LMFDB - Embedded newform 726.2.e.b.487.1

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			487.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	726.487
Dual form			726.2.e.b.565.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{6} +(-0.618034 + 1.90211i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{6} +(-0.618034 + 1.90211i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.00000 q^{12} +(-3.23607 + 2.35114i) q^{13} +(-0.618034 - 1.90211i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-4.85410 - 3.52671i) q^{17} +(0.309017 - 0.951057i) q^{18} +(1.23607 + 3.80423i) q^{19} -2.00000 q^{21} +6.00000 q^{23} +(-0.809017 + 0.587785i) q^{24} +(-1.54508 - 4.75528i) q^{25} +(1.23607 - 3.80423i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(1.61803 + 1.17557i) q^{28} +(-1.85410 + 5.70634i) q^{29} +(-6.47214 + 4.70228i) q^{31} +1.00000 q^{32} +6.00000 q^{34} +(0.309017 + 0.951057i) q^{36} +(-3.09017 + 9.51057i) q^{37} +(-3.23607 - 2.35114i) q^{38} +(-3.23607 - 2.35114i) q^{39} +(-1.85410 - 5.70634i) q^{41} +(1.61803 - 1.17557i) q^{42} -8.00000 q^{43} +(-4.85410 + 3.52671i) q^{46} +(-1.85410 - 5.70634i) q^{47} +(0.309017 - 0.951057i) q^{48} +(2.42705 + 1.76336i) q^{49} +(4.04508 + 2.93893i) q^{50} +(1.85410 - 5.70634i) q^{51} +(1.23607 + 3.80423i) q^{52} +1.00000 q^{54} -2.00000 q^{56} +(-3.23607 + 2.35114i) q^{57} +(-1.85410 - 5.70634i) q^{58} +(6.47214 + 4.70228i) q^{61} +(2.47214 - 7.60845i) q^{62} +(-0.618034 - 1.90211i) q^{63} +(-0.809017 + 0.587785i) q^{64} -4.00000 q^{67} +(-4.85410 + 3.52671i) q^{68} +(1.85410 + 5.70634i) q^{69} +(-4.85410 - 3.52671i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-0.618034 + 1.90211i) q^{73} +(-3.09017 - 9.51057i) q^{74} +(4.04508 - 2.93893i) q^{75} +4.00000 q^{76} +4.00000 q^{78} +(11.3262 - 8.22899i) q^{79} +(0.309017 - 0.951057i) q^{81} +(4.85410 + 3.52671i) q^{82} +(-9.70820 - 7.05342i) q^{83} +(-0.618034 + 1.90211i) q^{84} +(6.47214 - 4.70228i) q^{86} -6.00000 q^{87} -6.00000 q^{89} +(-2.47214 - 7.60845i) q^{91} +(1.85410 - 5.70634i) q^{92} +(-6.47214 - 4.70228i) q^{93} +(4.85410 + 3.52671i) q^{94} +(0.309017 + 0.951057i) q^{96} +(-11.3262 + 8.22899i) q^{97} -3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$5$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	−0.618034	+	1.90211i	−0.233595	+	0.718931i	0.763710	+	0.645560i	$0.223376\pi$
$7$	−0.618034	+	1.90211i	−0.233595	+	0.718931i	−0.997305	+	0.0733714i	$0.976624\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$		0			0
$11$		0			0
$12$	1.00000			0.288675
$13$	−3.23607	+	2.35114i	−0.897524	+	0.652089i	−0.937829	−	0.347098i	$-0.887167\pi$
$13$	−3.23607	+	2.35114i	−0.897524	+	0.652089i	0.0403050	+	0.999187i	$0.487167\pi$
$14$	−0.618034	−	1.90211i	−0.165177	−	0.508361i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−4.85410	−	3.52671i	−1.17729	−	0.855353i	−0.185429	−	0.982658i	$-0.559367\pi$
$17$	−4.85410	−	3.52671i	−1.17729	−	0.855353i	−0.991864	+	0.127304i	$0.959367\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$	1.23607	+	3.80423i	0.283573	+	0.872749i	0.986823	+	0.161806i	$0.0517318\pi$
$19$	1.23607	+	3.80423i	0.283573	+	0.872749i	−0.703249	+	0.710943i	$0.748268\pi$
$20$		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	$0.284877\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	−1.54508	−	4.75528i	−0.309017	−	0.951057i
$26$	1.23607	−	3.80423i	0.242413	−	0.746070i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	1.61803	+	1.17557i	0.305780	+	0.222162i
$29$	−1.85410	+	5.70634i	−0.344298	+	1.05964i	0.617660	+	0.786445i	$0.288081\pi$
$29$	−1.85410	+	5.70634i	−0.344298	+	1.05964i	−0.961958	+	0.273196i	$0.911919\pi$
$30$		0			0
$31$	−6.47214	+	4.70228i	−1.16243	+	0.844555i	−0.990083	−	0.140482i	$-0.955135\pi$
$31$	−6.47214	+	4.70228i	−1.16243	+	0.844555i	−0.172347	+	0.985036i	$0.555135\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	6.00000			1.02899
$35$		0			0
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−3.09017	+	9.51057i	−0.508021	+	1.56353i	0.287611	+	0.957747i	$0.407139\pi$
$37$	−3.09017	+	9.51057i	−0.508021	+	1.56353i	−0.795632	+	0.605780i	$0.792861\pi$
$38$	−3.23607	−	2.35114i	−0.524960	−	0.381405i
$39$	−3.23607	−	2.35114i	−0.518186	−	0.376484i
$40$		0			0
$41$	−1.85410	−	5.70634i	−0.289562	−	0.891180i	−0.984994	−	0.172588i	$-0.944787\pi$
$41$	−1.85410	−	5.70634i	−0.289562	−	0.891180i	0.695432	−	0.718592i	$-0.255213\pi$
$42$	1.61803	−	1.17557i	0.249668	−	0.181394i
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$		0			0
$45$		0			0
$46$	−4.85410	+	3.52671i	−0.715698	+	0.519985i
$47$	−1.85410	−	5.70634i	−0.270449	−	0.832355i	−0.990388	−	0.138318i	$-0.955830\pi$
$47$	−1.85410	−	5.70634i	−0.270449	−	0.832355i	0.719939	−	0.694037i	$-0.244170\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	2.42705	+	1.76336i	0.346722	+	0.251908i
$50$	4.04508	+	2.93893i	0.572061	+	0.415627i
$51$	1.85410	−	5.70634i	0.259626	−	0.799047i
$52$	1.23607	+	3.80423i	0.171412	+	0.527551i
$53$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$53$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$54$	1.00000			0.136083
$55$		0			0
$56$	−2.00000			−0.267261
$57$	−3.23607	+	2.35114i	−0.428628	+	0.311416i
$58$	−1.85410	−	5.70634i	−0.243456	−	0.749279i
$59$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$59$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$60$		0			0
$61$	6.47214	+	4.70228i	0.828672	+	0.602066i	0.919183	−	0.393830i	$-0.128850\pi$
$61$	6.47214	+	4.70228i	0.828672	+	0.602066i	−0.0905112	+	0.995895i	$0.528850\pi$
$62$	2.47214	−	7.60845i	0.313962	−	0.966274i
$63$	−0.618034	−	1.90211i	−0.0778650	−	0.239644i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$		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	$0.578571\pi$
$68$	−4.85410	+	3.52671i	−0.588646	+	0.427677i
$69$	1.85410	+	5.70634i	0.223208	+	0.686963i
$70$		0			0
$71$	−4.85410	−	3.52671i	−0.576076	−	0.418544i	0.261231	−	0.965276i	$-0.415871\pi$
$71$	−4.85410	−	3.52671i	−0.576076	−	0.418544i	−0.837307	+	0.546733i	$0.815871\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	−0.618034	+	1.90211i	−0.0723354	+	0.222625i	−0.980688	−	0.195580i	$-0.937341\pi$
$73$	−0.618034	+	1.90211i	−0.0723354	+	0.222625i	0.908352	+	0.418206i	$0.137341\pi$
$74$	−3.09017	−	9.51057i	−0.359225	−	1.10558i
$75$	4.04508	−	2.93893i	0.467086	−	0.339358i
$76$	4.00000			0.458831
$77$		0			0
$78$	4.00000			0.452911
$79$	11.3262	−	8.22899i	1.27430	−	0.925834i	0.274936	−	0.961462i	$-0.411343\pi$
$79$	11.3262	−	8.22899i	1.27430	−	0.925834i	0.999365	+	0.0356284i	$0.0113433\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	4.85410	+	3.52671i	0.536046	+	0.389460i
$83$	−9.70820	−	7.05342i	−1.06561	−	0.774214i	−0.0904951	−	0.995897i	$-0.528845\pi$
$83$	−9.70820	−	7.05342i	−1.06561	−	0.774214i	−0.975119	+	0.221683i	$0.928845\pi$
$84$	−0.618034	+	1.90211i	−0.0674330	+	0.207538i
$85$		0			0
$86$	6.47214	−	4.70228i	0.697908	−	0.507060i
$87$	−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
$91$	−2.47214	−	7.60845i	−0.259150	−	0.797582i
$92$	1.85410	−	5.70634i	0.193303	−	0.594927i
$93$	−6.47214	−	4.70228i	−0.671129	−	0.487604i
$94$	4.85410	+	3.52671i	0.500662	+	0.363753i
$95$		0			0
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	−11.3262	+	8.22899i	−1.15001	+	0.835528i	−0.988482	−	0.151341i	$-0.951641\pi$
$97$	−11.3262	+	8.22899i	−1.15001	+	0.835528i	−0.161524	+	0.986869i	$0.551641\pi$
$98$	−3.00000			−0.303046
$99$		0			0
$100$	−5.00000			−0.500000
$101$	4.85410	−	3.52671i	0.483001	−	0.350921i	−0.319485	−	0.947591i	$-0.603510\pi$
$101$	4.85410	−	3.52671i	0.483001	−	0.350921i	0.802486	+	0.596670i	$0.203510\pi$
$102$	1.85410	+	5.70634i	0.183583	+	0.565012i
$103$	−1.23607	+	3.80423i	−0.121793	+	0.374842i	−0.993303	−	0.115536i	$-0.963141\pi$
$103$	−1.23607	+	3.80423i	−0.121793	+	0.374842i	0.871510	+	0.490378i	$0.163141\pi$
$104$	−3.23607	−	2.35114i	−0.317323	−	0.230548i
$105$		0			0
$106$		0			0
$107$	3.70820	+	11.4127i	0.358486	+	1.10331i	0.953961	+	0.299932i	$0.0969638\pi$
$107$	3.70820	+	11.4127i	0.358486	+	1.10331i	−0.595475	+	0.803374i	$0.703036\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	4.00000			0.383131			0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$110$		0			0
$111$	−10.0000			−0.949158
$112$	1.61803	−	1.17557i	0.152890	−	0.111081i
$113$	5.56231	+	17.1190i	0.523258	+	1.61042i	0.767736	+	0.640767i	$0.221383\pi$
$113$	5.56231	+	17.1190i	0.523258	+	1.61042i	−0.244478	+	0.969655i	$0.578617\pi$
$114$	1.23607	−	3.80423i	0.115768	−	0.356298i
$115$		0			0
$116$	4.85410	+	3.52671i	0.450692	+	0.327447i
$117$	1.23607	−	3.80423i	0.114275	−	0.351701i
$118$		0			0
$119$	9.70820	−	7.05342i	0.889950	−	0.646586i
$120$		0			0
$121$		0			0
$122$	−8.00000			−0.724286
$123$	4.85410	−	3.52671i	0.437680	−	0.317993i
$124$	2.47214	+	7.60845i	0.222004	+	0.683259i
$125$		0			0
$126$	1.61803	+	1.17557i	0.144146	+	0.104728i
$127$	11.3262	+	8.22899i	1.00504	+	0.730205i	0.963163	−	0.268918i	$-0.0866659\pi$
$127$	11.3262	+	8.22899i	1.00504	+	0.730205i	0.0418779	+	0.999123i	$0.486666\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−2.47214	−	7.60845i	−0.217659	−	0.669887i
$130$		0			0
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$	−8.00000			−0.693688
$134$	3.23607	−	2.35114i	0.279554	−	0.203108i
$135$		0			0
$136$	1.85410	−	5.70634i	0.158988	−	0.489315i
$137$	14.5623	+	10.5801i	1.24414	+	0.903922i	0.997867	−	0.0652782i	$-0.0207935\pi$
$137$	14.5623	+	10.5801i	1.24414	+	0.903922i	0.246275	+	0.969200i	$0.420793\pi$
$138$	−4.85410	−	3.52671i	−0.413209	−	0.300214i
$139$	1.23607	−	3.80423i	0.104842	−	0.322670i	−0.884851	−	0.465873i	$-0.845740\pi$
$139$	1.23607	−	3.80423i	0.104842	−	0.322670i	0.989693	+	0.143203i	$0.0457402\pi$
$140$		0			0
$141$	4.85410	−	3.52671i	0.408789	−	0.297003i
$142$	6.00000			0.503509
$143$		0			0
$144$	1.00000			0.0833333
$145$		0			0
$146$	−0.618034	−	1.90211i	−0.0511489	−	0.157420i
$147$	−0.927051	+	2.85317i	−0.0764619	+	0.235325i
$148$	8.09017	+	5.87785i	0.665008	+	0.483157i
$149$	−4.85410	−	3.52671i	−0.397664	−	0.288919i	0.370925	−	0.928663i	$-0.379041\pi$
$149$	−4.85410	−	3.52671i	−0.397664	−	0.288919i	−0.768589	+	0.639743i	$0.779041\pi$
$150$	−1.54508	+	4.75528i	−0.126156	+	0.388267i
$151$	3.09017	+	9.51057i	0.251474	+	0.773959i	0.994504	+	0.104700i	$0.0333882\pi$
$151$	3.09017	+	9.51057i	0.251474	+	0.773959i	−0.743029	+	0.669259i	$0.766612\pi$
$152$	−3.23607	+	2.35114i	−0.262480	+	0.190703i
$153$	6.00000			0.485071
$154$		0			0
$155$		0			0
$156$	−3.23607	+	2.35114i	−0.259093	+	0.188242i
$157$	0.618034	+	1.90211i	0.0493245	+	0.151805i	0.972685	−	0.232129i	$-0.0745691\pi$
$157$	0.618034	+	1.90211i	0.0493245	+	0.151805i	−0.923361	+	0.383934i	$0.874569\pi$
$158$	−4.32624	+	13.3148i	−0.344177	+	1.05927i
$159$		0			0
$160$		0			0
$161$	−3.70820	+	11.4127i	−0.292247	+	0.899445i
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	3.23607	−	2.35114i	0.253468	−	0.184156i	−0.453794	−	0.891107i	$-0.649930\pi$
$163$	3.23607	−	2.35114i	0.253468	−	0.184156i	0.707263	+	0.706951i	$0.249930\pi$
$164$	−6.00000			−0.468521
$165$		0			0
$166$	12.0000			0.931381
$167$	9.70820	−	7.05342i	0.751243	−	0.545810i	−0.144969	−	0.989436i	$-0.546308\pi$
$167$	9.70820	−	7.05342i	0.751243	−	0.545810i	0.896212	+	0.443626i	$0.146308\pi$
$168$	−0.618034	−	1.90211i	−0.0476824	−	0.146751i
$169$	0.927051	−	2.85317i	0.0713116	−	0.219475i
$170$		0			0
$171$	−3.23607	−	2.35114i	−0.247468	−	0.179796i
$172$	−2.47214	+	7.60845i	−0.188499	+	0.580139i
$173$	−1.85410	−	5.70634i	−0.140965	−	0.433845i	0.855505	−	0.517794i	$-0.173247\pi$
$173$	−1.85410	−	5.70634i	−0.140965	−	0.433845i	−0.996470	+	0.0839492i	$0.973247\pi$
$174$	4.85410	−	3.52671i	0.367989	−	0.267359i
$175$	10.0000			0.755929
$176$		0			0
$177$		0			0
$178$	4.85410	−	3.52671i	0.363830	−	0.264338i
$179$	7.41641	+	22.8254i	0.554328	+	1.70605i	0.697710	+	0.716380i	$0.254202\pi$
$179$	7.41641	+	22.8254i	0.554328	+	1.70605i	−0.143382	+	0.989667i	$0.545798\pi$
$180$		0			0
$181$	17.7984	+	12.9313i	1.32294	+	0.961174i	0.999891	+	0.0147930i	$0.00470892\pi$
$181$	17.7984	+	12.9313i	1.32294	+	0.961174i	0.323052	+	0.946381i	$0.395291\pi$
$182$	6.47214	+	4.70228i	0.479747	+	0.348556i
$183$	−2.47214	+	7.60845i	−0.182746	+	0.562433i
$184$	1.85410	+	5.70634i	0.136686	+	0.420677i
$185$		0			0
$186$	8.00000			0.586588
$187$		0			0
$188$	−6.00000			−0.437595
$189$	1.61803	−	1.17557i	0.117695	−	0.0855102i
$190$		0			0
$191$	5.56231	−	17.1190i	0.402474	−	1.23869i	−0.520511	−	0.853855i	$-0.674259\pi$
$191$	5.56231	−	17.1190i	0.402474	−	1.23869i	0.922986	−	0.384834i	$-0.125741\pi$
$192$	−0.809017	−	0.587785i	−0.0583858	−	0.0424197i
$193$	11.3262	+	8.22899i	0.815280	+	0.592336i	0.915357	−	0.402644i	$-0.131909\pi$
$193$	11.3262	+	8.22899i	0.815280	+	0.592336i	−0.100076	+	0.994980i	$0.531909\pi$
$194$	4.32624	−	13.3148i	0.310606	−	0.955946i
$195$		0			0
$196$	2.42705	−	1.76336i	0.173361	−	0.125954i
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	−4.00000			−0.283552			−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$	4.04508	−	2.93893i	0.286031	−	0.207813i
$201$	−1.23607	−	3.80423i	−0.0871855	−	0.268329i
$202$	−1.85410	+	5.70634i	−0.130454	+	0.401497i
$203$	−9.70820	−	7.05342i	−0.681382	−	0.495053i
$204$	−4.85410	−	3.52671i	−0.339855	−	0.246919i
$205$		0			0
$206$	−1.23607	−	3.80423i	−0.0861209	−	0.265053i
$207$	−4.85410	+	3.52671i	−0.337383	+	0.245123i
$208$	4.00000			0.277350
$209$		0			0
$210$		0			0
$211$	6.47214	−	4.70228i	0.445560	−	0.323718i	−0.342280	−	0.939598i	$-0.611199\pi$
$211$	6.47214	−	4.70228i	0.445560	−	0.323718i	0.787840	+	0.615880i	$0.211199\pi$
$212$		0			0
$213$	1.85410	−	5.70634i	0.127041	−	0.390992i
$214$	−9.70820	−	7.05342i	−0.663639	−	0.482162i
$215$		0			0
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	−4.94427	−	15.2169i	−0.335639	−	1.03299i
$218$	−3.23607	+	2.35114i	−0.219174	+	0.159239i
$219$	−2.00000			−0.135147
$220$		0			0
$221$	24.0000			1.61441
$222$	8.09017	−	5.87785i	0.542977	−	0.394496i
$223$	−4.94427	−	15.2169i	−0.331093	−	1.01900i	−0.968615	−	0.248567i	$-0.920040\pi$
$223$	−4.94427	−	15.2169i	−0.331093	−	1.01900i	0.637522	−	0.770432i	$-0.279960\pi$
$224$	−0.618034	+	1.90211i	−0.0412941	+	0.127090i
$225$	4.04508	+	2.93893i	0.269672	+	0.195928i
$226$	−14.5623	−	10.5801i	−0.968670	−	0.703780i
$227$	3.70820	−	11.4127i	0.246122	−	0.757486i	−0.749328	−	0.662199i	$-0.769623\pi$
$227$	3.70820	−	11.4127i	0.246122	−	0.757486i	0.995450	−	0.0952867i	$-0.0303768\pi$
$228$	1.23607	+	3.80423i	0.0818606	+	0.251941i
$229$	17.7984	−	12.9313i	1.17615	−	0.854523i	0.184418	−	0.982848i	$-0.440960\pi$
$229$	17.7984	−	12.9313i	1.17615	−	0.854523i	0.991732	+	0.128325i	$0.0409601\pi$
$230$		0			0
$231$		0			0
$232$	−6.00000			−0.393919
$233$	−14.5623	+	10.5801i	−0.954008	+	0.693128i	−0.951752	−	0.306870i	$-0.900718\pi$
$233$	−14.5623	+	10.5801i	−0.954008	+	0.693128i	−0.00225687	+	0.999997i	$0.500718\pi$
$234$	1.23607	+	3.80423i	0.0808043	+	0.248690i
$235$		0			0
$236$		0			0
$237$	11.3262	+	8.22899i	0.735718	+	0.534531i
$238$	−3.70820	+	11.4127i	−0.240367	+	0.739774i
$239$	3.70820	+	11.4127i	0.239864	+	0.738225i	0.996439	+	0.0843180i	$0.0268712\pi$
$239$	3.70820	+	11.4127i	0.239864	+	0.738225i	−0.756575	+	0.653907i	$0.773129\pi$
$240$		0			0
$241$	10.0000			0.644157			0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000			0.644157			0.322078	+	0.946713i	$0.395619\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	6.47214	−	4.70228i	0.414336	−	0.301033i
$245$		0			0
$246$	−1.85410	+	5.70634i	−0.118213	+	0.363823i
$247$	−12.9443	−	9.40456i	−0.823624	−	0.598398i
$248$	−6.47214	−	4.70228i	−0.410981	−	0.298595i
$249$	3.70820	−	11.4127i	0.234998	−	0.723249i
$250$		0			0
$251$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$251$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$252$	−2.00000			−0.125988
$253$		0			0
$254$	−14.0000			−0.878438
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−9.27051	+	28.5317i	−0.578279	+	1.77976i	0.0464552	+	0.998920i	$0.485208\pi$
$257$	−9.27051	+	28.5317i	−0.578279	+	1.77976i	−0.624734	+	0.780838i	$0.714792\pi$
$258$	6.47214	+	4.70228i	0.402938	+	0.292751i
$259$	−16.1803	−	11.7557i	−1.00540	−	0.730464i
$260$		0			0
$261$	−1.85410	−	5.70634i	−0.114766	−	0.353214i
$262$	−9.70820	+	7.05342i	−0.599775	+	0.435762i
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$		0			0
$266$	6.47214	−	4.70228i	0.396832	−	0.288315i
$267$	−1.85410	−	5.70634i	−0.113469	−	0.349222i
$268$	−1.23607	+	3.80423i	−0.0755049	+	0.232380i
$269$	19.4164	+	14.1068i	1.18384	+	0.860110i	0.992600	−	0.121434i	$-0.0387492\pi$
$269$	19.4164	+	14.1068i	1.18384	+	0.860110i	0.191240	+	0.981543i	$0.438749\pi$
$270$		0			0
$271$	−0.618034	+	1.90211i	−0.0375429	+	0.115545i	−0.968072	−	0.250674i	$-0.919348\pi$
$271$	−0.618034	+	1.90211i	−0.0375429	+	0.115545i	0.930529	+	0.366219i	$0.119348\pi$
$272$	1.85410	+	5.70634i	0.112421	+	0.345998i
$273$	6.47214	−	4.70228i	0.391711	−	0.284595i
$274$	−18.0000			−1.08742
$275$		0			0
$276$	6.00000			0.361158
$277$	−12.9443	+	9.40456i	−0.777746	+	0.565065i	−0.904302	−	0.426894i	$-0.859608\pi$
$277$	−12.9443	+	9.40456i	−0.777746	+	0.565065i	0.126556	+	0.991959i	$0.459608\pi$
$278$	1.23607	+	3.80423i	0.0741344	+	0.228162i
$279$	2.47214	−	7.60845i	0.148003	−	0.455506i
$280$		0			0
$281$	−4.85410	−	3.52671i	−0.289571	−	0.210386i	0.433510	−	0.901149i	$-0.357275\pi$
$281$	−4.85410	−	3.52671i	−0.289571	−	0.210386i	−0.723081	+	0.690763i	$0.757275\pi$
$282$	−1.85410	+	5.70634i	−0.110410	+	0.339808i
$283$	−2.47214	−	7.60845i	−0.146953	−	0.452276i	0.850304	−	0.526292i	$-0.176418\pi$
$283$	−2.47214	−	7.60845i	−0.146953	−	0.452276i	−0.997257	+	0.0740167i	$0.976418\pi$
$284$	−4.85410	+	3.52671i	−0.288038	+	0.209272i
$285$		0			0
$286$		0			0
$287$	12.0000			0.708338
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	5.87132	+	18.0701i	0.345372	+	1.06295i
$290$		0			0
$291$	−11.3262	−	8.22899i	−0.663956	−	0.482392i
$292$	1.61803	+	1.17557i	0.0946883	+	0.0687951i
$293$	1.85410	−	5.70634i	0.108318	−	0.333368i	−0.882177	−	0.470918i	$-0.843923\pi$
$293$	1.85410	−	5.70634i	0.108318	−	0.333368i	0.990495	+	0.137550i	$0.0439228\pi$
$294$	−0.927051	−	2.85317i	−0.0540667	−	0.166400i
$295$		0			0
$296$	−10.0000			−0.581238
$297$		0			0
$298$	6.00000			0.347571
$299$	−19.4164	+	14.1068i	−1.12288	+	0.815820i
$300$	−1.54508	−	4.75528i	−0.0892055	−	0.274546i
$301$	4.94427	−	15.2169i	0.284983	−	0.877088i
$302$	−8.09017	−	5.87785i	−0.465537	−	0.338232i
$303$	4.85410	+	3.52671i	0.278861	+	0.202604i
$304$	1.23607	−	3.80423i	0.0708934	−	0.218187i
$305$		0			0
$306$	−4.85410	+	3.52671i	−0.277491	+	0.201609i
$307$	−20.0000			−1.14146			−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000			−1.14146			−0.570730	+	0.821138i	$0.693340\pi$
$308$		0			0
$309$	−4.00000			−0.227552
$310$		0			0
$311$	−5.56231	−	17.1190i	−0.315409	−	0.970730i	−0.975586	−	0.219620i	$-0.929518\pi$
$311$	−5.56231	−	17.1190i	−0.315409	−	0.970730i	0.660176	−	0.751111i	$-0.270482\pi$
$312$	1.23607	−	3.80423i	0.0699786	−	0.215372i
$313$	−21.0344	−	15.2824i	−1.18894	−	0.863813i	−0.195785	−	0.980647i	$-0.562726\pi$
$313$	−21.0344	−	15.2824i	−1.18894	−	0.863813i	−0.993152	+	0.116834i	$0.962726\pi$
$314$	−1.61803	−	1.17557i	−0.0913109	−	0.0663413i
$315$		0			0
$316$	−4.32624	−	13.3148i	−0.243370	−	0.749016i
$317$	−9.70820	+	7.05342i	−0.545267	+	0.396160i	−0.826037	−	0.563615i	$-0.809410\pi$
$317$	−9.70820	+	7.05342i	−0.545267	+	0.396160i	0.280770	+	0.959775i	$0.409410\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−9.70820	+	7.05342i	−0.541859	+	0.393684i
$322$	−3.70820	−	11.4127i	−0.206650	−	0.636004i
$323$	7.41641	−	22.8254i	0.412660	−	1.27004i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	16.1803	+	11.7557i	0.897524	+	0.652089i
$326$	−1.23607	+	3.80423i	−0.0684595	+	0.210697i
$327$	1.23607	+	3.80423i	0.0683547	+	0.210374i
$328$	4.85410	−	3.52671i	0.268023	−	0.194730i
$329$	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	$0.535063\pi$
$332$	−9.70820	+	7.05342i	−0.532807	+	0.387107i
$333$	−3.09017	−	9.51057i	−0.169340	−	0.521176i
$334$	−3.70820	+	11.4127i	−0.202904	+	0.624474i
$335$		0			0
$336$	1.61803	+	1.17557i	0.0882710	+	0.0641326i
$337$	−0.618034	+	1.90211i	−0.0336665	+	0.103615i	−0.966478	−	0.256751i	$-0.917348\pi$
$337$	−0.618034	+	1.90211i	−0.0336665	+	0.103615i	0.932811	+	0.360366i	$0.117348\pi$
$338$	0.927051	+	2.85317i	0.0504249	+	0.155192i
$339$	−14.5623	+	10.5801i	−0.790916	+	0.574634i
$340$		0			0
$341$		0			0
$342$	4.00000			0.216295
$343$	−16.1803	+	11.7557i	−0.873656	+	0.634748i
$344$	−2.47214	−	7.60845i	−0.133289	−	0.410220i
$345$		0			0
$346$	4.85410	+	3.52671i	0.260958	+	0.189597i
$347$	29.1246	+	21.1603i	1.56349	+	1.13594i	0.933073	+	0.359687i	$0.117117\pi$
$347$	29.1246	+	21.1603i	1.56349	+	1.13594i	0.630418	+	0.776256i	$0.282883\pi$
$348$	−1.85410	+	5.70634i	−0.0993903	+	0.305892i
$349$	1.23607	+	3.80423i	0.0661652	+	0.203636i	0.978673	−	0.205423i	$-0.0658571\pi$
$349$	1.23607	+	3.80423i	0.0661652	+	0.203636i	−0.912508	+	0.409059i	$0.865857\pi$
$350$	−8.09017	+	5.87785i	−0.432438	+	0.314184i
$351$	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
$356$	−1.85410	+	5.70634i	−0.0982672	+	0.302435i
$357$	9.70820	+	7.05342i	0.513813	+	0.373307i
$358$	−19.4164	−	14.1068i	−1.02619	−	0.745570i
$359$	3.70820	−	11.4127i	0.195712	−	0.602338i	−0.804256	−	0.594283i	$-0.797436\pi$
$359$	3.70820	−	11.4127i	0.195712	−	0.602338i	0.999968	−	0.00805517i	$-0.00256407\pi$
$360$		0			0
$361$	2.42705	−	1.76336i	0.127740	−	0.0928082i
$362$	−22.0000			−1.15629
$363$		0			0
$364$	−8.00000			−0.419314
$365$		0			0
$366$	−2.47214	−	7.60845i	−0.129221	−	0.397700i
$367$	2.47214	−	7.60845i	0.129044	−	0.397158i	−0.865572	−	0.500785i	$-0.833045\pi$
$367$	2.47214	−	7.60845i	0.129044	−	0.397158i	0.994616	+	0.103627i	$0.0330448\pi$
$368$	−4.85410	−	3.52671i	−0.253038	−	0.183843i
$369$	4.85410	+	3.52671i	0.252694	+	0.183593i
$370$		0			0
$371$		0			0
$372$	−6.47214	+	4.70228i	−0.335565	+	0.243802i
$373$	−20.0000			−1.03556			−0.517780	−	0.855514i	$-0.673242\pi$
$373$	−20.0000			−1.03556			−0.517780	+	0.855514i	$0.673242\pi$
$374$		0			0
$375$		0			0
$376$	4.85410	−	3.52671i	0.250331	−	0.181876i
$377$	−7.41641	−	22.8254i	−0.381964	−	1.17557i
$378$	−0.618034	+	1.90211i	−0.0317882	+	0.0978341i
$379$	−16.1803	−	11.7557i	−0.831128	−	0.603850i	0.0887501	−	0.996054i	$-0.471713\pi$
$379$	−16.1803	−	11.7557i	−0.831128	−	0.603850i	−0.919878	+	0.392204i	$0.871713\pi$
$380$		0			0
$381$	−4.32624	+	13.3148i	−0.221640	+	0.682137i
$382$	5.56231	+	17.1190i	0.284592	+	0.875885i
$383$	−4.85410	+	3.52671i	−0.248033	+	0.180207i	−0.704855	−	0.709352i	$-0.748988\pi$
$383$	−4.85410	+	3.52671i	−0.248033	+	0.180207i	0.456822	+	0.889558i	$0.348988\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−14.0000			−0.712581
$387$	6.47214	−	4.70228i	0.328997	−	0.239030i
$388$	4.32624	+	13.3148i	0.219631	+	0.675956i
$389$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$389$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$390$		0			0
$391$	−29.1246	−	21.1603i	−1.47289	−	1.07012i
$392$	−0.927051	+	2.85317i	−0.0468231	+	0.144107i
$393$	3.70820	+	11.4127i	0.187054	+	0.575693i
$394$	4.85410	−	3.52671i	0.244546	−	0.177673i
$395$		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	$0.273741\pi$
$398$	3.23607	−	2.35114i	0.162209	−	0.117852i
$399$	−2.47214	−	7.60845i	−0.123762	−	0.380899i
$400$	−1.54508	+	4.75528i	−0.0772542	+	0.237764i
$401$	−24.2705	−	17.6336i	−1.21201	−	0.880578i	−0.216600	−	0.976261i	$-0.569497\pi$
$401$	−24.2705	−	17.6336i	−1.21201	−	0.880578i	−0.995412	+	0.0956827i	$0.969497\pi$
$402$	3.23607	+	2.35114i	0.161400	+	0.117264i
$403$	9.88854	−	30.4338i	0.492583	−	1.51602i
$404$	−1.85410	−	5.70634i	−0.0922450	−	0.283901i
$405$		0			0
$406$	12.0000			0.595550
$407$		0			0
$408$	6.00000			0.297044
$409$	−27.5066	+	19.9847i	−1.36011	+	0.988180i	−0.361675	+	0.932304i	$0.617795\pi$
$409$	−27.5066	+	19.9847i	−1.36011	+	0.988180i	−0.998438	+	0.0558755i	$0.982205\pi$
$410$		0			0
$411$	−5.56231	+	17.1190i	−0.274368	+	0.844419i
$412$	3.23607	+	2.35114i	0.159430	+	0.115832i
$413$		0			0
$414$	1.85410	−	5.70634i	0.0911241	−	0.280451i
$415$		0			0
$416$	−3.23607	+	2.35114i	−0.158661	+	0.115274i
$417$	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
$421$	−3.09017	−	9.51057i	−0.150606	−	0.463517i	0.847084	−	0.531460i	$-0.178356\pi$
$421$	−3.09017	−	9.51057i	−0.150606	−	0.463517i	−0.997689	+	0.0679432i	$0.978356\pi$
$422$	−2.47214	+	7.60845i	−0.120342	+	0.370374i
$423$	4.85410	+	3.52671i	0.236015	+	0.171475i
$424$		0			0
$425$	−9.27051	+	28.5317i	−0.449686	+	1.38399i
$426$	1.85410	+	5.70634i	0.0898315	+	0.276473i
$427$	−12.9443	+	9.40456i	−0.626417	+	0.455119i
$428$	12.0000			0.580042
$429$		0			0
$430$		0			0
$431$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$431$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	8.03444	−	24.7275i	0.386111	−	1.18833i	−0.549561	−	0.835454i	$-0.685205\pi$
$433$	8.03444	−	24.7275i	0.386111	−	1.18833i	0.935671	−	0.352873i	$-0.114795\pi$
$434$	12.9443	+	9.40456i	0.621345	+	0.451434i
$435$		0			0
$436$	1.23607	−	3.80423i	0.0591969	−	0.182189i
$437$	7.41641	+	22.8254i	0.354775	+	1.09188i
$438$	1.61803	−	1.17557i	0.0773127	−	0.0561709i
$439$	10.0000			0.477274			0.238637	−	0.971109i	$-0.423299\pi$
$439$	10.0000			0.477274			0.238637	+	0.971109i	$0.423299\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	−19.4164	+	14.1068i	−0.923544	+	0.670994i
$443$	−7.41641	−	22.8254i	−0.352364	−	1.08447i	−0.957522	−	0.288360i	$-0.906890\pi$
$443$	−7.41641	−	22.8254i	−0.352364	−	1.08447i	0.605158	−	0.796105i	$-0.293110\pi$
$444$	−3.09017	+	9.51057i	−0.146653	+	0.451351i
$445$		0			0
$446$	12.9443	+	9.40456i	0.612929	+	0.445319i
$447$	1.85410	−	5.70634i	0.0876960	−	0.269901i
$448$	−0.618034	−	1.90211i	−0.0291994	−	0.0898664i
$449$	−4.85410	+	3.52671i	−0.229079	+	0.166436i	−0.696404	−	0.717650i	$-0.745218\pi$
$449$	−4.85410	+	3.52671i	−0.229079	+	0.166436i	0.467325	+	0.884086i	$0.345218\pi$
$450$	−5.00000			−0.235702
$451$		0			0
$452$	18.0000			0.846649
$453$	−8.09017	+	5.87785i	−0.380109	+	0.276166i
$454$	3.70820	+	11.4127i	0.174035	+	0.535624i
$455$		0			0
$456$	−3.23607	−	2.35114i	−0.151543	−	0.110102i
$457$	−8.09017	−	5.87785i	−0.378442	−	0.274954i	0.382261	−	0.924054i	$-0.375146\pi$
$457$	−8.09017	−	5.87785i	−0.378442	−	0.274954i	−0.760703	+	0.649100i	$0.775146\pi$
$458$	−6.79837	+	20.9232i	−0.317667	+	0.977679i
$459$	1.85410	+	5.70634i	0.0865421	+	0.266349i
$460$		0			0
$461$	−42.0000			−1.95614			−0.978068	−	0.208288i	$-0.933211\pi$
$461$	−42.0000			−1.95614			−0.978068	+	0.208288i	$0.933211\pi$
$462$		0			0
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	4.85410	−	3.52671i	0.225346	−	0.163723i
$465$		0			0
$466$	5.56231	−	17.1190i	0.257669	−	0.793023i
$467$	9.70820	+	7.05342i	0.449242	+	0.326393i	0.789296	−	0.614012i	$-0.210445\pi$
$467$	9.70820	+	7.05342i	0.449242	+	0.326393i	−0.340054	+	0.940406i	$0.610445\pi$
$468$	−3.23607	−	2.35114i	−0.149587	−	0.108682i
$469$	2.47214	−	7.60845i	0.114153	−	0.351326i
$470$		0			0
$471$	−1.61803	+	1.17557i	−0.0745551	+	0.0541674i
$472$		0			0
$473$		0			0
$474$	−14.0000			−0.643041
$475$	16.1803	−	11.7557i	0.742405	−	0.539389i
$476$	−3.70820	−	11.4127i	−0.169965	−	0.523099i
$477$		0			0
$478$	−9.70820	−	7.05342i	−0.444043	−	0.322616i
$479$	−19.4164	−	14.1068i	−0.887158	−	0.644558i	0.0479772	−	0.998848i	$-0.484723\pi$
$479$	−19.4164	−	14.1068i	−0.887158	−	0.644558i	−0.935136	+	0.354290i	$0.884723\pi$
$480$		0			0
$481$	−12.3607	−	38.0423i	−0.563598	−	1.73458i
$482$	−8.09017	+	5.87785i	−0.368497	+	0.267729i
$483$	−12.0000			−0.546019
$484$		0			0
$485$		0			0
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	6.18034	+	19.0211i	0.280058	+	0.861930i	0.987837	+	0.155495i	$0.0496974\pi$
$487$	6.18034	+	19.0211i	0.280058	+	0.861930i	−0.707779	+	0.706434i	$0.750303\pi$
$488$	−2.47214	+	7.60845i	−0.111908	+	0.344418i
$489$	3.23607	+	2.35114i	0.146340	+	0.106322i
$490$		0			0
$491$	−3.70820	+	11.4127i	−0.167349	+	0.515047i	−0.999202	−	0.0399494i	$-0.987280\pi$
$491$	−3.70820	+	11.4127i	−0.167349	+	0.515047i	0.831853	+	0.554996i	$0.187280\pi$
$492$	−1.85410	−	5.70634i	−0.0835894	−	0.257262i
$493$	29.1246	−	21.1603i	1.31171	−	0.953011i
$494$	16.0000			0.719874
$495$		0			0
$496$	8.00000			0.359211
$497$	9.70820	−	7.05342i	0.435472	−	0.316389i
$498$	3.70820	+	11.4127i	0.166169	+	0.511414i
$499$	−1.23607	+	3.80423i	−0.0553340	+	0.170301i	−0.974904	−	0.222626i	$-0.928537\pi$
$499$	−1.23607	+	3.80423i	−0.0553340	+	0.170301i	0.919570	+	0.392926i	$0.128537\pi$
$500$		0			0
$501$	9.70820	+	7.05342i	0.433731	+	0.315124i
$502$		0			0
$503$	−3.70820	−	11.4127i	−0.165341	−	0.508866i	0.833721	−	0.552187i	$-0.186206\pi$
$503$	−3.70820	−	11.4127i	−0.165341	−	0.508866i	−0.999061	+	0.0433204i	$0.986206\pi$
$504$	1.61803	−	1.17557i	0.0720730	−	0.0523641i
$505$		0			0
$506$		0			0
$507$	3.00000			0.133235
$508$	11.3262	−	8.22899i	0.502521	−	0.365103i
$509$	7.41641	+	22.8254i	0.328726	+	1.01172i	0.969730	+	0.244178i	$0.0785183\pi$
$509$	7.41641	+	22.8254i	0.328726	+	1.01172i	−0.641004	+	0.767538i	$0.721482\pi$
$510$		0			0
$511$	−3.23607	−	2.35114i	−0.143155	−	0.104008i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	1.23607	−	3.80423i	0.0545737	−	0.167961i
$514$	−9.27051	−	28.5317i	−0.408905	−	1.25848i
$515$		0			0
$516$	−8.00000			−0.352180
$517$		0			0
$518$	20.0000			0.878750
$519$	4.85410	−	3.52671i	0.213071	−	0.154805i
$520$		0			0
$521$	−5.56231	+	17.1190i	−0.243689	+	0.749998i	0.752160	+	0.658980i	$0.229012\pi$
$521$	−5.56231	+	17.1190i	−0.243689	+	0.749998i	−0.995849	+	0.0910175i	$0.970988\pi$
$522$	4.85410	+	3.52671i	0.212458	+	0.154360i
$523$	−12.9443	−	9.40456i	−0.566013	−	0.411233i	0.267641	−	0.963519i	$-0.413756\pi$
$523$	−12.9443	−	9.40456i	−0.566013	−	0.411233i	−0.833655	+	0.552286i	$0.813756\pi$
$524$	3.70820	−	11.4127i	0.161994	−	0.498565i
$525$	3.09017	+	9.51057i	0.134866	+	0.415075i
$526$		0			0
$527$	48.0000			2.09091
$528$		0			0
$529$	13.0000			0.565217
$530$		0			0
$531$		0			0
$532$	−2.47214	+	7.60845i	−0.107181	+	0.329868i
$533$	19.4164	+	14.1068i	0.841018	+	0.611035i
$534$	4.85410	+	3.52671i	0.210058	+	0.152616i
$535$		0			0
$536$	−1.23607	−	3.80423i	−0.0533900	−	0.164318i
$537$	−19.4164	+	14.1068i	−0.837880	+	0.608755i
$538$	−24.0000			−1.03471
$539$		0			0
$540$		0			0
$541$	16.1803	−	11.7557i	0.695647	−	0.505417i	−0.182865	−	0.983138i	$-0.558537\pi$
$541$	16.1803	−	11.7557i	0.695647	−	0.505417i	0.878512	+	0.477721i	$0.158537\pi$
$542$	−0.618034	−	1.90211i	−0.0265468	−	0.0817028i
$543$	−6.79837	+	20.9232i	−0.291746	+	0.897902i
$544$	−4.85410	−	3.52671i	−0.208118	−	0.151207i
$545$		0			0
$546$	−2.47214	+	7.60845i	−0.105798	+	0.325612i
$547$	8.65248	+	26.6296i	0.369953	+	1.13860i	0.946821	+	0.321761i	$0.104275\pi$
$547$	8.65248	+	26.6296i	0.369953	+	1.13860i	−0.576868	+	0.816838i	$0.695725\pi$
$548$	14.5623	−	10.5801i	0.622071	−	0.451961i
$549$	−8.00000			−0.341432
$550$		0			0
$551$	−24.0000			−1.02243
$552$	−4.85410	+	3.52671i	−0.206604	+	0.150107i
$553$	8.65248	+	26.6296i	0.367941	+	1.13241i
$554$	4.94427	−	15.2169i	0.210062	−	0.646504i
$555$		0			0
$556$	−3.23607	−	2.35114i	−0.137240	−	0.0997106i
$557$	−5.56231	+	17.1190i	−0.235682	+	0.725356i	0.761348	+	0.648344i	$0.224538\pi$
$557$	−5.56231	+	17.1190i	−0.235682	+	0.725356i	−0.997030	+	0.0770122i	$0.975462\pi$
$558$	2.47214	+	7.60845i	0.104654	+	0.322091i
$559$	25.8885	−	18.8091i	1.09497	−	0.795541i
$560$		0			0
$561$		0			0
$562$	6.00000			0.253095
$563$	−9.70820	+	7.05342i	−0.409152	+	0.297266i	−0.773258	−	0.634091i	$-0.781374\pi$
$563$	−9.70820	+	7.05342i	−0.409152	+	0.297266i	0.364106	+	0.931357i	$0.381374\pi$
$564$	−1.85410	−	5.70634i	−0.0780718	−	0.240280i
$565$		0			0
$566$	6.47214	+	4.70228i	0.272044	+	0.197652i
$567$	1.61803	+	1.17557i	0.0679510	+	0.0493693i
$568$	1.85410	−	5.70634i	0.0777964	−	0.239433i
$569$	−5.56231	−	17.1190i	−0.233184	−	0.717667i	−0.997357	−	0.0726553i	$-0.976853\pi$
$569$	−5.56231	−	17.1190i	−0.233184	−	0.717667i	0.764173	−	0.645011i	$-0.223147\pi$
$570$		0			0
$571$	28.0000			1.17176			0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000			1.17176			0.585882	+	0.810397i	$0.300748\pi$
$572$		0			0
$573$	18.0000			0.751961
$574$	−9.70820	+	7.05342i	−0.405213	+	0.294404i
$575$	−9.27051	−	28.5317i	−0.386607	−	1.18985i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	27.5066	+	19.9847i	1.14511	+	0.831974i	0.987824	−	0.155579i	$-0.0497242\pi$
$577$	27.5066	+	19.9847i	1.14511	+	0.831974i	0.157290	+	0.987552i	$0.449724\pi$
$578$	−15.3713	−	11.1679i	−0.639363	−	0.464524i
$579$	−4.32624	+	13.3148i	−0.179792	+	0.553344i
$580$		0			0
$581$	19.4164	−	14.1068i	0.805528	−	0.585251i
$582$	14.0000			0.580319
$583$		0			0
$584$	−2.00000			−0.0827606
$585$		0			0
$586$	1.85410	+	5.70634i	0.0765922	+	0.235727i
$587$	7.41641	−	22.8254i	0.306108	−	0.942103i	−0.673154	−	0.739503i	$-0.735061\pi$
$587$	7.41641	−	22.8254i	0.306108	−	0.942103i	0.979261	−	0.202601i	$-0.0649393\pi$
$588$	2.42705	+	1.76336i	0.100090	+	0.0727196i
$589$	−25.8885	−	18.8091i	−1.06672	−	0.775017i
$590$		0			0
$591$	−1.85410	−	5.70634i	−0.0762676	−	0.234727i
$592$	8.09017	−	5.87785i	0.332504	−	0.241578i
$593$	30.0000			1.23195			0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000			1.23195			0.615976	+	0.787765i	$0.288762\pi$
$594$		0			0
$595$		0			0
$596$	−4.85410	+	3.52671i	−0.198832	+	0.144460i
$597$	−1.23607	−	3.80423i	−0.0505889	−	0.155697i
$598$	7.41641	−	22.8254i	0.303279	−	0.933398i
$599$	−24.2705	−	17.6336i	−0.991666	−	0.720488i	−0.0313808	−	0.999508i	$-0.509990\pi$
$599$	−24.2705	−	17.6336i	−0.991666	−	0.720488i	−0.960285	+	0.279020i	$0.909990\pi$
$600$	4.04508	+	2.93893i	0.165140	+	0.119981i
$601$	6.79837	−	20.9232i	0.277311	−	0.853477i	−0.711287	−	0.702902i	$-0.751887\pi$
$601$	6.79837	−	20.9232i	0.277311	−	0.853477i	0.988599	−	0.150575i	$-0.0481126\pi$
$602$	4.94427	+	15.2169i	0.201513	+	0.620195i
$603$	3.23607	−	2.35114i	0.131783	−	0.0957459i
$604$	10.0000			0.406894
$605$		0			0
$606$	−6.00000			−0.243733
$607$	11.3262	−	8.22899i	0.459718	−	0.334005i	−0.333703	−	0.942678i	$-0.608298\pi$
$607$	11.3262	−	8.22899i	0.459718	−	0.334005i	0.793421	+	0.608674i	$0.208298\pi$
$608$	1.23607	+	3.80423i	0.0501292	+	0.154282i
$609$	3.70820	−	11.4127i	0.150264	−	0.462465i
$610$		0			0
$611$	19.4164	+	14.1068i	0.785504	+	0.570702i
$612$	1.85410	−	5.70634i	0.0749476	−	0.230665i
$613$	4.94427	+	15.2169i	0.199697	+	0.614605i	0.999890	+	0.0148615i	$0.00473072\pi$
$613$	4.94427	+	15.2169i	0.199697	+	0.614605i	−0.800192	+	0.599744i	$0.795269\pi$
$614$	16.1803	−	11.7557i	0.652985	−	0.474422i
$615$		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	$0.706378\pi$
$618$	3.23607	−	2.35114i	0.130174	−	0.0945768i
$619$	13.5967	+	41.8465i	0.546499	+	1.68195i	0.717398	+	0.696664i	$0.245333\pi$
$619$	13.5967	+	41.8465i	0.546499	+	1.68195i	−0.170898	+	0.985289i	$0.554667\pi$
$620$		0			0
$621$	−4.85410	−	3.52671i	−0.194788	−	0.141522i
$622$	14.5623	+	10.5801i	0.583895	+	0.424225i
$623$	3.70820	−	11.4127i	0.148566	−	0.457239i
$624$	1.23607	+	3.80423i	0.0494823	+	0.152291i
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$	26.0000			1.03917
$627$		0			0
$628$	2.00000			0.0798087
$629$	48.5410	−	35.2671i	1.93546	−	1.40619i
$630$		0			0
$631$	−4.94427	+	15.2169i	−0.196828	+	0.605775i	0.803122	+	0.595815i	$0.203171\pi$
$631$	−4.94427	+	15.2169i	−0.196828	+	0.605775i	−0.999950	+	0.00996082i	$0.996829\pi$
$632$	11.3262	+	8.22899i	0.450534	+	0.327332i
$633$	6.47214	+	4.70228i	0.257244	+	0.186899i
$634$	3.70820	−	11.4127i	0.147272	−	0.453255i
$635$		0			0
$636$		0			0
$637$	−12.0000			−0.475457
$638$		0			0
$639$	6.00000			0.237356
$640$		0			0
$641$	1.85410	+	5.70634i	0.0732326	+	0.225387i	0.980973	−	0.194147i	$-0.0621937\pi$
$641$	1.85410	+	5.70634i	0.0732326	+	0.225387i	−0.907740	+	0.419533i	$0.862194\pi$
$642$	3.70820	−	11.4127i	0.146351	−	0.450422i
$643$	3.23607	+	2.35114i	0.127618	+	0.0927200i	0.649763	−	0.760137i	$-0.274868\pi$
$643$	3.23607	+	2.35114i	0.127618	+	0.0927200i	−0.522145	+	0.852857i	$0.674868\pi$
$644$	9.70820	+	7.05342i	0.382557	+	0.277944i
$645$		0			0
$646$	7.41641	+	22.8254i	0.291795	+	0.898052i
$647$	−4.85410	+	3.52671i	−0.190834	+	0.138649i	−0.679100	−	0.734046i	$-0.737630\pi$
$647$	−4.85410	+	3.52671i	−0.190834	+	0.138649i	0.488266	+	0.872695i	$0.337630\pi$
$648$	1.00000			0.0392837
$649$		0			0
$650$	−20.0000			−0.784465
$651$	12.9443	−	9.40456i	0.507326	−	0.368594i
$652$	−1.23607	−	3.80423i	−0.0484082	−	0.148985i
$653$	−11.1246	+	34.2380i	−0.435340	+	1.33984i	0.457398	+	0.889262i	$0.348781\pi$
$653$	−11.1246	+	34.2380i	−0.435340	+	1.33984i	−0.892738	+	0.450576i	$0.851219\pi$
$654$	−3.23607	−	2.35114i	−0.126540	−	0.0919369i
$655$		0			0
$656$	−1.85410	+	5.70634i	−0.0723905	+	0.222795i
$657$	−0.618034	−	1.90211i	−0.0241118	−	0.0742085i
$658$	−9.70820	+	7.05342i	−0.378465	+	0.274971i
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$	−22.0000			−0.855701			−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000			−0.855701			−0.427850	+	0.903850i	$0.640729\pi$
$662$	3.23607	−	2.35114i	0.125773	−	0.0913797i
$663$	7.41641	+	22.8254i	0.288029	+	0.886463i
$664$	3.70820	−	11.4127i	0.143906	−	0.442898i
$665$		0			0
$666$	8.09017	+	5.87785i	0.313488	+	0.227762i
$667$	−11.1246	+	34.2380i	−0.430747	+	1.32570i
$668$	−3.70820	−	11.4127i	−0.143475	−	0.441570i
$669$	12.9443	−	9.40456i	0.500454	−	0.363601i
$670$		0			0
$671$		0			0
$672$	−2.00000			−0.0771517
$673$	11.3262	−	8.22899i	0.436594	−	0.317204i	−0.347686	−	0.937611i	$-0.613032\pi$
$673$	11.3262	−	8.22899i	0.436594	−	0.317204i	0.784280	+	0.620407i	$0.213032\pi$
$674$	−0.618034	−	1.90211i	−0.0238058	−	0.0732667i
$675$	−1.54508	+	4.75528i	−0.0594703	+	0.183031i
$676$	−2.42705	−	1.76336i	−0.0933481	−	0.0678214i
$677$	24.2705	+	17.6336i	0.932791	+	0.677713i	0.946675	−	0.322191i	$-0.104419\pi$
$677$	24.2705	+	17.6336i	0.932791	+	0.677713i	−0.0138832	+	0.999904i	$0.504419\pi$
$678$	5.56231	−	17.1190i	0.213619	−	0.657452i
$679$	−8.65248	−	26.6296i	−0.332052	−	1.02195i
$680$		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	$0.651852\pi$
$684$	−3.23607	+	2.35114i	−0.123734	+	0.0898981i
$685$		0			0
$686$	6.18034	−	19.0211i	0.235966	−	0.726230i
$687$	17.7984	+	12.9313i	0.679050	+	0.493359i
$688$	6.47214	+	4.70228i	0.246748	+	0.179273i
$689$		0			0
$690$		0			0
$691$	−16.1803	+	11.7557i	−0.615529	+	0.447208i	−0.851357	−	0.524587i	$-0.824220\pi$
$691$	−16.1803	+	11.7557i	−0.615529	+	0.447208i	0.235828	+	0.971795i	$0.424220\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−36.0000			−1.36654
$695$		0			0
$696$	−1.85410	−	5.70634i	−0.0702796	−	0.216298i
$697$	−11.1246	+	34.2380i	−0.421375	+	1.29686i
$698$	−3.23607	−	2.35114i	−0.122487	−	0.0889920i
$699$	−14.5623	−	10.5801i	−0.550797	−	0.400177i
$700$	3.09017	−	9.51057i	0.116797	−	0.359466i
$701$	1.85410	+	5.70634i	0.0700285	+	0.215525i	0.979946	−	0.199264i	$-0.0638552\pi$
$701$	1.85410	+	5.70634i	0.0700285	+	0.215525i	−0.909917	+	0.414790i	$0.863855\pi$
$702$	−3.23607	+	2.35114i	−0.122138	+	0.0887381i
$703$	−40.0000			−1.50863
$704$		0			0
$705$		0			0
$706$	4.85410	−	3.52671i	0.182687	−	0.132730i
$707$	3.70820	+	11.4127i	0.139461	+	0.429218i
$708$		0			0
$709$	−21.0344	−	15.2824i	−0.789965	−	0.573943i	0.117988	−	0.993015i	$-0.462356\pi$
$709$	−21.0344	−	15.2824i	−0.789965	−	0.573943i	−0.907953	+	0.419072i	$0.862356\pi$
$710$		0			0
$711$	−4.32624	+	13.3148i	−0.162247	+	0.499344i
$712$	−1.85410	−	5.70634i	−0.0694854	−	0.213854i
$713$	−38.8328	+	28.2137i	−1.45430	+	1.05661i
$714$	−12.0000			−0.449089
$715$		0			0
$716$	24.0000			0.896922
$717$	−9.70820	+	7.05342i	−0.362560	+	0.263415i
$718$	3.70820	+	11.4127i	0.138389	+	0.425917i
$719$	9.27051	−	28.5317i	0.345732	−	1.06405i	−0.615459	−	0.788169i	$-0.711029\pi$
$719$	9.27051	−	28.5317i	0.345732	−	1.06405i	0.961191	−	0.275884i	$-0.0889706\pi$
$720$		0			0
$721$	−6.47214	−	4.70228i	−0.241035	−	0.175122i
$722$	−0.927051	+	2.85317i	−0.0345013	+	0.106184i
$723$	3.09017	+	9.51057i	0.114925	+	0.353702i
$724$	17.7984	−	12.9313i	0.661471	−	0.480587i
$725$	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	$0.673782\pi$
$728$	6.47214	−	4.70228i	0.239873	−	0.174278i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	38.8328	+	28.2137i	1.43628	+	1.04352i
$732$	6.47214	+	4.70228i	0.239217	+	0.173801i
$733$	1.23607	−	3.80423i	0.0456552	−	0.140512i	−0.925630	−	0.378429i	$-0.876464\pi$
$733$	1.23607	−	3.80423i	0.0456552	−	0.140512i	0.971286	+	0.237917i	$0.0764645\pi$
$734$	2.47214	+	7.60845i	0.0912482	+	0.280833i
$735$		0			0
$736$	6.00000			0.221163
$737$		0			0
$738$	−6.00000			−0.220863
$739$	6.47214	−	4.70228i	0.238081	−	0.172976i	−0.462347	−	0.886699i	$-0.652992\pi$
$739$	6.47214	−	4.70228i	0.238081	−	0.172976i	0.700428	+	0.713723i	$0.252992\pi$
$740$		0			0
$741$	4.94427	−	15.2169i	0.181632	−	0.559007i
$742$		0			0
$743$	29.1246	+	21.1603i	1.06848	+	0.776295i	0.975638	−	0.219386i	$-0.0704054\pi$
$743$	29.1246	+	21.1603i	1.06848	+	0.776295i	0.0928402	+	0.995681i	$0.470405\pi$
$744$	2.47214	−	7.60845i	0.0906329	−	0.278939i
$745$		0			0
$746$	16.1803	−	11.7557i	0.592404	−	0.430407i
$747$	12.0000			0.439057
$748$		0			0
$749$	−24.0000			−0.876941
$750$		0			0
$751$	2.47214	+	7.60845i	0.0902095	+	0.277636i	0.985976	−	0.166889i	$-0.0533723\pi$
$751$	2.47214	+	7.60845i	0.0902095	+	0.277636i	−0.895766	+	0.444526i	$0.853372\pi$
$752$	−1.85410	+	5.70634i	−0.0676121	+	0.208089i
$753$		0			0
$754$	19.4164	+	14.1068i	0.707104	+	0.513741i
$755$		0			0
$756$	−0.618034	−	1.90211i	−0.0224777	−	0.0691792i
$757$	27.5066	−	19.9847i	0.999744	−	0.726356i	0.0377104	−	0.999289i	$-0.487994\pi$
$757$	27.5066	−	19.9847i	0.999744	−	0.726356i	0.962033	+	0.272932i	$0.0879936\pi$
$758$	20.0000			0.726433
$759$		0			0
$760$		0			0
$761$	14.5623	−	10.5801i	0.527883	−	0.383530i	−0.291682	−	0.956515i	$-0.594215\pi$
$761$	14.5623	−	10.5801i	0.527883	−	0.383530i	0.819565	+	0.572986i	$0.194215\pi$
$762$	−4.32624	−	13.3148i	−0.156723	−	0.482344i
$763$	−2.47214	+	7.60845i	−0.0894973	+	0.275444i
$764$	−14.5623	−	10.5801i	−0.526846	−	0.382776i
$765$		0			0
$766$	1.85410	−	5.70634i	0.0669914	−	0.206178i
$767$		0			0
$768$	−0.809017	+	0.587785i	−0.0291929	+	0.0212099i
$769$	34.0000			1.22607			0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000			1.22607			0.613036	+	0.790055i	$0.289948\pi$
$770$		0			0
$771$	−30.0000			−1.08042
$772$	11.3262	−	8.22899i	0.407640	−	0.296168i
$773$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$773$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$774$	−2.47214	+	7.60845i	−0.0888591	+	0.273480i
$775$	32.3607	+	23.5114i	1.16243	+	0.844555i
$776$	−11.3262	−	8.22899i	−0.406588	−	0.295404i
$777$	6.18034	−	19.0211i	0.221718	−	0.682379i
$778$		0			0
$779$	19.4164	−	14.1068i	0.695665	−	0.505430i
$780$		0			0
$781$		0			0
$782$	36.0000			1.28736
$783$	4.85410	−	3.52671i	0.173471	−	0.126034i
$784$	−0.927051	−	2.85317i	−0.0331090	−	0.101899i
$785$		0			0
$786$	−9.70820	−	7.05342i	−0.346280	−	0.251587i
$787$	25.8885	+	18.8091i	0.922827	+	0.670473i	0.944226	−	0.329298i	$-0.106812\pi$
$787$	25.8885	+	18.8091i	0.922827	+	0.670473i	−0.0213991	+	0.999771i	$0.506812\pi$
$788$	−1.85410	+	5.70634i	−0.0660496	+	0.203280i
$789$		0			0
$790$		0			0
$791$	−36.0000			−1.28001
$792$		0			0
$793$	−32.0000			−1.13635
$794$	−21.0344	+	15.2824i	−0.746484	+	0.542353i
$795$		0			0
$796$	−1.23607	+	3.80423i	−0.0438113	+	0.134837i
$797$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$797$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$798$	6.47214	+	4.70228i	0.229111	+	0.166459i
$799$	−11.1246	+	34.2380i	−0.393560	+	1.21125i
$800$	−1.54508	−	4.75528i	−0.0546270	−	0.168125i
$801$	4.85410	−	3.52671i	0.171511	−	0.124610i
$802$	30.0000			1.05934
$803$		0			0
$804$	−4.00000			−0.141069
$805$		0			0
$806$	9.88854	+	30.4338i	0.348309	+	1.07199i
$807$	−7.41641	+	22.8254i	−0.261070	+	0.803491i
$808$	4.85410	+	3.52671i	0.170767	+	0.124069i
$809$	−33.9787	−	24.6870i	−1.19463	−	0.867948i	−0.200882	−	0.979615i	$-0.564381\pi$
$809$	−33.9787	−	24.6870i	−1.19463	−	0.867948i	−0.993746	+	0.111667i	$0.964381\pi$
$810$		0			0
$811$	−2.47214	−	7.60845i	−0.0868084	−	0.267169i	0.898224	−	0.439538i	$-0.144858\pi$
$811$	−2.47214	−	7.60845i	−0.0868084	−	0.267169i	−0.985032	+	0.172369i	$0.944858\pi$
$812$	−9.70820	+	7.05342i	−0.340691	+	0.247527i
$813$	−2.00000			−0.0701431
$814$		0			0
$815$		0			0
$816$	−4.85410	+	3.52671i	−0.169928	+	0.123460i
$817$	−9.88854	−	30.4338i	−0.345956	−	1.06474i
$818$	10.5066	−	32.3359i	0.367354	−	1.13060i
$819$	6.47214	+	4.70228i	0.226155	+	0.164311i
$820$		0			0
$821$	5.56231	−	17.1190i	0.194126	−	0.597458i	−0.805860	−	0.592106i	$-0.798297\pi$
$821$	5.56231	−	17.1190i	0.194126	−	0.597458i	0.999986	−	0.00535152i	$-0.00170345\pi$
$822$	−5.56231	−	17.1190i	−0.194008	−	0.597094i
$823$	−6.47214	+	4.70228i	−0.225604	+	0.163911i	−0.694846	−	0.719159i	$-0.744527\pi$
$823$	−6.47214	+	4.70228i	−0.225604	+	0.163911i	0.469241	+	0.883070i	$0.344527\pi$
$824$	−4.00000			−0.139347
$825$		0			0
$826$		0			0
$827$	−9.70820	+	7.05342i	−0.337587	+	0.245272i	−0.743643	−	0.668577i	$-0.766904\pi$
$827$	−9.70820	+	7.05342i	−0.337587	+	0.245272i	0.406056	+	0.913848i	$0.366904\pi$
$828$	1.85410	+	5.70634i	0.0644345	+	0.198309i
$829$	4.32624	−	13.3148i	0.150256	−	0.462442i	−0.847393	−	0.530966i	$-0.821829\pi$
$829$	4.32624	−	13.3148i	0.150256	−	0.462442i	0.997649	+	0.0685244i	$0.0218291\pi$
$830$		0			0
$831$	−12.9443	−	9.40456i	−0.449032	−	0.326241i
$832$	1.23607	−	3.80423i	0.0428529	−	0.131888i
$833$	−5.56231	−	17.1190i	−0.192722	−	0.593139i
$834$	−3.23607	+	2.35114i	−0.112056	+	0.0814134i
$835$		0			0
$836$		0			0
$837$	8.00000			0.276520
$838$	−19.4164	+	14.1068i	−0.670729	+	0.487313i
$839$	5.56231	+	17.1190i	0.192032	+	0.591014i	0.999998	+	0.00178539i	$0.000568307\pi$
$839$	5.56231	+	17.1190i	0.192032	+	0.591014i	−0.807966	+	0.589229i	$0.799432\pi$
$840$		0			0
$841$	−5.66312	−	4.11450i	−0.195280	−	0.141879i
$842$	8.09017	+	5.87785i	0.278806	+	0.202564i
$843$	1.85410	−	5.70634i	0.0638587	−	0.196537i
$844$	−2.47214	−	7.60845i	−0.0850944	−	0.261894i
$845$		0			0
$846$	−6.00000			−0.206284
$847$		0			0
$848$		0			0
$849$	6.47214	−	4.70228i	0.222123	−	0.161382i
$850$	−9.27051	−	28.5317i	−0.317976	−	0.978629i
$851$	−18.5410	+	57.0634i	−0.635578	+	1.95611i
$852$	−4.85410	−	3.52671i	−0.166299	−	0.120823i
$853$	6.47214	+	4.70228i	0.221602	+	0.161003i	0.693047	−	0.720892i	$-0.256268\pi$
$853$	6.47214	+	4.70228i	0.221602	+	0.161003i	−0.471446	+	0.881895i	$0.656268\pi$
$854$	4.94427	−	15.2169i	0.169190	−	0.520712i
$855$		0			0
$856$	−9.70820	+	7.05342i	−0.331820	+	0.241081i
$857$	−54.0000			−1.84460			−0.922302	−	0.386469i	$-0.873695\pi$
$857$	−54.0000			−1.84460			−0.922302	+	0.386469i	$0.873695\pi$
$858$		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
$861$	3.70820	+	11.4127i	0.126375	+	0.388943i
$862$		0			0
$863$	−33.9787	−	24.6870i	−1.15665	−	0.840355i	−0.167298	−	0.985906i	$-0.553504\pi$
$863$	−33.9787	−	24.6870i	−1.15665	−	0.840355i	−0.989351	+	0.145552i	$0.953504\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$		0			0
$866$	8.03444	+	24.7275i	0.273021	+	0.840274i
$867$	−15.3713	+	11.1679i	−0.522037	+	0.379282i
$868$	−16.0000			−0.543075
$869$		0			0
$870$		0			0
$871$	12.9443	−	9.40456i	0.438600	−	0.318661i
$872$	1.23607	+	3.80423i	0.0418585	+	0.128827i
$873$	4.32624	−	13.3148i	0.146421	−	0.450637i
$874$	−19.4164	−	14.1068i	−0.656770	−	0.477171i
$875$		0			0
$876$	−0.618034	+	1.90211i	−0.0208814	+	0.0642664i
$877$	16.0689	+	49.4549i	0.542608	+	1.66997i	0.726611	+	0.687049i	$0.241094\pi$
$877$	16.0689	+	49.4549i	0.542608	+	1.66997i	−0.184003	+	0.982926i	$0.558906\pi$
$878$	−8.09017	+	5.87785i	−0.273030	+	0.198368i
$879$	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	$0.668641\pi$
$882$	2.42705	−	1.76336i	0.0817231	−	0.0593753i
$883$	−8.65248	−	26.6296i	−0.291179	−	0.896157i	−0.984478	−	0.175507i	$-0.943844\pi$
$883$	−8.65248	−	26.6296i	−0.291179	−	0.896157i	0.693299	−	0.720650i	$-0.256156\pi$
$884$	7.41641	−	22.8254i	0.249441	−	0.767700i
$885$		0			0
$886$	19.4164	+	14.1068i	0.652307	+	0.473929i
$887$	11.1246	−	34.2380i	0.373528	−	1.14960i	−0.570939	−	0.820993i	$-0.693421\pi$
$887$	11.1246	−	34.2380i	0.373528	−	1.14960i	0.944466	−	0.328608i	$-0.106579\pi$
$888$	−3.09017	−	9.51057i	−0.103699	−	0.319154i
$889$	−22.6525	+	16.4580i	−0.759740	+	0.551983i
$890$		0			0
$891$		0			0
$892$	−16.0000			−0.535720
$893$	19.4164	−	14.1068i	0.649745	−	0.472068i
$894$	1.85410	+	5.70634i	0.0620104	+	0.190849i
$895$		0			0
$896$	1.61803	+	1.17557i	0.0540547	+	0.0392731i
$897$	−19.4164	−	14.1068i	−0.648295	−	0.471014i
$898$	1.85410	−	5.70634i	0.0618722	−	0.190423i
$899$	−14.8328	−	45.6507i	−0.494702	−	1.52254i
$900$	4.04508	−	2.93893i	0.134836	−	0.0979642i
$901$		0			0
$902$		0			0
$903$	16.0000			0.532447
$904$	−14.5623	+	10.5801i	−0.484335	+	0.351890i
$905$		0			0
$906$	3.09017	−	9.51057i	0.102664	−	0.315967i
$907$	−16.1803	−	11.7557i	−0.537259	−	0.390342i	0.285807	−	0.958287i	$-0.407738\pi$
$907$	−16.1803	−	11.7557i	−0.537259	−	0.390342i	−0.823066	+	0.567945i	$0.807738\pi$
$908$	−9.70820	−	7.05342i	−0.322178	−	0.234076i
$909$	−1.85410	+	5.70634i	−0.0614967	+	0.189267i
$910$		0			0
$911$	33.9787	−	24.6870i	1.12577	−	0.817916i	0.140692	−	0.990053i	$-0.455067\pi$
$911$	33.9787	−	24.6870i	1.12577	−	0.817916i	0.985073	+	0.172137i	$0.0550673\pi$
$912$	4.00000			0.132453
$913$		0			0
$914$	10.0000			0.330771
$915$		0			0
$916$	−6.79837	−	20.9232i	−0.224625	−	0.691323i
$917$	−7.41641	+	22.8254i	−0.244911	+	0.753760i
$918$	−4.85410	−	3.52671i	−0.160209	−	0.116399i
$919$	1.61803	+	1.17557i	0.0533740	+	0.0387785i	0.614152	−	0.789187i	$-0.289498\pi$
$919$	1.61803	+	1.17557i	0.0533740	+	0.0387785i	−0.560778	+	0.827966i	$0.689498\pi$
$920$		0			0
$921$	−6.18034	−	19.0211i	−0.203649	−	0.626768i
$922$	33.9787	−	24.6870i	1.11903	−	0.813022i
$923$	24.0000			0.789970
$924$		0			0
$925$	50.0000			1.64399
$926$	3.23607	−	2.35114i	0.106344	−	0.0772633i
$927$	−1.23607	−	3.80423i	−0.0405978	−	0.124947i
$928$	−1.85410	+	5.70634i	−0.0608639	+	0.187320i
$929$	−24.2705	−	17.6336i	−0.796290	−	0.578538i	0.113534	−	0.993534i	$-0.463783\pi$
$929$	−24.2705	−	17.6336i	−0.796290	−	0.578538i	−0.909823	+	0.414996i	$0.863783\pi$
$930$		0			0
$931$	−3.70820	+	11.4127i	−0.121531	+	0.374035i
$932$	5.56231	+	17.1190i	0.182199	+	0.560752i
$933$	14.5623	−	10.5801i	0.476748	−	0.346378i
$934$	−12.0000			−0.392652
$935$		0			0
$936$	4.00000			0.130744
$937$	−17.7984	+	12.9313i	−0.581448	+	0.422446i	−0.839246	−	0.543752i	$-0.817003\pi$
$937$	−17.7984	+	12.9313i	−0.581448	+	0.422446i	0.257798	+	0.966199i	$0.417003\pi$
$938$	2.47214	+	7.60845i	0.0807181	+	0.248425i
$939$	8.03444	−	24.7275i	0.262194	−	0.806950i
$940$		0			0
$941$	−14.5623	−	10.5801i	−0.474718	−	0.344903i	0.324559	−	0.945865i	$-0.394784\pi$
$941$	−14.5623	−	10.5801i	−0.474718	−	0.344903i	−0.799277	+	0.600963i	$0.794784\pi$
$942$	0.618034	−	1.90211i	0.0201366	−	0.0619742i
$943$	−11.1246	−	34.2380i	−0.362267	−	1.11494i
$944$		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	$0.437538\pi$
$948$	11.3262	−	8.22899i	0.367859	−	0.267265i
$949$	−2.47214	−	7.60845i	−0.0802489	−	0.246981i
$950$	−6.18034	+	19.0211i	−0.200517	+	0.617127i
$951$	−9.70820	−	7.05342i	−0.314810	−	0.228723i
$952$	9.70820	+	7.05342i	0.314645	+	0.228603i
$953$	12.9787	−	39.9444i	0.420422	−	1.29393i	−0.486889	−	0.873464i	$-0.661868\pi$
$953$	12.9787	−	39.9444i	0.420422	−	1.29393i	0.907311	−	0.420461i	$-0.138132\pi$
$954$		0			0
$955$		0			0
$956$	12.0000			0.388108
$957$		0			0
$958$	24.0000			0.775405
$959$	−29.1246	+	21.1603i	−0.940483	+	0.683301i
$960$		0			0
$961$	10.1976	−	31.3849i	0.328954	−	1.01242i
$962$	32.3607	+	23.5114i	1.04335	+	0.758038i
$963$	−9.70820	−	7.05342i	−0.312842	−	0.227293i
$964$	3.09017	−	9.51057i	0.0995277	−	0.306315i
$965$		0			0
$966$	9.70820	−	7.05342i	0.312356	−	0.226940i
$967$	−14.0000			−0.450210			−0.225105	−	0.974335i	$-0.572272\pi$
$967$	−14.0000			−0.450210			−0.225105	+	0.974335i	$0.572272\pi$
$968$		0			0
$969$	24.0000			0.770991
$970$		0			0
$971$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$971$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	6.47214	+	4.70228i	0.207487	+	0.150748i
$974$	−16.1803	−	11.7557i	−0.518452	−	0.376677i
$975$	−6.18034	+	19.0211i	−0.197929	+	0.609164i
$976$	−2.47214	−	7.60845i	−0.0791311	−	0.243541i
$977$	−43.6869	+	31.7404i	−1.39767	+	1.01547i	−0.402694	+	0.915335i	$0.631926\pi$
$977$	−43.6869	+	31.7404i	−1.39767	+	1.01547i	−0.994974	+	0.100131i	$0.968074\pi$
$978$	−4.00000			−0.127906
$979$		0			0
$980$		0			0
$981$	−3.23607	+	2.35114i	−0.103320	+	0.0750662i
$982$	−3.70820	−	11.4127i	−0.118334	−	0.364193i
$983$	9.27051	−	28.5317i	0.295683	−	0.910020i	−0.687308	−	0.726366i	$-0.741208\pi$
$983$	9.27051	−	28.5317i	0.295683	−	0.910020i	0.982991	−	0.183653i	$-0.0587924\pi$
$984$	4.85410	+	3.52671i	0.154743	+	0.112427i
$985$		0			0
$986$	−11.1246	+	34.2380i	−0.354280	+	1.09036i
$987$	3.70820	+	11.4127i	0.118033	+	0.363270i
$988$	−12.9443	+	9.40456i	−0.411812	+	0.299199i
$989$	−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	$0.151088\pi$
$992$	−6.47214	+	4.70228i	−0.205491	+	0.149298i
$993$	−1.23607	−	3.80423i	−0.0392254	−	0.120723i
$994$	−3.70820	+	11.4127i	−0.117617	+	0.361988i
$995$		0			0
$996$	−9.70820	−	7.05342i	−0.307616	−	0.223496i
$997$	−13.5967	+	41.8465i	−0.430613	+	1.32529i	0.466902	+	0.884309i	$0.345370\pi$
$997$	−13.5967	+	41.8465i	−0.430613	+	1.32529i	−0.897516	+	0.440983i	$0.854630\pi$
$998$	−1.23607	−	3.80423i	−0.0391270	−	0.120421i
$999$	8.09017	−	5.87785i	0.255962	−	0.185967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.e.b.487.1		4
11.2	odd	10		66.2.a.a.1.1	✓	1
11.3	even	5	inner	726.2.e.b.511.1		4
11.4	even	5	inner	726.2.e.b.565.1		4
11.5	even	5	inner	726.2.e.b.493.1		4
11.6	odd	10		726.2.e.k.493.1		4
11.7	odd	10		726.2.e.k.565.1		4
11.8	odd	10		726.2.e.k.511.1		4
11.9	even	5		726.2.a.i.1.1		1
11.10	odd	2		726.2.e.k.487.1		4
33.2	even	10		198.2.a.e.1.1		1
33.20	odd	10		2178.2.a.b.1.1		1
44.31	odd	10		5808.2.a.l.1.1		1
44.35	even	10		528.2.a.d.1.1		1
55.2	even	20		1650.2.c.d.199.1		2
55.13	even	20		1650.2.c.d.199.2		2
55.24	odd	10		1650.2.a.m.1.1		1
77.13	even	10		3234.2.a.d.1.1		1
88.13	odd	10		2112.2.a.i.1.1		1
88.35	even	10		2112.2.a.v.1.1		1
99.2	even	30		1782.2.e.f.595.1		2
99.13	odd	30		1782.2.e.s.1189.1		2
99.68	even	30		1782.2.e.f.1189.1		2
99.79	odd	30		1782.2.e.s.595.1		2
132.35	odd	10		1584.2.a.h.1.1		1
165.2	odd	20		4950.2.c.r.199.2		2
165.68	odd	20		4950.2.c.r.199.1		2
165.134	even	10		4950.2.a.g.1.1		1
231.167	odd	10		9702.2.a.bu.1.1		1
264.35	odd	10		6336.2.a.bf.1.1		1
264.101	even	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	11.2	odd	10
198.2.a.e.1.1		1	33.2	even	10
528.2.a.d.1.1		1	44.35	even	10
726.2.a.i.1.1		1	11.9	even	5
726.2.e.b.487.1		4	1.1	even	1	trivial
726.2.e.b.493.1		4	11.5	even	5	inner
726.2.e.b.511.1		4	11.3	even	5	inner
726.2.e.b.565.1		4	11.4	even	5	inner
726.2.e.k.487.1		4	11.10	odd	2
726.2.e.k.493.1		4	11.6	odd	10
726.2.e.k.511.1		4	11.8	odd	10
726.2.e.k.565.1		4	11.7	odd	10
1584.2.a.h.1.1		1	132.35	odd	10
1650.2.a.m.1.1		1	55.24	odd	10
1650.2.c.d.199.1		2	55.2	even	20
1650.2.c.d.199.2		2	55.13	even	20
1782.2.e.f.595.1		2	99.2	even	30
1782.2.e.f.1189.1		2	99.68	even	30
1782.2.e.s.595.1		2	99.79	odd	30
1782.2.e.s.1189.1		2	99.13	odd	30
2112.2.a.i.1.1		1	88.13	odd	10
2112.2.a.v.1.1		1	88.35	even	10
2178.2.a.b.1.1		1	33.20	odd	10
3234.2.a.d.1.1		1	77.13	even	10
4950.2.a.g.1.1		1	165.134	even	10
4950.2.c.r.199.1		2	165.68	odd	20
4950.2.c.r.199.2		2	165.2	odd	20
5808.2.a.l.1.1		1	44.31	odd	10
6336.2.a.bf.1.1		1	264.35	odd	10
6336.2.a.bj.1.1		1	264.101	even	10
9702.2.a.bu.1.1		1	231.167	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{6} +(-0.618034 + 1.90211i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{6} +(-0.618034 + 1.90211i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.00000 q^{12} +(-3.23607 + 2.35114i) q^{13} +(-0.618034 - 1.90211i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-4.85410 - 3.52671i) q^{17} +(0.309017 - 0.951057i) q^{18} +(1.23607 + 3.80423i) q^{19} -2.00000 q^{21} +6.00000 q^{23} +(-0.809017 + 0.587785i) q^{24} +(-1.54508 - 4.75528i) q^{25} +(1.23607 - 3.80423i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(1.61803 + 1.17557i) q^{28} +(-1.85410 + 5.70634i) q^{29} +(-6.47214 + 4.70228i) q^{31} +1.00000 q^{32} +6.00000 q^{34} +(0.309017 + 0.951057i) q^{36} +(-3.09017 + 9.51057i) q^{37} +(-3.23607 - 2.35114i) q^{38} +(-3.23607 - 2.35114i) q^{39} +(-1.85410 - 5.70634i) q^{41} +(1.61803 - 1.17557i) q^{42} -8.00000 q^{43} +(-4.85410 + 3.52671i) q^{46} +(-1.85410 - 5.70634i) q^{47} +(0.309017 - 0.951057i) q^{48} +(2.42705 + 1.76336i) q^{49} +(4.04508 + 2.93893i) q^{50} +(1.85410 - 5.70634i) q^{51} +(1.23607 + 3.80423i) q^{52} +1.00000 q^{54} -2.00000 q^{56} +(-3.23607 + 2.35114i) q^{57} +(-1.85410 - 5.70634i) q^{58} +(6.47214 + 4.70228i) q^{61} +(2.47214 - 7.60845i) q^{62} +(-0.618034 - 1.90211i) q^{63} +(-0.809017 + 0.587785i) q^{64} -4.00000 q^{67} +(-4.85410 + 3.52671i) q^{68} +(1.85410 + 5.70634i) q^{69} +(-4.85410 - 3.52671i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-0.618034 + 1.90211i) q^{73} +(-3.09017 - 9.51057i) q^{74} +(4.04508 - 2.93893i) q^{75} +4.00000 q^{76} +4.00000 q^{78} +(11.3262 - 8.22899i) q^{79} +(0.309017 - 0.951057i) q^{81} +(4.85410 + 3.52671i) q^{82} +(-9.70820 - 7.05342i) q^{83} +(-0.618034 + 1.90211i) q^{84} +(6.47214 - 4.70228i) q^{86} -6.00000 q^{87} -6.00000 q^{89} +(-2.47214 - 7.60845i) q^{91} +(1.85410 - 5.70634i) q^{92} +(-6.47214 - 4.70228i) q^{93} +(4.85410 + 3.52671i) q^{94} +(0.309017 + 0.951057i) q^{96} +(-11.3262 + 8.22899i) q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{3} - q^{4} - q^{6} + 2 q^{7} - q^{8} - q^{9}+O(q^{10}) \) 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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