LMFDB - Embedded newform 726.2.e.k.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.k.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	$-0.776624\pi$
$7$	0.618034	−	1.90211i	0.233595	−	0.718931i	0.997305	−	0.0733714i	$-0.0233759\pi$
$8$	−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	−0.0403050	−	0.999187i	$-0.512833\pi$
$13$	3.23607	−	2.35114i	0.897524	−	0.652089i	0.937829	+	0.347098i	$0.112833\pi$
$14$	−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	0.991864	−	0.127304i	$-0.0406325\pi$
$17$	4.85410	+	3.52671i	1.17729	+	0.855353i	0.185429	+	0.982658i	$0.440633\pi$
$18$	−0.309017	+	0.951057i	−0.0728360	+	0.224166i
$19$	−1.23607	−	3.80423i	−0.283573	−	0.872749i	−0.986823	−	0.161806i	$-0.948268\pi$
$19$	−1.23607	−	3.80423i	−0.283573	−	0.872749i	0.703249	−	0.710943i	$-0.251732\pi$
$20$		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	$-0.711919\pi$
$29$	1.85410	−	5.70634i	0.344298	−	1.05964i	0.961958	−	0.273196i	$-0.0880806\pi$
$30$		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	$0.0552131\pi$
$41$	1.85410	+	5.70634i	0.289562	+	0.891180i	−0.695432	+	0.718592i	$0.744787\pi$
$42$	1.61803	−	1.17557i	0.249668	−	0.181394i
$43$	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
$46$	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	0.0905112	−	0.995895i	$-0.471150\pi$
$61$	−6.47214	−	4.70228i	−0.828672	−	0.602066i	−0.919183	+	0.393830i	$0.871150\pi$
$62$	−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	−0.908352	−	0.418206i	$-0.862659\pi$
$73$	0.618034	−	1.90211i	0.0723354	−	0.222625i	0.980688	+	0.195580i	$0.0626591\pi$
$74$	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	−0.999365	−	0.0356284i	$-0.988657\pi$
$79$	−11.3262	+	8.22899i	−1.27430	+	0.925834i	−0.274936	+	0.961462i	$0.588657\pi$
$80$		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	0.975119	−	0.221683i	$-0.0711551\pi$
$83$	9.70820	+	7.05342i	1.06561	+	0.774214i	0.0904951	+	0.995897i	$0.471155\pi$
$84$	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	−0.802486	−	0.596670i	$-0.796490\pi$
$101$	−4.85410	+	3.52671i	−0.483001	+	0.350921i	0.319485	+	0.947591i	$0.396490\pi$
$102$	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	$-0.903036\pi$
$107$	−3.70820	−	11.4127i	−0.358486	−	1.10331i	0.595475	−	0.803374i	$-0.296964\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	−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
$112$	−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	−0.0418779	−	0.999123i	$-0.513334\pi$
$127$	−11.3262	−	8.22899i	−1.00504	−	0.730205i	−0.963163	+	0.268918i	$0.913334\pi$
$128$	−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	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		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	−0.989693	−	0.143203i	$-0.954260\pi$
$139$	−1.23607	+	3.80423i	−0.104842	+	0.322670i	0.884851	+	0.465873i	$0.154260\pi$
$140$		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	0.768589	−	0.639743i	$-0.220959\pi$
$149$	4.85410	+	3.52671i	0.397664	+	0.288919i	−0.370925	+	0.928663i	$0.620959\pi$
$150$	1.54508	−	4.75528i	0.126156	−	0.388267i
$151$	−3.09017	−	9.51057i	−0.251474	−	0.773959i	−0.994504	−	0.104700i	$-0.966612\pi$
$151$	−3.09017	−	9.51057i	−0.251474	−	0.773959i	0.743029	−	0.669259i	$-0.233388\pi$
$152$	−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	−0.896212	−	0.443626i	$-0.853692\pi$
$167$	−9.70820	+	7.05342i	−0.751243	+	0.545810i	0.144969	+	0.989436i	$0.453692\pi$
$168$	−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	0.996470	−	0.0839492i	$-0.0267533\pi$
$173$	1.85410	+	5.70634i	0.140965	+	0.433845i	−0.855505	+	0.517794i	$0.826753\pi$
$174$	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	0.100076	−	0.994980i	$-0.468091\pi$
$193$	−11.3262	−	8.22899i	−0.815280	−	0.592336i	−0.915357	+	0.402644i	$0.868091\pi$
$194$	−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	$-0.431435\pi$
$197$	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	$0.545281\pi$
$200$	−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	−0.787840	−	0.615880i	$-0.788801\pi$
$211$	−6.47214	+	4.70228i	−0.445560	+	0.323718i	0.342280	+	0.939598i	$0.388801\pi$
$212$		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	$0.230377\pi$
$227$	−3.70820	+	11.4127i	−0.246122	+	0.757486i	−0.995450	+	0.0952867i	$0.969623\pi$
$228$	−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	0.00225687	−	0.999997i	$-0.499282\pi$
$233$	14.5623	−	10.5801i	0.954008	−	0.693128i	0.951752	+	0.306870i	$0.0992816\pi$
$234$	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	$-0.973129\pi$
$239$	−3.70820	−	11.4127i	−0.239864	−	0.738225i	0.756575	−	0.653907i	$-0.226871\pi$
$240$		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
$244$	−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	−0.930529	−	0.366219i	$-0.880652\pi$
$271$	0.618034	−	1.90211i	0.0375429	−	0.115545i	0.968072	+	0.250674i	$0.0806521\pi$
$272$	−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	−0.126556	−	0.991959i	$-0.540392\pi$
$277$	12.9443	−	9.40456i	0.777746	−	0.565065i	0.904302	+	0.426894i	$0.140392\pi$
$278$	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	0.723081	−	0.690763i	$-0.242725\pi$
$281$	4.85410	+	3.52671i	0.289571	+	0.210386i	−0.433510	+	0.901149i	$0.642725\pi$
$282$	1.85410	−	5.70634i	0.110410	−	0.339808i
$283$	2.47214	+	7.60845i	0.146953	+	0.452276i	0.997257	−	0.0740167i	$-0.0235818\pi$
$283$	2.47214	+	7.60845i	0.146953	+	0.452276i	−0.850304	+	0.526292i	$0.823582\pi$
$284$	−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	−0.990495	−	0.137550i	$-0.956077\pi$
$293$	−1.85410	+	5.70634i	−0.108318	+	0.333368i	0.882177	+	0.470918i	$0.156077\pi$
$294$	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	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$	−4.00000			−0.227552
$310$		0			0
$311$	−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	−0.932811	−	0.360366i	$-0.882652\pi$
$337$	0.618034	−	1.90211i	0.0336665	−	0.103615i	0.966478	+	0.256751i	$0.0826520\pi$
$338$	−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	$-0.882883\pi$
$347$	−29.1246	−	21.1603i	−1.56349	−	1.13594i	−0.630418	−	0.776256i	$-0.717117\pi$
$348$	1.85410	−	5.70634i	0.0993903	−	0.305892i
$349$	−1.23607	−	3.80423i	−0.0661652	−	0.203636i	0.912508	−	0.409059i	$-0.134143\pi$
$349$	−1.23607	−	3.80423i	−0.0661652	−	0.203636i	−0.978673	+	0.205423i	$0.934143\pi$
$350$	−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	$0.202564\pi$
$359$	−3.70820	+	11.4127i	−0.195712	+	0.602338i	−0.999968	+	0.00805517i	$0.997436\pi$
$360$		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	$-0.326758\pi$
$373$	20.0000			1.03556			0.517780	+	0.855514i	$0.326758\pi$
$374$		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	$-0.382205\pi$
$409$	27.5066	−	19.9847i	1.36011	−	0.988180i	0.998438	−	0.0558755i	$-0.0177950\pi$
$410$		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	$-0.576701\pi$
$439$	−10.0000			−0.477274			−0.238637	+	0.971109i	$0.576701\pi$
$440$		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	0.760703	−	0.649100i	$-0.224854\pi$
$457$	8.09017	+	5.87785i	0.378442	+	0.274954i	−0.382261	+	0.924054i	$0.624854\pi$
$458$	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	$-0.0667892\pi$
$461$	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	$0.529629\pi$
$464$	−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	0.935136	−	0.354290i	$-0.115277\pi$
$479$	19.4164	+	14.1068i	0.887158	+	0.644558i	−0.0479772	+	0.998848i	$0.515277\pi$
$480$		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	−0.831853	−	0.554996i	$-0.812720\pi$
$491$	3.70820	−	11.4127i	0.167349	−	0.515047i	0.999202	+	0.0399494i	$0.0127197\pi$
$492$	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	0.999061	−	0.0433204i	$-0.0137936\pi$
$503$	3.70820	+	11.4127i	0.165341	+	0.508866i	−0.833721	+	0.552187i	$0.813794\pi$
$504$	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	0.833655	−	0.552286i	$-0.186244\pi$
$523$	12.9443	+	9.40456i	0.566013	+	0.411233i	−0.267641	+	0.963519i	$0.586244\pi$
$524$	−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	−0.878512	−	0.477721i	$-0.841463\pi$
$541$	−16.1803	+	11.7557i	−0.695647	+	0.505417i	0.182865	+	0.983138i	$0.441463\pi$
$542$	−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	$-0.895725\pi$
$547$	−8.65248	−	26.6296i	−0.369953	−	1.13860i	0.576868	−	0.816838i	$-0.304275\pi$
$548$	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	$-0.775462\pi$
$557$	5.56231	−	17.1190i	0.235682	−	0.725356i	0.997030	−	0.0770122i	$-0.0245380\pi$
$558$	−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	−0.364106	−	0.931357i	$-0.618626\pi$
$563$	9.70820	−	7.05342i	0.409152	−	0.297266i	0.773258	+	0.634091i	$0.218626\pi$
$564$	−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	$0.0231473\pi$
$569$	5.56231	+	17.1190i	0.233184	+	0.717667i	−0.764173	+	0.645011i	$0.776853\pi$
$570$		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
$574$	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	$-0.711238\pi$
$593$	−30.0000			−1.23195			−0.615976	+	0.787765i	$0.711238\pi$
$594$		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	$0.248113\pi$
$601$	−6.79837	+	20.9232i	−0.277311	+	0.853477i	−0.988599	+	0.150575i	$0.951887\pi$
$602$	−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	−0.793421	−	0.608674i	$-0.791702\pi$
$607$	−11.3262	+	8.22899i	−0.459718	+	0.334005i	0.333703	+	0.942678i	$0.391702\pi$
$608$	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	$-0.995269\pi$
$613$	−4.94427	−	15.2169i	−0.199697	−	0.614605i	0.800192	−	0.599744i	$-0.204731\pi$
$614$	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	$-0.252657\pi$
$659$	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	$0.640729\pi$
$662$	−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	−0.784280	−	0.620407i	$-0.786968\pi$
$673$	−11.3262	+	8.22899i	−0.436594	+	0.317204i	0.347686	+	0.937611i	$0.386968\pi$
$674$	−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	0.0138832	−	0.999904i	$-0.495581\pi$
$677$	−24.2705	−	17.6336i	−0.932791	−	0.677713i	−0.946675	+	0.322191i	$0.895581\pi$
$678$	−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	0.909917	−	0.414790i	$-0.136145\pi$
$701$	−1.85410	−	5.70634i	−0.0700285	−	0.215525i	−0.979946	+	0.199264i	$0.936145\pi$
$702$	−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	−0.971286	−	0.237917i	$-0.923536\pi$
$733$	−1.23607	+	3.80423i	−0.0456552	+	0.140512i	0.925630	+	0.378429i	$0.123536\pi$
$734$	−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	−0.700428	−	0.713723i	$-0.747008\pi$
$739$	−6.47214	+	4.70228i	−0.238081	+	0.172976i	0.462347	+	0.886699i	$0.347008\pi$
$740$		0			0
$741$	4.94427	−	15.2169i	0.181632	−	0.559007i
$742$		0			0
$743$	−29.1246	−	21.1603i	−1.06848	−	0.776295i	−0.0928402	−	0.995681i	$-0.529595\pi$
$743$	−29.1246	−	21.1603i	−1.06848	−	0.776295i	−0.975638	+	0.219386i	$0.929595\pi$
$744$	−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	−0.819565	−	0.572986i	$-0.805785\pi$
$761$	−14.5623	+	10.5801i	−0.527883	+	0.383530i	0.291682	+	0.956515i	$0.405785\pi$
$762$	−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	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$		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	0.0213991	−	0.999771i	$-0.493188\pi$
$787$	−25.8885	−	18.8091i	−0.922827	−	0.670473i	−0.944226	+	0.329298i	$0.893188\pi$
$788$	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	0.993746	−	0.111667i	$-0.0356191\pi$
$809$	33.9787	+	24.6870i	1.19463	+	0.867948i	0.200882	+	0.979615i	$0.435619\pi$
$810$		0			0
$811$	2.47214	+	7.60845i	0.0868084	+	0.267169i	0.985032	−	0.172369i	$-0.0551422\pi$
$811$	2.47214	+	7.60845i	0.0868084	+	0.267169i	−0.898224	+	0.439538i	$0.855142\pi$
$812$	−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	$0.201703\pi$
$821$	−5.56231	+	17.1190i	−0.194126	+	0.597458i	−0.999986	+	0.00535152i	$0.998297\pi$
$822$	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	−0.406056	−	0.913848i	$-0.633096\pi$
$827$	9.70820	−	7.05342i	0.337587	−	0.245272i	0.743643	+	0.668577i	$0.233096\pi$
$828$	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	0.471446	−	0.881895i	$-0.343732\pi$
$853$	−6.47214	−	4.70228i	−0.221602	−	0.161003i	−0.693047	+	0.720892i	$0.743732\pi$
$854$	−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	$-0.126305\pi$
$857$	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
$861$	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	$-0.758906\pi$
$877$	−16.0689	−	49.4549i	−0.542608	−	1.66997i	0.184003	−	0.982926i	$-0.441094\pi$
$878$	−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	$0.306579\pi$
$887$	−11.1246	+	34.2380i	−0.373528	+	1.14960i	−0.944466	+	0.328608i	$0.893421\pi$
$888$	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	0.560778	−	0.827966i	$-0.310502\pi$
$919$	−1.61803	−	1.17557i	−0.0533740	−	0.0387785i	−0.614152	+	0.789187i	$0.710502\pi$
$920$		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	−0.257798	−	0.966199i	$-0.582997\pi$
$937$	17.7984	−	12.9313i	0.581448	−	0.422446i	0.839246	+	0.543752i	$0.182997\pi$
$938$	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	0.799277	−	0.600963i	$-0.205216\pi$
$941$	14.5623	+	10.5801i	0.474718	+	0.344903i	−0.324559	+	0.945865i	$0.605216\pi$
$942$	−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	$0.338132\pi$
$953$	−12.9787	+	39.9444i	−0.420422	+	1.29393i	−0.907311	+	0.420461i	$0.861868\pi$
$954$		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	$-0.427728\pi$
$967$	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		0.951057	−	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	$-0.654630\pi$
$997$	13.5967	−	41.8465i	0.430613	−	1.32529i	0.897516	−	0.440983i	$-0.145370\pi$
$998$	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.k.487.1		4
11.2	odd	10		726.2.a.i.1.1		1
11.3	even	5	inner	726.2.e.k.511.1		4
11.4	even	5	inner	726.2.e.k.565.1		4
11.5	even	5	inner	726.2.e.k.493.1		4
11.6	odd	10		726.2.e.b.493.1		4
11.7	odd	10		726.2.e.b.565.1		4
11.8	odd	10		726.2.e.b.511.1		4
11.9	even	5		66.2.a.a.1.1	✓	1
11.10	odd	2		726.2.e.b.487.1		4
33.2	even	10		2178.2.a.b.1.1		1
33.20	odd	10		198.2.a.e.1.1		1
44.31	odd	10		528.2.a.d.1.1		1
44.35	even	10		5808.2.a.l.1.1		1
55.9	even	10		1650.2.a.m.1.1		1
55.42	odd	20		1650.2.c.d.199.1		2
55.53	odd	20		1650.2.c.d.199.2		2
77.20	odd	10		3234.2.a.d.1.1		1
88.53	even	10		2112.2.a.i.1.1		1
88.75	odd	10		2112.2.a.v.1.1		1
99.20	odd	30		1782.2.e.f.595.1		2
99.31	even	15		1782.2.e.s.1189.1		2
99.86	odd	30		1782.2.e.f.1189.1		2
99.97	even	15		1782.2.e.s.595.1		2
132.119	even	10		1584.2.a.h.1.1		1
165.53	even	20		4950.2.c.r.199.1		2
165.119	odd	10		4950.2.a.g.1.1		1
165.152	even	20		4950.2.c.r.199.2		2
231.20	even	10		9702.2.a.bu.1.1		1
264.53	odd	10		6336.2.a.bj.1.1		1
264.251	even	10		6336.2.a.bf.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.a.a.1.1	✓	1	11.9	even	5
198.2.a.e.1.1		1	33.20	odd	10
528.2.a.d.1.1		1	44.31	odd	10
726.2.a.i.1.1		1	11.2	odd	10
726.2.e.b.487.1		4	11.10	odd	2
726.2.e.b.493.1		4	11.6	odd	10
726.2.e.b.511.1		4	11.8	odd	10
726.2.e.b.565.1		4	11.7	odd	10
726.2.e.k.487.1		4	1.1	even	1	trivial
726.2.e.k.493.1		4	11.5	even	5	inner
726.2.e.k.511.1		4	11.3	even	5	inner
726.2.e.k.565.1		4	11.4	even	5	inner
1584.2.a.h.1.1		1	132.119	even	10
1650.2.a.m.1.1		1	55.9	even	10
1650.2.c.d.199.1		2	55.42	odd	20
1650.2.c.d.199.2		2	55.53	odd	20
1782.2.e.f.595.1		2	99.20	odd	30
1782.2.e.f.1189.1		2	99.86	odd	30
1782.2.e.s.595.1		2	99.97	even	15
1782.2.e.s.1189.1		2	99.31	even	15
2112.2.a.i.1.1		1	88.53	even	10
2112.2.a.v.1.1		1	88.75	odd	10
2178.2.a.b.1.1		1	33.2	even	10
3234.2.a.d.1.1		1	77.20	odd	10
4950.2.a.g.1.1		1	165.119	odd	10
4950.2.c.r.199.1		2	165.53	even	20
4950.2.c.r.199.2		2	165.152	even	20
5808.2.a.l.1.1		1	44.35	even	10
6336.2.a.bf.1.1		1	264.251	even	10
6336.2.a.bj.1.1		1	264.53	odd	10
9702.2.a.bu.1.1		1	231.20	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)

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