LMFDB - Embedded newform 726.2.e.d.487.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(487,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("726.487"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [4,-1,-1,-1,1,-1,-4,-1,-1,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	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.d.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^{5} +(-0.809017 - 0.587785i) q^{6} +(1.23607 - 3.80423i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.00000 q^{10} +1.00000 q^{12} +(4.04508 - 2.93893i) q^{13} +(1.23607 + 3.80423i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.66312 - 4.11450i) q^{17} +(0.309017 - 0.951057i) q^{18} +(0.809017 - 0.587785i) q^{20} +4.00000 q^{21} +(-0.809017 + 0.587785i) q^{24} +(-1.23607 - 3.80423i) q^{25} +(-1.54508 + 4.75528i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-3.23607 - 2.35114i) q^{28} +(2.16312 - 6.65740i) q^{29} +(-0.309017 - 0.951057i) q^{30} +(6.47214 - 4.70228i) q^{31} +1.00000 q^{32} +7.00000 q^{34} +(3.23607 - 2.35114i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-1.54508 + 4.75528i) q^{37} +(4.04508 + 2.93893i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(3.39919 + 10.4616i) q^{41} +(-3.23607 + 2.35114i) q^{42} -8.00000 q^{43} -1.00000 q^{45} +(1.23607 + 3.80423i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-7.28115 - 5.29007i) q^{49} +(3.23607 + 2.35114i) q^{50} +(2.16312 - 6.65740i) q^{51} +(-1.54508 - 4.75528i) q^{52} +(4.04508 - 2.93893i) q^{53} +1.00000 q^{54} +4.00000 q^{56} +(2.16312 + 6.65740i) q^{58} +(0.809017 + 0.587785i) q^{60} +(1.61803 + 1.17557i) q^{61} +(-2.47214 + 7.60845i) q^{62} +(1.23607 + 3.80423i) q^{63} +(-0.809017 + 0.587785i) q^{64} +5.00000 q^{65} +12.0000 q^{67} +(-5.66312 + 4.11450i) q^{68} +(-1.23607 + 3.80423i) q^{70} +(12.9443 + 9.40456i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-1.85410 + 5.70634i) q^{73} +(-1.54508 - 4.75528i) q^{74} +(3.23607 - 2.35114i) q^{75} -5.00000 q^{78} +(-3.23607 + 2.35114i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-8.89919 - 6.46564i) q^{82} +(6.47214 + 4.70228i) q^{83} +(1.23607 - 3.80423i) q^{84} +(-2.16312 - 6.65740i) q^{85} +(6.47214 - 4.70228i) q^{86} +7.00000 q^{87} -17.0000 q^{89} +(0.809017 - 0.587785i) q^{90} +(-6.18034 - 19.0211i) q^{91} +(6.47214 + 4.70228i) q^{93} +(-3.23607 - 2.35114i) q^{94} +(0.309017 + 0.951057i) q^{96} +(4.04508 - 2.93893i) q^{97} +9.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 4 q^{7} - q^{8} - q^{9} - 4 q^{10} + 4 q^{12} + 5 q^{13} - 4 q^{14} + q^{15} - q^{16} - 7 q^{17} - q^{18} + q^{20} + 16 q^{21} - q^{24} + 4 q^{25}+ \cdots + 36 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^3 - q^4 + q^5 - q^6 - 4 * q^7 - q^8 - q^9 - 4 * q^10 + 4 * q^12 + 5 * q^13 - 4 * q^14 + q^15 - q^16 - 7 * q^17 - q^18 + q^20 + 16 * q^21 - q^24 + 4 * q^25 + 5 * q^26 - q^27 - 4 * q^28 - 7 * q^29 + q^30 + 8 * q^31 + 4 * q^32 + 28 * q^34 + 4 * q^35 - q^36 + 5 * q^37 + 5 * q^39 + q^40 - 11 * q^41 - 4 * q^42 - 32 * q^43 - 4 * q^45 - 4 * q^47 - q^48 - 9 * q^49 + 4 * q^50 - 7 * q^51 + 5 * q^52 + 5 * q^53 + 4 * q^54 + 16 * q^56 - 7 * q^58 + q^60 + 2 * q^61 + 8 * q^62 - 4 * q^63 - q^64 + 20 * q^65 + 48 * q^67 - 7 * q^68 + 4 * q^70 + 16 * q^71 - q^72 + 6 * q^73 + 5 * q^74 + 4 * q^75 - 20 * q^78 - 4 * q^79 + q^80 - q^81 - 11 * q^82 + 8 * q^83 - 4 * q^84 + 7 * q^85 + 8 * q^86 + 28 * q^87 - 68 * q^89 + q^90 + 20 * q^91 + 8 * q^93 - 4 * q^94 - q^96 + 5 * q^97 + 36 * q^98

Character values

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

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

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
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i	0.753804	−	0.657099i	$-0.228217\pi$
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i	−0.392000	+	0.919965i	$0.628217\pi$
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	1.23607	−	3.80423i	0.467190	−	1.43786i	−0.389018	−	0.921230i	$-0.627186\pi$
$7$	1.23607	−	3.80423i	0.467190	−	1.43786i	0.856208	−	0.516632i	$-0.172814\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−1.00000			−0.316228
$11$		0			0
$11$		0			0
$12$	1.00000			0.288675
$13$	4.04508	−	2.93893i	1.12190	−	0.815111i	0.137408	−	0.990515i	$-0.456123\pi$
$13$	4.04508	−	2.93893i	1.12190	−	0.815111i	0.984497	+	0.175403i	$0.0561229\pi$
$14$	1.23607	+	3.80423i	0.330353	+	1.01672i
$15$	−0.309017	+	0.951057i	−0.0797878	+	0.245562i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−5.66312	−	4.11450i	−1.37351	−	0.997912i	−0.997454	−	0.0713144i	$-0.977281\pi$
$17$	−5.66312	−	4.11450i	−1.37351	−	0.997912i	−0.376054	−	0.926598i	$-0.622719\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$19$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$	4.00000			0.872872
$22$		0			0
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	−1.23607	−	3.80423i	−0.247214	−	0.760845i
$26$	−1.54508	+	4.75528i	−0.303016	+	0.932588i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−3.23607	−	2.35114i	−0.611559	−	0.444324i
$29$	2.16312	−	6.65740i	0.401681	−	1.23625i	−0.521954	−	0.852974i	$-0.674797\pi$
$29$	2.16312	−	6.65740i	0.401681	−	1.23625i	0.923635	−	0.383274i	$-0.125203\pi$
$30$	−0.309017	−	0.951057i	−0.0564185	−	0.173638i
$31$	6.47214	−	4.70228i	1.16243	−	0.844555i	0.172347	−	0.985036i	$-0.444865\pi$
$31$	6.47214	−	4.70228i	1.16243	−	0.844555i	0.990083	+	0.140482i	$0.0448651\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	7.00000			1.20049
$35$	3.23607	−	2.35114i	0.546995	−	0.397415i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−1.54508	+	4.75528i	−0.254010	+	0.781764i	0.740013	+	0.672593i	$0.234819\pi$
$37$	−1.54508	+	4.75528i	−0.254010	+	0.781764i	−0.994023	+	0.109171i	$0.965181\pi$
$38$		0			0
$39$	4.04508	+	2.93893i	0.647732	+	0.470605i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	3.39919	+	10.4616i	0.530864	+	1.63383i	0.752420	+	0.658683i	$0.228886\pi$
$41$	3.39919	+	10.4616i	0.530864	+	1.63383i	−0.221557	+	0.975148i	$0.571114\pi$
$42$	−3.23607	+	2.35114i	−0.499336	+	0.362789i
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	1.23607	+	3.80423i	0.180299	+	0.554903i	0.999836	−	0.0181233i	$-0.00576913\pi$
$47$	1.23607	+	3.80423i	0.180299	+	0.554903i	−0.819537	+	0.573027i	$0.805769\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−7.28115	−	5.29007i	−1.04016	−	0.755724i
$50$	3.23607	+	2.35114i	0.457649	+	0.332502i
$51$	2.16312	−	6.65740i	0.302897	−	0.932222i
$52$	−1.54508	−	4.75528i	−0.214265	−	0.659439i
$53$	4.04508	−	2.93893i	0.555635	−	0.403693i	−0.274224	−	0.961666i	$-0.588421\pi$
$53$	4.04508	−	2.93893i	0.555635	−	0.403693i	0.829859	+	0.557973i	$0.188421\pi$
$54$	1.00000			0.136083
$55$		0			0
$56$	4.00000			0.534522
$57$		0			0
$58$	2.16312	+	6.65740i	0.284031	+	0.874159i
$59$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$59$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$60$	0.809017	+	0.587785i	0.104444	+	0.0758827i
$61$	1.61803	+	1.17557i	0.207168	+	0.150516i	0.686531	−	0.727100i	$-0.259132\pi$
$61$	1.61803	+	1.17557i	0.207168	+	0.150516i	−0.479363	+	0.877616i	$0.659132\pi$
$62$	−2.47214	+	7.60845i	−0.313962	+	0.966274i
$63$	1.23607	+	3.80423i	0.155730	+	0.479287i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	5.00000			0.620174
$66$		0			0
$67$	12.0000			1.46603			0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000			1.46603			0.733017	+	0.680211i	$0.238112\pi$
$68$	−5.66312	+	4.11450i	−0.686754	+	0.498956i
$69$		0			0
$70$	−1.23607	+	3.80423i	−0.147738	+	0.454692i
$71$	12.9443	+	9.40456i	1.53620	+	1.11612i	0.952662	+	0.304033i	$0.0983332\pi$
$71$	12.9443	+	9.40456i	1.53620	+	1.11612i	0.583541	+	0.812084i	$0.301667\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	−1.85410	+	5.70634i	−0.217006	+	0.667876i	0.781999	+	0.623280i	$0.214200\pi$
$73$	−1.85410	+	5.70634i	−0.217006	+	0.667876i	−0.999005	+	0.0445966i	$0.985800\pi$
$74$	−1.54508	−	4.75528i	−0.179612	−	0.552790i
$75$	3.23607	−	2.35114i	0.373669	−	0.271486i
$76$		0			0
$77$		0			0
$78$	−5.00000			−0.566139
$79$	−3.23607	+	2.35114i	−0.364086	+	0.264524i	−0.754754	−	0.656007i	$-0.772244\pi$
$79$	−3.23607	+	2.35114i	−0.364086	+	0.264524i	0.390668	+	0.920532i	$0.372244\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−8.89919	−	6.46564i	−0.982751	−	0.714010i
$83$	6.47214	+	4.70228i	0.710409	+	0.516143i	0.883306	−	0.468798i	$-0.155313\pi$
$83$	6.47214	+	4.70228i	0.710409	+	0.516143i	−0.172896	+	0.984940i	$0.555313\pi$
$84$	1.23607	−	3.80423i	0.134866	−	0.415075i
$85$	−2.16312	−	6.65740i	−0.234623	−	0.722096i
$86$	6.47214	−	4.70228i	0.697908	−	0.507060i
$87$	7.00000			0.750479
$88$		0			0
$89$	−17.0000			−1.80200			−0.900998	−	0.433823i	$-0.857164\pi$
$89$	−17.0000			−1.80200			−0.900998	+	0.433823i	$0.857164\pi$
$90$	0.809017	−	0.587785i	0.0852779	−	0.0619580i
$91$	−6.18034	−	19.0211i	−0.647876	−	1.99396i
$92$		0			0
$93$	6.47214	+	4.70228i	0.671129	+	0.487604i
$94$	−3.23607	−	2.35114i	−0.333775	−	0.242502i
$95$		0			0
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	4.04508	−	2.93893i	0.410716	−	0.298403i	−0.363176	−	0.931721i	$-0.618307\pi$
$97$	4.04508	−	2.93893i	0.410716	−	0.298403i	0.773892	+	0.633318i	$0.218307\pi$
$98$	9.00000			0.909137
$99$		0			0
$100$	−4.00000			−0.400000
$101$	8.09017	−	5.87785i	0.805002	−	0.584868i	−0.107375	−	0.994219i	$-0.534245\pi$
$101$	8.09017	−	5.87785i	0.805002	−	0.584868i	0.912377	+	0.409350i	$0.134245\pi$
$102$	2.16312	+	6.65740i	0.214181	+	0.659180i
$103$	1.23607	−	3.80423i	0.121793	−	0.374842i	−0.871510	−	0.490378i	$-0.836859\pi$
$103$	1.23607	−	3.80423i	0.121793	−	0.374842i	0.993303	+	0.115536i	$0.0368587\pi$
$104$	4.04508	+	2.93893i	0.396653	+	0.288185i
$105$	3.23607	+	2.35114i	0.315808	+	0.229448i
$106$	−1.54508	+	4.75528i	−0.150072	+	0.461874i
$107$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$107$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	−1.00000			−0.0957826			−0.0478913	−	0.998853i	$-0.515250\pi$
$109$	−1.00000			−0.0957826			−0.0478913	+	0.998853i	$0.515250\pi$
$110$		0			0
$111$	−5.00000			−0.474579
$112$	−3.23607	+	2.35114i	−0.305780	+	0.222162i
$113$	0.927051	+	2.85317i	0.0872096	+	0.268404i	0.985145	−	0.171723i	$-0.0549335\pi$
$113$	0.927051	+	2.85317i	0.0872096	+	0.268404i	−0.897936	+	0.440127i	$0.854933\pi$
$114$		0			0
$115$		0			0
$116$	−5.66312	−	4.11450i	−0.525807	−	0.382021i
$117$	−1.54508	+	4.75528i	−0.142843	+	0.439626i
$118$		0			0
$119$	−22.6525	+	16.4580i	−2.07655	+	1.50870i
$120$	−1.00000			−0.0912871
$121$		0			0
$122$	−2.00000			−0.181071
$123$	−8.89919	+	6.46564i	−0.802413	+	0.582987i
$124$	−2.47214	−	7.60845i	−0.222004	−	0.683259i
$125$	2.78115	−	8.55951i	0.248754	−	0.765586i
$126$	−3.23607	−	2.35114i	−0.288292	−	0.209456i
$127$	3.23607	+	2.35114i	0.287155	+	0.208630i	0.722032	−	0.691860i	$-0.243208\pi$
$127$	3.23607	+	2.35114i	0.287155	+	0.208630i	−0.434877	+	0.900490i	$0.643208\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−2.47214	−	7.60845i	−0.217659	−	0.669887i
$130$	−4.04508	+	2.93893i	−0.354777	+	0.257761i
$131$	−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
$134$	−9.70820	+	7.05342i	−0.838661	+	0.609323i
$135$	−0.309017	−	0.951057i	−0.0265959	−	0.0818539i
$136$	2.16312	−	6.65740i	0.185486	−	0.570867i
$137$	−8.09017	−	5.87785i	−0.691190	−	0.502179i	0.185861	−	0.982576i	$-0.440493\pi$
$137$	−8.09017	−	5.87785i	−0.691190	−	0.502179i	−0.877051	+	0.480397i	$0.840493\pi$
$138$		0			0
$139$	−3.70820	+	11.4127i	−0.314526	+	0.968011i	0.661423	+	0.750013i	$0.269953\pi$
$139$	−3.70820	+	11.4127i	−0.314526	+	0.968011i	−0.975949	+	0.217998i	$0.930047\pi$
$140$	−1.23607	−	3.80423i	−0.104467	−	0.321516i
$141$	−3.23607	+	2.35114i	−0.272526	+	0.198002i
$142$	−16.0000			−1.34269
$143$		0			0
$144$	1.00000			0.0833333
$145$	5.66312	−	4.11450i	0.470296	−	0.341690i
$146$	−1.85410	−	5.70634i	−0.153447	−	0.472260i
$147$	2.78115	−	8.55951i	0.229386	−	0.705976i
$148$	4.04508	+	2.93893i	0.332504	+	0.241578i
$149$	0.809017	+	0.587785i	0.0662773	+	0.0481532i	0.620431	−	0.784261i	$-0.286958\pi$
$149$	0.809017	+	0.587785i	0.0662773	+	0.0481532i	−0.554153	+	0.832415i	$0.686958\pi$
$150$	−1.23607	+	3.80423i	−0.100925	+	0.310614i
$151$	6.18034	+	19.0211i	0.502949	+	1.54792i	0.804192	+	0.594370i	$0.202599\pi$
$151$	6.18034	+	19.0211i	0.502949	+	1.54792i	−0.301243	+	0.953548i	$0.597401\pi$
$152$		0			0
$153$	7.00000			0.565916
$154$		0			0
$155$	8.00000			0.642575
$156$	4.04508	−	2.93893i	0.323866	−	0.235302i
$157$	−5.56231	−	17.1190i	−0.443920	−	1.36625i	−0.883663	−	0.468123i	$-0.844931\pi$
$157$	−5.56231	−	17.1190i	−0.443920	−	1.36625i	0.439743	−	0.898124i	$-0.355069\pi$
$158$	1.23607	−	3.80423i	0.0983363	−	0.302648i
$159$	4.04508	+	2.93893i	0.320796	+	0.233072i
$160$	0.809017	+	0.587785i	0.0639584	+	0.0464685i
$161$		0			0
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	−3.23607	+	2.35114i	−0.253468	+	0.184156i	−0.707263	−	0.706951i	$-0.750070\pi$
$163$	−3.23607	+	2.35114i	−0.253468	+	0.184156i	0.453794	+	0.891107i	$0.350070\pi$
$164$	11.0000			0.858956
$165$		0			0
$166$	−8.00000			−0.620920
$167$	−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	$0.453692\pi$
$168$	1.23607	+	3.80423i	0.0953647	+	0.293502i
$169$	3.70820	−	11.4127i	0.285246	−	0.877898i
$170$	5.66312	+	4.11450i	0.434341	+	0.315567i
$171$		0			0
$172$	−2.47214	+	7.60845i	−0.188499	+	0.580139i
$173$	−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	$-0.339873\pi$
$174$	−5.66312	+	4.11450i	−0.429320	+	0.311919i
$175$	−16.0000			−1.20949
$176$		0			0
$177$		0			0
$178$	13.7533	−	9.99235i	1.03085	−	0.748958i
$179$	3.70820	+	11.4127i	0.277164	+	0.853024i	0.988639	+	0.150312i	$0.0480277\pi$
$179$	3.70820	+	11.4127i	0.277164	+	0.853024i	−0.711474	+	0.702712i	$0.751972\pi$
$180$	−0.309017	+	0.951057i	−0.0230328	+	0.0708876i
$181$	0.809017	+	0.587785i	0.0601338	+	0.0436897i	0.617446	−	0.786613i	$-0.288167\pi$
$181$	0.809017	+	0.587785i	0.0601338	+	0.0436897i	−0.557312	+	0.830303i	$0.688167\pi$
$182$	16.1803	+	11.7557i	1.19937	+	0.871391i
$183$	−0.618034	+	1.90211i	−0.0456864	+	0.140608i
$184$		0			0
$185$	−4.04508	+	2.93893i	−0.297401	+	0.216074i
$186$	−8.00000			−0.586588
$187$		0			0
$188$	4.00000			0.291730
$189$	−3.23607	+	2.35114i	−0.235389	+	0.171020i
$190$		0			0
$191$	1.23607	−	3.80423i	0.0894387	−	0.275264i	−0.896326	−	0.443396i	$-0.853773\pi$
$191$	1.23607	−	3.80423i	0.0894387	−	0.275264i	0.985764	+	0.168132i	$0.0537735\pi$
$192$	−0.809017	−	0.587785i	−0.0583858	−	0.0424197i
$193$	−8.89919	−	6.46564i	−0.640577	−	0.465407i	0.219471	−	0.975619i	$-0.429567\pi$
$193$	−8.89919	−	6.46564i	−0.640577	−	0.465407i	−0.860049	+	0.510212i	$0.829567\pi$
$194$	−1.54508	+	4.75528i	−0.110931	+	0.341409i
$195$	1.54508	+	4.75528i	0.110646	+	0.340533i
$196$	−7.28115	+	5.29007i	−0.520082	+	0.377862i
$197$	−9.00000			−0.641223			−0.320612	−	0.947211i	$-0.603888\pi$
$197$	−9.00000			−0.641223			−0.320612	+	0.947211i	$0.603888\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$	3.23607	−	2.35114i	0.228825	−	0.166251i
$201$	3.70820	+	11.4127i	0.261557	+	0.804988i
$202$	−3.09017	+	9.51057i	−0.217424	+	0.669161i
$203$	−22.6525	−	16.4580i	−1.58989	−	1.15512i
$204$	−5.66312	−	4.11450i	−0.396498	−	0.288072i
$205$	−3.39919	+	10.4616i	−0.237410	+	0.730671i
$206$	1.23607	+	3.80423i	0.0861209	+	0.265053i
$207$		0			0
$208$	−5.00000			−0.346688
$209$		0			0
$210$	−4.00000			−0.276026
$211$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$211$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$212$	−1.54508	−	4.75528i	−0.106117	−	0.326594i
$213$	−4.94427	+	15.2169i	−0.338776	+	1.04265i
$214$		0			0
$215$	−6.47214	−	4.70228i	−0.441396	−	0.320693i
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	−9.88854	−	30.4338i	−0.671278	−	2.06598i
$218$	0.809017	−	0.587785i	0.0547935	−	0.0398098i
$219$	−6.00000			−0.405442
$220$		0			0
$221$	−35.0000			−2.35435
$222$	4.04508	−	2.93893i	0.271488	−	0.197248i
$223$	6.18034	+	19.0211i	0.413866	+	1.27375i	0.913261	+	0.407375i	$0.133556\pi$
$223$	6.18034	+	19.0211i	0.413866	+	1.27375i	−0.499395	+	0.866374i	$0.666444\pi$
$224$	1.23607	−	3.80423i	0.0825883	−	0.254181i
$225$	3.23607	+	2.35114i	0.215738	+	0.156743i
$226$	−2.42705	−	1.76336i	−0.161445	−	0.117297i
$227$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$227$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$228$		0			0
$229$	4.04508	−	2.93893i	0.267307	−	0.194210i	−0.446055	−	0.895005i	$-0.647172\pi$
$229$	4.04508	−	2.93893i	0.267307	−	0.194210i	0.713362	+	0.700796i	$0.247172\pi$
$230$		0			0
$231$		0			0
$232$	7.00000			0.459573
$233$	7.28115	−	5.29007i	0.477004	−	0.346564i	−0.323161	−	0.946344i	$-0.604745\pi$
$233$	7.28115	−	5.29007i	0.477004	−	0.346564i	0.800165	+	0.599780i	$0.204745\pi$
$234$	−1.54508	−	4.75528i	−0.101005	−	0.310863i
$235$	−1.23607	+	3.80423i	−0.0806322	+	0.248160i
$236$		0			0
$237$	−3.23607	−	2.35114i	−0.210205	−	0.152723i
$238$	8.65248	−	26.6296i	0.560857	−	1.72614i
$239$	1.23607	+	3.80423i	0.0799546	+	0.246075i	0.983042	−	0.183383i	$-0.0587048\pi$
$239$	1.23607	+	3.80423i	0.0799546	+	0.246075i	−0.903087	+	0.429458i	$0.858705\pi$
$240$	0.809017	−	0.587785i	0.0522218	−	0.0379414i
$241$	18.0000			1.15948			0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000			1.15948			0.579741	+	0.814801i	$0.303154\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	1.61803	−	1.17557i	0.103584	−	0.0752582i
$245$	−2.78115	−	8.55951i	−0.177681	−	0.546847i
$246$	3.39919	−	10.4616i	0.216724	−	0.667009i
$247$		0			0
$248$	6.47214	+	4.70228i	0.410981	+	0.298595i
$249$	−2.47214	+	7.60845i	−0.156665	+	0.482166i
$250$	2.78115	+	8.55951i	0.175896	+	0.541351i
$251$	−12.9443	+	9.40456i	−0.817035	+	0.593611i	−0.915862	−	0.401494i	$-0.868491\pi$
$251$	−12.9443	+	9.40456i	−0.817035	+	0.593611i	0.0988265	+	0.995105i	$0.468491\pi$
$252$	4.00000			0.251976
$253$		0			0
$254$	−4.00000			−0.250982
$255$	5.66312	−	4.11450i	0.354638	−	0.257660i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	0.927051	−	2.85317i	0.0578279	−	0.177976i	−0.917970	−	0.396649i	$-0.870173\pi$
$257$	0.927051	−	2.85317i	0.0578279	−	0.177976i	0.975798	+	0.218673i	$0.0701729\pi$
$258$	6.47214	+	4.70228i	0.402938	+	0.292751i
$259$	16.1803	+	11.7557i	1.00540	+	0.730464i
$260$	1.54508	−	4.75528i	0.0958221	−	0.294910i
$261$	2.16312	+	6.65740i	0.133894	+	0.412082i
$262$	9.70820	−	7.05342i	0.599775	−	0.435762i
$263$	8.00000			0.493301			0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000			0.493301			0.246651	+	0.969104i	$0.420670\pi$
$264$		0			0
$265$	5.00000			0.307148
$266$		0			0
$267$	−5.25329	−	16.1680i	−0.321496	−	0.989463i
$268$	3.70820	−	11.4127i	0.226515	−	0.697140i
$269$	4.04508	+	2.93893i	0.246633	+	0.179189i	0.704233	−	0.709969i	$-0.251291\pi$
$269$	4.04508	+	2.93893i	0.246633	+	0.179189i	−0.457600	+	0.889158i	$0.651291\pi$
$270$	0.809017	+	0.587785i	0.0492352	+	0.0357715i
$271$	−2.47214	+	7.60845i	−0.150172	+	0.462181i	−0.997640	−	0.0686657i	$-0.978126\pi$
$271$	−2.47214	+	7.60845i	−0.150172	+	0.462181i	0.847468	+	0.530846i	$0.178126\pi$
$272$	2.16312	+	6.65740i	0.131158	+	0.403664i
$273$	16.1803	−	11.7557i	0.979279	−	0.711488i
$274$	10.0000			0.604122
$275$		0			0
$276$		0			0
$277$	−18.6074	+	13.5191i	−1.11801	+	0.812282i	−0.983906	−	0.178686i	$-0.942815\pi$
$277$	−18.6074	+	13.5191i	−1.11801	+	0.812282i	−0.134104	+	0.990967i	$0.542815\pi$
$278$	−3.70820	−	11.4127i	−0.222403	−	0.684487i
$279$	−2.47214	+	7.60845i	−0.148003	+	0.455506i
$280$	3.23607	+	2.35114i	0.193392	+	0.140508i
$281$	−8.09017	−	5.87785i	−0.482619	−	0.350643i	0.319720	−	0.947512i	$-0.396411\pi$
$281$	−8.09017	−	5.87785i	−0.482619	−	0.350643i	−0.802339	+	0.596869i	$0.796411\pi$
$282$	1.23607	−	3.80423i	0.0736068	−	0.226538i
$283$	1.23607	+	3.80423i	0.0734766	+	0.226138i	0.981050	−	0.193756i	$-0.0620672\pi$
$283$	1.23607	+	3.80423i	0.0734766	+	0.226138i	−0.907573	+	0.419894i	$0.862067\pi$
$284$	12.9443	−	9.40456i	0.768101	−	0.558058i
$285$		0			0
$286$		0			0
$287$	44.0000			2.59724
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	9.88854	+	30.4338i	0.581679	+	1.79022i
$290$	−2.16312	+	6.65740i	−0.127023	+	0.390936i
$291$	4.04508	+	2.93893i	0.237127	+	0.172283i
$292$	4.85410	+	3.52671i	0.284065	+	0.206385i
$293$	7.10739	−	21.8743i	0.415218	−	1.27791i	−0.496837	−	0.867844i	$-0.665505\pi$
$293$	7.10739	−	21.8743i	0.415218	−	1.27791i	0.912056	−	0.410067i	$-0.134495\pi$
$294$	2.78115	+	8.55951i	0.162200	+	0.499201i
$295$		0			0
$296$	−5.00000			−0.290619
$297$		0			0
$298$	−1.00000			−0.0579284
$299$		0			0
$300$	−1.23607	−	3.80423i	−0.0713644	−	0.219637i
$301$	−9.88854	+	30.4338i	−0.569966	+	1.75418i
$302$	−16.1803	−	11.7557i	−0.931074	−	0.676465i
$303$	8.09017	+	5.87785i	0.464768	+	0.337674i
$304$		0			0
$305$	0.618034	+	1.90211i	0.0353885	+	0.108915i
$306$	−5.66312	+	4.11450i	−0.323739	+	0.235210i
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$		0			0
$309$	4.00000			0.227552
$310$	−6.47214	+	4.70228i	−0.367593	+	0.267072i
$311$	6.18034	+	19.0211i	0.350455	+	1.07859i	0.958598	+	0.284762i	$0.0919146\pi$
$311$	6.18034	+	19.0211i	0.350455	+	1.07859i	−0.608143	+	0.793827i	$0.708085\pi$
$312$	−1.54508	+	4.75528i	−0.0874732	+	0.269215i
$313$	7.28115	+	5.29007i	0.411555	+	0.299012i	0.774231	−	0.632903i	$-0.218137\pi$
$313$	7.28115	+	5.29007i	0.411555	+	0.299012i	−0.362676	+	0.931915i	$0.618137\pi$
$314$	14.5623	+	10.5801i	0.821798	+	0.597072i
$315$	−1.23607	+	3.80423i	−0.0696445	+	0.214344i
$316$	1.23607	+	3.80423i	0.0695343	+	0.214004i
$317$	1.61803	−	1.17557i	0.0908778	−	0.0660266i	−0.541418	−	0.840753i	$-0.682113\pi$
$317$	1.61803	−	1.17557i	0.0908778	−	0.0660266i	0.632296	+	0.774727i	$0.282113\pi$
$318$	−5.00000			−0.280386
$319$		0			0
$320$	−1.00000			−0.0559017
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−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
$327$	−0.309017	−	0.951057i	−0.0170887	−	0.0525935i
$328$	−8.89919	+	6.46564i	−0.491375	+	0.357005i
$329$	16.0000			0.882109
$330$		0			0
$331$	32.0000			1.75888			0.879440	−	0.476011i	$-0.157918\pi$
$331$	32.0000			1.75888			0.879440	+	0.476011i	$0.157918\pi$
$332$	6.47214	−	4.70228i	0.355205	−	0.258071i
$333$	−1.54508	−	4.75528i	−0.0846701	−	0.260588i
$334$	3.70820	−	11.4127i	0.202904	−	0.624474i
$335$	9.70820	+	7.05342i	0.530416	+	0.385370i
$336$	−3.23607	−	2.35114i	−0.176542	−	0.128265i
$337$	−0.309017	+	0.951057i	−0.0168332	+	0.0518073i	−0.959120	−	0.282999i	$-0.908671\pi$
$337$	−0.309017	+	0.951057i	−0.0168332	+	0.0518073i	0.942287	+	0.334806i	$0.108671\pi$
$338$	3.70820	+	11.4127i	0.201700	+	0.620768i
$339$	−2.42705	+	1.76336i	−0.131819	+	0.0957723i
$340$	−7.00000			−0.379628
$341$		0			0
$342$		0			0
$343$	−6.47214	+	4.70228i	−0.349462	+	0.253899i
$344$	−2.47214	−	7.60845i	−0.133289	−	0.410220i
$345$		0			0
$346$	14.5623	+	10.5801i	0.782874	+	0.568792i
$347$	−19.4164	−	14.1068i	−1.04233	−	0.757295i	−0.0715889	−	0.997434i	$-0.522807\pi$
$347$	−19.4164	−	14.1068i	−1.04233	−	0.757295i	−0.970739	+	0.240139i	$0.922807\pi$
$348$	2.16312	−	6.65740i	0.115955	−	0.356874i
$349$	2.16312	+	6.65740i	0.115789	+	0.356362i	0.992111	−	0.125364i	$-0.0400099\pi$
$349$	2.16312	+	6.65740i	0.115789	+	0.356362i	−0.876322	+	0.481726i	$0.840010\pi$
$350$	12.9443	−	9.40456i	0.691900	−	0.502695i
$351$	−5.00000			−0.266880
$352$		0			0
$353$	27.0000			1.43706			0.718532	−	0.695493i	$-0.244814\pi$
$353$	27.0000			1.43706			0.718532	+	0.695493i	$0.244814\pi$
$354$		0			0
$355$	4.94427	+	15.2169i	0.262415	+	0.807629i
$356$	−5.25329	+	16.1680i	−0.278424	+	0.856900i
$357$	−22.6525	−	16.4580i	−1.19890	−	0.871049i
$358$	−9.70820	−	7.05342i	−0.513095	−	0.372785i
$359$	1.23607	−	3.80423i	0.0652372	−	0.200779i	−0.913125	−	0.407680i	$-0.866338\pi$
$359$	1.23607	−	3.80423i	0.0652372	−	0.200779i	0.978362	+	0.206901i	$0.0663378\pi$
$360$	−0.309017	−	0.951057i	−0.0162866	−	0.0501251i
$361$	15.3713	−	11.1679i	0.809017	−	0.587785i
$362$	−1.00000			−0.0525588
$363$		0			0
$364$	−20.0000			−1.04828
$365$	−4.85410	+	3.52671i	−0.254075	+	0.184597i
$366$	−0.618034	−	1.90211i	−0.0323052	−	0.0994250i
$367$	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	$0.0330448\pi$
$368$		0			0
$369$	−8.89919	−	6.46564i	−0.463273	−	0.336588i
$370$	1.54508	−	4.75528i	0.0803251	−	0.247215i
$371$	−6.18034	−	19.0211i	−0.320867	−	0.987528i
$372$	6.47214	−	4.70228i	0.335565	−	0.243802i
$373$	22.0000			1.13912			0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000			1.13912			0.569558	+	0.821951i	$0.307114\pi$
$374$		0			0
$375$	9.00000			0.464758
$376$	−3.23607	+	2.35114i	−0.166887	+	0.121251i
$377$	−10.8156	−	33.2870i	−0.557031	−	1.71437i
$378$	1.23607	−	3.80423i	0.0635765	−	0.195668i
$379$	16.1803	+	11.7557i	0.831128	+	0.603850i	0.919878	−	0.392204i	$-0.128287\pi$
$379$	16.1803	+	11.7557i	0.831128	+	0.603850i	−0.0887501	+	0.996054i	$0.528287\pi$
$380$		0			0
$381$	−1.23607	+	3.80423i	−0.0633257	+	0.194896i
$382$	1.23607	+	3.80423i	0.0632427	+	0.194641i
$383$	29.1246	−	21.1603i	1.48820	−	1.08124i	0.513400	−	0.858149i	$-0.328386\pi$
$383$	29.1246	−	21.1603i	1.48820	−	1.08124i	0.974798	−	0.223090i	$-0.0716144\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	11.0000			0.559885
$387$	6.47214	−	4.70228i	0.328997	−	0.239030i
$388$	−1.54508	−	4.75528i	−0.0784398	−	0.241413i
$389$	−8.96149	+	27.5806i	−0.454366	+	1.39839i	0.417513	+	0.908671i	$0.362902\pi$
$389$	−8.96149	+	27.5806i	−0.454366	+	1.39839i	−0.871878	+	0.489723i	$0.837098\pi$
$390$	−4.04508	−	2.93893i	−0.204831	−	0.148818i
$391$		0			0
$392$	2.78115	−	8.55951i	0.140469	−	0.432320i
$393$	−3.70820	−	11.4127i	−0.187054	−	0.575693i
$394$	7.28115	−	5.29007i	0.366819	−	0.266510i
$395$	−4.00000			−0.201262
$396$		0			0
$397$	−21.0000			−1.05396			−0.526980	−	0.849878i	$-0.676676\pi$
$397$	−21.0000			−1.05396			−0.526980	+	0.849878i	$0.676676\pi$
$398$	12.9443	−	9.40456i	0.648838	−	0.471408i
$399$		0			0
$400$	−1.23607	+	3.80423i	−0.0618034	+	0.190211i
$401$	−12.1353	−	8.81678i	−0.606006	−	0.440289i	0.242000	−	0.970276i	$-0.422197\pi$
$401$	−12.1353	−	8.81678i	−0.606006	−	0.440289i	−0.848006	+	0.529987i	$0.822197\pi$
$402$	−9.70820	−	7.05342i	−0.484201	−	0.351793i
$403$	12.3607	−	38.0423i	0.615729	−	1.89502i
$404$	−3.09017	−	9.51057i	−0.153742	−	0.473168i
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	28.0000			1.38962
$407$		0			0
$408$	7.00000			0.346552
$409$	0.809017	−	0.587785i	0.0400033	−	0.0290641i	−0.567604	−	0.823302i	$-0.692129\pi$
$409$	0.809017	−	0.587785i	0.0400033	−	0.0290641i	0.607607	+	0.794238i	$0.292129\pi$
$410$	−3.39919	−	10.4616i	−0.167874	−	0.516663i
$411$	3.09017	−	9.51057i	0.152427	−	0.469122i
$412$	−3.23607	−	2.35114i	−0.159430	−	0.115832i
$413$		0			0
$414$		0			0
$415$	2.47214	+	7.60845i	0.121352	+	0.373484i
$416$	4.04508	−	2.93893i	0.198327	−	0.144093i
$417$	−12.0000			−0.587643
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	3.23607	−	2.35114i	0.157904	−	0.114724i
$421$	4.63525	+	14.2658i	0.225909	+	0.695275i	0.998198	+	0.0600043i	$0.0191114\pi$
$421$	4.63525	+	14.2658i	0.225909	+	0.695275i	−0.772290	+	0.635271i	$0.780889\pi$
$422$		0			0
$423$	−3.23607	−	2.35114i	−0.157343	−	0.114316i
$424$	4.04508	+	2.93893i	0.196447	+	0.142727i
$425$	−8.65248	+	26.6296i	−0.419707	+	1.29172i
$426$	−4.94427	−	15.2169i	−0.239551	−	0.737261i
$427$	6.47214	−	4.70228i	0.313209	−	0.227559i
$428$		0			0
$429$		0			0
$430$	8.00000			0.385794
$431$	−16.1803	+	11.7557i	−0.779380	+	0.566252i	−0.904793	−	0.425852i	$-0.859974\pi$
$431$	−16.1803	+	11.7557i	−0.779380	+	0.566252i	0.125413	+	0.992105i	$0.459974\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	−6.48936	+	19.9722i	−0.311859	+	0.959802i	0.665170	+	0.746692i	$0.268359\pi$
$433$	−6.48936	+	19.9722i	−0.311859	+	0.959802i	−0.977028	+	0.213110i	$0.931641\pi$
$434$	25.8885	+	18.8091i	1.24269	+	0.902867i
$435$	5.66312	+	4.11450i	0.271526	+	0.197275i
$436$	−0.309017	+	0.951057i	−0.0147992	+	0.0455473i
$437$		0			0
$438$	4.85410	−	3.52671i	0.231938	−	0.168513i
$439$	16.0000			0.763638			0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000			0.763638			0.381819	+	0.924237i	$0.375298\pi$
$440$		0			0
$441$	9.00000			0.428571
$442$	28.3156	−	20.5725i	1.34684	−	0.978533i
$443$	11.1246	+	34.2380i	0.528546	+	1.62670i	0.757195	+	0.653189i	$0.226569\pi$
$443$	11.1246	+	34.2380i	0.528546	+	1.62670i	−0.228649	+	0.973509i	$0.573431\pi$
$444$	−1.54508	+	4.75528i	−0.0733265	+	0.225676i
$445$	−13.7533	−	9.99235i	−0.651968	−	0.473683i
$446$	−16.1803	−	11.7557i	−0.766161	−	0.556649i
$447$	−0.309017	+	0.951057i	−0.0146160	+	0.0449834i
$448$	1.23607	+	3.80423i	0.0583987	+	0.179733i
$449$	−12.1353	+	8.81678i	−0.572698	+	0.416090i	−0.836084	−	0.548601i	$-0.815161\pi$
$449$	−12.1353	+	8.81678i	−0.572698	+	0.416090i	0.263386	+	0.964690i	$0.415161\pi$
$450$	−4.00000			−0.188562
$451$		0			0
$452$	3.00000			0.141108
$453$	−16.1803	+	11.7557i	−0.760219	+	0.552331i
$454$		0			0
$455$	6.18034	−	19.0211i	0.289739	−	0.891724i
$456$		0			0
$457$	13.7533	+	9.99235i	0.643352	+	0.467422i	0.861000	−	0.508605i	$-0.169839\pi$
$457$	13.7533	+	9.99235i	0.643352	+	0.467422i	−0.217648	+	0.976027i	$0.569839\pi$
$458$	−1.54508	+	4.75528i	−0.0721971	+	0.222200i
$459$	2.16312	+	6.65740i	0.100966	+	0.310741i
$460$		0			0
$461$	−33.0000			−1.53696			−0.768482	−	0.639872i	$-0.778987\pi$
$461$	−33.0000			−1.53696			−0.768482	+	0.639872i	$0.778987\pi$
$462$		0			0
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$	−5.66312	+	4.11450i	−0.262904	+	0.191011i
$465$	2.47214	+	7.60845i	0.114643	+	0.352834i
$466$	−2.78115	+	8.55951i	−0.128834	+	0.396512i
$467$	−22.6525	−	16.4580i	−1.04823	−	0.761585i	−0.0763562	−	0.997081i	$-0.524329\pi$
$467$	−22.6525	−	16.4580i	−1.04823	−	0.761585i	−0.971875	+	0.235496i	$0.924329\pi$
$468$	4.04508	+	2.93893i	0.186984	+	0.135852i
$469$	14.8328	−	45.6507i	0.684916	−	2.10795i
$470$	−1.23607	−	3.80423i	−0.0570156	−	0.175476i
$471$	14.5623	−	10.5801i	0.670996	−	0.487507i
$472$		0			0
$473$		0			0
$474$	4.00000			0.183726
$475$		0			0
$476$	8.65248	+	26.6296i	0.396586	+	1.22056i
$477$	−1.54508	+	4.75528i	−0.0707446	+	0.217729i
$478$	−3.23607	−	2.35114i	−0.148014	−	0.107539i
$479$	−3.23607	−	2.35114i	−0.147860	−	0.107426i	0.511396	−	0.859345i	$-0.329129\pi$
$479$	−3.23607	−	2.35114i	−0.147860	−	0.107426i	−0.659256	+	0.751919i	$0.729129\pi$
$480$	−0.309017	+	0.951057i	−0.0141046	+	0.0434096i
$481$	7.72542	+	23.7764i	0.352249	+	1.08411i
$482$	−14.5623	+	10.5801i	−0.663295	+	0.481912i
$483$		0			0
$484$		0			0
$485$	5.00000			0.227038
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−6.18034	−	19.0211i	−0.280058	−	0.861930i	−0.987837	−	0.155495i	$-0.950303\pi$
$487$	−6.18034	−	19.0211i	−0.280058	−	0.861930i	0.707779	−	0.706434i	$-0.249697\pi$
$488$	−0.618034	+	1.90211i	−0.0279771	+	0.0861046i
$489$	−3.23607	−	2.35114i	−0.146340	−	0.106322i
$490$	7.28115	+	5.29007i	0.328929	+	0.238981i
$491$	−3.70820	+	11.4127i	−0.167349	+	0.515047i	−0.999202	−	0.0399494i	$-0.987280\pi$
$491$	−3.70820	+	11.4127i	−0.167349	+	0.515047i	0.831853	+	0.554996i	$0.187280\pi$
$492$	3.39919	+	10.4616i	0.153247	+	0.471646i
$493$	−39.6418	+	28.8015i	−1.78538	+	1.29715i
$494$		0			0
$495$		0			0
$496$	−8.00000			−0.359211
$497$	51.7771	−	37.6183i	2.32252	−	1.68741i
$498$	−2.47214	−	7.60845i	−0.110779	−	0.340943i
$499$	12.3607	−	38.0423i	0.553340	−	1.70301i	−0.146947	−	0.989144i	$-0.546945\pi$
$499$	12.3607	−	38.0423i	0.553340	−	1.70301i	0.700287	−	0.713861i	$-0.253055\pi$
$500$	−7.28115	−	5.29007i	−0.325623	−	0.236579i
$501$	−9.70820	−	7.05342i	−0.433731	−	0.315124i
$502$	4.94427	−	15.2169i	0.220674	−	0.679164i
$503$	4.94427	+	15.2169i	0.220454	+	0.678488i	0.998721	+	0.0505549i	$0.0160990\pi$
$503$	4.94427	+	15.2169i	0.220454	+	0.678488i	−0.778267	+	0.627933i	$0.783901\pi$
$504$	−3.23607	+	2.35114i	−0.144146	+	0.104728i
$505$	10.0000			0.444994
$506$		0			0
$507$	12.0000			0.532939
$508$	3.23607	−	2.35114i	0.143577	−	0.104315i
$509$	−0.618034	−	1.90211i	−0.0273939	−	0.0843097i	0.936425	−	0.350868i	$-0.114113\pi$
$509$	−0.618034	−	1.90211i	−0.0273939	−	0.0843097i	−0.963819	+	0.266558i	$0.914113\pi$
$510$	−2.16312	+	6.65740i	−0.0957845	+	0.294794i
$511$	19.4164	+	14.1068i	0.858931	+	0.624050i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$		0			0
$514$	0.927051	+	2.85317i	0.0408905	+	0.125848i
$515$	3.23607	−	2.35114i	0.142598	−	0.103604i
$516$	−8.00000			−0.352180
$517$		0			0
$518$	−20.0000			−0.878750
$519$	14.5623	−	10.5801i	0.639214	−	0.464416i
$520$	1.54508	+	4.75528i	0.0677565	+	0.208533i
$521$	−1.85410	+	5.70634i	−0.0812297	+	0.249999i	−0.983421	−	0.181337i	$-0.941958\pi$
$521$	−1.85410	+	5.70634i	−0.0812297	+	0.249999i	0.902191	+	0.431336i	$0.141958\pi$
$522$	−5.66312	−	4.11450i	−0.247868	−	0.180087i
$523$	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
$525$	−4.94427	−	15.2169i	−0.215786	−	0.664120i
$526$	−6.47214	+	4.70228i	−0.282199	+	0.205029i
$527$	−56.0000			−2.43940
$528$		0			0
$529$	−23.0000			−1.00000
$530$	−4.04508	+	2.93893i	−0.175707	+	0.127659i
$531$		0			0
$532$		0			0
$533$	44.4959	+	32.3282i	1.92733	+	1.40029i
$534$	13.7533	+	9.99235i	0.595163	+	0.432411i
$535$		0			0
$536$	3.70820	+	11.4127i	0.160170	+	0.492953i
$537$	−9.70820	+	7.05342i	−0.418940	+	0.304378i
$538$	−5.00000			−0.215565
$539$		0			0
$540$	−1.00000			−0.0430331
$541$	−24.2705	+	17.6336i	−1.04347	+	0.758126i	−0.970960	−	0.239242i	$-0.923101\pi$
$541$	−24.2705	+	17.6336i	−1.04347	+	0.758126i	−0.0725107	+	0.997368i	$0.523101\pi$
$542$	−2.47214	−	7.60845i	−0.106187	−	0.326811i
$543$	−0.309017	+	0.951057i	−0.0132612	+	0.0408137i
$544$	−5.66312	−	4.11450i	−0.242804	−	0.176408i
$545$	−0.809017	−	0.587785i	−0.0346545	−	0.0251780i
$546$	−6.18034	+	19.0211i	−0.264494	+	0.814029i
$547$	1.23607	+	3.80423i	0.0528505	+	0.162657i	0.973998	−	0.226557i	$-0.0727468\pi$
$547$	1.23607	+	3.80423i	0.0528505	+	0.162657i	−0.921148	+	0.389214i	$0.872747\pi$
$548$	−8.09017	+	5.87785i	−0.345595	+	0.251089i
$549$	−2.00000			−0.0853579
$550$		0			0
$551$		0			0
$552$		0			0
$553$	4.94427	+	15.2169i	0.210252	+	0.647089i
$554$	7.10739	−	21.8743i	0.301964	−	0.929350i
$555$	−4.04508	−	2.93893i	−0.171704	−	0.124750i
$556$	9.70820	+	7.05342i	0.411720	+	0.299132i
$557$	4.32624	−	13.3148i	0.183309	−	0.564166i	−0.816607	−	0.577195i	$-0.804147\pi$
$557$	4.32624	−	13.3148i	0.183309	−	0.564166i	0.999915	+	0.0130289i	$0.00414735\pi$
$558$	−2.47214	−	7.60845i	−0.104654	−	0.322091i
$559$	−32.3607	+	23.5114i	−1.36871	+	0.994427i
$560$	−4.00000			−0.169031
$561$		0			0
$562$	10.0000			0.421825
$563$	−29.1246	+	21.1603i	−1.22746	+	0.891799i	−0.996697	−	0.0812119i	$-0.974121\pi$
$563$	−29.1246	+	21.1603i	−1.22746	+	0.891799i	−0.230759	+	0.973011i	$0.574121\pi$
$564$	1.23607	+	3.80423i	0.0520479	+	0.160187i
$565$	−0.927051	+	2.85317i	−0.0390013	+	0.120034i
$566$	−3.23607	−	2.35114i	−0.136022	−	0.0988258i
$567$	−3.23607	−	2.35114i	−0.135902	−	0.0987386i
$568$	−4.94427	+	15.2169i	−0.207457	+	0.638487i
$569$	8.03444	+	24.7275i	0.336821	+	1.03663i	0.965818	+	0.259221i	$0.0834659\pi$
$569$	8.03444	+	24.7275i	0.336821	+	1.03663i	−0.628997	+	0.777408i	$0.716534\pi$
$570$		0			0
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$		0			0
$573$	4.00000			0.167102
$574$	−35.5967	+	25.8626i	−1.48578	+	1.07948i
$575$		0			0
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−5.66312	−	4.11450i	−0.235759	−	0.171289i	0.463633	−	0.886027i	$-0.346546\pi$
$577$	−5.66312	−	4.11450i	−0.235759	−	0.171289i	−0.699392	+	0.714739i	$0.746546\pi$
$578$	−25.8885	−	18.8091i	−1.07682	−	0.782357i
$579$	3.39919	−	10.4616i	0.141265	−	0.434770i
$580$	−2.16312	−	6.65740i	−0.0898186	−	0.276433i
$581$	25.8885	−	18.8091i	1.07404	−	0.780334i
$582$	−5.00000			−0.207257
$583$		0			0
$584$	−6.00000			−0.248282
$585$	−4.04508	+	2.93893i	−0.167244	+	0.121510i
$586$	7.10739	+	21.8743i	0.293604	+	0.903619i
$587$	−8.65248	+	26.6296i	−0.357126	+	1.09912i	0.597641	+	0.801764i	$0.296105\pi$
$587$	−8.65248	+	26.6296i	−0.357126	+	1.09912i	−0.954767	+	0.297356i	$0.903895\pi$
$588$	−7.28115	−	5.29007i	−0.300270	−	0.218159i
$589$		0			0
$590$		0			0
$591$	−2.78115	−	8.55951i	−0.114401	−	0.352091i
$592$	4.04508	−	2.93893i	0.166252	−	0.120789i
$593$	35.0000			1.43728			0.718639	−	0.695383i	$-0.244765\pi$
$593$	35.0000			1.43728			0.718639	+	0.695383i	$0.244765\pi$
$594$		0			0
$595$	−28.0000			−1.14789
$596$	0.809017	−	0.587785i	0.0331386	−	0.0240766i
$597$	−4.94427	−	15.2169i	−0.202356	−	0.622786i
$598$		0			0
$599$	−29.1246	−	21.1603i	−1.19000	−	0.864585i	−0.196735	−	0.980457i	$-0.563034\pi$
$599$	−29.1246	−	21.1603i	−1.19000	−	0.864585i	−0.993264	+	0.115872i	$0.963034\pi$
$600$	3.23607	+	2.35114i	0.132112	+	0.0959849i
$601$	−13.9058	+	42.7975i	−0.567228	+	1.74575i	0.0940092	+	0.995571i	$0.470032\pi$
$601$	−13.9058	+	42.7975i	−0.567228	+	1.74575i	−0.661237	+	0.750177i	$0.729968\pi$
$602$	−9.88854	−	30.4338i	−0.403027	−	1.24039i
$603$	−9.70820	+	7.05342i	−0.395349	+	0.287238i
$604$	20.0000			0.813788
$605$		0			0
$606$	−10.0000			−0.406222
$607$	32.3607	−	23.5114i	1.31348	−	0.954299i	0.313491	−	0.949591i	$-0.398502\pi$
$607$	32.3607	−	23.5114i	1.31348	−	0.954299i	0.999989	−	0.00470738i	$-0.00149841\pi$
$608$		0			0
$609$	8.65248	−	26.6296i	0.350616	−	1.07909i
$610$	−1.61803	−	1.17557i	−0.0655123	−	0.0475975i
$611$	16.1803	+	11.7557i	0.654586	+	0.475585i
$612$	2.16312	−	6.65740i	0.0874389	−	0.269109i
$613$	−7.72542	−	23.7764i	−0.312027	−	0.960320i	−0.976961	−	0.213418i	$-0.931540\pi$
$613$	−7.72542	−	23.7764i	−0.312027	−	0.960320i	0.664934	−	0.746902i	$-0.268460\pi$
$614$	−6.47214	+	4.70228i	−0.261194	+	0.189769i
$615$	−11.0000			−0.443563
$616$		0			0
$617$	−25.0000			−1.00646			−0.503231	−	0.864152i	$-0.667856\pi$
$617$	−25.0000			−1.00646			−0.503231	+	0.864152i	$0.667856\pi$
$618$	−3.23607	+	2.35114i	−0.130174	+	0.0945768i
$619$	1.23607	+	3.80423i	0.0496818	+	0.152905i	0.972820	−	0.231565i	$-0.0743845\pi$
$619$	1.23607	+	3.80423i	0.0496818	+	0.152905i	−0.923138	+	0.384469i	$0.874384\pi$
$620$	2.47214	−	7.60845i	0.0992834	−	0.305563i
$621$		0			0
$622$	−16.1803	−	11.7557i	−0.648773	−	0.471361i
$623$	−21.0132	+	64.6718i	−0.841874	+	2.59102i
$624$	−1.54508	−	4.75528i	−0.0618529	−	0.190364i
$625$	−8.89919	+	6.46564i	−0.355967	+	0.258626i
$626$	−9.00000			−0.359712
$627$		0			0
$628$	−18.0000			−0.718278
$629$	28.3156	−	20.5725i	1.12902	−	0.820279i
$630$	−1.23607	−	3.80423i	−0.0492461	−	0.151564i
$631$	−7.41641	+	22.8254i	−0.295243	+	0.908663i	0.687897	+	0.725808i	$0.258534\pi$
$631$	−7.41641	+	22.8254i	−0.295243	+	0.908663i	−0.983140	+	0.182855i	$0.941466\pi$
$632$	−3.23607	−	2.35114i	−0.128724	−	0.0935234i
$633$		0			0
$634$	−0.618034	+	1.90211i	−0.0245453	+	0.0755426i
$635$	1.23607	+	3.80423i	0.0490519	+	0.150966i
$636$	4.04508	−	2.93893i	0.160398	−	0.116536i
$637$	−45.0000			−1.78296
$638$		0			0
$639$	−16.0000			−0.632950
$640$	0.809017	−	0.587785i	0.0319792	−	0.0232343i
$641$	−10.1976	−	31.3849i	−0.402779	−	1.23963i	−0.922735	−	0.385434i	$-0.874052\pi$
$641$	−10.1976	−	31.3849i	−0.402779	−	1.23963i	0.519956	−	0.854193i	$-0.325948\pi$
$642$		0			0
$643$	12.9443	+	9.40456i	0.510472	+	0.370880i	0.813003	−	0.582260i	$-0.197831\pi$
$643$	12.9443	+	9.40456i	0.510472	+	0.370880i	−0.302530	+	0.953140i	$0.597831\pi$
$644$		0			0
$645$	2.47214	−	7.60845i	0.0973403	−	0.299583i
$646$		0			0
$647$	3.23607	−	2.35114i	0.127223	−	0.0924329i	−0.522354	−	0.852729i	$-0.674946\pi$
$647$	3.23607	−	2.35114i	0.127223	−	0.0924329i	0.649577	+	0.760296i	$0.274946\pi$
$648$	1.00000			0.0392837
$649$		0			0
$650$	20.0000			0.784465
$651$	25.8885	−	18.8091i	1.01465	−	0.737188i
$652$	1.23607	+	3.80423i	0.0484082	+	0.148985i
$653$	9.27051	−	28.5317i	0.362783	−	1.11653i	−0.588575	−	0.808443i	$-0.700311\pi$
$653$	9.27051	−	28.5317i	0.362783	−	1.11653i	0.951358	−	0.308089i	$-0.0996893\pi$
$654$	0.809017	+	0.587785i	0.0316351	+	0.0229842i
$655$	−9.70820	−	7.05342i	−0.379331	−	0.275600i
$656$	3.39919	−	10.4616i	0.132716	−	0.408458i
$657$	−1.85410	−	5.70634i	−0.0723354	−	0.222625i
$658$	−12.9443	+	9.40456i	−0.504620	+	0.366628i
$659$	28.0000			1.09073			0.545363	−	0.838200i	$-0.316392\pi$
$659$	28.0000			1.09073			0.545363	+	0.838200i	$0.316392\pi$
$660$		0			0
$661$	−9.00000			−0.350059			−0.175030	−	0.984563i	$-0.556002\pi$
$661$	−9.00000			−0.350059			−0.175030	+	0.984563i	$0.556002\pi$
$662$	−25.8885	+	18.8091i	−1.00619	+	0.731038i
$663$	−10.8156	−	33.2870i	−0.420043	−	1.29276i
$664$	−2.47214	+	7.60845i	−0.0959375	+	0.295265i
$665$		0			0
$666$	4.04508	+	2.93893i	0.156744	+	0.113881i
$667$		0			0
$668$	3.70820	+	11.4127i	0.143475	+	0.441570i
$669$	−16.1803	+	11.7557i	−0.625568	+	0.454502i
$670$	−12.0000			−0.463600
$671$		0			0
$672$	4.00000			0.154303
$673$	−1.61803	+	1.17557i	−0.0623706	+	0.0453149i	−0.618534	−	0.785758i	$-0.712273\pi$
$673$	−1.61803	+	1.17557i	−0.0623706	+	0.0453149i	0.556163	+	0.831073i	$0.312273\pi$
$674$	−0.309017	−	0.951057i	−0.0119029	−	0.0366333i
$675$	−1.23607	+	3.80423i	−0.0475763	+	0.146425i
$676$	−9.70820	−	7.05342i	−0.373392	−	0.271286i
$677$	20.2254	+	14.6946i	0.777326	+	0.564761i	0.904175	−	0.427161i	$-0.140486\pi$
$677$	20.2254	+	14.6946i	0.777326	+	0.564761i	−0.126849	+	0.991922i	$0.540486\pi$
$678$	0.927051	−	2.85317i	0.0356032	−	0.109575i
$679$	−6.18034	−	19.0211i	−0.237180	−	0.729964i
$680$	5.66312	−	4.11450i	0.217171	−	0.157784i
$681$		0			0
$682$		0			0
$683$	−52.0000			−1.98972			−0.994862	−	0.101237i	$-0.967720\pi$
$683$	−52.0000			−1.98972			−0.994862	+	0.101237i	$0.967720\pi$
$684$		0			0
$685$	−3.09017	−	9.51057i	−0.118069	−	0.363380i
$686$	2.47214	−	7.60845i	0.0943866	−	0.290492i
$687$	4.04508	+	2.93893i	0.154330	+	0.112127i
$688$	6.47214	+	4.70228i	0.246748	+	0.179273i
$689$	7.72542	−	23.7764i	0.294315	−	0.905809i
$690$		0			0
$691$	−3.23607	+	2.35114i	−0.123106	+	0.0894416i	−0.647634	−	0.761951i	$-0.724242\pi$
$691$	−3.23607	+	2.35114i	−0.123106	+	0.0894416i	0.524529	+	0.851393i	$0.324242\pi$
$692$	−18.0000			−0.684257
$693$		0			0
$694$	24.0000			0.911028
$695$	−9.70820	+	7.05342i	−0.368253	+	0.267552i
$696$	2.16312	+	6.65740i	0.0819928	+	0.252348i
$697$	23.7943	−	73.2314i	0.901274	−	2.77384i
$698$	−5.66312	−	4.11450i	−0.214352	−	0.155736i
$699$	7.28115	+	5.29007i	0.275398	+	0.200089i
$700$	−4.94427	+	15.2169i	−0.186876	+	0.575145i
$701$	−10.1976	−	31.3849i	−0.385157	−	1.18539i	−0.936367	−	0.351024i	$-0.885834\pi$
$701$	−10.1976	−	31.3849i	−0.385157	−	1.18539i	0.551210	−	0.834366i	$-0.314166\pi$
$702$	4.04508	−	2.93893i	0.152672	−	0.110923i
$703$		0			0
$704$		0			0
$705$	−4.00000			−0.150649
$706$	−21.8435	+	15.8702i	−0.822089	+	0.597283i
$707$	−12.3607	−	38.0423i	−0.464871	−	1.43073i
$708$		0			0
$709$	21.0344	+	15.2824i	0.789965	+	0.573943i	0.907953	−	0.419072i	$-0.137644\pi$
$709$	21.0344	+	15.2824i	0.789965	+	0.573943i	−0.117988	+	0.993015i	$0.537644\pi$
$710$	−12.9443	−	9.40456i	−0.485790	−	0.352947i
$711$	1.23607	−	3.80423i	0.0463562	−	0.142670i
$712$	−5.25329	−	16.1680i	−0.196875	−	0.605920i
$713$		0			0
$714$	28.0000			1.04787
$715$		0			0
$716$	12.0000			0.448461
$717$	−3.23607	+	2.35114i	−0.120853	+	0.0878050i
$718$	1.23607	+	3.80423i	0.0461296	+	0.141972i
$719$	1.23607	−	3.80423i	0.0460976	−	0.141874i	−0.925359	−	0.379093i	$-0.876236\pi$
$719$	1.23607	−	3.80423i	0.0460976	−	0.141874i	0.971456	+	0.237219i	$0.0762360\pi$
$720$	0.809017	+	0.587785i	0.0301503	+	0.0219055i
$721$	−12.9443	−	9.40456i	−0.482070	−	0.350244i
$722$	−5.87132	+	18.0701i	−0.218508	+	0.672499i
$723$	5.56231	+	17.1190i	0.206864	+	0.636663i
$724$	0.809017	−	0.587785i	0.0300669	−	0.0218449i
$725$	−28.0000			−1.03989
$726$		0			0
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$	16.1803	−	11.7557i	0.599683	−	0.435695i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	1.85410	−	5.70634i	0.0686234	−	0.211201i
$731$	45.3050	+	32.9160i	1.67566	+	1.21744i
$732$	1.61803	+	1.17557i	0.0598043	+	0.0434503i
$733$	−5.25329	+	16.1680i	−0.194035	+	0.597177i	0.805952	+	0.591981i	$0.201654\pi$
$733$	−5.25329	+	16.1680i	−0.194035	+	0.597177i	−0.999986	+	0.00519616i	$0.998346\pi$
$734$	2.47214	+	7.60845i	0.0912482	+	0.280833i
$735$	7.28115	−	5.29007i	0.268569	−	0.195127i
$736$		0			0
$737$		0			0
$738$	11.0000			0.404916
$739$	−16.1803	+	11.7557i	−0.595203	+	0.432441i	−0.844173	−	0.536071i	$-0.819908\pi$
$739$	−16.1803	+	11.7557i	−0.595203	+	0.432441i	0.248970	+	0.968511i	$0.419908\pi$
$740$	1.54508	+	4.75528i	0.0567985	+	0.174808i
$741$		0			0
$742$	16.1803	+	11.7557i	0.593999	+	0.431566i
$743$	12.9443	+	9.40456i	0.474879	+	0.345020i	0.799340	−	0.600879i	$-0.205183\pi$
$743$	12.9443	+	9.40456i	0.474879	+	0.345020i	−0.324461	+	0.945899i	$0.605183\pi$
$744$	−2.47214	+	7.60845i	−0.0906329	+	0.278939i
$745$	0.309017	+	0.951057i	0.0113215	+	0.0348440i
$746$	−17.7984	+	12.9313i	−0.651645	+	0.473448i
$747$	−8.00000			−0.292705
$748$		0			0
$749$		0			0
$750$	−7.28115	+	5.29007i	−0.265870	+	0.193166i
$751$	−9.88854	−	30.4338i	−0.360838	−	1.11055i	−0.952546	−	0.304393i	$-0.901546\pi$
$751$	−9.88854	−	30.4338i	−0.360838	−	1.11055i	0.591708	−	0.806152i	$-0.298454\pi$
$752$	1.23607	−	3.80423i	0.0450748	−	0.138726i
$753$	−12.9443	−	9.40456i	−0.471715	−	0.342721i
$754$	28.3156	+	20.5725i	1.03119	+	0.749206i
$755$	−6.18034	+	19.0211i	−0.224926	+	0.692250i
$756$	1.23607	+	3.80423i	0.0449554	+	0.138358i
$757$	26.6976	−	19.3969i	0.970339	−	0.704993i	0.0148105	−	0.999890i	$-0.495286\pi$
$757$	26.6976	−	19.3969i	0.970339	−	0.704993i	0.955529	+	0.294898i	$0.0952855\pi$
$758$	−20.0000			−0.726433
$759$		0			0
$760$		0			0
$761$	−34.7877	+	25.2748i	−1.26105	+	0.916210i	−0.998809	−	0.0487917i	$-0.984463\pi$
$761$	−34.7877	+	25.2748i	−1.26105	+	0.916210i	−0.262245	+	0.965001i	$0.584463\pi$
$762$	−1.23607	−	3.80423i	−0.0447780	−	0.137813i
$763$	−1.23607	+	3.80423i	−0.0447487	+	0.137722i
$764$	−3.23607	−	2.35114i	−0.117077	−	0.0850613i
$765$	5.66312	+	4.11450i	0.204750	+	0.148760i
$766$	−11.1246	+	34.2380i	−0.401949	+	1.23707i
$767$		0			0
$768$	−0.809017	+	0.587785i	−0.0291929	+	0.0212099i
$769$	19.0000			0.685158			0.342579	−	0.939489i	$-0.388700\pi$
$769$	19.0000			0.685158			0.342579	+	0.939489i	$0.388700\pi$
$770$		0			0
$771$	3.00000			0.108042
$772$	−8.89919	+	6.46564i	−0.320289	+	0.232703i
$773$	−8.03444	−	24.7275i	−0.288979	−	0.889385i	−0.985178	−	0.171536i	$-0.945127\pi$
$773$	−8.03444	−	24.7275i	−0.288979	−	0.889385i	0.696199	−	0.717849i	$-0.254873\pi$
$774$	−2.47214	+	7.60845i	−0.0888591	+	0.273480i
$775$	−25.8885	−	18.8091i	−0.929944	−	0.675644i
$776$	4.04508	+	2.93893i	0.145210	+	0.105501i
$777$	−6.18034	+	19.0211i	−0.221718	+	0.682379i
$778$	−8.96149	−	27.5806i	−0.321285	−	0.988814i
$779$		0			0
$780$	5.00000			0.179029
$781$		0			0
$782$		0			0
$783$	−5.66312	+	4.11450i	−0.202383	+	0.147040i
$784$	2.78115	+	8.55951i	0.0993269	+	0.305697i
$785$	5.56231	−	17.1190i	0.198527	−	0.611004i
$786$	9.70820	+	7.05342i	0.346280	+	0.251587i
$787$	22.6525	+	16.4580i	0.807474	+	0.586664i	0.913097	−	0.407742i	$-0.133684\pi$
$787$	22.6525	+	16.4580i	0.807474	+	0.586664i	−0.105623	+	0.994406i	$0.533684\pi$
$788$	−2.78115	+	8.55951i	−0.0990745	+	0.304920i
$789$	2.47214	+	7.60845i	0.0880104	+	0.270868i
$790$	3.23607	−	2.35114i	0.115134	−	0.0836498i
$791$	12.0000			0.426671
$792$		0			0
$793$	10.0000			0.355110
$794$	16.9894	−	12.3435i	0.602930	−	0.438054i
$795$	1.54508	+	4.75528i	0.0547985	+	0.168652i
$796$	−4.94427	+	15.2169i	−0.175245	+	0.539349i
$797$	1.61803	+	1.17557i	0.0573137	+	0.0416408i	0.616073	−	0.787689i	$-0.288723\pi$
$797$	1.61803	+	1.17557i	0.0573137	+	0.0416408i	−0.558760	+	0.829330i	$0.688723\pi$
$798$		0			0
$799$	8.65248	−	26.6296i	0.306103	−	0.942087i
$800$	−1.23607	−	3.80423i	−0.0437016	−	0.134500i
$801$	13.7533	−	9.99235i	0.485949	−	0.353062i
$802$	15.0000			0.529668
$803$		0			0
$804$	12.0000			0.423207
$805$		0			0
$806$	12.3607	+	38.0423i	0.435386	+	1.33998i
$807$	−1.54508	+	4.75528i	−0.0543896	+	0.167394i
$808$	8.09017	+	5.87785i	0.284611	+	0.206782i
$809$	30.7426	+	22.3358i	1.08085	+	0.785286i	0.977832	−	0.209393i	$-0.0671487\pi$
$809$	30.7426	+	22.3358i	1.08085	+	0.785286i	0.103022	+	0.994679i	$0.467149\pi$
$810$	−0.309017	+	0.951057i	−0.0108578	+	0.0334167i
$811$	7.41641	+	22.8254i	0.260425	+	0.801507i	0.992712	+	0.120510i	$0.0384531\pi$
$811$	7.41641	+	22.8254i	0.260425	+	0.801507i	−0.732287	+	0.680996i	$0.761547\pi$
$812$	−22.6525	+	16.4580i	−0.794946	+	0.577562i
$813$	−8.00000			−0.280572
$814$		0			0
$815$	−4.00000			−0.140114
$816$	−5.66312	+	4.11450i	−0.198249	+	0.144036i
$817$		0			0
$818$	−0.309017	+	0.951057i	−0.0108045	+	0.0332529i
$819$	16.1803	+	11.7557i	0.565387	+	0.410778i
$820$	8.89919	+	6.46564i	0.310773	+	0.225790i
$821$	6.79837	−	20.9232i	0.237265	−	0.730226i	−0.759548	−	0.650451i	$-0.774580\pi$
$821$	6.79837	−	20.9232i	0.237265	−	0.730226i	0.996813	−	0.0797750i	$-0.0254202\pi$
$822$	3.09017	+	9.51057i	0.107782	+	0.331719i
$823$	19.4164	−	14.1068i	0.676813	−	0.491734i	−0.195486	−	0.980707i	$-0.562628\pi$
$823$	19.4164	−	14.1068i	0.676813	−	0.491734i	0.872299	+	0.488973i	$0.162628\pi$
$824$	4.00000			0.139347
$825$		0			0
$826$		0			0
$827$	−9.70820	+	7.05342i	−0.337587	+	0.245272i	−0.743643	−	0.668577i	$-0.766904\pi$
$827$	−9.70820	+	7.05342i	−0.337587	+	0.245272i	0.406056	+	0.913848i	$0.366904\pi$
$828$		0			0
$829$	−6.48936	+	19.9722i	−0.225385	+	0.693663i	0.772868	+	0.634567i	$0.218822\pi$
$829$	−6.48936	+	19.9722i	−0.225385	+	0.693663i	−0.998252	+	0.0590955i	$0.981178\pi$
$830$	−6.47214	−	4.70228i	−0.224651	−	0.163219i
$831$	−18.6074	−	13.5191i	−0.645483	−	0.468971i
$832$	−1.54508	+	4.75528i	−0.0535662	+	0.164860i
$833$	19.4681	+	59.9166i	0.674529	+	2.07599i
$834$	9.70820	−	7.05342i	0.336168	−	0.244240i
$835$	−12.0000			−0.415277
$836$		0			0
$837$	−8.00000			−0.276520
$838$		0			0
$839$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$839$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$840$	−1.23607	+	3.80423i	−0.0426484	+	0.131258i
$841$	−16.1803	−	11.7557i	−0.557943	−	0.405369i
$842$	−12.1353	−	8.81678i	−0.418209	−	0.303846i
$843$	3.09017	−	9.51057i	0.106431	−	0.327561i
$844$		0			0
$845$	9.70820	−	7.05342i	0.333972	−	0.242645i
$846$	4.00000			0.137523
$847$		0			0
$848$	−5.00000			−0.171701
$849$	−3.23607	+	2.35114i	−0.111062	+	0.0806910i
$850$	−8.65248	−	26.6296i	−0.296777	−	0.913387i
$851$		0			0
$852$	12.9443	+	9.40456i	0.443463	+	0.322195i
$853$	16.9894	+	12.3435i	0.581705	+	0.422633i	0.839338	−	0.543610i	$-0.182943\pi$
$853$	16.9894	+	12.3435i	0.581705	+	0.422633i	−0.257634	+	0.966243i	$0.582943\pi$
$854$	−2.47214	+	7.60845i	−0.0845948	+	0.260356i
$855$		0			0
$856$		0			0
$857$	26.0000			0.888143			0.444072	−	0.895991i	$-0.353534\pi$
$857$	26.0000			0.888143			0.444072	+	0.895991i	$0.353534\pi$
$858$		0			0
$859$	−56.0000			−1.91070			−0.955348	−	0.295484i	$-0.904519\pi$
$859$	−56.0000			−1.91070			−0.955348	+	0.295484i	$0.904519\pi$
$860$	−6.47214	+	4.70228i	−0.220698	+	0.160346i
$861$	13.5967	+	41.8465i	0.463376	+	1.42612i
$862$	6.18034	−	19.0211i	0.210503	−	0.647862i
$863$	−9.70820	−	7.05342i	−0.330471	−	0.240101i	0.410159	−	0.912014i	$-0.365473\pi$
$863$	−9.70820	−	7.05342i	−0.330471	−	0.240101i	−0.740630	+	0.671913i	$0.765473\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	5.56231	−	17.1190i	0.189124	−	0.582064i
$866$	−6.48936	−	19.9722i	−0.220517	−	0.678683i
$867$	−25.8885	+	18.8091i	−0.879221	+	0.638791i
$868$	−32.0000			−1.08615
$869$		0			0
$870$	−7.00000			−0.237322
$871$	48.5410	−	35.2671i	1.64475	−	1.19498i
$872$	−0.309017	−	0.951057i	−0.0104646	−	0.0322068i
$873$	−1.54508	+	4.75528i	−0.0522932	+	0.160942i
$874$		0			0
$875$	−29.1246	−	21.1603i	−0.984592	−	0.715348i
$876$	−1.85410	+	5.70634i	−0.0626443	+	0.192799i
$877$	−1.54508	−	4.75528i	−0.0521738	−	0.160574i	0.921575	−	0.388201i	$-0.126903\pi$
$877$	−1.54508	−	4.75528i	−0.0521738	−	0.160574i	−0.973748	+	0.227627i	$0.926903\pi$
$878$	−12.9443	+	9.40456i	−0.436848	+	0.317389i
$879$	23.0000			0.775771
$880$		0			0
$881$	19.0000			0.640126			0.320063	−	0.947396i	$-0.396296\pi$
$881$	19.0000			0.640126			0.320063	+	0.947396i	$0.396296\pi$
$882$	−7.28115	+	5.29007i	−0.245169	+	0.178126i
$883$	−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	$-0.256156\pi$
$884$	−10.8156	+	33.2870i	−0.363768	+	1.11956i
$885$		0			0
$886$	−29.1246	−	21.1603i	−0.978460	−	0.710893i
$887$	3.70820	−	11.4127i	0.124509	−	0.383200i	−0.869302	−	0.494281i	$-0.835431\pi$
$887$	3.70820	−	11.4127i	0.124509	−	0.383200i	0.993811	+	0.111081i	$0.0354313\pi$
$888$	−1.54508	−	4.75528i	−0.0518497	−	0.159577i
$889$	12.9443	−	9.40456i	0.434137	−	0.315419i
$890$	17.0000			0.569841
$891$		0			0
$892$	20.0000			0.669650
$893$		0			0
$894$	−0.309017	−	0.951057i	−0.0103351	−	0.0318081i
$895$	−3.70820	+	11.4127i	−0.123952	+	0.381484i
$896$	−3.23607	−	2.35114i	−0.108109	−	0.0785461i
$897$		0			0
$898$	4.63525	−	14.2658i	0.154680	−	0.476058i
$899$	−17.3050	−	53.2592i	−0.577152	−	1.77629i
$900$	3.23607	−	2.35114i	0.107869	−	0.0783714i
$901$	−35.0000			−1.16602
$902$		0			0
$903$	−32.0000			−1.06489
$904$	−2.42705	+	1.76336i	−0.0807225	+	0.0586483i
$905$	0.309017	+	0.951057i	0.0102721	+	0.0316142i
$906$	6.18034	−	19.0211i	0.205328	−	0.631935i
$907$	−38.8328	−	28.2137i	−1.28942	−	0.936820i	−0.289629	−	0.957139i	$-0.593532\pi$
$907$	−38.8328	−	28.2137i	−1.28942	−	0.936820i	−0.999794	+	0.0203187i	$0.993532\pi$
$908$		0			0
$909$	−3.09017	+	9.51057i	−0.102494	+	0.315446i
$910$	6.18034	+	19.0211i	0.204876	+	0.630544i
$911$	−16.1803	+	11.7557i	−0.536079	+	0.389484i	−0.822627	−	0.568582i	$-0.807492\pi$
$911$	−16.1803	+	11.7557i	−0.536079	+	0.389484i	0.286548	+	0.958066i	$0.407492\pi$
$912$		0			0
$913$		0			0
$914$	−17.0000			−0.562310
$915$	−1.61803	+	1.17557i	−0.0534906	+	0.0388632i
$916$	−1.54508	−	4.75528i	−0.0510510	−	0.157119i
$917$	−14.8328	+	45.6507i	−0.489823	+	1.50752i
$918$	−5.66312	−	4.11450i	−0.186911	−	0.135799i
$919$	−16.1803	−	11.7557i	−0.533740	−	0.387785i	0.288015	−	0.957626i	$-0.407005\pi$
$919$	−16.1803	−	11.7557i	−0.533740	−	0.387785i	−0.821755	+	0.569841i	$0.807005\pi$
$920$		0			0
$921$	2.47214	+	7.60845i	0.0814596	+	0.250707i
$922$	26.6976	−	19.3969i	0.879237	−	0.638803i
$923$	80.0000			2.63323
$924$		0			0
$925$	20.0000			0.657596
$926$	6.47214	−	4.70228i	0.212688	−	0.154527i
$927$	1.23607	+	3.80423i	0.0405978	+	0.124947i
$928$	2.16312	−	6.65740i	0.0710079	−	0.218540i
$929$	7.28115	+	5.29007i	0.238887	+	0.173561i	0.700787	−	0.713370i	$-0.252832\pi$
$929$	7.28115	+	5.29007i	0.238887	+	0.173561i	−0.461900	+	0.886932i	$0.652832\pi$
$930$	−6.47214	−	4.70228i	−0.212230	−	0.154194i
$931$		0			0
$932$	−2.78115	−	8.55951i	−0.0910997	−	0.280376i
$933$	−16.1803	+	11.7557i	−0.529721	+	0.384865i
$934$	28.0000			0.916188
$935$		0			0
$936$	−5.00000			−0.163430
$937$	42.8779	−	31.1526i	1.40076	−	1.01771i	0.406174	−	0.913796i	$-0.366863\pi$
$937$	42.8779	−	31.1526i	1.40076	−	1.01771i	0.994586	−	0.103916i	$-0.0331373\pi$
$938$	14.8328	+	45.6507i	0.484309	+	1.49055i
$939$	−2.78115	+	8.55951i	−0.0907595	+	0.279329i
$940$	3.23607	+	2.35114i	0.105549	+	0.0766858i
$941$	26.6976	+	19.3969i	0.870316	+	0.632321i	0.930672	−	0.365856i	$-0.119224\pi$
$941$	26.6976	+	19.3969i	0.870316	+	0.632321i	−0.0603560	+	0.998177i	$0.519224\pi$
$942$	−5.56231	+	17.1190i	−0.181230	+	0.557768i
$943$		0			0
$944$		0			0
$945$	−4.00000			−0.130120
$946$		0			0
$947$	52.0000			1.68977			0.844886	−	0.534946i	$-0.179668\pi$
$947$	52.0000			1.68977			0.844886	+	0.534946i	$0.179668\pi$
$948$	−3.23607	+	2.35114i	−0.105103	+	0.0763615i
$949$	9.27051	+	28.5317i	0.300933	+	0.926178i
$950$		0			0
$951$	1.61803	+	1.17557i	0.0524683	+	0.0381205i
$952$	−22.6525	−	16.4580i	−0.734171	−	0.533406i
$953$	0.927051	−	2.85317i	0.0300301	−	0.0924232i	−0.934918	−	0.354864i	$-0.884527\pi$
$953$	0.927051	−	2.85317i	0.0300301	−	0.0924232i	0.964948	+	0.262440i	$0.0845273\pi$
$954$	−1.54508	−	4.75528i	−0.0500240	−	0.153958i
$955$	3.23607	−	2.35114i	0.104717	−	0.0760811i
$956$	4.00000			0.129369
$957$		0			0
$958$	4.00000			0.129234
$959$	−32.3607	+	23.5114i	−1.04498	+	0.759223i
$960$	−0.309017	−	0.951057i	−0.00997348	−	0.0306952i
$961$	10.1976	−	31.3849i	0.328954	−	1.01242i
$962$	−20.2254	−	14.6946i	−0.652094	−	0.473774i
$963$		0			0
$964$	5.56231	−	17.1190i	0.179150	−	0.551366i
$965$	−3.39919	−	10.4616i	−0.109424	−	0.336772i
$966$		0			0
$967$	−40.0000			−1.28631			−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000			−1.28631			−0.643157	+	0.765735i	$0.722376\pi$
$968$		0			0
$969$		0			0
$970$	−4.04508	+	2.93893i	−0.129880	+	0.0943632i
$971$	6.18034	+	19.0211i	0.198337	+	0.610417i	0.999921	+	0.0125361i	$0.00399048\pi$
$971$	6.18034	+	19.0211i	0.198337	+	0.610417i	−0.801585	+	0.597881i	$0.796010\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	38.8328	+	28.2137i	1.24492	+	0.904489i
$974$	16.1803	+	11.7557i	0.518452	+	0.376677i
$975$	6.18034	−	19.0211i	0.197929	−	0.609164i
$976$	−0.618034	−	1.90211i	−0.0197828	−	0.0608852i
$977$	39.6418	−	28.8015i	1.26825	−	0.921441i	0.269123	−	0.963106i	$-0.413266\pi$
$977$	39.6418	−	28.8015i	1.26825	−	0.921441i	0.999132	+	0.0416649i	$0.0132662\pi$
$978$	4.00000			0.127906
$979$		0			0
$980$	−9.00000			−0.287494
$981$	0.809017	−	0.587785i	0.0258299	−	0.0187665i
$982$	−3.70820	−	11.4127i	−0.118334	−	0.364193i
$983$	−8.65248	+	26.6296i	−0.275971	+	0.849352i	0.712990	+	0.701175i	$0.247341\pi$
$983$	−8.65248	+	26.6296i	−0.275971	+	0.849352i	−0.988961	+	0.148177i	$0.952659\pi$
$984$	−8.89919	−	6.46564i	−0.283696	−	0.206117i
$985$	−7.28115	−	5.29007i	−0.231997	−	0.168556i
$986$	15.1418	−	46.6018i	0.482214	−	1.48410i
$987$	4.94427	+	15.2169i	0.157378	+	0.484359i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−20.0000			−0.635321			−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000			−0.635321			−0.317660	+	0.948205i	$0.602897\pi$
$992$	6.47214	−	4.70228i	0.205491	−	0.149298i
$993$	9.88854	+	30.4338i	0.313803	+	0.965788i
$994$	−19.7771	+	60.8676i	−0.627291	+	1.93060i
$995$	−12.9443	−	9.40456i	−0.410361	−	0.298145i
$996$	6.47214	+	4.70228i	0.205077	+	0.148998i
$997$	−11.4336	+	35.1891i	−0.362107	+	1.11445i	0.589666	+	0.807647i	$0.299259\pi$
$997$	−11.4336	+	35.1891i	−0.362107	+	1.11445i	−0.951773	+	0.306803i	$0.900741\pi$
$998$	12.3607	+	38.0423i	0.391270	+	1.20421i
$999$	4.04508	−	2.93893i	0.127981	−	0.0929835i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(1.23607 - 3.80423i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.00000 q^{10} +1.00000 q^{12} +(4.04508 - 2.93893i) q^{13} +(1.23607 + 3.80423i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.66312 - 4.11450i) q^{17} +(0.309017 - 0.951057i) q^{18} +(0.809017 - 0.587785i) q^{20} +4.00000 q^{21} +(-0.809017 + 0.587785i) q^{24} +(-1.23607 - 3.80423i) q^{25} +(-1.54508 + 4.75528i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-3.23607 - 2.35114i) q^{28} +(2.16312 - 6.65740i) q^{29} +(-0.309017 - 0.951057i) q^{30} +(6.47214 - 4.70228i) q^{31} +1.00000 q^{32} +7.00000 q^{34} +(3.23607 - 2.35114i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-1.54508 + 4.75528i) q^{37} +(4.04508 + 2.93893i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(3.39919 + 10.4616i) q^{41} +(-3.23607 + 2.35114i) q^{42} -8.00000 q^{43} -1.00000 q^{45} +(1.23607 + 3.80423i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-7.28115 - 5.29007i) q^{49} +(3.23607 + 2.35114i) q^{50} +(2.16312 - 6.65740i) q^{51} +(-1.54508 - 4.75528i) q^{52} +(4.04508 - 2.93893i) q^{53} +1.00000 q^{54} +4.00000 q^{56} +(2.16312 + 6.65740i) q^{58} +(0.809017 + 0.587785i) q^{60} +(1.61803 + 1.17557i) q^{61} +(-2.47214 + 7.60845i) q^{62} +(1.23607 + 3.80423i) q^{63} +(-0.809017 + 0.587785i) q^{64} +5.00000 q^{65} +12.0000 q^{67} +(-5.66312 + 4.11450i) q^{68} +(-1.23607 + 3.80423i) q^{70} +(12.9443 + 9.40456i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-1.85410 + 5.70634i) q^{73} +(-1.54508 - 4.75528i) q^{74} +(3.23607 - 2.35114i) q^{75} -5.00000 q^{78} +(-3.23607 + 2.35114i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-8.89919 - 6.46564i) q^{82} +(6.47214 + 4.70228i) q^{83} +(1.23607 - 3.80423i) q^{84} +(-2.16312 - 6.65740i) q^{85} +(6.47214 - 4.70228i) q^{86} +7.00000 q^{87} -17.0000 q^{89} +(0.809017 - 0.587785i) q^{90} +(-6.18034 - 19.0211i) q^{91} +(6.47214 + 4.70228i) q^{93} +(-3.23607 - 2.35114i) q^{94} +(0.309017 + 0.951057i) q^{96} +(4.04508 - 2.93893i) q^{97} +9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 4 q^{7} - q^{8} - q^{9} - 4 q^{10} + 4 q^{12} + 5 q^{13} - 4 q^{14} + q^{15} - q^{16} - 7 q^{17} - q^{18} + q^{20} + 16 q^{21} - q^{24} + 4 q^{25}+ \cdots + 36 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^3 - q^4 + q^5 - q^6 - 4 * q^7 - q^8 - q^9 - 4 * q^10 + 4 * q^12 + 5 * q^13 - 4 * q^14 + q^15 - q^16 - 7 * q^17 - q^18 + q^20 + 16 * q^21 - q^24 + 4 * q^25 + 5 * q^26 - q^27 - 4 * q^28 - 7 * q^29 + q^30 + 8 * q^31 + 4 * q^32 + 28 * q^34 + 4 * q^35 - q^36 + 5 * q^37 + 5 * q^39 + q^40 - 11 * q^41 - 4 * q^42 - 32 * q^43 - 4 * q^45 - 4 * q^47 - q^48 - 9 * q^49 + 4 * q^50 - 7 * q^51 + 5 * q^52 + 5 * q^53 + 4 * q^54 + 16 * q^56 - 7 * q^58 + q^60 + 2 * q^61 + 8 * q^62 - 4 * q^63 - q^64 + 20 * q^65 + 48 * q^67 - 7 * q^68 + 4 * q^70 + 16 * q^71 - q^72 + 6 * q^73 + 5 * q^74 + 4 * q^75 - 20 * q^78 - 4 * q^79 + q^80 - q^81 - 11 * q^82 + 8 * q^83 - 4 * q^84 + 7 * q^85 + 8 * q^86 + 28 * q^87 - 68 * q^89 + q^90 + 20 * q^91 + 8 * q^93 - 4 * q^94 - q^96 + 5 * q^97 + 36 * q^98

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