LMFDB - Embedded newform 726.2.e.h.511.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(487,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("726.487"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.e (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1,1,-1,0,1,0,-1,-1,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			511.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	726.511
Dual form			726.2.e.h.493.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{6} +(-0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} -1.00000 q^{12} +(1.85410 + 5.70634i) q^{13} +(0.309017 - 0.951057i) q^{16} +(-1.85410 + 5.70634i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(-4.85410 - 3.52671i) q^{19} +6.00000 q^{23} +(-0.309017 - 0.951057i) q^{24} +(4.04508 + 2.93893i) q^{25} +(-4.85410 + 3.52671i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-4.85410 + 3.52671i) q^{29} +(1.23607 + 3.80423i) q^{31} +1.00000 q^{32} -6.00000 q^{34} +(-0.809017 - 0.587785i) q^{36} +(1.61803 - 1.17557i) q^{37} +(1.85410 - 5.70634i) q^{38} +(-1.85410 + 5.70634i) q^{39} +(-4.85410 - 3.52671i) q^{41} +6.00000 q^{43} +(1.85410 + 5.70634i) q^{46} +(-4.85410 - 3.52671i) q^{47} +(0.809017 - 0.587785i) q^{48} +(-2.16312 + 6.65740i) q^{49} +(-1.54508 + 4.75528i) q^{50} +(-4.85410 + 3.52671i) q^{51} +(-4.85410 - 3.52671i) q^{52} +(-3.70820 - 11.4127i) q^{53} -1.00000 q^{54} +(-1.85410 - 5.70634i) q^{57} +(-4.85410 - 3.52671i) q^{58} +(9.70820 - 7.05342i) q^{59} +(1.85410 - 5.70634i) q^{61} +(-3.23607 + 2.35114i) q^{62} +(0.309017 + 0.951057i) q^{64} +4.00000 q^{67} +(-1.85410 - 5.70634i) q^{68} +(4.85410 + 3.52671i) q^{69} +(-1.85410 + 5.70634i) q^{71} +(0.309017 - 0.951057i) q^{72} +(9.70820 - 7.05342i) q^{73} +(1.61803 + 1.17557i) q^{74} +(1.54508 + 4.75528i) q^{75} +6.00000 q^{76} -6.00000 q^{78} +(3.70820 + 11.4127i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(1.85410 - 5.70634i) q^{82} +(1.85410 + 5.70634i) q^{86} -6.00000 q^{87} -6.00000 q^{89} +(-4.85410 + 3.52671i) q^{92} +(-1.23607 + 3.80423i) q^{93} +(1.85410 - 5.70634i) q^{94} +(0.809017 + 0.587785i) q^{96} +(-3.09017 - 9.51057i) q^{97} -7.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} - q^{4} + q^{6} - q^{8} - q^{9} - 4 q^{12} - 6 q^{13} - q^{16} + 6 q^{17} - q^{18} - 6 q^{19} + 24 q^{23} + q^{24} + 5 q^{25} - 6 q^{26} + q^{27} - 6 q^{29} - 4 q^{31} + 4 q^{32}+ \cdots - 28 q^{98}+O(q^{100}) $ 4 * q - q^2 + q^3 - q^4 + q^6 - q^8 - q^9 - 4 * q^12 - 6 * q^13 - q^16 + 6 * q^17 - q^18 - 6 * q^19 + 24 * q^23 + q^24 + 5 * q^25 - 6 * q^26 + q^27 - 6 * q^29 - 4 * q^31 + 4 * q^32 - 24 * q^34 - q^36 + 2 * q^37 - 6 * q^38 + 6 * q^39 - 6 * q^41 + 24 * q^43 - 6 * q^46 - 6 * q^47 + q^48 + 7 * q^49 + 5 * q^50 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 4 * q^54 + 6 * q^57 - 6 * q^58 + 12 * q^59 - 6 * q^61 - 4 * q^62 - q^64 + 16 * q^67 + 6 * q^68 + 6 * q^69 + 6 * q^71 - q^72 + 12 * q^73 + 2 * q^74 - 5 * q^75 + 24 * q^76 - 24 * q^78 - 12 * q^79 - q^81 - 6 * q^82 - 6 * q^86 - 24 * q^87 - 24 * q^89 - 6 * q^92 + 4 * q^93 - 6 * q^94 + q^96 + 10 * q^97 - 28 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$5$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$6$	−0.309017	+	0.951057i	−0.126156	+	0.388267i
$7$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$7$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$		0			0
$11$		0			0
$12$	−1.00000			−0.288675
$13$	1.85410	+	5.70634i	0.514235	+	1.58265i	0.784669	+	0.619915i	$0.212833\pi$
$13$	1.85410	+	5.70634i	0.514235	+	1.58265i	−0.270434	+	0.962739i	$0.587167\pi$
$14$		0			0
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−1.85410	+	5.70634i	−0.449686	+	1.38399i	0.427576	+	0.903979i	$0.359367\pi$
$17$	−1.85410	+	5.70634i	−0.449686	+	1.38399i	−0.877262	+	0.480011i	$0.840633\pi$
$18$	−0.809017	+	0.587785i	−0.190687	+	0.138542i
$19$	−4.85410	−	3.52671i	−1.11361	−	0.809083i	−0.130379	−	0.991464i	$-0.541620\pi$
$19$	−4.85410	−	3.52671i	−1.11361	−	0.809083i	−0.983228	+	0.182381i	$0.941620\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$	−0.309017	−	0.951057i	−0.0630778	−	0.194134i
$25$	4.04508	+	2.93893i	0.809017	+	0.587785i
$26$	−4.85410	+	3.52671i	−0.951968	+	0.691645i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$		0			0
$29$	−4.85410	+	3.52671i	−0.901384	+	0.654894i	−0.938821	−	0.344405i	$-0.888081\pi$
$29$	−4.85410	+	3.52671i	−0.901384	+	0.654894i	0.0374370	+	0.999299i	$0.488081\pi$
$30$		0			0
$31$	1.23607	+	3.80423i	0.222004	+	0.683259i	0.998582	+	0.0532375i	$0.0169540\pi$
$31$	1.23607	+	3.80423i	0.222004	+	0.683259i	−0.776578	+	0.630022i	$0.783046\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−6.00000			−1.02899
$35$		0			0
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	1.61803	−	1.17557i	0.266003	−	0.193263i	−0.446786	−	0.894641i	$-0.647432\pi$
$37$	1.61803	−	1.17557i	0.266003	−	0.193263i	0.712789	+	0.701378i	$0.247432\pi$
$38$	1.85410	−	5.70634i	0.300775	−	0.925690i
$39$	−1.85410	+	5.70634i	−0.296894	+	0.913746i
$40$		0			0
$41$	−4.85410	−	3.52671i	−0.758083	−	0.550780i	0.140238	−	0.990118i	$-0.455213\pi$
$41$	−4.85410	−	3.52671i	−0.758083	−	0.550780i	−0.898322	+	0.439338i	$0.855213\pi$
$42$		0			0
$43$	6.00000			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$44$		0			0
$45$		0			0
$46$	1.85410	+	5.70634i	0.273372	+	0.841354i
$47$	−4.85410	−	3.52671i	−0.708044	−	0.514424i	0.174498	−	0.984657i	$-0.444170\pi$
$47$	−4.85410	−	3.52671i	−0.708044	−	0.514424i	−0.882542	+	0.470234i	$0.844170\pi$
$48$	0.809017	−	0.587785i	0.116772	−	0.0848395i
$49$	−2.16312	+	6.65740i	−0.309017	+	0.951057i
$50$	−1.54508	+	4.75528i	−0.218508	+	0.672499i
$51$	−4.85410	+	3.52671i	−0.679710	+	0.493838i
$52$	−4.85410	−	3.52671i	−0.673143	−	0.489067i
$53$	−3.70820	−	11.4127i	−0.509361	−	1.56765i	−0.793313	−	0.608814i	$-0.791646\pi$
$53$	−3.70820	−	11.4127i	−0.509361	−	1.56765i	0.283952	−	0.958838i	$-0.408354\pi$
$54$	−1.00000			−0.136083
$55$		0			0
$56$		0			0
$57$	−1.85410	−	5.70634i	−0.245582	−	0.755823i
$58$	−4.85410	−	3.52671i	−0.637375	−	0.463080i
$59$	9.70820	−	7.05342i	1.26390	−	0.918277i	0.264958	−	0.964260i	$-0.414642\pi$
$59$	9.70820	−	7.05342i	1.26390	−	0.918277i	0.998942	+	0.0459824i	$0.0146418\pi$
$60$		0			0
$61$	1.85410	−	5.70634i	0.237393	−	0.730622i	−0.759401	−	0.650622i	$-0.774508\pi$
$61$	1.85410	−	5.70634i	0.237393	−	0.730622i	0.996795	−	0.0799995i	$-0.0254919\pi$
$62$	−3.23607	+	2.35114i	−0.410981	+	0.298595i
$63$		0			0
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$		0			0
$66$		0			0
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$	−1.85410	−	5.70634i	−0.224843	−	0.691995i
$69$	4.85410	+	3.52671i	0.584365	+	0.424566i
$70$		0			0
$71$	−1.85410	+	5.70634i	−0.220041	+	0.677218i	0.778716	+	0.627377i	$0.215871\pi$
$71$	−1.85410	+	5.70634i	−0.220041	+	0.677218i	−0.998757	+	0.0498409i	$0.984129\pi$
$72$	0.309017	−	0.951057i	0.0364180	−	0.112083i
$73$	9.70820	−	7.05342i	1.13626	−	0.825541i	0.149666	−	0.988737i	$-0.452180\pi$
$73$	9.70820	−	7.05342i	1.13626	−	0.825541i	0.986594	+	0.163196i	$0.0521803\pi$
$74$	1.61803	+	1.17557i	0.188093	+	0.136657i
$75$	1.54508	+	4.75528i	0.178411	+	0.549093i
$76$	6.00000			0.688247
$77$		0			0
$78$	−6.00000			−0.679366
$79$	3.70820	+	11.4127i	0.417206	+	1.28403i	0.910263	+	0.414030i	$0.135879\pi$
$79$	3.70820	+	11.4127i	0.417206	+	1.28403i	−0.493058	+	0.869997i	$0.664121\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	1.85410	−	5.70634i	0.204751	−	0.630160i
$83$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$83$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$84$		0			0
$85$		0			0
$86$	1.85410	+	5.70634i	0.199933	+	0.615330i
$87$	−6.00000			−0.643268
$88$		0			0
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$		0			0
$92$	−4.85410	+	3.52671i	−0.506075	+	0.367685i
$93$	−1.23607	+	3.80423i	−0.128174	+	0.394480i
$94$	1.85410	−	5.70634i	0.191236	−	0.588564i
$95$		0			0
$96$	0.809017	+	0.587785i	0.0825700	+	0.0599906i
$97$	−3.09017	−	9.51057i	−0.313759	−	0.965652i	−0.976262	−	0.216592i	$-0.930506\pi$
$97$	−3.09017	−	9.51057i	−0.313759	−	0.965652i	0.662503	−	0.749059i	$-0.269494\pi$
$98$	−7.00000			−0.707107
$99$		0			0
$100$	−5.00000			−0.500000
$101$	−1.85410	−	5.70634i	−0.184490	−	0.567802i	0.815449	−	0.578829i	$-0.196490\pi$
$101$	−1.85410	−	5.70634i	−0.184490	−	0.567802i	−0.999939	+	0.0110267i	$0.996490\pi$
$102$	−4.85410	−	3.52671i	−0.480628	−	0.349196i
$103$	3.23607	−	2.35114i	0.318859	−	0.231665i	−0.416829	−	0.908985i	$-0.636859\pi$
$103$	3.23607	−	2.35114i	0.318859	−	0.231665i	0.735689	+	0.677320i	$0.236859\pi$
$104$	1.85410	−	5.70634i	0.181810	−	0.559553i
$105$		0			0
$106$	9.70820	−	7.05342i	0.942944	−	0.685089i
$107$	9.70820	+	7.05342i	0.938527	+	0.681880i	0.948066	−	0.318074i	$-0.103036\pi$
$107$	9.70820	+	7.05342i	0.938527	+	0.681880i	−0.00953827	+	0.999955i	$0.503036\pi$
$108$	−0.309017	−	0.951057i	−0.0297352	−	0.0915155i
$109$	6.00000			0.574696			0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000			0.574696			0.287348	+	0.957826i	$0.407226\pi$
$110$		0			0
$111$	2.00000			0.189832
$112$		0			0
$113$	−4.85410	−	3.52671i	−0.456636	−	0.331765i	0.335575	−	0.942014i	$-0.391070\pi$
$113$	−4.85410	−	3.52671i	−0.456636	−	0.331765i	−0.792210	+	0.610249i	$0.791070\pi$
$114$	4.85410	−	3.52671i	0.454628	−	0.330307i
$115$		0			0
$116$	1.85410	−	5.70634i	0.172149	−	0.529820i
$117$	−4.85410	+	3.52671i	−0.448762	+	0.326045i
$118$	9.70820	+	7.05342i	0.893713	+	0.649320i
$119$		0			0
$120$		0			0
$121$		0			0
$122$	6.00000			0.543214
$123$	−1.85410	−	5.70634i	−0.167179	−	0.514523i
$124$	−3.23607	−	2.35114i	−0.290607	−	0.211139i
$125$		0			0
$126$		0			0
$127$	3.70820	−	11.4127i	0.329050	−	1.01271i	−0.640529	−	0.767934i	$-0.721285\pi$
$127$	3.70820	−	11.4127i	0.329050	−	1.01271i	0.969579	−	0.244778i	$-0.0787150\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	4.85410	+	3.52671i	0.427380	+	0.310510i
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		0			0
$133$		0			0
$134$	1.23607	+	3.80423i	0.106780	+	0.328635i
$135$		0			0
$136$	4.85410	−	3.52671i	0.416236	−	0.302413i
$137$	−1.85410	+	5.70634i	−0.158407	+	0.487525i	−0.998490	−	0.0549317i	$-0.982506\pi$
$137$	−1.85410	+	5.70634i	−0.158407	+	0.487525i	0.840083	+	0.542457i	$0.182506\pi$
$138$	−1.85410	+	5.70634i	−0.157832	+	0.485756i
$139$	14.5623	−	10.5801i	1.23516	−	0.897395i	0.237893	−	0.971291i	$-0.423543\pi$
$139$	14.5623	−	10.5801i	1.23516	−	0.897395i	0.997266	+	0.0738961i	$0.0235433\pi$
$140$		0			0
$141$	−1.85410	−	5.70634i	−0.156144	−	0.480560i
$142$	−6.00000			−0.503509
$143$		0			0
$144$	1.00000			0.0833333
$145$		0			0
$146$	9.70820	+	7.05342i	0.803457	+	0.583745i
$147$	−5.66312	+	4.11450i	−0.467086	+	0.339358i
$148$	−0.618034	+	1.90211i	−0.0508021	+	0.156353i
$149$	1.85410	−	5.70634i	0.151894	−	0.467482i	−0.845939	−	0.533280i	$-0.820959\pi$
$149$	1.85410	−	5.70634i	0.151894	−	0.467482i	0.997833	+	0.0657982i	$0.0209593\pi$
$150$	−4.04508	+	2.93893i	−0.330280	+	0.239962i
$151$	9.70820	+	7.05342i	0.790042	+	0.573999i	0.907976	−	0.419022i	$-0.137627\pi$
$151$	9.70820	+	7.05342i	0.790042	+	0.573999i	−0.117934	+	0.993021i	$0.537627\pi$
$152$	1.85410	+	5.70634i	0.150388	+	0.462845i
$153$	−6.00000			−0.485071
$154$		0			0
$155$		0			0
$156$	−1.85410	−	5.70634i	−0.148447	−	0.456873i
$157$	11.3262	+	8.22899i	0.903932	+	0.656745i	0.939473	−	0.342623i	$-0.111315\pi$
$157$	11.3262	+	8.22899i	0.903932	+	0.656745i	−0.0355408	+	0.999368i	$0.511315\pi$
$158$	−9.70820	+	7.05342i	−0.772343	+	0.561140i
$159$	3.70820	−	11.4127i	0.294080	−	0.905084i
$160$		0			0
$161$		0			0
$162$	−0.809017	−	0.587785i	−0.0635624	−	0.0461808i
$163$	6.18034	+	19.0211i	0.484082	+	1.48985i	0.833307	+	0.552811i	$0.186445\pi$
$163$	6.18034	+	19.0211i	0.484082	+	1.48985i	−0.349225	+	0.937039i	$0.613555\pi$
$164$	6.00000			0.468521
$165$		0			0
$166$		0			0
$167$	−7.41641	−	22.8254i	−0.573899	−	1.76628i	−0.639898	−	0.768459i	$-0.721024\pi$
$167$	−7.41641	−	22.8254i	−0.573899	−	1.76628i	0.0659996	−	0.997820i	$-0.478976\pi$
$168$		0			0
$169$	−18.6074	+	13.5191i	−1.43134	+	1.03993i
$170$		0			0
$171$	1.85410	−	5.70634i	0.141787	−	0.436375i
$172$	−4.85410	+	3.52671i	−0.370122	+	0.268909i
$173$	14.5623	+	10.5801i	1.10715	+	0.804393i	0.982213	−	0.187772i	$-0.0601265\pi$
$173$	14.5623	+	10.5801i	1.10715	+	0.804393i	0.124939	+	0.992164i	$0.460127\pi$
$174$	−1.85410	−	5.70634i	−0.140559	−	0.432596i
$175$		0			0
$176$		0			0
$177$	12.0000			0.901975
$178$	−1.85410	−	5.70634i	−0.138971	−	0.427708i
$179$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$179$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$180$		0			0
$181$	0.618034	−	1.90211i	0.0459381	−	0.141383i	−0.925457	−	0.378854i	$-0.876318\pi$
$181$	0.618034	−	1.90211i	0.0459381	−	0.141383i	0.971395	+	0.237471i	$0.0763184\pi$
$182$		0			0
$183$	4.85410	−	3.52671i	0.358826	−	0.260702i
$184$	−4.85410	−	3.52671i	−0.357849	−	0.259993i
$185$		0			0
$186$	−4.00000			−0.293294
$187$		0			0
$188$	6.00000			0.437595
$189$		0			0
$190$		0			0
$191$	14.5623	−	10.5801i	1.05369	−	0.765552i	0.0807805	−	0.996732i	$-0.474259\pi$
$191$	14.5623	−	10.5801i	1.05369	−	0.765552i	0.972911	+	0.231180i	$0.0742587\pi$
$192$	−0.309017	+	0.951057i	−0.0223014	+	0.0686366i
$193$	3.70820	−	11.4127i	0.266922	−	0.821503i	−0.724322	−	0.689462i	$-0.757847\pi$
$193$	3.70820	−	11.4127i	0.266922	−	0.821503i	0.991244	−	0.132041i	$-0.0421529\pi$
$194$	8.09017	−	5.87785i	0.580840	−	0.422005i
$195$		0			0
$196$	−2.16312	−	6.65740i	−0.154508	−	0.475528i
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	16.0000			1.13421			0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000			1.13421			0.567105	+	0.823646i	$0.308063\pi$
$200$	−1.54508	−	4.75528i	−0.109254	−	0.336249i
$201$	3.23607	+	2.35114i	0.228255	+	0.165837i
$202$	4.85410	−	3.52671i	0.341533	−	0.248139i
$203$		0			0
$204$	1.85410	−	5.70634i	0.129813	−	0.399524i
$205$		0			0
$206$	3.23607	+	2.35114i	0.225468	+	0.163812i
$207$	1.85410	+	5.70634i	0.128869	+	0.396618i
$208$	6.00000			0.416025
$209$		0			0
$210$		0			0
$211$	−1.85410	−	5.70634i	−0.127642	−	0.392841i	0.866731	−	0.498775i	$-0.166217\pi$
$211$	−1.85410	−	5.70634i	−0.127642	−	0.392841i	−0.994373	+	0.105934i	$0.966217\pi$
$212$	9.70820	+	7.05342i	0.666762	+	0.484431i
$213$	−4.85410	+	3.52671i	−0.332598	+	0.241646i
$214$	−3.70820	+	11.4127i	−0.253488	+	0.780155i
$215$		0			0
$216$	0.809017	−	0.587785i	0.0550466	−	0.0399937i
$217$		0			0
$218$	1.85410	+	5.70634i	0.125576	+	0.386482i
$219$	12.0000			0.810885
$220$		0			0
$221$	−36.0000			−2.42162
$222$	0.618034	+	1.90211i	0.0414797	+	0.127661i
$223$	−6.47214	−	4.70228i	−0.433406	−	0.314888i	0.349603	−	0.936898i	$-0.386316\pi$
$223$	−6.47214	−	4.70228i	−0.433406	−	0.314888i	−0.783009	+	0.622010i	$0.786316\pi$
$224$		0			0
$225$	−1.54508	+	4.75528i	−0.103006	+	0.317019i
$226$	1.85410	−	5.70634i	0.123333	−	0.379580i
$227$	−9.70820	+	7.05342i	−0.644356	+	0.468152i	−0.861344	−	0.508022i	$-0.830377\pi$
$227$	−9.70820	+	7.05342i	−0.644356	+	0.468152i	0.216988	+	0.976174i	$0.430377\pi$
$228$	4.85410	+	3.52671i	0.321471	+	0.233562i
$229$	−4.32624	−	13.3148i	−0.285886	−	0.879866i	−0.986132	−	0.165964i	$-0.946926\pi$
$229$	−4.32624	−	13.3148i	−0.285886	−	0.879866i	0.700246	−	0.713902i	$-0.253074\pi$
$230$		0			0
$231$		0			0
$232$	6.00000			0.393919
$233$	1.85410	+	5.70634i	0.121466	+	0.373835i	0.993241	−	0.116073i	$-0.0370306\pi$
$233$	1.85410	+	5.70634i	0.121466	+	0.373835i	−0.871774	+	0.489907i	$0.837031\pi$
$234$	−4.85410	−	3.52671i	−0.317323	−	0.230548i
$235$		0			0
$236$	−3.70820	+	11.4127i	−0.241384	+	0.742902i
$237$	−3.70820	+	11.4127i	−0.240874	+	0.741333i
$238$		0			0
$239$	−19.4164	−	14.1068i	−1.25594	−	0.912496i	−0.257392	−	0.966307i	$-0.582863\pi$
$239$	−19.4164	−	14.1068i	−1.25594	−	0.912496i	−0.998551	+	0.0538111i	$0.982863\pi$
$240$		0			0
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$	1.85410	+	5.70634i	0.118697	+	0.365311i
$245$		0			0
$246$	4.85410	−	3.52671i	0.309486	−	0.224855i
$247$	11.1246	−	34.2380i	0.707842	−	2.17851i
$248$	1.23607	−	3.80423i	0.0784904	−	0.241569i
$249$		0			0
$250$		0			0
$251$	7.41641	+	22.8254i	0.468120	+	1.44072i	0.855017	+	0.518601i	$0.173547\pi$
$251$	7.41641	+	22.8254i	0.468120	+	1.44072i	−0.386897	+	0.922123i	$0.626453\pi$
$252$		0			0
$253$		0			0
$254$	12.0000			0.752947
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−14.5623	+	10.5801i	−0.908372	+	0.659971i	−0.940603	−	0.339510i	$-0.889739\pi$
$257$	−14.5623	+	10.5801i	−0.908372	+	0.659971i	0.0322308	+	0.999480i	$0.489739\pi$
$258$	−1.85410	+	5.70634i	−0.115431	+	0.355261i
$259$		0			0
$260$		0			0
$261$	−4.85410	−	3.52671i	−0.300461	−	0.218298i
$262$	−3.70820	−	11.4127i	−0.229094	−	0.705078i
$263$	24.0000			1.47990			0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000			1.47990			0.739952	+	0.672660i	$0.234848\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−4.85410	−	3.52671i	−0.297066	−	0.215831i
$268$	−3.23607	+	2.35114i	−0.197674	+	0.143619i
$269$	3.70820	−	11.4127i	0.226093	−	0.695843i	−0.772086	−	0.635519i	$-0.780786\pi$
$269$	3.70820	−	11.4127i	0.226093	−	0.695843i	0.998179	−	0.0603247i	$-0.0192136\pi$
$270$		0			0
$271$	−9.70820	+	7.05342i	−0.589731	+	0.428465i	−0.842219	−	0.539135i	$-0.818751\pi$
$271$	−9.70820	+	7.05342i	−0.589731	+	0.428465i	0.252488	+	0.967600i	$0.418751\pi$
$272$	4.85410	+	3.52671i	0.294323	+	0.213838i
$273$		0			0
$274$	−6.00000			−0.362473
$275$		0			0
$276$	−6.00000			−0.361158
$277$	−1.85410	−	5.70634i	−0.111402	−	0.342861i	0.879777	−	0.475386i	$-0.157691\pi$
$277$	−1.85410	−	5.70634i	−0.111402	−	0.342861i	−0.991180	+	0.132525i	$0.957691\pi$
$278$	14.5623	+	10.5801i	0.873389	+	0.634554i
$279$	−3.23607	+	2.35114i	−0.193738	+	0.140759i
$280$		0			0
$281$	1.85410	−	5.70634i	0.110606	−	0.340412i	−0.880399	−	0.474234i	$-0.842725\pi$
$281$	1.85410	−	5.70634i	0.110606	−	0.340412i	0.991005	+	0.133822i	$0.0427251\pi$
$282$	4.85410	−	3.52671i	0.289058	−	0.210013i
$283$	−4.85410	−	3.52671i	−0.288546	−	0.209641i	0.434090	−	0.900869i	$-0.357070\pi$
$283$	−4.85410	−	3.52671i	−0.288546	−	0.209641i	−0.722637	+	0.691228i	$0.757070\pi$
$284$	−1.85410	−	5.70634i	−0.110021	−	0.338609i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.309017	+	0.951057i	0.0182090	+	0.0560415i
$289$	−15.3713	−	11.1679i	−0.904195	−	0.656936i
$290$		0			0
$291$	3.09017	−	9.51057i	0.181149	−	0.557519i
$292$	−3.70820	+	11.4127i	−0.217006	+	0.667876i
$293$	24.2705	−	17.6336i	1.41790	−	1.03016i	0.425784	−	0.904825i	$-0.359998\pi$
$293$	24.2705	−	17.6336i	1.41790	−	1.03016i	0.992114	−	0.125339i	$-0.0400018\pi$
$294$	−5.66312	−	4.11450i	−0.330280	−	0.239962i
$295$		0			0
$296$	−2.00000			−0.116248
$297$		0			0
$298$	6.00000			0.347571
$299$	11.1246	+	34.2380i	0.643353	+	1.98004i
$300$	−4.04508	−	2.93893i	−0.233543	−	0.169679i
$301$		0			0
$302$	−3.70820	+	11.4127i	−0.213383	+	0.656726i
$303$	1.85410	−	5.70634i	0.106515	−	0.327821i
$304$	−4.85410	+	3.52671i	−0.278402	+	0.202271i
$305$		0			0
$306$	−1.85410	−	5.70634i	−0.105992	−	0.326210i
$307$	−18.0000			−1.02731			−0.513657	−	0.857996i	$-0.671710\pi$
$307$	−18.0000			−1.02731			−0.513657	+	0.857996i	$0.671710\pi$
$308$		0			0
$309$	4.00000			0.227552
$310$		0			0
$311$	−4.85410	−	3.52671i	−0.275251	−	0.199981i	0.441592	−	0.897216i	$-0.354414\pi$
$311$	−4.85410	−	3.52671i	−0.275251	−	0.199981i	−0.716843	+	0.697234i	$0.754414\pi$
$312$	4.85410	−	3.52671i	0.274809	−	0.199661i
$313$	−8.03444	+	24.7275i	−0.454134	+	1.39768i	0.418016	+	0.908440i	$0.362726\pi$
$313$	−8.03444	+	24.7275i	−0.454134	+	1.39768i	−0.872149	+	0.489240i	$0.837274\pi$
$314$	−4.32624	+	13.3148i	−0.244144	+	0.751397i
$315$		0			0
$316$	−9.70820	−	7.05342i	−0.546129	−	0.396786i
$317$	−3.70820	−	11.4127i	−0.208273	−	0.641000i	−0.999563	−	0.0295583i	$-0.990590\pi$
$317$	−3.70820	−	11.4127i	−0.208273	−	0.641000i	0.791290	−	0.611442i	$-0.209410\pi$
$318$	12.0000			0.672927
$319$		0			0
$320$		0			0
$321$	3.70820	+	11.4127i	0.206972	+	0.636994i
$322$		0			0
$323$	29.1246	−	21.1603i	1.62054	−	1.17739i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	−9.27051	+	28.5317i	−0.514235	+	1.58265i
$326$	−16.1803	+	11.7557i	−0.896146	+	0.651088i
$327$	4.85410	+	3.52671i	0.268432	+	0.195028i
$328$	1.85410	+	5.70634i	0.102376	+	0.315080i
$329$		0			0
$330$		0			0
$331$	−28.0000			−1.53902			−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000			−1.53902			−0.769510	+	0.638635i	$0.779499\pi$
$332$		0			0
$333$	1.61803	+	1.17557i	0.0886677	+	0.0644209i
$334$	19.4164	−	14.1068i	1.06242	−	0.771892i
$335$		0			0
$336$		0			0
$337$	−29.1246	+	21.1603i	−1.58652	+	1.15267i	−0.677814	+	0.735233i	$0.737073\pi$
$337$	−29.1246	+	21.1603i	−1.58652	+	1.15267i	−0.908704	+	0.417440i	$0.862927\pi$
$338$	−18.6074	−	13.5191i	−1.01211	−	0.735340i
$339$	−1.85410	−	5.70634i	−0.100701	−	0.309926i
$340$		0			0
$341$		0			0
$342$	6.00000			0.324443
$343$		0			0
$344$	−4.85410	−	3.52671i	−0.261716	−	0.190148i
$345$		0			0
$346$	−5.56231	+	17.1190i	−0.299031	+	0.920324i
$347$	−7.41641	+	22.8254i	−0.398134	+	1.22533i	0.528361	+	0.849020i	$0.322807\pi$
$347$	−7.41641	+	22.8254i	−0.398134	+	1.22533i	−0.926494	+	0.376309i	$0.877193\pi$
$348$	4.85410	−	3.52671i	0.260207	−	0.189052i
$349$	−14.5623	−	10.5801i	−0.779502	−	0.566342i	0.125327	−	0.992115i	$-0.460002\pi$
$349$	−14.5623	−	10.5801i	−0.779502	−	0.566342i	−0.904830	+	0.425774i	$0.860002\pi$
$350$		0			0
$351$	−6.00000			−0.320256
$352$		0			0
$353$	−30.0000			−1.59674			−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000			−1.59674			−0.798369	+	0.602168i	$0.794304\pi$
$354$	3.70820	+	11.4127i	0.197089	+	0.606577i
$355$		0			0
$356$	4.85410	−	3.52671i	0.257267	−	0.186915i
$357$		0			0
$358$		0			0
$359$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$359$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$360$		0			0
$361$	5.25329	+	16.1680i	0.276489	+	0.850945i
$362$	2.00000			0.105118
$363$		0			0
$364$		0			0
$365$		0			0
$366$	4.85410	+	3.52671i	0.253728	+	0.184344i
$367$	−6.47214	+	4.70228i	−0.337843	+	0.245457i	−0.743751	−	0.668457i	$-0.766955\pi$
$367$	−6.47214	+	4.70228i	−0.337843	+	0.245457i	0.405908	+	0.913914i	$0.366955\pi$
$368$	1.85410	−	5.70634i	0.0966517	−	0.297463i
$369$	1.85410	−	5.70634i	0.0965207	−	0.297060i
$370$		0			0
$371$		0			0
$372$	−1.23607	−	3.80423i	−0.0640871	−	0.197240i
$373$	−6.00000			−0.310668			−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000			−0.310668			−0.155334	+	0.987862i	$0.549645\pi$
$374$		0			0
$375$		0			0
$376$	1.85410	+	5.70634i	0.0956180	+	0.294282i
$377$	−29.1246	−	21.1603i	−1.49999	−	1.08981i
$378$		0			0
$379$	6.18034	−	19.0211i	0.317463	−	0.977050i	−0.657266	−	0.753659i	$-0.728287\pi$
$379$	6.18034	−	19.0211i	0.317463	−	0.977050i	0.974729	−	0.223391i	$-0.0717128\pi$
$380$		0			0
$381$	9.70820	−	7.05342i	0.497366	−	0.361358i
$382$	14.5623	+	10.5801i	0.745072	+	0.541327i
$383$	−5.56231	−	17.1190i	−0.284221	−	0.874741i	−0.986631	−	0.162969i	$-0.947893\pi$
$383$	−5.56231	−	17.1190i	−0.284221	−	0.874741i	0.702411	−	0.711772i	$-0.252107\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	12.0000			0.610784
$387$	1.85410	+	5.70634i	0.0942493	+	0.290070i
$388$	8.09017	+	5.87785i	0.410716	+	0.298403i
$389$	−19.4164	+	14.1068i	−0.984451	+	0.715245i	−0.958699	−	0.284423i	$-0.908198\pi$
$389$	−19.4164	+	14.1068i	−0.984451	+	0.715245i	−0.0257520	+	0.999668i	$0.508198\pi$
$390$		0			0
$391$	−11.1246	+	34.2380i	−0.562596	+	1.73149i
$392$	5.66312	−	4.11450i	0.286031	−	0.207813i
$393$	−9.70820	−	7.05342i	−0.489714	−	0.355798i
$394$	−1.85410	−	5.70634i	−0.0934083	−	0.287481i
$395$		0			0
$396$		0			0
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$	4.94427	+	15.2169i	0.247834	+	0.762754i
$399$		0			0
$400$	4.04508	−	2.93893i	0.202254	−	0.146946i
$401$	−1.85410	+	5.70634i	−0.0925894	+	0.284961i	−0.986618	−	0.163049i	$-0.947867\pi$
$401$	−1.85410	+	5.70634i	−0.0925894	+	0.284961i	0.894029	+	0.448010i	$0.147867\pi$
$402$	−1.23607	+	3.80423i	−0.0616495	+	0.189738i
$403$	−19.4164	+	14.1068i	−0.967200	+	0.702712i
$404$	4.85410	+	3.52671i	0.241501	+	0.175460i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	6.00000			0.297044
$409$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$409$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$410$		0			0
$411$	−4.85410	+	3.52671i	−0.239435	+	0.173960i
$412$	−1.23607	+	3.80423i	−0.0608967	+	0.187421i
$413$		0			0
$414$	−4.85410	+	3.52671i	−0.238566	+	0.173328i
$415$		0			0
$416$	1.85410	+	5.70634i	0.0909048	+	0.279776i
$417$	18.0000			0.881464
$418$		0			0
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$		0			0
$421$	21.0344	+	15.2824i	1.02516	+	0.744819i	0.967333	−	0.253507i	$-0.0815842\pi$
$421$	21.0344	+	15.2824i	1.02516	+	0.744819i	0.0578225	+	0.998327i	$0.481584\pi$
$422$	4.85410	−	3.52671i	0.236294	−	0.171678i
$423$	1.85410	−	5.70634i	0.0901495	−	0.277452i
$424$	−3.70820	+	11.4127i	−0.180086	+	0.554249i
$425$	−24.2705	+	17.6336i	−1.17729	+	0.855353i
$426$	−4.85410	−	3.52671i	−0.235182	−	0.170870i
$427$		0			0
$428$	−12.0000			−0.580042
$429$		0			0
$430$		0			0
$431$	7.41641	+	22.8254i	0.357236	+	1.09946i	0.954702	+	0.297564i	$0.0961743\pi$
$431$	7.41641	+	22.8254i	0.357236	+	1.09946i	−0.597466	+	0.801894i	$0.703826\pi$
$432$	0.809017	+	0.587785i	0.0389238	+	0.0282798i
$433$	−1.61803	+	1.17557i	−0.0777578	+	0.0564943i	−0.625985	−	0.779835i	$-0.715303\pi$
$433$	−1.61803	+	1.17557i	−0.0777578	+	0.0564943i	0.548227	+	0.836329i	$0.315303\pi$
$434$		0			0
$435$		0			0
$436$	−4.85410	+	3.52671i	−0.232469	+	0.168899i
$437$	−29.1246	−	21.1603i	−1.39322	−	1.01223i
$438$	3.70820	+	11.4127i	0.177185	+	0.545319i
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$	−7.00000			−0.333333
$442$	−11.1246	−	34.2380i	−0.529144	−	1.62854i
$443$	9.70820	+	7.05342i	0.461251	+	0.335118i	0.794022	−	0.607889i	$-0.207984\pi$
$443$	9.70820	+	7.05342i	0.461251	+	0.335118i	−0.332771	+	0.943008i	$0.607984\pi$
$444$	−1.61803	+	1.17557i	−0.0767885	+	0.0557901i
$445$		0			0
$446$	2.47214	−	7.60845i	0.117059	−	0.360271i
$447$	4.85410	−	3.52671i	0.229591	−	0.166808i
$448$		0			0
$449$	1.85410	+	5.70634i	0.0875005	+	0.269299i	0.985227	−	0.171255i	$-0.0547822\pi$
$449$	1.85410	+	5.70634i	0.0875005	+	0.269299i	−0.897726	+	0.440554i	$0.854782\pi$
$450$	−5.00000			−0.235702
$451$		0			0
$452$	6.00000			0.282216
$453$	3.70820	+	11.4127i	0.174227	+	0.536214i
$454$	−9.70820	−	7.05342i	−0.455629	−	0.331034i
$455$		0			0
$456$	−1.85410	+	5.70634i	−0.0868263	+	0.267224i
$457$	−7.41641	+	22.8254i	−0.346925	+	1.06773i	0.613620	+	0.789601i	$0.289713\pi$
$457$	−7.41641	+	22.8254i	−0.346925	+	1.06773i	−0.960545	+	0.278124i	$0.910287\pi$
$458$	11.3262	−	8.22899i	0.529240	−	0.384516i
$459$	−4.85410	−	3.52671i	−0.226570	−	0.164613i
$460$		0			0
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$		0			0
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	1.85410	+	5.70634i	0.0860745	+	0.264910i
$465$		0			0
$466$	−4.85410	+	3.52671i	−0.224862	+	0.163372i
$467$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$467$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$468$	1.85410	−	5.70634i	0.0857059	−	0.263776i
$469$		0			0
$470$		0			0
$471$	4.32624	+	13.3148i	0.199343	+	0.613513i
$472$	−12.0000			−0.552345
$473$		0			0
$474$	−12.0000			−0.551178
$475$	−9.27051	−	28.5317i	−0.425360	−	1.30912i
$476$		0			0
$477$	9.70820	−	7.05342i	0.444508	−	0.322954i
$478$	7.41641	−	22.8254i	0.339219	−	1.04401i
$479$	7.41641	−	22.8254i	0.338864	−	1.04292i	−0.625923	−	0.779885i	$-0.715277\pi$
$479$	7.41641	−	22.8254i	0.338864	−	1.04292i	0.964787	−	0.263032i	$-0.0847225\pi$
$480$		0			0
$481$	9.70820	+	7.05342i	0.442656	+	0.321608i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$	−0.309017	−	0.951057i	−0.0140173	−	0.0431408i
$487$	−12.9443	−	9.40456i	−0.586561	−	0.426161i	0.254523	−	0.967067i	$-0.418082\pi$
$487$	−12.9443	−	9.40456i	−0.586561	−	0.426161i	−0.841083	+	0.540905i	$0.818082\pi$
$488$	−4.85410	+	3.52671i	−0.219735	+	0.159647i
$489$	−6.18034	+	19.0211i	−0.279485	+	0.860165i
$490$		0			0
$491$	29.1246	−	21.1603i	1.31438	−	0.954950i	0.314391	−	0.949293i	$-0.398200\pi$
$491$	29.1246	−	21.1603i	1.31438	−	0.954950i	0.999984	−	0.00565610i	$-0.00180040\pi$
$492$	4.85410	+	3.52671i	0.218840	+	0.158996i
$493$	−11.1246	−	34.2380i	−0.501027	−	1.54200i
$494$	36.0000			1.61972
$495$		0			0
$496$	4.00000			0.179605
$497$		0			0
$498$		0			0
$499$	−3.23607	+	2.35114i	−0.144866	+	0.105252i	−0.657858	−	0.753142i	$-0.728537\pi$
$499$	−3.23607	+	2.35114i	−0.144866	+	0.105252i	0.512992	+	0.858394i	$0.328537\pi$
$500$		0			0
$501$	7.41641	−	22.8254i	0.331341	−	1.01976i
$502$	−19.4164	+	14.1068i	−0.866597	+	0.629619i
$503$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$503$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−23.0000			−1.02147
$508$	3.70820	+	11.4127i	0.164525	+	0.506356i
$509$	9.70820	+	7.05342i	0.430309	+	0.312637i	0.781772	−	0.623564i	$-0.214316\pi$
$509$	9.70820	+	7.05342i	0.430309	+	0.312637i	−0.351464	+	0.936202i	$0.614316\pi$
$510$		0			0
$511$		0			0
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	4.85410	−	3.52671i	0.214314	−	0.155708i
$514$	−14.5623	−	10.5801i	−0.642316	−	0.466670i
$515$		0			0
$516$	−6.00000			−0.264135
$517$		0			0
$518$		0			0
$519$	5.56231	+	17.1190i	0.244158	+	0.751441i
$520$		0			0
$521$	−33.9787	+	24.6870i	−1.48863	+	1.08156i	−0.513990	+	0.857796i	$0.671833\pi$
$521$	−33.9787	+	24.6870i	−1.48863	+	1.08156i	−0.974644	+	0.223760i	$0.928167\pi$
$522$	1.85410	−	5.70634i	0.0811518	−	0.249760i
$523$	1.85410	−	5.70634i	0.0810742	−	0.249521i	−0.902301	−	0.431107i	$-0.858123\pi$
$523$	1.85410	−	5.70634i	0.0810742	−	0.249521i	0.983375	+	0.181586i	$0.0581231\pi$
$524$	9.70820	−	7.05342i	0.424105	−	0.308130i
$525$		0			0
$526$	7.41641	+	22.8254i	0.323371	+	0.995233i
$527$	−24.0000			−1.04546
$528$		0			0
$529$	13.0000			0.565217
$530$		0			0
$531$	9.70820	+	7.05342i	0.421300	+	0.306092i
$532$		0			0
$533$	11.1246	−	34.2380i	0.481860	−	1.48301i
$534$	1.85410	−	5.70634i	0.0802348	−	0.246937i
$535$		0			0
$536$	−3.23607	−	2.35114i	−0.139777	−	0.101554i
$537$		0			0
$538$	12.0000			0.517357
$539$		0			0
$540$		0			0
$541$	−5.56231	−	17.1190i	−0.239142	−	0.736004i	−0.996545	−	0.0830560i	$-0.973532\pi$
$541$	−5.56231	−	17.1190i	−0.239142	−	0.736004i	0.757403	−	0.652948i	$-0.226468\pi$
$542$	−9.70820	−	7.05342i	−0.417003	−	0.302970i
$543$	1.61803	−	1.17557i	0.0694365	−	0.0504486i
$544$	−1.85410	+	5.70634i	−0.0794940	+	0.244657i
$545$		0			0
$546$		0			0
$547$	4.85410	+	3.52671i	0.207546	+	0.150791i	0.686703	−	0.726938i	$-0.259057\pi$
$547$	4.85410	+	3.52671i	0.207546	+	0.150791i	−0.479156	+	0.877730i	$0.659057\pi$
$548$	−1.85410	−	5.70634i	−0.0792033	−	0.243763i
$549$	6.00000			0.256074
$550$		0			0
$551$	36.0000			1.53365
$552$	−1.85410	−	5.70634i	−0.0789158	−	0.242878i
$553$		0			0
$554$	4.85410	−	3.52671i	0.206231	−	0.149836i
$555$		0			0
$556$	−5.56231	+	17.1190i	−0.235894	+	0.726008i
$557$	−14.5623	+	10.5801i	−0.617025	+	0.448295i	−0.851881	−	0.523735i	$-0.824538\pi$
$557$	−14.5623	+	10.5801i	−0.617025	+	0.448295i	0.234856	+	0.972030i	$0.424538\pi$
$558$	−3.23607	−	2.35114i	−0.136994	−	0.0995317i
$559$	11.1246	+	34.2380i	0.470521	+	1.44811i
$560$		0			0
$561$		0			0
$562$	6.00000			0.253095
$563$	−7.41641	−	22.8254i	−0.312564	−	0.961974i	−0.976745	−	0.214402i	$-0.931220\pi$
$563$	−7.41641	−	22.8254i	−0.312564	−	0.961974i	0.664181	−	0.747572i	$-0.268780\pi$
$564$	4.85410	+	3.52671i	0.204395	+	0.148501i
$565$		0			0
$566$	1.85410	−	5.70634i	0.0779337	−	0.239855i
$567$		0			0
$568$	4.85410	−	3.52671i	0.203674	−	0.147978i
$569$	24.2705	+	17.6336i	1.01747	+	0.739237i	0.965763	−	0.259425i	$-0.0835330\pi$
$569$	24.2705	+	17.6336i	1.01747	+	0.739237i	0.0517094	+	0.998662i	$0.483533\pi$
$570$		0			0
$571$	18.0000			0.753277			0.376638	−	0.926360i	$-0.377080\pi$
$571$	18.0000			0.753277			0.376638	+	0.926360i	$0.377080\pi$
$572$		0			0
$573$	18.0000			0.751961
$574$		0			0
$575$	24.2705	+	17.6336i	1.01215	+	0.735370i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	−11.7426	+	36.1401i	−0.488853	+	1.50453i	0.337470	+	0.941336i	$0.390429\pi$
$577$	−11.7426	+	36.1401i	−0.488853	+	1.50453i	−0.826322	+	0.563198i	$0.809571\pi$
$578$	5.87132	−	18.0701i	0.244215	−	0.751616i
$579$	9.70820	−	7.05342i	0.403459	−	0.293130i
$580$		0			0
$581$		0			0
$582$	10.0000			0.414513
$583$		0			0
$584$	−12.0000			−0.496564
$585$		0			0
$586$	24.2705	+	17.6336i	1.00261	+	0.728436i
$587$	9.70820	−	7.05342i	0.400700	−	0.291126i	−0.369126	−	0.929379i	$-0.620343\pi$
$587$	9.70820	−	7.05342i	0.400700	−	0.291126i	0.769826	+	0.638254i	$0.220343\pi$
$588$	2.16312	−	6.65740i	0.0892055	−	0.274546i
$589$	7.41641	−	22.8254i	0.305588	−	0.940502i
$590$		0			0
$591$	−4.85410	−	3.52671i	−0.199671	−	0.145070i
$592$	−0.618034	−	1.90211i	−0.0254010	−	0.0781764i
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$		0			0
$595$		0			0
$596$	1.85410	+	5.70634i	0.0759470	+	0.233741i
$597$	12.9443	+	9.40456i	0.529774	+	0.384903i
$598$	−29.1246	+	21.1603i	−1.19099	+	0.865308i
$599$	−5.56231	+	17.1190i	−0.227270	+	0.699464i	0.770784	+	0.637097i	$0.219865\pi$
$599$	−5.56231	+	17.1190i	−0.227270	+	0.699464i	−0.998053	+	0.0623671i	$0.980135\pi$
$600$	1.54508	−	4.75528i	0.0630778	−	0.194134i
$601$	19.4164	−	14.1068i	0.792012	−	0.575430i	−0.116548	−	0.993185i	$-0.537183\pi$
$601$	19.4164	−	14.1068i	0.792012	−	0.575430i	0.908560	+	0.417755i	$0.137183\pi$
$602$		0			0
$603$	1.23607	+	3.80423i	0.0503366	+	0.154920i
$604$	−12.0000			−0.488273
$605$		0			0
$606$	6.00000			0.243733
$607$	−11.1246	−	34.2380i	−0.451534	−	1.38968i	−0.875156	−	0.483840i	$-0.839242\pi$
$607$	−11.1246	−	34.2380i	−0.451534	−	1.38968i	0.423622	−	0.905839i	$-0.360758\pi$
$608$	−4.85410	−	3.52671i	−0.196860	−	0.143027i
$609$		0			0
$610$		0			0
$611$	11.1246	−	34.2380i	0.450054	−	1.38512i
$612$	4.85410	−	3.52671i	0.196215	−	0.142559i
$613$	33.9787	+	24.6870i	1.37239	+	0.997098i	0.997546	+	0.0700086i	$0.0223027\pi$
$613$	33.9787	+	24.6870i	1.37239	+	0.997098i	0.374841	+	0.927089i	$0.377697\pi$
$614$	−5.56231	−	17.1190i	−0.224476	−	0.690867i
$615$		0			0
$616$		0			0
$617$	30.0000			1.20775			0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000			1.20775			0.603877	+	0.797077i	$0.293622\pi$
$618$	1.23607	+	3.80423i	0.0497219	+	0.153028i
$619$	22.6525	+	16.4580i	0.910480	+	0.661502i	0.941136	−	0.338028i	$-0.109760\pi$
$619$	22.6525	+	16.4580i	0.910480	+	0.661502i	−0.0306563	+	0.999530i	$0.509760\pi$
$620$		0			0
$621$	−1.85410	+	5.70634i	−0.0744025	+	0.228988i
$622$	1.85410	−	5.70634i	0.0743427	−	0.228803i
$623$		0			0
$624$	4.85410	+	3.52671i	0.194320	+	0.141181i
$625$	7.72542	+	23.7764i	0.309017	+	0.951057i
$626$	−26.0000			−1.03917
$627$		0			0
$628$	−14.0000			−0.558661
$629$	3.70820	+	11.4127i	0.147856	+	0.455053i
$630$		0			0
$631$	16.1803	−	11.7557i	0.644129	−	0.467987i	−0.217137	−	0.976141i	$-0.569672\pi$
$631$	16.1803	−	11.7557i	0.644129	−	0.467987i	0.861266	+	0.508154i	$0.169672\pi$
$632$	3.70820	−	11.4127i	0.147504	−	0.453972i
$633$	1.85410	−	5.70634i	0.0736939	−	0.226807i
$634$	9.70820	−	7.05342i	0.385562	−	0.280127i
$635$		0			0
$636$	3.70820	+	11.4127i	0.147040	+	0.452542i
$637$	−42.0000			−1.66410
$638$		0			0
$639$	−6.00000			−0.237356
$640$		0			0
$641$	−24.2705	−	17.6336i	−0.958628	−	0.696484i	−0.00579592	−	0.999983i	$-0.501845\pi$
$641$	−24.2705	−	17.6336i	−0.958628	−	0.696484i	−0.952832	+	0.303500i	$0.901845\pi$
$642$	−9.70820	+	7.05342i	−0.383152	+	0.278376i
$643$	−1.23607	+	3.80423i	−0.0487458	+	0.150024i	−0.972467	−	0.233042i	$-0.925132\pi$
$643$	−1.23607	+	3.80423i	−0.0487458	+	0.150024i	0.923721	+	0.383066i	$0.125132\pi$
$644$		0			0
$645$		0			0
$646$	29.1246	+	21.1603i	1.14589	+	0.832540i
$647$	−12.9787	−	39.9444i	−0.510246	−	1.57038i	−0.791769	−	0.610821i	$-0.790840\pi$
$647$	−12.9787	−	39.9444i	−0.510246	−	1.57038i	0.281523	−	0.959555i	$-0.409160\pi$
$648$	1.00000			0.0392837
$649$		0			0
$650$	−30.0000			−1.17670
$651$		0			0
$652$	−16.1803	−	11.7557i	−0.633671	−	0.460389i
$653$	19.4164	−	14.1068i	0.759823	−	0.552044i	−0.139033	−	0.990288i	$-0.544399\pi$
$653$	19.4164	−	14.1068i	0.759823	−	0.552044i	0.898856	+	0.438244i	$0.144399\pi$
$654$	−1.85410	+	5.70634i	−0.0725011	+	0.223136i
$655$		0			0
$656$	−4.85410	+	3.52671i	−0.189521	+	0.137695i
$657$	9.70820	+	7.05342i	0.378753	+	0.275180i
$658$		0			0
$659$	24.0000			0.934907			0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000			0.934907			0.467454	+	0.884018i	$0.345171\pi$
$660$		0			0
$661$	−14.0000			−0.544537			−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000			−0.544537			−0.272268	+	0.962221i	$0.587774\pi$
$662$	−8.65248	−	26.6296i	−0.336288	−	1.03499i
$663$	−29.1246	−	21.1603i	−1.13111	−	0.821797i
$664$		0			0
$665$		0			0
$666$	−0.618034	+	1.90211i	−0.0239483	+	0.0737054i
$667$	−29.1246	+	21.1603i	−1.12771	+	0.819329i
$668$	19.4164	+	14.1068i	0.751243	+	0.545810i
$669$	−2.47214	−	7.60845i	−0.0955783	−	0.294160i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−3.70820	−	11.4127i	−0.142941	−	0.439926i	0.853800	−	0.520602i	$-0.174292\pi$
$673$	−3.70820	−	11.4127i	−0.142941	−	0.439926i	−0.996740	+	0.0806753i	$0.974292\pi$
$674$	−29.1246	−	21.1603i	−1.12184	−	0.815063i
$675$	−4.04508	+	2.93893i	−0.155695	+	0.113119i
$676$	7.10739	−	21.8743i	0.273361	−	0.841319i
$677$	−1.85410	+	5.70634i	−0.0712589	+	0.219312i	−0.980343	−	0.197300i	$-0.936783\pi$
$677$	−1.85410	+	5.70634i	−0.0712589	+	0.219312i	0.909084	+	0.416612i	$0.136783\pi$
$678$	4.85410	−	3.52671i	0.186421	−	0.135443i
$679$		0			0
$680$		0			0
$681$	−12.0000			−0.459841
$682$		0			0
$683$	24.0000			0.918334			0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000			0.918334			0.459167	+	0.888350i	$0.348148\pi$
$684$	1.85410	+	5.70634i	0.0708934	+	0.218187i
$685$		0			0
$686$		0			0
$687$	4.32624	−	13.3148i	0.165056	−	0.507991i
$688$	1.85410	−	5.70634i	0.0706870	−	0.217552i
$689$	58.2492	−	42.3205i	2.21912	−	1.61228i
$690$		0			0
$691$	−8.65248	−	26.6296i	−0.329156	−	1.01304i	−0.969530	−	0.244974i	$-0.921221\pi$
$691$	−8.65248	−	26.6296i	−0.329156	−	1.01304i	0.640374	−	0.768063i	$-0.278779\pi$
$692$	−18.0000			−0.684257
$693$		0			0
$694$	−24.0000			−0.911028
$695$		0			0
$696$	4.85410	+	3.52671i	0.183994	+	0.133680i
$697$	29.1246	−	21.1603i	1.10317	−	0.801502i
$698$	5.56231	−	17.1190i	0.210536	−	0.647964i
$699$	−1.85410	+	5.70634i	−0.0701286	+	0.215834i
$700$		0			0
$701$	4.85410	+	3.52671i	0.183337	+	0.133202i	0.675668	−	0.737206i	$-0.263855\pi$
$701$	4.85410	+	3.52671i	0.183337	+	0.133202i	−0.492331	+	0.870408i	$0.663855\pi$
$702$	−1.85410	−	5.70634i	−0.0699786	−	0.215372i
$703$	−12.0000			−0.452589
$704$		0			0
$705$		0			0
$706$	−9.27051	−	28.5317i	−0.348900	−	1.07380i
$707$		0			0
$708$	−9.70820	+	7.05342i	−0.364857	+	0.265084i
$709$	3.09017	−	9.51057i	0.116054	−	0.357177i	−0.876112	−	0.482108i	$-0.839871\pi$
$709$	3.09017	−	9.51057i	0.116054	−	0.357177i	0.992165	+	0.124932i	$0.0398711\pi$
$710$		0			0
$711$	−9.70820	+	7.05342i	−0.364086	+	0.264524i
$712$	4.85410	+	3.52671i	0.181915	+	0.132169i
$713$	7.41641	+	22.8254i	0.277747	+	0.854816i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−7.41641	−	22.8254i	−0.276971	−	0.852429i
$718$		0			0
$719$	−14.5623	+	10.5801i	−0.543082	+	0.394572i	−0.825229	−	0.564799i	$-0.808954\pi$
$719$	−14.5623	+	10.5801i	−0.543082	+	0.394572i	0.282146	+	0.959371i	$0.408954\pi$
$720$		0			0
$721$		0			0
$722$	−13.7533	+	9.99235i	−0.511844	+	0.371877i
$723$		0			0
$724$	0.618034	+	1.90211i	0.0229691	+	0.0706915i
$725$	−30.0000			−1.11417
$726$		0			0
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	−11.1246	+	34.2380i	−0.411459	+	1.26634i
$732$	−1.85410	+	5.70634i	−0.0685296	+	0.210912i
$733$	−4.85410	+	3.52671i	−0.179290	+	0.130262i	−0.673811	−	0.738904i	$-0.735344\pi$
$733$	−4.85410	+	3.52671i	−0.179290	+	0.130262i	0.494520	+	0.869166i	$0.335344\pi$
$734$	−6.47214	−	4.70228i	−0.238891	−	0.173564i
$735$		0			0
$736$	6.00000			0.221163
$737$		0			0
$738$	6.00000			0.220863
$739$	9.27051	+	28.5317i	0.341021	+	1.04956i	0.963679	+	0.267062i	$0.0860527\pi$
$739$	9.27051	+	28.5317i	0.341021	+	1.04956i	−0.622658	+	0.782494i	$0.713947\pi$
$740$		0			0
$741$	29.1246	−	21.1603i	1.06992	−	0.777342i
$742$		0			0
$743$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$743$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$744$	3.23607	−	2.35114i	0.118640	−	0.0861970i
$745$		0			0
$746$	−1.85410	−	5.70634i	−0.0678835	−	0.208924i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−3.23607	−	2.35114i	−0.118086	−	0.0857944i	0.527175	−	0.849757i	$-0.323251\pi$
$751$	−3.23607	−	2.35114i	−0.118086	−	0.0857944i	−0.645261	+	0.763962i	$0.723251\pi$
$752$	−4.85410	+	3.52671i	−0.177011	+	0.128606i
$753$	−7.41641	+	22.8254i	−0.270269	+	0.831802i
$754$	11.1246	−	34.2380i	0.405134	−	1.24688i
$755$		0			0
$756$		0			0
$757$	−0.618034	−	1.90211i	−0.0224628	−	0.0691335i	0.939197	−	0.343380i	$-0.111572\pi$
$757$	−0.618034	−	1.90211i	−0.0224628	−	0.0691335i	−0.961660	+	0.274246i	$0.911572\pi$
$758$	20.0000			0.726433
$759$		0			0
$760$		0			0
$761$	−1.85410	−	5.70634i	−0.0672111	−	0.206855i	0.911810	−	0.410612i	$-0.134685\pi$
$761$	−1.85410	−	5.70634i	−0.0672111	−	0.206855i	−0.979022	+	0.203757i	$0.934685\pi$
$762$	9.70820	+	7.05342i	0.351691	+	0.255519i
$763$		0			0
$764$	−5.56231	+	17.1190i	−0.201237	+	0.619344i
$765$		0			0
$766$	14.5623	−	10.5801i	0.526157	−	0.382276i
$767$	58.2492	+	42.3205i	2.10326	+	1.52811i
$768$	−0.309017	−	0.951057i	−0.0111507	−	0.0343183i
$769$	−12.0000			−0.432731			−0.216366	−	0.976312i	$-0.569420\pi$
$769$	−12.0000			−0.432731			−0.216366	+	0.976312i	$0.569420\pi$
$770$		0			0
$771$	−18.0000			−0.648254
$772$	3.70820	+	11.4127i	0.133461	+	0.410751i
$773$	29.1246	+	21.1603i	1.04754	+	0.761082i	0.971743	−	0.236041i	$-0.0758501\pi$
$773$	29.1246	+	21.1603i	1.04754	+	0.761082i	0.0757965	+	0.997123i	$0.475850\pi$
$774$	−4.85410	+	3.52671i	−0.174477	+	0.126765i
$775$	−6.18034	+	19.0211i	−0.222004	+	0.683259i
$776$	−3.09017	+	9.51057i	−0.110931	+	0.341409i
$777$		0			0
$778$	−19.4164	−	14.1068i	−0.696112	−	0.505755i
$779$	11.1246	+	34.2380i	0.398581	+	1.22670i
$780$		0			0
$781$		0			0
$782$	−36.0000			−1.28736
$783$	−1.85410	−	5.70634i	−0.0662602	−	0.203928i
$784$	5.66312	+	4.11450i	0.202254	+	0.146946i
$785$		0			0
$786$	3.70820	−	11.4127i	0.132267	−	0.407077i
$787$	1.85410	−	5.70634i	0.0660916	−	0.203409i	−0.912557	−	0.408949i	$-0.865895\pi$
$787$	1.85410	−	5.70634i	0.0660916	−	0.203409i	0.978649	+	0.205540i	$0.0658952\pi$
$788$	4.85410	−	3.52671i	0.172920	−	0.125634i
$789$	19.4164	+	14.1068i	0.691242	+	0.502217i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	36.0000			1.27840
$794$	0.618034	+	1.90211i	0.0219332	+	0.0675035i
$795$		0			0
$796$	−12.9443	+	9.40456i	−0.458798	+	0.333336i
$797$	14.8328	−	45.6507i	0.525405	−	1.61703i	−0.238108	−	0.971239i	$-0.576527\pi$
$797$	14.8328	−	45.6507i	0.525405	−	1.61703i	0.763513	−	0.645792i	$-0.223473\pi$
$798$		0			0
$799$	29.1246	−	21.1603i	1.03035	−	0.748597i
$800$	4.04508	+	2.93893i	0.143015	+	0.103907i
$801$	−1.85410	−	5.70634i	−0.0655115	−	0.201624i
$802$	−6.00000			−0.211867
$803$		0			0
$804$	−4.00000			−0.141069
$805$		0			0
$806$	−19.4164	−	14.1068i	−0.683914	−	0.496892i
$807$	9.70820	−	7.05342i	0.341745	−	0.248292i
$808$	−1.85410	+	5.70634i	−0.0652271	+	0.200748i
$809$	5.56231	−	17.1190i	0.195560	−	0.601873i	−0.804409	−	0.594075i	$-0.797518\pi$
$809$	5.56231	−	17.1190i	0.195560	−	0.601873i	0.999970	−	0.00779717i	$-0.00248194\pi$
$810$		0			0
$811$	4.85410	+	3.52671i	0.170451	+	0.123840i	0.669740	−	0.742596i	$-0.266406\pi$
$811$	4.85410	+	3.52671i	0.170451	+	0.123840i	−0.499289	+	0.866435i	$0.666406\pi$
$812$		0			0
$813$	−12.0000			−0.420858
$814$		0			0
$815$		0			0
$816$	1.85410	+	5.70634i	0.0649066	+	0.199762i
$817$	−29.1246	−	21.1603i	−1.01894	−	0.740304i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−33.9787	+	24.6870i	−1.18587	+	0.861582i	−0.992821	−	0.119609i	$-0.961836\pi$
$821$	−33.9787	+	24.6870i	−1.18587	+	0.861582i	−0.193044	+	0.981190i	$0.561836\pi$
$822$	−4.85410	−	3.52671i	−0.169306	−	0.123008i
$823$	−12.3607	−	38.0423i	−0.430866	−	1.32607i	−0.897264	−	0.441495i	$-0.854448\pi$
$823$	−12.3607	−	38.0423i	−0.430866	−	1.32607i	0.466398	−	0.884575i	$-0.345552\pi$
$824$	−4.00000			−0.139347
$825$		0			0
$826$		0			0
$827$	−14.8328	−	45.6507i	−0.515788	−	1.58743i	−0.781844	−	0.623474i	$-0.785721\pi$
$827$	−14.8328	−	45.6507i	−0.515788	−	1.58743i	0.266057	−	0.963957i	$-0.414279\pi$
$828$	−4.85410	−	3.52671i	−0.168692	−	0.122562i
$829$	27.5066	−	19.9847i	0.955343	−	0.694097i	0.00327844	−	0.999995i	$-0.498956\pi$
$829$	27.5066	−	19.9847i	0.955343	−	0.694097i	0.952064	+	0.305897i	$0.0989564\pi$
$830$		0			0
$831$	1.85410	−	5.70634i	0.0643181	−	0.197951i
$832$	−4.85410	+	3.52671i	−0.168286	+	0.122267i
$833$	−33.9787	−	24.6870i	−1.17729	−	0.855353i
$834$	5.56231	+	17.1190i	0.192607	+	0.592783i
$835$		0			0
$836$		0			0
$837$	−4.00000			−0.138260
$838$	7.41641	+	22.8254i	0.256196	+	0.788489i
$839$	24.2705	+	17.6336i	0.837911	+	0.608778i	0.921786	−	0.387698i	$-0.126730\pi$
$839$	24.2705	+	17.6336i	0.837911	+	0.608778i	−0.0838753	+	0.996476i	$0.526730\pi$
$840$		0			0
$841$	2.16312	−	6.65740i	0.0745903	−	0.229565i
$842$	−8.03444	+	24.7275i	−0.276885	+	0.852165i
$843$	4.85410	−	3.52671i	0.167184	−	0.121466i
$844$	4.85410	+	3.52671i	0.167085	+	0.121394i
$845$		0			0
$846$	6.00000			0.206284
$847$		0			0
$848$	−12.0000			−0.412082
$849$	−1.85410	−	5.70634i	−0.0636326	−	0.195841i
$850$	−24.2705	−	17.6336i	−0.832472	−	0.604826i
$851$	9.70820	−	7.05342i	0.332793	−	0.241788i
$852$	1.85410	−	5.70634i	0.0635205	−	0.195496i
$853$	9.27051	−	28.5317i	0.317416	−	0.976907i	−0.657332	−	0.753601i	$-0.728315\pi$
$853$	9.27051	−	28.5317i	0.317416	−	0.976907i	0.974748	−	0.223306i	$-0.0716848\pi$
$854$		0			0
$855$		0			0
$856$	−3.70820	−	11.4127i	−0.126744	−	0.390077i
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$		0			0
$859$	−4.00000			−0.136478			−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000			−0.136478			−0.0682391	+	0.997669i	$0.521738\pi$
$860$		0			0
$861$		0			0
$862$	−19.4164	+	14.1068i	−0.661325	+	0.480481i
$863$	−16.6869	+	51.3571i	−0.568029	+	1.74821i	0.0907454	+	0.995874i	$0.471075\pi$
$863$	−16.6869	+	51.3571i	−0.568029	+	1.74821i	−0.658775	+	0.752340i	$0.728925\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$		0			0
$866$	−1.61803	−	1.17557i	−0.0549830	−	0.0399475i
$867$	−5.87132	−	18.0701i	−0.199401	−	0.613692i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	7.41641	+	22.8254i	0.251295	+	0.773408i
$872$	−4.85410	−	3.52671i	−0.164381	−	0.119430i
$873$	8.09017	−	5.87785i	0.273811	−	0.198935i
$874$	11.1246	−	34.2380i	0.376296	−	1.15812i
$875$		0			0
$876$	−9.70820	+	7.05342i	−0.328010	+	0.238313i
$877$	−14.5623	−	10.5801i	−0.491734	−	0.357266i	0.314117	−	0.949384i	$-0.398292\pi$
$877$	−14.5623	−	10.5801i	−0.491734	−	0.357266i	−0.805851	+	0.592119i	$0.798292\pi$
$878$		0			0
$879$	30.0000			1.01187
$880$		0			0
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$	−2.16312	−	6.65740i	−0.0728360	−	0.224166i
$883$	−42.0689	−	30.5648i	−1.41573	−	1.02859i	−0.992458	−	0.122586i	$-0.960881\pi$
$883$	−42.0689	−	30.5648i	−1.41573	−	1.02859i	−0.423273	−	0.906002i	$-0.639119\pi$
$884$	29.1246	−	21.1603i	0.979567	−	0.711697i
$885$		0			0
$886$	−3.70820	+	11.4127i	−0.124580	+	0.383416i
$887$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$887$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$888$	−1.61803	−	1.17557i	−0.0542977	−	0.0394496i
$889$		0			0
$890$		0			0
$891$		0			0
$892$	8.00000			0.267860
$893$	11.1246	+	34.2380i	0.372271	+	1.14573i
$894$	4.85410	+	3.52671i	0.162345	+	0.117951i
$895$		0			0
$896$		0			0
$897$	−11.1246	+	34.2380i	−0.371440	+	1.14317i
$898$	−4.85410	+	3.52671i	−0.161983	+	0.117688i
$899$	−19.4164	−	14.1068i	−0.647573	−	0.470490i
$900$	−1.54508	−	4.75528i	−0.0515028	−	0.158509i
$901$	72.0000			2.39867
$902$		0			0
$903$		0			0
$904$	1.85410	+	5.70634i	0.0616665	+	0.189790i
$905$		0			0
$906$	−9.70820	+	7.05342i	−0.322533	+	0.234334i
$907$	−8.65248	+	26.6296i	−0.287301	+	0.884221i	0.698399	+	0.715709i	$0.253896\pi$
$907$	−8.65248	+	26.6296i	−0.287301	+	0.884221i	−0.985700	+	0.168512i	$0.946104\pi$
$908$	3.70820	−	11.4127i	0.123061	−	0.378743i
$909$	4.85410	−	3.52671i	0.161000	−	0.116974i
$910$		0			0
$911$	−1.85410	−	5.70634i	−0.0614291	−	0.189059i	0.915632	−	0.402017i	$-0.131691\pi$
$911$	−1.85410	−	5.70634i	−0.0614291	−	0.189059i	−0.977062	+	0.212957i	$0.931691\pi$
$912$	−6.00000			−0.198680
$913$		0			0
$914$	−24.0000			−0.793849
$915$		0			0
$916$	11.3262	+	8.22899i	0.374229	+	0.271894i
$917$		0			0
$918$	1.85410	−	5.70634i	0.0611945	−	0.188337i
$919$	11.1246	−	34.2380i	0.366967	−	1.12941i	−0.581773	−	0.813351i	$-0.697641\pi$
$919$	11.1246	−	34.2380i	0.366967	−	1.12941i	0.948740	−	0.316057i	$-0.102359\pi$
$920$		0			0
$921$	−14.5623	−	10.5801i	−0.479844	−	0.348627i
$922$	5.56231	+	17.1190i	0.183185	+	0.563785i
$923$	−36.0000			−1.18495
$924$		0			0
$925$	10.0000			0.328798
$926$	−1.23607	−	3.80423i	−0.0406197	−	0.125015i
$927$	3.23607	+	2.35114i	0.106286	+	0.0772216i
$928$	−4.85410	+	3.52671i	−0.159344	+	0.115770i
$929$	−1.85410	+	5.70634i	−0.0608311	+	0.187219i	−0.976854	−	0.213907i	$-0.931381\pi$
$929$	−1.85410	+	5.70634i	−0.0608311	+	0.187219i	0.916023	+	0.401126i	$0.131381\pi$
$930$		0			0
$931$	33.9787	−	24.6870i	1.11361	−	0.809083i
$932$	−4.85410	−	3.52671i	−0.159001	−	0.115521i
$933$	−1.85410	−	5.70634i	−0.0607006	−	0.186817i
$934$		0			0
$935$		0			0
$936$	6.00000			0.196116
$937$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$937$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$938$		0			0
$939$	−21.0344	+	15.2824i	−0.686433	+	0.498723i
$940$		0			0
$941$	−9.27051	+	28.5317i	−0.302210	+	0.930107i	0.678494	+	0.734606i	$0.262633\pi$
$941$	−9.27051	+	28.5317i	−0.302210	+	0.930107i	−0.980704	+	0.195500i	$0.937367\pi$
$942$	−11.3262	+	8.22899i	−0.369029	+	0.268115i
$943$	−29.1246	−	21.1603i	−0.948428	−	0.689073i
$944$	−3.70820	−	11.4127i	−0.120692	−	0.371451i
$945$		0			0
$946$		0			0
$947$	36.0000			1.16984			0.584921	−	0.811090i	$-0.301125\pi$
$947$	36.0000			1.16984			0.584921	+	0.811090i	$0.301125\pi$
$948$	−3.70820	−	11.4127i	−0.120437	−	0.370667i
$949$	58.2492	+	42.3205i	1.89085	+	1.37378i
$950$	24.2705	−	17.6336i	0.787439	−	0.572108i
$951$	3.70820	−	11.4127i	0.120247	−	0.370081i
$952$		0			0
$953$	−14.5623	+	10.5801i	−0.471719	+	0.342724i	−0.798111	−	0.602510i	$-0.794167\pi$
$953$	−14.5623	+	10.5801i	−0.471719	+	0.342724i	0.326392	+	0.945235i	$0.394167\pi$
$954$	9.70820	+	7.05342i	0.314315	+	0.228363i
$955$		0			0
$956$	24.0000			0.776215
$957$		0			0
$958$	24.0000			0.775405
$959$		0			0
$960$		0			0
$961$	12.1353	−	8.81678i	0.391460	−	0.284412i
$962$	−3.70820	+	11.4127i	−0.119557	+	0.367960i
$963$	−3.70820	+	11.4127i	−0.119495	+	0.367768i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−12.0000			−0.385894			−0.192947	−	0.981209i	$-0.561805\pi$
$967$	−12.0000			−0.385894			−0.192947	+	0.981209i	$0.561805\pi$
$968$		0			0
$969$	36.0000			1.15649
$970$		0			0
$971$	9.70820	+	7.05342i	0.311551	+	0.226355i	0.732562	−	0.680701i	$-0.238325\pi$
$971$	9.70820	+	7.05342i	0.311551	+	0.226355i	−0.421011	+	0.907056i	$0.638325\pi$
$972$	0.809017	−	0.587785i	0.0259492	−	0.0188532i
$973$		0			0
$974$	4.94427	−	15.2169i	0.158425	−	0.487581i
$975$	−24.2705	+	17.6336i	−0.777278	+	0.564726i
$976$	−4.85410	−	3.52671i	−0.155376	−	0.112887i
$977$	12.9787	+	39.9444i	0.415226	+	1.27793i	0.912049	+	0.410082i	$0.134500\pi$
$977$	12.9787	+	39.9444i	0.415226	+	1.27793i	−0.496823	+	0.867852i	$0.665500\pi$
$978$	−20.0000			−0.639529
$979$		0			0
$980$		0			0
$981$	1.85410	+	5.70634i	0.0591969	+	0.182189i
$982$	29.1246	+	21.1603i	0.929404	+	0.675251i
$983$	−24.2705	+	17.6336i	−0.774109	+	0.562423i	−0.903205	−	0.429209i	$-0.858792\pi$
$983$	−24.2705	+	17.6336i	−0.774109	+	0.562423i	0.129096	+	0.991632i	$0.458792\pi$
$984$	−1.85410	+	5.70634i	−0.0591066	+	0.181911i
$985$		0			0
$986$	29.1246	−	21.1603i	0.927517	−	0.673880i
$987$		0			0
$988$	11.1246	+	34.2380i	0.353921	+	1.08926i
$989$	36.0000			1.14473
$990$		0			0
$991$	−20.0000			−0.635321			−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000			−0.635321			−0.317660	+	0.948205i	$0.602897\pi$
$992$	1.23607	+	3.80423i	0.0392452	+	0.120784i
$993$	−22.6525	−	16.4580i	−0.718855	−	0.522278i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−14.5623	+	10.5801i	−0.461193	+	0.335076i	−0.793999	−	0.607919i	$-0.792005\pi$
$997$	−14.5623	+	10.5801i	−0.461193	+	0.335076i	0.332806	+	0.942995i	$0.392005\pi$
$998$	−3.23607	−	2.35114i	−0.102436	−	0.0744241i
$999$	0.618034	+	1.90211i	0.0195537	+	0.0601802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.e.h.511.1		4
11.2	odd	10		726.2.e.p.493.1		4
11.3	even	5		726.2.a.g.1.1	yes	1
11.4	even	5	inner	726.2.e.h.487.1		4
11.5	even	5	inner	726.2.e.h.565.1		4
11.6	odd	10		726.2.e.p.565.1		4
11.7	odd	10		726.2.e.p.487.1		4
11.8	odd	10		726.2.a.b.1.1	✓	1
11.9	even	5	inner	726.2.e.h.493.1		4
11.10	odd	2		726.2.e.p.511.1		4
33.8	even	10		2178.2.a.i.1.1		1
33.14	odd	10		2178.2.a.c.1.1		1
44.3	odd	10		5808.2.a.bb.1.1		1
44.19	even	10		5808.2.a.ba.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
726.2.a.b.1.1	✓	1	11.8	odd	10
726.2.a.g.1.1	yes	1	11.3	even	5
726.2.e.h.487.1		4	11.4	even	5	inner
726.2.e.h.493.1		4	11.9	even	5	inner
726.2.e.h.511.1		4	1.1	even	1	trivial
726.2.e.h.565.1		4	11.5	even	5	inner
726.2.e.p.487.1		4	11.7	odd	10
726.2.e.p.493.1		4	11.2	odd	10
726.2.e.p.511.1		4	11.10	odd	2
726.2.e.p.565.1		4	11.6	odd	10
2178.2.a.c.1.1		1	33.14	odd	10
2178.2.a.i.1.1		1	33.8	even	10
5808.2.a.ba.1.1		1	44.19	even	10
5808.2.a.bb.1.1		1	44.3	odd	10

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:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{6} +(-0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} -1.00000 q^{12} +(1.85410 + 5.70634i) q^{13} +(0.309017 - 0.951057i) q^{16} +(-1.85410 + 5.70634i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(-4.85410 - 3.52671i) q^{19} +6.00000 q^{23} +(-0.309017 - 0.951057i) q^{24} +(4.04508 + 2.93893i) q^{25} +(-4.85410 + 3.52671i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-4.85410 + 3.52671i) q^{29} +(1.23607 + 3.80423i) q^{31} +1.00000 q^{32} -6.00000 q^{34} +(-0.809017 - 0.587785i) q^{36} +(1.61803 - 1.17557i) q^{37} +(1.85410 - 5.70634i) q^{38} +(-1.85410 + 5.70634i) q^{39} +(-4.85410 - 3.52671i) q^{41} +6.00000 q^{43} +(1.85410 + 5.70634i) q^{46} +(-4.85410 - 3.52671i) q^{47} +(0.809017 - 0.587785i) q^{48} +(-2.16312 + 6.65740i) q^{49} +(-1.54508 + 4.75528i) q^{50} +(-4.85410 + 3.52671i) q^{51} +(-4.85410 - 3.52671i) q^{52} +(-3.70820 - 11.4127i) q^{53} -1.00000 q^{54} +(-1.85410 - 5.70634i) q^{57} +(-4.85410 - 3.52671i) q^{58} +(9.70820 - 7.05342i) q^{59} +(1.85410 - 5.70634i) q^{61} +(-3.23607 + 2.35114i) q^{62} +(0.309017 + 0.951057i) q^{64} +4.00000 q^{67} +(-1.85410 - 5.70634i) q^{68} +(4.85410 + 3.52671i) q^{69} +(-1.85410 + 5.70634i) q^{71} +(0.309017 - 0.951057i) q^{72} +(9.70820 - 7.05342i) q^{73} +(1.61803 + 1.17557i) q^{74} +(1.54508 + 4.75528i) q^{75} +6.00000 q^{76} -6.00000 q^{78} +(3.70820 + 11.4127i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(1.85410 - 5.70634i) q^{82} +(1.85410 + 5.70634i) q^{86} -6.00000 q^{87} -6.00000 q^{89} +(-4.85410 + 3.52671i) q^{92} +(-1.23607 + 3.80423i) q^{93} +(1.85410 - 5.70634i) q^{94} +(0.809017 + 0.587785i) q^{96} +(-3.09017 - 9.51057i) q^{97} -7.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} - q^{4} + q^{6} - q^{8} - q^{9} - 4 q^{12} - 6 q^{13} - q^{16} + 6 q^{17} - q^{18} - 6 q^{19} + 24 q^{23} + q^{24} + 5 q^{25} - 6 q^{26} + q^{27} - 6 q^{29} - 4 q^{31} + 4 q^{32}+ \cdots - 28 q^{98}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 + q^6 - q^8 - q^9 - 4 * q^12 - 6 * q^13 - q^16 + 6 * q^17 - q^18 - 6 * q^19 + 24 * q^23 + q^24 + 5 * q^25 - 6 * q^26 + q^27 - 6 * q^29 - 4 * q^31 + 4 * q^32 - 24 * q^34 - q^36 + 2 * q^37 - 6 * q^38 + 6 * q^39 - 6 * q^41 + 24 * q^43 - 6 * q^46 - 6 * q^47 + q^48 + 7 * q^49 + 5 * q^50 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 4 * q^54 + 6 * q^57 - 6 * q^58 + 12 * q^59 - 6 * q^61 - 4 * q^62 - q^64 + 16 * q^67 + 6 * q^68 + 6 * q^69 + 6 * q^71 - q^72 + 12 * q^73 + 2 * q^74 - 5 * q^75 + 24 * q^76 - 24 * q^78 - 12 * q^79 - q^81 - 6 * q^82 - 6 * q^86 - 24 * q^87 - 24 * q^89 - 6 * q^92 + 4 * q^93 - 6 * q^94 + q^96 + 10 * q^97 - 28 * q^98

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