19.0255	−	7.88063i	−1.82232	−	0.754828i	−0.847869	−	0.530205i	$-0.822115\pi$
$110$		0			0
$111$		0			0
$112$	4.79015	−	19.9524i	0.452627	−	1.88533i
$113$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$113$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$114$		0			0
$115$	1.49594	+	9.44501i	0.139497	+	0.880752i
$116$	−1.68863	−	21.4561i	−0.156786	−	1.99215i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	12.3486	−	5.11497i	1.12727	−	0.466930i
$121$	9.80107	+	4.99390i	0.891007	+	0.453990i
$122$			21.5412i			1.95024i
$123$	−11.8285	+	6.57302i	−1.06654	+	0.592669i
$124$		0			0
$125$	5.07577	−	9.96176i	0.453990	−	0.891007i
$126$	4.07076	+	9.82769i	0.362652	+	0.875520i
$127$	12.7252	+	17.5147i	1.12918	+	1.55418i	0.789621	+	0.613595i	$0.210277\pi$
$127$	12.7252	+	17.5147i	1.12918	+	1.55418i	0.339557	+	0.940585i	$0.389723\pi$
$128$	−1.76985	+	11.1744i	−0.156434	+	0.987688i
$129$	−10.7753	−	0.848035i	−0.948712	−	0.0746653i
$130$		0			0
$131$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$131$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$132$		0			0
$133$		0			0
$134$	−16.3351	−	3.92171i	−1.41114	−	0.338784i
$135$	3.78694	−	6.17973i	0.325928	−	0.531867i
$136$		0			0
$137$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$137$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$138$	12.4285	−	2.98381i	1.05798	−	0.253999i
$139$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$139$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$140$	−19.5607	+	11.9868i	−1.65318	+	1.01307i
$141$	−6.68364	−	20.5701i	−0.562864	−	1.73232i
$142$		0			0
$143$		0			0
$144$	−2.66271	−	5.22586i	−0.221893	−	0.435489i
$145$	−15.6276	+	18.2975i	−1.29780	+	1.51953i
$146$		0			0
$147$	−21.3284	−	34.8048i	−1.75914	−	2.87065i
$148$		0			0
$149$	1.17953	+	4.91308i	0.0966306	+	0.402495i	0.999632	−	0.0271432i	$-0.00864100\pi$
$149$	1.17953	+	4.91308i	0.0966306	+	0.402495i	−0.903001	+	0.429638i	$0.858641\pi$
$150$	−13.8062	−	5.71870i	−1.12727	−	0.466930i
$151$		0			0		−0.649448	−	0.760406i	$-0.725000\pi$
$151$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.0784591	−	0.996917i	$-0.525000\pi$
$157$		0			0		0.0784591	+	0.996917i	$0.475000\pi$
$158$		0			0
$159$		0			0
$160$	10.2333	−	7.43496i	0.809017	−	0.587785i
$161$	−20.2683	+	8.39539i	−1.59736	+	0.661650i
$162$	−14.1744	−	7.22221i	−1.11365	−	0.567431i
$163$			6.65248i			0.521062i	0.965465	+	0.260531i	$0.0838976\pi$
$163$			6.65248i			0.521062i	−0.965465	+	0.260531i	$0.916102\pi$
$164$	−9.43259	+	8.66177i	−0.736561	+	0.676371i
$165$		0			0
$166$	−10.7983	+	21.1929i	−0.838113	+	1.64489i
$167$	8.88713	+	21.4554i	0.687707	+	1.66027i	0.749351	+	0.662173i	$0.230366\pi$
$167$	8.88713	+	21.4554i	0.687707	+	1.66027i	−0.0616444	+	0.998098i	$0.519634\pi$
$168$	18.0236	+	24.8073i	1.39055	+	1.91392i
$169$	2.03365	−	12.8399i	0.156434	−	0.987688i
$170$		0			0
$171$		0			0
$172$	−10.1029	+	1.60015i	−0.770341	+	0.122010i
$173$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$173$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$174$	26.0200	+	18.9047i	1.97257	+	1.43316i
$175$	24.9405	+	5.98769i	1.88533	+	0.452627i
$176$		0			0
$177$		0			0
$178$	5.25278	−	12.6813i	0.393712	−	0.950506i
$179$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$179$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$180$	−2.02635	+	6.23647i	−0.151035	+	0.464839i
$181$	16.1553	−	9.89995i	1.20081	−	0.735858i	0.229416	−	0.973328i	$-0.426318\pi$
$181$	16.1553	−	9.89995i	1.20081	−	0.735858i	0.971395	+	0.237471i	$0.0763184\pi$
$182$		0			0
$183$	−24.4778	−	20.9060i	−1.80945	−	1.54542i
$184$	10.7776	−	5.49148i	0.794538	−	0.404837i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−10.6948	−	17.4523i	−0.779999	−	1.27284i
$189$	15.8135	+	5.13813i	1.15027	+	0.373744i
$190$		0			0
$191$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$191$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$192$	−10.9801	−	12.8561i	−0.792423	−	0.927808i
$193$		0			0		−0.852640	−	0.522499i	$-0.825000\pi$
$193$		0			0		0.852640	+	0.522499i	$0.175000\pi$
$194$		0			0
$195$		0			0
$196$	−27.3159	−	27.3159i	−1.95114	−	1.95114i
$197$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$197$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$198$		0			0
$199$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$199$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$200$	−13.9680	−	2.21232i	−0.987688	−	0.156434i
$201$	20.3098	−	14.7559i	1.43254	−	1.04080i
$202$	9.80502	−	4.06137i	0.689879	−	0.285757i
$203$	−49.1866	−	25.0618i	−3.45222	−	1.75900i
$204$		0			0
$205$	14.3048	+	0.609385i	0.999094	+	0.0425613i
$206$	−7.51004			−0.523249
$207$	−2.84683	+	5.58722i	−0.197868	+	0.388339i
$208$		0			0
$209$		0			0
$210$	5.36302	−	33.8608i	0.370083	−	2.33661i
$211$		0			0		−0.996917	−	0.0784591i	$-0.975000\pi$
$211$		0			0		0.996917	+	0.0784591i	$0.0250000\pi$
$212$		0			0
$213$		0			0
$214$	16.7993	−	16.7993i	1.14838	−	1.14838i
$215$	9.25209	+	6.72204i	0.630987	+	0.458439i
$216$	−8.91447	−	2.14017i	−0.606553	−	0.145620i
$217$		0			0
$218$	22.1453	−	18.9139i	1.49987	−	1.28101i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−6.85024	−	21.0829i	−0.458726	−	1.41181i	−0.866705	−	0.498822i	$-0.833766\pi$
$223$	−6.85024	−	21.0829i	−0.458726	−	1.41181i	0.407979	−	0.912991i	$-0.366234\pi$
$224$	22.0660	+	18.8462i	1.47435	+	1.25921i
$225$	6.53233	−	3.32839i	0.435489	−	0.221893i
$226$		0			0
$227$	12.4006	−	14.5193i	0.823058	−	0.963677i	−0.176730	−	0.984259i	$-0.556552\pi$
$227$	12.4006	−	14.5193i	0.823058	−	0.963677i	0.999788	+	0.0205821i	$0.00655195\pi$
$228$		0			0
$229$	−8.39244	−	13.6952i	−0.554588	−	0.905005i	−0.999953	−	0.00965614i	$-0.996926\pi$
$229$	−8.39244	−	13.6952i	−0.554588	−	0.905005i	0.445366	−	0.895349i	$-0.353074\pi$
$230$	−12.8619	−	4.17907i	−0.848086	−	0.275560i
$231$		0			0
$232$	28.1205	+	11.6479i	1.84620	+	0.764721i
$233$		0			0		−0.649448	−	0.760406i	$-0.725000\pi$
$233$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$234$		0			0
$235$	−5.34230	+	22.2523i	−0.348493	+	1.45158i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.0784591	−	0.996917i	$-0.525000\pi$
$239$		0			0		0.0784591	+	0.996917i	$0.475000\pi$
$240$	−1.48307	+	18.8442i	−0.0957317	+	1.21639i
$241$	−8.76185	−	1.38774i	−0.564400	−	0.0893922i	−0.132287	−	0.991211i	$-0.542232\pi$
$241$	−8.76185	−	1.38774i	−0.564400	−	0.0893922i	−0.432113	+	0.901819i	$0.642232\pi$
$242$	−12.5854	+	9.14379i	−0.809017	+	0.587785i
$243$	12.9796	−	5.37631i	0.832640	−	0.344891i
$244$	−27.1434	−	13.8303i	−1.73768	−	0.885393i
$245$			43.1902i			2.75932i
$246$	−0.688137	−	19.1249i	−0.0438740	−	1.21936i
$247$		0			0
$248$		0			0
$249$	−13.6022	−	32.8385i	−0.862002	−	2.08106i
$250$	9.29370	+	12.7917i	0.587785	+	0.809017i
$251$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$251$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$252$	−14.9972	−	1.18031i	−0.944735	−	0.0743522i
$253$		0			0
$254$	−30.2399	+	4.78953i	−1.89742	+	0.300522i
$255$		0			0
$256$	−12.9443	−	9.40456i	−0.809017	−	0.587785i
$257$		0			0		−0.972370	−	0.233445i	$-0.925000\pi$
$257$		0			0		0.972370	+	0.233445i	$0.0750000\pi$
$258$	7.98676	−	13.0332i	0.497234	−	0.811412i
$259$		0			0
$260$		0			0
$261$	−15.3430	+	3.68353i	−0.949709	+	0.228005i
$262$		0			0
$263$	−1.36985	+	0.839447i	−0.0844688	+	0.0517625i	−0.564092	−	0.825712i	$-0.690774\pi$
$263$	−1.36985	+	0.839447i	−0.0844688	+	0.0517625i	0.479623	+	0.877475i	$0.340774\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	9.31224	+	18.2763i	0.569900	+	1.11849i
$268$	15.4294	−	18.0655i	0.942502	−	1.10353i
$269$	15.1366	−	4.91817i	0.922893	−	0.299866i	0.191240	−	0.981543i	$-0.438749\pi$
$269$	15.1366	−	4.91817i	0.922893	−	0.299866i	0.731653	+	0.681677i	$0.238749\pi$
$270$	5.35555	+	8.73946i	0.325928	+	0.531867i
$271$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$271$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−4.21974	+	17.5765i	−0.253999	+	1.05798i
$277$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$277$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$278$		0			0
$279$		0			0
$280$	−2.54552	−	32.3439i	−0.152124	−	1.93292i
$281$	−2.16850	+	27.5534i	−0.129362	+	1.64370i	0.499594	+	0.866260i	$0.333483\pi$
$281$	−2.16850	+	27.5534i	−0.129362	+	1.64370i	−0.628956	+	0.777441i	$0.716517\pi$
$282$	30.2111	+	4.78496i	1.79904	+	0.284940i
$283$	25.7318	−	18.6953i	1.52960	−	1.11132i	0.573137	−	0.819459i	$-0.305726\pi$
$283$	25.7318	−	18.6953i	1.52960	−	1.11132i	0.956461	−	0.291859i	$-0.0942738\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.30165	+	32.2369i	0.371975	+	1.90288i
$288$	8.29454			0.488760
$289$	7.71784	−	15.1471i	0.453990	−	0.891007i
$290$	−13.0227	−	31.4396i	−0.764721	−	1.84620i
$291$		0			0
$292$		0			0
$293$		0			0		−0.996917	−	0.0784591i	$-0.975000\pi$
$293$		0			0		0.996917	+	0.0784591i	$0.0250000\pi$
$294$	57.5503	−	4.52931i	3.35640	−	0.264155i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−6.94815	−	1.66810i	−0.402495	−	0.0966306i
$299$		0			0
$300$	16.0701	−	13.7252i	0.927808	−	0.792423i
$301$	−10.0402	+	24.2391i	−0.578705	+	1.39712i
$302$		0			0
$303$	−4.90087	+	15.0833i	−0.281548	+	0.866515i
$304$		0			0
$305$	10.5250	+	32.3926i	0.602659	+	1.85479i
$306$		0			0
$307$	−1.11480	+	0.568021i	−0.0636253	+	0.0324187i	−0.485514	−	0.874229i	$-0.661367\pi$
$307$	−1.11480	+	0.568021i	−0.0636253	+	0.0324187i	0.421888	+	0.906648i	$0.361367\pi$
$308$		0			0
$309$	7.28861	−	8.53386i	0.414634	−	0.485474i
$310$		0			0
$311$		0			0		−0.522499	−	0.852640i	$-0.675000\pi$
$311$		0			0		0.522499	+	0.852640i	$0.325000\pi$
$312$		0			0
$313$		0			0		−0.233445	−	0.972370i	$-0.575000\pi$
$313$		0			0		0.233445	+	0.972370i	$0.425000\pi$
$314$		0			0
$315$	10.9232	+	12.7894i	0.615453	+	0.720603i
$316$		0			0
$317$		0			0		0.233445	−	0.972370i	$-0.425000\pi$
$317$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$318$		0			0
$319$		0			0
$320$	2.79838	+	17.6683i	0.156434	+	0.987688i
$321$	2.78554	+	35.3936i	0.155473	+	1.97548i
$322$	2.43422	−	30.9297i	0.135654	−	1.72364i
$323$		0			0
$324$	18.2010	−	13.2238i	1.01117	−	0.734657i
$325$		0			0
$326$	−8.38261	−	4.27115i	−0.464270	−	0.236557i
$327$			43.5206i			2.40669i
$328$	−4.85837	−	17.4470i	−0.268259	−	0.963347i
$329$	−52.5003			−2.89443
$330$		0			0
$331$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$331$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$332$	−19.7717	−	27.2134i	−1.08511	−	1.49353i
$333$		0			0
$334$	−32.7413	−	2.57680i	−1.79152	−	0.140996i
$335$	−26.4801	+	2.08403i	−1.44676	+	0.113863i
$336$	−42.8309	+	6.78374i	−2.33661	+	0.370083i
$337$		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
$343$	−61.4298	+	14.7480i	−3.31690	+	0.796316i
$344$	4.47018	−	13.7578i	0.241016	−	0.741770i
$345$	17.2314	−	10.5594i	0.927709	−	0.568501i
$346$		0			0
$347$	−4.58353	−	3.91471i	−0.246057	−	0.210152i	0.517863	−	0.855464i	$-0.326728\pi$
$347$	−4.58353	−	3.91471i	−0.246057	−	0.210152i	−0.763920	+	0.645311i	$0.776728\pi$
$348$	−40.5272	+	20.6496i	−2.17248	+	1.10694i
$349$	13.8784	+	27.2379i	0.742893	+	1.45801i	0.883740	+	0.467978i	$0.155017\pi$
$349$	13.8784	+	27.2379i	0.742893	+	1.45801i	−0.140848	+	0.990031i	$0.544983\pi$
$350$	−23.5577	+	27.5825i	−1.25921	+	1.47435i
$351$		0			0
$352$		0			0
$353$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$353$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$354$		0			0
$355$		0			0
$356$	12.6069	+	14.7608i	0.668165	+	0.782321i
$357$		0			0
$358$		0			0
$359$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$359$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$360$	−6.55741	−	6.55741i	−0.345606	−	0.345606i
$361$	2.97225	+	18.7661i	0.156434	+	0.987688i
$362$	2.10236	+	26.7130i	0.110497	+	1.40400i
$363$	1.82393	−	23.1753i	0.0957317	−	1.21639i
$364$		0			0
$365$		0			0
$366$	42.0589	−	17.4213i	2.19845	−	0.910628i
$367$	31.4861	+	16.0430i	1.64356	+	0.837437i	0.997230	+	0.0743821i	$0.0236984\pi$
$367$	31.4861	+	16.0430i	1.64356	+	0.837437i	0.646333	+	0.763055i	$0.276302\pi$
$368$			17.1064i			0.891731i
$369$	7.35392	+	5.83687i	0.382830	+	0.303855i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$373$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$374$		0			0
$375$	−23.5552	−	1.85384i	−1.21639	−	0.0957317i
$376$	28.8577	−	2.27115i	1.48822	−	0.117126i
$377$		0			0
$378$	−16.6273	+	16.6273i	−0.855218	+	0.855218i
$379$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$379$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$380$		0			0
$381$	23.9058	−	39.0108i	1.22473	−	1.99858i
$382$		0			0
$383$	0.745673	−	1.80021i	0.0381021	−	0.0919866i	−0.903683	−	0.428202i	$-0.859147\pi$
$383$	0.745673	−	1.80021i	0.0381021	−	0.0919866i	0.941785	+	0.336216i	$0.109147\pi$
$384$	23.2493	−	5.58166i	1.18643	−	0.284838i
$385$		0			0
$386$		0			0
$387$	2.31738	+	7.13216i	0.117799	+	0.362548i
$388$		0			0
$389$	35.1351	−	17.9022i	1.78142	−	0.907680i	0.879020	−	0.476785i	$-0.158198\pi$
$389$	35.1351	−	17.9022i	1.78142	−	0.907680i	0.902402	−	0.430895i	$-0.141802\pi$
$390$		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		−0.649448	−	0.760406i	$-0.725000\pi$
$397$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$398$		0			0
$399$		0			0
$400$	11.7557	−	16.1803i	0.587785	−	0.809017i
$401$	−16.5287	−	16.5287i	−0.825406	−	0.825406i	0.161472	−	0.986877i	$-0.448376\pi$
$401$	−16.5287	−	16.5287i	−0.825406	−	0.825406i	−0.986877	+	0.161472i	$0.948376\pi$
$402$	5.55387	+	35.0658i	0.277002	+	1.74892i
$403$		0			0
$404$	−1.17758	+	14.9626i	−0.0585869	+	0.744417i
$405$	−24.8435	−	3.93483i	−1.23449	−	0.195523i
$406$	63.1595	−	45.8881i	3.13455	−	2.27739i
$407$		0			0
$408$		0			0
$409$			34.0464i			1.68348i	0.539880	+	0.841742i	$0.318470\pi$
$409$			34.0464i			1.68348i	−0.539880	+	0.841742i	$0.681530\pi$
$410$	−9.95215	+	17.6339i	−0.491501	+	0.870877i
$411$		0			0
$412$	4.82174	−	9.46320i	0.237550	−	0.466218i
$413$		0			0
$414$	−5.21253	−	7.17443i	−0.256182	−	0.352604i
$415$	−5.88318	+	37.1450i	−0.288794	+	1.82337i
$416$		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	$0.750000\pi$
$420$	39.2238	+	28.4977i	1.91392	+	1.39055i
$421$	39.8717	+	9.57236i	1.94323	+	0.466528i	0.980814	+	0.194948i	$0.0624538\pi$
$421$	39.8717	+	9.57236i	1.94323	+	0.466528i	0.962416	+	0.271580i	$0.0875462\pi$
$422$		0			0
$423$	−11.4109	+	9.74585i	−0.554818	+	0.473859i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−66.6229	+	40.8266i	−3.22411	+	1.97574i
$428$	10.3826	+	31.9543i	0.501860	+	1.54457i
$429$		0			0
$430$	−14.4105	+	7.34250i	−0.694935	+	0.354087i
$431$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$431$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$432$	8.42022	−	9.85881i	0.405118	−	0.474332i
$433$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$433$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$434$		0			0
$435$	48.3645	+	15.7146i	2.31890	+	0.753456i
$436$	9.61472	+	40.0482i	0.460462	+	1.91796i
$437$		0			0
$438$		0			0
$439$		0			0		−0.852640	−	0.522499i	$-0.825000\pi$
$439$		0			0		0.852640	+	0.522499i	$0.175000\pi$
$440$		0			0
$441$	−16.6470	+	22.9127i	−0.792715	+	1.09108i
$442$		0			0
$443$	−6.56889	−	41.4743i	−0.312097	−	1.97051i	−0.225367	−	0.974274i	$-0.572358\pi$
$443$	−6.56889	−	41.4743i	−0.312097	−	1.97051i	−0.0867309	−	0.996232i	$-0.527642\pi$
$444$		0			0
$445$	1.70280	−	21.6361i	0.0807203	−	1.02565i
$446$	30.9641	+	4.90423i	1.46619	+	0.232222i
$447$	8.63879	−	6.27645i	0.408601	−	0.296866i
$448$	−37.9148	+	15.7048i	−1.79131	+	0.741984i
$449$	37.6610	+	19.1892i	1.77733	+	0.905595i	0.921554	+	0.388250i	$0.126920\pi$
$449$	37.6610	+	19.1892i	1.77733	+	0.905595i	0.855777	+	0.517345i	$0.173080\pi$
$450$			10.3682i			0.488760i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	10.3336	+	24.9476i	0.484982	+	1.17085i
$455$		0			0
$456$		0			0
$457$		0			0		−0.996917	−	0.0784591i	$-0.975000\pi$
$457$		0			0		0.996917	+	0.0784591i	$0.0250000\pi$
$458$	22.6452	−	1.78222i	1.05814	−	0.0832776i
$459$		0			0
$460$	13.5238	−	13.5238i	0.630549	−	0.630549i
$461$	−25.8263	−	18.7639i	−1.20285	−	0.873922i	−0.208288	−	0.978068i	$-0.566789\pi$
$461$	−25.8263	−	18.7639i	−1.20285	−	0.873922i	−0.994562	+	0.104146i	$0.966789\pi$
$462$		0			0
$463$	−19.0069	+	31.0164i	−0.883326	+	1.44146i	0.0139095	+	0.999903i	$0.495572\pi$
$463$	−19.0069	+	31.0164i	−0.883326	+	1.44146i	−0.897235	+	0.441553i	$0.854428\pi$
$464$	−32.7316	+	27.9555i	−1.51953	+	1.29780i
$465$		0			0
$466$		0			0
$467$	12.9486	−	39.8516i	0.599189	−	1.84411i	0.0665285	−	0.997785i	$-0.478808\pi$
$467$	12.9486	−	39.8516i	0.599189	−	1.84411i	0.532660	−	0.846329i	$-0.321192\pi$
$468$		0			0
$469$	−18.8305	−	57.9543i	−0.869511	−	2.67608i
$470$	−24.6095	−	21.0185i	−1.13515	−	0.969512i
$471$		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		−0.649448	−	0.760406i	$-0.725000\pi$
$479$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$480$	−22.7929	−	13.9675i	−1.04035	−	0.637525i
$481$		0			0
$482$	7.37411	−	10.1496i	0.335881	−	0.462301i
$483$	32.7838	+	32.7838i	1.49172	+	1.49172i
$484$	−3.44156	−	21.7291i	−0.156434	−	0.987688i
$485$		0			0
$486$	−1.55885	+	19.8070i	−0.0707107	+	0.898464i
$487$	43.5289	+	6.89430i	1.97248	+	0.312411i	0.994706	+	0.102762i	$0.0327679\pi$
$487$	43.5289	+	6.89430i	1.97248	+	0.312411i	0.977777	+	0.209649i	$0.0672321\pi$
$488$	34.8543	−	25.3231i	1.57778	−	1.14633i
$489$	12.9889	−	5.38017i	0.587377	−	0.243300i
$490$	−54.4229	−	27.7298i	−2.45857	−	1.25271i
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$	24.5406	+	11.4118i	1.10637	+	0.514485i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	50.1121	+	3.94390i	2.24557	+	0.176731i
$499$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$499$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$500$	−22.0854	+	3.49798i	−0.987688	+	0.156434i
$501$	34.7040	−	34.7040i	1.55046	−	1.55046i
$502$		0			0
$503$	−31.5276	−	7.56910i	−1.40574	−	0.337489i	−0.541559	−	0.840663i	$-0.682166\pi$
$503$	−31.5276	−	7.56910i	−1.40574	−	0.337489i	−0.864185	+	0.503174i	$0.832166\pi$
$504$	11.1161	−	18.1398i	0.495149	−	0.808010i
$505$	12.7599	−	10.8980i	0.567810	−	0.484955i
$506$		0			0
$507$	−26.7146	+	6.41360i	−1.18643	+	0.284838i
$508$	13.3801	−	41.1796i	0.593644	−	1.82705i
$509$	37.1864	−	22.7879i	1.64826	−	1.01005i	0.690143	−	0.723673i	$-0.257548\pi$
$509$	37.1864	−	22.7879i	1.64826	−	1.01005i	0.958116	−	0.286381i	$-0.0924523\pi$
$510$		0			0
$511$		0			0
$512$	20.1612	−	10.2726i	0.891007	−	0.453990i
$513$		0			0
$514$		0			0
$515$	−11.2932	+	3.66939i	−0.497639	+	0.161693i
$516$	11.2950	+	18.4317i	0.497234	+	0.811412i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.47118	−	3.96554i	−0.283507	−	0.173734i	0.373473	−	0.927641i	$-0.378167\pi$
$521$	−6.47118	−	3.96554i	−0.283507	−	0.173734i	−0.656981	+	0.753907i	$0.728167\pi$
$522$	5.20930	−	21.6983i	0.228005	−	0.949709i
$523$	−26.8011	+	36.8885i	−1.17193	+	1.61302i	−0.522346	+	0.852734i	$0.674943\pi$
$523$	−26.8011	+	36.8885i	−1.17193	+	1.61302i	−0.649584	+	0.760290i	$0.725057\pi$
$524$		0			0
$525$	−8.47968	−	53.5386i	−0.370083	−	2.33661i
$526$	−0.178265	−	2.26507i	−0.00777273	−	0.0987619i
$527$		0			0
$528$		0			0
$529$	−3.81110	+	2.76893i	−0.165700	+	0.120388i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−29.0083			−1.25531
$535$	17.0539	−	33.4702i	0.737305	−	1.44704i
$536$	12.8576	+	31.0410i	0.555364	+	1.34077i
$537$		0			0
$538$	−3.52102	+	22.2308i	−0.151802	+	0.958440i
$539$		0			0
$540$	−14.4508	+	1.13731i	−0.621865	+	0.0489418i
$541$	−0.619908	+	0.0981838i	−0.0266519	+	0.00422125i	−0.169746	−	0.985488i	$-0.554295\pi$
$541$	−0.619908	+	0.0981838i	−0.0266519	+	0.00422125i	0.143094	+	0.989709i	$0.454295\pi$
$542$		0			0
$543$	−32.3951	−	23.5364i	−1.39020	−	1.01004i
$544$		0			0
$545$	24.0598	−	39.2620i	1.03061	−	1.68180i
$546$		0			0
$547$	17.7095	−	42.7544i	0.757202	−	1.82805i	0.244014	−	0.969772i	$-0.421536\pi$
$547$	17.7095	−	42.7544i	0.757202	−	1.82805i	0.513188	−	0.858276i	$-0.328464\pi$
$548$		0			0
$549$	−6.90166	+	21.2411i	−0.294556	+	0.906549i
$550$		0			0
$551$		0			0
$552$	−19.4384	−	16.6020i	−0.827354	−	0.706627i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.522499	−	0.852640i	$-0.675000\pi$
$557$		0			0		0.522499	+	0.852640i	$0.325000\pi$
$558$		0			0
$559$		0			0
$560$	42.3901	+	17.5585i	1.79131	+	0.741984i
$561$		0			0
$562$	−33.3271	−	20.4229i	−1.40582	−	0.861487i
$563$	8.20578	−	34.1795i	0.345833	−	1.44050i	−0.480342	−	0.877081i	$-0.659487\pi$
$563$	8.20578	−	34.1795i	0.345833	−	1.44050i	0.826174	−	0.563415i	$-0.190513\pi$
$564$	−25.4261	+	34.9960i	−1.07063	+	1.47360i
$565$		0			0
$566$	7.03656	+	44.4271i	0.295769	+	1.86741i
$567$	−4.52747	−	57.5270i	−0.190136	−	2.41591i
$568$		0			0
$569$	−18.4186	−	2.91722i	−0.772147	−	0.122296i	−0.242085	−	0.970255i	$-0.577831\pi$
$569$	−18.4186	−	2.91722i	−0.772147	−	0.122296i	−0.530062	+	0.847959i	$0.677831\pi$
$570$		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
$574$	−44.6667	−	12.7568i	−1.86435	−	0.532458i
$575$	−21.3829			−0.891731
$576$	−5.32542	+	10.4517i	−0.221893	+	0.435489i
$577$		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
$580$	47.9774	+	3.77590i	1.99215	+	0.156786i
$581$	−86.0118	+	6.76928i	−3.56837	+	0.280837i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	33.3153	−	28.4540i	1.37507	−	1.17442i	0.410108	−	0.912037i	$-0.365491\pi$
$587$	33.3153	−	28.4540i	1.37507	−	1.17442i	0.964963	−	0.262384i	$-0.0845089\pi$
$588$	−31.2423	+	75.4256i	−1.28841	+	3.11050i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.760406	−	0.649448i	$-0.775000\pi$
$593$		0			0		0.760406	+	0.649448i	$0.225000\pi$
$594$		0			0
$595$		0			0
$596$	6.56292	−	7.68419i	0.268828	−	0.314757i
$597$		0			0
$598$		0			0
$599$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$599$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$600$	6.97707	+	29.0616i	0.284838	+	1.18643i
$601$	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	$0.556528\pi$
$602$	−24.0969	−	28.2138i	−0.982115	−	1.14991i
$603$	−14.8511	−	9.10076i	−0.604783	−	0.370612i
$604$		0			0
$605$	−14.4576	+	19.8992i	−0.587785	+	0.809017i
$606$	−15.8596	−	15.8596i	−0.644251	−	0.644251i
$607$	1.11057	+	7.01185i	0.0450766	+	0.284602i	0.999922	−	0.0125012i	$-0.00397937\pi$
$607$	1.11057	+	7.01185i	0.0450766	+	0.284602i	−0.954845	+	0.297103i	$0.903979\pi$
$608$		0			0
$609$	−9.15340	+	116.305i	−0.370914	+	4.71291i
$610$	−47.5745	−	7.53506i	−1.92623	−	0.305085i
$611$		0			0
$612$		0			0
$613$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$613$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$614$		−	1.76943i		−	0.0714083i
$615$	−10.3792	−	28.4229i	−0.418529	−	1.14612i
$616$		0			0
$617$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$617$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$618$	6.07372	+	14.6633i	0.244321	+	0.589843i
$619$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$619$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$620$		0			0
$621$	−13.8190	−	1.08758i	−0.554536	−	0.0436429i
$622$		0			0
$623$	49.1766	−	7.78880i	1.97022	−	0.312052i
$624$		0			0
$625$	20.2254	+	14.6946i	0.809017	+	0.587785i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−23.1288	+	5.55273i	−0.921472	+	0.221226i
$631$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$631$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−43.1332	+	21.9775i	−1.71169	+	0.872149i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−24.0600	−	7.81758i	−0.951057	−	0.309017i
$641$	−3.69373	−	15.3855i	−0.145894	−	0.607691i	−0.996625	−	0.0820899i	$-0.973841\pi$
$641$	−3.69373	−	15.3855i	−0.145894	−	0.607691i	0.850731	−	0.525601i	$-0.176159\pi$
$642$	−46.3869	−	19.2141i	−1.83075	−	0.758320i
$643$	−32.8281	−	38.4367i	−1.29461	−	1.51580i	−0.709015	−	0.705193i	$-0.750860\pi$
$643$	−32.8281	−	38.4367i	−1.29461	−	1.51580i	−0.585597	−	0.810602i	$-0.699140\pi$
$644$	37.4108	+	22.9254i	1.47419	+	0.903386i
$645$	5.64210	−	23.5010i	0.222157	−	0.925352i
$646$		0			0
$647$	30.2321	+	30.2321i	1.18855	+	1.18855i	0.977469	+	0.211079i	$0.0676977\pi$
$647$	30.2321	+	30.2321i	1.18855	+	1.18855i	0.211079	+	0.977469i	$0.432302\pi$
$648$	4.97721	+	31.4249i	0.195523	+	1.23449i
$649$		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	$0.875000\pi$
$654$	−54.8391	−	27.9419i	−2.14438	−	1.09262i
$655$		0			0
$656$	25.1037	+	5.07973i	0.980135	+	0.198330i
$657$		0			0
$658$	33.7073	−	66.1542i	1.31405	−	2.57896i
$659$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$659$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$660$		0			0
$661$	−7.75077	+	48.9364i	−0.301470	+	1.90341i	0.113440	+	0.993545i	$0.463813\pi$
$661$	−7.75077	+	48.9364i	−0.301470	+	1.90341i	−0.414910	+	0.909862i	$0.636187\pi$
$662$		0			0
$663$		0			0
$664$	46.9851	−	7.44171i	1.82337	−	0.288794i
$665$		0			0
$666$		0			0
$667$	44.7498	+	10.7435i	1.73272	+	0.415989i
$668$	24.2682	−	39.6020i	0.938964	−	1.53225i
$669$	−35.6239	+	30.4257i	−1.37730	+	1.17633i
$670$	14.3752	−	34.7049i	0.555364	−	1.34077i
$671$		0			0
$672$	18.9511	−	58.3255i	0.731054	−	2.24995i
$673$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$673$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$674$		0			0
$675$	12.3235	+	10.5253i	0.474332	+	0.405118i
$676$	−23.1662	+	11.8038i	−0.891007	+	0.453990i
$677$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$677$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−38.3777	−	12.4697i	−1.47063	−	0.477838i
$682$		0			0
$683$	42.4416	+	17.5799i	1.62398	+	0.672676i	0.994539	−	0.104370i	$-0.0332826\pi$
$683$	42.4416	+	17.5799i	1.62398	+	0.672676i	0.629444	+	0.777046i	$0.283283\pi$
$684$		0			0
$685$		0			0
$686$	20.8568	−	86.8748i	0.796316	−	3.31690i
$687$	−19.9524	+	27.4621i	−0.761231	+	1.04774i
$688$	14.4658	+	14.4658i	0.551503	+	0.551503i
$689$		0			0
$690$	2.24240	+	28.4924i	0.0853669	+	1.08469i
$691$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$691$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$692$		0			0
$693$		0			0
$694$	7.87563	−	3.26219i	0.298955	−	0.123831i
$695$		0			0
$696$		−	64.3251i		−	2.43824i
$697$		0			0
$698$	−43.2322			−1.63636
$699$		0			0
$700$	−19.6310	−	47.3935i	−0.741984	−	1.79131i
$701$	−10.6564	−	14.6673i	−0.402486	−	0.553975i	0.558879	−	0.829249i	$-0.311231\pi$
$701$	−10.6564	−	14.6673i	−0.402486	−	0.553975i	−0.961366	+	0.275274i	$0.911231\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	47.7679	−	7.56569i	1.79904	−	0.284940i
$706$		0			0
$707$	31.1444	+	22.6277i	1.17130	+	0.851003i
$708$		0			0
$709$	−16.8401	+	27.4806i	−0.632444	+	1.03205i	0.362535	+	0.931970i	$0.381911\pi$
$709$	−16.8401	+	27.4806i	−0.632444	+	1.03205i	−0.994979	+	0.100085i	$0.968089\pi$
$710$		0			0
$711$		0			0
$712$	−26.6938	+	6.40862i	−1.00039	+	0.240173i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.649448	−	0.760406i	$-0.275000\pi$
$719$		0			0		−0.649448	+	0.760406i	$0.725000\pi$
$720$	12.4729	−	4.05270i	0.464839	−	0.151035i
$721$	−14.2336	−	23.2272i	−0.530088	−	0.865026i
$722$	−25.5549	−	8.30330i	−0.951057	−	0.309017i
$723$	4.37657	+	18.2297i	0.162766	+	0.677971i
$724$	−35.0101	−	14.5017i	−1.30114	−	0.538950i
$725$	−34.9443	−	40.9145i	−1.29780	−	1.51953i
$726$	28.0315	+	17.1777i	1.04035	+	0.637525i
$727$	12.4342	−	51.7921i	0.461158	−	1.92086i	0.0786754	−	0.996900i	$-0.474931\pi$
$727$	12.4342	−	51.7921i	0.461158	−	1.92086i	0.382483	−	0.923963i	$-0.375069\pi$
$728$		0			0
$729$	2.86807	+	2.86807i	0.106225	+	0.106225i
$730$		0			0
$731$		0			0
$732$	−5.05127	+	64.1824i	−0.186700	+	2.37225i
$733$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$733$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$734$	−40.4307	+	29.3746i	−1.49232	+	1.08424i
$735$	84.3284	−	34.9300i	3.11050	−	1.28841i
$736$	−21.5553	−	10.9830i	−0.794538	−	0.404837i
$737$		0			0
$738$	−12.0764	+	5.51898i	−0.444538	+	0.203157i
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	2.99086	−	18.8835i	0.109724	−	0.692769i	−0.870095	−	0.492883i	$-0.835943\pi$
$743$	2.99086	−	18.8835i	0.109724	−	0.692769i	0.979819	−	0.199886i	$-0.0640571\pi$
$744$		0			0
$745$	−11.2633	+	0.886443i	−0.412656	+	0.0324768i
$746$		0			0
$747$	−17.4380	+	17.4380i	−0.638024	+	0.638024i
$748$		0			0
$749$	83.7968	+	20.1178i	3.06187	+	0.735090i
$750$	17.4594	−	28.4911i	0.637525	−	1.04035i
$751$		0			0		0.760406	−	0.649448i	$-0.225000\pi$
$751$		0			0		−0.760406	+	0.649448i	$0.775000\pi$
$752$	−15.6660	+	37.8210i	−0.571279	+	1.37919i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−10.2763	−	31.6271i	−0.373744	−	1.15027i
$757$		0			0		−0.760406	−	0.649448i	$-0.775000\pi$
$757$		0			0		0.760406	+	0.649448i	$0.225000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−48.4518	+	15.7429i	−1.75638	+	0.570681i	−0.996815	−	0.0797547i	$-0.974586\pi$
$761$	−48.4518	+	15.7429i	−1.75638	+	0.570681i	−0.759561	+	0.650436i	$0.774586\pi$
$762$	33.8079	+	55.1696i	1.22473	+	1.99858i
$763$	100.469	+	32.6443i	3.63722	+	1.18180i
$764$		0			0
$765$		0			0
$766$	1.78965	+	2.09541i	0.0646627	+	0.0757103i
$767$		0			0
$768$	−7.89366	+	32.8794i	−0.284838	+	1.18643i
$769$	3.19313	−	4.39497i	0.115147	−	0.158487i	−0.747553	−	0.664202i	$-0.768771\pi$
$769$	3.19313	−	4.39497i	0.115147	−	0.158487i	0.862700	+	0.505715i	$0.168771\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$773$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$774$	−10.4749	−	1.65906i	−0.376512	−	0.0596337i
$775$		0			0
$776$		0			0
$777$		0			0
$778$			55.7668i			1.99934i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−20.5022	−	28.2188i	−0.732687	−	1.00846i
$784$	−12.0863	+	76.3098i	−0.431653	+	2.72535i
$785$		0			0
$786$		0			0
$787$	−6.64486	+	1.05244i	−0.236864	+	0.0375155i	−0.273738	−	0.961804i	$-0.588260\pi$
$787$	−6.64486	+	1.05244i	−0.236864	+	0.0375155i	0.0368739	+	0.999320i	$0.488260\pi$
$788$		0			0
$789$	2.74688	+	1.99572i	0.0977913	+	0.0710496i
$790$		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	$-0.600000\pi$
$797$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$798$		0			0
$799$		0			0
$800$	12.8408	+	25.2015i	0.453990	+	0.891007i
$801$	9.24264	−	10.8217i	0.326573	−	0.382367i
$802$	31.4395	−	10.2153i	1.11017	−	0.360715i
$803$		0			0
$804$	−47.7512	−	15.5153i	−1.68406	−	0.547183i
$805$	−11.4517	−	47.7000i	−0.403621	−	1.68120i
$806$		0			0
$807$	−21.8443	−	25.5764i	−0.768956	−	0.900332i
$808$	−18.0979	−	11.0904i	−0.636683	−	0.390160i
$809$	−12.9304	+	53.8589i	−0.454608	+	1.89358i	−0.00573251	+	0.999984i	$0.501825\pi$
$809$	−12.9304	+	53.8589i	−0.454608	+	1.89358i	−0.448875	+	0.893594i	$0.648175\pi$
$810$	20.9087	−	28.7784i	0.734657	−	1.01117i
$811$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$811$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$812$	17.2714	+	109.048i	0.606109	+	3.82682i
$813$		0			0
$814$		0			0
$815$	−14.6922	−	2.32702i	−0.514647	−	0.0815121i
$816$		0			0
$817$		0			0
$818$	−42.9009	−	21.8591i	−1.50000	−	0.764286i
$819$		0			0
$820$	−15.8304	−	23.8621i	−0.552820	−	0.833301i
$821$	20.4322			0.713090			0.356545	−	0.934278i	$-0.383955\pi$
$821$	20.4322			0.713090			0.356545	+	0.934278i	$0.383955\pi$
$822$		0			0
$823$	7.68811	+	18.5607i	0.267991	+	0.646987i	0.999389	−	0.0349641i	$-0.0111317\pi$
$823$	7.68811	+	18.5607i	0.267991	+	0.646987i	−0.731398	+	0.681951i	$0.761132\pi$
$824$	8.82858	+	12.1515i	0.307558	+	0.423317i
$825$		0			0
$826$		0			0
$827$	−55.3685	+	4.35759i	−1.92535	+	0.151528i	−0.983062	−	0.183274i	$-0.941331\pi$
$827$	−55.3685	+	4.35759i	−1.92535	+	0.151528i	−0.942289	+	0.334802i	$0.891331\pi$
$828$	12.3870	−	1.96190i	0.430477	−	0.0681808i
$829$	−9.52428	+	9.52428i	−0.330792	+	0.330792i	−0.852887	−	0.522095i	$-0.825151\pi$
$829$	−9.52428	+	9.52428i	−0.330792	+	0.330792i	0.522095	+	0.852887i	$0.325151\pi$
$830$	−43.0282	−	31.2618i	−1.49353	−	1.08511i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−50.4938	+	12.1225i	−1.74741	+	0.419516i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.760406	−	0.649448i	$-0.775000\pi$
$839$		0			0		0.760406	+	0.649448i	$0.225000\pi$
$840$	−61.0925	+	31.1282i	−2.10789	+	1.07402i
$841$	39.4083	+	77.3431i	1.35891	+	2.66700i
$842$	−37.6611	+	44.0955i	−1.29789	+	1.51963i
$843$	55.5515	−	18.0498i	1.91330	−	0.621668i
$844$		0			0
$845$	27.6462	+	8.98278i	0.951057	+	0.309017i
$846$	−4.95422	−	20.6358i	−0.170330	−	0.709474i
$847$	−52.1329	−	21.5942i	−1.79131	−	0.741984i
$848$		0			0
$849$	−57.3128	−	35.1213i	−1.96697	−	1.20536i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$853$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$854$	−8.66994	−	110.162i	−0.296679	−	3.76967i
$855$		0			0
$856$	−46.9307	−	7.43310i	−1.60406	−	0.254058i
$857$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$857$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$858$		0			0
$859$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$859$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$860$		−	22.8724i		−	0.779943i
$861$	57.8456	−	38.3754i	1.97137	−	1.30783i
$862$		0			0
$863$	−4.30693	+	8.45283i	−0.146610	+	0.287738i	−0.952620	−	0.304164i	$-0.901623\pi$
$863$	−4.30693	+	8.45283i	−0.146610	+	0.287738i	0.806010	+	0.591902i	$0.201623\pi$
$864$	7.01671	+	16.9398i	0.238713	+	0.576305i
$865$		0			0
$866$		0			0
$867$	−35.8163	−	2.81881i	−1.21639	−	0.0957317i
$868$		0			0
$869$		0			0
$870$	−50.8534	+	50.8534i	−1.72409	+	1.72409i
$871$		0			0
$872$	−56.6367	−	13.5973i	−1.91796	−	0.460462i
$873$		0			0
$874$		0			0
$875$	−21.9482	+	52.9876i	−0.741984	+	1.79131i
$876$		0			0
$877$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$877$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	49.4908	−	25.2168i	1.66739	−	0.849576i	0.673497	−	0.739190i	$-0.264791\pi$
$881$	49.4908	−	25.2168i	1.66739	−	0.849576i	0.993889	−	0.110386i	$-0.0352087\pi$
$882$	−18.1836	−	35.6873i	−0.612273	−	1.20165i
$883$	−26.9895	+	31.6006i	−0.908269	+	1.06345i	0.0894534	+	0.995991i	$0.471488\pi$
$883$	−26.9895	+	31.6006i	−0.908269	+	1.06345i	−0.997722	+	0.0674553i	$0.978512\pi$
$884$		0			0
$885$		0			0
$886$	56.4782	+	18.3509i	1.89742	+	0.616510i
$887$	−3.60881	−	15.0318i	−0.121172	−	0.504717i	−0.999638	−	0.0269122i	$-0.991433\pi$
$887$	−3.60881	−	15.0318i	−0.121172	−	0.504717i	0.878466	−	0.477805i	$-0.158567\pi$
$888$		0			0
$889$	−72.1263	−	84.4491i	−2.41904	−	2.83233i
$890$	26.1698	+	16.0369i	0.877213	+	0.537557i
$891$		0			0
$892$	−26.0599	+	35.8683i	−0.872549	+	1.20096i
$893$		0			0
$894$	2.36234	+	14.9152i	0.0790086	+	0.498840i
$895$		0			0
$896$	4.55357	−	57.8586i	0.152124	−	1.93292i
$897$		0			0
$898$	−48.3597	+	35.1353i	−1.61378	+	1.17248i
$899$		0			0
$900$	−13.0647	−	6.65678i	−0.435489	−	0.221893i
$901$		0			0
$902$		0			0
$903$	55.4465			1.84514
$904$		0			0
$905$	16.2133	+	39.1425i	0.538950	+	1.30114i
$906$		0			0
$907$	−4.85846	+	30.6751i	−0.161322	+	1.01855i	0.765606	+	0.643310i	$0.222439\pi$
$907$	−4.85846	+	30.6751i	−0.161322	+	1.01855i	−0.926928	+	0.375239i	$0.877561\pi$
$908$	−38.0705	−	2.99621i	−1.26341	−	0.0994327i
$909$	10.9697	−	0.863334i	0.363842	−	0.0286350i
$910$		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
$915$	54.7340	−	46.7473i	1.80945	−	1.54542i
$916$	−12.2934	+	29.6789i	−0.406186	+	0.980619i
$917$		0			0
$918$		0			0
$919$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$919$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$920$	8.35815	+	25.7237i	0.275560	+	0.848086i
$921$	2.01065	+	1.71726i	0.0662532	+	0.0565856i
$922$	40.2254	−	20.4959i	1.32475	−	0.674995i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−26.8798	−	43.8639i	−0.883326	−	1.44146i
$927$	−7.40543	−	2.40617i	−0.243226	−	0.0790290i
$928$	−14.2109	−	59.1928i	−0.466497	−	1.94310i
$929$	−4.61156	−	1.91017i	−0.151300	−	0.0626706i	0.305748	−	0.952112i	$-0.401093\pi$
$929$	−4.61156	−	1.91017i	−0.151300	−	0.0626706i	−0.457049	+	0.889442i	$0.651093\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	41.9025	+	41.9025i	1.37109	+	1.37109i
$935$		0			0
$936$		0			0
$937$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$937$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$938$	85.1166	+	13.4811i	2.77915	+	0.440175i
$939$		0			0
$940$	42.2852	−	17.5151i	1.37919	−	0.571279i
$941$	−51.4337	−	26.2068i	−1.67669	−	0.854316i	−0.992109	−	0.125379i	$-0.959985\pi$
$941$	−51.4337	−	26.2068i	−1.67669	−	0.854316i	−0.684580	−	0.728937i	$-0.740015\pi$
$942$		0			0
$943$	−11.3822	−	24.9059i	−0.370654	−	0.811048i
$944$		0			0
$945$	−16.8793	+	33.1275i	−0.549084	+	1.07764i
$946$		0			0
$947$	−29.2177	−	40.2148i	−0.949449	−	1.30680i	−0.951772	−	0.306808i	$-0.900739\pi$
$947$	−29.2177	−	40.2148i	−0.949449	−	1.30680i	0.00232231	−	0.999997i	$-0.499261\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$953$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	32.2340	−	19.7530i	1.04035	−	0.637525i
$961$	−9.57953	−	29.4828i	−0.309017	−	0.951057i
$962$		0			0
$963$	21.9478	−	11.1829i	0.707257	−	0.360365i
$964$	8.05476	+	15.8084i	0.259426	+	0.509153i
$965$		0			0
$966$	−62.3585	+	20.2615i	−2.00635	+	0.651903i
$967$	10.5131	+	17.1558i	0.338079	+	0.551695i	0.975825	−	0.218552i	$-0.0701332\pi$
$967$	10.5131	+	17.1558i	0.338079	+	0.551695i	−0.637746	+	0.770246i	$0.720133\pi$
$968$	29.5899	+	9.61435i	0.951057	+	0.309017i
$969$		0			0
$970$		0			0
$971$		0			0		−0.649448	−	0.760406i	$-0.725000\pi$
$971$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$972$	−23.9575	−	14.6811i	−0.768436	−	0.470898i
$973$		0			0
$974$	−36.6346	+	50.4232i	−1.17385	+	1.61566i
$975$		0			0
$976$	9.53118	+	60.1775i	0.305085	+	1.92623i
$977$		0			0		−0.0784591	−	0.996917i	$-0.525000\pi$
$977$		0			0		0.0784591	+	0.996917i	$0.475000\pi$
$978$	−1.55996	+	19.8212i	−0.0498822	+	0.633813i
$979$		0			0
$980$	69.8833	−	50.7732i	2.23234	−	1.62189i
$981$	27.8968	−	11.5552i	0.890676	−	0.368930i
$982$		0			0
$983$		−	40.4345i		−	1.28966i	−0.764327	−	0.644829i	$-0.776928\pi$
$983$		−	40.4345i		−	1.28966i	0.764327	−	0.644829i	$-0.223072\pi$
$984$	−30.1358	+	23.5961i	−0.960693	+	0.752216i
$985$		0			0
$986$		0			0
$987$	42.4595	+	102.506i	1.35150	+	3.26281i
$988$		0			0
$989$	3.42158	−	21.6030i	0.108800	−	0.686937i
$990$		0			0
$991$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$991$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−37.1435	+	60.6127i	−1.17694	+	1.92059i
$997$		0			0		0.760406	−	0.649448i	$-0.225000\pi$
$997$		0			0		−0.760406	+	0.649448i	$0.775000\pi$
$998$		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.539.1	yes	16
4.3	odd	2		820.2.cc.f.539.1	yes	16
5.4	even	2		820.2.cc.f.539.1	yes	16
20.19	odd	2	CM	820.2.cc.a.539.1	yes	16
41.7	odd	40	inner	820.2.cc.a.499.1	✓	16
164.7	even	40		820.2.cc.f.499.1	yes	16
205.89	odd	40		820.2.cc.f.499.1	yes	16
820.499	even	40	inner	820.2.cc.a.499.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.cc.a.499.1	✓	16	41.7	odd	40	inner
820.2.cc.a.499.1	✓	16	820.499	even	40	inner
820.2.cc.a.539.1	yes	16	1.1	even	1	trivial
820.2.cc.a.539.1	yes	16	20.19	odd	2	CM
820.2.cc.f.499.1	yes	16	164.7	even	40
820.2.cc.f.499.1	yes	16	205.89	odd	40
820.2.cc.f.539.1	yes	16	4.3	odd	2
820.2.cc.f.539.1	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)

\(f(q)\)	\(=\)	\(q+(-0.642040 + 1.26007i) q^{2} +(-0.808747 - 1.95249i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-0.349798 + 2.20854i) q^{5} +(2.97953 + 0.234494i) q^{6} +(-5.11403 + 0.402483i) q^{7} +(2.79360 - 0.442463i) q^{8} +(-1.03682 + 1.03682i) q^{9} +(-2.55834 - 1.85874i) q^{10} +(-2.20845 + 3.60387i) q^{12} +(2.77625 - 6.70246i) q^{14} +(4.59504 - 1.10317i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-0.640788 - 1.97214i) q^{18} +(3.98470 - 2.03031i) q^{20} +(4.92180 + 9.65957i) q^{21} +(4.06728 - 1.32154i) q^{23} +(-3.12322 - 5.09664i) q^{24} +(-4.75528 - 1.54508i) q^{25} +(-2.99457 - 1.24039i) q^{27} +(6.66313 + 7.80152i) q^{28} +(9.17546 + 5.62273i) q^{29} +(-1.56012 + 6.49837i) q^{30} +(-4.00000 - 4.00000i) q^{32} +(0.899978 - 11.4353i) q^{35} +(2.89646 + 0.458754i) q^{36} +6.32456i q^{40} +(-0.731592 - 6.36119i) q^{41} -15.3318 q^{42} +(2.32190 - 4.55699i) q^{43} +(-1.92717 - 2.65253i) q^{45} +(-0.946117 + 5.97355i) q^{46} +(10.2027 + 0.802973i) q^{47} +(8.42737 - 0.663249i) q^{48} +(19.0775 - 3.02157i) q^{49} +(5.00000 - 5.00000i) q^{50} +(3.48561 - 2.97700i) q^{54} +(-14.1085 + 3.38715i) q^{56} +(-12.9761 + 7.95174i) q^{58} +(-7.18677 - 6.13808i) q^{60} +(13.5717 - 6.91514i) q^{61} +(4.88501 - 5.71961i) q^{63} +(7.60845 - 2.47214i) q^{64} +(2.77307 + 11.5507i) q^{67} +(-5.86969 - 6.87252i) q^{69} +(13.8315 + 8.47596i) q^{70} +(-2.43770 + 3.35521i) q^{72} +(0.829061 + 10.5342i) q^{75} +(-7.96940 - 4.06061i) q^{80} +11.2489i q^{81} +(8.48528 + 3.16228i) q^{82} +16.8188 q^{83} +(9.84359 - 19.3191i) q^{84} +(4.25139 + 5.85154i) q^{86} +(3.55769 - 22.4623i) q^{87} +(-9.67595 + 0.761514i) q^{89} +(4.57970 - 0.725353i) q^{90} +(-6.91967 - 5.02743i) q^{92} +(-7.56237 + 12.3407i) q^{94} +(-4.57496 + 11.0449i) q^{96} +(-8.44108 + 25.9790i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 12 q^{3} + 20 q^{6} + 16 q^{7} + 8 q^{8} + 12 q^{9} - 16 q^{12} + 20 q^{15} + 16 q^{16} + 4 q^{18} + 4 q^{21} + 8 q^{24} - 48 q^{27} + 8 q^{28} - 80 q^{30} - 64 q^{32} - 20 q^{35} + 24 q^{36}+ \cdots - 104 q^{98}+O(q^{100}) \) 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

Properties

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