LMFDB - Embedded newform 726.2.e.f.493.1

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,-7,1,-1,-1,-1,-2] 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:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			493.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	726.493
Dual form			726.2.e.f.511.1

$q$-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} +(-1.19098 - 3.66547i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.92705 - 1.40008i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} -3.85410 q^{10} -1.00000 q^{12} +(0.381966 - 1.17557i) q^{13} +(-1.92705 + 1.40008i) q^{14} +(-3.11803 - 2.26538i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.00000 + 6.15537i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-1.00000 + 0.726543i) q^{19} +(-1.19098 + 3.66547i) q^{20} -2.38197 q^{21} +1.23607 q^{23} +(-0.309017 + 0.951057i) q^{24} +(-7.97214 + 5.79210i) q^{25} +(-1.00000 - 0.726543i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.736068 + 2.26538i) q^{28} +(2.11803 + 1.53884i) q^{29} +(-3.11803 + 2.26538i) q^{30} +(1.97214 - 6.06961i) q^{31} +1.00000 q^{32} +6.47214 q^{34} +(-2.83688 + 8.73102i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-8.47214 - 6.15537i) q^{37} +(0.381966 + 1.17557i) q^{38} +(-0.381966 - 1.17557i) q^{39} +(3.11803 + 2.26538i) q^{40} +(-1.00000 + 0.726543i) q^{41} +(-0.736068 + 2.26538i) q^{42} +1.23607 q^{43} -3.85410 q^{45} +(0.381966 - 1.17557i) q^{46} +(5.23607 - 3.80423i) q^{47} +(0.809017 + 0.587785i) q^{48} +(-0.409830 - 1.26133i) q^{49} +(3.04508 + 9.37181i) q^{50} +(5.23607 + 3.80423i) q^{51} +(-1.00000 + 0.726543i) q^{52} +(0.881966 - 2.71441i) q^{53} -1.00000 q^{54} +2.38197 q^{56} +(-0.381966 + 1.17557i) q^{57} +(2.11803 - 1.53884i) q^{58} +(-2.30902 - 1.67760i) q^{59} +(1.19098 + 3.66547i) q^{60} +(-3.47214 - 10.6861i) q^{61} +(-5.16312 - 3.75123i) q^{62} +(-1.92705 + 1.40008i) q^{63} +(0.309017 - 0.951057i) q^{64} -4.76393 q^{65} +4.00000 q^{67} +(2.00000 - 6.15537i) q^{68} +(1.00000 - 0.726543i) q^{69} +(7.42705 + 5.39607i) q^{70} +(1.09017 + 3.35520i) q^{71} +(0.309017 + 0.951057i) q^{72} +(-3.50000 - 2.54290i) q^{73} +(-8.47214 + 6.15537i) q^{74} +(-3.04508 + 9.37181i) q^{75} +1.23607 q^{76} -1.23607 q^{78} +(1.95492 - 6.01661i) q^{79} +(3.11803 - 2.26538i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.381966 + 1.17557i) q^{82} +(-5.04508 - 15.5272i) q^{83} +(1.92705 + 1.40008i) q^{84} +(20.1803 - 14.6619i) q^{85} +(0.381966 - 1.17557i) q^{86} +2.61803 q^{87} +1.70820 q^{89} +(-1.19098 + 3.66547i) q^{90} +(-2.38197 + 1.73060i) q^{91} +(-1.00000 - 0.726543i) q^{92} +(-1.97214 - 6.06961i) q^{93} +(-2.00000 - 6.15537i) q^{94} +(3.85410 + 2.80017i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-1.33688 + 4.11450i) q^{97} -1.32624 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} - q^{4} - 7 q^{5} + q^{6} - q^{7} - q^{8} - q^{9} - 2 q^{10} - 4 q^{12} + 6 q^{13} - q^{14} - 8 q^{15} - q^{16} + 8 q^{17} - q^{18} - 4 q^{19} - 7 q^{20} - 14 q^{21} - 4 q^{23}+ \cdots + 26 q^{98}+O(q^{100}) $ 4 * q - q^2 + q^3 - q^4 - 7 * q^5 + q^6 - q^7 - q^8 - q^9 - 2 * q^10 - 4 * q^12 + 6 * q^13 - q^14 - 8 * q^15 - q^16 + 8 * q^17 - q^18 - 4 * q^19 - 7 * q^20 - 14 * q^21 - 4 * q^23 + q^24 - 14 * q^25 - 4 * q^26 + q^27 - 6 * q^28 + 4 * q^29 - 8 * q^30 - 10 * q^31 + 4 * q^32 + 8 * q^34 - 27 * q^35 - q^36 - 16 * q^37 + 6 * q^38 - 6 * q^39 + 8 * q^40 - 4 * q^41 + 6 * q^42 - 4 * q^43 - 2 * q^45 + 6 * q^46 + 12 * q^47 + q^48 - 24 * q^49 + q^50 + 12 * q^51 - 4 * q^52 + 8 * q^53 - 4 * q^54 + 14 * q^56 - 6 * q^57 + 4 * q^58 - 7 * q^59 + 7 * q^60 + 4 * q^61 - 5 * q^62 - q^63 - q^64 - 28 * q^65 + 16 * q^67 + 8 * q^68 + 4 * q^69 + 23 * q^70 - 18 * q^71 - q^72 - 14 * q^73 - 16 * q^74 - q^75 - 4 * q^76 + 4 * q^78 + 19 * q^79 + 8 * q^80 - q^81 + 6 * q^82 - 9 * q^83 + q^84 + 36 * q^85 + 6 * q^86 + 6 * q^87 - 20 * q^89 - 7 * q^90 - 14 * q^91 - 4 * q^92 + 10 * q^93 - 8 * q^94 + 2 * q^95 + q^96 - 21 * q^97 + 26 * q^98

Character values

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

$n$	$485$	$607$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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
$5$	−1.19098	−	3.66547i	−0.532624	−	1.63925i	−0.748728	−	0.662877i	$-0.769335\pi$
$5$	−1.19098	−	3.66547i	−0.532624	−	1.63925i	0.216104	−	0.976370i	$-0.430665\pi$
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$	−1.92705	−	1.40008i	−0.728357	−	0.529182i	0.160686	−	0.987006i	$-0.448629\pi$
$7$	−1.92705	−	1.40008i	−0.728357	−	0.529182i	−0.889043	+	0.457823i	$0.848629\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−3.85410			−1.21877
$11$		0			0
$11$		0			0
$12$	−1.00000			−0.288675
$13$	0.381966	−	1.17557i	0.105938	−	0.326045i	−0.884011	−	0.467466i	$-0.845167\pi$
$13$	0.381966	−	1.17557i	0.105938	−	0.326045i	0.989950	+	0.141421i	$0.0451671\pi$
$14$	−1.92705	+	1.40008i	−0.515026	+	0.374188i
$15$	−3.11803	−	2.26538i	−0.805073	−	0.584920i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	2.00000	+	6.15537i	0.485071	+	1.49290i	0.831878	+	0.554959i	$0.187266\pi$
$17$	2.00000	+	6.15537i	0.485071	+	1.49290i	−0.346806	+	0.937937i	$0.612734\pi$
$18$	−0.809017	−	0.587785i	−0.190687	−	0.138542i
$19$	−1.00000	+	0.726543i	−0.229416	+	0.166680i	−0.696555	−	0.717504i	$-0.745285\pi$
$19$	−1.00000	+	0.726543i	−0.229416	+	0.166680i	0.467139	+	0.884184i	$0.345285\pi$
$20$	−1.19098	+	3.66547i	−0.266312	+	0.819624i
$21$	−2.38197			−0.519788
$22$		0			0
$23$	1.23607			0.257738			0.128869	−	0.991662i	$-0.458865\pi$
$23$	1.23607			0.257738			0.128869	+	0.991662i	$0.458865\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	−7.97214	+	5.79210i	−1.59443	+	1.15842i
$26$	−1.00000	−	0.726543i	−0.196116	−	0.142487i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	0.736068	+	2.26538i	0.139104	+	0.428117i
$29$	2.11803	+	1.53884i	0.393309	+	0.285756i	0.766810	−	0.641874i	$-0.221843\pi$
$29$	2.11803	+	1.53884i	0.393309	+	0.285756i	−0.373501	+	0.927630i	$0.621843\pi$
$30$	−3.11803	+	2.26538i	−0.569273	+	0.413601i
$31$	1.97214	−	6.06961i	0.354206	−	1.09013i	−0.602262	−	0.798298i	$-0.705734\pi$
$31$	1.97214	−	6.06961i	0.354206	−	1.09013i	0.956468	−	0.291836i	$-0.0942661\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	6.47214			1.10996
$35$	−2.83688	+	8.73102i	−0.479520	+	1.47581i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	−8.47214	−	6.15537i	−1.39281	−	1.01194i	−0.995550	−	0.0942301i	$-0.969961\pi$
$37$	−8.47214	−	6.15537i	−1.39281	−	1.01194i	−0.397260	−	0.917706i	$-0.630039\pi$
$38$	0.381966	+	1.17557i	0.0619631	+	0.190703i
$39$	−0.381966	−	1.17557i	−0.0611635	−	0.188242i
$40$	3.11803	+	2.26538i	0.493004	+	0.358189i
$41$	−1.00000	+	0.726543i	−0.156174	+	0.113467i	−0.663128	−	0.748506i	$-0.730771\pi$
$41$	−1.00000	+	0.726543i	−0.156174	+	0.113467i	0.506954	+	0.861973i	$0.330771\pi$
$42$	−0.736068	+	2.26538i	−0.113578	+	0.349556i
$43$	1.23607			0.188499			0.0942493	−	0.995549i	$-0.469955\pi$
$43$	1.23607			0.188499			0.0942493	+	0.995549i	$0.469955\pi$
$44$		0			0
$45$	−3.85410			−0.574536
$46$	0.381966	−	1.17557i	0.0563178	−	0.173328i
$47$	5.23607	−	3.80423i	0.763759	−	0.554903i	−0.136302	−	0.990667i	$-0.543522\pi$
$47$	5.23607	−	3.80423i	0.763759	−	0.554903i	0.900061	+	0.435764i	$0.143522\pi$
$48$	0.809017	+	0.587785i	0.116772	+	0.0848395i
$49$	−0.409830	−	1.26133i	−0.0585472	−	0.180190i
$50$	3.04508	+	9.37181i	0.430640	+	1.32537i
$51$	5.23607	+	3.80423i	0.733196	+	0.532698i
$52$	−1.00000	+	0.726543i	−0.138675	+	0.100753i
$53$	0.881966	−	2.71441i	0.121147	−	0.372853i	−0.872032	−	0.489449i	$-0.837198\pi$
$53$	0.881966	−	2.71441i	0.121147	−	0.372853i	0.993179	+	0.116595i	$0.0371981\pi$
$54$	−1.00000			−0.136083
$55$		0			0
$56$	2.38197			0.318304
$57$	−0.381966	+	1.17557i	−0.0505926	+	0.155708i
$58$	2.11803	−	1.53884i	0.278111	−	0.202060i
$59$	−2.30902	−	1.67760i	−0.300608	−	0.218405i	0.427248	−	0.904135i	$-0.359483\pi$
$59$	−2.30902	−	1.67760i	−0.300608	−	0.218405i	−0.727856	+	0.685730i	$0.759483\pi$
$60$	1.19098	+	3.66547i	0.153755	+	0.473210i
$61$	−3.47214	−	10.6861i	−0.444561	−	1.36822i	−0.882964	−	0.469441i	$-0.844456\pi$
$61$	−3.47214	−	10.6861i	−0.444561	−	1.36822i	0.438403	−	0.898779i	$-0.355544\pi$
$62$	−5.16312	−	3.75123i	−0.655717	−	0.476406i
$63$	−1.92705	+	1.40008i	−0.242786	+	0.176394i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−4.76393			−0.590893
$66$		0			0
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$	2.00000	−	6.15537i	0.242536	−	0.746448i
$69$	1.00000	−	0.726543i	0.120386	−	0.0874654i
$70$	7.42705	+	5.39607i	0.887702	+	0.644954i
$71$	1.09017	+	3.35520i	0.129379	+	0.398189i	0.994674	−	0.103076i	$-0.0328684\pi$
$71$	1.09017	+	3.35520i	0.129379	+	0.398189i	−0.865294	+	0.501264i	$0.832868\pi$
$72$	0.309017	+	0.951057i	0.0364180	+	0.112083i
$73$	−3.50000	−	2.54290i	−0.409644	−	0.297624i	0.363814	−	0.931472i	$-0.381474\pi$
$73$	−3.50000	−	2.54290i	−0.409644	−	0.297624i	−0.773458	+	0.633848i	$0.781474\pi$
$74$	−8.47214	+	6.15537i	−0.984866	+	0.715547i
$75$	−3.04508	+	9.37181i	−0.351616	+	1.08216i
$76$	1.23607			0.141787
$77$		0			0
$78$	−1.23607			−0.139957
$79$	1.95492	−	6.01661i	0.219945	−	0.676921i	−0.778820	−	0.627247i	$-0.784182\pi$
$79$	1.95492	−	6.01661i	0.219945	−	0.676921i	0.998765	−	0.0496744i	$-0.0158184\pi$
$80$	3.11803	−	2.26538i	0.348607	−	0.253278i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	0.381966	+	1.17557i	0.0421811	+	0.129820i
$83$	−5.04508	−	15.5272i	−0.553770	−	1.70433i	−0.699170	−	0.714956i	$-0.746447\pi$
$83$	−5.04508	−	15.5272i	−0.553770	−	1.70433i	0.145400	−	0.989373i	$-0.453553\pi$
$84$	1.92705	+	1.40008i	0.210258	+	0.152762i
$85$	20.1803	−	14.6619i	2.18887	−	1.59030i
$86$	0.381966	−	1.17557i	0.0411885	−	0.126765i
$87$	2.61803			0.280683
$88$		0			0
$89$	1.70820			0.181069			0.0905346	−	0.995893i	$-0.471142\pi$
$89$	1.70820			0.181069			0.0905346	+	0.995893i	$0.471142\pi$
$90$	−1.19098	+	3.66547i	−0.125541	+	0.386374i
$91$	−2.38197	+	1.73060i	−0.249698	+	0.181416i
$92$	−1.00000	−	0.726543i	−0.104257	−	0.0757473i
$93$	−1.97214	−	6.06961i	−0.204501	−	0.629389i
$94$	−2.00000	−	6.15537i	−0.206284	−	0.634878i
$95$	3.85410	+	2.80017i	0.395423	+	0.287291i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	−1.33688	+	4.11450i	−0.135740	+	0.417764i	−0.995704	−	0.0925898i	$-0.970485\pi$
$97$	−1.33688	+	4.11450i	−0.135740	+	0.417764i	0.859965	+	0.510354i	$0.170485\pi$
$98$	−1.32624			−0.133970
$99$		0			0
$100$	9.85410			0.985410
$101$	−4.51722	+	13.9026i	−0.449480	+	1.38336i	0.428014	+	0.903772i	$0.359213\pi$
$101$	−4.51722	+	13.9026i	−0.449480	+	1.38336i	−0.877495	+	0.479586i	$0.840787\pi$
$102$	5.23607	−	3.80423i	0.518448	−	0.376675i
$103$	13.7812	+	10.0126i	1.35790	+	0.986570i	0.998576	+	0.0533565i	$0.0169920\pi$
$103$	13.7812	+	10.0126i	1.35790	+	0.986570i	0.359322	+	0.933214i	$0.383008\pi$
$104$	0.381966	+	1.17557i	0.0374548	+	0.115274i
$105$	2.83688	+	8.73102i	0.276851	+	0.852061i
$106$	−2.30902	−	1.67760i	−0.224272	−	0.162943i
$107$	−6.16312	+	4.47777i	−0.595811	+	0.432882i	−0.844390	−	0.535730i	$-0.820037\pi$
$107$	−6.16312	+	4.47777i	−0.595811	+	0.432882i	0.248578	+	0.968612i	$0.420037\pi$
$108$	−0.309017	+	0.951057i	−0.0297352	+	0.0915155i
$109$	−9.41641			−0.901928			−0.450964	−	0.892542i	$-0.648920\pi$
$109$	−9.41641			−0.901928			−0.450964	+	0.892542i	$0.648920\pi$
$110$		0			0
$111$	−10.4721			−0.993971
$112$	0.736068	−	2.26538i	0.0695519	−	0.214059i
$113$	2.85410	−	2.07363i	0.268491	−	0.195070i	−0.445391	−	0.895336i	$-0.646935\pi$
$113$	2.85410	−	2.07363i	0.268491	−	0.195070i	0.713882	+	0.700266i	$0.246935\pi$
$114$	1.00000	+	0.726543i	0.0936586	+	0.0680469i
$115$	−1.47214	−	4.53077i	−0.137277	−	0.422496i
$116$	−0.809017	−	2.48990i	−0.0751153	−	0.231181i
$117$	−1.00000	−	0.726543i	−0.0924500	−	0.0671689i
$118$	−2.30902	+	1.67760i	−0.212562	+	0.154436i
$119$	4.76393	−	14.6619i	0.436709	−	1.34405i
$120$	3.85410			0.351830
$121$		0			0
$122$	−11.2361			−1.01727
$123$	−0.381966	+	1.17557i	−0.0344407	+	0.105998i
$124$	−5.16312	+	3.75123i	−0.463662	+	0.336870i
$125$	15.1353	+	10.9964i	1.35374	+	0.983548i
$126$	0.736068	+	2.26538i	0.0655741	+	0.201816i
$127$	3.70820	+	11.4127i	0.329050	+	1.01271i	0.969579	+	0.244778i	$0.0787150\pi$
$127$	3.70820	+	11.4127i	0.329050	+	1.01271i	−0.640529	+	0.767934i	$0.721285\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	1.00000	−	0.726543i	0.0880451	−	0.0639685i
$130$	−1.47214	+	4.53077i	−0.129115	+	0.397375i
$131$	18.2705			1.59630			0.798151	−	0.602458i	$-0.205812\pi$
$131$	18.2705			1.59630			0.798151	+	0.602458i	$0.205812\pi$
$132$		0			0
$133$	2.94427			0.255301
$134$	1.23607	−	3.80423i	0.106780	−	0.328635i
$135$	−3.11803	+	2.26538i	−0.268358	+	0.194973i
$136$	−5.23607	−	3.80423i	−0.448989	−	0.326210i
$137$	5.29180	+	16.2865i	0.452109	+	1.39145i	0.874496	+	0.485032i	$0.161192\pi$
$137$	5.29180	+	16.2865i	0.452109	+	1.39145i	−0.422388	+	0.906415i	$0.638808\pi$
$138$	−0.381966	−	1.17557i	−0.0325151	−	0.100071i
$139$	−7.09017	−	5.15131i	−0.601380	−	0.436928i	0.244988	−	0.969526i	$-0.421216\pi$
$139$	−7.09017	−	5.15131i	−0.601380	−	0.436928i	−0.846369	+	0.532598i	$0.821216\pi$
$140$	7.42705	−	5.39607i	0.627700	−	0.456051i
$141$	2.00000	−	6.15537i	0.168430	−	0.518375i
$142$	3.52786			0.296052
$143$		0			0
$144$	1.00000			0.0833333
$145$	3.11803	−	9.59632i	0.258939	−	0.796931i
$146$	−3.50000	+	2.54290i	−0.289662	+	0.210452i
$147$	−1.07295	−	0.779543i	−0.0884953	−	0.0642956i
$148$	3.23607	+	9.95959i	0.266003	+	0.818674i
$149$	1.11803	+	3.44095i	0.0915929	+	0.281894i	0.986351	−	0.164658i	$-0.0526519\pi$
$149$	1.11803	+	3.44095i	0.0915929	+	0.281894i	−0.894758	+	0.446552i	$0.852652\pi$
$150$	7.97214	+	5.79210i	0.650922	+	0.472923i
$151$	5.11803	−	3.71847i	0.416500	−	0.302605i	−0.359728	−	0.933057i	$-0.617131\pi$
$151$	5.11803	−	3.71847i	0.416500	−	0.302605i	0.776228	+	0.630452i	$0.217131\pi$
$152$	0.381966	−	1.17557i	0.0309815	−	0.0953514i
$153$	6.47214			0.523241
$154$		0			0
$155$	−24.5967			−1.97566
$156$	−0.381966	+	1.17557i	−0.0305818	+	0.0941210i
$157$	3.61803	−	2.62866i	0.288751	−	0.209790i	−0.433975	−	0.900925i	$-0.642889\pi$
$157$	3.61803	−	2.62866i	0.288751	−	0.209790i	0.722725	+	0.691136i	$0.242889\pi$
$158$	−5.11803	−	3.71847i	−0.407169	−	0.295826i
$159$	−0.881966	−	2.71441i	−0.0699445	−	0.215267i
$160$	−1.19098	−	3.66547i	−0.0941555	−	0.289781i
$161$	−2.38197	−	1.73060i	−0.187725	−	0.136390i
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	4.14590	−	12.7598i	0.324732	−	0.999422i	−0.646830	−	0.762634i	$-0.723906\pi$
$163$	4.14590	−	12.7598i	0.324732	−	0.999422i	0.971562	−	0.236787i	$-0.0760944\pi$
$164$	1.23607			0.0965207
$165$		0			0
$166$	−16.3262			−1.26716
$167$	0.854102	−	2.62866i	0.0660924	−	0.203411i	−0.912556	−	0.408951i	$-0.865895\pi$
$167$	0.854102	−	2.62866i	0.0660924	−	0.203411i	0.978649	+	0.205539i	$0.0658948\pi$
$168$	1.92705	−	1.40008i	0.148675	−	0.108019i
$169$	9.28115	+	6.74315i	0.713935	+	0.518704i
$170$	−7.70820	−	23.7234i	−0.591192	−	1.81950i
$171$	0.381966	+	1.17557i	0.0292097	+	0.0898981i
$172$	−1.00000	−	0.726543i	−0.0762493	−	0.0553983i
$173$	8.78115	−	6.37988i	0.667619	−	0.485053i	−0.201609	−	0.979466i	$-0.564617\pi$
$173$	8.78115	−	6.37988i	0.667619	−	0.485053i	0.869227	+	0.494413i	$0.164617\pi$
$174$	0.809017	−	2.48990i	0.0613314	−	0.188759i
$175$	23.4721			1.77433
$176$		0			0
$177$	−2.85410			−0.214527
$178$	0.527864	−	1.62460i	0.0395651	−	0.121769i
$179$	6.97214	−	5.06555i	0.521122	−	0.378617i	−0.295904	−	0.955218i	$-0.595621\pi$
$179$	6.97214	−	5.06555i	0.521122	−	0.378617i	0.817026	+	0.576600i	$0.195621\pi$
$180$	3.11803	+	2.26538i	0.232405	+	0.168852i
$181$	−2.32624	−	7.15942i	−0.172908	−	0.532156i	0.826624	−	0.562755i	$-0.190258\pi$
$181$	−2.32624	−	7.15942i	−0.172908	−	0.532156i	−0.999532	+	0.0305991i	$0.990258\pi$
$182$	0.909830	+	2.80017i	0.0674411	+	0.207562i
$183$	−9.09017	−	6.60440i	−0.671965	−	0.488211i
$184$	−1.00000	+	0.726543i	−0.0737210	+	0.0535614i
$185$	−12.4721	+	38.3853i	−0.916970	+	2.82214i
$186$	−6.38197			−0.467948
$187$		0			0
$188$	−6.47214			−0.472029
$189$	−0.736068	+	2.26538i	−0.0535411	+	0.164782i
$190$	3.85410	−	2.80017i	0.279606	−	0.203146i
$191$	−10.9443	−	7.95148i	−0.791900	−	0.575349i	0.116627	−	0.993176i	$-0.462792\pi$
$191$	−10.9443	−	7.95148i	−0.791900	−	0.575349i	−0.908527	+	0.417827i	$0.862792\pi$
$192$	−0.309017	−	0.951057i	−0.0223014	−	0.0686366i
$193$	−4.73607	−	14.5761i	−0.340910	−	1.04921i	−0.963737	−	0.266853i	$-0.914016\pi$
$193$	−4.73607	−	14.5761i	−0.340910	−	1.04921i	0.622828	−	0.782359i	$-0.285984\pi$
$194$	3.50000	+	2.54290i	0.251285	+	0.182569i
$195$	−3.85410	+	2.80017i	−0.275998	+	0.200524i
$196$	−0.409830	+	1.26133i	−0.0292736	+	0.0900948i
$197$	−5.09017			−0.362660			−0.181330	−	0.983422i	$-0.558040\pi$
$197$	−5.09017			−0.362660			−0.181330	+	0.983422i	$0.558040\pi$
$198$		0			0
$199$	19.8541			1.40742			0.703710	−	0.710487i	$-0.251525\pi$
$199$	19.8541			1.40742			0.703710	+	0.710487i	$0.251525\pi$
$200$	3.04508	−	9.37181i	0.215320	−	0.662687i
$201$	3.23607	−	2.35114i	0.228255	−	0.165837i
$202$	11.8262	+	8.59226i	0.832091	+	0.604550i
$203$	−1.92705	−	5.93085i	−0.135252	−	0.416264i
$204$	−2.00000	−	6.15537i	−0.140028	−	0.430962i
$205$	3.85410	+	2.80017i	0.269182	+	0.195572i
$206$	13.7812	−	10.0126i	0.960178	−	0.697610i
$207$	0.381966	−	1.17557i	0.0265485	−	0.0817078i
$208$	1.23607			0.0857059
$209$		0			0
$210$	9.18034			0.633504
$211$	8.23607	−	25.3480i	0.566994	−	1.74503i	−0.0949562	−	0.995481i	$-0.530271\pi$
$211$	8.23607	−	25.3480i	0.566994	−	1.74503i	0.661950	−	0.749548i	$-0.269729\pi$
$212$	−2.30902	+	1.67760i	−0.158584	+	0.115218i
$213$	2.85410	+	2.07363i	0.195560	+	0.142083i
$214$	2.35410	+	7.24518i	0.160923	+	0.495270i
$215$	−1.47214	−	4.53077i	−0.100399	−	0.308996i
$216$	0.809017	+	0.587785i	0.0550466	+	0.0399937i
$217$	−12.2984	+	8.93529i	−0.834868	+	0.606567i
$218$	−2.90983	+	8.95554i	−0.197079	+	0.606545i
$219$	−4.32624			−0.292340
$220$		0			0
$221$	8.00000			0.538138
$222$	−3.23607	+	9.95959i	−0.217191	+	0.668444i
$223$	10.5902	−	7.69421i	0.709170	−	0.515242i	−0.173736	−	0.984792i	$-0.555584\pi$
$223$	10.5902	−	7.69421i	0.709170	−	0.515242i	0.882906	+	0.469550i	$0.155584\pi$
$224$	−1.92705	−	1.40008i	−0.128757	−	0.0935471i
$225$	3.04508	+	9.37181i	0.203006	+	0.624787i
$226$	−1.09017	−	3.35520i	−0.0725170	−	0.223184i
$227$	11.2082	+	8.14324i	0.743915	+	0.540486i	0.893935	−	0.448197i	$-0.147934\pi$
$227$	11.2082	+	8.14324i	0.743915	+	0.540486i	−0.150020	+	0.988683i	$0.547934\pi$
$228$	1.00000	−	0.726543i	0.0662266	−	0.0481165i
$229$	1.56231	−	4.80828i	0.103240	−	0.317740i	−0.886073	−	0.463545i	$-0.846577\pi$
$229$	1.56231	−	4.80828i	0.103240	−	0.317740i	0.989313	+	0.145805i	$0.0465772\pi$
$230$	−4.76393			−0.314124
$231$		0			0
$232$	−2.61803			−0.171882
$233$	2.76393	−	8.50651i	0.181071	−	0.557280i	−0.818787	−	0.574097i	$-0.805353\pi$
$233$	2.76393	−	8.50651i	0.181071	−	0.557280i	0.999859	+	0.0168170i	$0.00535327\pi$
$234$	−1.00000	+	0.726543i	−0.0653720	+	0.0474956i
$235$	−20.1803	−	14.6619i	−1.31642	−	0.956435i
$236$	0.881966	+	2.71441i	0.0574111	+	0.176693i
$237$	−1.95492	−	6.01661i	−0.126985	−	0.390821i
$238$	−12.4721	−	9.06154i	−0.808448	−	0.587372i
$239$	6.09017	−	4.42477i	0.393940	−	0.286214i	−0.373128	−	0.927780i	$-0.621715\pi$
$239$	6.09017	−	4.42477i	0.393940	−	0.286214i	0.767068	+	0.641565i	$0.221715\pi$
$240$	1.19098	−	3.66547i	0.0768776	−	0.236605i
$241$	−22.5623			−1.45337			−0.726683	−	0.686973i	$-0.758939\pi$
$241$	−22.5623			−1.45337			−0.726683	+	0.686973i	$0.758939\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$	−3.47214	+	10.6861i	−0.222281	+	0.684110i
$245$	−4.13525	+	3.00444i	−0.264192	+	0.191947i
$246$	1.00000	+	0.726543i	0.0637577	+	0.0463227i
$247$	0.472136	+	1.45309i	0.0300413	+	0.0924576i
$248$	1.97214	+	6.06961i	0.125231	+	0.385421i
$249$	−13.2082	−	9.59632i	−0.837036	−	0.608142i
$250$	15.1353	−	10.9964i	0.957238	−	0.695474i
$251$	−1.13525	+	3.49396i	−0.0716567	+	0.220537i	−0.980471	−	0.196665i	$-0.936989\pi$
$251$	−1.13525	+	3.49396i	−0.0716567	+	0.220537i	0.908814	+	0.417201i	$0.136989\pi$
$252$	2.38197			0.150050
$253$		0			0
$254$	12.0000			0.752947
$255$	7.70820	−	23.7234i	0.482706	−	1.48562i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	19.5623	+	14.2128i	1.22026	+	0.886573i	0.996122	−	0.0879836i	$-0.0280423\pi$
$257$	19.5623	+	14.2128i	1.22026	+	0.886573i	0.224141	+	0.974557i	$0.428042\pi$
$258$	−0.381966	−	1.17557i	−0.0237802	−	0.0731878i
$259$	7.70820	+	23.7234i	0.478964	+	1.47410i
$260$	3.85410	+	2.80017i	0.239021	+	0.173659i
$261$	2.11803	−	1.53884i	0.131103	−	0.0952519i
$262$	5.64590	−	17.3763i	0.348805	−	1.07351i
$263$	−5.70820			−0.351983			−0.175991	−	0.984392i	$-0.556313\pi$
$263$	−5.70820			−0.351983			−0.175991	+	0.984392i	$0.556313\pi$
$264$		0			0
$265$	−11.0000			−0.675725
$266$	0.909830	−	2.80017i	0.0557853	−	0.171689i
$267$	1.38197	−	1.00406i	0.0845749	−	0.0614473i
$268$	−3.23607	−	2.35114i	−0.197674	−	0.143619i
$269$	4.61803	+	14.2128i	0.281567	+	0.866573i	0.987407	+	0.158202i	$0.0505696\pi$
$269$	4.61803	+	14.2128i	0.281567	+	0.866573i	−0.705840	+	0.708371i	$0.749430\pi$
$270$	1.19098	+	3.66547i	0.0724809	+	0.223073i
$271$	2.76393	+	2.00811i	0.167897	+	0.121984i	0.668561	−	0.743658i	$-0.266911\pi$
$271$	2.76393	+	2.00811i	0.167897	+	0.121984i	−0.500664	+	0.865642i	$0.666911\pi$
$272$	−5.23607	+	3.80423i	−0.317483	+	0.230665i
$273$	−0.909830	+	2.80017i	−0.0550654	+	0.169474i
$274$	17.1246			1.03454
$275$		0			0
$276$	−1.23607			−0.0744025
$277$	−9.00000	+	27.6992i	−0.540758	+	1.66428i	0.190111	+	0.981763i	$0.439115\pi$
$277$	−9.00000	+	27.6992i	−0.540758	+	1.66428i	−0.730869	+	0.682518i	$0.760885\pi$
$278$	−7.09017	+	5.15131i	−0.425240	+	0.308955i
$279$	−5.16312	−	3.75123i	−0.309108	−	0.224580i
$280$	−2.83688	−	8.73102i	−0.169536	−	0.521778i
$281$	−5.29180	−	16.2865i	−0.315682	−	0.971570i	−0.975473	−	0.220120i	$-0.929355\pi$
$281$	−5.29180	−	16.2865i	−0.315682	−	0.971570i	0.659791	−	0.751449i	$-0.270645\pi$
$282$	−5.23607	−	3.80423i	−0.311803	−	0.226538i
$283$	−9.61803	+	6.98791i	−0.571733	+	0.415388i	−0.835734	−	0.549134i	$-0.814958\pi$
$283$	−9.61803	+	6.98791i	−0.571733	+	0.415388i	0.264001	+	0.964522i	$0.414958\pi$
$284$	1.09017	−	3.35520i	0.0646897	−	0.199094i
$285$	4.76393			0.282191
$286$		0			0
$287$	2.94427			0.173795
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	−20.1353	+	14.6291i	−1.18443	+	0.860536i
$290$	−8.16312	−	5.93085i	−0.479355	−	0.348272i
$291$	1.33688	+	4.11450i	0.0783694	+	0.241196i
$292$	1.33688	+	4.11450i	0.0782350	+	0.240783i
$293$	19.3992	+	14.0943i	1.13331	+	0.823400i	0.986174	−	0.165716i	$-0.0529935\pi$
$293$	19.3992	+	14.0943i	1.13331	+	0.823400i	0.147139	+	0.989116i	$0.452994\pi$
$294$	−1.07295	+	0.779543i	−0.0625757	+	0.0454639i
$295$	−3.39919	+	10.4616i	−0.197908	+	0.609099i
$296$	10.4721			0.608681
$297$		0			0
$298$	3.61803			0.209587
$299$	0.472136	−	1.45309i	0.0273043	−	0.0840341i
$300$	7.97214	−	5.79210i	0.460271	−	0.334407i
$301$	−2.38197	−	1.73060i	−0.137294	−	0.0997501i
$302$	−1.95492	−	6.01661i	−0.112493	−	0.346217i
$303$	4.51722	+	13.9026i	0.259508	+	0.798682i
$304$	−1.00000	−	0.726543i	−0.0573539	−	0.0416701i
$305$	−35.0344	+	25.4540i	−2.00607	+	1.45749i
$306$	2.00000	−	6.15537i	0.114332	−	0.351879i
$307$	14.6525			0.836261			0.418130	−	0.908387i	$-0.362685\pi$
$307$	14.6525			0.836261			0.418130	+	0.908387i	$0.362685\pi$
$308$		0			0
$309$	17.0344			0.969056
$310$	−7.60081	+	23.3929i	−0.431697	+	1.32863i
$311$	−9.61803	+	6.98791i	−0.545389	+	0.396248i	−0.826082	−	0.563549i	$-0.809435\pi$
$311$	−9.61803	+	6.98791i	−0.545389	+	0.396248i	0.280694	+	0.959797i	$0.409435\pi$
$312$	1.00000	+	0.726543i	0.0566139	+	0.0411324i
$313$	6.75329	+	20.7845i	0.381718	+	1.17481i	0.938833	+	0.344373i	$0.111908\pi$
$313$	6.75329	+	20.7845i	0.381718	+	1.17481i	−0.557114	+	0.830436i	$0.688092\pi$
$314$	−1.38197	−	4.25325i	−0.0779889	−	0.240025i
$315$	7.42705	+	5.39607i	0.418467	+	0.304034i
$316$	−5.11803	+	3.71847i	−0.287912	+	0.209180i
$317$	4.90983	−	15.1109i	0.275764	−	0.848713i	−0.713253	−	0.700907i	$-0.752779\pi$
$317$	4.90983	−	15.1109i	0.275764	−	0.848713i	0.989016	−	0.147806i	$-0.0472211\pi$
$318$	−2.85410			−0.160050
$319$		0			0
$320$	−3.85410			−0.215451
$321$	−2.35410	+	7.24518i	−0.131393	+	0.404387i
$322$	−2.38197	+	1.73060i	−0.132742	+	0.0964425i
$323$	−6.47214	−	4.70228i	−0.360119	−	0.261642i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	3.76393	+	11.5842i	0.208785	+	0.642575i
$326$	−10.8541	−	7.88597i	−0.601153	−	0.436763i
$327$	−7.61803	+	5.53483i	−0.421278	+	0.306077i
$328$	0.381966	−	1.17557i	0.0210905	−	0.0649100i
$329$	−15.4164			−0.849934
$330$		0			0
$331$	−8.94427			−0.491622			−0.245811	−	0.969318i	$-0.579054\pi$
$331$	−8.94427			−0.491622			−0.245811	+	0.969318i	$0.579054\pi$
$332$	−5.04508	+	15.5272i	−0.276885	+	0.852164i
$333$	−8.47214	+	6.15537i	−0.464270	+	0.337312i
$334$	−2.23607	−	1.62460i	−0.122352	−	0.0888941i
$335$	−4.76393	−	14.6619i	−0.260281	−	0.801064i
$336$	−0.736068	−	2.26538i	−0.0401558	−	0.123587i
$337$	8.85410	+	6.43288i	0.482314	+	0.350421i	0.802221	−	0.597028i	$-0.203652\pi$
$337$	8.85410	+	6.43288i	0.482314	+	0.350421i	−0.319907	+	0.947449i	$0.603652\pi$
$338$	9.28115	−	6.74315i	0.504828	−	0.366779i
$339$	1.09017	−	3.35520i	0.0592099	−	0.182229i
$340$	−24.9443			−1.35279
$341$		0			0
$342$	1.23607			0.0668389
$343$	−6.12868	+	18.8621i	−0.330917	+	1.01846i
$344$	−1.00000	+	0.726543i	−0.0539164	+	0.0391725i
$345$	−3.85410	−	2.80017i	−0.207498	−	0.150756i
$346$	−3.35410	−	10.3229i	−0.180318	−	0.554961i
$347$	1.59017	+	4.89404i	0.0853648	+	0.262726i	0.984623	−	0.174692i	$-0.0558930\pi$
$347$	1.59017	+	4.89404i	0.0853648	+	0.262726i	−0.899258	+	0.437418i	$0.855893\pi$
$348$	−2.11803	−	1.53884i	−0.113539	−	0.0824906i
$349$	7.09017	−	5.15131i	0.379528	−	0.275743i	−0.381623	−	0.924318i	$-0.624635\pi$
$349$	7.09017	−	5.15131i	0.379528	−	0.275743i	0.761151	+	0.648575i	$0.224635\pi$
$350$	7.25329	−	22.3233i	0.387705	−	1.19323i
$351$	−1.23607			−0.0659764
$352$		0			0
$353$	27.5967			1.46883			0.734413	−	0.678702i	$-0.237457\pi$
$353$	27.5967			1.46883			0.734413	+	0.678702i	$0.237457\pi$
$354$	−0.881966	+	2.71441i	−0.0468760	+	0.144269i
$355$	11.0000	−	7.99197i	0.583819	−	0.424170i
$356$	−1.38197	−	1.00406i	−0.0732441	−	0.0532149i
$357$	−4.76393	−	14.6619i	−0.252134	−	0.775989i
$358$	−2.66312	−	8.19624i	−0.140750	−	0.433185i
$359$	−13.9443	−	10.1311i	−0.735951	−	0.534699i	0.155490	−	0.987838i	$-0.450304\pi$
$359$	−13.9443	−	10.1311i	−0.735951	−	0.534699i	−0.891440	+	0.453138i	$0.850304\pi$
$360$	3.11803	−	2.26538i	0.164335	−	0.119396i
$361$	−5.39919	+	16.6170i	−0.284168	+	0.874578i
$362$	−7.52786			−0.395656
$363$		0			0
$364$	2.94427			0.154322
$365$	−5.15248	+	15.8577i	−0.269693	+	0.830029i
$366$	−9.09017	+	6.60440i	−0.475151	+	0.345217i
$367$	−0.409830	−	0.297759i	−0.0213930	−	0.0155429i	0.577037	−	0.816718i	$-0.304209\pi$
$367$	−0.409830	−	0.297759i	−0.0213930	−	0.0155429i	−0.598430	+	0.801175i	$0.704209\pi$
$368$	0.381966	+	1.17557i	0.0199114	+	0.0612808i
$369$	0.381966	+	1.17557i	0.0198844	+	0.0611978i
$370$	32.6525	+	23.7234i	1.69752	+	1.23332i
$371$	−5.50000	+	3.99598i	−0.285546	+	0.207461i
$372$	−1.97214	+	6.06961i	−0.102250	+	0.314695i
$373$	−18.4721			−0.956451			−0.478225	−	0.878237i	$-0.658720\pi$
$373$	−18.4721			−0.956451			−0.478225	+	0.878237i	$0.658720\pi$
$374$		0			0
$375$	18.7082			0.966087
$376$	−2.00000	+	6.15537i	−0.103142	+	0.317439i
$377$	2.61803	−	1.90211i	0.134836	−	0.0979638i
$378$	1.92705	+	1.40008i	0.0991168	+	0.0720126i
$379$	−3.00000	−	9.23305i	−0.154100	−	0.474270i	0.843969	−	0.536392i	$-0.180213\pi$
$379$	−3.00000	−	9.23305i	−0.154100	−	0.474270i	−0.998069	+	0.0621221i	$0.980213\pi$
$380$	−1.47214	−	4.53077i	−0.0755190	−	0.232424i
$381$	9.70820	+	7.05342i	0.497366	+	0.361358i
$382$	−10.9443	+	7.95148i	−0.559958	+	0.406833i
$383$	2.70820	−	8.33499i	0.138383	−	0.425898i	−0.857718	−	0.514120i	$-0.828118\pi$
$383$	2.70820	−	8.33499i	0.138383	−	0.425898i	0.996101	+	0.0882220i	$0.0281185\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−15.3262			−0.780085
$387$	0.381966	−	1.17557i	0.0194164	−	0.0597576i
$388$	3.50000	−	2.54290i	0.177686	−	0.129096i
$389$	−17.0344	−	12.3762i	−0.863680	−	0.627501i	0.0652033	−	0.997872i	$-0.479230\pi$
$389$	−17.0344	−	12.3762i	−0.863680	−	0.627501i	−0.928884	+	0.370371i	$0.879230\pi$
$390$	1.47214	+	4.53077i	0.0745445	+	0.229424i
$391$	2.47214	+	7.60845i	0.125021	+	0.384776i
$392$	1.07295	+	0.779543i	0.0541921	+	0.0393729i
$393$	14.7812	−	10.7391i	0.745611	−	0.541718i
$394$	−1.57295	+	4.84104i	−0.0792440	+	0.243888i
$395$	−24.3820			−1.22679
$396$		0			0
$397$	−25.8885			−1.29931			−0.649654	−	0.760230i	$-0.725086\pi$
$397$	−25.8885			−1.29931			−0.649654	+	0.760230i	$0.725086\pi$
$398$	6.13525	−	18.8824i	0.307533	−	0.946488i
$399$	2.38197	−	1.73060i	0.119247	−	0.0866383i
$400$	−7.97214	−	5.79210i	−0.398607	−	0.289605i
$401$	7.32624	+	22.5478i	0.365855	+	1.12599i	0.949444	+	0.313936i	$0.101648\pi$
$401$	7.32624	+	22.5478i	0.365855	+	1.12599i	−0.583589	+	0.812049i	$0.698352\pi$
$402$	−1.23607	−	3.80423i	−0.0616495	−	0.189738i
$403$	−6.38197	−	4.63677i	−0.317908	−	0.230974i
$404$	11.8262	−	8.59226i	0.588377	−	0.427481i
$405$	−1.19098	+	3.66547i	−0.0591804	+	0.182139i
$406$	−6.23607			−0.309491
$407$		0			0
$408$	−6.47214			−0.320418
$409$	−0.281153	+	0.865300i	−0.0139021	+	0.0427863i	−0.957767	−	0.287546i	$-0.907161\pi$
$409$	−0.281153	+	0.865300i	−0.0139021	+	0.0427863i	0.943865	+	0.330332i	$0.107161\pi$
$410$	3.85410	−	2.80017i	0.190341	−	0.138290i
$411$	13.8541	+	10.0656i	0.683372	+	0.496499i
$412$	−5.26393	−	16.2007i	−0.259335	−	0.798152i
$413$	2.10081	+	6.46564i	0.103374	+	0.318153i
$414$	−1.00000	−	0.726543i	−0.0491473	−	0.0357076i
$415$	−50.9058	+	36.9852i	−2.49887	+	1.81553i
$416$	0.381966	−	1.17557i	0.0187274	−	0.0576371i
$417$	−8.76393			−0.429172
$418$		0			0
$419$	28.9787			1.41570			0.707851	−	0.706361i	$-0.249665\pi$
$419$	28.9787			1.41570			0.707851	+	0.706361i	$0.249665\pi$
$420$	2.83688	−	8.73102i	0.138426	−	0.426030i
$421$	4.14590	−	3.01217i	0.202059	−	0.146804i	−0.482155	−	0.876086i	$-0.660146\pi$
$421$	4.14590	−	3.01217i	0.202059	−	0.146804i	0.684213	+	0.729282i	$0.260146\pi$
$422$	−21.5623	−	15.6659i	−1.04964	−	0.762606i
$423$	−2.00000	−	6.15537i	−0.0972433	−	0.299284i
$424$	0.881966	+	2.71441i	0.0428321	+	0.131824i
$425$	−51.5967	−	37.4872i	−2.50281	−	1.81840i
$426$	2.85410	−	2.07363i	0.138282	−	0.100468i
$427$	−8.27051	+	25.4540i	−0.400238	+	1.23181i
$428$	7.61803			0.368232
$429$		0			0
$430$	−4.76393			−0.229737
$431$	−0.854102	+	2.62866i	−0.0411406	+	0.126618i	−0.969517	−	0.245023i	$-0.921205\pi$
$431$	−0.854102	+	2.62866i	−0.0411406	+	0.126618i	0.928377	+	0.371641i	$0.121205\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	2.69098	+	1.95511i	0.129320	+	0.0939568i	0.650565	−	0.759451i	$-0.274532\pi$
$433$	2.69098	+	1.95511i	0.129320	+	0.0939568i	−0.521245	+	0.853407i	$0.674532\pi$
$434$	4.69756	+	14.4576i	0.225490	+	0.693987i
$435$	−3.11803	−	9.59632i	−0.149498	−	0.460108i
$436$	7.61803	+	5.53483i	0.364838	+	0.265070i
$437$	−1.23607	+	0.898056i	−0.0591292	+	0.0429598i
$438$	−1.33688	+	4.11450i	−0.0638786	+	0.196598i
$439$	−13.0344			−0.622100			−0.311050	−	0.950394i	$-0.600681\pi$
$439$	−13.0344			−0.622100			−0.311050	+	0.950394i	$0.600681\pi$
$440$		0			0
$441$	−1.32624			−0.0631542
$442$	2.47214	−	7.60845i	0.117588	−	0.361897i
$443$	14.0172	−	10.1841i	0.665978	−	0.483862i	−0.202698	−	0.979241i	$-0.564971\pi$
$443$	14.0172	−	10.1841i	0.665978	−	0.483862i	0.868677	+	0.495380i	$0.164971\pi$
$444$	8.47214	+	6.15537i	0.402070	+	0.292121i
$445$	−2.03444	−	6.26137i	−0.0964418	−	0.296817i
$446$	−4.04508	−	12.4495i	−0.191540	−	0.589501i
$447$	2.92705	+	2.12663i	0.138445	+	0.100586i
$448$	−1.92705	+	1.40008i	−0.0910446	+	0.0661478i
$449$	0.0344419	−	0.106001i	0.00162541	−	0.00500250i	−0.950241	−	0.311517i	$-0.899163\pi$
$449$	0.0344419	−	0.106001i	0.00162541	−	0.00500250i	0.951866	+	0.306515i	$0.0991629\pi$
$450$	9.85410			0.464527
$451$		0			0
$452$	−3.52786			−0.165937
$453$	1.95492	−	6.01661i	0.0918499	−	0.282685i
$454$	11.2082	−	8.14324i	0.526027	−	0.382181i
$455$	9.18034	+	6.66991i	0.430381	+	0.312690i
$456$	−0.381966	−	1.17557i	−0.0178872	−	0.0550511i
$457$	7.71885	+	23.7562i	0.361072	+	1.11127i	0.952404	+	0.304838i	$0.0986024\pi$
$457$	7.71885	+	23.7562i	0.361072	+	1.11127i	−0.591332	+	0.806428i	$0.701398\pi$
$458$	−4.09017	−	2.97168i	−0.191121	−	0.138858i
$459$	5.23607	−	3.80423i	0.244399	−	0.177566i
$460$	−1.47214	+	4.53077i	−0.0686387	+	0.211248i
$461$	−12.8328			−0.597684			−0.298842	−	0.954303i	$-0.596600\pi$
$461$	−12.8328			−0.597684			−0.298842	+	0.954303i	$0.596600\pi$
$462$		0			0
$463$	7.90983			0.367601			0.183800	−	0.982964i	$-0.441160\pi$
$463$	7.90983			0.367601			0.183800	+	0.982964i	$0.441160\pi$
$464$	−0.809017	+	2.48990i	−0.0375577	+	0.115591i
$465$	−19.8992	+	14.4576i	−0.922803	+	0.670455i
$466$	−7.23607	−	5.25731i	−0.335204	−	0.243540i
$467$	−0.173762	−	0.534785i	−0.00804075	−	0.0247469i	0.946956	−	0.321364i	$-0.104141\pi$
$467$	−0.173762	−	0.534785i	−0.00804075	−	0.0247469i	−0.954996	+	0.296617i	$0.904141\pi$
$468$	0.381966	+	1.17557i	0.0176564	+	0.0543408i
$469$	−7.70820	−	5.60034i	−0.355932	−	0.258600i
$470$	−20.1803	+	14.6619i	−0.930850	+	0.676302i
$471$	1.38197	−	4.25325i	0.0636776	−	0.195980i
$472$	2.85410			0.131371
$473$		0			0
$474$	−6.32624			−0.290574
$475$	3.76393	−	11.5842i	0.172701	−	0.531519i
$476$	−12.4721	+	9.06154i	−0.571659	+	0.415335i
$477$	−2.30902	−	1.67760i	−0.105723	−	0.0768120i
$478$	−2.32624	−	7.15942i	−0.106400	−	0.327464i
$479$	−0.854102	−	2.62866i	−0.0390249	−	0.120106i	0.929646	−	0.368454i	$-0.120113\pi$
$479$	−0.854102	−	2.62866i	−0.0390249	−	0.120106i	−0.968671	+	0.248347i	$0.920113\pi$
$480$	−3.11803	−	2.26538i	−0.142318	−	0.103400i
$481$	−10.4721	+	7.60845i	−0.477488	+	0.346916i
$482$	−6.97214	+	21.4580i	−0.317572	+	0.977386i
$483$	−2.94427			−0.133969
$484$		0			0
$485$	16.6738			0.757117
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	17.7812	−	12.9188i	0.805741	−	0.585405i	−0.106852	−	0.994275i	$-0.534077\pi$
$487$	17.7812	−	12.9188i	0.805741	−	0.585405i	0.912593	+	0.408870i	$0.134077\pi$
$488$	9.09017	+	6.60440i	0.411493	+	0.298967i
$489$	−4.14590	−	12.7598i	−0.187484	−	0.577016i
$490$	1.57953	+	4.86128i	0.0713557	+	0.219610i
$491$	30.9443	+	22.4823i	1.39650	+	1.01461i	0.995117	+	0.0987010i	$0.0314687\pi$
$491$	30.9443	+	22.4823i	1.39650	+	1.01461i	0.401378	+	0.915912i	$0.368531\pi$
$492$	1.00000	−	0.726543i	0.0450835	−	0.0327551i
$493$	−5.23607	+	16.1150i	−0.235821	+	0.725781i
$494$	1.52786			0.0687419
$495$		0			0
$496$	6.38197			0.286559
$497$	2.59675	−	7.99197i	0.116480	−	0.358489i
$498$	−13.2082	+	9.59632i	−0.591874	+	0.430021i
$499$	−15.7082	−	11.4127i	−0.703196	−	0.510902i	0.177776	−	0.984071i	$-0.443110\pi$
$499$	−15.7082	−	11.4127i	−0.703196	−	0.510902i	−0.880971	+	0.473169i	$0.843110\pi$
$500$	−5.78115	−	17.7926i	−0.258541	−	0.795707i
$501$	−0.854102	−	2.62866i	−0.0381585	−	0.117440i
$502$	2.97214	+	2.15938i	0.132653	+	0.0963780i
$503$	32.6525	−	23.7234i	1.45590	−	1.05777i	0.471495	−	0.881869i	$-0.343715\pi$
$503$	32.6525	−	23.7234i	1.45590	−	1.05777i	0.984407	−	0.175906i	$-0.0562855\pi$
$504$	0.736068	−	2.26538i	0.0327871	−	0.100908i
$505$	56.3394			2.50707
$506$		0			0
$507$	11.4721			0.509495
$508$	3.70820	−	11.4127i	0.164525	−	0.506356i
$509$	−22.4894	+	16.3395i	−0.996823	+	0.724234i	−0.961405	−	0.275138i	$-0.911276\pi$
$509$	−22.4894	+	16.3395i	−0.996823	+	0.724234i	−0.0354185	+	0.999373i	$0.511276\pi$
$510$	−20.1803	−	14.6619i	−0.893600	−	0.649239i
$511$	3.18441	+	9.80059i	0.140870	+	0.433553i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	1.00000	+	0.726543i	0.0441511	+	0.0320776i
$514$	19.5623	−	14.2128i	0.862856	−	0.626902i
$515$	20.2877	−	62.4392i	0.893984	−	2.75140i
$516$	−1.23607			−0.0544149
$517$		0			0
$518$	24.9443			1.09599
$519$	3.35410	−	10.3229i	0.147229	−	0.453123i
$520$	3.85410	−	2.80017i	0.169014	−	0.122796i
$521$	−3.70820	−	2.69417i	−0.162459	−	0.118034i	0.503585	−	0.863946i	$-0.332014\pi$
$521$	−3.70820	−	2.69417i	−0.162459	−	0.118034i	−0.666045	+	0.745912i	$0.732014\pi$
$522$	−0.809017	−	2.48990i	−0.0354097	−	0.108980i
$523$	−9.14590	−	28.1482i	−0.399922	−	1.23083i	−0.925061	−	0.379818i	$-0.875987\pi$
$523$	−9.14590	−	28.1482i	−0.399922	−	1.23083i	0.525139	−	0.851016i	$-0.324013\pi$
$524$	−14.7812	−	10.7391i	−0.645718	−	0.469141i
$525$	18.9894	−	13.7966i	0.828763	−	0.602132i
$526$	−1.76393	+	5.42882i	−0.0769111	+	0.236708i
$527$	41.3050			1.79927
$528$		0			0
$529$	−21.4721			−0.933571
$530$	−3.39919	+	10.4616i	−0.147651	+	0.454424i
$531$	−2.30902	+	1.67760i	−0.100203	+	0.0728016i
$532$	−2.38197	−	1.73060i	−0.103271	−	0.0750310i
$533$	0.472136	+	1.45309i	0.0204505	+	0.0629401i
$534$	−0.527864	−	1.62460i	−0.0228429	−	0.0703033i
$535$	23.7533	+	17.2578i	1.02694	+	0.746119i
$536$	−3.23607	+	2.35114i	−0.139777	+	0.101554i
$537$	2.66312	−	8.19624i	0.114922	−	0.353694i
$538$	14.9443			0.644293
$539$		0			0
$540$	3.85410			0.165854
$541$	5.09017	−	15.6659i	0.218843	−	0.673531i	−0.780015	−	0.625761i	$-0.784789\pi$
$541$	5.09017	−	15.6659i	0.218843	−	0.673531i	0.998858	−	0.0477700i	$-0.0152115\pi$
$542$	2.76393	−	2.00811i	0.118721	−	0.0862559i
$543$	−6.09017	−	4.42477i	−0.261354	−	0.189885i
$544$	2.00000	+	6.15537i	0.0857493	+	0.263909i
$545$	11.2148	+	34.5155i	0.480388	+	1.47848i
$546$	2.38197	+	1.73060i	0.101939	+	0.0740628i
$547$	3.38197	−	2.45714i	0.144602	−	0.105060i	−0.513132	−	0.858310i	$-0.671515\pi$
$547$	3.38197	−	2.45714i	0.144602	−	0.105060i	0.657734	+	0.753250i	$0.271515\pi$
$548$	5.29180	−	16.2865i	0.226054	−	0.695724i
$549$	−11.2361			−0.479544
$550$		0			0
$551$	−3.23607			−0.137861
$552$	−0.381966	+	1.17557i	−0.0162576	+	0.0500356i
$553$	−12.1910	+	8.85727i	−0.518413	+	0.376649i
$554$	23.5623	+	17.1190i	1.00107	+	0.727317i
$555$	12.4721	+	38.3853i	0.529413	+	1.62936i
$556$	2.70820	+	8.33499i	0.114853	+	0.353483i
$557$	10.4894	+	7.62096i	0.444448	+	0.322911i	0.787400	−	0.616442i	$-0.211427\pi$
$557$	10.4894	+	7.62096i	0.444448	+	0.322911i	−0.342952	+	0.939353i	$0.611427\pi$
$558$	−5.16312	+	3.75123i	−0.218572	+	0.158802i
$559$	0.472136	−	1.45309i	0.0199692	−	0.0614589i
$560$	−9.18034			−0.387940
$561$		0			0
$562$	−17.1246			−0.722358
$563$	2.11146	−	6.49839i	0.0889873	−	0.273875i	−0.896653	−	0.442734i	$-0.854008\pi$
$563$	2.11146	−	6.49839i	0.0889873	−	0.273875i	0.985640	+	0.168860i	$0.0540085\pi$
$564$	−5.23607	+	3.80423i	−0.220478	+	0.160187i
$565$	−11.0000	−	7.99197i	−0.462773	−	0.336225i
$566$	3.67376	+	11.3067i	0.154420	+	0.475255i
$567$	0.736068	+	2.26538i	0.0309119	+	0.0951372i
$568$	−2.85410	−	2.07363i	−0.119755	−	0.0870074i
$569$	13.6180	−	9.89408i	0.570898	−	0.414781i	−0.264534	−	0.964376i	$-0.585218\pi$
$569$	13.6180	−	9.89408i	0.570898	−	0.414781i	0.835431	+	0.549595i	$0.185218\pi$
$570$	1.47214	−	4.53077i	0.0616610	−	0.189773i
$571$	−39.5967			−1.65707			−0.828536	−	0.559936i	$-0.810826\pi$
$571$	−39.5967			−1.65707			−0.828536	+	0.559936i	$0.810826\pi$
$572$		0			0
$573$	−13.5279			−0.565135
$574$	0.909830	−	2.80017i	0.0379756	−	0.116877i
$575$	−9.85410	+	7.15942i	−0.410944	+	0.298569i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−1.26393	−	3.88998i	−0.0526182	−	0.161942i	0.921294	−	0.388866i	$-0.127133\pi$
$577$	−1.26393	−	3.88998i	−0.0526182	−	0.161942i	−0.973912	+	0.226924i	$0.927133\pi$
$578$	7.69098	+	23.6704i	0.319903	+	0.984559i
$579$	−12.3992	−	9.00854i	−0.515293	−	0.374382i
$580$	−8.16312	+	5.93085i	−0.338955	+	0.246265i
$581$	−12.0172	+	36.9852i	−0.498558	+	1.53440i
$582$	4.32624			0.179328
$583$		0			0
$584$	4.32624			0.179021
$585$	−1.47214	+	4.53077i	−0.0608653	+	0.187324i
$586$	19.3992	−	14.0943i	0.801373	−	0.582232i
$587$	10.4443	+	7.58821i	0.431081	+	0.313199i	0.782081	−	0.623177i	$-0.214158\pi$
$587$	10.4443	+	7.58821i	0.431081	+	0.313199i	−0.351000	+	0.936376i	$0.614158\pi$
$588$	0.409830	+	1.26133i	0.0169011	+	0.0520163i
$589$	2.43769	+	7.50245i	0.100443	+	0.309133i
$590$	8.89919	+	6.46564i	0.366374	+	0.266186i
$591$	−4.11803	+	2.99193i	−0.169393	+	0.123071i
$592$	3.23607	−	9.95959i	0.133002	−	0.409337i
$593$	15.5279			0.637653			0.318826	−	0.947813i	$-0.396711\pi$
$593$	15.5279			0.637653			0.318826	+	0.947813i	$0.396711\pi$
$594$		0			0
$595$	−59.4164			−2.43584
$596$	1.11803	−	3.44095i	0.0457965	−	0.140947i
$597$	16.0623	−	11.6699i	0.657386	−	0.477619i
$598$	−1.23607	−	0.898056i	−0.0505466	−	0.0367242i
$599$	−11.2361	−	34.5811i	−0.459093	−	1.41294i	−0.866262	−	0.499591i	$-0.833484\pi$
$599$	−11.2361	−	34.5811i	−0.459093	−	1.41294i	0.407168	−	0.913353i	$-0.366516\pi$
$600$	−3.04508	−	9.37181i	−0.124315	−	0.382602i
$601$	−15.1631	−	11.0167i	−0.618517	−	0.449379i	0.233886	−	0.972264i	$-0.424856\pi$
$601$	−15.1631	−	11.0167i	−0.618517	−	0.449379i	−0.852403	+	0.522885i	$0.824856\pi$
$602$	−2.38197	+	1.73060i	−0.0970817	+	0.0705340i
$603$	1.23607	−	3.80423i	0.0503366	−	0.154920i
$604$	−6.32624			−0.257411
$605$		0			0
$606$	14.6180			0.593817
$607$	−14.7639	+	45.4387i	−0.599250	+	1.84430i	−0.0669285	+	0.997758i	$0.521320\pi$
$607$	−14.7639	+	45.4387i	−0.599250	+	1.84430i	−0.532321	+	0.846543i	$0.678680\pi$
$608$	−1.00000	+	0.726543i	−0.0405554	+	0.0294652i
$609$	−5.04508	−	3.66547i	−0.204437	−	0.148532i
$610$	13.3820	+	41.1855i	0.541820	+	1.66755i
$611$	−2.47214	−	7.60845i	−0.100012	−	0.307805i
$612$	−5.23607	−	3.80423i	−0.211656	−	0.153777i
$613$	22.4164	−	16.2865i	0.905390	−	0.657804i	−0.0344546	−	0.999406i	$-0.510969\pi$
$613$	22.4164	−	16.2865i	0.905390	−	0.657804i	0.939845	+	0.341602i	$0.110969\pi$
$614$	4.52786	−	13.9353i	0.182730	−	0.562384i
$615$	4.76393			0.192100
$616$		0			0
$617$	−43.7082			−1.75963			−0.879813	−	0.475320i	$-0.842332\pi$
$617$	−43.7082			−1.75963			−0.879813	+	0.475320i	$0.842332\pi$
$618$	5.26393	−	16.2007i	0.211746	−	0.651688i
$619$	−30.1803	+	21.9273i	−1.21305	+	0.881333i	−0.995504	−	0.0947174i	$-0.969805\pi$
$619$	−30.1803	+	21.9273i	−1.21305	+	0.881333i	−0.217546	+	0.976050i	$0.569805\pi$
$620$	19.8992	+	14.4576i	0.799171	+	0.580631i
$621$	−0.381966	−	1.17557i	−0.0153278	−	0.0471740i
$622$	3.67376	+	11.3067i	0.147304	+	0.453356i
$623$	−3.29180	−	2.39163i	−0.131883	−	0.0958186i
$624$	1.00000	−	0.726543i	0.0400320	−	0.0290850i
$625$	7.05573	−	21.7153i	0.282229	−	0.868612i
$626$	21.8541			0.873466
$627$		0			0
$628$	−4.47214			−0.178458
$629$	20.9443	−	64.4598i	0.835103	−	2.57018i
$630$	7.42705	−	5.39607i	0.295901	−	0.214985i
$631$	19.2984	+	14.0211i	0.768256	+	0.558171i	0.901432	−	0.432922i	$-0.142517\pi$
$631$	19.2984	+	14.0211i	0.768256	+	0.558171i	−0.133175	+	0.991092i	$0.542517\pi$
$632$	1.95492	+	6.01661i	0.0777623	+	0.239328i
$633$	−8.23607	−	25.3480i	−0.327354	−	1.00749i
$634$	−12.8541	−	9.33905i	−0.510502	−	0.370901i
$635$	37.4164	−	27.1846i	1.48482	−	1.07879i
$636$	−0.881966	+	2.71441i	−0.0349722	+	0.107633i
$637$	−1.63932			−0.0649522
$638$		0			0
$639$	3.52786			0.139560
$640$	−1.19098	+	3.66547i	−0.0470777	+	0.144890i
$641$	−5.56231	+	4.04125i	−0.219698	+	0.159620i	−0.692191	−	0.721715i	$-0.743354\pi$
$641$	−5.56231	+	4.04125i	−0.219698	+	0.159620i	0.472493	+	0.881335i	$0.343354\pi$
$642$	6.16312	+	4.47777i	0.243239	+	0.176723i
$643$	−2.14590	−	6.60440i	−0.0846260	−	0.260452i	0.899786	−	0.436332i	$-0.143723\pi$
$643$	−2.14590	−	6.60440i	−0.0846260	−	0.260452i	−0.984412	+	0.175880i	$0.943723\pi$
$644$	0.909830	+	2.80017i	0.0358523	+	0.110342i
$645$	−3.85410	−	2.80017i	−0.151755	−	0.110257i
$646$	−6.47214	+	4.70228i	−0.254643	+	0.185009i
$647$	−13.3262	+	41.0139i	−0.523908	+	1.61242i	0.242556	+	0.970137i	$0.422014\pi$
$647$	−13.3262	+	41.0139i	−0.523908	+	1.61242i	−0.766464	+	0.642287i	$0.777986\pi$
$648$	1.00000			0.0392837
$649$		0			0
$650$	12.1803			0.477752
$651$	−4.69756	+	14.4576i	−0.184112	+	0.566638i
$652$	−10.8541	+	7.88597i	−0.425079	+	0.308838i
$653$	22.5344	+	16.3722i	0.881841	+	0.640695i	0.933738	−	0.357958i	$-0.116527\pi$
$653$	22.5344	+	16.3722i	0.881841	+	0.640695i	−0.0518970	+	0.998652i	$0.516527\pi$
$654$	2.90983	+	8.95554i	0.113783	+	0.350189i
$655$	−21.7599	−	66.9700i	−0.850228	−	2.61673i
$656$	−1.00000	−	0.726543i	−0.0390434	−	0.0283667i
$657$	−3.50000	+	2.54290i	−0.136548	+	0.0992079i
$658$	−4.76393	+	14.6619i	−0.185717	+	0.571579i
$659$	49.8541			1.94204			0.971020	−	0.238998i	$-0.0768190\pi$
$659$	49.8541			1.94204			0.971020	+	0.238998i	$0.0768190\pi$
$660$		0			0
$661$	28.1803			1.09609			0.548044	−	0.836449i	$-0.315373\pi$
$661$	28.1803			1.09609			0.548044	+	0.836449i	$0.315373\pi$
$662$	−2.76393	+	8.50651i	−0.107423	+	0.330615i
$663$	6.47214	−	4.70228i	0.251357	−	0.182622i
$664$	13.2082	+	9.59632i	0.512578	+	0.372410i
$665$	−3.50658	−	10.7921i	−0.135979	−	0.418501i
$666$	3.23607	+	9.95959i	0.125395	+	0.385926i
$667$	2.61803	+	1.90211i	0.101371	+	0.0736501i
$668$	−2.23607	+	1.62460i	−0.0865161	+	0.0628576i
$669$	4.04508	−	12.4495i	0.156392	−	0.481325i
$670$	−15.4164			−0.595588
$671$		0			0
$672$	−2.38197			−0.0918863
$673$	−11.1353	+	34.2708i	−0.429233	+	1.32104i	0.469650	+	0.882853i	$0.344380\pi$
$673$	−11.1353	+	34.2708i	−0.429233	+	1.32104i	−0.898883	+	0.438189i	$0.855620\pi$
$674$	8.85410	−	6.43288i	0.341047	−	0.247785i
$675$	7.97214	+	5.79210i	0.306848	+	0.222938i
$676$	−3.54508	−	10.9106i	−0.136349	−	0.419640i
$677$	−0.770510	−	2.37139i	−0.0296131	−	0.0911397i	0.935158	−	0.354232i	$-0.115258\pi$
$677$	−0.770510	−	2.37139i	−0.0296131	−	0.0911397i	−0.964771	+	0.263092i	$0.915258\pi$
$678$	−2.85410	−	2.07363i	−0.109611	−	0.0796371i
$679$	8.33688	−	6.05710i	0.319940	−	0.232450i
$680$	−7.70820	+	23.7234i	−0.295596	+	0.909751i
$681$	13.8541			0.530890
$682$		0			0
$683$	3.25735			0.124639			0.0623196	−	0.998056i	$-0.480150\pi$
$683$	3.25735			0.124639			0.0623196	+	0.998056i	$0.480150\pi$
$684$	0.381966	−	1.17557i	0.0146048	−	0.0449491i
$685$	53.3951	−	38.7938i	2.04012	−	1.48224i
$686$	16.0451	+	11.6574i	0.612604	+	0.445083i
$687$	−1.56231	−	4.80828i	−0.0596057	−	0.183447i
$688$	0.381966	+	1.17557i	0.0145623	+	0.0448182i
$689$	−2.85410	−	2.07363i	−0.108733	−	0.0789989i
$690$	−3.85410	+	2.80017i	−0.146723	+	0.106601i
$691$	−4.23607	+	13.0373i	−0.161148	+	0.495961i	−0.998732	−	0.0503469i	$-0.983967\pi$
$691$	−4.23607	+	13.0373i	−0.161148	+	0.495961i	0.837584	+	0.546308i	$0.183967\pi$
$692$	−10.8541			−0.412611
$693$		0			0
$694$	5.14590			0.195336
$695$	−10.4377	+	32.1239i	−0.395924	+	1.21853i
$696$	−2.11803	+	1.53884i	−0.0802839	+	0.0583296i
$697$	−6.47214	−	4.70228i	−0.245150	−	0.178112i
$698$	−2.70820	−	8.33499i	−0.102507	−	0.315484i
$699$	−2.76393	−	8.50651i	−0.104542	−	0.321746i
$700$	−18.9894	−	13.7966i	−0.717730	−	0.521462i
$701$	−15.3262	+	11.1352i	−0.578864	+	0.420569i	−0.838314	−	0.545187i	$-0.816459\pi$
$701$	−15.3262	+	11.1352i	−0.578864	+	0.420569i	0.259450	+	0.965756i	$0.416459\pi$
$702$	−0.381966	+	1.17557i	−0.0144164	+	0.0443690i
$703$	12.9443			0.488202
$704$		0			0
$705$	−24.9443			−0.939456
$706$	8.52786	−	26.2461i	0.320950	−	0.987784i
$707$	28.1697	−	20.4665i	1.05943	−	0.769721i
$708$	2.30902	+	1.67760i	0.0867782	+	0.0630480i
$709$	−12.6738	−	39.0058i	−0.475973	−	1.46489i	−0.844641	−	0.535333i	$-0.820186\pi$
$709$	−12.6738	−	39.0058i	−0.475973	−	1.46489i	0.368668	−	0.929561i	$-0.379814\pi$
$710$	−4.20163	−	12.9313i	−0.157684	−	0.485302i
$711$	−5.11803	−	3.71847i	−0.191941	−	0.139453i
$712$	−1.38197	+	1.00406i	−0.0517914	+	0.0376286i
$713$	2.43769	−	7.50245i	0.0912924	−	0.280969i
$714$	−15.4164			−0.576945
$715$		0			0
$716$	−8.61803			−0.322071
$717$	2.32624	−	7.15942i	0.0868749	−	0.267374i
$718$	−13.9443	+	10.1311i	−0.520396	+	0.378090i
$719$	5.61803	+	4.08174i	0.209517	+	0.152223i	0.687595	−	0.726094i	$-0.258666\pi$
$719$	5.61803	+	4.08174i	0.209517	+	0.152223i	−0.478078	+	0.878317i	$0.658666\pi$
$720$	−1.19098	−	3.66547i	−0.0443853	−	0.136604i
$721$	−12.5385	−	38.5896i	−0.466958	−	1.43715i
$722$	14.1353	+	10.2699i	0.526060	+	0.382205i
$723$	−18.2533	+	13.2618i	−0.678847	+	0.493211i
$724$	−2.32624	+	7.15942i	−0.0864540	+	0.266078i
$725$	−25.7984			−0.958128
$726$		0			0
$727$	−23.4164			−0.868466			−0.434233	−	0.900800i	$-0.642981\pi$
$727$	−23.4164			−0.868466			−0.434233	+	0.900800i	$0.642981\pi$
$728$	0.909830	−	2.80017i	0.0337205	−	0.103781i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	13.4894	+	9.80059i	0.499263	+	0.362736i
$731$	2.47214	+	7.60845i	0.0914353	+	0.281409i
$732$	3.47214	+	10.6861i	0.128334	+	0.394971i
$733$	24.5066	+	17.8051i	0.905171	+	0.657645i	0.939789	−	0.341755i	$-0.111021\pi$
$733$	24.5066	+	17.8051i	0.905171	+	0.657645i	−0.0346179	+	0.999401i	$0.511021\pi$
$734$	−0.409830	+	0.297759i	−0.0151271	+	0.0109905i
$735$	−1.57953	+	4.86128i	−0.0582617	+	0.179311i
$736$	1.23607			0.0455621
$737$		0			0
$738$	1.23607			0.0455003
$739$	10.1803	−	31.3319i	0.374490	−	1.15256i	−0.569332	−	0.822107i	$-0.692798\pi$
$739$	10.1803	−	31.3319i	0.374490	−	1.15256i	0.943822	−	0.330454i	$-0.107202\pi$
$740$	32.6525	−	23.7234i	1.20033	−	0.872090i
$741$	1.23607	+	0.898056i	0.0454081	+	0.0329909i
$742$	2.10081	+	6.46564i	0.0771233	+	0.237361i
$743$	10.4377	+	32.1239i	0.382922	+	1.17851i	0.937977	+	0.346698i	$0.112697\pi$
$743$	10.4377	+	32.1239i	0.382922	+	1.17851i	−0.555055	+	0.831814i	$0.687303\pi$
$744$	5.16312	+	3.75123i	0.189289	+	0.137527i
$745$	11.2812	−	8.19624i	0.413309	−	0.300287i
$746$	−5.70820	+	17.5680i	−0.208992	+	0.643212i
$747$	−16.3262			−0.597346
$748$		0			0
$749$	18.1459			0.663037
$750$	5.78115	−	17.7926i	0.211098	−	0.649692i
$751$	37.1246	−	26.9726i	1.35470	−	0.984244i	0.355934	−	0.934511i	$-0.384163\pi$
$751$	37.1246	−	26.9726i	1.35470	−	0.984244i	0.998763	−	0.0497333i	$-0.0158371\pi$
$752$	5.23607	+	3.80423i	0.190940	+	0.138726i
$753$	1.13525	+	3.49396i	0.0413710	+	0.127327i
$754$	−1.00000	−	3.07768i	−0.0364179	−	0.112083i
$755$	−19.7254	−	14.3314i	−0.717882	−	0.521572i
$756$	1.92705	−	1.40008i	0.0700862	−	0.0509206i
$757$	11.2918	−	34.7526i	0.410407	−	1.26310i	−0.505888	−	0.862599i	$-0.668835\pi$
$757$	11.2918	−	34.7526i	0.410407	−	1.26310i	0.916295	−	0.400504i	$-0.131165\pi$
$758$	−9.70820			−0.352618
$759$		0			0
$760$	−4.76393			−0.172806
$761$	7.32624	−	22.5478i	0.265576	−	0.817359i	−0.725984	−	0.687711i	$-0.758615\pi$
$761$	7.32624	−	22.5478i	0.265576	−	0.817359i	0.991560	−	0.129647i	$-0.0413845\pi$
$762$	9.70820	−	7.05342i	0.351691	−	0.255519i
$763$	18.1459	+	13.1838i	0.656926	+	0.477284i
$764$	4.18034	+	12.8658i	0.151239	+	0.465467i
$765$	−7.70820	−	23.7234i	−0.278691	−	0.857722i
$766$	−7.09017	−	5.15131i	−0.256178	−	0.186124i
$767$	−2.85410	+	2.07363i	−0.103056	+	0.0748743i
$768$	−0.309017	+	0.951057i	−0.0111507	+	0.0343183i
$769$	29.2705			1.05552			0.527761	−	0.849393i	$-0.323032\pi$
$769$	29.2705			1.05552			0.527761	+	0.849393i	$0.323032\pi$
$770$		0			0
$771$	24.1803			0.870834
$772$	−4.73607	+	14.5761i	−0.170455	+	0.524606i
$773$	23.0623	−	16.7557i	0.829493	−	0.602662i	−0.0899225	−	0.995949i	$-0.528662\pi$
$773$	23.0623	−	16.7557i	0.829493	−	0.602662i	0.919416	+	0.393286i	$0.128662\pi$
$774$	−1.00000	−	0.726543i	−0.0359443	−	0.0261150i
$775$	19.4336	+	59.8106i	0.698077	+	2.14846i
$776$	−1.33688	−	4.11450i	−0.0479912	−	0.147702i
$777$	20.1803	+	14.6619i	0.723966	+	0.525992i
$778$	−17.0344	+	12.3762i	−0.610714	+	0.443710i
$779$	0.472136	−	1.45309i	0.0169160	−	0.0520622i
$780$	4.76393			0.170576
$781$		0			0
$782$	8.00000			0.286079
$783$	0.809017	−	2.48990i	0.0289119	−	0.0889817i
$784$	1.07295	−	0.779543i	0.0383196	−	0.0278408i
$785$	−13.9443	−	10.1311i	−0.497692	−	0.361595i
$786$	−5.64590	−	17.3763i	−0.201383	−	0.619792i
$787$	14.6738	+	45.1612i	0.523063	+	1.60982i	0.768114	+	0.640313i	$0.221195\pi$
$787$	14.6738	+	45.1612i	0.523063	+	1.60982i	−0.245051	+	0.969510i	$0.578805\pi$
$788$	4.11803	+	2.99193i	0.146699	+	0.106583i
$789$	−4.61803	+	3.35520i	−0.164406	+	0.119448i
$790$	−7.53444	+	23.1886i	−0.268063	+	0.825014i
$791$	−8.40325			−0.298785
$792$		0			0
$793$	−13.8885			−0.493197
$794$	−8.00000	+	24.6215i	−0.283909	+	0.873783i
$795$	−8.89919	+	6.46564i	−0.315622	+	0.229313i
$796$	−16.0623	−	11.6699i	−0.569313	−	0.413630i
$797$	−6.29837	−	19.3844i	−0.223100	−	0.686631i	−0.998479	−	0.0551347i	$-0.982441\pi$
$797$	−6.29837	−	19.3844i	−0.223100	−	0.686631i	0.775379	−	0.631496i	$-0.217559\pi$
$798$	−0.909830	−	2.80017i	−0.0322076	−	0.0991249i
$799$	33.8885	+	24.6215i	1.19889	+	0.871045i
$800$	−7.97214	+	5.79210i	−0.281858	+	0.204782i
$801$	0.527864	−	1.62460i	0.0186512	−	0.0574024i
$802$	23.7082			0.837166
$803$		0			0
$804$	−4.00000			−0.141069
$805$	−3.50658	+	10.7921i	−0.123591	+	0.380373i
$806$	−6.38197	+	4.63677i	−0.224795	+	0.163323i
$807$	12.0902	+	8.78402i	0.425594	+	0.309212i
$808$	−4.51722	−	13.9026i	−0.158915	−	0.489091i
$809$	−15.5279	−	47.7899i	−0.545931	−	1.68020i	−0.718767	−	0.695251i	$-0.755293\pi$
$809$	−15.5279	−	47.7899i	−0.545931	−	1.68020i	0.172836	−	0.984951i	$-0.444707\pi$
$810$	3.11803	+	2.26538i	0.109557	+	0.0795975i
$811$	36.5967	−	26.5891i	1.28509	−	0.933669i	0.285392	−	0.958411i	$-0.407876\pi$
$811$	36.5967	−	26.5891i	1.28509	−	0.933669i	0.999694	+	0.0247416i	$0.00787630\pi$
$812$	−1.92705	+	5.93085i	−0.0676262	+	0.208132i
$813$	3.41641			0.119819
$814$		0			0
$815$	−51.7082			−1.81126
$816$	−2.00000	+	6.15537i	−0.0700140	+	0.215481i
$817$	−1.23607	+	0.898056i	−0.0432445	+	0.0314190i
$818$	0.736068	+	0.534785i	0.0257360	+	0.0186983i
$819$	0.909830	+	2.80017i	0.0317920	+	0.0978458i
$820$	−1.47214	−	4.53077i	−0.0514092	−	0.158221i
$821$	−8.01722	−	5.82485i	−0.279803	−	0.203289i	0.439029	−	0.898473i	$-0.355323\pi$
$821$	−8.01722	−	5.82485i	−0.279803	−	0.203289i	−0.718831	+	0.695184i	$0.755323\pi$
$822$	13.8541	−	10.0656i	0.483217	−	0.351078i
$823$	14.8992	−	45.8550i	0.519353	−	1.59840i	−0.255866	−	0.966712i	$-0.582361\pi$
$823$	14.8992	−	45.8550i	0.519353	−	1.59840i	0.775219	−	0.631692i	$-0.217639\pi$
$824$	−17.0344			−0.593423
$825$		0			0
$826$	6.79837			0.236546
$827$	−15.3541	+	47.2551i	−0.533914	+	1.64322i	0.212069	+	0.977255i	$0.431980\pi$
$827$	−15.3541	+	47.2551i	−0.533914	+	1.64322i	−0.745983	+	0.665965i	$0.768020\pi$
$828$	−1.00000	+	0.726543i	−0.0347524	+	0.0252491i
$829$	44.7426	+	32.5074i	1.55398	+	1.12903i	0.940739	+	0.339131i	$0.110133\pi$
$829$	44.7426	+	32.5074i	1.55398	+	1.12903i	0.613237	+	0.789899i	$0.289867\pi$
$830$	19.4443	+	59.8433i	0.674921	+	2.07719i
$831$	9.00000	+	27.6992i	0.312207	+	0.960873i
$832$	−1.00000	−	0.726543i	−0.0346688	−	0.0251883i
$833$	6.94427	−	5.04531i	0.240605	−	0.174810i
$834$	−2.70820	+	8.33499i	−0.0937774	+	0.288617i
$835$	−10.6525			−0.368644
$836$		0			0
$837$	−6.38197			−0.220593
$838$	8.95492	−	27.5604i	0.309342	−	0.952058i
$839$	−30.0344	+	21.8213i	−1.03690	+	0.753355i	−0.969679	−	0.244383i	$-0.921415\pi$
$839$	−30.0344	+	21.8213i	−1.03690	+	0.753355i	−0.0672253	+	0.997738i	$0.521415\pi$
$840$	−7.42705	−	5.39607i	−0.256258	−	0.186182i
$841$	−6.84346	−	21.0620i	−0.235981	−	0.726276i
$842$	−1.58359	−	4.87380i	−0.0545742	−	0.167962i
$843$	−13.8541	−	10.0656i	−0.477161	−	0.346677i
$844$	−21.5623	+	15.6659i	−0.742205	+	0.539244i
$845$	13.6631	−	42.0508i	0.470026	−	1.44659i
$846$	−6.47214			−0.222517
$847$		0			0
$848$	2.85410			0.0980103
$849$	−3.67376	+	11.3067i	−0.126083	+	0.388044i
$850$	−51.5967	+	37.4872i	−1.76975	+	1.28580i
$851$	−10.4721	−	7.60845i	−0.358980	−	0.260814i
$852$	−1.09017	−	3.35520i	−0.0373486	−	0.114947i
$853$	10.1803	+	31.3319i	0.348568	+	1.07278i	0.959646	+	0.281212i	$0.0907364\pi$
$853$	10.1803	+	31.3319i	0.348568	+	1.07278i	−0.611078	+	0.791571i	$0.709264\pi$
$854$	21.6525	+	15.7314i	0.740932	+	0.538319i
$855$	3.85410	−	2.80017i	0.131808	−	0.0957638i
$856$	2.35410	−	7.24518i	0.0804615	−	0.247635i
$857$	13.2361			0.452135			0.226068	−	0.974112i	$-0.427413\pi$
$857$	13.2361			0.452135			0.226068	+	0.974112i	$0.427413\pi$
$858$		0			0
$859$	53.5967			1.82870			0.914349	−	0.404928i	$-0.132703\pi$
$859$	53.5967			1.82870			0.914349	+	0.404928i	$0.132703\pi$
$860$	−1.47214	+	4.53077i	−0.0501994	+	0.154498i
$861$	2.38197	−	1.73060i	0.0811772	−	0.0589787i
$862$	2.23607	+	1.62460i	0.0761608	+	0.0553340i
$863$	2.23607	+	6.88191i	0.0761166	+	0.234263i	0.981874	−	0.189533i	$-0.0606974\pi$
$863$	2.23607	+	6.88191i	0.0761166	+	0.234263i	−0.905758	+	0.423796i	$0.860697\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	−33.8435	−	24.5887i	−1.15071	−	0.836041i
$866$	2.69098	−	1.95511i	0.0914433	−	0.0664375i
$867$	−7.69098	+	23.6704i	−0.261199	+	0.803889i
$868$	15.2016			0.515977
$869$		0			0
$870$	−10.0902			−0.342089
$871$	1.52786	−	4.70228i	0.0517697	−	0.159331i
$872$	7.61803	−	5.53483i	0.257979	−	0.187433i
$873$	3.50000	+	2.54290i	0.118457	+	0.0860641i
$874$	0.472136	+	1.45309i	0.0159702	+	0.0491513i
$875$	−13.7705	−	42.3813i	−0.465528	−	1.43275i
$876$	3.50000	+	2.54290i	0.118254	+	0.0859166i
$877$	−11.6180	+	8.44100i	−0.392313	+	0.285032i	−0.766403	−	0.642360i	$-0.777955\pi$
$877$	−11.6180	+	8.44100i	−0.392313	+	0.285032i	0.374090	+	0.927393i	$0.377955\pi$
$878$	−4.02786	+	12.3965i	−0.135934	+	0.418361i
$879$	23.9787			0.808782
$880$		0			0
$881$	−25.7082			−0.866131			−0.433066	−	0.901362i	$-0.642568\pi$
$881$	−25.7082			−0.866131			−0.433066	+	0.901362i	$0.642568\pi$
$882$	−0.409830	+	1.26133i	−0.0137997	+	0.0424711i
$883$	−40.5967	+	29.4953i	−1.36619	+	0.992595i	−0.368165	+	0.929760i	$0.620014\pi$
$883$	−40.5967	+	29.4953i	−1.36619	+	0.992595i	−0.998024	+	0.0628343i	$0.979986\pi$
$884$	−6.47214	−	4.70228i	−0.217681	−	0.158155i
$885$	3.39919	+	10.4616i	0.114262	+	0.351664i
$886$	−5.35410	−	16.4782i	−0.179875	−	0.553597i
$887$	−31.1803	−	22.6538i	−1.04693	−	0.760642i	−0.0753064	−	0.997160i	$-0.523994\pi$
$887$	−31.1803	−	22.6538i	−1.04693	−	0.760642i	−0.971627	+	0.236519i	$0.923994\pi$
$888$	8.47214	−	6.15537i	0.284306	−	0.206561i
$889$	8.83282	−	27.1846i	0.296243	−	0.911743i
$890$	−6.58359			−0.220683
$891$		0			0
$892$	−13.0902			−0.438291
$893$	−2.47214	+	7.60845i	−0.0827269	+	0.254607i
$894$	2.92705	−	2.12663i	0.0978952	−	0.0711250i
$895$	−26.8713	−	19.5232i	−0.898209	−	0.652587i
$896$	0.736068	+	2.26538i	0.0245903	+	0.0756812i
$897$	−0.472136	−	1.45309i	−0.0157642	−	0.0485171i
$898$	−0.0901699	−	0.0655123i	−0.00300901	−	0.00218617i
$899$	13.5172	−	9.82084i	0.450825	−	0.327543i
$900$	3.04508	−	9.37181i	0.101503	−	0.312394i
$901$	18.4721			0.615396
$902$		0			0
$903$	−2.94427			−0.0979792
$904$	−1.09017	+	3.35520i	−0.0362585	+	0.111592i
$905$	−23.4721	+	17.0535i	−0.780240	+	0.566878i
$906$	−5.11803	−	3.71847i	−0.170035	−	0.123538i
$907$	4.38197	+	13.4863i	0.145501	+	0.447805i	0.997075	−	0.0764286i	$-0.0243517\pi$
$907$	4.38197	+	13.4863i	0.145501	+	0.447805i	−0.851574	+	0.524234i	$0.824352\pi$
$908$	−4.28115	−	13.1760i	−0.142075	−	0.437262i
$909$	11.8262	+	8.59226i	0.392252	+	0.284987i
$910$	9.18034	−	6.66991i	0.304325	−	0.221105i
$911$	9.36068	−	28.8092i	0.310133	−	0.954492i	−0.667578	−	0.744539i	$-0.732669\pi$
$911$	9.36068	−	28.8092i	0.310133	−	0.954492i	0.977712	−	0.209952i	$-0.0673309\pi$
$912$	−1.23607			−0.0409303
$913$		0			0
$914$	24.9787			0.826222
$915$	−13.3820	+	41.1855i	−0.442394	+	1.36155i
$916$	−4.09017	+	2.97168i	−0.135143	+	0.0981872i
$917$	−35.2082	−	25.5803i	−1.16268	−	0.844735i
$918$	−2.00000	−	6.15537i	−0.0660098	−	0.203157i
$919$	5.16970	+	15.9107i	0.170533	+	0.524845i	0.999401	−	0.0345978i	$-0.0110150\pi$
$919$	5.16970	+	15.9107i	0.170533	+	0.524845i	−0.828869	+	0.559443i	$0.811015\pi$
$920$	3.85410	+	2.80017i	0.127066	+	0.0923188i
$921$	11.8541	−	8.61251i	0.390606	−	0.283792i
$922$	−3.96556	+	12.2047i	−0.130599	+	0.401941i
$923$	4.36068			0.143534
$924$		0			0
$925$	103.193			3.39298
$926$	2.44427	−	7.52270i	0.0803238	−	0.247211i
$927$	13.7812	−	10.0126i	0.452632	−	0.328857i
$928$	2.11803	+	1.53884i	0.0695279	+	0.0505150i
$929$	5.29180	+	16.2865i	0.173618	+	0.534342i	0.999568	−	0.0294023i	$-0.00936039\pi$
$929$	5.29180	+	16.2865i	0.173618	+	0.534342i	−0.825949	+	0.563744i	$0.809360\pi$
$930$	7.60081	+	23.3929i	0.249240	+	0.767083i
$931$	1.32624	+	0.963568i	0.0434657	+	0.0315797i
$932$	−7.23607	+	5.25731i	−0.237025	+	0.172209i
$933$	−3.67376	+	11.3067i	−0.120274	+	0.370164i
$934$	−0.562306			−0.0183992
$935$		0			0
$936$	1.23607			0.0404021
$937$	−8.79180	+	27.0584i	−0.287215	+	0.883958i	0.698510	+	0.715600i	$0.253847\pi$
$937$	−8.79180	+	27.0584i	−0.287215	+	0.883958i	−0.985726	+	0.168358i	$0.946153\pi$
$938$	−7.70820	+	5.60034i	−0.251682	+	0.182858i
$939$	17.6803	+	12.8455i	0.576976	+	0.419198i
$940$	7.70820	+	23.7234i	0.251414	+	0.773772i
$941$	13.8541	+	42.6385i	0.451631	+	1.38998i	0.875045	+	0.484041i	$0.160831\pi$
$941$	13.8541	+	42.6385i	0.451631	+	1.38998i	−0.423415	+	0.905936i	$0.639169\pi$
$942$	−3.61803	−	2.62866i	−0.117882	−	0.0856462i
$943$	−1.23607	+	0.898056i	−0.0402519	+	0.0292447i
$944$	0.881966	−	2.71441i	0.0287055	−	0.0883466i
$945$	9.18034			0.298636
$946$		0			0
$947$	−13.3262			−0.433045			−0.216522	−	0.976278i	$-0.569471\pi$
$947$	−13.3262			−0.433045			−0.216522	+	0.976278i	$0.569471\pi$
$948$	−1.95492	+	6.01661i	−0.0634927	+	0.195410i
$949$	−4.32624	+	3.14320i	−0.140436	+	0.102032i
$950$	−9.85410	−	7.15942i	−0.319709	−	0.232282i
$951$	−4.90983	−	15.1109i	−0.159212	−	0.490005i
$952$	4.76393	+	14.6619i	0.154400	+	0.475194i
$953$	32.9443	+	23.9354i	1.06717	+	0.775344i	0.975401	−	0.220436i	$-0.0707481\pi$
$953$	32.9443	+	23.9354i	1.06717	+	0.775344i	0.0917683	+	0.995780i	$0.470748\pi$
$954$	−2.30902	+	1.67760i	−0.0747572	+	0.0543143i
$955$	−16.1115	+	49.5860i	−0.521354	+	1.60456i
$956$	−7.52786			−0.243469
$957$		0			0
$958$	−2.76393			−0.0892986
$959$	12.6049	−	38.7938i	0.407033	−	1.25272i
$960$	−3.11803	+	2.26538i	−0.100634	+	0.0731150i
$961$	−7.87132	−	5.71885i	−0.253914	−	0.184479i
$962$	4.00000	+	12.3107i	0.128965	+	0.396914i
$963$	2.35410	+	7.24518i	0.0758599	+	0.233473i
$964$	18.2533	+	13.2618i	0.587899	+	0.427134i
$965$	−47.7877	+	34.7198i	−1.53834	+	1.11767i
$966$	−0.909830	+	2.80017i	−0.0292733	+	0.0900940i
$967$	−46.6869			−1.50135			−0.750675	−	0.660672i	$-0.770272\pi$
$967$	−46.6869			−1.50135			−0.750675	+	0.660672i	$0.770272\pi$
$968$		0			0
$969$	−8.00000			−0.256997
$970$	5.15248	−	15.8577i	0.165436	−	0.509160i
$971$	−43.1246	+	31.3319i	−1.38393	+	1.00549i	−0.387434	+	0.921897i	$0.626639\pi$
$971$	−43.1246	+	31.3319i	−1.38393	+	1.00549i	−0.996500	+	0.0835901i	$0.973361\pi$
$972$	0.809017	+	0.587785i	0.0259492	+	0.0188532i
$973$	6.45085	+	19.8537i	0.206805	+	0.636480i
$974$	−6.79180	−	20.9030i	−0.217623	−	0.669775i
$975$	9.85410	+	7.15942i	0.315584	+	0.229285i
$976$	9.09017	−	6.60440i	0.290969	−	0.211402i
$977$	−12.7426	+	39.2178i	−0.407673	+	1.25469i	0.510969	+	0.859599i	$0.329287\pi$
$977$	−12.7426	+	39.2178i	−0.407673	+	1.25469i	−0.918642	+	0.395090i	$0.870713\pi$
$978$	−13.4164			−0.429009
$979$		0			0
$980$	5.11146			0.163279
$981$	−2.90983	+	8.95554i	−0.0929037	+	0.285928i
$982$	30.9443	−	22.4823i	0.987471	−	0.717440i
$983$	−25.1803	−	18.2946i	−0.803128	−	0.583507i	0.108702	−	0.994074i	$-0.465331\pi$
$983$	−25.1803	−	18.2946i	−0.803128	−	0.583507i	−0.911830	+	0.410568i	$0.865331\pi$
$984$	−0.381966	−	1.17557i	−0.0121766	−	0.0374758i
$985$	6.06231	+	18.6579i	0.193161	+	0.594489i
$986$	13.7082	+	9.95959i	0.436558	+	0.317178i
$987$	−12.4721	+	9.06154i	−0.396992	+	0.288432i
$988$	0.472136	−	1.45309i	0.0150206	−	0.0462288i
$989$	1.52786			0.0485833
$990$		0			0
$991$	14.6869			0.466545			0.233273	−	0.972411i	$-0.425057\pi$
$991$	14.6869			0.466545			0.233273	+	0.972411i	$0.425057\pi$
$992$	1.97214	−	6.06961i	0.0626154	−	0.192710i
$993$	−7.23607	+	5.25731i	−0.229630	+	0.166836i
$994$	−6.79837	−	4.93931i	−0.215631	−	0.156665i
$995$	−23.6459	−	72.7746i	−0.749625	−	2.30711i
$996$	5.04508	+	15.5272i	0.159860	+	0.491997i
$997$	29.0902	+	21.1352i	0.921295	+	0.669360i	0.943846	−	0.330386i	$-0.107179\pi$
$997$	29.0902	+	21.1352i	0.921295	+	0.669360i	−0.0225511	+	0.999746i	$0.507179\pi$
$998$	−15.7082	+	11.4127i	−0.497235	+	0.361262i
$999$	−3.23607	+	9.95959i	−0.102385	+	0.315108i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.e.f.493.1		4
11.2	odd	10		726.2.e.r.487.1		4
11.3	even	5		66.2.e.a.37.1	yes	4
11.4	even	5		726.2.a.l.1.1		2
11.5	even	5	inner	726.2.e.f.511.1		4
11.6	odd	10		726.2.e.n.511.1		4
11.7	odd	10		726.2.a.j.1.1		2
11.8	odd	10		726.2.e.r.565.1		4
11.9	even	5		66.2.e.a.25.1	✓	4
11.10	odd	2		726.2.e.n.493.1		4
33.14	odd	10		198.2.f.c.37.1		4
33.20	odd	10		198.2.f.c.91.1		4
33.26	odd	10		2178.2.a.t.1.2		2
33.29	even	10		2178.2.a.bb.1.2		2
44.3	odd	10		528.2.y.d.433.1		4
44.7	even	10		5808.2.a.cg.1.1		2
44.15	odd	10		5808.2.a.cb.1.1		2
44.31	odd	10		528.2.y.d.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.e.a.25.1	✓	4	11.9	even	5
66.2.e.a.37.1	yes	4	11.3	even	5
198.2.f.c.37.1		4	33.14	odd	10
198.2.f.c.91.1		4	33.20	odd	10
528.2.y.d.289.1		4	44.31	odd	10
528.2.y.d.433.1		4	44.3	odd	10
726.2.a.j.1.1		2	11.7	odd	10
726.2.a.l.1.1		2	11.4	even	5
726.2.e.f.493.1		4	1.1	even	1	trivial
726.2.e.f.511.1		4	11.5	even	5	inner
726.2.e.n.493.1		4	11.10	odd	2
726.2.e.n.511.1		4	11.6	odd	10
726.2.e.r.487.1		4	11.2	odd	10
726.2.e.r.565.1		4	11.8	odd	10
2178.2.a.t.1.2		2	33.26	odd	10
2178.2.a.bb.1.2		2	33.29	even	10
5808.2.a.cb.1.1		2	44.15	odd	10
5808.2.a.cg.1.1		2	44.7	even	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} +(-1.19098 - 3.66547i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.92705 - 1.40008i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} -3.85410 q^{10} -1.00000 q^{12} +(0.381966 - 1.17557i) q^{13} +(-1.92705 + 1.40008i) q^{14} +(-3.11803 - 2.26538i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.00000 + 6.15537i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-1.00000 + 0.726543i) q^{19} +(-1.19098 + 3.66547i) q^{20} -2.38197 q^{21} +1.23607 q^{23} +(-0.309017 + 0.951057i) q^{24} +(-7.97214 + 5.79210i) q^{25} +(-1.00000 - 0.726543i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.736068 + 2.26538i) q^{28} +(2.11803 + 1.53884i) q^{29} +(-3.11803 + 2.26538i) q^{30} +(1.97214 - 6.06961i) q^{31} +1.00000 q^{32} +6.47214 q^{34} +(-2.83688 + 8.73102i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-8.47214 - 6.15537i) q^{37} +(0.381966 + 1.17557i) q^{38} +(-0.381966 - 1.17557i) q^{39} +(3.11803 + 2.26538i) q^{40} +(-1.00000 + 0.726543i) q^{41} +(-0.736068 + 2.26538i) q^{42} +1.23607 q^{43} -3.85410 q^{45} +(0.381966 - 1.17557i) q^{46} +(5.23607 - 3.80423i) q^{47} +(0.809017 + 0.587785i) q^{48} +(-0.409830 - 1.26133i) q^{49} +(3.04508 + 9.37181i) q^{50} +(5.23607 + 3.80423i) q^{51} +(-1.00000 + 0.726543i) q^{52} +(0.881966 - 2.71441i) q^{53} -1.00000 q^{54} +2.38197 q^{56} +(-0.381966 + 1.17557i) q^{57} +(2.11803 - 1.53884i) q^{58} +(-2.30902 - 1.67760i) q^{59} +(1.19098 + 3.66547i) q^{60} +(-3.47214 - 10.6861i) q^{61} +(-5.16312 - 3.75123i) q^{62} +(-1.92705 + 1.40008i) q^{63} +(0.309017 - 0.951057i) q^{64} -4.76393 q^{65} +4.00000 q^{67} +(2.00000 - 6.15537i) q^{68} +(1.00000 - 0.726543i) q^{69} +(7.42705 + 5.39607i) q^{70} +(1.09017 + 3.35520i) q^{71} +(0.309017 + 0.951057i) q^{72} +(-3.50000 - 2.54290i) q^{73} +(-8.47214 + 6.15537i) q^{74} +(-3.04508 + 9.37181i) q^{75} +1.23607 q^{76} -1.23607 q^{78} +(1.95492 - 6.01661i) q^{79} +(3.11803 - 2.26538i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.381966 + 1.17557i) q^{82} +(-5.04508 - 15.5272i) q^{83} +(1.92705 + 1.40008i) q^{84} +(20.1803 - 14.6619i) q^{85} +(0.381966 - 1.17557i) q^{86} +2.61803 q^{87} +1.70820 q^{89} +(-1.19098 + 3.66547i) q^{90} +(-2.38197 + 1.73060i) q^{91} +(-1.00000 - 0.726543i) q^{92} +(-1.97214 - 6.06961i) q^{93} +(-2.00000 - 6.15537i) q^{94} +(3.85410 + 2.80017i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-1.33688 + 4.11450i) q^{97} -1.32624 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} - q^{4} - 7 q^{5} + q^{6} - q^{7} - q^{8} - q^{9} - 2 q^{10} - 4 q^{12} + 6 q^{13} - q^{14} - 8 q^{15} - q^{16} + 8 q^{17} - q^{18} - 4 q^{19} - 7 q^{20} - 14 q^{21} - 4 q^{23}+ \cdots + 26 q^{98}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 - 7 * q^5 + q^6 - q^7 - q^8 - q^9 - 2 * q^10 - 4 * q^12 + 6 * q^13 - q^14 - 8 * q^15 - q^16 + 8 * q^17 - q^18 - 4 * q^19 - 7 * q^20 - 14 * q^21 - 4 * q^23 + q^24 - 14 * q^25 - 4 * q^26 + q^27 - 6 * q^28 + 4 * q^29 - 8 * q^30 - 10 * q^31 + 4 * q^32 + 8 * q^34 - 27 * q^35 - q^36 - 16 * q^37 + 6 * q^38 - 6 * q^39 + 8 * q^40 - 4 * q^41 + 6 * q^42 - 4 * q^43 - 2 * q^45 + 6 * q^46 + 12 * q^47 + q^48 - 24 * q^49 + q^50 + 12 * q^51 - 4 * q^52 + 8 * q^53 - 4 * q^54 + 14 * q^56 - 6 * q^57 + 4 * q^58 - 7 * q^59 + 7 * q^60 + 4 * q^61 - 5 * q^62 - q^63 - q^64 - 28 * q^65 + 16 * q^67 + 8 * q^68 + 4 * q^69 + 23 * q^70 - 18 * q^71 - q^72 - 14 * q^73 - 16 * q^74 - q^75 - 4 * q^76 + 4 * q^78 + 19 * q^79 + 8 * q^80 - q^81 + 6 * q^82 - 9 * q^83 + q^84 + 36 * q^85 + 6 * q^86 + 6 * q^87 - 20 * q^89 - 7 * q^90 - 14 * q^91 - 4 * q^92 + 10 * q^93 - 8 * q^94 + 2 * q^95 + q^96 - 21 * q^97 + 26 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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