LMFDB - Embedded newform 116.2.l.a.19.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [116,2,Mod(3,116)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("116.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(116, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([14, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 116 = 2^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	116.l (of order $28$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.926264663447$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\Q(\zeta_{28})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{28}]$

Embedding invariants

Embedding label			19.1
Root			$-0.974928 - 0.222521i$ of defining polynomial
Character	$\chi$	$=$	116.19
Dual form			116.2.l.a.55.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.752407 - 1.19745i) q^{2} +(-0.867767 + 1.80194i) q^{4} +(3.95589 + 0.902906i) q^{5} +(2.81064 - 0.316683i) q^{8} +(-2.34549 - 1.87047i) q^{9} +(-1.89525 - 5.41633i) q^{10} +(2.86954 - 2.28838i) q^{13} +(-2.49396 - 3.12733i) q^{16} +(-4.03739 + 4.03739i) q^{17} +(-0.475025 + 4.21596i) q^{18} +(-5.05977 + 6.34475i) q^{20} +(10.3290 + 4.97417i) q^{25} +(-4.89928 - 1.71433i) q^{26} +(-5.15614 + 1.55379i) q^{29} +(-1.86834 + 5.33941i) q^{32} +(7.87233 + 1.79681i) q^{34} +(5.40581 - 2.60330i) q^{36} +(-11.9118 + 1.34214i) q^{37} +(11.4045 + 1.28498i) q^{40} +(-4.80592 - 4.80592i) q^{41} +(-7.58966 - 9.51713i) q^{45} +(4.36443 - 5.47282i) q^{49} +(-1.81528 - 16.1110i) q^{50} +(1.63343 + 7.15651i) q^{52} +(-3.23525 + 14.1745i) q^{53} +(5.74009 + 5.00513i) q^{58} +(4.90518 - 14.0182i) q^{61} +(7.79942 - 1.78017i) q^{64} +(13.4178 - 6.46166i) q^{65} +(-3.77161 - 10.7786i) q^{68} +(-7.18469 - 4.51444i) q^{72} +(1.82602 - 2.90610i) q^{73} +(10.5696 + 13.2539i) q^{74} +(-7.04215 - 14.6232i) q^{80} +(2.00269 + 8.77435i) q^{81} +(-2.13884 + 9.37086i) q^{82} +(-19.6168 + 12.3261i) q^{85} +(6.23997 + 9.93085i) q^{89} +(-5.68576 + 16.2490i) q^{90} +(0.530443 + 1.51592i) q^{97} +(-9.83725 - 1.10839i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 4 q^{8} - 8 q^{10} + 8 q^{16} - 10 q^{17} - 6 q^{18} - 40 q^{20} + 22 q^{25} - 2 q^{26} + 4 q^{29} - 8 q^{32} + 42 q^{34} + 12 q^{36} - 14 q^{37} + 68 q^{40} - 2 q^{41} - 60 q^{45} - 14 q^{49}+ \cdots + 14 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 - 4 * q^8 - 8 * q^10 + 8 * q^16 - 10 * q^17 - 6 * q^18 - 40 * q^20 + 22 * q^25 - 2 * q^26 + 4 * q^29 - 8 * q^32 + 42 * q^34 + 12 * q^36 - 14 * q^37 + 68 * q^40 - 2 * q^41 - 60 * q^45 - 14 * q^49 - 22 * q^50 - 24 * q^52 - 20 * q^53 + 6 * q^58 + 2 * q^61 + 8 * q^65 + 20 * q^68 - 12 * q^72 + 90 * q^73 + 28 * q^74 + 18 * q^81 + 4 * q^82 + 40 * q^85 + 6 * q^89 - 24 * q^90 - 116 * q^97 + 14 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/116\mathbb{Z}\right)^\times$.

$n$	$59$	$89$
$\chi(n)$	$-1$	$e\left(\frac{9}{28}\right)$

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 $

$2$	−0.752407	−	1.19745i	−0.532032	−	0.846724i
$2$	−0.752407	−	1.19745i	−0.532032	−	0.846724i
$3$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$3$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$4$	−0.867767	+	1.80194i	−0.433884	+	0.900969i
$5$	3.95589	+	0.902906i	1.76913	+	0.403792i	0.978124	−	0.208021i	$-0.0667021\pi$
$5$	3.95589	+	0.902906i	1.76913	+	0.403792i	0.791003	+	0.611812i	$0.209559\pi$
$6$		0			0
$7$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$7$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$8$	2.81064	−	0.316683i	0.993712	−	0.111964i
$9$	−2.34549	−	1.87047i	−0.781831	−	0.623490i
$10$	−1.89525	−	5.41633i	−0.599332	−	1.71279i
$11$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$11$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$12$		0			0
$13$	2.86954	−	2.28838i	0.795867	−	0.634683i	−0.138755	−	0.990327i	$-0.544310\pi$
$13$	2.86954	−	2.28838i	0.795867	−	0.634683i	0.934621	+	0.355644i	$0.115738\pi$
$14$		0			0
$15$		0			0
$16$	−2.49396	−	3.12733i	−0.623490	−	0.781831i
$17$	−4.03739	+	4.03739i	−0.979211	+	0.979211i	−0.999788	−	0.0205777i	$-0.993449\pi$
$17$	−4.03739	+	4.03739i	−0.979211	+	0.979211i	0.0205777	+	0.999788i	$0.493449\pi$
$18$	−0.475025	+	4.21596i	−0.111964	+	0.993712i
$19$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$19$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$20$	−5.05977	+	6.34475i	−1.13140	+	1.41873i
$21$		0			0
$22$		0			0
$23$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$23$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$24$		0			0
$25$	10.3290	+	4.97417i	2.06580	+	0.994834i
$26$	−4.89928	−	1.71433i	−0.960828	−	0.336208i
$27$		0			0
$28$		0			0
$29$	−5.15614	+	1.55379i	−0.957471	+	0.288531i
$29$	−5.15614	+	1.55379i	−0.957471	+	0.288531i
$30$		0			0
$31$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$31$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$32$	−1.86834	+	5.33941i	−0.330279	+	0.943883i
$33$		0			0
$34$	7.87233	+	1.79681i	1.35009	+	0.308150i
$35$		0			0
$36$	5.40581	−	2.60330i	0.900969	−	0.433884i
$37$	−11.9118	+	1.34214i	−1.95829	+	0.220646i	−0.998245	−	0.0592161i	$-0.981140\pi$
$37$	−11.9118	+	1.34214i	−1.95829	+	0.220646i	−0.960040	+	0.279862i	$0.909711\pi$
$38$		0			0
$39$		0			0
$40$	11.4045	+	1.28498i	1.80321	+	0.203173i
$41$	−4.80592	−	4.80592i	−0.750559	−	0.750559i	0.224025	−	0.974584i	$-0.428080\pi$
$41$	−4.80592	−	4.80592i	−0.750559	−	0.750559i	−0.974584	+	0.224025i	$0.928080\pi$
$42$		0			0
$43$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$43$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$44$		0			0
$45$	−7.58966	−	9.51713i	−1.13140	−	1.41873i
$46$		0			0
$47$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$47$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$48$		0			0
$49$	4.36443	−	5.47282i	0.623490	−	0.781831i
$50$	−1.81528	−	16.1110i	−0.256719	−	2.27844i
$51$		0			0
$52$	1.63343	+	7.15651i	0.226516	+	0.992430i
$53$	−3.23525	+	14.1745i	−0.444396	+	1.94702i	−0.169674	+	0.985500i	$0.554272\pi$
$53$	−3.23525	+	14.1745i	−0.444396	+	1.94702i	−0.274721	+	0.961524i	$0.588586\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	5.74009	+	5.00513i	0.753711	+	0.657206i
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$		0			0
$61$	4.90518	−	14.0182i	0.628044	−	1.79485i	0.0215382	−	0.999768i	$-0.493144\pi$
$61$	4.90518	−	14.0182i	0.628044	−	1.79485i	0.606506	−	0.795079i	$-0.292571\pi$
$62$		0			0
$63$		0			0
$64$	7.79942	−	1.78017i	0.974928	−	0.222521i
$65$	13.4178	−	6.46166i	1.66427	−	0.801470i
$66$		0			0
$67$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$67$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$68$	−3.77161	−	10.7786i	−0.457375	−	1.30710i
$69$		0			0
$70$		0			0
$71$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$71$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$72$	−7.18469	−	4.51444i	−0.846724	−	0.532032i
$73$	1.82602	−	2.90610i	0.213720	−	0.340133i	−0.722609	−	0.691257i	$-0.757057\pi$
$73$	1.82602	−	2.90610i	0.213720	−	0.340133i	0.936329	+	0.351123i	$0.114200\pi$
$74$	10.5696	+	13.2539i	1.22870	+	1.54074i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$79$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$80$	−7.04215	−	14.6232i	−0.787336	−	1.63492i
$81$	2.00269	+	8.77435i	0.222521	+	0.974928i
$82$	−2.13884	+	9.37086i	−0.236195	+	1.03484i
$83$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$83$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$84$		0			0
$85$	−19.6168	+	12.3261i	−2.12775	+	1.33695i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.23997	+	9.93085i	0.661435	+	1.05267i	0.993978	+	0.109580i	$0.0349505\pi$
$89$	6.23997	+	9.93085i	0.661435	+	1.05267i	−0.332543	+	0.943088i	$0.607907\pi$
$90$	−5.68576	+	16.2490i	−0.599332	+	1.71279i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.530443	+	1.51592i	0.0538583	+	0.153918i	0.967670	−	0.252220i	$-0.0811608\pi$
$97$	0.530443	+	1.51592i	0.0538583	+	0.153918i	−0.913812	+	0.406138i	$0.866875\pi$
$98$	−9.83725	−	1.10839i	−0.993712	−	0.111964i
$99$		0			0
$100$	−17.9263	+	14.2957i	−1.79263	+	1.42957i
$101$	−0.213260	−	0.134000i	−0.0212202	−	0.0133335i	0.521380	−	0.853324i	$-0.325417\pi$
$101$	−0.213260	−	0.134000i	−0.0212202	−	0.0133335i	−0.542600	+	0.839991i	$0.682560\pi$
$102$		0			0
$103$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$103$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$104$	7.34056	−	7.34056i	0.719801	−	0.719801i
$105$		0			0
$106$	19.4075	−	6.79099i	1.88503	−	0.659599i
$107$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$107$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$108$		0			0
$109$	−8.94785	−	18.5804i	−0.857048	−	1.77968i	−0.569700	−	0.821853i	$-0.692941\pi$
$109$	−8.94785	−	18.5804i	−0.857048	−	1.77968i	−0.287348	−	0.957826i	$-0.592774\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	16.4867	+	5.76895i	1.55094	+	0.542697i	0.963763	−	0.266761i	$-0.0859536\pi$
$113$	16.4867	+	5.76895i	1.55094	+	0.542697i	0.587177	+	0.809459i	$0.300239\pi$
$114$		0			0
$115$		0			0
$116$	1.67450	−	10.6394i	0.155474	−	0.987840i
$117$	−11.0108			−1.01795
$118$		0			0
$119$		0			0
$120$		0			0
$121$	10.7242	+	2.44773i	0.974928	+	0.222521i
$122$	−20.4768	+	4.67369i	−1.85388	+	0.423136i
$123$		0			0
$124$		0			0
$125$	20.5072	+	16.3539i	1.83422	+	1.46274i
$126$		0			0
$127$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$127$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$		0			0
$130$	−17.8331	−	11.2053i	−1.56407	−	0.982770i
$131$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$131$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−10.0691	+	12.6262i	−0.863417	+	1.08269i
$137$	−0.614291	−	5.45198i	−0.0524824	−	0.465794i	−0.992276	−	0.124051i	$-0.960411\pi$
$137$	−0.614291	−	5.45198i	−0.0524824	−	0.465794i	0.939793	−	0.341743i	$-0.111017\pi$
$138$		0			0
$139$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$139$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$			12.0000i			1.00000i
$145$	−21.8000	+	1.49110i	−1.81039	+	0.123829i
$146$	−4.85382			−0.401705
$147$		0			0
$148$	7.91821	−	22.6290i	0.650873	−	1.86009i
$149$	9.81178	−	20.3744i	0.803813	−	1.66913i	0.0624318	−	0.998049i	$-0.480114\pi$
$149$	9.81178	−	20.3744i	0.803813	−	1.66913i	0.741381	−	0.671085i	$-0.234171\pi$
$150$		0			0
$151$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$151$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$152$		0			0
$153$	17.0215	−	1.91786i	1.37611	−	0.155050i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	16.4086	+	16.4086i	1.30955	+	1.30955i	0.921741	+	0.387807i	$0.126767\pi$
$157$	16.4086	+	16.4086i	1.30955	+	1.30955i	0.387807	+	0.921741i	$0.373233\pi$
$158$		0			0
$159$		0			0
$160$	−12.2119	+	19.4352i	−0.965438	+	1.53649i
$161$		0			0
$162$	9.00000	−	9.00000i	0.707107	−	0.707107i
$163$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$163$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$164$	12.8304	−	4.48955i	1.00189	−	0.350575i
$165$		0			0
$166$		0			0
$167$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$167$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$168$		0			0
$169$	0.104795	−	0.459135i	0.00806112	−	0.0353181i
$170$	29.5197	+	14.2159i	2.26406	+	1.09031i
$171$		0			0
$172$		0			0
$173$		−	9.68526i		−	0.736356i	−0.929755	−	0.368178i	$-0.879982\pi$
$173$		−	9.68526i		−	0.736356i	0.929755	−	0.368178i	$-0.120018\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	7.19669	−	14.9441i	0.539415	−	1.12011i
$179$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$179$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$180$	23.7353	−	5.41744i	1.76913	−	0.403792i
$181$	−3.97671	+	1.91508i	−0.295586	+	0.142347i	−0.575800	−	0.817591i	$-0.695309\pi$
$181$	−3.97671	+	1.91508i	−0.295586	+	0.142347i	0.280213	+	0.959938i	$0.409595\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−48.3335	−	5.44588i	−3.55355	−	0.400389i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$191$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$192$		0			0
$193$	10.5949	−	3.70732i	0.762639	−	0.266859i	0.0791925	−	0.996859i	$-0.474766\pi$
$193$	10.5949	−	3.70732i	0.762639	−	0.266859i	0.683447	+	0.730000i	$0.260480\pi$
$194$	1.41613	−	1.77576i	0.101672	−	0.127492i
$195$		0			0
$196$	6.07437	+	12.6136i	0.433884	+	0.900969i
$197$	4.59379	+	20.1267i	0.327294	+	1.43397i	0.824266	+	0.566202i	$0.191588\pi$
$197$	4.59379	+	20.1267i	0.327294	+	1.43397i	−0.496972	+	0.867766i	$0.665555\pi$
$198$		0			0
$199$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$199$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$200$	30.6063	+	10.7096i	2.16419	+	0.757283i
$201$		0			0
$202$			0.356191i			0.0250615i
$203$		0			0
$204$		0			0
$205$	−14.6724	−	23.3510i	−1.02476	−	1.63090i
$206$		0			0
$207$		0			0
$208$	−14.3130	−	3.26685i	−0.992430	−	0.226516i
$209$		0			0
$210$		0			0
$211$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$211$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$212$	−22.7342	−	18.1299i	−1.56139	−	1.24517i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−15.5166	+	24.6946i	−1.05092	+	1.67253i
$219$		0			0
$220$		0			0
$221$	−2.34636	+	20.8245i	−0.157833	+	1.40081i
$222$		0			0
$223$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$223$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$224$		0			0
$225$	−14.9225	−	30.9869i	−0.994834	−	2.06580i
$226$	−5.49670	−	24.0826i	−0.365635	−	1.60195i
$227$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$227$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$228$		0			0
$229$	−11.8685	−	4.15295i	−0.784289	−	0.274435i	−0.0917189	−	0.995785i	$-0.529236\pi$
$229$	−11.8685	−	4.15295i	−0.784289	−	0.274435i	−0.692570	+	0.721350i	$0.743522\pi$
$230$		0			0
$231$		0			0
$232$	−14.0000	+	6.00000i	−0.919145	+	0.393919i
$233$	−3.70143			−0.242489			−0.121244	−	0.992623i	$-0.538688\pi$
$233$	−3.70143			−0.242489			−0.121244	+	0.992623i	$0.538688\pi$
$234$	8.28463	+	13.1849i	0.541583	+	0.861925i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$239$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$240$		0			0
$241$	21.4751	+	17.1258i	1.38333	+	1.10317i	0.982343	+	0.187088i	$0.0599048\pi$
$241$	21.4751	+	17.1258i	1.38333	+	1.10317i	0.400989	+	0.916083i	$0.368667\pi$
$242$	−5.13794	−	14.6834i	−0.330279	−	0.943883i
$243$		0			0
$244$	21.0034	+	21.0034i	1.34460	+	1.34460i
$245$	22.2066	−	17.7092i	1.41873	−	1.13140i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	4.15325	−	36.8611i	0.262675	−	2.33130i
$251$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$251$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−3.56033	+	15.5988i	−0.222521	+	0.974928i
$257$	−25.1940	−	12.1328i	−1.57156	−	0.756823i	−0.573506	−	0.819201i	$-0.694417\pi$
$257$	−25.1940	−	12.1328i	−1.57156	−	0.756823i	−0.998053	+	0.0623783i	$0.980131\pi$
$258$		0			0
$259$		0			0
$260$			29.7852i			1.84720i
$261$	15.0000	+	6.00000i	0.928477	+	0.371391i
$262$		0			0
$263$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$263$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$264$		0			0
$265$	−25.5966	+	53.1518i	−1.57238	+	3.26509i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−16.8565	+	1.89927i	−1.02776	+	0.115801i	−0.609711	−	0.792624i	$-0.708714\pi$
$269$	−16.8565	+	1.89927i	−1.02776	+	0.115801i	−0.418049	+	0.908425i	$0.637286\pi$
$270$		0			0
$271$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$271$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$272$	22.6953	+	2.55715i	1.37611	+	0.155050i
$273$		0			0
$274$	−6.06627	+	4.83769i	−0.366477	+	0.292256i
$275$		0			0
$276$		0			0
$277$	−7.05673	−	8.84886i	−0.423998	−	0.531676i	0.523250	−	0.852179i	$-0.324720\pi$
$277$	−7.05673	−	8.84886i	−0.423998	−	0.531676i	−0.947248	+	0.320503i	$0.896148\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−14.2742	+	17.8992i	−0.851525	+	1.06778i	0.145397	+	0.989373i	$0.453554\pi$
$281$	−14.2742	+	17.8992i	−0.851525	+	1.06778i	−0.996922	+	0.0784048i	$0.975017\pi$
$282$		0			0
$283$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$283$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	14.3694	−	9.02888i	0.846724	−	0.532032i
$289$		−	15.6010i		−	0.917706i
$290$	18.1880	+	24.9825i	1.06804	+	1.46702i
$291$		0			0
$292$	3.65205	+	5.81220i	0.213720	+	0.340133i
$293$	−10.1630	+	29.0442i	−0.593728	+	1.69678i	0.116841	+	0.993151i	$0.462723\pi$
$293$	−10.1630	+	29.0442i	−0.593728	+	1.69678i	−0.710569	+	0.703627i	$0.751563\pi$
$294$		0			0
$295$		0			0
$296$	−33.0547	+	7.54453i	−1.92127	+	0.438517i
$297$		0			0
$298$	−31.7797	+	3.58072i	−1.84095	+	0.207425i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	32.0615	−	51.0255i	1.83583	−	2.92171i
$306$	−15.1036	−	18.9393i	−0.863417	−	1.08269i
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$311$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$312$		0			0
$313$	6.82886	+	29.9192i	0.385990	+	1.69113i	0.678280	+	0.734803i	$0.262726\pi$
$313$	6.82886	+	29.9192i	0.385990	+	1.69113i	−0.292290	+	0.956330i	$0.594417\pi$
$314$	7.30251	−	31.9944i	0.412104	−	1.80555i
$315$		0			0
$316$		0			0
$317$	29.9850	−	18.8408i	1.68413	−	1.05821i	0.786318	−	0.617822i	$-0.211985\pi$
$317$	29.9850	−	18.8408i	1.68413	−	1.05821i	0.897809	−	0.440386i	$-0.145158\pi$
$318$		0			0
$319$		0			0
$320$	32.4610			1.81462
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−17.5487	−	4.00538i	−0.974928	−	0.222521i
$325$	41.0222	−	9.36305i	2.27550	−	0.519369i
$326$		0			0
$327$		0			0
$328$	−15.0297	−	11.9858i	−0.829876	−	0.661804i
$329$		0			0
$330$		0			0
$331$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$331$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$332$		0			0
$333$	30.4495	+	19.1327i	1.66862	+	1.04846i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	3.08561	−	27.3855i	0.168084	−	1.49179i	−0.572546	−	0.819873i	$-0.694044\pi$
$337$	3.08561	−	27.3855i	0.168084	−	1.49179i	0.740630	−	0.671913i	$-0.234527\pi$
$338$	−0.628639	+	0.219970i	−0.0341934	+	0.0119648i
$339$		0			0
$340$	−5.18797	−	46.0445i	−0.281357	−	2.49711i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−11.5976	+	7.28725i	−0.623491	+	0.391765i
$347$		0			0			−	1.00000i	$-0.5\pi$
$347$		0			0				1.00000i	$0.5\pi$
$348$		0			0
$349$	−17.7600			−0.950673			−0.475336	−	0.879804i	$-0.657674\pi$
$349$	−17.7600			−0.950673			−0.475336	+	0.879804i	$0.657674\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	36.6330	+	8.36124i	1.94978	+	0.445024i	0.976882	+	0.213780i	$0.0685777\pi$
$353$	36.6330	+	8.36124i	1.94978	+	0.445024i	0.972896	+	0.231244i	$0.0742795\pi$
$354$		0			0
$355$		0			0
$356$	−23.3096	+	2.62636i	−1.23541	+	0.139197i
$357$		0			0
$358$		0			0
$359$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$359$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$360$	−24.3457	−	24.3457i	−1.28313	−	1.28313i
$361$	14.8548	−	11.8463i	0.781831	−	0.623490i
$362$	5.28532	+	3.32098i	0.277790	+	0.174547i
$363$		0			0
$364$		0			0
$365$	9.84748	−	9.84748i	0.515441	−	0.515441i
$366$		0			0
$367$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$367$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$368$		0			0
$369$	2.28293	+	20.2616i	0.118845	+	1.05478i
$370$	29.8453	+	61.9744i	1.55158	+	3.22190i
$371$		0			0
$372$		0			0
$373$	−33.2230	−	15.9994i	−1.72022	−	0.828416i	−0.989289	−	0.145968i	$-0.953370\pi$
$373$	−33.2230	−	15.9994i	−1.72022	−	0.828416i	−0.730934	−	0.682448i	$-0.760916\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−11.2401	+	16.2579i	−0.578894	+	0.837322i
$378$		0			0
$379$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$379$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$383$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$384$		0			0
$385$		0			0
$386$	−12.4110	−	9.89746i	−0.631705	−	0.503768i
$387$		0			0
$388$	−3.19189	−	0.359640i	−0.162044	−	0.0182579i
$389$	−0.816430	−	0.816430i	−0.0413947	−	0.0413947i	0.686106	−	0.727501i	$-0.259318\pi$
$389$	−0.816430	−	0.816430i	−0.0413947	−	0.0413947i	−0.727501	+	0.686106i	$0.759318\pi$
$390$		0			0
$391$		0			0
$392$	10.5337	−	16.7643i	0.532032	−	0.846724i
$393$		0			0
$394$	20.6443	−	20.6443i	1.04004	−	1.04004i
$395$		0			0
$396$		0			0
$397$	−2.02219	+	2.53574i	−0.101491	+	0.127265i	−0.829983	−	0.557789i	$-0.811650\pi$
$397$	−2.02219	+	2.53574i	−0.101491	+	0.127265i	0.728492	+	0.685054i	$0.240221\pi$
$398$		0			0
$399$		0			0
$400$	−10.2042	−	44.7075i	−0.510209	−	2.23537i
$401$	3.46096	−	15.1635i	0.172832	−	0.757227i	−0.811992	−	0.583669i	$-0.801617\pi$
$401$	3.46096	−	15.1635i	0.172832	−	0.757227i	0.984824	−	0.173558i	$-0.0555263\pi$
$402$		0			0
$403$		0			0
$404$	0.426521	−	0.268001i	0.0212202	−	0.0133335i
$405$			36.5186i			1.81462i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	13.3500	−	38.1520i	0.660114	−	1.88650i	0.295433	−	0.955363i	$-0.404536\pi$
$409$	13.3500	−	38.1520i	0.660114	−	1.88650i	0.364680	−	0.931133i	$-0.381178\pi$
$410$	−16.9220	+	35.1389i	−0.835718	+	1.73539i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	6.85733	+	19.5971i	0.336208	+	0.960828i
$417$		0			0
$418$		0			0
$419$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$419$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$420$		0			0
$421$	−0.752407	+	1.19745i	−0.0366701	+	0.0583601i	−0.864556	−	0.502536i	$-0.832400\pi$
$421$	−0.752407	+	1.19745i	−0.0366701	+	0.0583601i	0.827886	+	0.560896i	$0.189543\pi$
$422$		0			0
$423$		0			0
$424$	−4.60428	+	40.8641i	−0.223604	+	1.98454i
$425$	−61.7848	+	21.6194i	−2.99700	+	1.04870i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$431$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$432$		0			0
$433$	−5.98724	+	3.76203i	−0.287729	+	0.180792i	−0.668161	−	0.744017i	$-0.732918\pi$
$433$	−5.98724	+	3.76203i	−0.287729	+	0.180792i	0.380432	+	0.924809i	$0.375775\pi$
$434$		0			0
$435$		0			0
$436$	41.2454			1.97529
$437$		0			0
$438$		0			0
$439$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$439$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$440$		0			0
$441$	−20.4735	+	4.67294i	−0.974928	+	0.222521i
$442$	26.7017	−	12.8589i	1.27007	−	0.611634i
$443$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$443$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$444$		0			0
$445$	15.7180	+	44.9194i	0.745104	+	2.12939i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−28.0566	−	17.6291i	−1.32407	−	0.831969i	−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−28.0566	−	17.6291i	−1.32407	−	0.831969i	−0.993721	+	0.111889i	$0.964310\pi$
$450$	−25.8775	+	41.1837i	−1.21987	+	1.94142i
$451$		0			0
$452$	−24.7019	+	24.7019i	−1.16188	+	1.16188i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	8.64814	+	17.9580i	0.404543	+	0.840042i	0.999346	+	0.0361701i	$0.0115158\pi$
$457$	8.64814	+	17.9580i	0.404543	+	0.840042i	−0.594803	+	0.803872i	$0.702770\pi$
$458$	3.95696	+	17.3366i	0.184897	+	0.810085i
$459$		0			0
$460$		0			0
$461$	−12.0137	−	4.20377i	−0.559533	−	0.195789i	0.0356714	−	0.999364i	$-0.488643\pi$
$461$	−12.0137	−	4.20377i	−0.559533	−	0.195789i	−0.595204	+	0.803575i	$0.702929\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$	17.7184	+	12.2498i	0.822556	+	0.568685i
$465$		0			0
$466$	2.78498	+	4.43227i	0.129012	+	0.205321i
$467$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$467$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$468$	9.55484	−	19.8408i	0.441673	−	0.917143i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	34.1013	−	27.1949i	1.56139	−	1.24517i
$478$		0			0
$479$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$479$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$480$		0			0
$481$	−31.1100	+	31.1100i	−1.41849	+	1.41849i
$482$	4.34928	−	38.6009i	0.198104	−	1.75822i
$483$		0			0
$484$	−13.7168	+	17.2003i	−0.623490	+	0.781831i
$485$	0.729641	+	6.47574i	0.0331313	+	0.294048i
$486$		0			0
$487$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$487$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$488$	9.34738	−	40.9535i	0.423136	−	1.85388i
$489$		0			0
$490$	−37.9143	−	13.2668i	−1.71279	−	0.599332i
$491$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$491$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$492$		0			0
$493$	14.5441	−	27.0906i	0.655033	−	1.22010i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$499$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$500$	−47.2642	+	22.7613i	−2.11372	+	1.01791i
$501$		0			0
$502$		0			0
$503$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$503$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$504$		0			0
$505$	−0.722644	−	0.722644i	−0.0321573	−	0.0321573i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−22.0116	−	27.6016i	−0.975645	−	1.22342i	−0.974722	−	0.223421i	$-0.928278\pi$
$509$	−22.0116	−	27.6016i	−0.975645	−	1.22342i	−0.000922874	−	1.00000i	$-0.500294\pi$
$510$		0			0
$511$		0			0
$512$	21.3576	−	7.47336i	0.943883	−	0.330279i
$513$		0			0
$514$	4.42775	+	39.2973i	0.195299	+	1.73333i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	35.6663	−	22.4106i	1.56407	−	0.982770i
$521$		−	44.9900i		−	1.97105i	−0.169532	−	0.985525i	$-0.554226\pi$
$521$		−	44.9900i		−	1.97105i	0.169532	−	0.985525i	$-0.445774\pi$
$522$	−4.10141	−	22.4762i	−0.179514	−	0.983755i
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−20.7223	+	9.97933i	−0.900969	+	0.433884i
$530$	82.9056	−	9.34122i	3.60119	−	0.405757i
$531$		0			0
$532$		0			0
$533$	−24.7886	−	2.79300i	−1.07371	−	0.120978i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	14.9572	+	18.7558i	0.644852	+	0.808619i
$539$		0			0
$540$		0			0
$541$	30.9116	−	10.8164i	1.32899	−	0.465035i	0.429934	−	0.902861i	$-0.358537\pi$
$541$	30.9116	−	10.8164i	1.32899	−	0.465035i	0.899060	+	0.437826i	$0.144251\pi$
$542$		0			0
$543$		0			0
$544$	−14.0141	−	29.1005i	−0.600848	−	1.24767i
$545$	−18.6203	−	81.5810i	−0.797608	−	3.49455i
$546$		0			0
$547$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$547$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$548$	10.3572	+	3.62414i	0.442437	+	0.154816i
$549$	−37.7257	+	23.7046i	−1.61009	+	1.01169i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−5.28652	+	15.1080i	−0.224603	+	0.641878i
$555$		0			0
$556$		0			0
$557$	−8.52043	+	1.94473i	−0.361022	+	0.0824009i	−0.399185	−	0.916871i	$-0.630707\pi$
$557$	−8.52043	+	1.94473i	−0.361022	+	0.0824009i	0.0381624	+	0.999272i	$0.487850\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	32.1734	+	3.62507i	1.35715	+	0.152914i
$563$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$563$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$564$		0			0
$565$	60.0108	+	37.7073i	2.52467	+	1.58636i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.18872	+	46.0512i	−0.217523	+	1.93057i	0.127230	+	0.991873i	$0.459391\pi$
$569$	−5.18872	+	46.0512i	−0.217523	+	1.93057i	−0.344753	+	0.938693i	$0.612037\pi$
$570$		0			0
$571$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$571$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−21.6233	−	10.4132i	−0.900969	−	0.433884i
$577$	13.1819	+	4.61255i	0.548771	+	0.192023i	0.590401	−	0.807110i	$-0.298970\pi$
$577$	13.1819	+	4.61255i	0.548771	+	0.192023i	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	−18.6814	+	11.7383i	−0.777044	+	0.488249i
$579$		0			0
$580$	16.2305	−	40.5762i	0.673934	−	1.68484i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	4.21199	−	8.74628i	0.174293	−	0.361924i
$585$	−43.5576	−	9.94175i	−1.80089	−	0.411041i
$586$	42.4256	−	9.68337i	1.75259	−	0.400016i
$587$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$587$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	33.9048	+	33.9048i	1.39348	+	1.39348i
$593$	−20.1985	+	16.1077i	−0.829452	+	0.661466i	−0.943267	−	0.332036i	$-0.892264\pi$
$593$	−20.1985	+	16.1077i	−0.829452	+	0.661466i	0.113815	+	0.993502i	$0.463693\pi$
$594$		0			0
$595$		0			0
$596$	28.1990	+	35.3604i	1.15508	+	1.44842i
$597$		0			0
$598$		0			0
$599$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$599$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$600$		0			0
$601$	3.00849	+	26.7011i	0.122719	+	1.08916i	0.892561	+	0.450926i	$0.148906\pi$
$601$	3.00849	+	26.7011i	0.122719	+	1.08916i	−0.769842	+	0.638234i	$0.779665\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	40.2137	+	19.3659i	1.63492	+	0.787336i
$606$		0			0
$607$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$607$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$608$		0			0
$609$		0			0
$610$	−85.2237			−3.45061
$611$		0			0
$612$	−11.3148	+	32.3359i	−0.457375	+	1.30710i
$613$	20.4736	−	42.5140i	0.826923	−	1.71712i	0.140299	−	0.990109i	$-0.455194\pi$
$613$	20.4736	−	42.5140i	0.826923	−	1.71712i	0.686624	−	0.727013i	$-0.259092\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	33.9633	−	3.82674i	1.36731	−	0.154059i	0.602400	−	0.798195i	$-0.294211\pi$
$617$	33.9633	−	3.82674i	1.36731	−	0.154059i	0.764911	+	0.644136i	$0.222783\pi$
$618$		0			0
$619$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$619$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	30.6187	+	38.3947i	1.22475	+	1.53579i
$626$	30.6886	−	30.6886i	1.22656	−	1.22656i
$627$		0			0
$628$	−43.8061	+	15.3284i	−1.74805	+	0.611670i
$629$	42.6738	−	53.5112i	1.70152	−	2.13363i
$630$		0			0
$631$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$631$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$632$		0			0
$633$		0			0
$634$	−45.1219	−	21.7296i	−1.79202	−	0.862991i
$635$		0			0
$636$		0			0
$637$		−	25.6919i		−	1.01795i
$638$		0			0
$639$		0			0
$640$	−24.4239	−	38.8704i	−0.965438	−	1.53649i
$641$	9.80879	−	28.0319i	0.387424	−	1.10719i	−0.570779	−	0.821104i	$-0.693359\pi$
$641$	9.80879	−	28.0319i	0.387424	−	1.10719i	0.958203	−	0.286090i	$-0.0923556\pi$
$642$		0			0
$643$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$643$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$647$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$648$	8.40753	+	24.0273i	0.330279	+	0.943883i
$649$		0			0
$650$	−42.0772	−	42.0772i	−1.65040	−	1.65040i
$651$		0			0
$652$		0			0
$653$	−5.32494	+	8.47460i	−0.208381	+	0.331637i	−0.934520	−	0.355912i	$-0.884170\pi$
$653$	−5.32494	+	8.47460i	−0.208381	+	0.331637i	0.726138	+	0.687549i	$0.241313\pi$
$654$		0			0
$655$		0			0
$656$	−3.04391	+	27.0155i	−0.118845	+	1.05478i
$657$	−9.71870	+	3.40072i	−0.379163	+	0.132675i
$658$		0			0
$659$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$659$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$660$		0			0
$661$	7.23322	+	31.6908i	0.281340	+	1.23263i	0.896077	+	0.443898i	$0.146405\pi$
$661$	7.23322	+	31.6908i	0.281340	+	1.23263i	−0.614737	+	0.788732i	$0.710738\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		−	50.8572i		−	1.97068i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−20.4740	+	4.67305i	−0.789213	+	0.180133i	−0.598085	−	0.801432i	$-0.704072\pi$
$673$	−20.4740	+	4.67305i	−0.789213	+	0.180133i	−0.191128	+	0.981565i	$0.561215\pi$
$674$	−35.1144	+	16.9102i	−1.35256	+	0.651357i
$675$		0			0
$676$	0.736395	+	0.587256i	0.0283229	+	0.0225868i
$677$	17.1405	+	48.9847i	0.658762	+	1.88263i	0.398936	+	0.916979i	$0.369380\pi$
$677$	17.1405	+	48.9847i	0.658762	+	1.88263i	0.259826	+	0.965655i	$0.416335\pi$
$678$		0			0
$679$		0			0
$680$	−51.2325	+	40.8565i	−1.96468	+	1.56678i
$681$		0			0
$682$		0			0
$683$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$683$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$684$		0			0
$685$	2.49256	−	22.1221i	0.0952358	−	0.845241i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	23.1531	+	48.0779i	0.882063	+	1.83162i
$690$		0			0
$691$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$691$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$692$	17.4522	+	8.40455i	0.663434	+	0.319493i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	38.8068			1.46991
$698$	13.3628	+	21.2667i	0.505788	+	0.804958i
$699$		0			0
$700$		0			0
$701$	−47.2558	−	10.7858i	−1.78483	−	0.407375i	−0.802819	−	0.596222i	$-0.796668\pi$
$701$	−47.2558	−	10.7858i	−1.78483	−	0.407375i	−0.982006	+	0.188847i	$0.939525\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−17.5508	−	50.1572i	−0.660532	−	1.88769i
$707$		0			0
$708$		0			0
$709$	−41.5194	+	33.1106i	−1.55929	+	1.24349i	−0.733066	+	0.680158i	$0.761911\pi$
$709$	−41.5194	+	33.1106i	−1.55929	+	1.24349i	−0.826227	+	0.563337i	$0.809517\pi$
$710$		0			0
$711$		0			0
$712$	20.6833	+	25.9360i	0.775138	+	0.971992i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$719$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$720$	−10.8349	+	47.4707i	−0.403792	+	1.76913i
$721$		0			0
$722$	−25.3622	−	8.87462i	−0.943883	−	0.330279i
$723$		0			0
$724$		−	8.82763i		−	0.328076i
$725$	−60.9864	−	9.59850i	−2.26498	−	0.356479i
$726$		0			0
$727$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$727$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$728$		0			0
$729$	11.7149	−	24.3262i	0.433884	−	0.900969i
$730$	−19.2012	−	4.38254i	−0.710667	−	0.162205i
$731$		0			0
$732$		0			0
$733$	−35.1330	+	3.95854i	−1.29767	+	0.146212i	−0.733637	−	0.679541i	$-0.762179\pi$
$733$	−35.1330	+	3.95854i	−1.29767	+	0.146212i	−0.564031	+	0.825754i	$0.690750\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	22.5445	−	17.9787i	0.829876	−	0.661804i
$739$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$739$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$740$	51.7554	−	82.3682i	1.90257	−	3.02792i
$741$		0			0
$742$		0			0
$743$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$743$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$744$		0			0
$745$	57.2105	−	71.7397i	2.09603	−	2.62834i
$746$	5.83882	+	51.8209i	0.213774	+	1.89730i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$751$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$752$		0			0
$753$		0			0
$754$	27.9251	+	1.22690i	1.01697	+	0.0446810i
$755$		0			0
$756$		0			0
$757$	−7.83058	+	22.3785i	−0.284607	+	0.813361i	0.709475	+	0.704731i	$0.248932\pi$
$757$	−7.83058	+	22.3785i	−0.284607	+	0.813361i	−0.994082	+	0.108630i	$0.965354\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	4.29763	−	2.06963i	0.155789	−	0.0750239i	−0.354365	−	0.935107i	$-0.615303\pi$
$761$	4.29763	−	2.06963i	0.155789	−	0.0750239i	0.510154	+	0.860083i	$0.329589\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	69.0667	+	7.78195i	2.49711	+	0.281357i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−15.6669	+	24.9338i	−0.564963	+	0.899134i	−0.999999	−	0.00127898i	$-0.999593\pi$
$769$	−15.6669	+	24.9338i	−0.564963	+	0.899134i	0.435036	+	0.900413i	$0.356736\pi$
$770$		0			0
$771$		0			0
$772$	−2.51356	+	22.3085i	−0.0904651	+	0.802900i
$773$	−37.6766	+	13.1836i	−1.35513	+	0.474181i	−0.907506	−	0.420040i	$-0.862016\pi$
$773$	−37.6766	+	13.1836i	−1.35513	+	0.474181i	−0.447626	+	0.894221i	$0.647730\pi$
$774$		0			0
$775$		0			0
$776$	1.97095	+	4.09272i	0.0707530	+	0.146920i
$777$		0			0
$778$	−0.363346	+	1.59192i	−0.0130266	+	0.0570731i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−28.0000			−1.00000
$785$	50.0951	+	79.7259i	1.78797	+	2.84554i
$786$		0			0
$787$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$787$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$788$	−40.2534	−	9.18758i	−1.43397	−	0.327294i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−18.0034	−	51.4507i	−0.639319	−	1.82707i
$794$	4.55793	+	0.513556i	0.161755	+	0.0182254i
$795$		0			0
$796$		0			0
$797$	−32.1247	−	20.1853i	−1.13791	−	0.714999i	−0.174936	−	0.984580i	$-0.555972\pi$
$797$	−32.1247	−	20.1853i	−1.13791	−	0.714999i	−0.962978	+	0.269581i	$0.913115\pi$
$798$		0			0
$799$		0			0
$800$	−45.8572	+	45.8572i	−1.62130	+	1.62130i
$801$	3.93954	−	34.9644i	0.139197	−	1.23541i
$802$	−20.7615	+	7.26477i	−0.733114	+	0.256528i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−0.641834	−	0.309091i	−0.0225796	−	0.0108738i
$809$	46.7738	+	16.3669i	1.64448	+	0.575429i	0.984428	−	0.175791i	$-0.0562482\pi$
$809$	46.7738	+	16.3669i	1.64448	+	0.575429i	0.660053	+	0.751219i	$0.270534\pi$
$810$	43.7292	−	27.4768i	1.53649	−	0.965438i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−55.7297	+	12.7199i	−1.94854	+	0.444742i
$819$		0			0
$820$	54.8093	−	6.17552i	1.91402	−	0.215659i
$821$	−12.6437	−	10.0830i	−0.441269	−	0.351900i	0.377513	−	0.926004i	$-0.376779\pi$
$821$	−12.6437	−	10.0830i	−0.441269	−	0.351900i	−0.818783	+	0.574104i	$0.805351\pi$
$822$		0			0
$823$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$823$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$827$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$828$		0			0
$829$	−31.3702	+	31.3702i	−1.08953	+	1.08953i	−0.0939545	+	0.995576i	$0.529951\pi$
$829$	−31.3702	+	31.3702i	−1.08953	+	1.08953i	−0.995576	+	0.0939545i	$0.970049\pi$
$830$		0			0
$831$		0			0
$832$	18.3070	−	22.9563i	0.634683	−	0.795867i
$833$	4.47501	+	39.7168i	0.155050	+	1.37611i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$839$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$840$		0			0
$841$	24.1715	−	16.0231i	0.833500	−	0.552520i
$842$	2.00000			0.0689246
$843$		0			0
$844$		0			0
$845$	0.829111	−	1.72167i	0.0285223	−	0.0592272i
$846$		0			0
$847$		0			0
$848$	52.3970	−	25.2331i	1.79932	−	0.866507i
$849$		0			0
$850$	72.3754	+	57.7175i	2.48246	+	1.97969i
$851$		0			0
$852$		0			0
$853$	−28.9376	−	28.9376i	−0.990806	−	0.990806i	0.00915214	−	0.999958i	$-0.497087\pi$
$853$	−28.9376	−	28.9376i	−0.990806	−	0.990806i	−0.999958	+	0.00915214i	$0.997087\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.98792	−	6.25465i	−0.170384	−	0.213655i	0.689307	−	0.724470i	$-0.257915\pi$
$857$	−4.98792	−	6.25465i	−0.170384	−	0.213655i	−0.859691	+	0.510815i	$0.829344\pi$
$858$		0			0
$859$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$859$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$863$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$864$		0			0
$865$	8.74487	−	38.3138i	0.297335	−	1.30271i
$866$	9.00969	+	4.33884i	0.306162	+	0.147440i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−31.0333	−	49.3892i	−1.05092	−	1.67253i
$873$	1.59133	−	4.54775i	0.0538583	−	0.153918i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	10.8116	−	5.20660i	0.365083	−	0.175815i	−0.242344	−	0.970190i	$-0.577916\pi$
$877$	10.8116	−	5.20660i	0.365083	−	0.175815i	0.607427	+	0.794376i	$0.292202\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	53.3591	+	6.01213i	1.79772	+	0.202554i	0.946597	−	0.322420i	$-0.104496\pi$
$881$	53.3591	+	6.01213i	1.79772	+	0.202554i	0.851118	+	0.524974i	$0.175925\pi$
$882$	21.0000	+	21.0000i	0.707107	+	0.707107i
$883$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$883$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$884$	−35.4884	−	22.2988i	−1.19360	−	0.749991i
$885$		0			0
$886$		0			0
$887$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$887$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$888$		0			0
$889$		0			0
$890$	41.9624	−	52.6192i	1.40658	−	1.76380i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$			46.8606i			1.56376i
$899$		0			0
$900$	68.7858			2.29286
$901$	−44.1662	−	70.2901i	−1.47139	−	2.34170i
$902$		0			0
$903$		0			0
$904$	48.1652	+	10.9934i	1.60195	+	0.365635i
$905$	−17.4606	+	3.98526i	−0.580409	+	0.132474i
$906$		0			0
$907$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$907$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$908$		0			0
$909$	0.249557	+	0.713194i	0.00827729	+	0.0236551i
$910$		0			0
$911$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$911$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$912$		0			0
$913$		0			0
$914$	14.9969	−	23.8675i	0.496054	−	0.789465i
$915$		0			0
$916$	17.7824	−	17.7824i	0.587547	−	0.587547i
$917$		0			0
$918$		0			0
$919$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$919$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$920$		0			0
$921$		0			0
$922$	4.00538	+	17.5487i	0.131910	+	0.577936i
$923$		0			0
$924$		0			0
$925$	−129.713	−	45.3884i	−4.26492	−	1.49236i
$926$		0			0
$927$		0			0
$928$	1.33712	−	30.4337i	0.0438931	−	0.999036i
$929$	16.0801			0.527571			0.263786	−	0.964581i	$-0.415029\pi$
$929$	16.0801			0.527571			0.263786	+	0.964581i	$0.415029\pi$
$930$		0			0
$931$		0			0
$932$	3.21198	−	6.66975i	0.105212	−	0.218475i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−30.9475	+	3.48695i	−1.01155	+	0.113974i
$937$	−47.8641	−	38.1704i	−1.56365	−	1.24697i	−0.784046	−	0.620703i	$-0.786847\pi$
$937$	−47.8641	−	38.1704i	−1.56365	−	1.24697i	−0.779607	−	0.626269i	$-0.784581\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−15.6366	+	12.4698i	−0.509740	+	0.406504i	−0.844300	−	0.535870i	$-0.819984\pi$
$941$	−15.6366	+	12.4698i	−0.509740	+	0.406504i	0.334561	+	0.942374i	$0.391412\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$947$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$948$		0			0
$949$	−1.41042	−	12.5178i	−0.0457841	−	0.406345i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.785914	−	0.378476i	−0.0254583	−	0.0122600i	0.421111	−	0.907009i	$-0.361640\pi$
$953$	−0.785914	−	0.378476i	−0.0254583	−	0.0122600i	−0.446570	+	0.894749i	$0.647354\pi$
$954$	−58.2226	−	20.3730i	−1.88503	−	0.659599i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−13.4504	+	27.9300i	−0.433884	+	0.900969i
$962$	60.6600	+	13.8453i	1.95576	+	0.446389i
$963$		0			0
$964$	−49.4950	+	23.8356i	−1.59413	+	0.767691i
$965$	45.2597	−	5.09954i	1.45696	−	0.164160i
$966$		0			0
$967$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$967$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$968$	30.9171	+	3.48352i	0.993712	+	0.111964i
$969$		0			0
$970$	7.20538	−	5.74610i	0.231351	−	0.184496i
$971$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$971$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−56.0728	+	19.6207i	−1.79485	+	0.628044i
$977$	−33.3327	+	41.7979i	−1.06641	+	1.33723i	−0.127971	+	0.991778i	$0.540847\pi$
$977$	−33.3327	+	41.7979i	−1.06641	+	1.33723i	−0.938436	+	0.345454i	$0.887725\pi$
$978$		0			0
$979$		0			0
$980$	12.6407	+	55.3824i	0.403792	+	1.76913i
$981$	−13.7669	+	60.3169i	−0.439544	+	1.92577i
$982$		0			0
$983$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$983$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$984$		0			0
$985$			83.7668i			2.66903i
$986$	−43.3826	+	2.96733i	−1.38158	+	0.0944989i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$991$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	4.95142	+	0.557891i	0.156813	+	0.0176686i	0.190022	−	0.981780i	$-0.439144\pi$
$997$	4.95142	+	0.557891i	0.156813	+	0.0176686i	−0.0332089	+	0.999448i	$0.510573\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	116.2.l.a.19.1	✓	12
4.3	odd	2	CM	116.2.l.a.19.1	✓	12
29.26	odd	28	inner	116.2.l.a.55.1	yes	12
116.55	even	28	inner	116.2.l.a.55.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
116.2.l.a.19.1	✓	12	1.1	even	1	trivial
116.2.l.a.19.1	✓	12	4.3	odd	2	CM
116.2.l.a.55.1	yes	12	29.26	odd	28	inner
116.2.l.a.55.1	yes	12	116.55	even	28	inner

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:	\( N \)	\(=\)	\( 116 = 2^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	116.l (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.752407 - 1.19745i) q^{2} +(-0.867767 + 1.80194i) q^{4} +(3.95589 + 0.902906i) q^{5} +(2.81064 - 0.316683i) q^{8} +(-2.34549 - 1.87047i) q^{9} +(-1.89525 - 5.41633i) q^{10} +(2.86954 - 2.28838i) q^{13} +(-2.49396 - 3.12733i) q^{16} +(-4.03739 + 4.03739i) q^{17} +(-0.475025 + 4.21596i) q^{18} +(-5.05977 + 6.34475i) q^{20} +(10.3290 + 4.97417i) q^{25} +(-4.89928 - 1.71433i) q^{26} +(-5.15614 + 1.55379i) q^{29} +(-1.86834 + 5.33941i) q^{32} +(7.87233 + 1.79681i) q^{34} +(5.40581 - 2.60330i) q^{36} +(-11.9118 + 1.34214i) q^{37} +(11.4045 + 1.28498i) q^{40} +(-4.80592 - 4.80592i) q^{41} +(-7.58966 - 9.51713i) q^{45} +(4.36443 - 5.47282i) q^{49} +(-1.81528 - 16.1110i) q^{50} +(1.63343 + 7.15651i) q^{52} +(-3.23525 + 14.1745i) q^{53} +(5.74009 + 5.00513i) q^{58} +(4.90518 - 14.0182i) q^{61} +(7.79942 - 1.78017i) q^{64} +(13.4178 - 6.46166i) q^{65} +(-3.77161 - 10.7786i) q^{68} +(-7.18469 - 4.51444i) q^{72} +(1.82602 - 2.90610i) q^{73} +(10.5696 + 13.2539i) q^{74} +(-7.04215 - 14.6232i) q^{80} +(2.00269 + 8.77435i) q^{81} +(-2.13884 + 9.37086i) q^{82} +(-19.6168 + 12.3261i) q^{85} +(6.23997 + 9.93085i) q^{89} +(-5.68576 + 16.2490i) q^{90} +(0.530443 + 1.51592i) q^{97} +(-9.83725 - 1.10839i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 4 q^{8} - 8 q^{10} + 8 q^{16} - 10 q^{17} - 6 q^{18} - 40 q^{20} + 22 q^{25} - 2 q^{26} + 4 q^{29} - 8 q^{32} + 42 q^{34} + 12 q^{36} - 14 q^{37} + 68 q^{40} - 2 q^{41} - 60 q^{45} - 14 q^{49}+ \cdots + 14 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 - 4 * q^8 - 8 * q^10 + 8 * q^16 - 10 * q^17 - 6 * q^18 - 40 * q^20 + 22 * q^25 - 2 * q^26 + 4 * q^29 - 8 * q^32 + 42 * q^34 + 12 * q^36 - 14 * q^37 + 68 * q^40 - 2 * q^41 - 60 * q^45 - 14 * q^49 - 22 * q^50 - 24 * q^52 - 20 * q^53 + 6 * q^58 + 2 * q^61 + 8 * q^65 + 20 * q^68 - 12 * q^72 + 90 * q^73 + 28 * q^74 + 18 * q^81 + 4 * q^82 + 40 * q^85 + 6 * q^89 - 24 * q^90 - 116 * q^97 + 14 * q^98

Introduction

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