LMFDB - Embedded newform 726.2.e.h.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:	yes
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.h.565.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{6} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{6} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.00000 q^{12} +(-4.85410 + 3.52671i) q^{13} +(-0.809017 - 0.587785i) q^{16} +(4.85410 + 3.52671i) q^{17} +(0.309017 - 0.951057i) q^{18} +(1.85410 + 5.70634i) q^{19} +6.00000 q^{23} +(0.809017 - 0.587785i) q^{24} +(-1.54508 - 4.75528i) q^{25} +(1.85410 - 5.70634i) q^{26} +(0.809017 + 0.587785i) q^{27} +(1.85410 - 5.70634i) q^{29} +(-3.23607 + 2.35114i) q^{31} +1.00000 q^{32} -6.00000 q^{34} +(0.309017 + 0.951057i) q^{36} +(-0.618034 + 1.90211i) q^{37} +(-4.85410 - 3.52671i) q^{38} +(4.85410 + 3.52671i) q^{39} +(1.85410 + 5.70634i) q^{41} +6.00000 q^{43} +(-4.85410 + 3.52671i) q^{46} +(1.85410 + 5.70634i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(5.66312 + 4.11450i) q^{49} +(4.04508 + 2.93893i) q^{50} +(1.85410 - 5.70634i) q^{51} +(1.85410 + 5.70634i) q^{52} +(9.70820 - 7.05342i) q^{53} -1.00000 q^{54} +(4.85410 - 3.52671i) q^{57} +(1.85410 + 5.70634i) q^{58} +(-3.70820 + 11.4127i) q^{59} +(-4.85410 - 3.52671i) q^{61} +(1.23607 - 3.80423i) q^{62} +(-0.809017 + 0.587785i) q^{64} +4.00000 q^{67} +(4.85410 - 3.52671i) q^{68} +(-1.85410 - 5.70634i) q^{69} +(4.85410 + 3.52671i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-3.70820 + 11.4127i) q^{73} +(-0.618034 - 1.90211i) q^{74} +(-4.04508 + 2.93893i) q^{75} +6.00000 q^{76} -6.00000 q^{78} +(-9.70820 + 7.05342i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-4.85410 - 3.52671i) q^{82} +(-4.85410 + 3.52671i) q^{86} -6.00000 q^{87} -6.00000 q^{89} +(1.85410 - 5.70634i) q^{92} +(3.23607 + 2.35114i) q^{93} +(-4.85410 - 3.52671i) q^{94} +(-0.309017 - 0.951057i) q^{96} +(8.09017 - 5.87785i) q^{97} -7.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} - q^{4} + q^{6} - q^{8} - q^{9}+O(q^{10}) $ 4 * q - q^2 + q^3 - q^4 + q^6 - q^8 - q^9	$ 4 q - q^{2} + q^{3} - q^{4} + q^{6} - q^{8} - q^{9} - 4 q^{12} - 6 q^{13} - q^{16} + 6 q^{17} - q^{18} - 6 q^{19} + 24 q^{23} + q^{24} + 5 q^{25} - 6 q^{26} + q^{27} - 6 q^{29} - 4 q^{31} + 4 q^{32} - 24 q^{34} - q^{36} + 2 q^{37} - 6 q^{38} + 6 q^{39} - 6 q^{41} + 24 q^{43} - 6 q^{46} - 6 q^{47} + q^{48} + 7 q^{49} + 5 q^{50} - 6 q^{51} - 6 q^{52} + 12 q^{53} - 4 q^{54} + 6 q^{57} - 6 q^{58} + 12 q^{59} - 6 q^{61} - 4 q^{62} - q^{64} + 16 q^{67} + 6 q^{68} + 6 q^{69} + 6 q^{71} - q^{72} + 12 q^{73} + 2 q^{74} - 5 q^{75} + 24 q^{76} - 24 q^{78} - 12 q^{79} - q^{81} - 6 q^{82} - 6 q^{86} - 24 q^{87} - 24 q^{89} - 6 q^{92} + 4 q^{93} - 6 q^{94} + q^{96} + 10 q^{97} - 28 q^{98}+O(q^{100}) $ 4 * q - q^2 + q^3 - q^4 + q^6 - q^8 - q^9 - 4 * q^12 - 6 * q^13 - q^16 + 6 * q^17 - q^18 - 6 * q^19 + 24 * q^23 + q^24 + 5 * q^25 - 6 * q^26 + q^27 - 6 * q^29 - 4 * q^31 + 4 * q^32 - 24 * q^34 - q^36 + 2 * q^37 - 6 * q^38 + 6 * q^39 - 6 * q^41 + 24 * q^43 - 6 * q^46 - 6 * q^47 + q^48 + 7 * q^49 + 5 * q^50 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 4 * q^54 + 6 * q^57 - 6 * q^58 + 12 * q^59 - 6 * q^61 - 4 * q^62 - q^64 + 16 * q^67 + 6 * q^68 + 6 * q^69 + 6 * q^71 - q^72 + 12 * q^73 + 2 * q^74 - 5 * q^75 + 24 * q^76 - 24 * q^78 - 12 * q^79 - q^81 - 6 * q^82 - 6 * q^86 - 24 * q^87 - 24 * q^89 - 6 * q^92 + 4 * q^93 - 6 * q^94 + q^96 + 10 * q^97 - 28 * q^98

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			0		−0.951057	−	0.309017i	$-0.900000\pi$
$7$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$8$	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
$13$	−4.85410	+	3.52671i	−1.34629	+	0.978134i	−0.347098	+	0.937829i	$0.612833\pi$
$13$	−4.85410	+	3.52671i	−1.34629	+	0.978134i	−0.999187	+	0.0403050i	$0.987167\pi$
$14$		0			0
$15$		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
$19$	1.85410	+	5.70634i	0.425360	+	1.30912i	0.902649	+	0.430377i	$0.141620\pi$
$19$	1.85410	+	5.70634i	0.425360	+	1.30912i	−0.477289	+	0.878746i	$0.658380\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	−1.54508	−	4.75528i	−0.309017	−	0.951057i
$26$	1.85410	−	5.70634i	0.363619	−	1.11911i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$		0			0
$29$	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
$31$	−3.23607	+	2.35114i	−0.581215	+	0.422277i	−0.839162	−	0.543882i	$-0.816954\pi$
$31$	−3.23607	+	2.35114i	−0.581215	+	0.422277i	0.257947	+	0.966159i	$0.416954\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−6.00000			−1.02899
$35$		0			0
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−0.618034	+	1.90211i	−0.101604	+	0.312705i	−0.988918	−	0.148460i	$-0.952568\pi$
$37$	−0.618034	+	1.90211i	−0.101604	+	0.312705i	0.887314	+	0.461165i	$0.152568\pi$
$38$	−4.85410	−	3.52671i	−0.787439	−	0.572108i
$39$	4.85410	+	3.52671i	0.777278	+	0.564726i
$40$		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	$0.744787\pi$
$42$		0			0
$43$	6.00000			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$44$		0			0
$45$		0			0
$46$	−4.85410	+	3.52671i	−0.715698	+	0.519985i
$47$	1.85410	+	5.70634i	0.270449	+	0.832355i	0.990388	+	0.138318i	$0.0441696\pi$
$47$	1.85410	+	5.70634i	0.270449	+	0.832355i	−0.719939	+	0.694037i	$0.755830\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	5.66312	+	4.11450i	0.809017	+	0.587785i
$50$	4.04508	+	2.93893i	0.572061	+	0.415627i
$51$	1.85410	−	5.70634i	0.259626	−	0.799047i
$52$	1.85410	+	5.70634i	0.257118	+	0.791327i
$53$	9.70820	−	7.05342i	1.33352	−	0.968862i	0.333869	−	0.942620i	$-0.391646\pi$
$53$	9.70820	−	7.05342i	1.33352	−	0.968862i	0.999656	−	0.0262426i	$-0.00835424\pi$
$54$	−1.00000			−0.136083
$55$		0			0
$56$		0			0
$57$	4.85410	−	3.52671i	0.642942	−	0.467124i
$58$	1.85410	+	5.70634i	0.243456	+	0.749279i
$59$	−3.70820	+	11.4127i	−0.482767	+	1.48580i	0.352422	+	0.935841i	$0.385358\pi$
$59$	−3.70820	+	11.4127i	−0.482767	+	1.48580i	−0.835189	+	0.549963i	$0.814642\pi$
$60$		0			0
$61$	−4.85410	−	3.52671i	−0.621504	−	0.451549i	0.231942	−	0.972730i	$-0.425492\pi$
$61$	−4.85410	−	3.52671i	−0.621504	−	0.451549i	−0.853447	+	0.521180i	$0.825492\pi$
$62$	1.23607	−	3.80423i	0.156981	−	0.483137i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$		0			0
$66$		0			0
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$	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	0.837307	−	0.546733i	$-0.184129\pi$
$71$	4.85410	+	3.52671i	0.576076	+	0.418544i	−0.261231	+	0.965276i	$0.584129\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	−3.70820	+	11.4127i	−0.434012	+	1.33575i	0.460083	+	0.887876i	$0.347820\pi$
$73$	−3.70820	+	11.4127i	−0.434012	+	1.33575i	−0.894095	+	0.447877i	$0.852180\pi$
$74$	−0.618034	−	1.90211i	−0.0718450	−	0.221116i
$75$	−4.04508	+	2.93893i	−0.467086	+	0.339358i
$76$	6.00000			0.688247
$77$		0			0
$78$	−6.00000			−0.679366
$79$	−9.70820	+	7.05342i	−1.09226	+	0.793572i	−0.979779	−	0.200082i	$-0.935879\pi$
$79$	−9.70820	+	7.05342i	−1.09226	+	0.793572i	−0.112479	+	0.993654i	$0.535879\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−4.85410	−	3.52671i	−0.536046	−	0.389460i
$83$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$83$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$84$		0			0
$85$		0			0
$86$	−4.85410	+	3.52671i	−0.523431	+	0.380295i
$87$	−6.00000			−0.643268
$88$		0			0
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$		0			0
$92$	1.85410	−	5.70634i	0.193303	−	0.594927i
$93$	3.23607	+	2.35114i	0.335565	+	0.243802i
$94$	−4.85410	−	3.52671i	−0.500662	−	0.363753i
$95$		0			0
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	8.09017	−	5.87785i	0.821432	−	0.596806i	−0.0956901	−	0.995411i	$-0.530506\pi$
$97$	8.09017	−	5.87785i	0.821432	−	0.596806i	0.917122	+	0.398606i	$0.130506\pi$
$98$	−7.00000			−0.707107
$99$		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	$0.163141\pi$
$104$	−4.85410	−	3.52671i	−0.475984	−	0.345823i
$105$		0			0
$106$	−3.70820	+	11.4127i	−0.360173	+	1.10850i
$107$	−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
$109$	6.00000			0.574696			0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000			0.574696			0.287348	+	0.957826i	$0.407226\pi$
$110$		0			0
$111$	2.00000			0.189832
$112$		0			0
$113$	1.85410	+	5.70634i	0.174419	+	0.536807i	0.999606	−	0.0280521i	$-0.00893043\pi$
$113$	1.85410	+	5.70634i	0.174419	+	0.536807i	−0.825187	+	0.564859i	$0.808930\pi$
$114$	−1.85410	+	5.70634i	−0.173653	+	0.534448i
$115$		0			0
$116$	−4.85410	−	3.52671i	−0.450692	−	0.327447i
$117$	1.85410	−	5.70634i	0.171412	−	0.527551i
$118$	−3.70820	−	11.4127i	−0.341368	−	1.05062i
$119$		0			0
$120$		0			0
$121$		0			0
$122$	6.00000			0.543214
$123$	4.85410	−	3.52671i	0.437680	−	0.317993i
$124$	1.23607	+	3.80423i	0.111002	+	0.341630i
$125$		0			0
$126$		0			0
$127$	−9.70820	−	7.05342i	−0.861464	−	0.625890i	0.0668190	−	0.997765i	$-0.478715\pi$
$127$	−9.70820	−	7.05342i	−0.861464	−	0.625890i	−0.928283	+	0.371875i	$0.878715\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−1.85410	−	5.70634i	−0.163245	−	0.502415i
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		0			0
$133$		0			0
$134$	−3.23607	+	2.35114i	−0.279554	+	0.203108i
$135$		0			0
$136$	−1.85410	+	5.70634i	−0.158988	+	0.489315i
$137$	4.85410	+	3.52671i	0.414714	+	0.301307i	0.775507	−	0.631338i	$-0.217494\pi$
$137$	4.85410	+	3.52671i	0.414714	+	0.301307i	−0.360794	+	0.932646i	$0.617494\pi$
$138$	4.85410	+	3.52671i	0.413209	+	0.300214i
$139$	−5.56231	+	17.1190i	−0.471789	+	1.45202i	0.378452	+	0.925621i	$0.376457\pi$
$139$	−5.56231	+	17.1190i	−0.471789	+	1.45202i	−0.850240	+	0.526395i	$0.823543\pi$
$140$		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
$146$	−3.70820	−	11.4127i	−0.306893	−	0.944520i
$147$	2.16312	−	6.65740i	0.178411	−	0.549093i
$148$	1.61803	+	1.17557i	0.133002	+	0.0966313i
$149$	−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
$151$	−3.70820	−	11.4127i	−0.301769	−	0.928751i	−0.980863	−	0.194699i	$-0.937627\pi$
$151$	−3.70820	−	11.4127i	−0.301769	−	0.928751i	0.679094	−	0.734052i	$-0.262373\pi$
$152$	−4.85410	+	3.52671i	−0.393720	+	0.286054i
$153$	−6.00000			−0.485071
$154$		0			0
$155$		0			0
$156$	4.85410	−	3.52671i	0.388639	−	0.282363i
$157$	−4.32624	−	13.3148i	−0.345271	−	1.06264i	−0.961438	−	0.275020i	$-0.911315\pi$
$157$	−4.32624	−	13.3148i	−0.345271	−	1.06264i	0.616167	−	0.787616i	$-0.288685\pi$
$158$	3.70820	−	11.4127i	0.295009	−	0.907944i
$159$	−9.70820	−	7.05342i	−0.769911	−	0.559373i
$160$		0			0
$161$		0			0
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	−16.1803	+	11.7557i	−1.26734	+	0.920778i	−0.999093	−	0.0425718i	$-0.986445\pi$
$163$	−16.1803	+	11.7557i	−1.26734	+	0.920778i	−0.268249	+	0.963350i	$0.586445\pi$
$164$	6.00000			0.468521
$165$		0			0
$166$		0			0
$167$	19.4164	−	14.1068i	1.50249	−	1.09162i	0.533109	−	0.846047i	$-0.321024\pi$
$167$	19.4164	−	14.1068i	1.50249	−	1.09162i	0.969378	−	0.245574i	$-0.0789764\pi$
$168$		0			0
$169$	7.10739	−	21.8743i	0.546722	−	1.68264i
$170$		0			0
$171$	−4.85410	−	3.52671i	−0.371202	−	0.269694i
$172$	1.85410	−	5.70634i	0.141374	−	0.435104i
$173$	−5.56231	−	17.1190i	−0.422894	−	1.30153i	−0.904996	−	0.425420i	$-0.860127\pi$
$173$	−5.56231	−	17.1190i	−0.422894	−	1.30153i	0.482102	−	0.876115i	$-0.339873\pi$
$174$	4.85410	−	3.52671i	0.367989	−	0.267359i
$175$		0			0
$176$		0			0
$177$	12.0000			0.901975
$178$	4.85410	−	3.52671i	0.363830	−	0.264338i
$179$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$179$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$180$		0			0
$181$	−1.61803	−	1.17557i	−0.120268	−	0.0873795i	0.526026	−	0.850469i	$-0.323682\pi$
$181$	−1.61803	−	1.17557i	−0.120268	−	0.0873795i	−0.646293	+	0.763089i	$0.723682\pi$
$182$		0			0
$183$	−1.85410	+	5.70634i	−0.137059	+	0.421825i
$184$	1.85410	+	5.70634i	0.136686	+	0.420677i
$185$		0			0
$186$	−4.00000			−0.293294
$187$		0			0
$188$	6.00000			0.437595
$189$		0			0
$190$		0			0
$191$	−5.56231	+	17.1190i	−0.402474	+	1.23869i	0.520511	+	0.853855i	$0.325741\pi$
$191$	−5.56231	+	17.1190i	−0.402474	+	1.23869i	−0.922986	+	0.384834i	$0.874259\pi$
$192$	0.809017	+	0.587785i	0.0583858	+	0.0424197i
$193$	−9.70820	−	7.05342i	−0.698812	−	0.507716i	0.180733	−	0.983532i	$-0.442153\pi$
$193$	−9.70820	−	7.05342i	−0.698812	−	0.507716i	−0.879545	+	0.475816i	$0.842153\pi$
$194$	−3.09017	+	9.51057i	−0.221861	+	0.682819i
$195$		0			0
$196$	5.66312	−	4.11450i	0.404508	−	0.293893i
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	16.0000			1.13421			0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000			1.13421			0.567105	+	0.823646i	$0.308063\pi$
$200$	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
$203$		0			0
$204$	−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
$208$	6.00000			0.416025
$209$		0			0
$210$		0			0
$211$	4.85410	−	3.52671i	0.334170	−	0.242789i	−0.408028	−	0.912969i	$-0.633783\pi$
$211$	4.85410	−	3.52671i	0.334170	−	0.242789i	0.742198	+	0.670181i	$0.233783\pi$
$212$	−3.70820	−	11.4127i	−0.254680	−	0.783826i
$213$	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
$217$		0			0
$218$	−4.85410	+	3.52671i	−0.328761	+	0.238859i
$219$	12.0000			0.810885
$220$		0			0
$221$	−36.0000			−2.42162
$222$	−1.61803	+	1.17557i	−0.108595	+	0.0788991i
$223$	2.47214	+	7.60845i	0.165546	+	0.509500i	0.999076	−	0.0429750i	$-0.0136836\pi$
$223$	2.47214	+	7.60845i	0.165546	+	0.509500i	−0.833530	+	0.552475i	$0.813684\pi$
$224$		0			0
$225$	4.04508	+	2.93893i	0.269672	+	0.195928i
$226$	−4.85410	−	3.52671i	−0.322890	−	0.234593i
$227$	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	$-0.0303768\pi$
$228$	−1.85410	−	5.70634i	−0.122791	−	0.377912i
$229$	11.3262	−	8.22899i	0.748459	−	0.543787i	−0.146890	−	0.989153i	$-0.546926\pi$
$229$	11.3262	−	8.22899i	0.748459	−	0.543787i	0.895349	+	0.445366i	$0.146926\pi$
$230$		0			0
$231$		0			0
$232$	6.00000			0.393919
$233$	−4.85410	+	3.52671i	−0.318003	+	0.231043i	−0.735323	−	0.677717i	$-0.762969\pi$
$233$	−4.85410	+	3.52671i	−0.318003	+	0.231043i	0.417320	+	0.908760i	$0.362969\pi$
$234$	1.85410	+	5.70634i	0.121206	+	0.373035i
$235$		0			0
$236$	9.70820	+	7.05342i	0.631950	+	0.459139i
$237$	9.70820	+	7.05342i	0.630616	+	0.458169i
$238$		0			0
$239$	7.41641	+	22.8254i	0.479728	+	1.47645i	0.839474	+	0.543400i	$0.182863\pi$
$239$	7.41641	+	22.8254i	0.479728	+	1.47645i	−0.359747	+	0.933050i	$0.617137\pi$
$240$		0			0
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$	−4.85410	+	3.52671i	−0.310752	+	0.225775i
$245$		0			0
$246$	−1.85410	+	5.70634i	−0.118213	+	0.363823i
$247$	−29.1246	−	21.1603i	−1.85315	−	1.34640i
$248$	−3.23607	−	2.35114i	−0.205491	−	0.149298i
$249$		0			0
$250$		0			0
$251$	−19.4164	+	14.1068i	−1.22555	+	0.890416i	−0.996549	−	0.0830092i	$-0.973547\pi$
$251$	−19.4164	+	14.1068i	−1.22555	+	0.890416i	−0.229004	+	0.973425i	$0.573547\pi$
$252$		0			0
$253$		0			0
$254$	12.0000			0.752947
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	5.56231	−	17.1190i	0.346967	−	1.06785i	−0.613555	−	0.789652i	$-0.710261\pi$
$257$	5.56231	−	17.1190i	0.346967	−	1.06785i	0.960522	−	0.278203i	$-0.0897388\pi$
$258$	4.85410	+	3.52671i	0.302203	+	0.219563i
$259$		0			0
$260$		0			0
$261$	1.85410	+	5.70634i	0.114766	+	0.353214i
$262$	9.70820	−	7.05342i	0.599775	−	0.435762i
$263$	24.0000			1.47990			0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000			1.47990			0.739952	+	0.672660i	$0.234848\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.85410	+	5.70634i	0.113469	+	0.349222i
$268$	1.23607	−	3.80423i	0.0755049	−	0.232380i
$269$	−9.70820	−	7.05342i	−0.591920	−	0.430055i	0.251082	−	0.967966i	$-0.419214\pi$
$269$	−9.70820	−	7.05342i	−0.591920	−	0.430055i	−0.843002	+	0.537911i	$0.819214\pi$
$270$		0			0
$271$	3.70820	−	11.4127i	0.225257	−	0.693271i	−0.773008	−	0.634396i	$-0.781249\pi$
$271$	3.70820	−	11.4127i	0.225257	−	0.693271i	0.998265	−	0.0588746i	$-0.0187512\pi$
$272$	−1.85410	−	5.70634i	−0.112421	−	0.345998i
$273$		0			0
$274$	−6.00000			−0.362473
$275$		0			0
$276$	−6.00000			−0.361158
$277$	4.85410	−	3.52671i	0.291655	−	0.211900i	−0.432330	−	0.901715i	$-0.642309\pi$
$277$	4.85410	−	3.52671i	0.291655	−	0.211900i	0.723985	+	0.689816i	$0.242309\pi$
$278$	−5.56231	−	17.1190i	−0.333605	−	1.02673i
$279$	1.23607	−	3.80423i	0.0740015	−	0.227753i
$280$		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
$283$	1.85410	+	5.70634i	0.110215	+	0.339207i	0.990919	−	0.134460i	$-0.0429301\pi$
$283$	1.85410	+	5.70634i	0.110215	+	0.339207i	−0.880704	+	0.473667i	$0.842930\pi$
$284$	4.85410	−	3.52671i	0.288038	−	0.209272i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	5.87132	+	18.0701i	0.345372	+	1.06295i
$290$		0			0
$291$	−8.09017	−	5.87785i	−0.474254	−	0.344566i
$292$	9.70820	+	7.05342i	0.568130	+	0.412770i
$293$	−9.27051	+	28.5317i	−0.541589	+	1.66684i	0.187376	+	0.982288i	$0.440002\pi$
$293$	−9.27051	+	28.5317i	−0.541589	+	1.66684i	−0.728965	+	0.684551i	$0.759998\pi$
$294$	2.16312	+	6.65740i	0.126156	+	0.388267i
$295$		0			0
$296$	−2.00000			−0.116248
$297$		0			0
$298$	6.00000			0.347571
$299$	−29.1246	+	21.1603i	−1.68432	+	1.22373i
$300$	1.54508	+	4.75528i	0.0892055	+	0.274546i
$301$		0			0
$302$	9.70820	+	7.05342i	0.558644	+	0.405879i
$303$	−4.85410	−	3.52671i	−0.278861	−	0.202604i
$304$	1.85410	−	5.70634i	0.106340	−	0.327281i
$305$		0			0
$306$	4.85410	−	3.52671i	0.277491	−	0.201609i
$307$	−18.0000			−1.02731			−0.513657	−	0.857996i	$-0.671710\pi$
$307$	−18.0000			−1.02731			−0.513657	+	0.857996i	$0.671710\pi$
$308$		0			0
$309$	4.00000			0.227552
$310$		0			0
$311$	1.85410	+	5.70634i	0.105136	+	0.323577i	0.989762	−	0.142724i	$-0.0455863\pi$
$311$	1.85410	+	5.70634i	0.105136	+	0.323577i	−0.884626	+	0.466301i	$0.845586\pi$
$312$	−1.85410	+	5.70634i	−0.104968	+	0.323058i
$313$	21.0344	+	15.2824i	1.18894	+	0.863813i	0.993152	−	0.116834i	$-0.0372744\pi$
$313$	21.0344	+	15.2824i	1.18894	+	0.863813i	0.195785	+	0.980647i	$0.437274\pi$
$314$	11.3262	+	8.22899i	0.639177	+	0.464389i
$315$		0			0
$316$	3.70820	+	11.4127i	0.208603	+	0.642013i
$317$	9.70820	−	7.05342i	0.545267	−	0.396160i	−0.280770	−	0.959775i	$-0.590590\pi$
$317$	9.70820	−	7.05342i	0.545267	−	0.396160i	0.826037	+	0.563615i	$0.190590\pi$
$318$	12.0000			0.672927
$319$		0			0
$320$		0			0
$321$	−9.70820	+	7.05342i	−0.541859	+	0.393684i
$322$		0			0
$323$	−11.1246	+	34.2380i	−0.618990	+	1.90506i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	24.2705	+	17.6336i	1.34629	+	0.978134i
$326$	6.18034	−	19.0211i	0.342297	−	1.05348i
$327$	−1.85410	−	5.70634i	−0.102532	−	0.315561i
$328$	−4.85410	+	3.52671i	−0.268023	+	0.194730i
$329$		0			0
$330$		0			0
$331$	−28.0000			−1.53902			−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000			−1.53902			−0.769510	+	0.638635i	$0.779499\pi$
$332$		0			0
$333$	−0.618034	−	1.90211i	−0.0338681	−	0.104235i
$334$	−7.41641	+	22.8254i	−0.405808	+	1.24895i
$335$		0			0
$336$		0			0
$337$	11.1246	−	34.2380i	0.605996	−	1.86506i	0.116204	−	0.993225i	$-0.462927\pi$
$337$	11.1246	−	34.2380i	0.605996	−	1.86506i	0.489792	−	0.871839i	$-0.337073\pi$
$338$	7.10739	+	21.8743i	0.386591	+	1.18981i
$339$	4.85410	−	3.52671i	0.263639	−	0.191545i
$340$		0			0
$341$		0			0
$342$	6.00000			0.324443
$343$		0			0
$344$	1.85410	+	5.70634i	0.0999665	+	0.307665i
$345$		0			0
$346$	14.5623	+	10.5801i	0.782874	+	0.568792i
$347$	19.4164	+	14.1068i	1.04233	+	0.757295i	0.970739	−	0.240139i	$-0.0771930\pi$
$347$	19.4164	+	14.1068i	1.04233	+	0.757295i	0.0715889	+	0.997434i	$0.477193\pi$
$348$	−1.85410	+	5.70634i	−0.0993903	+	0.305892i
$349$	5.56231	+	17.1190i	0.297743	+	0.916360i	0.982286	+	0.187387i	$0.0600019\pi$
$349$	5.56231	+	17.1190i	0.297743	+	0.916360i	−0.684543	+	0.728973i	$0.739998\pi$
$350$		0			0
$351$	−6.00000			−0.320256
$352$		0			0
$353$	−30.0000			−1.59674			−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000			−1.59674			−0.798369	+	0.602168i	$0.794304\pi$
$354$	−9.70820	+	7.05342i	−0.515985	+	0.374885i
$355$		0			0
$356$	−1.85410	+	5.70634i	−0.0982672	+	0.302435i
$357$		0			0
$358$		0			0
$359$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$359$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$360$		0			0
$361$	−13.7533	+	9.99235i	−0.723857	+	0.525913i
$362$	2.00000			0.105118
$363$		0			0
$364$		0			0
$365$		0			0
$366$	−1.85410	−	5.70634i	−0.0969155	−	0.298275i
$367$	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
$372$	3.23607	−	2.35114i	0.167782	−	0.121901i
$373$	−6.00000			−0.310668			−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000			−0.310668			−0.155334	+	0.987862i	$0.549645\pi$
$374$		0			0
$375$		0			0
$376$	−4.85410	+	3.52671i	−0.250331	+	0.181876i
$377$	11.1246	+	34.2380i	0.572947	+	1.76335i
$378$		0			0
$379$	−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
$381$	−3.70820	+	11.4127i	−0.189977	+	0.584689i
$382$	−5.56231	−	17.1190i	−0.284592	−	0.875885i
$383$	14.5623	−	10.5801i	0.744099	−	0.540620i	−0.149893	−	0.988702i	$-0.547893\pi$
$383$	14.5623	−	10.5801i	0.744099	−	0.540620i	0.893992	+	0.448083i	$0.147893\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	12.0000			0.610784
$387$	−4.85410	+	3.52671i	−0.246748	+	0.179273i
$388$	−3.09017	−	9.51057i	−0.156880	−	0.482826i
$389$	7.41641	−	22.8254i	0.376027	−	1.15729i	−0.566756	−	0.823885i	$-0.691802\pi$
$389$	7.41641	−	22.8254i	0.376027	−	1.15729i	0.942783	−	0.333406i	$-0.108198\pi$
$390$		0			0
$391$	29.1246	+	21.1603i	1.47289	+	1.07012i
$392$	−2.16312	+	6.65740i	−0.109254	+	0.336249i
$393$	3.70820	+	11.4127i	0.187054	+	0.575693i
$394$	4.85410	−	3.52671i	0.244546	−	0.177673i
$395$		0			0
$396$		0			0
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$	−12.9443	+	9.40456i	−0.648838	+	0.471408i
$399$		0			0
$400$	−1.54508	+	4.75528i	−0.0772542	+	0.237764i
$401$	4.85410	+	3.52671i	0.242402	+	0.176116i	0.702353	−	0.711829i	$-0.252133\pi$
$401$	4.85410	+	3.52671i	0.242402	+	0.176116i	−0.459951	+	0.887945i	$0.652133\pi$
$402$	3.23607	+	2.35114i	0.161400	+	0.117264i
$403$	7.41641	−	22.8254i	0.369438	−	1.13701i
$404$	−1.85410	−	5.70634i	−0.0922450	−	0.283901i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	6.00000			0.297044
$409$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$409$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$410$		0			0
$411$	1.85410	−	5.70634i	0.0914561	−	0.281473i
$412$	3.23607	+	2.35114i	0.159430	+	0.115832i
$413$		0			0
$414$	1.85410	−	5.70634i	0.0911241	−	0.280451i
$415$		0			0
$416$	−4.85410	+	3.52671i	−0.237992	+	0.172911i
$417$	18.0000			0.881464
$418$		0			0
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$		0			0
$421$	−8.03444	−	24.7275i	−0.391575	−	1.20514i	−0.931597	−	0.363492i	$-0.881584\pi$
$421$	−8.03444	−	24.7275i	−0.391575	−	1.20514i	0.540022	−	0.841651i	$-0.318416\pi$
$422$	−1.85410	+	5.70634i	−0.0902563	+	0.277780i
$423$	−4.85410	−	3.52671i	−0.236015	−	0.171475i
$424$	9.70820	+	7.05342i	0.471472	+	0.342545i
$425$	9.27051	−	28.5317i	0.449686	−	1.38399i
$426$	1.85410	+	5.70634i	0.0898315	+	0.276473i
$427$		0			0
$428$	−12.0000			−0.580042
$429$		0			0
$430$		0			0
$431$	−19.4164	+	14.1068i	−0.935255	+	0.679503i	−0.947274	−	0.320425i	$-0.896174\pi$
$431$	−19.4164	+	14.1068i	−0.935255	+	0.679503i	0.0120185	+	0.999928i	$0.496174\pi$
$432$	−0.309017	−	0.951057i	−0.0148676	−	0.0457577i
$433$	0.618034	−	1.90211i	0.0297008	−	0.0914097i	−0.935107	−	0.354365i	$-0.884697\pi$
$433$	0.618034	−	1.90211i	0.0297008	−	0.0914097i	0.964808	+	0.262955i	$0.0846971\pi$
$434$		0			0
$435$		0			0
$436$	1.85410	−	5.70634i	0.0887954	−	0.273284i
$437$	11.1246	+	34.2380i	0.532162	+	1.63783i
$438$	−9.70820	+	7.05342i	−0.463876	+	0.337026i
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$	−7.00000			−0.333333
$442$	29.1246	−	21.1603i	1.38532	−	1.00649i
$443$	−3.70820	−	11.4127i	−0.176182	−	0.542233i	0.823503	−	0.567311i	$-0.192016\pi$
$443$	−3.70820	−	11.4127i	−0.176182	−	0.542233i	−0.999685	+	0.0250786i	$0.992016\pi$
$444$	0.618034	−	1.90211i	0.0293306	−	0.0902703i
$445$		0			0
$446$	−6.47214	−	4.70228i	−0.306465	−	0.222660i
$447$	−1.85410	+	5.70634i	−0.0876960	+	0.269901i
$448$		0			0
$449$	−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
$452$	6.00000			0.282216
$453$	−9.70820	+	7.05342i	−0.456131	+	0.331399i
$454$	3.70820	+	11.4127i	0.174035	+	0.535624i
$455$		0			0
$456$	4.85410	+	3.52671i	0.227314	+	0.165153i
$457$	19.4164	+	14.1068i	0.908261	+	0.659890i	0.940575	−	0.339587i	$-0.110287\pi$
$457$	19.4164	+	14.1068i	0.908261	+	0.659890i	−0.0323133	+	0.999478i	$0.510287\pi$
$458$	−4.32624	+	13.3148i	−0.202152	+	0.622159i
$459$	1.85410	+	5.70634i	0.0865421	+	0.266349i
$460$		0			0
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$		0			0
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	−4.85410	+	3.52671i	−0.225346	+	0.163723i
$465$		0			0
$466$	1.85410	−	5.70634i	0.0858896	−	0.264341i
$467$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$467$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$468$	−4.85410	−	3.52671i	−0.224381	−	0.163022i
$469$		0			0
$470$		0			0
$471$	−11.3262	+	8.22899i	−0.521885	+	0.379172i
$472$	−12.0000			−0.552345
$473$		0			0
$474$	−12.0000			−0.551178
$475$	24.2705	−	17.6336i	1.11361	−	0.809083i
$476$		0			0
$477$	−3.70820	+	11.4127i	−0.169787	+	0.522551i
$478$	−19.4164	−	14.1068i	−0.888086	−	0.645232i
$479$	−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
$481$	−3.70820	−	11.4127i	−0.169080	−	0.520373i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	4.94427	+	15.2169i	0.224046	+	0.689544i	0.998387	+	0.0567748i	$0.0180817\pi$
$487$	4.94427	+	15.2169i	0.224046	+	0.689544i	−0.774341	+	0.632769i	$0.781918\pi$
$488$	1.85410	−	5.70634i	0.0839313	−	0.258314i
$489$	16.1803	+	11.7557i	0.731700	+	0.531611i
$490$		0			0
$491$	−11.1246	+	34.2380i	−0.502047	+	1.54514i	0.303633	+	0.952789i	$0.401800\pi$
$491$	−11.1246	+	34.2380i	−0.502047	+	1.54514i	−0.805679	+	0.592352i	$0.798200\pi$
$492$	−1.85410	−	5.70634i	−0.0835894	−	0.257262i
$493$	29.1246	−	21.1603i	1.31171	−	0.953011i
$494$	36.0000			1.61972
$495$		0			0
$496$	4.00000			0.179605
$497$		0			0
$498$		0			0
$499$	1.23607	−	3.80423i	0.0553340	−	0.170301i	−0.919570	−	0.392926i	$-0.871463\pi$
$499$	1.23607	−	3.80423i	0.0553340	−	0.170301i	0.974904	+	0.222626i	$0.0714628\pi$
$500$		0			0
$501$	−19.4164	−	14.1068i	−0.867461	−	0.630247i
$502$	7.41641	−	22.8254i	0.331010	−	1.01875i
$503$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$503$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−23.0000			−1.02147
$508$	−9.70820	+	7.05342i	−0.430732	+	0.312945i
$509$	−3.70820	−	11.4127i	−0.164363	−	0.505858i	0.834626	−	0.550818i	$-0.185684\pi$
$509$	−3.70820	−	11.4127i	−0.164363	−	0.505858i	−0.998989	+	0.0449597i	$0.985684\pi$
$510$		0			0
$511$		0			0
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−1.85410	+	5.70634i	−0.0818606	+	0.251941i
$514$	5.56231	+	17.1190i	0.245343	+	0.755087i
$515$		0			0
$516$	−6.00000			−0.264135
$517$		0			0
$518$		0			0
$519$	−14.5623	+	10.5801i	−0.639214	+	0.464416i
$520$		0			0
$521$	12.9787	−	39.9444i	0.568608	−	1.74999i	−0.0883730	−	0.996087i	$-0.528167\pi$
$521$	12.9787	−	39.9444i	0.568608	−	1.74999i	0.656981	−	0.753907i	$-0.271833\pi$
$522$	−4.85410	−	3.52671i	−0.212458	−	0.154360i
$523$	−4.85410	−	3.52671i	−0.212255	−	0.154212i	0.476578	−	0.879132i	$-0.341877\pi$
$523$	−4.85410	−	3.52671i	−0.212255	−	0.154212i	−0.688833	+	0.724920i	$0.741877\pi$
$524$	−3.70820	+	11.4127i	−0.161994	+	0.498565i
$525$		0			0
$526$	−19.4164	+	14.1068i	−0.846596	+	0.615088i
$527$	−24.0000			−1.04546
$528$		0			0
$529$	13.0000			0.565217
$530$		0			0
$531$	−3.70820	−	11.4127i	−0.160922	−	0.495268i
$532$		0			0
$533$	−29.1246	−	21.1603i	−1.26153	−	0.916553i
$534$	−4.85410	−	3.52671i	−0.210058	−	0.152616i
$535$		0			0
$536$	1.23607	+	3.80423i	0.0533900	+	0.164318i
$537$		0			0
$538$	12.0000			0.517357
$539$		0			0
$540$		0			0
$541$	14.5623	−	10.5801i	0.626082	−	0.454876i	−0.228958	−	0.973436i	$-0.573532\pi$
$541$	14.5623	−	10.5801i	0.626082	−	0.454876i	0.855041	+	0.518561i	$0.173532\pi$
$542$	3.70820	+	11.4127i	0.159281	+	0.490217i
$543$	−0.618034	+	1.90211i	−0.0265224	+	0.0816275i
$544$	4.85410	+	3.52671i	0.208118	+	0.151207i
$545$		0			0
$546$		0			0
$547$	−1.85410	−	5.70634i	−0.0792757	−	0.243985i	0.903562	−	0.428457i	$-0.140943\pi$
$547$	−1.85410	−	5.70634i	−0.0792757	−	0.243985i	−0.982838	+	0.184472i	$0.940943\pi$
$548$	4.85410	−	3.52671i	0.207357	−	0.150654i
$549$	6.00000			0.256074
$550$		0			0
$551$	36.0000			1.53365
$552$	4.85410	−	3.52671i	0.206604	−	0.150107i
$553$		0			0
$554$	−1.85410	+	5.70634i	−0.0787732	+	0.242439i
$555$		0			0
$556$	14.5623	+	10.5801i	0.617579	+	0.448698i
$557$	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	$-0.0245380\pi$
$558$	1.23607	+	3.80423i	0.0523269	+	0.161046i
$559$	−29.1246	+	21.1603i	−1.23184	+	0.894984i
$560$		0			0
$561$		0			0
$562$	6.00000			0.253095
$563$	19.4164	−	14.1068i	0.818304	−	0.594533i	−0.0979222	−	0.995194i	$-0.531220\pi$
$563$	19.4164	−	14.1068i	0.818304	−	0.594533i	0.916226	+	0.400661i	$0.131220\pi$
$564$	−1.85410	−	5.70634i	−0.0780718	−	0.240280i
$565$		0			0
$566$	−4.85410	−	3.52671i	−0.204033	−	0.148239i
$567$		0			0
$568$	−1.85410	+	5.70634i	−0.0777964	+	0.239433i
$569$	−9.27051	−	28.5317i	−0.388640	−	1.19611i	−0.933805	−	0.357782i	$-0.883533\pi$
$569$	−9.27051	−	28.5317i	−0.388640	−	1.19611i	0.545165	−	0.838329i	$-0.316467\pi$
$570$		0			0
$571$	18.0000			0.753277			0.376638	−	0.926360i	$-0.377080\pi$
$571$	18.0000			0.753277			0.376638	+	0.926360i	$0.377080\pi$
$572$		0			0
$573$	18.0000			0.751961
$574$		0			0
$575$	−9.27051	−	28.5317i	−0.386607	−	1.18985i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	30.7426	+	22.3358i	1.27983	+	0.929853i	0.999548	−	0.0300636i	$-0.00957099\pi$
$577$	30.7426	+	22.3358i	1.27983	+	0.929853i	0.280285	+	0.959917i	$0.409571\pi$
$578$	−15.3713	−	11.1679i	−0.639363	−	0.464524i
$579$	−3.70820	+	11.4127i	−0.154108	+	0.474295i
$580$		0			0
$581$		0			0
$582$	10.0000			0.414513
$583$		0			0
$584$	−12.0000			−0.496564
$585$		0			0
$586$	−9.27051	−	28.5317i	−0.382961	−	1.17863i
$587$	−3.70820	+	11.4127i	−0.153054	+	0.471052i	−0.997959	−	0.0638654i	$-0.979657\pi$
$587$	−3.70820	+	11.4127i	−0.153054	+	0.471052i	0.844905	+	0.534917i	$0.179657\pi$
$588$	−5.66312	−	4.11450i	−0.233543	−	0.169679i
$589$	−19.4164	−	14.1068i	−0.800039	−	0.581262i
$590$		0			0
$591$	1.85410	+	5.70634i	0.0762676	+	0.234727i
$592$	1.61803	−	1.17557i	0.0665008	−	0.0483157i
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$		0			0
$595$		0			0
$596$	−4.85410	+	3.52671i	−0.198832	+	0.144460i
$597$	−4.94427	−	15.2169i	−0.202356	−	0.622786i
$598$	11.1246	−	34.2380i	0.454919	−	1.40010i
$599$	14.5623	+	10.5801i	0.595000	+	0.432293i	0.844101	−	0.536185i	$-0.180135\pi$
$599$	14.5623	+	10.5801i	0.595000	+	0.432293i	−0.249101	+	0.968478i	$0.580135\pi$
$600$	−4.04508	−	2.93893i	−0.165140	−	0.119981i
$601$	−7.41641	+	22.8254i	−0.302522	+	0.931066i	0.678069	+	0.734998i	$0.262817\pi$
$601$	−7.41641	+	22.8254i	−0.302522	+	0.931066i	−0.980590	+	0.196067i	$0.937183\pi$
$602$		0			0
$603$	−3.23607	+	2.35114i	−0.131783	+	0.0957459i
$604$	−12.0000			−0.488273
$605$		0			0
$606$	6.00000			0.243733
$607$	29.1246	−	21.1603i	1.18213	−	0.858869i	0.189721	−	0.981838i	$-0.439242\pi$
$607$	29.1246	−	21.1603i	1.18213	−	0.858869i	0.992410	+	0.122969i	$0.0392416\pi$
$608$	1.85410	+	5.70634i	0.0751938	+	0.231423i
$609$		0			0
$610$		0			0
$611$	−29.1246	−	21.1603i	−1.17826	−	0.856053i
$612$	−1.85410	+	5.70634i	−0.0749476	+	0.230665i
$613$	−12.9787	−	39.9444i	−0.524205	−	1.61334i	−0.765882	−	0.642981i	$-0.777697\pi$
$613$	−12.9787	−	39.9444i	−0.524205	−	1.61334i	0.241677	−	0.970357i	$-0.422303\pi$
$614$	14.5623	−	10.5801i	0.587687	−	0.426979i
$615$		0			0
$616$		0			0
$617$	30.0000			1.20775			0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000			1.20775			0.603877	+	0.797077i	$0.293622\pi$
$618$	−3.23607	+	2.35114i	−0.130174	+	0.0945768i
$619$	−8.65248	−	26.6296i	−0.347772	−	1.07033i	−0.960083	−	0.279716i	$-0.909760\pi$
$619$	−8.65248	−	26.6296i	−0.347772	−	1.07033i	0.612310	−	0.790617i	$-0.290240\pi$
$620$		0			0
$621$	4.85410	+	3.52671i	0.194788	+	0.141522i
$622$	−4.85410	−	3.52671i	−0.194632	−	0.141408i
$623$		0			0
$624$	−1.85410	−	5.70634i	−0.0742235	−	0.228436i
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$	−26.0000			−1.03917
$627$		0			0
$628$	−14.0000			−0.558661
$629$	−9.70820	+	7.05342i	−0.387091	+	0.281238i
$630$		0			0
$631$	−6.18034	+	19.0211i	−0.246035	+	0.757219i	0.749429	+	0.662085i	$0.230328\pi$
$631$	−6.18034	+	19.0211i	−0.246035	+	0.757219i	−0.995464	+	0.0951345i	$0.969672\pi$
$632$	−9.70820	−	7.05342i	−0.386172	−	0.280570i
$633$	−4.85410	−	3.52671i	−0.192933	−	0.140174i
$634$	−3.70820	+	11.4127i	−0.147272	+	0.453255i
$635$		0			0
$636$	−9.70820	+	7.05342i	−0.384955	+	0.279686i
$637$	−42.0000			−1.66410
$638$		0			0
$639$	−6.00000			−0.237356
$640$		0			0
$641$	9.27051	+	28.5317i	0.366163	+	1.12693i	0.949250	+	0.314524i	$0.101845\pi$
$641$	9.27051	+	28.5317i	0.366163	+	1.12693i	−0.583086	+	0.812410i	$0.698155\pi$
$642$	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	$0.674868\pi$
$644$		0			0
$645$		0			0
$646$	−11.1246	−	34.2380i	−0.437692	−	1.34708i
$647$	33.9787	−	24.6870i	1.33584	−	0.970545i	0.336255	−	0.941771i	$-0.390840\pi$
$647$	33.9787	−	24.6870i	1.33584	−	0.970545i	0.999586	−	0.0287744i	$-0.00916045\pi$
$648$	1.00000			0.0392837
$649$		0			0
$650$	−30.0000			−1.17670
$651$		0			0
$652$	6.18034	+	19.0211i	0.242041	+	0.744925i
$653$	−7.41641	+	22.8254i	−0.290226	+	0.893225i	0.694557	+	0.719438i	$0.255601\pi$
$653$	−7.41641	+	22.8254i	−0.290226	+	0.893225i	−0.984783	+	0.173787i	$0.944399\pi$
$654$	4.85410	+	3.52671i	0.189810	+	0.137905i
$655$		0			0
$656$	1.85410	−	5.70634i	0.0723905	−	0.222795i
$657$	−3.70820	−	11.4127i	−0.144671	−	0.445251i
$658$		0			0
$659$	24.0000			0.934907			0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000			0.934907			0.467454	+	0.884018i	$0.345171\pi$
$660$		0			0
$661$	−14.0000			−0.544537			−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000			−0.544537			−0.272268	+	0.962221i	$0.587774\pi$
$662$	22.6525	−	16.4580i	0.880413	−	0.639658i
$663$	11.1246	+	34.2380i	0.432044	+	1.32970i
$664$		0			0
$665$		0			0
$666$	1.61803	+	1.17557i	0.0626975	+	0.0455524i
$667$	11.1246	−	34.2380i	0.430747	−	1.32570i
$668$	−7.41641	−	22.8254i	−0.286949	−	0.883140i
$669$	6.47214	−	4.70228i	0.250227	−	0.181801i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	9.70820	−	7.05342i	0.374224	−	0.271889i	−0.384736	−	0.923026i	$-0.625708\pi$
$673$	9.70820	−	7.05342i	0.374224	−	0.271889i	0.758960	+	0.651137i	$0.225708\pi$
$674$	11.1246	+	34.2380i	0.428504	+	1.31880i
$675$	1.54508	−	4.75528i	0.0594703	−	0.183031i
$676$	−18.6074	−	13.5191i	−0.715669	−	0.519964i
$677$	4.85410	+	3.52671i	0.186558	+	0.135543i	0.677144	−	0.735850i	$-0.263217\pi$
$677$	4.85410	+	3.52671i	0.186558	+	0.135543i	−0.490586	+	0.871393i	$0.663217\pi$
$678$	−1.85410	+	5.70634i	−0.0712064	+	0.219151i
$679$		0			0
$680$		0			0
$681$	−12.0000			−0.459841
$682$		0			0
$683$	24.0000			0.918334			0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000			0.918334			0.459167	+	0.888350i	$0.348148\pi$
$684$	−4.85410	+	3.52671i	−0.185601	+	0.134847i
$685$		0			0
$686$		0			0
$687$	−11.3262	−	8.22899i	−0.432123	−	0.313956i
$688$	−4.85410	−	3.52671i	−0.185061	−	0.134455i
$689$	−22.2492	+	68.4761i	−0.847628	+	2.60873i
$690$		0			0
$691$	22.6525	−	16.4580i	0.861741	−	0.626091i	−0.0666172	−	0.997779i	$-0.521221\pi$
$691$	22.6525	−	16.4580i	0.861741	−	0.626091i	0.928358	+	0.371687i	$0.121221\pi$
$692$	−18.0000			−0.684257
$693$		0			0
$694$	−24.0000			−0.911028
$695$		0			0
$696$	−1.85410	−	5.70634i	−0.0702796	−	0.216298i
$697$	−11.1246	+	34.2380i	−0.421375	+	1.29686i
$698$	−14.5623	−	10.5801i	−0.551191	−	0.400464i
$699$	4.85410	+	3.52671i	0.183599	+	0.133392i
$700$		0			0
$701$	−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	$0.936145\pi$
$702$	4.85410	−	3.52671i	0.183206	−	0.133107i
$703$	−12.0000			−0.452589
$704$		0			0
$705$		0			0
$706$	24.2705	−	17.6336i	0.913433	−	0.663648i
$707$		0			0
$708$	3.70820	−	11.4127i	0.139363	−	0.428915i
$709$	−8.09017	−	5.87785i	−0.303833	−	0.220747i	0.425413	−	0.904999i	$-0.360129\pi$
$709$	−8.09017	−	5.87785i	−0.303833	−	0.220747i	−0.729246	+	0.684252i	$0.760129\pi$
$710$		0			0
$711$	3.70820	−	11.4127i	0.139069	−	0.428009i
$712$	−1.85410	−	5.70634i	−0.0694854	−	0.213854i
$713$	−19.4164	+	14.1068i	−0.727150	+	0.528306i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	19.4164	−	14.1068i	0.725119	−	0.526830i
$718$		0			0
$719$	5.56231	−	17.1190i	0.207439	−	0.638432i	−0.792165	−	0.610306i	$-0.791046\pi$
$719$	5.56231	−	17.1190i	0.207439	−	0.638432i	0.999604	−	0.0281252i	$-0.00895370\pi$
$720$		0			0
$721$		0			0
$722$	5.25329	−	16.1680i	0.195507	−	0.601709i
$723$		0			0
$724$	−1.61803	+	1.17557i	−0.0601338	+	0.0436897i
$725$	−30.0000			−1.11417
$726$		0			0
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	29.1246	+	21.1603i	1.07721	+	0.782641i
$732$	4.85410	+	3.52671i	0.179413	+	0.130351i
$733$	1.85410	−	5.70634i	0.0684828	−	0.210768i	−0.910958	−	0.412498i	$-0.864656\pi$
$733$	1.85410	−	5.70634i	0.0684828	−	0.210768i	0.979441	+	0.201730i	$0.0646563\pi$
$734$	2.47214	+	7.60845i	0.0912482	+	0.280833i
$735$		0			0
$736$	6.00000			0.221163
$737$		0			0
$738$	6.00000			0.220863
$739$	−24.2705	+	17.6336i	−0.892805	+	0.648661i	−0.936608	−	0.350379i	$-0.886053\pi$
$739$	−24.2705	+	17.6336i	−0.892805	+	0.648661i	0.0438028	+	0.999040i	$0.486053\pi$
$740$		0			0
$741$	−11.1246	+	34.2380i	−0.408673	+	1.25777i
$742$		0			0
$743$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$743$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$744$	−1.23607	+	3.80423i	−0.0453165	+	0.139470i
$745$		0			0
$746$	4.85410	−	3.52671i	0.177721	−	0.129122i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.23607	+	3.80423i	0.0451048	+	0.138818i	0.971073	−	0.238784i	$-0.0767487\pi$
$751$	1.23607	+	3.80423i	0.0451048	+	0.138818i	−0.925968	+	0.377602i	$0.876749\pi$
$752$	1.85410	−	5.70634i	0.0676121	−	0.208089i
$753$	19.4164	+	14.1068i	0.707573	+	0.514082i
$754$	−29.1246	−	21.1603i	−1.06066	−	0.770612i
$755$		0			0
$756$		0			0
$757$	1.61803	−	1.17557i	0.0588084	−	0.0427268i	−0.557993	−	0.829846i	$-0.688428\pi$
$757$	1.61803	−	1.17557i	0.0588084	−	0.0427268i	0.616801	+	0.787119i	$0.288428\pi$
$758$	20.0000			0.726433
$759$		0			0
$760$		0			0
$761$	4.85410	−	3.52671i	0.175961	−	0.127843i	−0.496319	−	0.868140i	$-0.665315\pi$
$761$	4.85410	−	3.52671i	0.175961	−	0.127843i	0.672280	+	0.740297i	$0.265315\pi$
$762$	−3.70820	−	11.4127i	−0.134334	−	0.413438i
$763$		0			0
$764$	14.5623	+	10.5801i	0.526846	+	0.382776i
$765$		0			0
$766$	−5.56231	+	17.1190i	−0.200974	+	0.618535i
$767$	−22.2492	−	68.4761i	−0.803373	−	2.47253i
$768$	0.809017	−	0.587785i	0.0291929	−	0.0212099i
$769$	−12.0000			−0.432731			−0.216366	−	0.976312i	$-0.569420\pi$
$769$	−12.0000			−0.432731			−0.216366	+	0.976312i	$0.569420\pi$
$770$		0			0
$771$	−18.0000			−0.648254
$772$	−9.70820	+	7.05342i	−0.349406	+	0.253858i
$773$	−11.1246	−	34.2380i	−0.400124	−	1.23146i	−0.924898	−	0.380215i	$-0.875850\pi$
$773$	−11.1246	−	34.2380i	−0.400124	−	1.23146i	0.524774	−	0.851242i	$-0.324150\pi$
$774$	1.85410	−	5.70634i	0.0666443	−	0.205110i
$775$	16.1803	+	11.7557i	0.581215	+	0.422277i
$776$	8.09017	+	5.87785i	0.290420	+	0.211003i
$777$		0			0
$778$	7.41641	+	22.8254i	0.265891	+	0.818329i
$779$	−29.1246	+	21.1603i	−1.04350	+	0.758145i
$780$		0			0
$781$		0			0
$782$	−36.0000			−1.28736
$783$	4.85410	−	3.52671i	0.173471	−	0.126034i
$784$	−2.16312	−	6.65740i	−0.0772542	−	0.237764i
$785$		0			0
$786$	−9.70820	−	7.05342i	−0.346280	−	0.251587i
$787$	−4.85410	−	3.52671i	−0.173030	−	0.125714i	0.497900	−	0.867235i	$-0.334105\pi$
$787$	−4.85410	−	3.52671i	−0.173030	−	0.125714i	−0.670930	+	0.741521i	$0.734105\pi$
$788$	−1.85410	+	5.70634i	−0.0660496	+	0.203280i
$789$	−7.41641	−	22.8254i	−0.264031	−	0.812604i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	36.0000			1.27840
$794$	−1.61803	+	1.17557i	−0.0574219	+	0.0417194i
$795$		0			0
$796$	4.94427	−	15.2169i	0.175245	−	0.539349i
$797$	−38.8328	−	28.2137i	−1.37553	−	0.999380i	−0.997282	−	0.0736754i	$-0.976527\pi$
$797$	−38.8328	−	28.2137i	−1.37553	−	0.999380i	−0.378247	−	0.925705i	$-0.623473\pi$
$798$		0			0
$799$	−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
$802$	−6.00000			−0.211867
$803$		0			0
$804$	−4.00000			−0.141069
$805$		0			0
$806$	7.41641	+	22.8254i	0.261232	+	0.803989i
$807$	−3.70820	+	11.4127i	−0.130535	+	0.401745i
$808$	4.85410	+	3.52671i	0.170767	+	0.124069i
$809$	−14.5623	−	10.5801i	−0.511983	−	0.371978i	0.301592	−	0.953437i	$-0.402482\pi$
$809$	−14.5623	−	10.5801i	−0.511983	−	0.371978i	−0.813575	+	0.581459i	$0.802482\pi$
$810$		0			0
$811$	−1.85410	−	5.70634i	−0.0651063	−	0.200377i	0.913211	−	0.407486i	$-0.133594\pi$
$811$	−1.85410	−	5.70634i	−0.0651063	−	0.200377i	−0.978318	+	0.207109i	$0.933594\pi$
$812$		0			0
$813$	−12.0000			−0.420858
$814$		0			0
$815$		0			0
$816$	−4.85410	+	3.52671i	−0.169928	+	0.123460i
$817$	11.1246	+	34.2380i	0.389201	+	1.19784i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	12.9787	−	39.9444i	0.452960	−	1.39407i	−0.420553	−	0.907268i	$-0.638164\pi$
$821$	12.9787	−	39.9444i	0.452960	−	1.39407i	0.873513	−	0.486800i	$-0.161836\pi$
$822$	1.85410	+	5.70634i	0.0646692	+	0.199031i
$823$	32.3607	−	23.5114i	1.12802	−	0.819556i	0.142617	−	0.989778i	$-0.454448\pi$
$823$	32.3607	−	23.5114i	1.12802	−	0.819556i	0.985406	+	0.170222i	$0.0544484\pi$
$824$	−4.00000			−0.139347
$825$		0			0
$826$		0			0
$827$	38.8328	−	28.2137i	1.35035	−	0.981086i	0.351355	−	0.936242i	$-0.385721\pi$
$827$	38.8328	−	28.2137i	1.35035	−	0.981086i	0.998994	−	0.0448440i	$-0.0142791\pi$
$828$	1.85410	+	5.70634i	0.0644345	+	0.198309i
$829$	−10.5066	+	32.3359i	−0.364909	+	1.12307i	0.585130	+	0.810940i	$0.301044\pi$
$829$	−10.5066	+	32.3359i	−0.364909	+	1.12307i	−0.950038	+	0.312133i	$0.898956\pi$
$830$		0			0
$831$	−4.85410	−	3.52671i	−0.168387	−	0.122340i
$832$	1.85410	−	5.70634i	0.0642794	−	0.197832i
$833$	12.9787	+	39.9444i	0.449686	+	1.38399i
$834$	−14.5623	+	10.5801i	−0.504251	+	0.366360i
$835$		0			0
$836$		0			0
$837$	−4.00000			−0.138260
$838$	−19.4164	+	14.1068i	−0.670729	+	0.487313i
$839$	−9.27051	−	28.5317i	−0.320054	−	0.985024i	−0.973624	−	0.228158i	$-0.926730\pi$
$839$	−9.27051	−	28.5317i	−0.320054	−	0.985024i	0.653571	−	0.756866i	$-0.273270\pi$
$840$		0			0
$841$	−5.66312	−	4.11450i	−0.195280	−	0.141879i
$842$	21.0344	+	15.2824i	0.724895	+	0.526667i
$843$	−1.85410	+	5.70634i	−0.0638587	+	0.196537i
$844$	−1.85410	−	5.70634i	−0.0638208	−	0.196420i
$845$		0			0
$846$	6.00000			0.206284
$847$		0			0
$848$	−12.0000			−0.412082
$849$	4.85410	−	3.52671i	0.166592	−	0.121036i
$850$	9.27051	+	28.5317i	0.317976	+	0.978629i
$851$	−3.70820	+	11.4127i	−0.127116	+	0.391222i
$852$	−4.85410	−	3.52671i	−0.166299	−	0.120823i
$853$	−24.2705	−	17.6336i	−0.831006	−	0.603762i	0.0888375	−	0.996046i	$-0.471685\pi$
$853$	−24.2705	−	17.6336i	−0.831006	−	0.603762i	−0.919844	+	0.392285i	$0.871685\pi$
$854$		0			0
$855$		0			0
$856$	9.70820	−	7.05342i	0.331820	−	0.241081i
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$		0			0
$859$	−4.00000			−0.136478			−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000			−0.136478			−0.0682391	+	0.997669i	$0.521738\pi$
$860$		0			0
$861$		0			0
$862$	7.41641	−	22.8254i	0.252604	−	0.777435i
$863$	43.6869	+	31.7404i	1.48712	+	1.08046i	0.975174	+	0.221438i	$0.0710750\pi$
$863$	43.6869	+	31.7404i	1.48712	+	1.08046i	0.511946	+	0.859018i	$0.328925\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$		0			0
$866$	0.618034	+	1.90211i	0.0210016	+	0.0646364i
$867$	15.3713	−	11.1679i	0.522037	−	0.379282i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−19.4164	+	14.1068i	−0.657900	+	0.477992i
$872$	1.85410	+	5.70634i	0.0627878	+	0.193241i
$873$	−3.09017	+	9.51057i	−0.104586	+	0.321884i
$874$	−29.1246	−	21.1603i	−0.985155	−	0.715757i
$875$		0			0
$876$	3.70820	−	11.4127i	0.125289	−	0.385599i
$877$	5.56231	+	17.1190i	0.187826	+	0.578068i	0.999986	−	0.00536681i	$-0.00170832\pi$
$877$	5.56231	+	17.1190i	0.187826	+	0.578068i	−0.812160	+	0.583435i	$0.801708\pi$
$878$		0			0
$879$	30.0000			1.01187
$880$		0			0
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$	5.66312	−	4.11450i	0.190687	−	0.138542i
$883$	16.0689	+	49.4549i	0.540761	+	1.66429i	0.730861	+	0.682526i	$0.239119\pi$
$883$	16.0689	+	49.4549i	0.540761	+	1.66429i	−0.190100	+	0.981765i	$0.560881\pi$
$884$	−11.1246	+	34.2380i	−0.374161	+	1.15155i
$885$		0			0
$886$	9.70820	+	7.05342i	0.326153	+	0.236964i
$887$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$887$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$888$	0.618034	+	1.90211i	0.0207399	+	0.0638307i
$889$		0			0
$890$		0			0
$891$		0			0
$892$	8.00000			0.267860
$893$	−29.1246	+	21.1603i	−0.974618	+	0.708101i
$894$	−1.85410	−	5.70634i	−0.0620104	−	0.190849i
$895$		0			0
$896$		0			0
$897$	29.1246	+	21.1603i	0.972442	+	0.706521i
$898$	1.85410	−	5.70634i	0.0618722	−	0.190423i
$899$	7.41641	+	22.8254i	0.247351	+	0.761268i
$900$	4.04508	−	2.93893i	0.134836	−	0.0979642i
$901$	72.0000			2.39867
$902$		0			0
$903$		0			0
$904$	−4.85410	+	3.52671i	−0.161445	+	0.117297i
$905$		0			0
$906$	3.70820	−	11.4127i	0.123197	−	0.379161i
$907$	22.6525	+	16.4580i	0.752163	+	0.546478i	0.896497	−	0.443051i	$-0.146104\pi$
$907$	22.6525	+	16.4580i	0.752163	+	0.546478i	−0.144333	+	0.989529i	$0.546104\pi$
$908$	−9.70820	−	7.05342i	−0.322178	−	0.234076i
$909$	−1.85410	+	5.70634i	−0.0614967	+	0.189267i
$910$		0			0
$911$	4.85410	−	3.52671i	0.160824	−	0.116845i	−0.504463	−	0.863433i	$-0.668309\pi$
$911$	4.85410	−	3.52671i	0.160824	−	0.116845i	0.665286	+	0.746588i	$0.268309\pi$
$912$	−6.00000			−0.198680
$913$		0			0
$914$	−24.0000			−0.793849
$915$		0			0
$916$	−4.32624	−	13.3148i	−0.142943	−	0.439933i
$917$		0			0
$918$	−4.85410	−	3.52671i	−0.160209	−	0.116399i
$919$	−29.1246	−	21.1603i	−0.960732	−	0.698013i	−0.00741159	−	0.999973i	$-0.502359\pi$
$919$	−29.1246	−	21.1603i	−0.960732	−	0.698013i	−0.953321	+	0.301960i	$0.902359\pi$
$920$		0			0
$921$	5.56231	+	17.1190i	0.183284	+	0.564091i
$922$	−14.5623	+	10.5801i	−0.479584	+	0.348438i
$923$	−36.0000			−1.18495
$924$		0			0
$925$	10.0000			0.328798
$926$	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
$929$	4.85410	+	3.52671i	0.159258	+	0.115708i	0.664560	−	0.747235i	$-0.268619\pi$
$929$	4.85410	+	3.52671i	0.159258	+	0.115708i	−0.505302	+	0.862942i	$0.668619\pi$
$930$		0			0
$931$	−12.9787	+	39.9444i	−0.425360	+	1.30912i
$932$	1.85410	+	5.70634i	0.0607331	+	0.186917i
$933$	4.85410	−	3.52671i	0.158916	−	0.115459i
$934$		0			0
$935$		0			0
$936$	6.00000			0.196116
$937$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$937$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$938$		0			0
$939$	8.03444	−	24.7275i	0.262194	−	0.806950i
$940$		0			0
$941$	24.2705	+	17.6336i	0.791196	+	0.574838i	0.908318	−	0.418280i	$-0.137367\pi$
$941$	24.2705	+	17.6336i	0.791196	+	0.574838i	−0.117122	+	0.993118i	$0.537367\pi$
$942$	4.32624	−	13.3148i	0.140956	−	0.433819i
$943$	11.1246	+	34.2380i	0.362267	+	1.11494i
$944$	9.70820	−	7.05342i	0.315975	−	0.229569i
$945$		0			0
$946$		0			0
$947$	36.0000			1.16984			0.584921	−	0.811090i	$-0.301125\pi$
$947$	36.0000			1.16984			0.584921	+	0.811090i	$0.301125\pi$
$948$	9.70820	−	7.05342i	0.315308	−	0.229085i
$949$	−22.2492	−	68.4761i	−0.722240	−	2.22283i
$950$	−9.27051	+	28.5317i	−0.300775	+	0.925690i
$951$	−9.70820	−	7.05342i	−0.314810	−	0.228723i
$952$		0			0
$953$	5.56231	−	17.1190i	0.180181	−	0.554539i	−0.819651	−	0.572863i	$-0.805833\pi$
$953$	5.56231	−	17.1190i	0.180181	−	0.554539i	0.999832	+	0.0183233i	$0.00583282\pi$
$954$	−3.70820	−	11.4127i	−0.120058	−	0.369499i
$955$		0			0
$956$	24.0000			0.776215
$957$		0			0
$958$	24.0000			0.775405
$959$		0			0
$960$		0			0
$961$	−4.63525	+	14.2658i	−0.149524	+	0.460189i
$962$	9.70820	+	7.05342i	0.313005	+	0.227411i
$963$	9.70820	+	7.05342i	0.312842	+	0.227293i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−12.0000			−0.385894			−0.192947	−	0.981209i	$-0.561805\pi$
$967$	−12.0000			−0.385894			−0.192947	+	0.981209i	$0.561805\pi$
$968$		0			0
$969$	36.0000			1.15649
$970$		0			0
$971$	−3.70820	−	11.4127i	−0.119002	−	0.366250i	0.873759	−	0.486360i	$-0.161675\pi$
$971$	−3.70820	−	11.4127i	−0.119002	−	0.366250i	−0.992761	+	0.120109i	$0.961675\pi$
$972$	−0.309017	+	0.951057i	−0.00991172	+	0.0305052i
$973$		0			0
$974$	−12.9443	−	9.40456i	−0.414761	−	0.301342i
$975$	9.27051	−	28.5317i	0.296894	−	0.913746i
$976$	1.85410	+	5.70634i	0.0593484	+	0.182655i
$977$	−33.9787	+	24.6870i	−1.08708	+	0.789806i	−0.978903	−	0.204326i	$-0.934500\pi$
$977$	−33.9787	+	24.6870i	−1.08708	+	0.789806i	−0.108172	+	0.994132i	$0.534500\pi$
$978$	−20.0000			−0.639529
$979$		0			0
$980$		0			0
$981$	−4.85410	+	3.52671i	−0.154980	+	0.112599i
$982$	−11.1246	−	34.2380i	−0.355001	−	1.09258i
$983$	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
$987$		0			0
$988$	−29.1246	+	21.1603i	−0.926577	+	0.673198i
$989$	36.0000			1.14473
$990$		0			0
$991$	−20.0000			−0.635321			−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000			−0.635321			−0.317660	+	0.948205i	$0.602897\pi$
$992$	−3.23607	+	2.35114i	−0.102745	+	0.0746488i
$993$	8.65248	+	26.6296i	0.274578	+	0.845064i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	5.56231	−	17.1190i	0.176160	−	0.542165i	−0.823525	−	0.567281i	$-0.807995\pi$
$997$	5.56231	−	17.1190i	0.176160	−	0.542165i	0.999685	+	0.0251159i	$0.00799548\pi$
$998$	1.23607	+	3.80423i	0.0391270	+	0.120421i
$999$	−1.61803	+	1.17557i	−0.0511923	+	0.0371934i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
726.2.a.b.1.1	✓	1	11.2	odd	10
726.2.a.g.1.1	yes	1	11.9	even	5
726.2.e.h.487.1		4	1.1	even	1	trivial
726.2.e.h.493.1		4	11.5	even	5	inner
726.2.e.h.511.1		4	11.3	even	5	inner
726.2.e.h.565.1		4	11.4	even	5	inner
726.2.e.p.487.1		4	11.10	odd	2
726.2.e.p.493.1		4	11.6	odd	10
726.2.e.p.511.1		4	11.8	odd	10
726.2.e.p.565.1		4	11.7	odd	10
2178.2.a.c.1.1		1	33.20	odd	10
2178.2.a.i.1.1		1	33.2	even	10
5808.2.a.ba.1.1		1	44.35	even	10
5808.2.a.bb.1.1		1	44.31	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{6} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{6} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.00000 q^{12} +(-4.85410 + 3.52671i) q^{13} +(-0.809017 - 0.587785i) q^{16} +(4.85410 + 3.52671i) q^{17} +(0.309017 - 0.951057i) q^{18} +(1.85410 + 5.70634i) q^{19} +6.00000 q^{23} +(0.809017 - 0.587785i) q^{24} +(-1.54508 - 4.75528i) q^{25} +(1.85410 - 5.70634i) q^{26} +(0.809017 + 0.587785i) q^{27} +(1.85410 - 5.70634i) q^{29} +(-3.23607 + 2.35114i) q^{31} +1.00000 q^{32} -6.00000 q^{34} +(0.309017 + 0.951057i) q^{36} +(-0.618034 + 1.90211i) q^{37} +(-4.85410 - 3.52671i) q^{38} +(4.85410 + 3.52671i) q^{39} +(1.85410 + 5.70634i) q^{41} +6.00000 q^{43} +(-4.85410 + 3.52671i) q^{46} +(1.85410 + 5.70634i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(5.66312 + 4.11450i) q^{49} +(4.04508 + 2.93893i) q^{50} +(1.85410 - 5.70634i) q^{51} +(1.85410 + 5.70634i) q^{52} +(9.70820 - 7.05342i) q^{53} -1.00000 q^{54} +(4.85410 - 3.52671i) q^{57} +(1.85410 + 5.70634i) q^{58} +(-3.70820 + 11.4127i) q^{59} +(-4.85410 - 3.52671i) q^{61} +(1.23607 - 3.80423i) q^{62} +(-0.809017 + 0.587785i) q^{64} +4.00000 q^{67} +(4.85410 - 3.52671i) q^{68} +(-1.85410 - 5.70634i) q^{69} +(4.85410 + 3.52671i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-3.70820 + 11.4127i) q^{73} +(-0.618034 - 1.90211i) q^{74} +(-4.04508 + 2.93893i) q^{75} +6.00000 q^{76} -6.00000 q^{78} +(-9.70820 + 7.05342i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-4.85410 - 3.52671i) q^{82} +(-4.85410 + 3.52671i) q^{86} -6.00000 q^{87} -6.00000 q^{89} +(1.85410 - 5.70634i) q^{92} +(3.23607 + 2.35114i) q^{93} +(-4.85410 - 3.52671i) q^{94} +(-0.309017 - 0.951057i) q^{96} +(8.09017 - 5.87785i) q^{97} -7.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} - q^{4} + q^{6} - q^{8} - q^{9}+O(q^{10}) \) 4 * q - q^2 + q^3 - q^4 + q^6 - q^8 - q^9	\( 4 q - q^{2} + q^{3} - q^{4} + q^{6} - q^{8} - q^{9} - 4 q^{12} - 6 q^{13} - q^{16} + 6 q^{17} - q^{18} - 6 q^{19} + 24 q^{23} + q^{24} + 5 q^{25} - 6 q^{26} + q^{27} - 6 q^{29} - 4 q^{31} + 4 q^{32} - 24 q^{34} - q^{36} + 2 q^{37} - 6 q^{38} + 6 q^{39} - 6 q^{41} + 24 q^{43} - 6 q^{46} - 6 q^{47} + q^{48} + 7 q^{49} + 5 q^{50} - 6 q^{51} - 6 q^{52} + 12 q^{53} - 4 q^{54} + 6 q^{57} - 6 q^{58} + 12 q^{59} - 6 q^{61} - 4 q^{62} - q^{64} + 16 q^{67} + 6 q^{68} + 6 q^{69} + 6 q^{71} - q^{72} + 12 q^{73} + 2 q^{74} - 5 q^{75} + 24 q^{76} - 24 q^{78} - 12 q^{79} - q^{81} - 6 q^{82} - 6 q^{86} - 24 q^{87} - 24 q^{89} - 6 q^{92} + 4 q^{93} - 6 q^{94} + q^{96} + 10 q^{97} - 28 q^{98}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 + q^6 - q^8 - q^9 - 4 * q^12 - 6 * q^13 - q^16 + 6 * q^17 - q^18 - 6 * q^19 + 24 * q^23 + q^24 + 5 * q^25 - 6 * q^26 + q^27 - 6 * q^29 - 4 * q^31 + 4 * q^32 - 24 * q^34 - q^36 + 2 * q^37 - 6 * q^38 + 6 * q^39 - 6 * q^41 + 24 * q^43 - 6 * q^46 - 6 * q^47 + q^48 + 7 * q^49 + 5 * q^50 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 4 * q^54 + 6 * q^57 - 6 * q^58 + 12 * q^59 - 6 * q^61 - 4 * q^62 - q^64 + 16 * q^67 + 6 * q^68 + 6 * q^69 + 6 * q^71 - q^72 + 12 * q^73 + 2 * q^74 - 5 * q^75 + 24 * q^76 - 24 * q^78 - 12 * q^79 - q^81 - 6 * q^82 - 6 * q^86 - 24 * q^87 - 24 * q^89 - 6 * q^92 + 4 * q^93 - 6 * q^94 + q^96 + 10 * q^97 - 28 * q^98

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