LMFDB - Embedded newform 820.2.u.a.141.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(141,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.141"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.u (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.5
Character	$\chi$	$=$	820.141
Dual form			820.2.u.a.221.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.34396 q^{3} +(-0.809017 + 0.587785i) q^{5} +(-1.10976 + 3.41550i) q^{7} -1.19376 q^{9} +(-1.76997 - 1.28596i) q^{11} +(-0.0445363 - 0.137069i) q^{13} +(-1.08729 + 0.789962i) q^{15} +(3.20771 + 2.33053i) q^{17} +(-1.32729 + 4.08498i) q^{19} +(-1.49148 + 4.59031i) q^{21} +(1.69503 + 5.21678i) q^{23} +(0.309017 - 0.951057i) q^{25} -5.63626 q^{27} +(-7.59594 + 5.51877i) q^{29} +(-3.27809 - 2.38168i) q^{31} +(-2.37877 - 1.72828i) q^{33} +(-1.10976 - 3.41550i) q^{35} +(-0.000202820 + 0.000147358i) q^{37} +(-0.0598552 - 0.184215i) q^{39} +(6.39614 - 0.299050i) q^{41} +(-2.93535 - 9.03406i) q^{43} +(0.965774 - 0.701676i) q^{45} +(3.24623 + 9.99087i) q^{47} +(-4.77096 - 3.46631i) q^{49} +(4.31104 + 3.13215i) q^{51} +(6.06700 - 4.40793i) q^{53} +2.18780 q^{55} +(-1.78383 + 5.49006i) q^{57} +(2.90058 + 8.92708i) q^{59} +(-1.71987 + 5.29322i) q^{61} +(1.32479 - 4.07730i) q^{63} +(0.116598 + 0.0847132i) q^{65} +(6.24294 - 4.53576i) q^{67} +(2.27806 + 7.01116i) q^{69} +(-3.85278 - 2.79921i) q^{71} -2.37813 q^{73} +(0.415308 - 1.27819i) q^{75} +(6.35643 - 4.61822i) q^{77} +17.0749 q^{79} -3.99365 q^{81} -10.6815 q^{83} -3.96494 q^{85} +(-10.2087 + 7.41703i) q^{87} +(5.08466 - 15.6490i) q^{89} +0.517584 q^{91} +(-4.40564 - 3.20088i) q^{93} +(-1.32729 - 4.08498i) q^{95} +(1.62250 - 1.17882i) q^{97} +(2.11292 + 1.53513i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} - 6 q^{5} + 5 q^{7} + 18 q^{9} - 7 q^{11} - 5 q^{13} + 2 q^{15} + 3 q^{17} - q^{19} + 2 q^{21} + 20 q^{23} - 6 q^{25} + 20 q^{27} - 15 q^{29} - q^{31} - 6 q^{33} + 5 q^{35} + q^{37} + 28 q^{41}+ \cdots + 34 q^{99}+O(q^{100}) $ 24 * q + 2 * q^3 - 6 * q^5 + 5 * q^7 + 18 * q^9 - 7 * q^11 - 5 * q^13 + 2 * q^15 + 3 * q^17 - q^19 + 2 * q^21 + 20 * q^23 - 6 * q^25 + 20 * q^27 - 15 * q^29 - q^31 - 6 * q^33 + 5 * q^35 + q^37 + 28 * q^41 - 4 * q^43 + 3 * q^45 + 3 * q^47 + 3 * q^49 + 37 * q^51 + 29 * q^53 - 12 * q^55 + 17 * q^57 - 4 * q^59 - 14 * q^61 - 10 * q^63 + 5 * q^65 - 14 * q^67 - 26 * q^69 + q^71 - 84 * q^73 - 3 * q^75 + 24 * q^77 + 18 * q^79 - 40 * q^81 - 6 * q^83 - 12 * q^85 + 39 * q^87 + 12 * q^89 - 2 * q^91 - 58 * q^93 - q^95 - 20 * q^97 + 34 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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			0
$2$		0			0
$3$	1.34396			0.775938			0.387969	−	0.921672i	$-0.373177\pi$
$3$	1.34396			0.775938			0.387969	+	0.921672i	$0.373177\pi$
$4$		0			0
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$6$		0			0
$7$	−1.10976	+	3.41550i	−0.419451	+	1.29094i	0.488757	+	0.872420i	$0.337451\pi$
$7$	−1.10976	+	3.41550i	−0.419451	+	1.29094i	−0.908208	+	0.418519i	$0.862549\pi$
$8$		0			0
$9$	−1.19376			−0.397921
$10$		0			0
$11$	−1.76997	−	1.28596i	−0.533665	−	0.387730i	0.288062	−	0.957612i	$-0.406989\pi$
$11$	−1.76997	−	1.28596i	−0.533665	−	0.387730i	−0.821727	+	0.569882i	$0.806989\pi$
$12$		0			0
$13$	−0.0445363	−	0.137069i	−0.0123522	−	0.0380160i	0.944690	−	0.327963i	$-0.106362\pi$
$13$	−0.0445363	−	0.137069i	−0.0123522	−	0.0380160i	−0.957043	+	0.289947i	$0.906362\pi$
$14$		0			0
$15$	−1.08729	+	0.789962i	−0.280737	+	0.203967i
$16$		0			0
$17$	3.20771	+	2.33053i	0.777983	+	0.565238i	0.904373	−	0.426743i	$-0.140339\pi$
$17$	3.20771	+	2.33053i	0.777983	+	0.565238i	−0.126390	+	0.991981i	$0.540339\pi$
$18$		0			0
$19$	−1.32729	+	4.08498i	−0.304501	+	0.937158i	0.675362	+	0.737486i	$0.263987\pi$
$19$	−1.32729	+	4.08498i	−0.304501	+	0.937158i	−0.979863	+	0.199671i	$0.936013\pi$
$20$		0			0
$21$	−1.49148	+	4.59031i	−0.325468	+	1.00169i
$22$		0			0
$23$	1.69503	+	5.21678i	0.353439	+	1.08777i	0.956909	+	0.290388i	$0.0937843\pi$
$23$	1.69503	+	5.21678i	0.353439	+	1.08777i	−0.603470	+	0.797386i	$0.706216\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$		0			0
$27$	−5.63626			−1.08470
$28$		0			0
$29$	−7.59594	+	5.51877i	−1.41053	+	1.02481i	−0.417285	+	0.908776i	$0.637018\pi$
$29$	−7.59594	+	5.51877i	−1.41053	+	1.02481i	−0.993245	+	0.116035i	$0.962982\pi$
$30$		0			0
$31$	−3.27809	−	2.38168i	−0.588763	−	0.427761i	0.253110	−	0.967438i	$-0.418547\pi$
$31$	−3.27809	−	2.38168i	−0.588763	−	0.427761i	−0.841873	+	0.539676i	$0.818547\pi$
$32$		0			0
$33$	−2.37877	−	1.72828i	−0.414091	−	0.300854i
$34$		0			0
$35$	−1.10976	−	3.41550i	−0.187584	−	0.577325i
$36$		0			0
$37$	−0.000202820	0	0.000147358i	−3.33434e−5	0	2.42254e-5i	−0.587802	−	0.809005i	$-0.700007\pi$
$37$	−0.000202820	0	0.000147358i	−3.33434e−5	0	2.42254e-5i	0.587769	+	0.809029i	$0.300007\pi$
$38$		0			0
$39$	−0.0598552	−	0.184215i	−0.00958451	−	0.0294981i
$40$		0			0
$41$	6.39614	−	0.299050i	0.998909	−	0.0467038i
$41$	6.39614	−	0.299050i	0.998909	−	0.0467038i
$42$		0			0
$43$	−2.93535	−	9.03406i	−0.447636	−	1.37768i	−0.879567	−	0.475775i	$-0.842168\pi$
$43$	−2.93535	−	9.03406i	−0.447636	−	1.37768i	0.431931	−	0.901907i	$-0.357832\pi$
$44$		0			0
$45$	0.965774	−	0.701676i	0.143969	−	0.104600i
$46$		0			0
$47$	3.24623	+	9.99087i	0.473511	+	1.45732i	0.847955	+	0.530069i	$0.177834\pi$
$47$	3.24623	+	9.99087i	0.473511	+	1.45732i	−0.374443	+	0.927250i	$0.622166\pi$
$48$		0			0
$49$	−4.77096	−	3.46631i	−0.681566	−	0.495187i
$50$		0			0
$51$	4.31104	+	3.13215i	0.603666	+	0.438589i
$52$		0			0
$53$	6.06700	−	4.40793i	0.833366	−	0.605476i	−0.0871434	−	0.996196i	$-0.527774\pi$
$53$	6.06700	−	4.40793i	0.833366	−	0.605476i	0.920510	+	0.390720i	$0.127774\pi$
$54$		0			0
$55$	2.18780			0.295003
$56$		0			0
$57$	−1.78383	+	5.49006i	−0.236274	+	0.727176i
$58$		0			0
$59$	2.90058	+	8.92708i	0.377624	+	1.16221i	0.941691	+	0.336478i	$0.109236\pi$
$59$	2.90058	+	8.92708i	0.377624	+	1.16221i	−0.564067	+	0.825729i	$0.690764\pi$
$60$		0			0
$61$	−1.71987	+	5.29322i	−0.220207	+	0.677727i	0.778536	+	0.627600i	$0.215963\pi$
$61$	−1.71987	+	5.29322i	−0.220207	+	0.677727i	−0.998743	+	0.0501272i	$0.984037\pi$
$62$		0			0
$63$	1.32479	−	4.07730i	0.166908	−	0.513691i
$64$		0			0
$65$	0.116598	+	0.0847132i	0.0144622	+	0.0105074i
$66$		0			0
$67$	6.24294	−	4.53576i	0.762696	−	0.554131i	−0.137040	−	0.990566i	$-0.543759\pi$
$67$	6.24294	−	4.53576i	0.762696	−	0.554131i	0.899736	+	0.436434i	$0.143759\pi$
$68$		0			0
$69$	2.27806	+	7.01116i	0.274247	+	0.844044i
$70$		0			0
$71$	−3.85278	−	2.79921i	−0.457241	−	0.332205i	0.335207	−	0.942145i	$-0.391194\pi$
$71$	−3.85278	−	2.79921i	−0.457241	−	0.332205i	−0.792448	+	0.609939i	$0.791194\pi$
$72$		0			0
$73$	−2.37813			−0.278339			−0.139169	−	0.990269i	$-0.544443\pi$
$73$	−2.37813			−0.278339			−0.139169	+	0.990269i	$0.544443\pi$
$74$		0			0
$75$	0.415308	−	1.27819i	0.0479556	−	0.147592i
$76$		0			0
$77$	6.35643	−	4.61822i	0.724382	−	0.526295i
$78$		0			0
$79$	17.0749			1.92108			0.960538	−	0.278148i	$-0.0897207\pi$
$79$	17.0749			1.92108			0.960538	+	0.278148i	$0.0897207\pi$
$80$		0			0
$81$	−3.99365			−0.443738
$82$		0			0
$83$	−10.6815			−1.17245			−0.586224	−	0.810149i	$-0.699386\pi$
$83$	−10.6815			−1.17245			−0.586224	+	0.810149i	$0.699386\pi$
$84$		0			0
$85$	−3.96494			−0.430058
$86$		0			0
$87$	−10.2087	+	7.41703i	−1.09448	+	0.795189i
$88$		0			0
$89$	5.08466	−	15.6490i	0.538973	−	1.65879i	−0.195931	−	0.980618i	$-0.562773\pi$
$89$	5.08466	−	15.6490i	0.538973	−	1.65879i	0.734904	−	0.678171i	$-0.237227\pi$
$90$		0			0
$91$	0.517584			0.0542575
$92$		0			0
$93$	−4.40564	−	3.20088i	−0.456844	−	0.331916i
$94$		0			0
$95$	−1.32729	−	4.08498i	−0.136177	−	0.419110i
$96$		0			0
$97$	1.62250	−	1.17882i	0.164740	−	0.119691i	−0.502361	−	0.864658i	$-0.667535\pi$
$97$	1.62250	−	1.17882i	0.164740	−	0.119691i	0.667101	+	0.744967i	$0.267535\pi$
$98$		0			0
$99$	2.11292	+	1.53513i	0.212356	+	0.154286i
$100$		0			0
$101$	−0.432423	+	1.33086i	−0.0430277	+	0.132426i	−0.970263	−	0.242054i	$-0.922179\pi$
$101$	−0.432423	+	1.33086i	−0.0430277	+	0.132426i	0.927235	+	0.374480i	$0.122179\pi$
$102$		0			0
$103$	0.715848	−	2.20315i	0.0705346	−	0.217083i	−0.909575	−	0.415540i	$-0.863593\pi$
$103$	0.715848	−	2.20315i	0.0705346	−	0.217083i	0.980110	+	0.198456i	$0.0635928\pi$
$104$		0			0
$105$	−1.49148	−	4.59031i	−0.145554	−	0.447968i
$106$		0			0
$107$	−5.59423	+	17.2173i	−0.540815	+	1.66446i	0.189924	+	0.981799i	$0.439176\pi$
$107$	−5.59423	+	17.2173i	−0.540815	+	1.66446i	−0.730738	+	0.682658i	$0.760824\pi$
$108$		0			0
$109$	2.04797			0.196160			0.0980800	−	0.995179i	$-0.468730\pi$
$109$	2.04797			0.196160			0.0980800	+	0.995179i	$0.468730\pi$
$110$		0			0
$111$	−0.000272583	0	0.000198043i	−2.58724e−5	0	1.87974e-5i
$112$		0			0
$113$	−6.10286	−	4.43399i	−0.574108	−	0.417114i	0.262487	−	0.964936i	$-0.415457\pi$
$113$	−6.10286	−	4.43399i	−0.574108	−	0.417114i	−0.836595	+	0.547821i	$0.815457\pi$
$114$		0			0
$115$	−4.43766	−	3.22415i	−0.413814	−	0.300653i
$116$		0			0
$117$	0.0531658	+	0.163628i	0.00491518	+	0.0151274i
$118$		0			0
$119$	−11.5197	+	8.36958i	−1.05601	+	0.767239i
$120$		0			0
$121$	−1.92009	−	5.90943i	−0.174554	−	0.537221i
$122$		0			0
$123$	8.59617	−	0.401913i	0.775091	−	0.0362392i
$124$		0			0
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$		0			0
$127$	16.0597	−	11.6681i	1.42507	−	1.03537i	0.434161	−	0.900835i	$-0.357045\pi$
$127$	16.0597	−	11.6681i	1.42507	−	1.03537i	0.990908	−	0.134539i	$-0.0429552\pi$
$128$		0			0
$129$	−3.94500	−	12.1415i	−0.347338	−	1.06900i
$130$		0			0
$131$	13.1855	+	9.57983i	1.15202	+	0.836994i	0.988749	−	0.149587i	$-0.0477943\pi$
$131$	13.1855	+	9.57983i	1.15202	+	0.836994i	0.163275	+	0.986581i	$0.447794\pi$
$132$		0			0
$133$	−12.4793	−	9.06672i	−1.08209	−	0.786184i
$134$		0			0
$135$	4.55983	−	3.31291i	0.392448	−	0.285130i
$136$		0			0
$137$	−0.876573			−0.0748907			−0.0374454	−	0.999299i	$-0.511922\pi$
$137$	−0.876573			−0.0748907			−0.0374454	+	0.999299i	$0.511922\pi$
$138$		0			0
$139$	−0.225290	+	0.693373i	−0.0191089	+	0.0588111i	−0.960156	−	0.279464i	$-0.909843\pi$
$139$	−0.225290	+	0.693373i	−0.0191089	+	0.0588111i	0.941047	+	0.338275i	$0.109843\pi$
$140$		0			0
$141$	4.36282	+	13.4274i	0.367415	+	1.13079i
$142$		0			0
$143$	−0.0974365	+	0.299879i	−0.00814805	+	0.0250771i
$144$		0			0
$145$	2.90139	−	8.92956i	0.240947	−	0.741560i
$146$		0			0
$147$	−6.41200	−	4.65859i	−0.528853	−	0.384234i
$148$		0			0
$149$	−1.44143	+	1.04726i	−0.118087	+	0.0857949i	−0.645261	−	0.763962i	$-0.723251\pi$
$149$	−1.44143	+	1.04726i	−0.118087	+	0.0857949i	0.527175	+	0.849757i	$0.323251\pi$
$150$		0			0
$151$	6.87654	+	21.1638i	0.559605	+	1.72229i	0.683461	+	0.729987i	$0.260474\pi$
$151$	6.87654	+	21.1638i	0.559605	+	1.72229i	−0.123856	+	0.992300i	$0.539526\pi$
$152$		0			0
$153$	−3.82924	−	2.78210i	−0.309576	−	0.224920i
$154$		0			0
$155$	4.05195			0.325460
$156$		0			0
$157$	0.799017	−	2.45912i	0.0637685	−	0.196259i	−0.914096	−	0.405497i	$-0.867098\pi$
$157$	0.799017	−	2.45912i	0.0637685	−	0.196259i	0.977865	+	0.209238i	$0.0670984\pi$
$158$		0			0
$159$	8.15382	−	5.92410i	0.646640	−	0.469812i
$160$		0			0
$161$	−19.6990			−1.55250
$162$		0			0
$163$	0.814220			0.0637746			0.0318873	−	0.999491i	$-0.489848\pi$
$163$	0.814220			0.0637746			0.0318873	+	0.999491i	$0.489848\pi$
$164$		0			0
$165$	2.94032			0.228904
$166$		0			0
$167$	−11.0173			−0.852546			−0.426273	−	0.904595i	$-0.640174\pi$
$167$	−11.0173			−0.852546			−0.426273	+	0.904595i	$0.640174\pi$
$168$		0			0
$169$	10.5004	−	7.62900i	0.807724	−	0.586846i
$170$		0			0
$171$	1.58447	−	4.87649i	0.121167	−	0.372915i
$172$		0			0
$173$	15.8936			1.20837			0.604183	−	0.796846i	$-0.293500\pi$
$173$	15.8936			1.20837			0.604183	+	0.796846i	$0.293500\pi$
$174$		0			0
$175$	2.90540	+	2.11090i	0.219628	+	0.159569i
$176$		0			0
$177$	3.89828	+	11.9977i	0.293013	+	0.901800i
$178$		0			0
$179$	−3.71625	+	2.70002i	−0.277766	+	0.201809i	−0.717942	−	0.696103i	$-0.754916\pi$
$179$	−3.71625	+	2.70002i	−0.277766	+	0.201809i	0.440177	+	0.897911i	$0.354916\pi$
$180$		0			0
$181$	2.35014	+	1.70748i	0.174684	+	0.126916i	0.671692	−	0.740831i	$-0.265568\pi$
$181$	2.35014	+	1.70748i	0.174684	+	0.126916i	−0.497007	+	0.867746i	$0.665568\pi$
$182$		0			0
$183$	−2.31144	+	7.11389i	−0.170867	+	0.525874i
$184$		0			0
$185$	7.74704e−5	0	0.000238429i	5.69574e−6	0	1.75297e-5i
$186$		0			0
$187$	−2.68057	−	8.24993i	−0.196022	−	0.603295i
$188$		0			0
$189$	6.25492	−	19.2507i	0.454979	−	1.40028i
$190$		0			0
$191$	−1.02847			−0.0744173			−0.0372087	−	0.999308i	$-0.511847\pi$
$191$	−1.02847			−0.0744173			−0.0372087	+	0.999308i	$0.511847\pi$
$192$		0			0
$193$	18.7560	−	13.6270i	1.35009	−	0.980895i	0.351079	−	0.936346i	$-0.385815\pi$
$193$	18.7560	−	13.6270i	1.35009	−	0.980895i	0.999007	−	0.0445495i	$-0.0141852\pi$
$194$		0			0
$195$	0.156703	+	0.113851i	0.0112217	+	0.00815307i
$196$		0			0
$197$	0.217238	+	0.157833i	0.0154776	+	0.0112451i	0.595497	−	0.803357i	$-0.296955\pi$
$197$	0.217238	+	0.157833i	0.0154776	+	0.0112451i	−0.580020	+	0.814603i	$0.696955\pi$
$198$		0			0
$199$	8.03555	+	24.7309i	0.569625	+	1.75313i	0.653792	+	0.756674i	$0.273177\pi$
$199$	8.03555	+	24.7309i	0.569625	+	1.75313i	−0.0841671	+	0.996452i	$0.526823\pi$
$200$		0			0
$201$	8.39028	−	6.09590i	0.591805	−	0.429971i
$202$		0			0
$203$	−10.4197	−	32.0685i	−0.731318	−	2.25077i
$204$		0			0
$205$	−4.99881	+	4.00149i	−0.349132	+	0.279476i
$206$		0			0
$207$	−2.02347	−	6.22759i	−0.140641	−	0.432847i
$208$		0			0
$209$	7.60235	−	5.52343i	0.525866	−	0.382064i
$210$		0			0
$211$	−0.918624	−	2.82723i	−0.0632407	−	0.194635i	0.914444	−	0.404712i	$-0.132628\pi$
$211$	−0.918624	−	2.82723i	−0.0632407	−	0.194635i	−0.977685	+	0.210078i	$0.932628\pi$
$212$		0			0
$213$	−5.17800	−	3.76204i	−0.354791	−	0.257770i
$214$		0			0
$215$	7.68483	+	5.58336i	0.524101	+	0.380782i
$216$		0			0
$217$	11.7725	−	8.55324i	0.799171	−	0.580632i
$218$		0			0
$219$	−3.19612			−0.215974
$220$		0			0
$221$	0.176584	−	0.543470i	0.0118783	−	0.0365577i
$222$		0			0
$223$	0.640462	+	1.97114i	0.0428885	+	0.131997i	0.970208	−	0.242273i	$-0.0778931\pi$
$223$	0.640462	+	1.97114i	0.0428885	+	0.131997i	−0.927319	+	0.374271i	$0.877893\pi$
$224$		0			0
$225$	−0.368893	+	1.13534i	−0.0245929	+	0.0756890i
$226$		0			0
$227$	−4.47882	+	13.7844i	−0.297270	+	0.914902i	0.685180	+	0.728374i	$0.259724\pi$
$227$	−4.47882	+	13.7844i	−0.297270	+	0.914902i	−0.982450	+	0.186528i	$0.940276\pi$
$228$		0			0
$229$	−16.4161	−	11.9270i	−1.08481	−	0.788159i	−0.106292	−	0.994335i	$-0.533898\pi$
$229$	−16.4161	−	11.9270i	−1.08481	−	0.788159i	−0.978515	+	0.206176i	$0.933898\pi$
$230$		0			0
$231$	8.54281	−	6.20671i	0.562076	−	0.408372i
$232$		0			0
$233$	−8.38802	−	25.8157i	−0.549517	−	1.69124i	−0.710000	−	0.704202i	$-0.751305\pi$
$233$	−8.38802	−	25.8157i	−0.549517	−	1.69124i	0.160483	−	0.987039i	$-0.448695\pi$
$234$		0			0
$235$	−8.49874	−	6.17470i	−0.554397	−	0.402793i
$236$		0			0
$237$	22.9480			1.49064
$238$		0			0
$239$	−3.20636	+	9.86816i	−0.207402	+	0.638318i	0.792204	+	0.610256i	$0.208934\pi$
$239$	−3.20636	+	9.86816i	−0.207402	+	0.638318i	−0.999606	+	0.0280618i	$0.991066\pi$
$240$		0			0
$241$	−16.4453	+	11.9482i	−1.05934	+	0.769653i	−0.973966	−	0.226696i	$-0.927208\pi$
$241$	−16.4453	+	11.9482i	−1.05934	+	0.769653i	−0.0853710	+	0.996349i	$0.527208\pi$
$242$		0			0
$243$	11.5415			0.740386
$244$		0			0
$245$	5.89723			0.376760
$246$		0			0
$247$	0.619035			0.0393883
$248$		0			0
$249$	−14.3556			−0.909747
$250$		0			0
$251$	−5.14358	+	3.73703i	−0.324660	+	0.235879i	−0.738161	−	0.674624i	$-0.764306\pi$
$251$	−5.14358	+	3.73703i	−0.324660	+	0.235879i	0.413501	+	0.910503i	$0.364306\pi$
$252$		0			0
$253$	3.70839	−	11.4133i	0.233145	−	0.717545i
$254$		0			0
$255$	−5.32874			−0.333699
$256$		0			0
$257$	−5.27245	−	3.83066i	−0.328886	−	0.238950i	0.411072	−	0.911603i	$-0.365155\pi$
$257$	−5.27245	−	3.83066i	−0.328886	−	0.238950i	−0.739958	+	0.672653i	$0.765155\pi$
$258$		0			0
$259$	−0.000278217	0	0.000856265i	−1.72876e−5	0	5.32057e-5i
$260$		0			0
$261$	9.06774	−	6.58810i	0.561279	−	0.407793i
$262$		0			0
$263$	−2.10069	−	1.52624i	−0.129534	−	0.0941118i	0.521132	−	0.853476i	$-0.325510\pi$
$263$	−2.10069	−	1.52624i	−0.129534	−	0.0941118i	−0.650666	+	0.759364i	$0.725510\pi$
$264$		0			0
$265$	−2.31739	+	7.13218i	−0.142356	+	0.438127i
$266$		0			0
$267$	6.83360	−	21.0317i	0.418210	−	1.28712i
$268$		0			0
$269$	−1.18852	−	3.65788i	−0.0724651	−	0.223025i	0.908264	−	0.418398i	$-0.137408\pi$
$269$	−1.18852	−	3.65788i	−0.0724651	−	0.223025i	−0.980729	+	0.195373i	$0.937408\pi$
$270$		0			0
$271$	−2.65924	+	8.18430i	−0.161537	+	0.497161i	−0.998764	−	0.0496946i	$-0.984175\pi$
$271$	−2.65924	+	8.18430i	−0.161537	+	0.497161i	0.837227	+	0.546855i	$0.184175\pi$
$272$		0			0
$273$	0.695613			0.0421004
$274$		0			0
$275$	−1.76997	+	1.28596i	−0.106733	+	0.0775460i
$276$		0			0
$277$	−12.8254	−	9.31823i	−0.770606	−	0.559878i	0.131539	−	0.991311i	$-0.458008\pi$
$277$	−12.8254	−	9.31823i	−0.770606	−	0.559878i	−0.902145	+	0.431433i	$0.858008\pi$
$278$		0			0
$279$	3.91327	+	2.84315i	0.234281	+	0.170215i
$280$		0			0
$281$	5.63004	+	17.3275i	0.335860	+	1.03367i	0.966297	+	0.257430i	$0.0828758\pi$
$281$	5.63004	+	17.3275i	0.335860	+	1.03367i	−0.630437	+	0.776241i	$0.717124\pi$
$282$		0			0
$283$	−2.64026	+	1.91826i	−0.156947	+	0.114029i	−0.663487	−	0.748188i	$-0.730924\pi$
$283$	−2.64026	+	1.91826i	−0.156947	+	0.114029i	0.506540	+	0.862217i	$0.330924\pi$
$284$		0			0
$285$	−1.78383	−	5.49006i	−0.105665	−	0.325203i
$286$		0			0
$287$	−6.07680	+	22.1779i	−0.358702	+	1.30912i
$288$		0			0
$289$	−0.395303	−	1.21662i	−0.0232531	−	0.0715658i
$290$		0			0
$291$	2.18058	−	1.58429i	0.127828	−	0.0928726i
$292$		0			0
$293$	−3.01441	−	9.27741i	−0.176104	−	0.541992i	0.823578	−	0.567203i	$-0.191974\pi$
$293$	−3.01441	−	9.27741i	−0.176104	−	0.541992i	−0.999682	+	0.0252105i	$0.991974\pi$
$294$		0			0
$295$	−7.59383	−	5.51724i	−0.442130	−	0.321226i
$296$		0			0
$297$	9.97599	+	7.24798i	0.578866	+	0.420571i
$298$		0			0
$299$	0.639567	−	0.464672i	0.0369871	−	0.0268727i
$300$		0			0
$301$	34.1134			1.96626
$302$		0			0
$303$	−0.581161	+	1.78863i	−0.0333868	+	0.102754i
$304$		0			0
$305$	−1.71987	−	5.29322i	−0.0984795	−	0.303089i
$306$		0			0
$307$	7.04255	−	21.6747i	0.401940	−	1.23704i	−0.521484	−	0.853261i	$-0.674621\pi$
$307$	7.04255	−	21.6747i	0.401940	−	1.23704i	0.923424	−	0.383782i	$-0.125379\pi$
$308$		0			0
$309$	0.962074	−	2.96096i	0.0547305	−	0.168443i
$310$		0			0
$311$	16.9805	+	12.3371i	0.962878	+	0.699572i	0.953817	−	0.300387i	$-0.0971159\pi$
$311$	16.9805	+	12.3371i	0.962878	+	0.699572i	0.00906068	+	0.999959i	$0.497116\pi$
$312$		0			0
$313$	18.8267	−	13.6784i	1.06415	−	0.773148i	0.0892954	−	0.996005i	$-0.471538\pi$
$313$	18.8267	−	13.6784i	1.06415	−	0.773148i	0.974851	+	0.222858i	$0.0715385\pi$
$314$		0			0
$315$	1.32479	+	4.07730i	0.0746437	+	0.229730i
$316$		0			0
$317$	6.81762	+	4.95329i	0.382916	+	0.278205i	0.762546	−	0.646934i	$-0.223949\pi$
$317$	6.81762	+	4.95329i	0.382916	+	0.278205i	−0.379631	+	0.925138i	$0.623949\pi$
$318$		0			0
$319$	20.5414			1.15010
$320$		0			0
$321$	−7.51844	+	23.1394i	−0.419639	+	1.29151i
$322$		0			0
$323$	−13.7777	+	10.0101i	−0.766614	+	0.556977i
$324$		0			0
$325$	−0.144123			−0.00799449
$326$		0			0
$327$	2.75240			0.152208
$328$		0			0
$329$	−37.7264			−2.07992
$330$		0			0
$331$	−26.6375			−1.46413			−0.732065	−	0.681235i	$-0.761443\pi$
$331$	−26.6375			−1.46413			−0.732065	+	0.681235i	$0.761443\pi$
$332$		0			0
$333$	0.000242119	0	0.000175910i	1.32680e−5	0	9.63980e-6i
$334$		0			0
$335$	−2.38459	+	7.33901i	−0.130284	+	0.400973i
$336$		0			0
$337$	−16.3498			−0.890632			−0.445316	−	0.895373i	$-0.646909\pi$
$337$	−16.3498			−0.890632			−0.445316	+	0.895373i	$0.646909\pi$
$338$		0			0
$339$	−8.20202	−	5.95911i	−0.445472	−	0.323655i
$340$		0			0
$341$	2.73939	+	8.43097i	0.148346	+	0.456562i
$342$		0			0
$343$	−3.20398	+	2.32783i	−0.172999	+	0.125691i
$344$		0			0
$345$	−5.96405	−	4.33313i	−0.321094	−	0.233288i
$346$		0			0
$347$	−4.53016	+	13.9424i	−0.243192	+	0.748467i	0.752737	+	0.658321i	$0.228733\pi$
$347$	−4.53016	+	13.9424i	−0.243192	+	0.748467i	−0.995929	+	0.0901456i	$0.971267\pi$
$348$		0			0
$349$	−8.11578	+	24.9778i	−0.434428	+	1.33703i	0.459244	+	0.888310i	$0.348120\pi$
$349$	−8.11578	+	24.9778i	−0.434428	+	1.33703i	−0.893672	+	0.448721i	$0.851880\pi$
$350$		0			0
$351$	0.251019	+	0.772556i	0.0133984	+	0.0412360i
$352$		0			0
$353$	−11.1118	+	34.1986i	−0.591421	+	1.82021i	−0.0196299	+	0.999807i	$0.506249\pi$
$353$	−11.1118	+	34.1986i	−0.591421	+	1.82021i	−0.571791	+	0.820399i	$0.693751\pi$
$354$		0			0
$355$	4.76230			0.252757
$356$		0			0
$357$	−15.4821	+	11.2484i	−0.819400	+	0.595329i
$358$		0			0
$359$	14.7480	+	10.7150i	0.778369	+	0.565518i	0.904489	−	0.426497i	$-0.140252\pi$
$359$	14.7480	+	10.7150i	0.778369	+	0.565518i	−0.126120	+	0.992015i	$0.540252\pi$
$360$		0			0
$361$	0.445988	+	0.324029i	0.0234730	+	0.0170542i
$362$		0			0
$363$	−2.58053	−	7.94205i	−0.135443	−	0.416850i
$364$		0			0
$365$	1.92395	−	1.39783i	0.100704	−	0.0731657i
$366$		0			0
$367$	−7.40649	−	22.7948i	−0.386615	−	1.18988i	−0.935302	−	0.353852i	$-0.884872\pi$
$367$	−7.40649	−	22.7948i	−0.386615	−	1.18988i	0.548686	−	0.836028i	$-0.315128\pi$
$368$		0			0
$369$	−7.63547	+	0.356995i	−0.397486	+	0.0185844i
$370$		0			0
$371$	8.32237	+	25.6136i	0.432076	+	1.32979i
$372$		0			0
$373$	9.09660	−	6.60906i	0.471004	−	0.342204i	−0.326829	−	0.945084i	$-0.605980\pi$
$373$	9.09660	−	6.60906i	0.471004	−	0.342204i	0.797832	+	0.602879i	$0.205980\pi$
$374$		0			0
$375$	0.415308	+	1.27819i	0.0214464	+	0.0660052i
$376$		0			0
$377$	1.09475	+	0.795380i	0.0563823	+	0.0409642i
$378$		0			0
$379$	8.70656	+	6.32569i	0.447226	+	0.324929i	0.788500	−	0.615035i	$-0.210858\pi$
$379$	8.70656	+	6.32569i	0.447226	+	0.324929i	−0.341274	+	0.939964i	$0.610858\pi$
$380$		0			0
$381$	21.5837	−	15.6815i	1.10577	−	0.803386i
$382$		0			0
$383$	25.7540			1.31597			0.657984	−	0.753032i	$-0.271409\pi$
$383$	25.7540			1.31597			0.657984	+	0.753032i	$0.271409\pi$
$384$		0			0
$385$	−2.42794	+	7.47243i	−0.123739	+	0.380830i
$386$		0			0
$387$	3.50410	+	10.7845i	0.178124	+	0.548208i
$388$		0			0
$389$	−1.59812	+	4.91851i	−0.0810280	+	0.249379i	−0.983361	−	0.181660i	$-0.941853\pi$
$389$	−1.59812	+	4.91851i	−0.0810280	+	0.249379i	0.902333	+	0.431039i	$0.141853\pi$
$390$		0			0
$391$	−6.72071	+	20.6842i	−0.339881	+	1.04605i
$392$		0			0
$393$	17.7208	+	12.8749i	0.893898	+	0.649455i
$394$		0			0
$395$	−13.8139	+	10.0364i	−0.695052	+	0.504985i
$396$		0			0
$397$	7.61404	+	23.4336i	0.382138	+	1.17610i	0.938536	+	0.345183i	$0.112183\pi$
$397$	7.61404	+	23.4336i	0.382138	+	1.17610i	−0.556398	+	0.830916i	$0.687817\pi$
$398$		0			0
$399$	−16.7717	−	12.1853i	−0.839634	−	0.610030i
$400$		0			0
$401$	−4.40023			−0.219737			−0.109869	−	0.993946i	$-0.535043\pi$
$401$	−4.40023			−0.219737			−0.109869	+	0.993946i	$0.535043\pi$
$402$		0			0
$403$	−0.180459	+	0.555396i	−0.00898930	+	0.0276662i
$404$		0			0
$405$	3.23093	−	2.34741i	0.160546	−	0.116644i
$406$		0			0
$407$	0.000548480	0		2.71871e−5	0
$408$		0			0
$409$	−23.4777			−1.16090			−0.580448	−	0.814297i	$-0.697122\pi$
$409$	−23.4777			−1.16090			−0.580448	+	0.814297i	$0.697122\pi$
$410$		0			0
$411$	−1.17808			−0.0581105
$412$		0			0
$413$	−33.7094			−1.65873
$414$		0			0
$415$	8.64153	−	6.27844i	0.424196	−	0.308196i
$416$		0			0
$417$	−0.302782	+	0.931868i	−0.0148273	+	0.0456337i
$418$		0			0
$419$	7.98845			0.390261			0.195131	−	0.980777i	$-0.437487\pi$
$419$	7.98845			0.390261			0.195131	+	0.980777i	$0.437487\pi$
$420$		0			0
$421$	−26.7367	−	19.4254i	−1.30307	−	0.946735i	−0.303088	−	0.952962i	$-0.598018\pi$
$421$	−26.7367	−	19.4254i	−1.30307	−	0.946735i	−0.999981	+	0.00622742i	$0.998018\pi$
$422$		0			0
$423$	−3.87523	−	11.9267i	−0.188420	−	0.579897i
$424$		0			0
$425$	3.20771	−	2.33053i	0.155597	−	0.113048i
$426$		0			0
$427$	−16.1704	−	11.7484i	−0.782538	−	0.568547i
$428$		0			0
$429$	−0.130951	+	0.403026i	−0.00632238	+	0.0194583i
$430$		0			0
$431$	−9.12240	+	28.0759i	−0.439411	+	1.35237i	0.449088	+	0.893488i	$0.351749\pi$
$431$	−9.12240	+	28.0759i	−0.439411	+	1.35237i	−0.888498	+	0.458880i	$0.848251\pi$
$432$		0			0
$433$	5.07986	+	15.6342i	0.244122	+	0.751331i	0.995780	+	0.0917773i	$0.0292548\pi$
$433$	5.07986	+	15.6342i	0.244122	+	0.751331i	−0.751657	+	0.659554i	$0.770745\pi$
$434$		0			0
$435$	3.89936	−	12.0010i	0.186960	−	0.575404i
$436$		0			0
$437$	−23.5602			−1.12704
$438$		0			0
$439$	10.5853	−	7.69064i	0.505207	−	0.367054i	−0.305796	−	0.952097i	$-0.598922\pi$
$439$	10.5853	−	7.69064i	0.505207	−	0.367054i	0.811002	+	0.585043i	$0.198922\pi$
$440$		0			0
$441$	5.69539	+	4.13795i	0.271209	+	0.197045i
$442$		0			0
$443$	−19.6914	−	14.3066i	−0.935567	−	0.679729i	0.0117828	−	0.999931i	$-0.496249\pi$
$443$	−19.6914	−	14.3066i	−0.935567	−	0.679729i	−0.947349	+	0.320202i	$0.896249\pi$
$444$		0			0
$445$	5.08466	+	15.6490i	0.241036	+	0.741833i
$446$		0			0
$447$	−1.93723	+	1.40748i	−0.0916278	+	0.0665715i
$448$		0			0
$449$	−0.0809089	−	0.249012i	−0.00381833	−	0.0117516i	0.949129	−	0.314887i	$-0.101967\pi$
$449$	−0.0809089	−	0.249012i	−0.00381833	−	0.0117516i	−0.952948	+	0.303135i	$0.901967\pi$
$450$		0			0
$451$	−11.7055	−	7.69584i	−0.551191	−	0.362383i
$452$		0			0
$453$	9.24182	+	28.4434i	0.434219	+	1.33639i
$454$		0			0
$455$	−0.418734	+	0.304228i	−0.0196305	+	0.0142624i
$456$		0			0
$457$	9.79806	+	30.1553i	0.458334	+	1.41061i	0.867176	+	0.498002i	$0.165933\pi$
$457$	9.79806	+	30.1553i	0.458334	+	1.41061i	−0.408842	+	0.912605i	$0.634067\pi$
$458$		0			0
$459$	−18.0795	−	13.1355i	−0.843878	−	0.613113i
$460$		0			0
$461$	−1.95260	−	1.41865i	−0.0909417	−	0.0660730i	0.541385	−	0.840775i	$-0.317900\pi$
$461$	−1.95260	−	1.41865i	−0.0909417	−	0.0660730i	−0.632327	+	0.774702i	$0.717900\pi$
$462$		0			0
$463$	14.3214	−	10.4051i	0.665571	−	0.483565i	−0.202969	−	0.979185i	$-0.565059\pi$
$463$	14.3214	−	10.4051i	0.665571	−	0.483565i	0.868540	+	0.495620i	$0.165059\pi$
$464$		0			0
$465$	5.44567			0.252537
$466$		0			0
$467$	0.685967	−	2.11119i	0.0317428	−	0.0976941i	−0.933930	−	0.357456i	$-0.883644\pi$
$467$	0.685967	−	2.11119i	0.0317428	−	0.0976941i	0.965673	+	0.259762i	$0.0836441\pi$
$468$		0			0
$469$	8.56371	+	26.3564i	0.395435	+	1.21703i
$470$		0			0
$471$	1.07385	−	3.30497i	0.0494804	−	0.152285i
$472$		0			0
$473$	−6.42194	+	19.7647i	−0.295281	+	0.908782i
$474$		0			0
$475$	3.47489	+	2.52465i	0.159439	+	0.115839i
$476$		0			0
$477$	−7.24255	+	5.26202i	−0.331614	+	0.240931i
$478$		0			0
$479$	7.26137	+	22.3482i	0.331780	+	1.02111i	0.968286	+	0.249843i	$0.0803790\pi$
$479$	7.26137	+	22.3482i	0.331780	+	1.02111i	−0.636506	+	0.771272i	$0.719621\pi$
$480$		0			0
$481$	2.92310e−5	0	2.12376e-5i	1.33282e−6	0	9.68349e-7i
$482$		0			0
$483$	−26.4747			−1.20464
$484$		0			0
$485$	−0.619741	+	1.90737i	−0.0281410	+	0.0866090i
$486$		0			0
$487$	0.804510	−	0.584511i	0.0364558	−	0.0264867i	−0.569408	−	0.822055i	$-0.692828\pi$
$487$	0.804510	−	0.584511i	0.0364558	−	0.0264867i	0.605864	+	0.795568i	$0.292828\pi$
$488$		0			0
$489$	1.09428			0.0494851
$490$		0			0
$491$	−6.01340			−0.271381			−0.135690	−	0.990751i	$-0.543325\pi$
$491$	−6.01340			−0.271381			−0.135690	+	0.990751i	$0.543325\pi$
$492$		0			0
$493$	−37.2272			−1.67663
$494$		0			0
$495$	−2.61171			−0.117388
$496$		0			0
$497$	13.8364	−	10.0527i	0.620647	−	0.450926i
$498$		0			0
$499$	0.0289521	−	0.0891055i	0.00129608	−	0.00398891i	−0.950406	−	0.311011i	$-0.899332\pi$
$499$	0.0289521	−	0.0891055i	0.00129608	−	0.00398891i	0.951702	+	0.307022i	$0.0993325\pi$
$500$		0			0
$501$	−14.8069			−0.661523
$502$		0			0
$503$	16.4727	+	11.9681i	0.734479	+	0.533630i	0.890977	−	0.454048i	$-0.150020\pi$
$503$	16.4727	+	11.9681i	0.734479	+	0.533630i	−0.156498	+	0.987678i	$0.550020\pi$
$504$		0			0
$505$	−0.432423	−	1.33086i	−0.0192426	−	0.0592226i
$506$		0			0
$507$	14.1122	−	10.2531i	0.626744	−	0.455356i
$508$		0			0
$509$	25.4729	+	18.5072i	1.12907	+	0.820315i	0.985559	−	0.169334i	$-0.0541616\pi$
$509$	25.4729	+	18.5072i	1.12907	+	0.820315i	0.143508	+	0.989649i	$0.454162\pi$
$510$		0			0
$511$	2.63916	−	8.12250i	0.116750	−	0.359318i
$512$		0			0
$513$	7.48095	−	23.0240i	0.330292	−	1.01653i
$514$		0			0
$515$	0.715848	+	2.20315i	0.0315440	+	0.0970826i
$516$		0			0
$517$	7.10210	−	21.8580i	0.312350	−	0.961314i
$518$		0			0
$519$	21.3604			0.937617
$520$		0			0
$521$	−3.51549	+	2.55416i	−0.154017	+	0.111900i	−0.662125	−	0.749394i	$-0.730345\pi$
$521$	−3.51549	+	2.55416i	−0.154017	+	0.111900i	0.508108	+	0.861293i	$0.330345\pi$
$522$		0			0
$523$	0.232185	+	0.168692i	0.0101527	+	0.00737638i	0.592850	−	0.805313i	$-0.298003\pi$
$523$	0.232185	+	0.168692i	0.0101527	+	0.00737638i	−0.582697	+	0.812689i	$0.698003\pi$
$524$		0			0
$525$	3.90475	+	2.83697i	0.170417	+	0.123815i
$526$		0			0
$527$	−4.96459	−	15.2794i	−0.216261	−	0.665582i
$528$		0			0
$529$	−5.73423	+	4.16617i	−0.249315	+	0.181138i
$530$		0			0
$531$	−3.46261	−	10.6568i	−0.150264	−	0.462466i
$532$		0			0
$533$	−0.325851	−	0.863392i	−0.0141142	−	0.0373977i
$534$		0			0
$535$	−5.59423	−	17.2173i	−0.241860	−	0.744368i
$536$		0			0
$537$	−4.99451	+	3.62872i	−0.215529	+	0.156591i
$538$		0			0
$539$	3.98692	+	12.2705i	0.171729	+	0.528527i
$540$		0			0
$541$	10.4025	+	7.55785i	0.447238	+	0.324937i	0.788504	−	0.615029i	$-0.210856\pi$
$541$	10.4025	+	7.55785i	0.447238	+	0.324937i	−0.341266	+	0.939967i	$0.610856\pi$
$542$		0			0
$543$	3.15850	+	2.29479i	0.135544	+	0.0984787i
$544$		0			0
$545$	−1.65684	+	1.20377i	−0.0709714	+	0.0515637i
$546$		0			0
$547$	2.76950			0.118415			0.0592077	−	0.998246i	$-0.481143\pi$
$547$	2.76950			0.118415			0.0592077	+	0.998246i	$0.481143\pi$
$548$		0			0
$549$	2.05312	−	6.31884i	0.0876249	−	0.269682i
$550$		0			0
$551$	−12.4620	−	38.3542i	−0.530901	−	1.63395i
$552$		0			0
$553$	−18.9491	+	58.3194i	−0.805798	+	2.47999i
$554$		0			0
$555$	0.000104117	0	0.000320440i	4.41954e−6	0	1.36019e-5i
$556$		0			0
$557$	3.46145	+	2.51489i	0.146666	+	0.106559i	0.658699	−	0.752407i	$-0.271107\pi$
$557$	3.46145	+	2.51489i	0.146666	+	0.106559i	−0.512032	+	0.858966i	$0.671107\pi$
$558$		0			0
$559$	−1.10756	+	0.804688i	−0.0468447	+	0.0340347i
$560$		0			0
$561$	−3.60258	−	11.0876i	−0.152101	−	0.468119i
$562$		0			0
$563$	15.1119	+	10.9794i	0.636891	+	0.462728i	0.858781	−	0.512343i	$-0.171222\pi$
$563$	15.1119	+	10.9794i	0.636891	+	0.462728i	−0.221890	+	0.975072i	$0.571222\pi$
$564$		0			0
$565$	7.54355			0.317359
$566$		0			0
$567$	4.43200	−	13.6403i	0.186127	−	0.572839i
$568$		0			0
$569$	26.8211	−	19.4866i	1.12440	−	0.816923i	0.139528	−	0.990218i	$-0.455442\pi$
$569$	26.8211	−	19.4866i	1.12440	−	0.816923i	0.984870	+	0.173296i	$0.0554416\pi$
$570$		0			0
$571$	−0.690623			−0.0289017			−0.0144508	−	0.999896i	$-0.504600\pi$
$571$	−0.690623			−0.0289017			−0.0144508	+	0.999896i	$0.504600\pi$
$572$		0			0
$573$	−1.38222			−0.0577432
$574$		0			0
$575$	5.48524			0.228750
$576$		0			0
$577$	15.5256			0.646339			0.323170	−	0.946341i	$-0.395252\pi$
$577$	15.5256			0.646339			0.323170	+	0.946341i	$0.395252\pi$
$578$		0			0
$579$	25.2074	−	18.3142i	1.04758	−	0.761114i
$580$		0			0
$581$	11.8540	−	36.4827i	0.491785	−	1.51356i
$582$		0			0
$583$	−16.4068			−0.679500
$584$		0			0
$585$	−0.139190	−	0.101127i	−0.00575479	−	0.00418110i
$586$		0			0
$587$	−5.94532	−	18.2978i	−0.245390	−	0.755232i	−0.995572	−	0.0940009i	$-0.970034\pi$
$587$	−5.94532	−	18.2978i	−0.245390	−	0.755232i	0.750182	−	0.661231i	$-0.229966\pi$
$588$		0			0
$589$	14.0801	−	10.2298i	0.580159	−	0.421510i
$590$		0			0
$591$	0.291960	+	0.212121i	0.0120096	+	0.00872550i
$592$		0			0
$593$	−4.49720	+	13.8410i	−0.184678	+	0.568380i	−0.999943	−	0.0107081i	$-0.996591\pi$
$593$	−4.49720	+	13.8410i	−0.184678	+	0.568380i	0.815265	+	0.579089i	$0.196591\pi$
$594$		0			0
$595$	4.40015	−	13.5423i	0.180389	−	0.555179i
$596$		0			0
$597$	10.7995	+	33.2374i	0.441994	+	1.36032i
$598$		0			0
$599$	3.59063	−	11.0508i	0.146709	−	0.451524i	−0.850518	−	0.525946i	$-0.823711\pi$
$599$	3.59063	−	11.0508i	0.146709	−	0.451524i	0.997227	+	0.0744224i	$0.0237113\pi$
$600$		0			0
$601$	−33.6461			−1.37245			−0.686226	−	0.727389i	$-0.740734\pi$
$601$	−33.6461			−1.37245			−0.686226	+	0.727389i	$0.740734\pi$
$602$		0			0
$603$	−7.45258	+	5.41462i	−0.303493	+	0.220500i
$604$		0			0
$605$	5.02686	+	3.65223i	0.204371	+	0.148484i
$606$		0			0
$607$	−2.83608	−	2.06054i	−0.115113	−	0.0836346i	0.528739	−	0.848784i	$-0.322665\pi$
$607$	−2.83608	−	2.06054i	−0.115113	−	0.0836346i	−0.643852	+	0.765150i	$0.722665\pi$
$608$		0			0
$609$	−14.0037	−	43.0989i	−0.567457	−	1.74645i
$610$		0			0
$611$	1.22486	−	0.889914i	0.0495526	−	0.0360021i
$612$		0			0
$613$	−2.42038	−	7.44916i	−0.0977581	−	0.300869i	0.890205	−	0.455561i	$-0.150561\pi$
$613$	−2.42038	−	7.44916i	−0.0977581	−	0.300869i	−0.987963	+	0.154692i	$0.950561\pi$
$614$		0			0
$615$	−6.71821	+	5.37786i	−0.270904	+	0.216856i
$616$		0			0
$617$	14.3193	+	44.0703i	0.576474	+	1.77421i	0.631103	+	0.775699i	$0.282602\pi$
$617$	14.3193	+	44.0703i	0.576474	+	1.77421i	−0.0546292	+	0.998507i	$0.517398\pi$
$618$		0			0
$619$	−8.95495	+	6.50615i	−0.359930	+	0.261504i	−0.753023	−	0.657994i	$-0.771405\pi$
$619$	−8.95495	+	6.50615i	−0.359930	+	0.261504i	0.393093	+	0.919499i	$0.371405\pi$
$620$		0			0
$621$	−9.55366	−	29.4031i	−0.383375	−	1.17991i
$622$		0			0
$623$	47.8064	+	34.7334i	1.91532	+	1.39156i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$		0			0
$627$	10.2173	−	7.42329i	0.408039	−	0.296458i
$628$		0			0
$629$	−0.000994009	0		−3.96338e−5	0
$630$		0			0
$631$	−3.09439	+	9.52355i	−0.123186	+	0.379127i	−0.993566	−	0.113253i	$-0.963873\pi$
$631$	−3.09439	+	9.52355i	−0.123186	+	0.379127i	0.870380	+	0.492380i	$0.163873\pi$
$632$		0			0
$633$	−1.23460	−	3.79970i	−0.0490708	−	0.151024i
$634$		0			0
$635$	−6.13427	+	18.8793i	−0.243431	+	0.749203i
$636$		0			0
$637$	−0.262641	+	0.808327i	−0.0104062	+	0.0320271i
$638$		0			0
$639$	4.59931	+	3.34159i	0.181946	+	0.132191i
$640$		0			0
$641$	19.1822	−	13.9367i	0.757651	−	0.550466i	−0.140538	−	0.990075i	$-0.544883\pi$
$641$	19.1822	−	13.9367i	0.757651	−	0.550466i	0.898189	+	0.439610i	$0.144883\pi$
$642$		0			0
$643$	−5.43819	−	16.7370i	−0.214461	−	0.660043i	−0.999191	−	0.0402061i	$-0.987199\pi$
$643$	−5.43819	−	16.7370i	−0.214461	−	0.660043i	0.784730	−	0.619837i	$-0.212801\pi$
$644$		0			0
$645$	10.3281	+	7.50383i	0.406670	+	0.295463i
$646$		0			0
$647$	−24.3217			−0.956183			−0.478091	−	0.878310i	$-0.658671\pi$
$647$	−24.3217			−0.956183			−0.478091	+	0.878310i	$0.658671\pi$
$648$		0			0
$649$	6.34589	−	19.5307i	0.249098	−	0.766645i
$650$		0			0
$651$	15.8218	−	11.4952i	0.620107	−	0.450534i
$652$		0			0
$653$	9.67667			0.378677			0.189339	−	0.981912i	$-0.439366\pi$
$653$	9.67667			0.378677			0.189339	+	0.981912i	$0.439366\pi$
$654$		0			0
$655$	−16.2982			−0.636823
$656$		0			0
$657$	2.83892			0.110757
$658$		0			0
$659$	−33.6251			−1.30985			−0.654923	−	0.755695i	$-0.727299\pi$
$659$	−33.6251			−1.30985			−0.654923	+	0.755695i	$0.727299\pi$
$660$		0			0
$661$	34.2851	−	24.9096i	1.33354	−	0.968871i	0.333881	−	0.942615i	$-0.391642\pi$
$661$	34.2851	−	24.9096i	1.33354	−	0.968871i	0.999655	−	0.0262556i	$-0.00835839\pi$
$662$		0			0
$663$	0.237323	−	0.730404i	0.00921684	−	0.0283665i
$664$		0			0
$665$	15.4252			0.598165
$666$		0			0
$667$	−41.6656	−	30.2718i	−1.61330	−	1.17213i
$668$		0			0
$669$	0.860758	+	2.64914i	0.0332788	+	0.102422i
$670$		0			0
$671$	9.85096	−	7.15714i	0.380292	−	0.276298i
$672$		0			0
$673$	31.5940	+	22.9544i	1.21786	+	0.884828i	0.995921	−	0.0902323i	$-0.0287610\pi$
$673$	31.5940	+	22.9544i	1.21786	+	0.884828i	0.221940	+	0.975060i	$0.428761\pi$
$674$		0			0
$675$	−1.74170	+	5.36040i	−0.0670381	+	0.206322i
$676$		0			0
$677$	−3.80805	+	11.7200i	−0.146355	+	0.450435i	−0.997183	−	0.0750101i	$-0.976101\pi$
$677$	−3.80805	+	11.7200i	−0.146355	+	0.450435i	0.850828	+	0.525445i	$0.176101\pi$
$678$		0			0
$679$	2.22566	+	6.84987i	0.0854129	+	0.262874i
$680$		0			0
$681$	−6.01937	+	18.5257i	−0.230663	+	0.709907i
$682$		0			0
$683$	−6.72705			−0.257404			−0.128702	−	0.991683i	$-0.541081\pi$
$683$	−6.72705			−0.257404			−0.128702	+	0.991683i	$0.541081\pi$
$684$		0			0
$685$	0.709163	−	0.515237i	0.0270957	−	0.0196862i
$686$		0			0
$687$	−22.0627	−	16.0295i	−0.841743	−	0.611562i
$688$		0			0
$689$	−0.874392	−	0.635283i	−0.0333117	−	0.0242024i
$690$		0			0
$691$	−6.72449	−	20.6958i	−0.255812	−	0.787307i	−0.993669	−	0.112350i	$-0.964162\pi$
$691$	−6.72449	−	20.6958i	−0.255812	−	0.787307i	0.737857	−	0.674957i	$-0.235838\pi$
$692$		0			0
$693$	−7.58806	+	5.51305i	−0.288247	+	0.209423i
$694$		0			0
$695$	−0.225290	−	0.693373i	−0.00854575	−	0.0263011i
$696$		0			0
$697$	21.2139	+	13.9472i	0.803533	+	0.528286i
$698$		0			0
$699$	−11.2732	−	34.6953i	−0.426391	−	1.31230i
$700$		0			0
$701$	−1.75450	+	1.27472i	−0.0662664	+	0.0481453i	−0.620425	−	0.784266i	$-0.713040\pi$
$701$	−1.75450	+	1.27472i	−0.0662664	+	0.0481453i	0.554159	+	0.832411i	$0.313040\pi$
$702$		0			0
$703$	−0.000332751	−	0.00102410i	−1.25499e−5	−	3.86247e-5i
$704$		0			0
$705$	−11.4220	−	8.29857i	−0.430177	−	0.312542i
$706$		0			0
$707$	−4.06567	−	2.95388i	−0.152905	−	0.111092i
$708$		0			0
$709$	−38.9072	+	28.2677i	−1.46119	+	1.06162i	−0.478139	+	0.878284i	$0.658688\pi$
$709$	−38.9072	+	28.2677i	−1.46119	+	1.06162i	−0.983051	+	0.183332i	$0.941312\pi$
$710$		0			0
$711$	−20.3834			−0.764436
$712$		0			0
$713$	6.86819	−	21.1381i	0.257216	−	0.791628i
$714$		0			0
$715$	−0.0974365	−	0.299879i	−0.00364392	−	0.0112148i
$716$		0			0
$717$	−4.30923	+	13.2624i	−0.160931	+	0.495295i
$718$		0			0
$719$	2.74923	−	8.46125i	0.102529	−	0.315551i	−0.886614	−	0.462511i	$-0.846949\pi$
$719$	2.74923	−	8.46125i	0.102529	−	0.315551i	0.989143	+	0.146959i	$0.0469487\pi$
$720$		0			0
$721$	6.73045	+	4.88996i	0.250655	+	0.182112i
$722$		0			0
$723$	−22.1019	+	16.0580i	−0.821979	+	0.597203i
$724$		0			0
$725$	2.90139	+	8.92956i	0.107755	+	0.331636i
$726$		0			0
$727$	−17.0308	−	12.3736i	−0.631639	−	0.458912i	0.225329	−	0.974283i	$-0.427654\pi$
$727$	−17.0308	−	12.3736i	−0.631639	−	0.458912i	−0.856968	+	0.515370i	$0.827654\pi$
$728$		0			0
$729$	27.4923			1.01823
$730$		0			0
$731$	11.6385	−	35.8195i	0.430465	−	1.32483i
$732$		0			0
$733$	40.1973	−	29.2051i	1.48472	−	1.07871i	0.508725	−	0.860929i	$-0.330117\pi$
$733$	40.1973	−	29.2051i	1.48472	−	1.07871i	0.975997	−	0.217784i	$-0.0698829\pi$
$734$		0			0
$735$	7.92567			0.292343
$736$		0			0
$737$	−16.8826			−0.621878
$738$		0			0
$739$	50.8996			1.87237			0.936185	−	0.351507i	$-0.114331\pi$
$739$	50.8996			1.87237			0.936185	+	0.351507i	$0.114331\pi$
$740$		0			0
$741$	0.831961			0.0305628
$742$		0			0
$743$	−12.4277	+	9.02928i	−0.455929	+	0.331252i	−0.791932	−	0.610609i	$-0.790925\pi$
$743$	−12.4277	+	9.02928i	−0.455929	+	0.331252i	0.336003	+	0.941861i	$0.390925\pi$
$744$		0			0
$745$	0.550577	−	1.69450i	0.0201716	−	0.0620817i
$746$		0			0
$747$	12.7512			0.466542
$748$		0			0
$749$	−52.5974	−	38.2142i	−1.92187	−	1.39632i
$750$		0			0
$751$	−11.6496	−	35.8537i	−0.425099	−	1.30832i	−0.902900	−	0.429852i	$-0.858566\pi$
$751$	−11.6496	−	35.8537i	−0.425099	−	1.30832i	0.477801	−	0.878468i	$-0.341434\pi$
$752$		0			0
$753$	−6.91278	+	5.02243i	−0.251916	+	0.183028i
$754$		0			0
$755$	−18.0030	−	13.0800i	−0.655197	−	0.476028i
$756$		0			0
$757$	1.02514	−	3.15506i	0.0372594	−	0.114673i	−0.930697	−	0.365791i	$-0.880798\pi$
$757$	1.02514	−	3.15506i	0.0372594	−	0.114673i	0.967956	+	0.251119i	$0.0807984\pi$
$758$		0			0
$759$	4.98394	−	15.3390i	0.180906	−	0.556770i
$760$		0			0
$761$	−7.64678	−	23.5344i	−0.277196	−	0.853121i	−0.988630	−	0.150368i	$-0.951954\pi$
$761$	−7.64678	−	23.5344i	−0.277196	−	0.853121i	0.711434	−	0.702753i	$-0.248046\pi$
$762$		0			0
$763$	−2.27276	+	6.99485i	−0.0822796	+	0.253231i
$764$		0			0
$765$	4.73320			0.171129
$766$		0			0
$767$	1.09444	−	0.795159i	0.0395180	−	0.0287115i
$768$		0			0
$769$	32.1809	+	23.3808i	1.16047	+	0.843133i	0.989838	−	0.142201i	$-0.0454179\pi$
$769$	32.1809	+	23.3808i	1.16047	+	0.843133i	0.170636	+	0.985334i	$0.445418\pi$
$770$		0			0
$771$	−7.08598	−	5.14827i	−0.255195	−	0.185410i
$772$		0			0
$773$	−1.31387	−	4.04369i	−0.0472567	−	0.145441i	0.924644	−	0.380833i	$-0.124363\pi$
$773$	−1.31387	−	4.04369i	−0.0472567	−	0.145441i	−0.971901	+	0.235392i	$0.924363\pi$
$774$		0			0
$775$	−3.27809	+	2.38168i	−0.117753	+	0.0855523i
$776$		0			0
$777$	−0.000373914	−	0.00115079i	−1.34141e−5	−	4.12843e-5i
$778$		0			0
$779$	−7.26791	+	26.5250i	−0.260400	+	0.950357i
$780$		0			0
$781$	3.21963	+	9.90901i	0.115208	+	0.354572i
$782$		0			0
$783$	42.8127	−	31.1053i	1.53000	−	1.11161i
$784$		0			0
$785$	0.799017	+	2.45912i	0.0285181	+	0.0877698i
$786$		0			0
$787$	11.6705	+	8.47913i	0.416009	+	0.302248i	0.776030	−	0.630696i	$-0.217231\pi$
$787$	11.6705	+	8.47913i	0.416009	+	0.302248i	−0.360021	+	0.932944i	$0.617231\pi$
$788$		0			0
$789$	−2.82324	−	2.05121i	−0.100510	−	0.0730249i
$790$		0			0
$791$	21.9170	−	15.9236i	0.779279	−	0.566180i
$792$		0			0
$793$	0.802132			0.0284845
$794$		0			0
$795$	−3.11448	+	9.58540i	−0.110459	+	0.339959i
$796$		0			0
$797$	7.85043	+	24.1611i	0.278076	+	0.855831i	0.988389	+	0.151945i	$0.0485536\pi$
$797$	7.85043	+	24.1611i	0.278076	+	0.855831i	−0.710313	+	0.703886i	$0.751446\pi$
$798$		0			0
$799$	−12.8711	+	39.6132i	−0.455347	+	1.40142i
$800$		0			0
$801$	−6.06988	+	18.6812i	−0.214469	+	0.660066i
$802$		0			0
$803$	4.20921	+	3.05817i	0.148540	+	0.107920i
$804$		0			0
$805$	15.9368	−	11.5788i	0.561699	−	0.408098i
$806$		0			0
$807$	−1.59732	−	4.91605i	−0.0562284	−	0.173053i
$808$		0			0
$809$	15.5797	+	11.3193i	0.547752	+	0.397965i	0.826956	−	0.562267i	$-0.190071\pi$
$809$	15.5797	+	11.3193i	0.547752	+	0.397965i	−0.279204	+	0.960232i	$0.590071\pi$
$810$		0			0
$811$	32.3382			1.13555			0.567774	−	0.823185i	$-0.307805\pi$
$811$	32.3382			1.13555			0.567774	+	0.823185i	$0.307805\pi$
$812$		0			0
$813$	−3.57392	+	10.9994i	−0.125343	+	0.385766i
$814$		0			0
$815$	−0.658718	+	0.478586i	−0.0230739	+	0.0167642i
$816$		0			0
$817$	40.8000			1.42741
$818$		0			0
$819$	−0.617872			−0.0215902
$820$		0			0
$821$	−41.7277			−1.45631			−0.728154	−	0.685414i	$-0.759621\pi$
$821$	−41.7277			−1.45631			−0.728154	+	0.685414i	$0.759621\pi$
$822$		0			0
$823$	15.1311			0.527436			0.263718	−	0.964600i	$-0.415051\pi$
$823$	15.1311			0.527436			0.263718	+	0.964600i	$0.415051\pi$
$824$		0			0
$825$	−2.37877	+	1.72828i	−0.0828181	+	0.0601709i
$826$		0			0
$827$	13.0225	−	40.0790i	0.452836	−	1.39369i	−0.420822	−	0.907143i	$-0.638258\pi$
$827$	13.0225	−	40.0790i	0.452836	−	1.39369i	0.873657	−	0.486542i	$-0.161742\pi$
$828$		0			0
$829$	−53.4115			−1.85506			−0.927530	−	0.373750i	$-0.878072\pi$
$829$	−53.4115			−1.85506			−0.927530	+	0.373750i	$0.878072\pi$
$830$		0			0
$831$	−17.2369	−	12.5234i	−0.597942	−	0.434431i
$832$		0			0
$833$	−7.22549	−	22.2378i	−0.250349	−	0.770494i
$834$		0			0
$835$	8.91320	−	6.47582i	0.308454	−	0.224105i
$836$		0			0
$837$	18.4762	+	13.4237i	0.638631	+	0.463993i
$838$		0			0
$839$	−12.2123	+	37.5856i	−0.421615	+	1.29760i	0.484583	+	0.874745i	$0.338971\pi$
$839$	−12.2123	+	37.5856i	−0.421615	+	1.29760i	−0.906198	+	0.422853i	$0.861029\pi$
$840$		0			0
$841$	18.2799	−	56.2599i	0.630343	−	1.94000i
$842$		0			0
$843$	7.56657	+	23.2875i	0.260606	+	0.802064i
$844$		0			0
$845$	−4.01080	+	12.3440i	−0.137976	+	0.424646i
$846$		0			0
$847$	22.3145			0.766736
$848$		0			0
$849$	−3.54842	+	2.57807i	−0.121781	+	0.0884793i
$850$		0			0
$851$	−0.00111252		0.000808292i	−3.81366e−5		2.77079e-5i
$852$		0			0
$853$	−14.2690	−	10.3670i	−0.488562	−	0.354961i	0.316069	−	0.948736i	$-0.397637\pi$
$853$	−14.2690	−	10.3670i	−0.488562	−	0.354961i	−0.804631	+	0.593775i	$0.797637\pi$
$854$		0			0
$855$	1.58447	+	4.87649i	0.0541877	+	0.166772i
$856$		0			0
$857$	42.3155	−	30.7440i	1.44547	−	1.05020i	0.458608	−	0.888639i	$-0.348348\pi$
$857$	42.3155	−	30.7440i	1.44547	−	1.05020i	0.986863	−	0.161557i	$-0.0516517\pi$
$858$		0			0
$859$	−11.2201	−	34.5320i	−0.382826	−	1.17822i	−0.938045	−	0.346513i	$-0.887366\pi$
$859$	−11.2201	−	34.5320i	−0.382826	−	1.17822i	0.555219	−	0.831704i	$-0.312634\pi$
$860$		0			0
$861$	−8.16699	+	29.8063i	−0.278330	+	1.01580i
$862$		0			0
$863$	12.1614	+	37.4290i	0.413979	+	1.27410i	0.913161	+	0.407600i	$0.133634\pi$
$863$	12.1614	+	37.4290i	0.413979	+	1.27410i	−0.499181	+	0.866498i	$0.666366\pi$
$864$		0			0
$865$	−12.8582	+	9.34201i	−0.437191	+	0.317638i
$866$		0			0
$867$	−0.531273	−	1.63509i	−0.0180430	−	0.0555306i
$868$		0			0
$869$	−30.2220	−	21.9576i	−1.02521	−	0.744859i
$870$		0			0
$871$	−0.899749	−	0.653706i	−0.0304868	−	0.0221500i
$872$		0			0
$873$	−1.93688	+	1.40723i	−0.0655535	+	0.0476274i
$874$		0			0
$875$	−3.59127			−0.121407
$876$		0			0
$877$	9.83740	−	30.2764i	0.332185	−	1.02236i	−0.635907	−	0.771766i	$-0.719374\pi$
$877$	9.83740	−	30.2764i	0.332185	−	1.02236i	0.968092	−	0.250595i	$-0.0806264\pi$
$878$		0			0
$879$	−4.05126	−	12.4685i	−0.136646	−	0.420552i
$880$		0			0
$881$	5.41672	−	16.6710i	0.182494	−	0.561659i	−0.817402	−	0.576068i	$-0.804587\pi$
$881$	5.41672	−	16.6710i	0.182494	−	0.561659i	0.999896	+	0.0144085i	$0.00458652\pi$
$882$		0			0
$883$	−14.9659	+	46.0603i	−0.503643	+	1.55005i	0.299398	+	0.954128i	$0.403214\pi$
$883$	−14.9659	+	46.0603i	−0.503643	+	1.55005i	−0.803040	+	0.595925i	$0.796786\pi$
$884$		0			0
$885$	−10.2058	−	7.41497i	−0.343065	−	0.249251i
$886$		0			0
$887$	21.6459	−	15.7267i	0.726800	−	0.528051i	−0.161750	−	0.986832i	$-0.551714\pi$
$887$	21.6459	−	15.7267i	0.726800	−	0.528051i	0.888549	+	0.458781i	$0.151714\pi$
$888$		0			0
$889$	22.0298	+	67.8008i	0.738856	+	2.27397i
$890$		0			0
$891$	7.06862	+	5.13565i	0.236808	+	0.172051i
$892$		0			0
$893$	−45.1212			−1.50992
$894$		0			0
$895$	1.41948	−	4.36872i	0.0474481	−	0.146030i
$896$		0			0
$897$	0.859554	−	0.624503i	0.0286997	−	0.0208515i
$898$		0			0
$899$	38.0441			1.26884
$900$		0			0
$901$	29.7340			0.990583
$902$		0			0
$903$	45.8472			1.52570
$904$		0			0
$905$	−2.90493			−0.0965632
$906$		0			0
$907$	−15.6204	+	11.3489i	−0.518667	+	0.376834i	−0.816102	−	0.577909i	$-0.803869\pi$
$907$	−15.6204	+	11.3489i	−0.518667	+	0.376834i	0.297434	+	0.954742i	$0.403869\pi$
$908$		0			0
$909$	0.516210	−	1.58873i	0.0171216	−	0.0526949i
$910$		0			0
$911$	−36.8878			−1.22215			−0.611074	−	0.791574i	$-0.709262\pi$
$911$	−36.8878			−1.22215			−0.611074	+	0.791574i	$0.709262\pi$
$912$		0			0
$913$	18.9059	+	13.7360i	0.625695	+	0.454594i
$914$		0			0
$915$	−2.31144	−	7.11389i	−0.0764140	−	0.235178i
$916$		0			0
$917$	−47.3528	+	34.4038i	−1.56373	+	1.13611i
$918$		0			0
$919$	−20.0401	−	14.5600i	−0.661063	−	0.480291i	0.205959	−	0.978561i	$-0.433969\pi$
$919$	−20.0401	−	14.5600i	−0.661063	−	0.480291i	−0.867022	+	0.498270i	$0.833969\pi$
$920$		0			0
$921$	9.46493	−	29.1301i	0.311880	−	0.959869i
$922$		0			0
$923$	−0.212096	+	0.652763i	−0.00698121	+	0.0214860i
$924$		0			0
$925$	7.74704e−5	0	0.000238429i	2.54721e−6	0	7.83951e-6i
$926$		0			0
$927$	−0.854552	+	2.63004i	−0.0280672	+	0.0863819i
$928$		0			0
$929$	2.82394			0.0926505			0.0463253	−	0.998926i	$-0.485249\pi$
$929$	2.82394			0.0926505			0.0463253	+	0.998926i	$0.485249\pi$
$930$		0			0
$931$	20.4922	−	14.8885i	0.671606	−	0.487950i
$932$		0			0
$933$	22.8212	+	16.5806i	0.747133	+	0.542824i
$934$		0			0
$935$	7.01781	+	5.09874i	0.229507	+	0.166747i
$936$		0			0
$937$	−10.3701	−	31.9158i	−0.338776	−	1.04265i	−0.964832	−	0.262867i	$-0.915332\pi$
$937$	−10.3701	−	31.9158i	−0.338776	−	1.04265i	0.626056	−	0.779778i	$-0.284668\pi$
$938$		0			0
$939$	25.3024	−	18.3832i	0.825711	−	0.599914i
$940$		0			0
$941$	5.64538	+	17.3747i	0.184034	+	0.566399i	0.999930	−	0.0117995i	$-0.00375598\pi$
$941$	5.64538	+	17.3747i	0.184034	+	0.566399i	−0.815896	+	0.578198i	$0.803756\pi$
$942$		0			0
$943$	12.4017	+	32.8603i	0.403856	+	1.07008i
$944$		0			0
$945$	6.25492	+	19.2507i	0.203473	+	0.626224i
$946$		0			0
$947$	14.7752	−	10.7348i	0.480131	−	0.348835i	−0.321246	−	0.946996i	$-0.604102\pi$
$947$	14.7752	−	10.7348i	0.480131	−	0.348835i	0.801376	+	0.598161i	$0.204102\pi$
$948$		0			0
$949$	0.105913	+	0.325967i	0.00343809	+	0.0105813i
$950$		0			0
$951$	9.16264	+	6.65704i	0.297119	+	0.215869i
$952$		0			0
$953$	8.63936	+	6.27687i	0.279856	+	0.203328i	0.718855	−	0.695160i	$-0.244667\pi$
$953$	8.63936	+	6.27687i	0.279856	+	0.203328i	−0.438998	+	0.898488i	$0.644667\pi$
$954$		0			0
$955$	0.832048	−	0.604518i	0.0269244	−	0.0195617i
$956$		0			0
$957$	27.6070			0.892406
$958$		0			0
$959$	0.972790	−	2.99394i	0.0314130	−	0.0966793i
$960$		0			0
$961$	−4.50600	−	13.8680i	−0.145355	−	0.447356i
$962$		0			0
$963$	6.67818	−	20.5533i	0.215201	−	0.662322i
$964$		0			0
$965$	−7.16415	+	22.0490i	−0.230622	+	0.709782i
$966$		0			0
$967$	−38.5792	−	28.0294i	−1.24062	−	0.901365i	−0.242983	−	0.970031i	$-0.578126\pi$
$967$	−38.5792	−	28.0294i	−1.24062	−	0.901365i	−0.997640	+	0.0686652i	$0.978126\pi$
$968$		0			0
$969$	−18.5168	+	13.4532i	−0.594844	+	0.432180i
$970$		0			0
$971$	−11.5005	−	35.3949i	−0.369069	−	1.13588i	−0.947394	−	0.320070i	$-0.896293\pi$
$971$	−11.5005	−	35.3949i	−0.369069	−	1.13588i	0.578325	−	0.815807i	$-0.303707\pi$
$972$		0			0
$973$	−2.11820	−	1.53896i	−0.0679063	−	0.0493368i
$974$		0			0
$975$	−0.193696			−0.00620322
$976$		0			0
$977$	8.09379	−	24.9101i	0.258943	−	0.796946i	−0.734084	−	0.679059i	$-0.762388\pi$
$977$	8.09379	−	24.9101i	0.258943	−	0.796946i	0.993027	−	0.117887i	$-0.0376120\pi$
$978$		0			0
$979$	−29.1236	+	21.1595i	−0.930793	+	0.676261i
$980$		0			0
$981$	−2.44479			−0.0780561
$982$		0			0
$983$	−6.85447			−0.218624			−0.109312	−	0.994008i	$-0.534865\pi$
$983$	−6.85447			−0.218624			−0.109312	+	0.994008i	$0.534865\pi$
$984$		0			0
$985$	−0.268521			−0.00855578
$986$		0			0
$987$	−50.7029			−1.61389
$988$		0			0
$989$	42.1532	−	30.6261i	1.34039	−	0.973853i
$990$		0			0
$991$	13.3019	−	40.9389i	0.422548	−	1.30047i	−0.482775	−	0.875744i	$-0.660371\pi$
$991$	13.3019	−	40.9389i	0.422548	−	1.30047i	0.905323	−	0.424724i	$-0.139629\pi$
$992$		0			0
$993$	−35.7998			−1.13607
$994$		0			0
$995$	−21.0373	−	15.2845i	−0.666929	−	0.484552i
$996$		0			0
$997$	−18.8798	−	58.1059i	−0.597928	−	1.84023i	−0.539577	−	0.841936i	$-0.681416\pi$
$997$	−18.8798	−	58.1059i	−0.597928	−	1.84023i	−0.0583506	−	0.998296i	$-0.518584\pi$
$998$		0			0
$999$	0.00114315		0.000830546i	3.61676e−5		2.62773e-5i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.u.a.141.5	✓	24
41.16	even	5	inner	820.2.u.a.221.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.u.a.141.5	✓	24	1.1	even	1	trivial
820.2.u.a.221.5	yes	24	41.16	even	5	inner

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.u (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+1.34396 q^{3} +(-0.809017 + 0.587785i) q^{5} +(-1.10976 + 3.41550i) q^{7} -1.19376 q^{9} +(-1.76997 - 1.28596i) q^{11} +(-0.0445363 - 0.137069i) q^{13} +(-1.08729 + 0.789962i) q^{15} +(3.20771 + 2.33053i) q^{17} +(-1.32729 + 4.08498i) q^{19} +(-1.49148 + 4.59031i) q^{21} +(1.69503 + 5.21678i) q^{23} +(0.309017 - 0.951057i) q^{25} -5.63626 q^{27} +(-7.59594 + 5.51877i) q^{29} +(-3.27809 - 2.38168i) q^{31} +(-2.37877 - 1.72828i) q^{33} +(-1.10976 - 3.41550i) q^{35} +(-0.000202820 + 0.000147358i) q^{37} +(-0.0598552 - 0.184215i) q^{39} +(6.39614 - 0.299050i) q^{41} +(-2.93535 - 9.03406i) q^{43} +(0.965774 - 0.701676i) q^{45} +(3.24623 + 9.99087i) q^{47} +(-4.77096 - 3.46631i) q^{49} +(4.31104 + 3.13215i) q^{51} +(6.06700 - 4.40793i) q^{53} +2.18780 q^{55} +(-1.78383 + 5.49006i) q^{57} +(2.90058 + 8.92708i) q^{59} +(-1.71987 + 5.29322i) q^{61} +(1.32479 - 4.07730i) q^{63} +(0.116598 + 0.0847132i) q^{65} +(6.24294 - 4.53576i) q^{67} +(2.27806 + 7.01116i) q^{69} +(-3.85278 - 2.79921i) q^{71} -2.37813 q^{73} +(0.415308 - 1.27819i) q^{75} +(6.35643 - 4.61822i) q^{77} +17.0749 q^{79} -3.99365 q^{81} -10.6815 q^{83} -3.96494 q^{85} +(-10.2087 + 7.41703i) q^{87} +(5.08466 - 15.6490i) q^{89} +0.517584 q^{91} +(-4.40564 - 3.20088i) q^{93} +(-1.32729 - 4.08498i) q^{95} +(1.62250 - 1.17882i) q^{97} +(2.11292 + 1.53513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} - 6 q^{5} + 5 q^{7} + 18 q^{9} - 7 q^{11} - 5 q^{13} + 2 q^{15} + 3 q^{17} - q^{19} + 2 q^{21} + 20 q^{23} - 6 q^{25} + 20 q^{27} - 15 q^{29} - q^{31} - 6 q^{33} + 5 q^{35} + q^{37} + 28 q^{41}+ \cdots + 34 q^{99}+O(q^{100}) \) 24 * q + 2 * q^3 - 6 * q^5 + 5 * q^7 + 18 * q^9 - 7 * q^11 - 5 * q^13 + 2 * q^15 + 3 * q^17 - q^19 + 2 * q^21 + 20 * q^23 - 6 * q^25 + 20 * q^27 - 15 * q^29 - q^31 - 6 * q^33 + 5 * q^35 + q^37 + 28 * q^41 - 4 * q^43 + 3 * q^45 + 3 * q^47 + 3 * q^49 + 37 * q^51 + 29 * q^53 - 12 * q^55 + 17 * q^57 - 4 * q^59 - 14 * q^61 - 10 * q^63 + 5 * q^65 - 14 * q^67 - 26 * q^69 + q^71 - 84 * q^73 - 3 * q^75 + 24 * q^77 + 18 * q^79 - 40 * q^81 - 6 * q^83 - 12 * q^85 + 39 * q^87 + 12 * q^89 - 2 * q^91 - 58 * q^93 - q^95 - 20 * q^97 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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