LMFDB - Embedded newform 726.2.e.k.493.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [726,2,Mod(487,726)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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.k.511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +1.00000 q^{12} +(-1.23607 + 3.80423i) q^{13} +(1.61803 - 1.17557i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-1.85410 - 5.70634i) q^{17} +(0.809017 + 0.587785i) q^{18} +(3.23607 - 2.35114i) q^{19} +2.00000 q^{21} +6.00000 q^{23} +(-0.309017 + 0.951057i) q^{24} +(4.04508 - 2.93893i) q^{25} +(-3.23607 - 2.35114i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.618034 + 1.90211i) q^{28} +(-4.85410 - 3.52671i) q^{29} +(2.47214 - 7.60845i) q^{31} -1.00000 q^{32} +6.00000 q^{34} +(-0.809017 + 0.587785i) q^{36} +(8.09017 + 5.87785i) q^{37} +(1.23607 + 3.80423i) q^{38} +(-1.23607 - 3.80423i) q^{39} +(-4.85410 + 3.52671i) q^{41} +(-0.618034 + 1.90211i) q^{42} +8.00000 q^{43} +(-1.85410 + 5.70634i) q^{46} +(4.85410 - 3.52671i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(-0.927051 - 2.85317i) q^{49} +(1.54508 + 4.75528i) q^{50} +(4.85410 + 3.52671i) q^{51} +(3.23607 - 2.35114i) q^{52} -1.00000 q^{54} -2.00000 q^{56} +(-1.23607 + 3.80423i) q^{57} +(4.85410 - 3.52671i) q^{58} +(2.47214 + 7.60845i) q^{61} +(6.47214 + 4.70228i) q^{62} +(-1.61803 + 1.17557i) q^{63} +(0.309017 - 0.951057i) q^{64} -4.00000 q^{67} +(-1.85410 + 5.70634i) q^{68} +(-4.85410 + 3.52671i) q^{69} +(1.85410 + 5.70634i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(-1.61803 - 1.17557i) q^{73} +(-8.09017 + 5.87785i) q^{74} +(-1.54508 + 4.75528i) q^{75} -4.00000 q^{76} +4.00000 q^{78} +(4.32624 - 13.3148i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-1.85410 - 5.70634i) q^{82} +(-3.70820 - 11.4127i) q^{83} +(-1.61803 - 1.17557i) q^{84} +(-2.47214 + 7.60845i) q^{86} +6.00000 q^{87} -6.00000 q^{89} +(6.47214 - 4.70228i) q^{91} +(-4.85410 - 3.52671i) q^{92} +(2.47214 + 7.60845i) q^{93} +(1.85410 + 5.70634i) q^{94} +(0.809017 - 0.587785i) q^{96} +(4.32624 - 13.3148i) q^{97} +3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9	$ 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9} + 4 q^{12} + 4 q^{13} + 2 q^{14} - q^{16} + 6 q^{17} + q^{18} + 4 q^{19} + 8 q^{21} + 24 q^{23} + q^{24} + 5 q^{25} - 4 q^{26} - q^{27} - 2 q^{28} - 6 q^{29} - 8 q^{31} - 4 q^{32} + 24 q^{34} - q^{36} + 10 q^{37} - 4 q^{38} + 4 q^{39} - 6 q^{41} + 2 q^{42} + 32 q^{43} + 6 q^{46} + 6 q^{47} - q^{48} + 3 q^{49} - 5 q^{50} + 6 q^{51} + 4 q^{52} - 4 q^{54} - 8 q^{56} + 4 q^{57} + 6 q^{58} - 8 q^{61} + 8 q^{62} - 2 q^{63} - q^{64} - 16 q^{67} + 6 q^{68} - 6 q^{69} - 6 q^{71} + q^{72} - 2 q^{73} - 10 q^{74} + 5 q^{75} - 16 q^{76} + 16 q^{78} - 14 q^{79} - q^{81} + 6 q^{82} + 12 q^{83} - 2 q^{84} + 8 q^{86} + 24 q^{87} - 24 q^{89} + 8 q^{91} - 6 q^{92} - 8 q^{93} - 6 q^{94} + q^{96} - 14 q^{97} + 12 q^{98}+O(q^{100}) $ 4 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9 + 4 * q^12 + 4 * q^13 + 2 * q^14 - q^16 + 6 * q^17 + q^18 + 4 * q^19 + 8 * q^21 + 24 * q^23 + q^24 + 5 * q^25 - 4 * q^26 - q^27 - 2 * q^28 - 6 * q^29 - 8 * q^31 - 4 * q^32 + 24 * q^34 - q^36 + 10 * q^37 - 4 * q^38 + 4 * q^39 - 6 * q^41 + 2 * q^42 + 32 * q^43 + 6 * q^46 + 6 * q^47 - q^48 + 3 * q^49 - 5 * q^50 + 6 * q^51 + 4 * q^52 - 4 * q^54 - 8 * q^56 + 4 * q^57 + 6 * q^58 - 8 * q^61 + 8 * q^62 - 2 * q^63 - q^64 - 16 * q^67 + 6 * q^68 - 6 * q^69 - 6 * q^71 + q^72 - 2 * q^73 - 10 * q^74 + 5 * q^75 - 16 * q^76 + 16 * q^78 - 14 * q^79 - q^81 + 6 * q^82 + 12 * q^83 - 2 * q^84 + 8 * q^86 + 24 * q^87 - 24 * q^89 + 8 * q^91 - 6 * q^92 - 8 * q^93 - 6 * q^94 + q^96 - 14 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

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
$5$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$5$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$	−1.61803	−	1.17557i	−0.611559	−	0.444324i	0.238404	−	0.971166i	$-0.423376\pi$
$7$	−1.61803	−	1.17557i	−0.611559	−	0.444324i	−0.849963	+	0.526842i	$0.823376\pi$
$8$	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
$13$	−1.23607	+	3.80423i	−0.342824	+	1.05510i	0.619915	+	0.784669i	$0.287167\pi$
$13$	−1.23607	+	3.80423i	−0.342824	+	1.05510i	−0.962739	+	0.270434i	$0.912833\pi$
$14$	1.61803	−	1.17557i	0.432438	−	0.314184i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−1.85410	−	5.70634i	−0.449686	−	1.38399i	−0.877262	−	0.480011i	$-0.840633\pi$
$17$	−1.85410	−	5.70634i	−0.449686	−	1.38399i	0.427576	−	0.903979i	$-0.359367\pi$
$18$	0.809017	+	0.587785i	0.190687	+	0.138542i
$19$	3.23607	−	2.35114i	0.742405	−	0.539389i	−0.151058	−	0.988525i	$-0.548268\pi$
$19$	3.23607	−	2.35114i	0.742405	−	0.539389i	0.893463	+	0.449136i	$0.148268\pi$
$20$		0			0
$21$	2.00000			0.436436
$22$		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
$26$	−3.23607	−	2.35114i	−0.634645	−	0.461097i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	0.618034	+	1.90211i	0.116797	+	0.359466i
$29$	−4.85410	−	3.52671i	−0.901384	−	0.654894i	0.0374370	−	0.999299i	$-0.488081\pi$
$29$	−4.85410	−	3.52671i	−0.901384	−	0.654894i	−0.938821	+	0.344405i	$0.888081\pi$
$30$		0			0
$31$	2.47214	−	7.60845i	0.444009	−	1.36652i	−0.439558	−	0.898214i	$-0.644865\pi$
$31$	2.47214	−	7.60845i	0.444009	−	1.36652i	0.883567	−	0.468304i	$-0.155135\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	6.00000			1.02899
$35$		0			0
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	8.09017	+	5.87785i	1.33002	+	0.966313i	0.999749	+	0.0224255i	$0.00713887\pi$
$37$	8.09017	+	5.87785i	1.33002	+	0.966313i	0.330267	+	0.943887i	$0.392861\pi$
$38$	1.23607	+	3.80423i	0.200517	+	0.617127i
$39$	−1.23607	−	3.80423i	−0.197929	−	0.609164i
$40$		0			0
$41$	−4.85410	+	3.52671i	−0.758083	+	0.550780i	−0.898322	−	0.439338i	$-0.855213\pi$
$41$	−4.85410	+	3.52671i	−0.758083	+	0.550780i	0.140238	+	0.990118i	$0.455213\pi$
$42$	−0.618034	+	1.90211i	−0.0953647	+	0.293502i
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		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	$-0.555830\pi$
$47$	4.85410	−	3.52671i	0.708044	−	0.514424i	0.882542	+	0.470234i	$0.155830\pi$
$48$	−0.809017	−	0.587785i	−0.116772	−	0.0848395i
$49$	−0.927051	−	2.85317i	−0.132436	−	0.407596i
$50$	1.54508	+	4.75528i	0.218508	+	0.672499i
$51$	4.85410	+	3.52671i	0.679710	+	0.493838i
$52$	3.23607	−	2.35114i	0.448762	−	0.326045i
$53$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$53$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$54$	−1.00000			−0.136083
$55$		0			0
$56$	−2.00000			−0.267261
$57$	−1.23607	+	3.80423i	−0.163721	+	0.503882i
$58$	4.85410	−	3.52671i	0.637375	−	0.463080i
$59$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$59$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$60$		0			0
$61$	2.47214	+	7.60845i	0.316525	+	0.974162i	0.975122	+	0.221667i	$0.0711499\pi$
$61$	2.47214	+	7.60845i	0.316525	+	0.974162i	−0.658598	+	0.752495i	$0.728850\pi$
$62$	6.47214	+	4.70228i	0.821962	+	0.597190i
$63$	−1.61803	+	1.17557i	−0.203853	+	0.148108i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$		0			0
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$	−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	0.998757	+	0.0498409i	$0.0158714\pi$
$71$	1.85410	+	5.70634i	0.220041	+	0.677218i	−0.778716	+	0.627377i	$0.784129\pi$
$72$	−0.309017	−	0.951057i	−0.0364180	−	0.112083i
$73$	−1.61803	−	1.17557i	−0.189377	−	0.137590i	0.489057	−	0.872252i	$-0.337341\pi$
$73$	−1.61803	−	1.17557i	−0.189377	−	0.137590i	−0.678434	+	0.734662i	$0.737341\pi$
$74$	−8.09017	+	5.87785i	−0.940463	+	0.683286i
$75$	−1.54508	+	4.75528i	−0.178411	+	0.549093i
$76$	−4.00000			−0.458831
$77$		0			0
$78$	4.00000			0.452911
$79$	4.32624	−	13.3148i	0.486740	−	1.49803i	−0.342705	−	0.939443i	$-0.611343\pi$
$79$	4.32624	−	13.3148i	0.486740	−	1.49803i	0.829445	−	0.558588i	$-0.188657\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−1.85410	−	5.70634i	−0.204751	−	0.630160i
$83$	−3.70820	−	11.4127i	−0.407028	−	1.25270i	−0.919190	−	0.393815i	$-0.871155\pi$
$83$	−3.70820	−	11.4127i	−0.407028	−	1.25270i	0.512161	−	0.858889i	$-0.328845\pi$
$84$	−1.61803	−	1.17557i	−0.176542	−	0.128265i
$85$		0			0
$86$	−2.47214	+	7.60845i	−0.266577	+	0.820440i
$87$	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
$91$	6.47214	−	4.70228i	0.678464	−	0.492933i
$92$	−4.85410	−	3.52671i	−0.506075	−	0.367685i
$93$	2.47214	+	7.60845i	0.256349	+	0.788960i
$94$	1.85410	+	5.70634i	0.191236	+	0.588564i
$95$		0			0
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	4.32624	−	13.3148i	0.439263	−	1.35191i	−0.449392	−	0.893335i	$-0.648359\pi$
$97$	4.32624	−	13.3148i	0.439263	−	1.35191i	0.888654	−	0.458577i	$-0.151641\pi$
$98$	3.00000			0.303046
$99$		0			0
$100$	−5.00000			−0.500000
$101$	1.85410	−	5.70634i	0.184490	−	0.567802i	−0.815449	−	0.578829i	$-0.803510\pi$
$101$	1.85410	−	5.70634i	0.184490	−	0.567802i	0.999939	+	0.0110267i	$0.00350999\pi$
$102$	−4.85410	+	3.52671i	−0.480628	+	0.349196i
$103$	3.23607	+	2.35114i	0.318859	+	0.231665i	0.735689	−	0.677320i	$-0.236859\pi$
$103$	3.23607	+	2.35114i	0.318859	+	0.231665i	−0.416829	+	0.908985i	$0.636859\pi$
$104$	1.23607	+	3.80423i	0.121206	+	0.373035i
$105$		0			0
$106$		0			0
$107$	9.70820	−	7.05342i	0.938527	−	0.681880i	−0.00953827	−	0.999955i	$-0.503036\pi$
$107$	9.70820	−	7.05342i	0.938527	−	0.681880i	0.948066	+	0.318074i	$0.103036\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	−4.00000			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$110$		0			0
$111$	−10.0000			−0.949158
$112$	0.618034	−	1.90211i	0.0583987	−	0.179733i
$113$	−14.5623	+	10.5801i	−1.36991	+	0.995295i	−0.372162	+	0.928168i	$0.621383\pi$
$113$	−14.5623	+	10.5801i	−1.36991	+	0.995295i	−0.997744	+	0.0671276i	$0.978617\pi$
$114$	−3.23607	−	2.35114i	−0.303086	−	0.220205i
$115$		0			0
$116$	1.85410	+	5.70634i	0.172149	+	0.529820i
$117$	3.23607	+	2.35114i	0.299175	+	0.217363i
$118$		0			0
$119$	−3.70820	+	11.4127i	−0.339930	+	1.04620i
$120$		0			0
$121$		0			0
$122$	−8.00000			−0.724286
$123$	1.85410	−	5.70634i	0.167179	−	0.514523i
$124$	−6.47214	+	4.70228i	−0.581215	+	0.422277i
$125$		0			0
$126$	−0.618034	−	1.90211i	−0.0550588	−	0.169454i
$127$	4.32624	+	13.3148i	0.383892	+	1.18150i	0.937281	+	0.348574i	$0.113334\pi$
$127$	4.32624	+	13.3148i	0.383892	+	1.18150i	−0.553390	+	0.832922i	$0.686666\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−6.47214	+	4.70228i	−0.569840	+	0.414013i
$130$		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
$133$	−8.00000			−0.693688
$134$	1.23607	−	3.80423i	0.106780	−	0.328635i
$135$		0			0
$136$	−4.85410	−	3.52671i	−0.416236	−	0.302413i
$137$	−5.56231	−	17.1190i	−0.475220	−	1.46258i	−0.845661	−	0.533720i	$-0.820793\pi$
$137$	−5.56231	−	17.1190i	−0.475220	−	1.46258i	0.370441	−	0.928856i	$-0.379207\pi$
$138$	−1.85410	−	5.70634i	−0.157832	−	0.485756i
$139$	3.23607	+	2.35114i	0.274480	+	0.199421i	0.716506	−	0.697581i	$-0.245740\pi$
$139$	3.23607	+	2.35114i	0.274480	+	0.199421i	−0.442026	+	0.897002i	$0.645740\pi$
$140$		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
$146$	1.61803	−	1.17557i	0.133909	−	0.0972909i
$147$	2.42705	+	1.76336i	0.200180	+	0.145439i
$148$	−3.09017	−	9.51057i	−0.254010	−	0.781764i
$149$	−1.85410	−	5.70634i	−0.151894	−	0.467482i	0.845939	−	0.533280i	$-0.179041\pi$
$149$	−1.85410	−	5.70634i	−0.151894	−	0.467482i	−0.997833	+	0.0657982i	$0.979041\pi$
$150$	−4.04508	−	2.93893i	−0.330280	−	0.239962i
$151$	8.09017	−	5.87785i	0.658369	−	0.478333i	−0.207743	−	0.978183i	$-0.566612\pi$
$151$	8.09017	−	5.87785i	0.658369	−	0.478333i	0.866112	+	0.499851i	$0.166612\pi$
$152$	1.23607	−	3.80423i	0.100258	−	0.308563i
$153$	−6.00000			−0.485071
$154$		0			0
$155$		0			0
$156$	−1.23607	+	3.80423i	−0.0989646	+	0.304582i
$157$	−1.61803	+	1.17557i	−0.129133	+	0.0938207i	−0.650477	−	0.759526i	$-0.725431\pi$
$157$	−1.61803	+	1.17557i	−0.129133	+	0.0938207i	0.521344	+	0.853347i	$0.325431\pi$
$158$	11.3262	+	8.22899i	0.901067	+	0.654664i
$159$		0			0
$160$		0			0
$161$	−9.70820	−	7.05342i	−0.765114	−	0.555888i
$162$	0.809017	−	0.587785i	0.0635624	−	0.0461808i
$163$	−1.23607	+	3.80423i	−0.0968163	+	0.297970i	−0.987723	−	0.156217i	$-0.950070\pi$
$163$	−1.23607	+	3.80423i	−0.0968163	+	0.297970i	0.890906	+	0.454187i	$0.150070\pi$
$164$	6.00000			0.468521
$165$		0			0
$166$	12.0000			0.931381
$167$	3.70820	−	11.4127i	0.286949	−	0.883140i	−0.698858	−	0.715260i	$-0.746308\pi$
$167$	3.70820	−	11.4127i	0.286949	−	0.883140i	0.985808	−	0.167879i	$-0.0536919\pi$
$168$	1.61803	−	1.17557i	0.124834	−	0.0906972i
$169$	−2.42705	−	1.76336i	−0.186696	−	0.135643i
$170$		0			0
$171$	−1.23607	−	3.80423i	−0.0945245	−	0.290916i
$172$	−6.47214	−	4.70228i	−0.493496	−	0.358546i
$173$	−4.85410	+	3.52671i	−0.369051	+	0.268131i	−0.756817	−	0.653627i	$-0.773247\pi$
$173$	−4.85410	+	3.52671i	−0.369051	+	0.268131i	0.387767	+	0.921758i	$0.373247\pi$
$174$	−1.85410	+	5.70634i	−0.140559	+	0.432596i
$175$	−10.0000			−0.755929
$176$		0			0
$177$		0			0
$178$	1.85410	−	5.70634i	0.138971	−	0.427708i
$179$	−19.4164	+	14.1068i	−1.45125	+	1.05440i	−0.465713	+	0.884936i	$0.654202\pi$
$179$	−19.4164	+	14.1068i	−1.45125	+	1.05440i	−0.985537	+	0.169460i	$0.945798\pi$
$180$		0			0
$181$	−6.79837	−	20.9232i	−0.505319	−	1.55521i	−0.800233	−	0.599689i	$-0.795291\pi$
$181$	−6.79837	−	20.9232i	−0.505319	−	1.55521i	0.294914	−	0.955524i	$-0.404709\pi$
$182$	2.47214	+	7.60845i	0.183247	+	0.563976i
$183$	−6.47214	−	4.70228i	−0.478434	−	0.347603i
$184$	4.85410	−	3.52671i	0.357849	−	0.259993i
$185$		0			0
$186$	−8.00000			−0.586588
$187$		0			0
$188$	−6.00000			−0.437595
$189$	0.618034	−	1.90211i	0.0449554	−	0.138358i
$190$		0			0
$191$	−14.5623	−	10.5801i	−1.05369	−	0.765552i	−0.0807805	−	0.996732i	$-0.525741\pi$
$191$	−14.5623	−	10.5801i	−1.05369	−	0.765552i	−0.972911	+	0.231180i	$0.925741\pi$
$192$	0.309017	+	0.951057i	0.0223014	+	0.0686366i
$193$	4.32624	+	13.3148i	0.311409	+	0.958420i	0.977207	+	0.212287i	$0.0680913\pi$
$193$	4.32624	+	13.3148i	0.311409	+	0.958420i	−0.665798	+	0.746132i	$0.731909\pi$
$194$	11.3262	+	8.22899i	0.813176	+	0.590807i
$195$		0			0
$196$	−0.927051	+	2.85317i	−0.0662179	+	0.203798i
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	−4.00000			−0.283552			−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$	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
$203$	3.70820	+	11.4127i	0.260265	+	0.801013i
$204$	−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
$208$	−4.00000			−0.277350
$209$		0			0
$210$		0			0
$211$	2.47214	−	7.60845i	0.170189	−	0.523787i	−0.829192	−	0.558963i	$-0.811199\pi$
$211$	2.47214	−	7.60845i	0.170189	−	0.523787i	0.999381	+	0.0351760i	$0.0111992\pi$
$212$		0			0
$213$	−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
$217$	−12.9443	+	9.40456i	−0.878714	+	0.638423i
$218$	1.23607	−	3.80423i	0.0837171	−	0.257655i
$219$	2.00000			0.135147
$220$		0			0
$221$	24.0000			1.61441
$222$	3.09017	−	9.51057i	0.207399	−	0.638307i
$223$	12.9443	−	9.40456i	0.866813	−	0.629776i	−0.0629172	−	0.998019i	$-0.520040\pi$
$223$	12.9443	−	9.40456i	0.866813	−	0.629776i	0.929730	+	0.368243i	$0.120040\pi$
$224$	1.61803	+	1.17557i	0.108109	+	0.0785461i
$225$	−1.54508	−	4.75528i	−0.103006	−	0.317019i
$226$	−5.56231	−	17.1190i	−0.369999	−	1.13874i
$227$	9.70820	+	7.05342i	0.644356	+	0.468152i	0.861344	−	0.508022i	$-0.169623\pi$
$227$	9.70820	+	7.05342i	0.644356	+	0.468152i	−0.216988	+	0.976174i	$0.569623\pi$
$228$	3.23607	−	2.35114i	0.214314	−	0.155708i
$229$	−6.79837	+	20.9232i	−0.449249	+	1.38265i	0.428507	+	0.903539i	$0.359040\pi$
$229$	−6.79837	+	20.9232i	−0.449249	+	1.38265i	−0.877756	+	0.479108i	$0.840960\pi$
$230$		0			0
$231$		0			0
$232$	−6.00000			−0.393919
$233$	−5.56231	+	17.1190i	−0.364399	+	1.12150i	0.585958	+	0.810341i	$0.300718\pi$
$233$	−5.56231	+	17.1190i	−0.364399	+	1.12150i	−0.950357	+	0.311163i	$0.899282\pi$
$234$	−3.23607	+	2.35114i	−0.211548	+	0.153699i
$235$		0			0
$236$		0			0
$237$	4.32624	+	13.3148i	0.281019	+	0.864889i
$238$	−9.70820	−	7.05342i	−0.629289	−	0.457206i
$239$	9.70820	−	7.05342i	0.627972	−	0.456248i	−0.227725	−	0.973725i	$-0.573129\pi$
$239$	9.70820	−	7.05342i	0.627972	−	0.456248i	0.855697	+	0.517477i	$0.173129\pi$
$240$		0			0
$241$	−10.0000			−0.644157			−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000			−0.644157			−0.322078	+	0.946713i	$0.604381\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	2.47214	−	7.60845i	0.158262	−	0.487081i
$245$		0			0
$246$	4.85410	+	3.52671i	0.309486	+	0.224855i
$247$	4.94427	+	15.2169i	0.314596	+	0.968228i
$248$	−2.47214	−	7.60845i	−0.156981	−	0.483137i
$249$	9.70820	+	7.05342i	0.615232	+	0.446993i
$250$		0			0
$251$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$251$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$252$	2.00000			0.125988
$253$		0			0
$254$	−14.0000			−0.878438
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	24.2705	+	17.6336i	1.51395	+	1.09995i	0.964385	+	0.264502i	$0.0852075\pi$
$257$	24.2705	+	17.6336i	1.51395	+	1.09995i	0.549568	+	0.835449i	$0.314792\pi$
$258$	−2.47214	−	7.60845i	−0.153908	−	0.473682i
$259$	−6.18034	−	19.0211i	−0.384028	−	1.18192i
$260$		0			0
$261$	−4.85410	+	3.52671i	−0.300461	+	0.218298i
$262$	3.70820	−	11.4127i	0.229094	−	0.705078i
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$		0			0
$266$	2.47214	−	7.60845i	0.151576	−	0.466504i
$267$	4.85410	−	3.52671i	0.297066	−	0.215831i
$268$	3.23607	+	2.35114i	0.197674	+	0.143619i
$269$	−7.41641	−	22.8254i	−0.452186	−	1.39169i	−0.874407	−	0.485193i	$-0.838749\pi$
$269$	−7.41641	−	22.8254i	−0.452186	−	1.39169i	0.422221	−	0.906493i	$-0.361251\pi$
$270$		0			0
$271$	−1.61803	−	1.17557i	−0.0982886	−	0.0714108i	0.537555	−	0.843228i	$-0.319348\pi$
$271$	−1.61803	−	1.17557i	−0.0982886	−	0.0714108i	−0.635844	+	0.771818i	$0.719348\pi$
$272$	4.85410	−	3.52671i	0.294323	−	0.213838i
$273$	−2.47214	+	7.60845i	−0.149620	+	0.460484i
$274$	18.0000			1.08742
$275$		0			0
$276$	6.00000			0.361158
$277$	−4.94427	+	15.2169i	−0.297073	+	0.914295i	0.685445	+	0.728124i	$0.259608\pi$
$277$	−4.94427	+	15.2169i	−0.297073	+	0.914295i	−0.982517	+	0.186171i	$0.940392\pi$
$278$	−3.23607	+	2.35114i	−0.194086	+	0.141012i
$279$	−6.47214	−	4.70228i	−0.387477	−	0.281518i
$280$		0			0
$281$	−1.85410	−	5.70634i	−0.110606	−	0.340412i	0.880399	−	0.474234i	$-0.157275\pi$
$281$	−1.85410	−	5.70634i	−0.110606	−	0.340412i	−0.991005	+	0.133822i	$0.957275\pi$
$282$	−4.85410	−	3.52671i	−0.289058	−	0.210013i
$283$	−6.47214	+	4.70228i	−0.384729	+	0.279522i	−0.763292	−	0.646054i	$-0.776418\pi$
$283$	−6.47214	+	4.70228i	−0.384729	+	0.279522i	0.378563	+	0.925575i	$0.376418\pi$
$284$	1.85410	−	5.70634i	0.110021	−	0.338609i
$285$		0			0
$286$		0			0
$287$	12.0000			0.708338
$288$	−0.309017	+	0.951057i	−0.0182090	+	0.0560415i
$289$	−15.3713	+	11.1679i	−0.904195	+	0.656936i
$290$		0			0
$291$	4.32624	+	13.3148i	0.253609	+	0.780527i
$292$	0.618034	+	1.90211i	0.0361677	+	0.111313i
$293$	4.85410	+	3.52671i	0.283580	+	0.206033i	0.720477	−	0.693479i	$-0.243923\pi$
$293$	4.85410	+	3.52671i	0.283580	+	0.206033i	−0.436898	+	0.899511i	$0.643923\pi$
$294$	−2.42705	+	1.76336i	−0.141548	+	0.102841i
$295$		0			0
$296$	10.0000			0.581238
$297$		0			0
$298$	6.00000			0.347571
$299$	−7.41641	+	22.8254i	−0.428902	+	1.32002i
$300$	4.04508	−	2.93893i	0.233543	−	0.169679i
$301$	−12.9443	−	9.40456i	−0.746095	−	0.542070i
$302$	3.09017	+	9.51057i	0.177819	+	0.547272i
$303$	1.85410	+	5.70634i	0.106515	+	0.327821i
$304$	3.23607	+	2.35114i	0.185601	+	0.134847i
$305$		0			0
$306$	1.85410	−	5.70634i	0.105992	−	0.326210i
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$	−4.00000			−0.227552
$310$		0			0
$311$	14.5623	−	10.5801i	0.825753	−	0.599944i	−0.0926019	−	0.995703i	$-0.529518\pi$
$311$	14.5623	−	10.5801i	0.825753	−	0.599944i	0.918354	+	0.395759i	$0.129518\pi$
$312$	−3.23607	−	2.35114i	−0.183206	−	0.133107i
$313$	8.03444	+	24.7275i	0.454134	+	1.39768i	0.872149	+	0.489240i	$0.162726\pi$
$313$	8.03444	+	24.7275i	0.454134	+	1.39768i	−0.418016	+	0.908440i	$0.637274\pi$
$314$	−0.618034	−	1.90211i	−0.0348777	−	0.107342i
$315$		0			0
$316$	−11.3262	+	8.22899i	−0.637151	+	0.462917i
$317$	3.70820	−	11.4127i	0.208273	−	0.641000i	−0.791290	−	0.611442i	$-0.790590\pi$
$317$	3.70820	−	11.4127i	0.208273	−	0.641000i	0.999563	−	0.0295583i	$-0.00941007\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−3.70820	+	11.4127i	−0.206972	+	0.636994i
$322$	9.70820	−	7.05342i	0.541017	−	0.393072i
$323$	−19.4164	−	14.1068i	−1.08036	−	0.784926i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	6.18034	+	19.0211i	0.342824	+	1.05510i
$326$	−3.23607	−	2.35114i	−0.179229	−	0.130218i
$327$	3.23607	−	2.35114i	0.178955	−	0.130018i
$328$	−1.85410	+	5.70634i	−0.102376	+	0.315080i
$329$	−12.0000			−0.661581
$330$		0			0
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$	−3.70820	+	11.4127i	−0.203514	+	0.626352i
$333$	8.09017	−	5.87785i	0.443339	−	0.322104i
$334$	9.70820	+	7.05342i	0.531209	+	0.385946i
$335$		0			0
$336$	0.618034	+	1.90211i	0.0337165	+	0.103769i
$337$	−1.61803	−	1.17557i	−0.0881399	−	0.0640374i	0.542843	−	0.839834i	$-0.317348\pi$
$337$	−1.61803	−	1.17557i	−0.0881399	−	0.0640374i	−0.630982	+	0.775797i	$0.717348\pi$
$338$	2.42705	−	1.76336i	0.132014	−	0.0959139i
$339$	5.56231	−	17.1190i	0.302103	−	0.929777i
$340$		0			0
$341$		0			0
$342$	4.00000			0.216295
$343$	−6.18034	+	19.0211i	−0.333707	+	1.02704i
$344$	6.47214	−	4.70228i	0.348954	−	0.253530i
$345$		0			0
$346$	−1.85410	−	5.70634i	−0.0996771	−	0.306775i
$347$	11.1246	+	34.2380i	0.597200	+	1.83799i	0.543453	+	0.839439i	$0.317117\pi$
$347$	11.1246	+	34.2380i	0.597200	+	1.83799i	0.0537472	+	0.998555i	$0.482883\pi$
$348$	−4.85410	−	3.52671i	−0.260207	−	0.189052i
$349$	3.23607	−	2.35114i	0.173223	−	0.125854i	−0.497796	−	0.867294i	$-0.665857\pi$
$349$	3.23607	−	2.35114i	0.173223	−	0.125854i	0.671019	+	0.741441i	$0.265857\pi$
$350$	3.09017	−	9.51057i	0.165177	−	0.508361i
$351$	−4.00000			−0.213504
$352$		0			0
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$		0			0
$355$		0			0
$356$	4.85410	+	3.52671i	0.257267	+	0.186915i
$357$	−3.70820	−	11.4127i	−0.196259	−	0.604023i
$358$	−7.41641	−	22.8254i	−0.391969	−	1.20636i
$359$	9.70820	+	7.05342i	0.512379	+	0.372265i	0.813725	−	0.581249i	$-0.197436\pi$
$359$	9.70820	+	7.05342i	0.512379	+	0.372265i	−0.301346	+	0.953515i	$0.597436\pi$
$360$		0			0
$361$	−0.927051	+	2.85317i	−0.0487922	+	0.150167i
$362$	22.0000			1.15629
$363$		0			0
$364$	−8.00000			−0.419314
$365$		0			0
$366$	6.47214	−	4.70228i	0.338304	−	0.245792i
$367$	−6.47214	−	4.70228i	−0.337843	−	0.245457i	0.405908	−	0.913914i	$-0.366955\pi$
$367$	−6.47214	−	4.70228i	−0.337843	−	0.245457i	−0.743751	+	0.668457i	$0.766955\pi$
$368$	1.85410	+	5.70634i	0.0966517	+	0.297463i
$369$	1.85410	+	5.70634i	0.0965207	+	0.297060i
$370$		0			0
$371$		0			0
$372$	2.47214	−	7.60845i	0.128174	−	0.394480i
$373$	20.0000			1.03556			0.517780	−	0.855514i	$-0.326758\pi$
$373$	20.0000			1.03556			0.517780	+	0.855514i	$0.326758\pi$
$374$		0			0
$375$		0			0
$376$	1.85410	−	5.70634i	0.0956180	−	0.294282i
$377$	19.4164	−	14.1068i	0.999996	−	0.726540i
$378$	1.61803	+	1.17557i	0.0832227	+	0.0604648i
$379$	6.18034	+	19.0211i	0.317463	+	0.977050i	0.974729	+	0.223391i	$0.0717128\pi$
$379$	6.18034	+	19.0211i	0.317463	+	0.977050i	−0.657266	+	0.753659i	$0.728287\pi$
$380$		0			0
$381$	−11.3262	−	8.22899i	−0.580261	−	0.421584i
$382$	14.5623	−	10.5801i	0.745072	−	0.541327i
$383$	1.85410	−	5.70634i	0.0947402	−	0.291580i	−0.892446	−	0.451155i	$-0.851012\pi$
$383$	1.85410	−	5.70634i	0.0947402	−	0.291580i	0.987186	+	0.159575i	$0.0510122\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−14.0000			−0.712581
$387$	2.47214	−	7.60845i	0.125666	−	0.386759i
$388$	−11.3262	+	8.22899i	−0.575003	+	0.417764i
$389$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$389$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$390$		0			0
$391$	−11.1246	−	34.2380i	−0.562596	−	1.73149i
$392$	−2.42705	−	1.76336i	−0.122585	−	0.0890629i
$393$	9.70820	−	7.05342i	0.489714	−	0.355798i
$394$	−1.85410	+	5.70634i	−0.0934083	+	0.287481i
$395$		0			0
$396$		0			0
$397$	26.0000			1.30490			0.652451	−	0.757831i	$-0.273741\pi$
$397$	26.0000			1.30490			0.652451	+	0.757831i	$0.273741\pi$
$398$	1.23607	−	3.80423i	0.0619585	−	0.190689i
$399$	6.47214	−	4.70228i	0.324012	−	0.235409i
$400$	4.04508	+	2.93893i	0.202254	+	0.146946i
$401$	9.27051	+	28.5317i	0.462947	+	1.42480i	0.861546	+	0.507679i	$0.169497\pi$
$401$	9.27051	+	28.5317i	0.462947	+	1.42480i	−0.398599	+	0.917125i	$0.630503\pi$
$402$	1.23607	+	3.80423i	0.0616495	+	0.189738i
$403$	25.8885	+	18.8091i	1.28960	+	0.936949i
$404$	−4.85410	+	3.52671i	−0.241501	+	0.175460i
$405$		0			0
$406$	−12.0000			−0.595550
$407$		0			0
$408$	6.00000			0.297044
$409$	−10.5066	+	32.3359i	−0.519517	+	1.59891i	0.255393	+	0.966837i	$0.417795\pi$
$409$	−10.5066	+	32.3359i	−0.519517	+	1.59891i	−0.774910	+	0.632071i	$0.782205\pi$
$410$		0			0
$411$	14.5623	+	10.5801i	0.718306	+	0.521880i
$412$	−1.23607	−	3.80423i	−0.0608967	−	0.187421i
$413$		0			0
$414$	4.85410	+	3.52671i	0.238566	+	0.173328i
$415$		0			0
$416$	1.23607	−	3.80423i	0.0606032	−	0.186518i
$417$	−4.00000			−0.195881
$418$		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
$421$	8.09017	−	5.87785i	0.394291	−	0.286469i	−0.372921	−	0.927863i	$-0.621644\pi$
$421$	8.09017	−	5.87785i	0.394291	−	0.286469i	0.767211	+	0.641394i	$0.221644\pi$
$422$	6.47214	+	4.70228i	0.315059	+	0.228904i
$423$	−1.85410	−	5.70634i	−0.0901495	−	0.277452i
$424$		0			0
$425$	−24.2705	−	17.6336i	−1.17729	−	0.855353i
$426$	4.85410	−	3.52671i	0.235182	−	0.170870i
$427$	4.94427	−	15.2169i	0.239270	−	0.736398i
$428$	−12.0000			−0.580042
$429$		0			0
$430$		0			0
$431$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$431$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	−21.0344	−	15.2824i	−1.01085	−	0.734426i	−0.0464634	−	0.998920i	$-0.514795\pi$
$433$	−21.0344	−	15.2824i	−1.01085	−	0.734426i	−0.964387	+	0.264494i	$0.914795\pi$
$434$	−4.94427	−	15.2169i	−0.237333	−	0.730435i
$435$		0			0
$436$	3.23607	+	2.35114i	0.154980	+	0.112599i
$437$	19.4164	−	14.1068i	0.928813	−	0.674822i
$438$	−0.618034	+	1.90211i	−0.0295308	+	0.0908865i
$439$	−10.0000			−0.477274			−0.238637	−	0.971109i	$-0.576701\pi$
$439$	−10.0000			−0.477274			−0.238637	+	0.971109i	$0.576701\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	−7.41641	+	22.8254i	−0.352763	+	1.08569i
$443$	19.4164	−	14.1068i	0.922501	−	0.670236i	−0.0216440	−	0.999766i	$-0.506890\pi$
$443$	19.4164	−	14.1068i	0.922501	−	0.670236i	0.944145	+	0.329529i	$0.106890\pi$
$444$	8.09017	+	5.87785i	0.383942	+	0.278951i
$445$		0			0
$446$	4.94427	+	15.2169i	0.234118	+	0.720541i
$447$	4.85410	+	3.52671i	0.229591	+	0.166808i
$448$	−1.61803	+	1.17557i	−0.0764449	+	0.0555405i
$449$	1.85410	−	5.70634i	0.0875005	−	0.269299i	−0.897726	−	0.440554i	$-0.854782\pi$
$449$	1.85410	−	5.70634i	0.0875005	−	0.269299i	0.985227	+	0.171255i	$0.0547822\pi$
$450$	5.00000			0.235702
$451$		0			0
$452$	18.0000			0.846649
$453$	−3.09017	+	9.51057i	−0.145189	+	0.446845i
$454$	−9.70820	+	7.05342i	−0.455629	+	0.331034i
$455$		0			0
$456$	1.23607	+	3.80423i	0.0578842	+	0.178149i
$457$	−3.09017	−	9.51057i	−0.144552	−	0.444885i	0.852401	−	0.522889i	$-0.175146\pi$
$457$	−3.09017	−	9.51057i	−0.144552	−	0.444885i	−0.996953	+	0.0780031i	$0.975146\pi$
$458$	−17.7984	−	12.9313i	−0.831663	−	0.604239i
$459$	4.85410	−	3.52671i	0.226570	−	0.164613i
$460$		0			0
$461$	42.0000			1.95614			0.978068	−	0.208288i	$-0.0667892\pi$
$461$	42.0000			1.95614			0.978068	+	0.208288i	$0.0667892\pi$
$462$		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
$466$	−14.5623	−	10.5801i	−0.674586	−	0.490115i
$467$	−3.70820	−	11.4127i	−0.171595	−	0.528116i	0.827866	−	0.560925i	$-0.189555\pi$
$467$	−3.70820	−	11.4127i	−0.171595	−	0.528116i	−0.999462	+	0.0328096i	$0.989555\pi$
$468$	−1.23607	−	3.80423i	−0.0571373	−	0.175850i
$469$	6.47214	+	4.70228i	0.298855	+	0.217131i
$470$		0			0
$471$	0.618034	−	1.90211i	0.0284775	−	0.0876447i
$472$		0			0
$473$		0			0
$474$	−14.0000			−0.643041
$475$	6.18034	−	19.0211i	0.283573	−	0.872749i
$476$	9.70820	−	7.05342i	0.444975	−	0.323293i
$477$		0			0
$478$	3.70820	+	11.4127i	0.169609	+	0.522004i
$479$	−7.41641	−	22.8254i	−0.338864	−	1.04292i	−0.964787	−	0.263032i	$-0.915277\pi$
$479$	−7.41641	−	22.8254i	−0.338864	−	1.04292i	0.625923	−	0.779885i	$-0.284723\pi$
$480$		0			0
$481$	−32.3607	+	23.5114i	−1.47552	+	1.07203i
$482$	3.09017	−	9.51057i	0.140753	−	0.433194i
$483$	12.0000			0.546019
$484$		0			0
$485$		0			0
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	−16.1803	+	11.7557i	−0.733201	+	0.532702i	−0.890575	−	0.454837i	$-0.849697\pi$
$487$	−16.1803	+	11.7557i	−0.733201	+	0.532702i	0.157373	+	0.987539i	$0.449697\pi$
$488$	6.47214	+	4.70228i	0.292980	+	0.212862i
$489$	−1.23607	−	3.80423i	−0.0558969	−	0.172033i
$490$		0			0
$491$	−9.70820	−	7.05342i	−0.438125	−	0.318317i	0.346764	−	0.937952i	$-0.387280\pi$
$491$	−9.70820	−	7.05342i	−0.438125	−	0.318317i	−0.784890	+	0.619636i	$0.787280\pi$
$492$	−4.85410	+	3.52671i	−0.218840	+	0.158996i
$493$	−11.1246	+	34.2380i	−0.501027	+	1.54200i
$494$	−16.0000			−0.719874
$495$		0			0
$496$	8.00000			0.359211
$497$	3.70820	−	11.4127i	0.166336	−	0.511929i
$498$	−9.70820	+	7.05342i	−0.435035	+	0.316071i
$499$	3.23607	+	2.35114i	0.144866	+	0.105252i	0.657858	−	0.753142i	$-0.271463\pi$
$499$	3.23607	+	2.35114i	0.144866	+	0.105252i	−0.512992	+	0.858394i	$0.671463\pi$
$500$		0			0
$501$	3.70820	+	11.4127i	0.165670	+	0.509881i
$502$		0			0
$503$	−9.70820	+	7.05342i	−0.432867	+	0.314497i	−0.782794	−	0.622280i	$-0.786206\pi$
$503$	−9.70820	+	7.05342i	−0.432867	+	0.314497i	0.349927	+	0.936777i	$0.386206\pi$
$504$	−0.618034	+	1.90211i	−0.0275294	+	0.0847268i
$505$		0			0
$506$		0			0
$507$	3.00000			0.133235
$508$	4.32624	−	13.3148i	0.191946	−	0.590748i
$509$	−19.4164	+	14.1068i	−0.860617	+	0.625275i	−0.928053	−	0.372449i	$-0.878518\pi$
$509$	−19.4164	+	14.1068i	−0.860617	+	0.625275i	0.0674356	+	0.997724i	$0.478518\pi$
$510$		0			0
$511$	1.23607	+	3.80423i	0.0546804	+	0.168289i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	3.23607	+	2.35114i	0.142876	+	0.103805i
$514$	−24.2705	+	17.6336i	−1.07053	+	0.777783i
$515$		0			0
$516$	8.00000			0.352180
$517$		0			0
$518$	20.0000			0.878750
$519$	1.85410	−	5.70634i	0.0813860	−	0.250480i
$520$		0			0
$521$	14.5623	+	10.5801i	0.637986	+	0.463524i	0.859158	−	0.511711i	$-0.170988\pi$
$521$	14.5623	+	10.5801i	0.637986	+	0.463524i	−0.221172	+	0.975235i	$0.570988\pi$
$522$	−1.85410	−	5.70634i	−0.0811518	−	0.249760i
$523$	−4.94427	−	15.2169i	−0.216198	−	0.665389i	−0.999066	−	0.0432015i	$-0.986244\pi$
$523$	−4.94427	−	15.2169i	−0.216198	−	0.665389i	0.782868	−	0.622187i	$-0.213756\pi$
$524$	9.70820	+	7.05342i	0.424105	+	0.308130i
$525$	8.09017	−	5.87785i	0.353084	−	0.256531i
$526$		0			0
$527$	−48.0000			−2.09091
$528$		0			0
$529$	13.0000			0.565217
$530$		0			0
$531$		0			0
$532$	6.47214	+	4.70228i	0.280603	+	0.203870i
$533$	−7.41641	−	22.8254i	−0.321240	−	0.988676i
$534$	1.85410	+	5.70634i	0.0802348	+	0.246937i
$535$		0			0
$536$	−3.23607	+	2.35114i	−0.139777	+	0.101554i
$537$	7.41641	−	22.8254i	0.320042	−	0.984987i
$538$	24.0000			1.03471
$539$		0			0
$540$		0			0
$541$	6.18034	−	19.0211i	0.265714	−	0.817782i	−0.725815	−	0.687890i	$-0.758537\pi$
$541$	6.18034	−	19.0211i	0.265714	−	0.817782i	0.991528	−	0.129892i	$-0.0414630\pi$
$542$	1.61803	−	1.17557i	0.0695005	−	0.0504951i
$543$	17.7984	+	12.9313i	0.763801	+	0.554934i
$544$	1.85410	+	5.70634i	0.0794940	+	0.244657i
$545$		0			0
$546$	−6.47214	−	4.70228i	−0.276982	−	0.201239i
$547$	22.6525	−	16.4580i	0.968550	−	0.703693i	0.0134293	−	0.999910i	$-0.495725\pi$
$547$	22.6525	−	16.4580i	0.968550	−	0.703693i	0.955121	+	0.296217i	$0.0957252\pi$
$548$	−5.56231	+	17.1190i	−0.237610	+	0.731288i
$549$	8.00000			0.341432
$550$		0			0
$551$	−24.0000			−1.02243
$552$	−1.85410	+	5.70634i	−0.0789158	+	0.242878i
$553$	−22.6525	+	16.4580i	−0.963281	+	0.699865i
$554$	−12.9443	−	9.40456i	−0.549949	−	0.399562i
$555$		0			0
$556$	−1.23607	−	3.80423i	−0.0524210	−	0.161335i
$557$	−14.5623	−	10.5801i	−0.617025	−	0.448295i	0.234856	−	0.972030i	$-0.424538\pi$
$557$	−14.5623	−	10.5801i	−0.617025	−	0.448295i	−0.851881	+	0.523735i	$0.824538\pi$
$558$	6.47214	−	4.70228i	0.273987	−	0.199063i
$559$	−9.88854	+	30.4338i	−0.418241	+	1.28721i
$560$		0			0
$561$		0			0
$562$	6.00000			0.253095
$563$	−3.70820	+	11.4127i	−0.156282	+	0.480987i	−0.998289	−	0.0584805i	$-0.981374\pi$
$563$	−3.70820	+	11.4127i	−0.156282	+	0.480987i	0.842006	+	0.539468i	$0.181374\pi$
$564$	4.85410	−	3.52671i	0.204395	−	0.148501i
$565$		0			0
$566$	−2.47214	−	7.60845i	−0.103912	−	0.319807i
$567$	0.618034	+	1.90211i	0.0259550	+	0.0798812i
$568$	4.85410	+	3.52671i	0.203674	+	0.147978i
$569$	−14.5623	+	10.5801i	−0.610484	+	0.443542i	−0.849585	−	0.527452i	$-0.823147\pi$
$569$	−14.5623	+	10.5801i	−0.610484	+	0.443542i	0.239101	+	0.970995i	$0.423147\pi$
$570$		0			0
$571$	−28.0000			−1.17176			−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000			−1.17176			−0.585882	+	0.810397i	$0.699252\pi$
$572$		0			0
$573$	18.0000			0.751961
$574$	−3.70820	+	11.4127i	−0.154777	+	0.476356i
$575$	24.2705	−	17.6336i	1.01215	−	0.735370i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−10.5066	−	32.3359i	−0.437395	−	1.34616i	−0.890613	−	0.454762i	$-0.849724\pi$
$577$	−10.5066	−	32.3359i	−0.437395	−	1.34616i	0.453218	−	0.891400i	$-0.350276\pi$
$578$	−5.87132	−	18.0701i	−0.244215	−	0.751616i
$579$	−11.3262	−	8.22899i	−0.470702	−	0.341985i
$580$		0			0
$581$	−7.41641	+	22.8254i	−0.307684	+	0.946955i
$582$	−14.0000			−0.580319
$583$		0			0
$584$	−2.00000			−0.0827606
$585$		0			0
$586$	−4.85410	+	3.52671i	−0.200521	+	0.145687i
$587$	−19.4164	−	14.1068i	−0.801401	−	0.582252i	0.109924	−	0.993940i	$-0.464939\pi$
$587$	−19.4164	−	14.1068i	−0.801401	−	0.582252i	−0.911325	+	0.411688i	$0.864939\pi$
$588$	−0.927051	−	2.85317i	−0.0382309	−	0.117663i
$589$	−9.88854	−	30.4338i	−0.407450	−	1.25400i
$590$		0			0
$591$	−4.85410	+	3.52671i	−0.199671	+	0.145070i
$592$	−3.09017	+	9.51057i	−0.127005	+	0.390882i
$593$	−30.0000			−1.23195			−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000			−1.23195			−0.615976	+	0.787765i	$0.711238\pi$
$594$		0			0
$595$		0			0
$596$	−1.85410	+	5.70634i	−0.0759470	+	0.233741i
$597$	3.23607	−	2.35114i	0.132443	−	0.0962258i
$598$	−19.4164	−	14.1068i	−0.793996	−	0.576872i
$599$	9.27051	+	28.5317i	0.378783	+	1.16577i	0.940891	+	0.338710i	$0.109990\pi$
$599$	9.27051	+	28.5317i	0.378783	+	1.16577i	−0.562108	+	0.827064i	$0.690010\pi$
$600$	1.54508	+	4.75528i	0.0630778	+	0.194134i
$601$	17.7984	+	12.9313i	0.726011	+	0.527478i	0.888299	−	0.459266i	$-0.151887\pi$
$601$	17.7984	+	12.9313i	0.726011	+	0.527478i	−0.162288	+	0.986743i	$0.551887\pi$
$602$	12.9443	−	9.40456i	0.527569	−	0.383301i
$603$	−1.23607	+	3.80423i	−0.0503366	+	0.154920i
$604$	−10.0000			−0.406894
$605$		0			0
$606$	−6.00000			−0.243733
$607$	4.32624	−	13.3148i	0.175597	−	0.540431i	−0.824064	−	0.566497i	$-0.808298\pi$
$607$	4.32624	−	13.3148i	0.175597	−	0.540431i	0.999660	+	0.0260665i	$0.00829818\pi$
$608$	−3.23607	+	2.35114i	−0.131240	+	0.0953514i
$609$	−9.70820	−	7.05342i	−0.393396	−	0.285819i
$610$		0			0
$611$	7.41641	+	22.8254i	0.300036	+	0.923415i
$612$	4.85410	+	3.52671i	0.196215	+	0.142559i
$613$	12.9443	−	9.40456i	0.522814	−	0.379847i	−0.294849	−	0.955544i	$-0.595269\pi$
$613$	12.9443	−	9.40456i	0.522814	−	0.379847i	0.817663	+	0.575697i	$0.195269\pi$
$614$	−6.18034	+	19.0211i	−0.249418	+	0.767630i
$615$		0			0
$616$		0			0
$617$	−30.0000			−1.20775			−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000			−1.20775			−0.603877	+	0.797077i	$0.706378\pi$
$618$	1.23607	−	3.80423i	0.0497219	−	0.153028i
$619$	−35.5967	+	25.8626i	−1.43075	+	1.03950i	−0.440878	+	0.897567i	$0.645333\pi$
$619$	−35.5967	+	25.8626i	−1.43075	+	1.03950i	−0.989876	+	0.141937i	$0.954667\pi$
$620$		0			0
$621$	1.85410	+	5.70634i	0.0744025	+	0.228988i
$622$	5.56231	+	17.1190i	0.223028	+	0.686410i
$623$	9.70820	+	7.05342i	0.388951	+	0.282589i
$624$	3.23607	−	2.35114i	0.129546	−	0.0941210i
$625$	7.72542	−	23.7764i	0.309017	−	0.951057i
$626$	−26.0000			−1.03917
$627$		0			0
$628$	2.00000			0.0798087
$629$	18.5410	−	57.0634i	0.739279	−	2.27527i
$630$		0			0
$631$	12.9443	+	9.40456i	0.515303	+	0.374390i	0.814832	−	0.579698i	$-0.196829\pi$
$631$	12.9443	+	9.40456i	0.515303	+	0.374390i	−0.299528	+	0.954087i	$0.596829\pi$
$632$	−4.32624	−	13.3148i	−0.172089	−	0.529634i
$633$	2.47214	+	7.60845i	0.0982586	+	0.302409i
$634$	9.70820	+	7.05342i	0.385562	+	0.280127i
$635$		0			0
$636$		0			0
$637$	12.0000			0.475457
$638$		0			0
$639$	6.00000			0.237356
$640$		0			0
$641$	−4.85410	+	3.52671i	−0.191726	+	0.139297i	−0.679507	−	0.733669i	$-0.737806\pi$
$641$	−4.85410	+	3.52671i	−0.191726	+	0.139297i	0.487781	+	0.872966i	$0.337806\pi$
$642$	−9.70820	−	7.05342i	−0.383152	−	0.278376i
$643$	−1.23607	−	3.80423i	−0.0487458	−	0.150024i	0.923721	−	0.383066i	$-0.125132\pi$
$643$	−1.23607	−	3.80423i	−0.0487458	−	0.150024i	−0.972467	+	0.233042i	$0.925132\pi$
$644$	3.70820	+	11.4127i	0.146124	+	0.449723i
$645$		0			0
$646$	19.4164	−	14.1068i	0.763928	−	0.555026i
$647$	1.85410	−	5.70634i	0.0728923	−	0.224339i	−0.907972	−	0.419030i	$-0.862370\pi$
$647$	1.85410	−	5.70634i	0.0728923	−	0.224339i	0.980865	+	0.194691i	$0.0623703\pi$
$648$	−1.00000			−0.0392837
$649$		0			0
$650$	−20.0000			−0.784465
$651$	4.94427	−	15.2169i	0.193781	−	0.596397i
$652$	3.23607	−	2.35114i	0.126734	−	0.0920778i
$653$	29.1246	+	21.1603i	1.13973	+	0.828065i	0.987082	−	0.160215i	$-0.0512187\pi$
$653$	29.1246	+	21.1603i	1.13973	+	0.828065i	0.152652	+	0.988280i	$0.451219\pi$
$654$	1.23607	+	3.80423i	0.0483341	+	0.148757i
$655$		0			0
$656$	−4.85410	−	3.52671i	−0.189521	−	0.137695i
$657$	−1.61803	+	1.17557i	−0.0631255	+	0.0458634i
$658$	3.70820	−	11.4127i	0.144561	−	0.444913i
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$		0			0
$661$	−22.0000			−0.855701			−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000			−0.855701			−0.427850	+	0.903850i	$0.640729\pi$
$662$	1.23607	−	3.80423i	0.0480411	−	0.147855i
$663$	−19.4164	+	14.1068i	−0.754071	+	0.547865i
$664$	−9.70820	−	7.05342i	−0.376751	−	0.273726i
$665$		0			0
$666$	3.09017	+	9.51057i	0.119742	+	0.368527i
$667$	−29.1246	−	21.1603i	−1.12771	−	0.819329i
$668$	−9.70820	+	7.05342i	−0.375622	+	0.272905i
$669$	−4.94427	+	15.2169i	−0.191157	+	0.588320i
$670$		0			0
$671$		0			0
$672$	−2.00000			−0.0771517
$673$	4.32624	−	13.3148i	0.166764	−	0.513247i	−0.832398	−	0.554179i	$-0.813032\pi$
$673$	4.32624	−	13.3148i	0.166764	−	0.513247i	0.999162	+	0.0409312i	$0.0130324\pi$
$674$	1.61803	−	1.17557i	0.0623243	−	0.0452813i
$675$	4.04508	+	2.93893i	0.155695	+	0.113119i
$676$	0.927051	+	2.85317i	0.0356558	+	0.109737i
$677$	9.27051	+	28.5317i	0.356295	+	1.09656i	0.955255	+	0.295783i	$0.0955807\pi$
$677$	9.27051	+	28.5317i	0.356295	+	1.09656i	−0.598960	+	0.800779i	$0.704419\pi$
$678$	14.5623	+	10.5801i	0.559262	+	0.406328i
$679$	−22.6525	+	16.4580i	−0.869322	+	0.631600i
$680$		0			0
$681$	−12.0000			−0.459841
$682$		0			0
$683$	−24.0000			−0.918334			−0.459167	−	0.888350i	$-0.651852\pi$
$683$	−24.0000			−0.918334			−0.459167	+	0.888350i	$0.651852\pi$
$684$	−1.23607	+	3.80423i	−0.0472622	+	0.145458i
$685$		0			0
$686$	−16.1803	−	11.7557i	−0.617768	−	0.448835i
$687$	−6.79837	−	20.9232i	−0.259374	−	0.798272i
$688$	2.47214	+	7.60845i	0.0942493	+	0.290070i
$689$		0			0
$690$		0			0
$691$	6.18034	−	19.0211i	0.235111	−	0.723598i	−0.761995	−	0.647582i	$-0.775780\pi$
$691$	6.18034	−	19.0211i	0.235111	−	0.723598i	0.997107	−	0.0760155i	$-0.0242198\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−36.0000			−1.36654
$695$		0			0
$696$	4.85410	−	3.52671i	0.183994	−	0.133680i
$697$	29.1246	+	21.1603i	1.10317	+	0.801502i
$698$	1.23607	+	3.80423i	0.0467859	+	0.143992i
$699$	−5.56231	−	17.1190i	−0.210386	−	0.647501i
$700$	8.09017	+	5.87785i	0.305780	+	0.222162i
$701$	4.85410	−	3.52671i	0.183337	−	0.133202i	−0.492331	−	0.870408i	$-0.663855\pi$
$701$	4.85410	−	3.52671i	0.183337	−	0.133202i	0.675668	+	0.737206i	$0.263855\pi$
$702$	1.23607	−	3.80423i	0.0466524	−	0.143581i
$703$	40.0000			1.50863
$704$		0			0
$705$		0			0
$706$	1.85410	−	5.70634i	0.0697800	−	0.214761i
$707$	−9.70820	+	7.05342i	−0.365115	+	0.265271i
$708$		0			0
$709$	8.03444	+	24.7275i	0.301740	+	0.928660i	0.980874	+	0.194645i	$0.0623555\pi$
$709$	8.03444	+	24.7275i	0.301740	+	0.928660i	−0.679134	+	0.734014i	$0.737644\pi$
$710$		0			0
$711$	−11.3262	−	8.22899i	−0.424767	−	0.308611i
$712$	−4.85410	+	3.52671i	−0.181915	+	0.132169i
$713$	14.8328	−	45.6507i	0.555493	−	1.70963i
$714$	12.0000			0.449089
$715$		0			0
$716$	24.0000			0.896922
$717$	−3.70820	+	11.4127i	−0.138485	+	0.426214i
$718$	−9.70820	+	7.05342i	−0.362307	+	0.263231i
$719$	−24.2705	−	17.6336i	−0.905137	−	0.657621i	0.0346431	−	0.999400i	$-0.488971\pi$
$719$	−24.2705	−	17.6336i	−0.905137	−	0.657621i	−0.939780	+	0.341779i	$0.888971\pi$
$720$		0			0
$721$	−2.47214	−	7.60845i	−0.0920672	−	0.283354i
$722$	−2.42705	−	1.76336i	−0.0903255	−	0.0656253i
$723$	8.09017	−	5.87785i	0.300877	−	0.218600i
$724$	−6.79837	+	20.9232i	−0.252660	+	0.777606i
$725$	−30.0000			−1.11417
$726$		0			0
$727$	−28.0000			−1.03846			−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000			−1.03846			−0.519231	+	0.854634i	$0.673782\pi$
$728$	2.47214	−	7.60845i	0.0916235	−	0.281988i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−14.8328	−	45.6507i	−0.548612	−	1.68845i
$732$	2.47214	+	7.60845i	0.0913728	+	0.281216i
$733$	3.23607	+	2.35114i	0.119527	+	0.0868414i	0.645943	−	0.763386i	$-0.276464\pi$
$733$	3.23607	+	2.35114i	0.119527	+	0.0868414i	−0.526416	+	0.850227i	$0.676464\pi$
$734$	6.47214	−	4.70228i	0.238891	−	0.173564i
$735$		0			0
$736$	−6.00000			−0.221163
$737$		0			0
$738$	−6.00000			−0.220863
$739$	2.47214	−	7.60845i	0.0909390	−	0.279881i	−0.895235	−	0.445594i	$-0.852992\pi$
$739$	2.47214	−	7.60845i	0.0909390	−	0.279881i	0.986174	+	0.165713i	$0.0529924\pi$
$740$		0			0
$741$	−12.9443	−	9.40456i	−0.475520	−	0.345485i
$742$		0			0
$743$	11.1246	+	34.2380i	0.408122	+	1.25607i	0.918260	+	0.395979i	$0.129595\pi$
$743$	11.1246	+	34.2380i	0.408122	+	1.25607i	−0.510137	+	0.860093i	$0.670405\pi$
$744$	6.47214	+	4.70228i	0.237280	+	0.172394i
$745$		0			0
$746$	−6.18034	+	19.0211i	−0.226278	+	0.696413i
$747$	−12.0000			−0.439057
$748$		0			0
$749$	−24.0000			−0.876941
$750$		0			0
$751$	−6.47214	+	4.70228i	−0.236172	+	0.171589i	−0.699576	−	0.714558i	$-0.746628\pi$
$751$	−6.47214	+	4.70228i	−0.236172	+	0.171589i	0.463404	+	0.886147i	$0.346628\pi$
$752$	4.85410	+	3.52671i	0.177011	+	0.128606i
$753$		0			0
$754$	7.41641	+	22.8254i	0.270090	+	0.831250i
$755$		0			0
$756$	−1.61803	+	1.17557i	−0.0588473	+	0.0427551i
$757$	−10.5066	+	32.3359i	−0.381868	+	1.17527i	0.556859	+	0.830607i	$0.312006\pi$
$757$	−10.5066	+	32.3359i	−0.381868	+	1.17527i	−0.938727	+	0.344662i	$0.887994\pi$
$758$	−20.0000			−0.726433
$759$		0			0
$760$		0			0
$761$	5.56231	−	17.1190i	0.201633	−	0.620564i	−0.798201	−	0.602391i	$-0.794215\pi$
$761$	5.56231	−	17.1190i	0.201633	−	0.620564i	0.999835	−	0.0181732i	$-0.00578504\pi$
$762$	11.3262	−	8.22899i	0.410306	−	0.298105i
$763$	6.47214	+	4.70228i	0.234307	+	0.170234i
$764$	5.56231	+	17.1190i	0.201237	+	0.619344i
$765$		0			0
$766$	4.85410	+	3.52671i	0.175386	+	0.127425i
$767$		0			0
$768$	0.309017	−	0.951057i	0.0111507	−	0.0343183i
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$		0			0
$771$	−30.0000			−1.08042
$772$	4.32624	−	13.3148i	0.155705	−	0.479210i
$773$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$773$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$774$	6.47214	+	4.70228i	0.232636	+	0.169020i
$775$	−12.3607	−	38.0423i	−0.444009	−	1.36652i
$776$	−4.32624	−	13.3148i	−0.155303	−	0.477973i
$777$	16.1803	+	11.7557i	0.580466	+	0.421734i
$778$		0			0
$779$	−7.41641	+	22.8254i	−0.265720	+	0.817803i
$780$		0			0
$781$		0			0
$782$	36.0000			1.28736
$783$	1.85410	−	5.70634i	0.0662602	−	0.203928i
$784$	2.42705	−	1.76336i	0.0866804	−	0.0629770i
$785$		0			0
$786$	3.70820	+	11.4127i	0.132267	+	0.407077i
$787$	9.88854	+	30.4338i	0.352489	+	1.08485i	0.957451	+	0.288594i	$0.0931879\pi$
$787$	9.88854	+	30.4338i	0.352489	+	1.08485i	−0.604963	+	0.796254i	$0.706812\pi$
$788$	−4.85410	−	3.52671i	−0.172920	−	0.125634i
$789$		0			0
$790$		0			0
$791$	36.0000			1.28001
$792$		0			0
$793$	−32.0000			−1.13635
$794$	−8.03444	+	24.7275i	−0.285132	+	0.877545i
$795$		0			0
$796$	3.23607	+	2.35114i	0.114699	+	0.0833340i
$797$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$797$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$798$	2.47214	+	7.60845i	0.0875127	+	0.269336i
$799$	−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
$802$	−30.0000			−1.05934
$803$		0			0
$804$	−4.00000			−0.141069
$805$		0			0
$806$	−25.8885	+	18.8091i	−0.911885	+	0.662523i
$807$	19.4164	+	14.1068i	0.683490	+	0.496584i
$808$	−1.85410	−	5.70634i	−0.0652271	−	0.200748i
$809$	−12.9787	−	39.9444i	−0.456307	−	1.40437i	−0.869594	−	0.493768i	$-0.835619\pi$
$809$	−12.9787	−	39.9444i	−0.456307	−	1.40437i	0.413286	−	0.910601i	$-0.364381\pi$
$810$		0			0
$811$	−6.47214	+	4.70228i	−0.227267	+	0.165119i	−0.695592	−	0.718437i	$-0.744858\pi$
$811$	−6.47214	+	4.70228i	−0.227267	+	0.165119i	0.468325	+	0.883557i	$0.344858\pi$
$812$	3.70820	−	11.4127i	0.130132	−	0.400506i
$813$	2.00000			0.0701431
$814$		0			0
$815$		0			0
$816$	−1.85410	+	5.70634i	−0.0649066	+	0.199762i
$817$	25.8885	−	18.8091i	0.905725	−	0.658048i
$818$	−27.5066	−	19.9847i	−0.961745	−	0.698749i
$819$	−2.47214	−	7.60845i	−0.0863834	−	0.265861i
$820$		0			0
$821$	14.5623	+	10.5801i	0.508228	+	0.369249i	0.812151	−	0.583447i	$-0.198297\pi$
$821$	14.5623	+	10.5801i	0.508228	+	0.369249i	−0.303923	+	0.952697i	$0.598297\pi$
$822$	−14.5623	+	10.5801i	−0.507919	+	0.369025i
$823$	2.47214	−	7.60845i	0.0861732	−	0.265214i	−0.898680	−	0.438605i	$-0.855473\pi$
$823$	2.47214	−	7.60845i	0.0861732	−	0.265214i	0.984853	+	0.173391i	$0.0554726\pi$
$824$	4.00000			0.139347
$825$		0			0
$826$		0			0
$827$	−3.70820	+	11.4127i	−0.128947	+	0.396858i	−0.994600	−	0.103787i	$-0.966904\pi$
$827$	−3.70820	+	11.4127i	−0.128947	+	0.396858i	0.865653	+	0.500645i	$0.166904\pi$
$828$	−4.85410	+	3.52671i	−0.168692	+	0.122562i
$829$	−11.3262	−	8.22899i	−0.393377	−	0.285805i	0.373461	−	0.927646i	$-0.378171\pi$
$829$	−11.3262	−	8.22899i	−0.393377	−	0.285805i	−0.766838	+	0.641841i	$0.778171\pi$
$830$		0			0
$831$	−4.94427	−	15.2169i	−0.171515	−	0.527869i
$832$	3.23607	+	2.35114i	0.112190	+	0.0815111i
$833$	−14.5623	+	10.5801i	−0.504554	+	0.366580i
$834$	1.23607	−	3.80423i	0.0428015	−	0.131730i
$835$		0			0
$836$		0			0
$837$	8.00000			0.276520
$838$	−7.41641	+	22.8254i	−0.256196	+	0.788489i
$839$	−14.5623	+	10.5801i	−0.502747	+	0.365267i	−0.810065	−	0.586340i	$-0.800568\pi$
$839$	−14.5623	+	10.5801i	−0.502747	+	0.365267i	0.307318	+	0.951607i	$0.400568\pi$
$840$		0			0
$841$	2.16312	+	6.65740i	0.0745903	+	0.229565i
$842$	3.09017	+	9.51057i	0.106494	+	0.327756i
$843$	4.85410	+	3.52671i	0.167184	+	0.121466i
$844$	−6.47214	+	4.70228i	−0.222780	+	0.161859i
$845$		0			0
$846$	6.00000			0.206284
$847$		0			0
$848$		0			0
$849$	2.47214	−	7.60845i	0.0848435	−	0.261121i
$850$	24.2705	−	17.6336i	0.832472	−	0.604826i
$851$	48.5410	+	35.2671i	1.66396	+	1.20894i
$852$	1.85410	+	5.70634i	0.0635205	+	0.195496i
$853$	2.47214	+	7.60845i	0.0846443	+	0.260508i	0.984417	−	0.175851i	$-0.0562677\pi$
$853$	2.47214	+	7.60845i	0.0846443	+	0.260508i	−0.899772	+	0.436359i	$0.856268\pi$
$854$	12.9443	+	9.40456i	0.442944	+	0.321818i
$855$		0			0
$856$	3.70820	−	11.4127i	0.126744	−	0.390077i
$857$	54.0000			1.84460			0.922302	−	0.386469i	$-0.126305\pi$
$857$	54.0000			1.84460			0.922302	+	0.386469i	$0.126305\pi$
$858$		0			0
$859$	20.0000			0.682391			0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000			0.682391			0.341196	+	0.939992i	$0.389168\pi$
$860$		0			0
$861$	−9.70820	+	7.05342i	−0.330855	+	0.240380i
$862$		0			0
$863$	12.9787	+	39.9444i	0.441801	+	1.35972i	0.885955	+	0.463772i	$0.153504\pi$
$863$	12.9787	+	39.9444i	0.441801	+	1.35972i	−0.444154	+	0.895950i	$0.646496\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$		0			0
$866$	21.0344	−	15.2824i	0.714779	−	0.519318i
$867$	5.87132	−	18.0701i	0.199401	−	0.613692i
$868$	16.0000			0.543075
$869$		0			0
$870$		0			0
$871$	4.94427	−	15.2169i	0.167530	−	0.515605i
$872$	−3.23607	+	2.35114i	−0.109587	+	0.0796197i
$873$	−11.3262	−	8.22899i	−0.383335	−	0.278509i
$874$	7.41641	+	22.8254i	0.250864	+	0.772079i
$875$		0			0
$876$	−1.61803	−	1.17557i	−0.0546683	−	0.0397188i
$877$	42.0689	−	30.5648i	1.42057	−	1.03210i	0.428887	−	0.903358i	$-0.358906\pi$
$877$	42.0689	−	30.5648i	1.42057	−	1.03210i	0.991678	−	0.128743i	$-0.0410942\pi$
$878$	3.09017	−	9.51057i	0.104288	−	0.320966i
$879$	−6.00000			−0.202375
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$	0.927051	−	2.85317i	0.0312154	−	0.0960712i
$883$	22.6525	−	16.4580i	0.762317	−	0.553855i	−0.137303	−	0.990529i	$-0.543844\pi$
$883$	22.6525	−	16.4580i	0.762317	−	0.553855i	0.899620	+	0.436674i	$0.143844\pi$
$884$	−19.4164	−	14.1068i	−0.653044	−	0.474465i
$885$		0			0
$886$	7.41641	+	22.8254i	0.249159	+	0.766833i
$887$	29.1246	+	21.1603i	0.977909	+	0.710492i	0.957240	−	0.289294i	$-0.0934205\pi$
$887$	29.1246	+	21.1603i	0.977909	+	0.710492i	0.0206685	+	0.999786i	$0.493421\pi$
$888$	−8.09017	+	5.87785i	−0.271488	+	0.197248i
$889$	8.65248	−	26.6296i	0.290195	−	0.893128i
$890$		0			0
$891$		0			0
$892$	−16.0000			−0.535720
$893$	7.41641	−	22.8254i	0.248181	−	0.763821i
$894$	−4.85410	+	3.52671i	−0.162345	+	0.117951i
$895$		0			0
$896$	−0.618034	−	1.90211i	−0.0206471	−	0.0635451i
$897$	−7.41641	−	22.8254i	−0.247627	−	0.762116i
$898$	4.85410	+	3.52671i	0.161983	+	0.117688i
$899$	−38.8328	+	28.2137i	−1.29515	+	0.940979i
$900$	−1.54508	+	4.75528i	−0.0515028	+	0.158509i
$901$		0			0
$902$		0			0
$903$	16.0000			0.532447
$904$	−5.56231	+	17.1190i	−0.185000	+	0.569370i
$905$		0			0
$906$	−8.09017	−	5.87785i	−0.268778	−	0.195279i
$907$	6.18034	+	19.0211i	0.205215	+	0.631586i	0.999705	+	0.0243086i	$0.00773844\pi$
$907$	6.18034	+	19.0211i	0.205215	+	0.631586i	−0.794490	+	0.607278i	$0.792262\pi$
$908$	−3.70820	−	11.4127i	−0.123061	−	0.378743i
$909$	−4.85410	−	3.52671i	−0.161000	−	0.116974i
$910$		0			0
$911$	−12.9787	+	39.9444i	−0.430004	+	1.32342i	0.468117	+	0.883667i	$0.344933\pi$
$911$	−12.9787	+	39.9444i	−0.430004	+	1.32342i	−0.898121	+	0.439749i	$0.855067\pi$
$912$	−4.00000			−0.132453
$913$		0			0
$914$	10.0000			0.330771
$915$		0			0
$916$	17.7984	−	12.9313i	0.588075	−	0.427261i
$917$	19.4164	+	14.1068i	0.641186	+	0.465849i
$918$	1.85410	+	5.70634i	0.0611945	+	0.188337i
$919$	0.618034	+	1.90211i	0.0203871	+	0.0627449i	0.960732	−	0.277476i	$-0.0894980\pi$
$919$	0.618034	+	1.90211i	0.0203871	+	0.0627449i	−0.940345	+	0.340221i	$0.889498\pi$
$920$		0			0
$921$	−16.1803	+	11.7557i	−0.533160	+	0.387364i
$922$	−12.9787	+	39.9444i	−0.427431	+	1.31550i
$923$	−24.0000			−0.789970
$924$		0			0
$925$	50.0000			1.64399
$926$	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
$929$	9.27051	+	28.5317i	0.304156	+	0.936095i	0.979991	+	0.199042i	$0.0637830\pi$
$929$	9.27051	+	28.5317i	0.304156	+	0.936095i	−0.675835	+	0.737053i	$0.736217\pi$
$930$		0			0
$931$	−9.70820	−	7.05342i	−0.318174	−	0.231167i
$932$	14.5623	−	10.5801i	0.477004	−	0.346564i
$933$	−5.56231	+	17.1190i	−0.182102	+	0.560451i
$934$	12.0000			0.392652
$935$		0			0
$936$	4.00000			0.130744
$937$	−6.79837	+	20.9232i	−0.222093	+	0.683533i	0.776480	+	0.630141i	$0.217003\pi$
$937$	−6.79837	+	20.9232i	−0.222093	+	0.683533i	−0.998574	+	0.0533913i	$0.982997\pi$
$938$	−6.47214	+	4.70228i	−0.211323	+	0.153535i
$939$	−21.0344	−	15.2824i	−0.686433	−	0.498723i
$940$		0			0
$941$	−5.56231	−	17.1190i	−0.181326	−	0.558064i	0.818540	−	0.574450i	$-0.194784\pi$
$941$	−5.56231	−	17.1190i	−0.181326	−	0.558064i	−0.999866	+	0.0163859i	$0.994784\pi$
$942$	1.61803	+	1.17557i	0.0527184	+	0.0383022i
$943$	−29.1246	+	21.1603i	−0.948428	+	0.689073i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$	4.32624	−	13.3148i	0.140510	−	0.432444i
$949$	6.47214	−	4.70228i	0.210094	−	0.152643i
$950$	16.1803	+	11.7557i	0.524960	+	0.381405i
$951$	3.70820	+	11.4127i	0.120247	+	0.370081i
$952$	3.70820	+	11.4127i	0.120184	+	0.369887i
$953$	33.9787	+	24.6870i	1.10068	+	0.799690i	0.981171	−	0.193143i	$-0.0618683\pi$
$953$	33.9787	+	24.6870i	1.10068	+	0.799690i	0.119508	+	0.992833i	$0.461868\pi$
$954$		0			0
$955$		0			0
$956$	−12.0000			−0.388108
$957$		0			0
$958$	24.0000			0.775405
$959$	−11.1246	+	34.2380i	−0.359232	+	1.10560i
$960$		0			0
$961$	−26.6976	−	19.3969i	−0.861212	−	0.625707i
$962$	−12.3607	−	38.0423i	−0.398524	−	1.22653i
$963$	−3.70820	−	11.4127i	−0.119495	−	0.367768i
$964$	8.09017	+	5.87785i	0.260567	+	0.189313i
$965$		0			0
$966$	−3.70820	+	11.4127i	−0.119310	+	0.367197i
$967$	14.0000			0.450210			0.225105	−	0.974335i	$-0.427728\pi$
$967$	14.0000			0.450210			0.225105	+	0.974335i	$0.427728\pi$
$968$		0			0
$969$	24.0000			0.770991
$970$		0			0
$971$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$971$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	−2.47214	−	7.60845i	−0.0792530	−	0.243916i
$974$	−6.18034	−	19.0211i	−0.198031	−	0.609476i
$975$	−16.1803	−	11.7557i	−0.518186	−	0.376484i
$976$	−6.47214	+	4.70228i	−0.207168	+	0.150516i
$977$	16.6869	−	51.3571i	0.533862	−	1.64306i	−0.212234	−	0.977219i	$-0.568074\pi$
$977$	16.6869	−	51.3571i	0.533862	−	1.64306i	0.746096	−	0.665839i	$-0.231926\pi$
$978$	4.00000			0.127906
$979$		0			0
$980$		0			0
$981$	−1.23607	+	3.80423i	−0.0394646	+	0.121460i
$982$	9.70820	−	7.05342i	0.309801	−	0.225084i
$983$	−24.2705	−	17.6336i	−0.774109	−	0.562423i	0.129096	−	0.991632i	$-0.458792\pi$
$983$	−24.2705	−	17.6336i	−0.774109	−	0.562423i	−0.903205	+	0.429209i	$0.858792\pi$
$984$	−1.85410	−	5.70634i	−0.0591066	−	0.181911i
$985$		0			0
$986$	−29.1246	−	21.1603i	−0.927517	−	0.673880i
$987$	9.70820	−	7.05342i	0.309016	−	0.224513i
$988$	4.94427	−	15.2169i	0.157298	−	0.484114i
$989$	48.0000			1.52631
$990$		0			0
$991$	56.0000			1.77890			0.889449	−	0.457034i	$-0.151088\pi$
$991$	56.0000			1.77890			0.889449	+	0.457034i	$0.151088\pi$
$992$	−2.47214	+	7.60845i	−0.0784904	+	0.241569i
$993$	3.23607	−	2.35114i	0.102694	−	0.0746112i
$994$	9.70820	+	7.05342i	0.307926	+	0.223721i
$995$		0			0
$996$	−3.70820	−	11.4127i	−0.117499	−	0.361625i
$997$	−35.5967	−	25.8626i	−1.12736	−	0.819075i	−0.142052	−	0.989859i	$-0.545370\pi$
$997$	−35.5967	−	25.8626i	−1.12736	−	0.819075i	−0.985308	+	0.170784i	$0.945370\pi$
$998$	−3.23607	+	2.35114i	−0.102436	+	0.0744241i
$999$	−3.09017	+	9.51057i	−0.0977687	+	0.300901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.e.k.493.1		4
11.2	odd	10		726.2.e.b.487.1		4
11.3	even	5	inner	726.2.e.k.565.1		4
11.4	even	5		66.2.a.a.1.1	✓	1
11.5	even	5	inner	726.2.e.k.511.1		4
11.6	odd	10		726.2.e.b.511.1		4
11.7	odd	10		726.2.a.i.1.1		1
11.8	odd	10		726.2.e.b.565.1		4
11.9	even	5	inner	726.2.e.k.487.1		4
11.10	odd	2		726.2.e.b.493.1		4
33.26	odd	10		198.2.a.e.1.1		1
33.29	even	10		2178.2.a.b.1.1		1
44.7	even	10		5808.2.a.l.1.1		1
44.15	odd	10		528.2.a.d.1.1		1
55.4	even	10		1650.2.a.m.1.1		1
55.37	odd	20		1650.2.c.d.199.1		2
55.48	odd	20		1650.2.c.d.199.2		2
77.48	odd	10		3234.2.a.d.1.1		1
88.37	even	10		2112.2.a.i.1.1		1
88.59	odd	10		2112.2.a.v.1.1		1
99.4	even	15		1782.2.e.s.1189.1		2
99.59	odd	30		1782.2.e.f.1189.1		2
99.70	even	15		1782.2.e.s.595.1		2
99.92	odd	30		1782.2.e.f.595.1		2
132.59	even	10		1584.2.a.h.1.1		1
165.59	odd	10		4950.2.a.g.1.1		1
165.92	even	20		4950.2.c.r.199.2		2
165.158	even	20		4950.2.c.r.199.1		2
231.125	even	10		9702.2.a.bu.1.1		1
264.59	even	10		6336.2.a.bf.1.1		1
264.125	odd	10		6336.2.a.bj.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.a.a.1.1	✓	1	11.4	even	5
198.2.a.e.1.1		1	33.26	odd	10
528.2.a.d.1.1		1	44.15	odd	10
726.2.a.i.1.1		1	11.7	odd	10
726.2.e.b.487.1		4	11.2	odd	10
726.2.e.b.493.1		4	11.10	odd	2
726.2.e.b.511.1		4	11.6	odd	10
726.2.e.b.565.1		4	11.8	odd	10
726.2.e.k.487.1		4	11.9	even	5	inner
726.2.e.k.493.1		4	1.1	even	1	trivial
726.2.e.k.511.1		4	11.5	even	5	inner
726.2.e.k.565.1		4	11.3	even	5	inner
1584.2.a.h.1.1		1	132.59	even	10
1650.2.a.m.1.1		1	55.4	even	10
1650.2.c.d.199.1		2	55.37	odd	20
1650.2.c.d.199.2		2	55.48	odd	20
1782.2.e.f.595.1		2	99.92	odd	30
1782.2.e.f.1189.1		2	99.59	odd	30
1782.2.e.s.595.1		2	99.70	even	15
1782.2.e.s.1189.1		2	99.4	even	15
2112.2.a.i.1.1		1	88.37	even	10
2112.2.a.v.1.1		1	88.59	odd	10
2178.2.a.b.1.1		1	33.29	even	10
3234.2.a.d.1.1		1	77.48	odd	10
4950.2.a.g.1.1		1	165.59	odd	10
4950.2.c.r.199.1		2	165.158	even	20
4950.2.c.r.199.2		2	165.92	even	20
5808.2.a.l.1.1		1	44.7	even	10
6336.2.a.bf.1.1		1	264.59	even	10
6336.2.a.bj.1.1		1	264.125	odd	10
9702.2.a.bu.1.1		1	231.125	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +1.00000 q^{12} +(-1.23607 + 3.80423i) q^{13} +(1.61803 - 1.17557i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-1.85410 - 5.70634i) q^{17} +(0.809017 + 0.587785i) q^{18} +(3.23607 - 2.35114i) q^{19} +2.00000 q^{21} +6.00000 q^{23} +(-0.309017 + 0.951057i) q^{24} +(4.04508 - 2.93893i) q^{25} +(-3.23607 - 2.35114i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.618034 + 1.90211i) q^{28} +(-4.85410 - 3.52671i) q^{29} +(2.47214 - 7.60845i) q^{31} -1.00000 q^{32} +6.00000 q^{34} +(-0.809017 + 0.587785i) q^{36} +(8.09017 + 5.87785i) q^{37} +(1.23607 + 3.80423i) q^{38} +(-1.23607 - 3.80423i) q^{39} +(-4.85410 + 3.52671i) q^{41} +(-0.618034 + 1.90211i) q^{42} +8.00000 q^{43} +(-1.85410 + 5.70634i) q^{46} +(4.85410 - 3.52671i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(-0.927051 - 2.85317i) q^{49} +(1.54508 + 4.75528i) q^{50} +(4.85410 + 3.52671i) q^{51} +(3.23607 - 2.35114i) q^{52} -1.00000 q^{54} -2.00000 q^{56} +(-1.23607 + 3.80423i) q^{57} +(4.85410 - 3.52671i) q^{58} +(2.47214 + 7.60845i) q^{61} +(6.47214 + 4.70228i) q^{62} +(-1.61803 + 1.17557i) q^{63} +(0.309017 - 0.951057i) q^{64} -4.00000 q^{67} +(-1.85410 + 5.70634i) q^{68} +(-4.85410 + 3.52671i) q^{69} +(1.85410 + 5.70634i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(-1.61803 - 1.17557i) q^{73} +(-8.09017 + 5.87785i) q^{74} +(-1.54508 + 4.75528i) q^{75} -4.00000 q^{76} +4.00000 q^{78} +(4.32624 - 13.3148i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-1.85410 - 5.70634i) q^{82} +(-3.70820 - 11.4127i) q^{83} +(-1.61803 - 1.17557i) q^{84} +(-2.47214 + 7.60845i) q^{86} +6.00000 q^{87} -6.00000 q^{89} +(6.47214 - 4.70228i) q^{91} +(-4.85410 - 3.52671i) q^{92} +(2.47214 + 7.60845i) q^{93} +(1.85410 + 5.70634i) q^{94} +(0.809017 - 0.587785i) q^{96} +(4.32624 - 13.3148i) q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9	\( 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9} + 4 q^{12} + 4 q^{13} + 2 q^{14} - q^{16} + 6 q^{17} + q^{18} + 4 q^{19} + 8 q^{21} + 24 q^{23} + q^{24} + 5 q^{25} - 4 q^{26} - q^{27} - 2 q^{28} - 6 q^{29} - 8 q^{31} - 4 q^{32} + 24 q^{34} - q^{36} + 10 q^{37} - 4 q^{38} + 4 q^{39} - 6 q^{41} + 2 q^{42} + 32 q^{43} + 6 q^{46} + 6 q^{47} - q^{48} + 3 q^{49} - 5 q^{50} + 6 q^{51} + 4 q^{52} - 4 q^{54} - 8 q^{56} + 4 q^{57} + 6 q^{58} - 8 q^{61} + 8 q^{62} - 2 q^{63} - q^{64} - 16 q^{67} + 6 q^{68} - 6 q^{69} - 6 q^{71} + q^{72} - 2 q^{73} - 10 q^{74} + 5 q^{75} - 16 q^{76} + 16 q^{78} - 14 q^{79} - q^{81} + 6 q^{82} + 12 q^{83} - 2 q^{84} + 8 q^{86} + 24 q^{87} - 24 q^{89} + 8 q^{91} - 6 q^{92} - 8 q^{93} - 6 q^{94} + q^{96} - 14 q^{97} + 12 q^{98}+O(q^{100}) \) 4 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9 + 4 * q^12 + 4 * q^13 + 2 * q^14 - q^16 + 6 * q^17 + q^18 + 4 * q^19 + 8 * q^21 + 24 * q^23 + q^24 + 5 * q^25 - 4 * q^26 - q^27 - 2 * q^28 - 6 * q^29 - 8 * q^31 - 4 * q^32 + 24 * q^34 - q^36 + 10 * q^37 - 4 * q^38 + 4 * q^39 - 6 * q^41 + 2 * q^42 + 32 * q^43 + 6 * q^46 + 6 * q^47 - q^48 + 3 * q^49 - 5 * q^50 + 6 * q^51 + 4 * q^52 - 4 * q^54 - 8 * q^56 + 4 * q^57 + 6 * q^58 - 8 * q^61 + 8 * q^62 - 2 * q^63 - q^64 - 16 * q^67 + 6 * q^68 - 6 * q^69 - 6 * q^71 + q^72 - 2 * q^73 - 10 * q^74 + 5 * q^75 - 16 * q^76 + 16 * q^78 - 14 * q^79 - q^81 + 6 * q^82 + 12 * q^83 - 2 * q^84 + 8 * q^86 + 24 * q^87 - 24 * q^89 + 8 * q^91 - 6 * q^92 - 8 * q^93 - 6 * q^94 + q^96 - 14 * q^97 + 12 * q^98

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