LMFDB - Embedded newform 2736.2.bm.r.559.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2736,2,Mod(559,2736)] 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("2736.559"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2736, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,-4,0,0,0,0,0,-6,0,-12,0,0,0, 12,0,-28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(31)] == traces)

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

Self dual:	no
Analytic conductor:	$21.8470699930$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 30x^{5} - 5x^{4} + 114x^{3} + 300x^{2} + 116x + 19 $ x^8 - 2x^7 - 30x^5 - 5x^4 + 114x^3 + 300x^2 + 116x + 19
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 912)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.4
Root			$3.14556 - 0.349646i$ of defining polynomial
Character	$\chi$	$=$	2736.559
Dual form			2736.2.bm.r.1855.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73843 - 3.01105i) q^{5} -3.36658i q^{7} +2.43134i q^{11} +(-5.02115 + 2.89896i) q^{13} +(-2.67711 + 4.63689i) q^{17} +(-2.84404 + 3.30325i) q^{19} +(-1.30585 + 0.753935i) q^{23} +(-3.54429 - 6.13888i) q^{25} +(4.21121 - 2.43134i) q^{29} -10.5654 q^{31} +(-10.1369 - 5.85256i) q^{35} -8.46521i q^{37} +(3.41146 + 1.96961i) q^{41} +(-9.02523 - 5.21072i) q^{43} +(-9.63084 + 5.56037i) q^{47} -4.33385 q^{49} +(4.41554 - 2.54931i) q^{53} +(7.32090 + 4.22672i) q^{55} +(-5.58247 + 9.66912i) q^{59} +(-2.80994 - 4.86695i) q^{61} +20.1586i q^{65} +(3.03818 + 5.26229i) q^{67} +(6.15397 - 10.6590i) q^{71} +(-3.97686 + 6.88813i) q^{73} +8.18531 q^{77} +(1.19415 - 2.06832i) q^{79} +5.59111i q^{83} +(9.30795 + 16.1218i) q^{85} +(5.04638 - 2.91353i) q^{89} +(9.75958 + 16.9041i) q^{91} +(5.00209 + 14.3060i) q^{95} +(2.47885 + 1.43117i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{5} - 4 q^{17} - 6 q^{23} - 12 q^{25} + 12 q^{29} - 28 q^{31} - 18 q^{35} + 12 q^{41} - 18 q^{43} - 12 q^{47} - 24 q^{49} + 6 q^{53} + 12 q^{55} - 10 q^{59} - 4 q^{61} + 6 q^{67} + 8 q^{71} - 8 q^{73}+ \cdots + 60 q^{97}+O(q^{100}) $ 8 * q + 2 * q^5 - 4 * q^17 - 6 * q^23 - 12 * q^25 + 12 * q^29 - 28 * q^31 - 18 * q^35 + 12 * q^41 - 18 * q^43 - 12 * q^47 - 24 * q^49 + 6 * q^53 + 12 * q^55 - 10 * q^59 - 4 * q^61 + 6 * q^67 + 8 * q^71 - 8 * q^73 - 28 * q^77 + 14 * q^79 - 8 * q^85 - 54 * q^89 + 26 * q^91 - 38 * q^95 + 60 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.73843	−	3.01105i	0.777450	−	1.34658i	−0.155957	−	0.987764i	$-0.549846\pi$
$5$	1.73843	−	3.01105i	0.777450	−	1.34658i	0.933407	−	0.358819i	$-0.116820\pi$
$6$		0			0
$7$		−	3.36658i		−	1.27245i	−0.771505	−	0.636223i	$-0.780496\pi$
$7$		−	3.36658i		−	1.27245i	0.771505	−	0.636223i	$-0.219504\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$			2.43134i			0.733078i	0.930403	+	0.366539i	$0.119457\pi$
$11$			2.43134i			0.733078i	−0.930403	+	0.366539i	$0.880543\pi$
$12$		0			0
$13$	−5.02115	+	2.89896i	−1.39262	+	0.804027i	−0.993604	−	0.112919i	$-0.963980\pi$
$13$	−5.02115	+	2.89896i	−1.39262	+	0.804027i	−0.399011	+	0.916946i	$0.630647\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.67711	+	4.63689i	−0.649295	+	1.12461i	0.333997	+	0.942574i	$0.391603\pi$
$17$	−2.67711	+	4.63689i	−0.649295	+	1.12461i	−0.983292	+	0.182037i	$0.941731\pi$
$18$		0			0
$19$	−2.84404	+	3.30325i	−0.652467	+	0.757817i
$19$	−2.84404	+	3.30325i	−0.652467	+	0.757817i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.30585	+	0.753935i	−0.272289	+	0.157206i	−0.629928	−	0.776654i	$-0.716915\pi$
$23$	−1.30585	+	0.753935i	−0.272289	+	0.157206i	0.357638	+	0.933860i	$0.383582\pi$
$24$		0			0
$25$	−3.54429	−	6.13888i	−0.708857	−	1.22778i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.21121	−	2.43134i	0.782002	−	0.451489i	−0.0551373	−	0.998479i	$-0.517560\pi$
$29$	4.21121	−	2.43134i	0.782002	−	0.451489i	0.837139	+	0.546990i	$0.184226\pi$
$30$		0			0
$31$	−10.5654			−1.89761			−0.948804	−	0.315866i	$-0.897705\pi$
$31$	−10.5654			−1.89761			−0.948804	+	0.315866i	$0.897705\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−10.1369	−	5.85256i	−1.71346	−	0.989264i
$36$		0			0
$37$		−	8.46521i		−	1.39167i	−0.718201	−	0.695836i	$-0.755034\pi$
$37$		−	8.46521i		−	1.39167i	0.718201	−	0.695836i	$-0.244966\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.41146	+	1.96961i	0.532780	+	0.307601i	0.742148	−	0.670236i	$-0.233807\pi$
$41$	3.41146	+	1.96961i	0.532780	+	0.307601i	−0.209368	+	0.977837i	$0.567141\pi$
$42$		0			0
$43$	−9.02523	−	5.21072i	−1.37633	−	0.794627i	−0.384619	−	0.923076i	$-0.625667\pi$
$43$	−9.02523	−	5.21072i	−1.37633	−	0.794627i	−0.991716	+	0.128448i	$0.959000\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−9.63084	+	5.56037i	−1.40480	+	0.811063i	−0.994881	−	0.101058i	$-0.967777\pi$
$47$	−9.63084	+	5.56037i	−1.40480	+	0.811063i	−0.409921	+	0.912121i	$0.634444\pi$
$48$		0			0
$49$	−4.33385			−0.619121
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.41554	−	2.54931i	0.606521	−	0.350175i	−0.165081	−	0.986280i	$-0.552789\pi$
$53$	4.41554	−	2.54931i	0.606521	−	0.350175i	0.771603	+	0.636105i	$0.219455\pi$
$54$		0			0
$55$	7.32090	+	4.22672i	0.987150	+	0.569931i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.58247	+	9.66912i	−0.726775	+	1.25881i	0.231464	+	0.972844i	$0.425649\pi$
$59$	−5.58247	+	9.66912i	−0.726775	+	1.25881i	−0.958239	+	0.285968i	$0.907685\pi$
$60$		0			0
$61$	−2.80994	−	4.86695i	−0.359776	−	0.623150i	0.628148	−	0.778094i	$-0.283813\pi$
$61$	−2.80994	−	4.86695i	−0.359776	−	0.623150i	−0.987923	+	0.154945i	$0.950480\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			20.1586i			2.50036i
$66$		0			0
$67$	3.03818	+	5.26229i	0.371173	+	0.642890i	0.989746	−	0.142837i	$-0.0456223\pi$
$67$	3.03818	+	5.26229i	0.371173	+	0.642890i	−0.618573	+	0.785727i	$0.712289\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.15397	−	10.6590i	0.730342	−	1.26499i	−0.226395	−	0.974036i	$-0.572694\pi$
$71$	6.15397	−	10.6590i	0.730342	−	1.26499i	0.956737	−	0.290954i	$-0.0939728\pi$
$72$		0			0
$73$	−3.97686	+	6.88813i	−0.465457	+	0.806194i	−0.999222	−	0.0394382i	$-0.987443\pi$
$73$	−3.97686	+	6.88813i	−0.465457	+	0.806194i	0.533766	+	0.845633i	$0.320777\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.18531			0.932802
$78$		0			0
$79$	1.19415	−	2.06832i	0.134352	−	0.232704i	−0.790998	−	0.611819i	$-0.790438\pi$
$79$	1.19415	−	2.06832i	0.134352	−	0.232704i	0.925350	+	0.379115i	$0.123771\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			5.59111i			0.613704i	0.951757	+	0.306852i	$0.0992757\pi$
$83$			5.59111i			0.613704i	−0.951757	+	0.306852i	$0.900724\pi$
$84$		0			0
$85$	9.30795	+	16.1218i	1.00959	+	1.74866i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.04638	−	2.91353i	0.534915	−	0.308833i	−0.208101	−	0.978107i	$-0.566728\pi$
$89$	5.04638	−	2.91353i	0.534915	−	0.308833i	0.743016	+	0.669274i	$0.233395\pi$
$90$		0			0
$91$	9.75958	+	16.9041i	1.02308	+	1.77203i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.00209	+	14.3060i	0.513204	+	1.46777i
$96$		0			0
$97$	2.47885	+	1.43117i	0.251689	+	0.145313i	0.620538	−	0.784177i	$-0.286914\pi$
$97$	2.47885	+	1.43117i	0.251689	+	0.145313i	−0.368848	+	0.929490i	$0.620248\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.24254	−	16.0086i	−0.919667	−	1.59291i	−0.799920	−	0.600106i	$-0.795125\pi$
$101$	−9.24254	−	16.0086i	−0.919667	−	1.59291i	−0.119747	−	0.992804i	$-0.538208\pi$
$102$		0			0
$103$	3.83108			0.377488			0.188744	−	0.982026i	$-0.439558\pi$
$103$	3.83108			0.377488			0.188744	+	0.982026i	$0.439558\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.17714			−0.597167			−0.298583	−	0.954384i	$-0.596514\pi$
$107$	−6.17714			−0.597167			−0.298583	+	0.954384i	$0.596514\pi$
$108$		0			0
$109$	−2.30994	−	1.33364i	−0.221252	−	0.127740i	0.385278	−	0.922801i	$-0.374106\pi$
$109$	−2.30994	−	1.33364i	−0.221252	−	0.127740i	−0.606530	+	0.795061i	$0.707439\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	5.29368i		−	0.497987i	−0.968505	−	0.248994i	$-0.919900\pi$
$113$		−	5.29368i		−	0.497987i	0.968505	−	0.248994i	$-0.0800998\pi$
$114$		0			0
$115$			5.24266i			0.488880i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	15.6105	+	9.01270i	1.43101	+	0.826193i
$120$		0			0
$121$	5.08857			0.462597
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−7.26167			−0.649504
$126$		0			0
$127$	−1.00000	−	1.73205i	−0.0887357	−	0.153695i	0.818241	−	0.574875i	$-0.194949\pi$
$127$	−1.00000	−	1.73205i	−0.0887357	−	0.153695i	−0.906977	+	0.421180i	$0.861616\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.03133	−	4.63689i	−0.701701	−	0.405127i	0.106280	−	0.994336i	$-0.466106\pi$
$131$	−8.03133	−	4.63689i	−0.701701	−	0.405127i	−0.807981	+	0.589209i	$0.799439\pi$
$132$		0			0
$133$	11.1206	+	9.57467i	0.964283	+	0.830229i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	0.965250	−	0.261329i	$-0.0841608\pi$
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	−0.708942	+	0.705266i	$0.750827\pi$
$138$		0			0
$139$	−1.23644	+	0.713859i	−0.104874	+	0.0605488i	−0.551519	−	0.834162i	$-0.685952\pi$
$139$	−1.23644	+	0.713859i	−0.104874	+	0.0605488i	0.446646	+	0.894711i	$0.352618\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−7.04837	−	12.2081i	−0.589414	−	1.02090i
$144$		0			0
$145$		−	16.9069i		−	1.40404i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.10361	+	15.7679i	−0.745797	+	1.29176i	0.204024	+	0.978966i	$0.434598\pi$
$149$	−9.10361	+	15.7679i	−0.745797	+	1.29176i	−0.949821	+	0.312793i	$0.898735\pi$
$150$		0			0
$151$	−1.04628			−0.0851447			−0.0425724	−	0.999093i	$-0.513555\pi$
$151$	−1.04628			−0.0851447			−0.0425724	+	0.999093i	$0.513555\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−18.3673	+	31.8131i	−1.47530	+	2.55529i
$156$		0			0
$157$	−8.85422	+	15.3360i	−0.706644	+	1.22394i	0.259451	+	0.965756i	$0.416458\pi$
$157$	−8.85422	+	15.3360i	−0.706644	+	1.22394i	−0.966095	+	0.258187i	$0.916875\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.53818	+	4.39626i	0.200037	+	0.346474i
$162$		0			0
$163$		−	11.6934i		−	0.915895i	−0.888979	−	0.457948i	$-0.848585\pi$
$163$		−	11.6934i		−	0.915895i	0.888979	−	0.457948i	$-0.151415\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.69415	−	13.3267i	−0.595391	−	1.03125i	−0.993492	−	0.113906i	$-0.963664\pi$
$167$	−7.69415	−	13.3267i	−0.595391	−	1.03125i	0.398101	−	0.917342i	$-0.369669\pi$
$168$		0			0
$169$	10.3079	−	17.8539i	0.792919	−	1.37338i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.42242	−	4.86269i	−0.640345	−	0.369703i	0.144403	−	0.989519i	$-0.453874\pi$
$173$	−8.42242	−	4.86269i	−0.640345	−	0.369703i	−0.784747	+	0.619816i	$0.787207\pi$
$174$		0			0
$175$	−20.6670	+	11.9321i	−1.56228	+	0.901983i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	14.4047			1.07666			0.538328	−	0.842735i	$-0.319056\pi$
$179$	14.4047			1.07666			0.538328	+	0.842735i	$0.319056\pi$
$180$		0			0
$181$	8.12065	−	4.68846i	0.603603	−	0.348490i	−0.166855	−	0.985982i	$-0.553361\pi$
$181$	8.12065	−	4.68846i	0.603603	−	0.348490i	0.770458	+	0.637491i	$0.220028\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−25.4892	−	14.7162i	−1.87400	−	1.08196i
$186$		0			0
$187$	−11.2739	−	6.50898i	−0.824428	−	0.475983i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			21.9024i			1.58480i	0.610001	+	0.792401i	$0.291169\pi$
$191$			21.9024i			1.58480i	−0.610001	+	0.792401i	$0.708831\pi$
$192$		0			0
$193$	−8.79773	−	5.07937i	−0.633275	−	0.365621i	0.148745	−	0.988876i	$-0.452477\pi$
$193$	−8.79773	−	5.07937i	−0.633275	−	0.365621i	−0.782019	+	0.623254i	$0.785810\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.52314			0.179766			0.0898831	−	0.995952i	$-0.471351\pi$
$197$	2.52314			0.179766			0.0898831	+	0.995952i	$0.471351\pi$
$198$		0			0
$199$	16.0472	−	9.26483i	1.13755	−	0.656766i	0.191729	−	0.981448i	$-0.438591\pi$
$199$	16.0472	−	9.26483i	1.13755	−	0.656766i	0.945823	+	0.324682i	$0.105257\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−8.18531	−	14.1774i	−0.574496	−	0.995056i
$204$		0			0
$205$	11.8612	−	6.84805i	0.828420	−	0.478289i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−8.03133	−	6.91483i	−0.555539	−	0.478309i
$210$		0			0
$211$	3.81402	−	6.60608i	0.262568	−	0.454781i	−0.704356	−	0.709847i	$-0.748764\pi$
$211$	3.81402	−	6.60608i	0.262568	−	0.454781i	0.966924	+	0.255066i	$0.0820973\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−31.3795	+	18.1170i	−2.14006	+	1.23557i
$216$		0			0
$217$			35.5694i			2.41461i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	31.0434i		−	2.08820i
$222$		0			0
$223$	−1.71728	+	2.97442i	−0.114998	+	0.199182i	−0.917779	−	0.397092i	$-0.870019\pi$
$223$	−1.71728	+	2.97442i	−0.114998	+	0.199182i	0.802781	+	0.596274i	$0.203353\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.4729			−0.761482			−0.380741	−	0.924682i	$-0.624331\pi$
$227$	−11.4729			−0.761482			−0.380741	+	0.924682i	$0.624331\pi$
$228$		0			0
$229$	4.13485			0.273238			0.136619	−	0.990624i	$-0.456376\pi$
$229$	4.13485			0.273238			0.136619	+	0.990624i	$0.456376\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.20025	−	3.81094i	0.144143	−	0.249663i	−0.784910	−	0.619610i	$-0.787291\pi$
$233$	2.20025	−	3.81094i	0.144143	−	0.249663i	0.929053	+	0.369947i	$0.120624\pi$
$234$		0			0
$235$			38.6652i			2.52224i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	7.09898i		−	0.459195i	−0.973286	−	0.229598i	$-0.926259\pi$
$239$		−	7.09898i		−	0.459195i	0.973286	−	0.229598i	$-0.0737410\pi$
$240$		0			0
$241$	7.09134	−	4.09418i	0.456793	−	0.263730i	−0.253902	−	0.967230i	$-0.581714\pi$
$241$	7.09134	−	4.09418i	0.456793	−	0.263730i	0.710695	+	0.703500i	$0.248381\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.53410	+	13.0494i	−0.481336	+	0.833698i
$246$		0			0
$247$	4.70433	−	24.8309i	0.299330	−	1.57995i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	8.66217	−	5.00111i	0.546751	−	0.315667i	−0.201059	−	0.979579i	$-0.564438\pi$
$251$	8.66217	−	5.00111i	0.546751	−	0.315667i	0.747811	+	0.663912i	$0.231105\pi$
$252$		0			0
$253$	−1.83308	−	3.17498i	−0.115244	−	0.199609i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	0.204332	−	0.117971i	0.0127459	−	0.00735885i	−0.493614	−	0.869681i	$-0.664324\pi$
$257$	0.204332	−	0.117971i	0.0127459	−	0.00735885i	0.506359	+	0.862323i	$0.330991\pi$
$258$		0			0
$259$	−28.4988			−1.77083
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.01096	+	2.89308i	0.308989	+	0.178395i	0.646474	−	0.762936i	$-0.276243\pi$
$263$	5.01096	+	2.89308i	0.308989	+	0.178395i	−0.337485	+	0.941331i	$0.609576\pi$
$264$		0			0
$265$		−	17.7272i		−	1.08898i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−8.79567	−	5.07818i	−0.536281	−	0.309622i	0.207289	−	0.978280i	$-0.433536\pi$
$269$	−8.79567	−	5.07818i	−0.536281	−	0.309622i	−0.743570	+	0.668658i	$0.766869\pi$
$270$		0			0
$271$	−11.0082	−	6.35557i	−0.668698	−	0.386073i	0.126885	−	0.991917i	$-0.459502\pi$
$271$	−11.0082	−	6.35557i	−0.668698	−	0.386073i	−0.795583	+	0.605844i	$0.792835\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	14.9257	−	8.61737i	0.900055	−	0.519647i
$276$		0			0
$277$	−3.39646			−0.204073			−0.102037	−	0.994781i	$-0.532536\pi$
$277$	−3.39646			−0.204073			−0.102037	+	0.994781i	$0.532536\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	24.4770	−	14.1318i	1.46017	−	0.843031i	0.461154	−	0.887320i	$-0.347435\pi$
$281$	24.4770	−	14.1318i	1.46017	−	0.843031i	0.999019	+	0.0442884i	$0.0141021\pi$
$282$		0			0
$283$	−17.6622	−	10.1973i	−1.04991	−	0.606164i	−0.127284	−	0.991866i	$-0.540626\pi$
$283$	−17.6622	−	10.1973i	−1.04991	−	0.606164i	−0.922623	+	0.385702i	$0.873959\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.63084	−	11.4849i	0.391406	−	0.677935i
$288$		0			0
$289$	−5.83385	−	10.1045i	−0.343168	−	0.594384i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			2.51388i			0.146862i	0.997300	+	0.0734311i	$0.0233949\pi$
$293$			2.51388i			0.146862i	−0.997300	+	0.0734311i	$0.976605\pi$
$294$		0			0
$295$	19.4095	+	33.6182i	1.13006	+	1.95733i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.37126	−	7.57124i	0.252796	−	0.437856i
$300$		0			0
$301$	−17.5423	+	30.3841i	−1.01112	+	1.75131i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−19.5395			−1.11883
$306$		0			0
$307$	4.84404	−	8.39012i	0.276464	−	0.478849i	−0.694040	−	0.719937i	$-0.744171\pi$
$307$	4.84404	−	8.39012i	0.276464	−	0.478849i	0.970503	+	0.241088i	$0.0775041\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		−	6.56560i		−	0.372301i	−0.982521	−	0.186151i	$-0.940399\pi$
$311$		−	6.56560i		−	0.372301i	0.982521	−	0.186151i	$-0.0596012\pi$
$312$		0			0
$313$	12.5975	+	21.8195i	0.712053	+	1.23331i	0.964085	+	0.265594i	$0.0855680\pi$
$313$	12.5975	+	21.8195i	0.712053	+	1.23331i	−0.252032	+	0.967719i	$0.581099\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.02321	+	4.63220i	−0.450628	+	0.260170i	−0.708096	−	0.706117i	$-0.750445\pi$
$317$	−8.02321	+	4.63220i	−0.450628	+	0.260170i	0.257467	+	0.966287i	$0.417112\pi$
$318$		0			0
$319$	5.91143	+	10.2389i	0.330977	+	0.573268i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−7.70301	−	22.0307i	−0.428607	−	1.22582i
$324$		0			0
$325$	35.5928	+	20.5495i	1.97433	+	1.13988i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	18.7194	+	32.4230i	1.03203	+	1.78754i
$330$		0			0
$331$	−16.9879			−0.933737			−0.466868	−	0.884327i	$-0.654618\pi$
$331$	−16.9879			−0.933737			−0.466868	+	0.884327i	$0.654618\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	21.1267			1.15427
$336$		0			0
$337$	−3.01298	−	1.73955i	−0.164128	−	0.0947591i	0.415686	−	0.909508i	$-0.363541\pi$
$337$	−3.01298	−	1.73955i	−0.164128	−	0.0947591i	−0.579814	+	0.814749i	$0.696875\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	25.6882i		−	1.39109i
$342$		0			0
$343$		−	8.97580i		−	0.484648i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−14.9790	−	8.64812i	−0.804114	−	0.464255i	0.0407937	−	0.999168i	$-0.487011\pi$
$347$	−14.9790	−	8.64812i	−0.804114	−	0.464255i	−0.844908	+	0.534912i	$0.820345\pi$
$348$		0			0
$349$	−31.3259			−1.67684			−0.838418	−	0.545028i	$-0.816519\pi$
$349$	−31.3259			−1.67684			−0.838418	+	0.545028i	$0.816519\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.408665			0.0217510			0.0108755	−	0.999941i	$-0.496538\pi$
$353$	0.408665			0.0217510			0.0108755	+	0.999941i	$0.496538\pi$
$354$		0			0
$355$	−21.3965	−	37.0599i	−1.13561	−	1.96693i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	14.0545	+	8.11437i	0.741768	+	0.428260i	0.822712	−	0.568459i	$-0.192460\pi$
$359$	14.0545	+	8.11437i	0.741768	+	0.428260i	−0.0809437	+	0.996719i	$0.525793\pi$
$360$		0			0
$361$	−2.82292	−	18.7891i	−0.148575	−	0.988901i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	13.8270	+	23.9491i	0.723738	+	1.25355i
$366$		0			0
$367$	5.15185	−	2.97442i	0.268924	−	0.155264i	−0.359474	−	0.933155i	$-0.617044\pi$
$367$	5.15185	−	2.97442i	0.268924	−	0.155264i	0.628399	+	0.777891i	$0.283711\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−8.58247	−	14.8653i	−0.445579	−	0.771766i
$372$		0			0
$373$		−	21.8930i		−	1.13358i	−0.823863	−	0.566788i	$-0.808186\pi$
$373$		−	21.8930i		−	1.13358i	0.823863	−	0.566788i	$-0.191814\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−14.0967	+	24.4163i	−0.726019	+	1.25750i
$378$		0			0
$379$	7.94158			0.407931			0.203966	−	0.978978i	$-0.434617\pi$
$379$	7.94158			0.407931			0.203966	+	0.978978i	$0.434617\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−15.0143	+	26.0055i	−0.767195	+	1.32882i	0.171883	+	0.985117i	$0.445015\pi$
$383$	−15.0143	+	26.0055i	−0.767195	+	1.32882i	−0.939078	+	0.343703i	$0.888319\pi$
$384$		0			0
$385$	14.2296	−	24.6464i	0.725207	−	1.25610i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	18.3462	+	31.7765i	0.930187	+	1.61113i	0.782999	+	0.622023i	$0.213689\pi$
$389$	18.3462	+	31.7765i	0.930187	+	1.61113i	0.147188	+	0.989109i	$0.452978\pi$
$390$		0			0
$391$		−	8.07347i		−	0.408293i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.15188	−	7.19127i	−0.208904	−	0.361832i
$396$		0			0
$397$	−15.3291	+	26.5508i	−0.769345	+	1.33254i	0.168573	+	0.985689i	$0.446084\pi$
$397$	−15.3291	+	26.5508i	−0.769345	+	1.33254i	−0.937918	+	0.346856i	$0.887249\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	13.8066	+	7.97126i	0.689470	+	0.398066i	0.803414	−	0.595421i	$-0.203015\pi$
$401$	13.8066	+	7.97126i	0.689470	+	0.398066i	−0.113943	+	0.993487i	$0.536348\pi$
$402$		0			0
$403$	53.0506	−	30.6288i	2.64264	−	1.52573i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	20.5818			1.02020
$408$		0			0
$409$	6.69006	−	3.86251i	0.330802	−	0.190989i	−0.325395	−	0.945578i	$-0.605497\pi$
$409$	6.69006	−	3.86251i	0.330802	−	0.190989i	0.656197	+	0.754589i	$0.272164\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	32.5518	+	18.7938i	1.60177	+	0.924783i
$414$		0			0
$415$	16.8351	+	9.71976i	0.826404	+	0.477124i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			22.5693i			1.10258i	0.834313	+	0.551292i	$0.185865\pi$
$419$			22.5693i			1.10258i	−0.834313	+	0.551292i	$0.814135\pi$
$420$		0			0
$421$	−35.2174	−	20.3328i	−1.71639	−	0.990960i	−0.925275	−	0.379297i	$-0.876166\pi$
$421$	−35.2174	−	20.3328i	−1.71639	−	0.990960i	−0.791118	−	0.611663i	$-0.790501\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	37.9538			1.84103
$426$		0			0
$427$	−16.3850	+	9.45987i	−0.792925	+	0.457795i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	14.0313	+	24.3030i	0.675866	+	1.17063i	0.976215	+	0.216804i	$0.0695633\pi$
$431$	14.0313	+	24.3030i	0.675866	+	1.17063i	−0.300350	+	0.953829i	$0.597103\pi$
$432$		0			0
$433$	15.6711	−	9.04772i	0.753105	−	0.434806i	−0.0737094	−	0.997280i	$-0.523484\pi$
$433$	15.6711	−	9.04772i	0.753105	−	0.434806i	0.826815	+	0.562474i	$0.190150\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.22346	−	6.45778i	0.0585260	−	0.308918i
$438$		0			0
$439$	−7.65806	+	13.2641i	−0.365499	+	0.633063i	−0.988856	−	0.148874i	$-0.952435\pi$
$439$	−7.65806	+	13.2641i	−0.365499	+	0.633063i	0.623357	+	0.781937i	$0.285768\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−24.2194	+	13.9831i	−1.15070	+	0.664355i	−0.949057	−	0.315104i	$-0.897961\pi$
$443$	−24.2194	+	13.9831i	−1.15070	+	0.664355i	−0.201640	+	0.979460i	$0.564627\pi$
$444$		0			0
$445$		−	20.2599i		−	0.960410i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			6.03148i			0.284643i	0.989820	+	0.142322i	$0.0454567\pi$
$449$			6.03148i			0.284643i	−0.989820	+	0.142322i	$0.954543\pi$
$450$		0			0
$451$	−4.78879	+	8.29443i	−0.225495	+	0.390569i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	67.8654			3.18158
$456$		0			0
$457$	−24.5573			−1.14874			−0.574370	−	0.818596i	$-0.694753\pi$
$457$	−24.5573			−1.14874			−0.574370	+	0.818596i	$0.694753\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	9.74939	−	16.8864i	0.454074	−	0.786480i	−0.544560	−	0.838722i	$-0.683303\pi$
$461$	9.74939	−	16.8864i	0.454074	−	0.786480i	0.998634	+	0.0522419i	$0.0166367\pi$
$462$		0			0
$463$			14.2072i			0.660267i	0.943934	+	0.330133i	$0.107094\pi$
$463$			14.2072i			0.660267i	−0.943934	+	0.330133i	$0.892906\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	16.9572i		−	0.784684i	−0.919819	−	0.392342i	$-0.871665\pi$
$467$		−	16.9572i		−	0.784684i	0.919819	−	0.392342i	$-0.128335\pi$
$468$		0			0
$469$	17.7159	−	10.2283i	0.818044	−	0.472298i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	12.6690	−	21.9434i	0.582523	−	1.00896i
$474$		0			0
$475$	30.3583	+	5.75154i	1.39294	+	0.263899i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	22.2645	−	12.8544i	1.01729	−	0.587332i	0.103972	−	0.994580i	$-0.466845\pi$
$479$	22.2645	−	12.8544i	1.01729	−	0.587332i	0.913318	+	0.407248i	$0.133512\pi$
$480$		0			0
$481$	24.5403	+	42.5051i	1.11894	+	1.93806i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	8.61863	−	4.97597i	0.391352	−	0.225947i
$486$		0			0
$487$	19.4607			0.881850			0.440925	−	0.897544i	$-0.354650\pi$
$487$	19.4607			0.881850			0.440925	+	0.897544i	$0.354650\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−35.1119	−	20.2719i	−1.58458	−	0.914856i	−0.994179	−	0.107744i	$-0.965637\pi$
$491$	−35.1119	−	20.2719i	−1.58458	−	0.914856i	−0.590398	−	0.807112i	$-0.701029\pi$
$492$		0			0
$493$			26.0359i			1.17260i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−35.8843	−	20.7178i	−1.60963	−	0.929322i
$498$		0			0
$499$	−6.51908	−	3.76379i	−0.291834	−	0.168491i	0.346934	−	0.937889i	$-0.387223\pi$
$499$	−6.51908	−	3.76379i	−0.291834	−	0.168491i	−0.638769	+	0.769399i	$0.720556\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.19084	−	0.687530i	0.0530968	−	0.0306554i	−0.473217	−	0.880946i	$-0.656907\pi$
$503$	1.19084	−	0.687530i	0.0530968	−	0.0306554i	0.526313	+	0.850291i	$0.323574\pi$
$504$		0			0
$505$	−64.2701			−2.85998
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−28.0830	+	16.2138i	−1.24476	+	0.718662i	−0.970059	−	0.242868i	$-0.921912\pi$
$509$	−28.0830	+	16.2138i	−1.24476	+	0.718662i	−0.274700	+	0.961530i	$0.588578\pi$
$510$		0			0
$511$	23.1894	+	13.3884i	1.02584	+	0.592269i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	6.66008	−	11.5356i	0.293478	−	0.508319i
$516$		0			0
$517$	−13.5192	−	23.4159i	−0.594572	−	1.02983i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	3.05664i		−	0.133914i	−0.997756	−	0.0669568i	$-0.978671\pi$
$521$		−	3.05664i		−	0.133914i	0.997756	−	0.0669568i	$-0.0213290\pi$
$522$		0			0
$523$	−10.2031	−	17.6723i	−0.446151	−	0.772756i	0.551980	−	0.833857i	$-0.313872\pi$
$523$	−10.2031	−	17.6723i	−0.446151	−	0.772756i	−0.998132	+	0.0611006i	$0.980539\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	28.2848	−	48.9908i	1.23211	−	2.13407i
$528$		0			0
$529$	−10.3632	+	17.9495i	−0.450572	+	0.780414i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−22.8393			−0.989278
$534$		0			0
$535$	−10.7385	+	18.5997i	−0.464267	+	0.804135i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	10.5371i		−	0.453864i
$540$		0			0
$541$	−8.20845	−	14.2174i	−0.352909	−	0.611256i	0.633849	−	0.773457i	$-0.281474\pi$
$541$	−8.20845	−	14.2174i	−0.352909	−	0.611256i	−0.986758	+	0.162201i	$0.948141\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−8.03133	+	4.63689i	−0.344025	+	0.198623i
$546$		0			0
$547$	−0.882218	−	1.52805i	−0.0377209	−	0.0653345i	0.846549	−	0.532311i	$-0.178676\pi$
$547$	−0.882218	−	1.52805i	−0.0377209	−	0.0653345i	−0.884270	+	0.466977i	$0.845343\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−3.94550	+	20.8255i	−0.168084	+	0.887196i
$552$		0			0
$553$	−6.96317	−	4.02019i	−0.296104	−	0.170956i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.388292	−	0.672541i	−0.0164525	−	0.0284965i	0.857682	−	0.514181i	$-0.171904\pi$
$557$	−0.388292	−	0.672541i	−0.0164525	−	0.0284965i	−0.874134	+	0.485684i	$0.838571\pi$
$558$		0			0
$559$	60.4227			2.55561
$560$		0			0
$561$		0			0
$562$		0			0
$563$	44.9019			1.89239			0.946195	−	0.323597i	$-0.104892\pi$
$563$	44.9019			1.89239			0.946195	+	0.323597i	$0.104892\pi$
$564$		0			0
$565$	−15.9395	−	9.20269i	−0.670581	−	0.387160i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	33.7523i		−	1.41497i	−0.706729	−	0.707485i	$-0.749830\pi$
$569$		−	33.7523i		−	1.41497i	0.706729	−	0.707485i	$-0.250170\pi$
$570$		0			0
$571$		−	21.1007i		−	0.883037i	−0.897252	−	0.441518i	$-0.854440\pi$
$571$		−	21.1007i		−	0.883037i	0.897252	−	0.441518i	$-0.145560\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	9.25664	+	5.34432i	0.386029	+	0.222874i
$576$		0			0
$577$	6.84882			0.285120			0.142560	−	0.989786i	$-0.454467\pi$
$577$	6.84882			0.285120			0.142560	+	0.989786i	$0.454467\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	18.8229			0.780906
$582$		0			0
$583$	6.19826	+	10.7357i	0.256706	+	0.444627i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.3018	+	6.52511i	0.466476	+	0.269320i	0.714763	−	0.699366i	$-0.246534\pi$
$587$	11.3018	+	6.52511i	0.466476	+	0.269320i	−0.248287	+	0.968686i	$0.579868\pi$
$588$		0			0
$589$	30.0485	−	34.9003i	1.23813	−	1.43804i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−18.0887	−	31.3305i	−0.742813	−	1.28659i	−0.951210	−	0.308545i	$-0.900158\pi$
$593$	−18.0887	−	31.3305i	−0.742813	−	1.28659i	0.208397	−	0.978044i	$-0.433175\pi$
$594$		0			0
$595$	54.2754	−	31.3359i	2.22508	−	1.28465i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	13.4449	+	23.2872i	0.549343	+	0.951490i	0.998320	+	0.0579467i	$0.0184553\pi$
$599$	13.4449	+	23.2872i	0.549343	+	0.951490i	−0.448977	+	0.893544i	$0.648211\pi$
$600$		0			0
$601$			3.73240i			0.152248i	0.997098	+	0.0761240i	$0.0242545\pi$
$601$			3.73240i			0.152248i	−0.997098	+	0.0761240i	$0.975746\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	8.84613	−	15.3219i	0.359646	−	0.622926i
$606$		0			0
$607$	−47.3177			−1.92057			−0.960284	−	0.279026i	$-0.909988\pi$
$607$	−47.3177			−1.92057			−0.960284	+	0.279026i	$0.909988\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	32.2386	−	55.8388i	1.30423	−	2.25900i
$612$		0			0
$613$	−8.52115	+	14.7591i	−0.344166	+	0.596113i	−0.985202	−	0.171398i	$-0.945172\pi$
$613$	−8.52115	+	14.7591i	−0.344166	+	0.596113i	0.641036	+	0.767511i	$0.278505\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.30107	+	9.18172i	0.213413	+	0.369642i	0.952780	−	0.303660i	$-0.0982087\pi$
$617$	5.30107	+	9.18172i	0.213413	+	0.369642i	−0.739367	+	0.673302i	$0.764875\pi$
$618$		0			0
$619$		−	23.0642i		−	0.927028i	−0.886090	−	0.463514i	$-0.846588\pi$
$619$		−	23.0642i		−	0.927028i	0.886090	−	0.463514i	$-0.153412\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−9.80862	−	16.9890i	−0.392974	−	0.680651i
$624$		0			0
$625$	5.09751	−	8.82915i	0.203900	−	0.353166i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	39.2523	+	22.6623i	1.56509	+	0.903605i
$630$		0			0
$631$	1.71405	−	0.989606i	0.0682352	−	0.0393956i	−0.465494	−	0.885051i	$-0.654123\pi$
$631$	1.71405	−	0.989606i	0.0682352	−	0.0393956i	0.533729	+	0.845655i	$0.320790\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6.95372			−0.275950
$636$		0			0
$637$	21.7609	−	12.5637i	0.862198	−	0.497790i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−21.2425	−	12.2644i	−0.839030	−	0.484414i	0.0179044	−	0.999840i	$-0.494301\pi$
$641$	−21.2425	−	12.2644i	−0.839030	−	0.484414i	−0.856934	+	0.515425i	$0.827634\pi$
$642$		0			0
$643$	29.9660	+	17.3009i	1.18174	+	0.682280i	0.956417	−	0.292003i	$-0.0943218\pi$
$643$	29.9660	+	17.3009i	1.18174	+	0.682280i	0.225326	+	0.974283i	$0.427655\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			40.0103i			1.57297i	0.617610	+	0.786484i	$0.288101\pi$
$647$			40.0103i			1.57297i	−0.617610	+	0.786484i	$0.711899\pi$
$648$		0			0
$649$	−23.5089	−	13.5729i	−0.922807	−	0.532783i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−23.7687			−0.930140			−0.465070	−	0.885274i	$-0.653971\pi$
$653$	−23.7687			−0.930140			−0.465070	+	0.885274i	$0.653971\pi$
$654$		0			0
$655$	−27.9238	+	16.1218i	−1.09107	+	0.629932i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−10.1016	−	17.4965i	−0.393503	−	0.681568i	0.599406	−	0.800446i	$-0.295404\pi$
$659$	−10.1016	−	17.4965i	−0.393503	−	0.681568i	−0.992909	+	0.118878i	$0.962070\pi$
$660$		0			0
$661$	20.2836	−	11.7107i	0.788940	−	0.455495i	−0.0506490	−	0.998717i	$-0.516129\pi$
$661$	20.2836	−	11.7107i	0.788940	−	0.455495i	0.839589	+	0.543222i	$0.182796\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	48.1623	−	16.8399i	1.86765	−	0.653025i
$666$		0			0
$667$	−3.66615	+	6.34996i	−0.141954	+	0.245871i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	11.8332	−	6.83192i	0.456817	−	0.263743i
$672$		0			0
$673$			43.0646i			1.66002i	0.557750	+	0.830009i	$0.311665\pi$
$673$			43.0646i			1.66002i	−0.557750	+	0.830009i	$0.688335\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			19.2557i			0.740057i	0.929020	+	0.370028i	$0.120652\pi$
$677$			19.2557i			0.740057i	−0.929020	+	0.370028i	$0.879348\pi$
$678$		0			0
$679$	4.81813	−	8.34525i	0.184903	−	0.320261i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	33.5654			1.28435			0.642173	−	0.766560i	$-0.278033\pi$
$683$	33.5654			1.28435			0.642173	+	0.766560i	$0.278033\pi$
$684$		0			0
$685$	20.8612			0.797064
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−14.7807	+	25.6010i	−0.563101	+	0.975319i
$690$		0			0
$691$		−	15.1717i		−	0.577159i	−0.957456	−	0.288580i	$-0.906817\pi$
$691$		−	15.1717i		−	0.577159i	0.957456	−	0.288580i	$-0.0931830\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			4.96398i			0.188295i
$696$		0			0
$697$	−18.2657	+	10.5457i	−0.691863	+	0.399447i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−15.6158	+	27.0473i	−0.589800	+	1.02156i	0.404458	+	0.914557i	$0.367460\pi$
$701$	−15.6158	+	27.0473i	−0.589800	+	1.02156i	−0.994258	+	0.107007i	$0.965873\pi$
$702$		0			0
$703$	27.9627	+	24.0754i	1.05463	+	0.908019i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−53.8941	+	31.1157i	−2.02689	+	1.17023i
$708$		0			0
$709$	−3.61248	−	6.25700i	−0.135670	−	0.234987i	0.790183	−	0.612870i	$-0.209985\pi$
$709$	−3.61248	−	6.25700i	−0.135670	−	0.234987i	−0.925853	+	0.377884i	$0.876652\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	13.7969	−	7.96565i	0.516698	−	0.298316i
$714$		0			0
$715$	−49.0124			−1.83296
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−12.7051	−	7.33530i	−0.473821	−	0.273560i	0.244017	−	0.969771i	$-0.421535\pi$
$719$	−12.7051	−	7.33530i	−0.473821	−	0.273560i	−0.717838	+	0.696211i	$0.754868\pi$
$720$		0			0
$721$		−	12.8976i		−	0.480333i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−29.8515	−	17.2347i	−1.10866	−	0.640082i
$726$		0			0
$727$	−25.2064	−	14.5529i	−0.934852	−	0.539737i	−0.0465091	−	0.998918i	$-0.514810\pi$
$727$	−25.2064	−	14.5529i	−0.934852	−	0.539737i	−0.888343	+	0.459181i	$0.848143\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	48.3231	−	27.8994i	1.78729	−	1.03189i
$732$		0			0
$733$	−21.2194			−0.783758			−0.391879	−	0.920017i	$-0.628175\pi$
$733$	−21.2194			−0.783758			−0.391879	+	0.920017i	$0.628175\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.7944	+	7.38686i	−0.471289	+	0.272099i
$738$		0			0
$739$	−2.07225	−	1.19641i	−0.0762290	−	0.0440108i	0.461401	−	0.887192i	$-0.347347\pi$
$739$	−2.07225	−	1.19641i	−0.0762290	−	0.0440108i	−0.537630	+	0.843181i	$0.680680\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5.71607	−	9.90052i	0.209702	−	0.363215i	−0.741919	−	0.670490i	$-0.766084\pi$
$743$	5.71607	−	9.90052i	0.209702	−	0.363215i	0.951621	+	0.307275i	$0.0994172\pi$
$744$		0			0
$745$	31.6520	+	54.8229i	1.15964	+	2.00856i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			20.7958i			0.759863i
$750$		0			0
$751$	−22.2195	−	38.4853i	−0.810801	−	1.40435i	−0.912304	−	0.409514i	$-0.865698\pi$
$751$	−22.2195	−	38.4853i	−0.810801	−	1.40435i	0.101503	−	0.994835i	$-0.467635\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−1.81888	+	3.15039i	−0.0661958	+	0.114654i
$756$		0			0
$757$	17.6289	−	30.5341i	0.640732	−	1.10978i	−0.344537	−	0.938773i	$-0.611964\pi$
$757$	17.6289	−	30.5341i	0.640732	−	1.10978i	0.985270	−	0.171008i	$-0.0547025\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−28.0983			−1.01856			−0.509282	−	0.860600i	$-0.670089\pi$
$761$	−28.0983			−1.01856			−0.509282	+	0.860600i	$0.670089\pi$
$762$		0			0
$763$	−4.48981	+	7.77659i	−0.162542	+	0.281531i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	64.7334i		−	2.33739i
$768$		0			0
$769$	3.36515	+	5.82862i	0.121351	+	0.210185i	0.920301	−	0.391212i	$-0.127944\pi$
$769$	3.36515	+	5.82862i	0.121351	+	0.210185i	−0.798950	+	0.601398i	$0.794611\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−15.5383	+	8.97107i	−0.558875	+	0.322667i	−0.752694	−	0.658371i	$-0.771246\pi$
$773$	−15.5383	+	8.97107i	−0.558875	+	0.322667i	0.193819	+	0.981037i	$0.437913\pi$
$774$		0			0
$775$	37.4469	+	64.8599i	1.34513	+	2.32984i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−16.2084	+	5.66727i	−0.580727	+	0.203051i
$780$		0			0
$781$	25.9157	+	14.9624i	0.927336	+	0.535398i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	30.7849	+	53.3210i	1.09876	+	1.90311i
$786$		0			0
$787$	−16.7441			−0.596861			−0.298431	−	0.954431i	$-0.596463\pi$
$787$	−16.7441			−0.596861			−0.298431	+	0.954431i	$0.596463\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−17.8216			−0.633662
$792$		0			0
$793$	28.2182	+	16.2918i	1.00206	+	0.578539i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	8.30004i		−	0.294002i	−0.989136	−	0.147001i	$-0.953038\pi$
$797$		−	8.30004i		−	0.294002i	0.989136	−	0.147001i	$-0.0469621\pi$
$798$		0			0
$799$		−	59.5429i		−	2.10648i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−16.7474	−	9.66912i	−0.591003	−	0.341216i
$804$		0			0
$805$	17.6498			0.622074
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−3.29972			−0.116012			−0.0580060	−	0.998316i	$-0.518474\pi$
$809$	−3.29972			−0.116012			−0.0580060	+	0.998316i	$0.518474\pi$
$810$		0			0
$811$	6.44279	+	11.1592i	0.226237	+	0.391854i	0.956690	−	0.291109i	$-0.0940243\pi$
$811$	6.44279	+	11.1592i	0.226237	+	0.391854i	−0.730453	+	0.682963i	$0.760691\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−35.2093	−	20.3281i	−1.23333	−	0.712063i
$816$		0			0
$817$	42.8804	−	14.9931i	1.50019	−	0.524543i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	8.00817	+	13.8706i	0.279487	+	0.484086i	0.971257	−	0.238032i	$-0.0765023\pi$
$821$	8.00817	+	13.8706i	0.279487	+	0.484086i	−0.691770	+	0.722118i	$0.743169\pi$
$822$		0			0
$823$	29.6825	−	17.1372i	1.03467	−	0.597366i	0.116350	−	0.993208i	$-0.462881\pi$
$823$	29.6825	−	17.1372i	1.03467	−	0.597366i	0.918319	+	0.395842i	$0.129547\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.865154	+	1.49849i	0.0300844	+	0.0521076i	0.880676	−	0.473720i	$-0.157089\pi$
$827$	0.865154	+	1.49849i	0.0300844	+	0.0521076i	−0.850591	+	0.525827i	$0.823756\pi$
$828$		0			0
$829$		−	29.4144i		−	1.02161i	−0.859698	−	0.510803i	$-0.829348\pi$
$829$		−	29.4144i		−	1.02161i	0.859698	−	0.510803i	$-0.170652\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	11.6022	−	20.0956i	0.401992	−	0.696271i
$834$		0			0
$835$	−53.5030			−1.85155
$836$		0			0
$837$		0			0
$838$		0			0
$839$	18.5894	−	32.1979i	0.641779	−	1.11159i	−0.343256	−	0.939242i	$-0.611530\pi$
$839$	18.5894	−	32.1979i	0.641779	−	1.11159i	0.985035	−	0.172352i	$-0.0551367\pi$
$840$		0			0
$841$	−2.67714	+	4.63694i	−0.0923152	+	0.159895i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−35.8393	−	62.0755i	−1.23291	−	2.13546i
$846$		0			0
$847$		−	17.1311i		−	0.588631i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	6.38222	+	11.0543i	0.218780	+	0.378937i
$852$		0			0
$853$	−16.5967	+	28.7464i	−0.568261	+	0.984258i	0.428477	+	0.903553i	$0.359050\pi$
$853$	−16.5967	+	28.7464i	−0.568261	+	0.984258i	−0.996738	+	0.0807048i	$0.974283\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−19.5371	−	11.2797i	−0.667375	−	0.385309i	0.127707	−	0.991812i	$-0.459238\pi$
$857$	−19.5371	−	11.2797i	−0.667375	−	0.385309i	−0.795081	+	0.606503i	$0.792572\pi$
$858$		0			0
$859$	−12.4006	+	7.15951i	−0.423104	+	0.244279i	−0.696404	−	0.717649i	$-0.745218\pi$
$859$	−12.4006	+	7.15951i	−0.423104	+	0.244279i	0.273300	+	0.961929i	$0.411885\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	31.0001			1.05525			0.527627	−	0.849476i	$-0.323082\pi$
$863$	31.0001			1.05525			0.527627	+	0.849476i	$0.323082\pi$
$864$		0			0
$865$	−29.2836	+	16.9069i	−0.995672	+	0.574852i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	5.02880	+	2.90338i	0.170590	+	0.0984904i
$870$		0			0
$871$	−30.5103	−	17.6151i	−1.03380	−	0.596866i
$872$		0			0
$873$		0			0
$874$		0			0
$875$			24.4470i			0.826459i
$876$		0			0
$877$	34.5764	+	19.9627i	1.16756	+	0.674093i	0.953105	−	0.302640i	$-0.0978681\pi$
$877$	34.5764	+	19.9627i	1.16756	+	0.674093i	0.214458	+	0.976733i	$0.431201\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	17.5857			0.592479			0.296239	−	0.955114i	$-0.404267\pi$
$881$	17.5857			0.592479			0.296239	+	0.955114i	$0.404267\pi$
$882$		0			0
$883$	−44.6874	+	25.8003i	−1.50385	+	0.868249i	−0.503861	+	0.863785i	$0.668088\pi$
$883$	−44.6874	+	25.8003i	−1.50385	+	0.868249i	−0.999990	+	0.00446371i	$0.998579\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.8360	+	29.1608i	0.565297	+	0.979122i	0.997022	+	0.0771174i	$0.0245716\pi$
$887$	16.8360	+	29.1608i	0.565297	+	0.979122i	−0.431725	+	0.902005i	$0.642095\pi$
$888$		0			0
$889$	−5.83108	+	3.36658i	−0.195568	+	0.112911i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	9.02317	−	47.6269i	0.301949	−	1.59377i
$894$		0			0
$895$	25.0415	−	43.3732i	0.837047	−	1.44981i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−44.4933	+	25.6882i	−1.48393	+	0.856749i
$900$		0			0
$901$			27.2992i			0.909468i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	32.6023i		−	1.08374i
$906$		0			0
$907$	0.788790	−	1.36622i	0.0261913	−	0.0453647i	−0.852633	−	0.522511i	$-0.824995\pi$
$907$	0.788790	−	1.36622i	0.0261913	−	0.0453647i	0.878824	+	0.477146i	$0.158329\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5.05186			−0.167376			−0.0836879	−	0.996492i	$-0.526670\pi$
$911$	−5.05186			−0.167376			−0.0836879	+	0.996492i	$0.526670\pi$
$912$		0			0
$913$	−13.5939			−0.449893
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.6105	+	27.0381i	−0.515503	+	0.892877i
$918$		0			0
$919$			15.7897i			0.520853i	0.965494	+	0.260426i	$0.0838631\pi$
$919$			15.7897i			0.520853i	−0.965494	+	0.260426i	$0.916137\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			71.3605i			2.34886i
$924$		0			0
$925$	−51.9669	+	30.0031i	−1.70866	+	0.986496i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−17.3039	+	29.9712i	−0.567721	+	0.983322i	0.429069	+	0.903272i	$0.358842\pi$
$929$	−17.3039	+	29.9712i	−0.567721	+	0.983322i	−0.996791	+	0.0800507i	$0.974492\pi$
$930$		0			0
$931$	12.3256	−	14.3158i	0.403956	−	0.469181i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−39.1977	+	22.6308i	−1.28190	+	0.740107i
$936$		0			0
$937$	22.6370	+	39.2085i	0.739520	+	1.28089i	0.952712	+	0.303876i	$0.0982807\pi$
$937$	22.6370	+	39.2085i	0.739520	+	1.28089i	−0.213192	+	0.977010i	$0.568386\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	37.0830	−	21.4099i	1.20887	−	0.697943i	0.246360	−	0.969178i	$-0.420766\pi$
$941$	37.0830	−	21.4099i	1.20887	−	0.697943i	0.962513	+	0.271236i	$0.0874322\pi$
$942$		0			0
$943$	−5.93982			−0.193427
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−29.4252	−	16.9887i	−0.956191	−	0.552057i	−0.0611923	−	0.998126i	$-0.519490\pi$
$947$	−29.4252	−	16.9887i	−0.956191	−	0.552057i	−0.894999	+	0.446069i	$0.852824\pi$
$948$		0			0
$949$		−	46.1151i		−	1.49696i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−32.4648	−	18.7435i	−1.05164	−	0.607163i	−0.128530	−	0.991706i	$-0.541026\pi$
$953$	−32.4648	−	18.7435i	−1.05164	−	0.607163i	−0.923107	+	0.384543i	$0.874359\pi$
$954$		0			0
$955$	65.9492	+	38.0758i	2.13407	+	1.23210i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	17.4933	−	10.0997i	0.564887	−	0.326137i
$960$		0			0
$961$	80.6284			2.60091
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−30.5885	+	17.6603i	−0.984679	+	0.568504i
$966$		0			0
$967$	−36.7557	−	21.2209i	−1.18198	−	0.682418i	−0.225510	−	0.974241i	$-0.572405\pi$
$967$	−36.7557	−	21.2209i	−1.18198	−	0.682418i	−0.956472	+	0.291823i	$0.905738\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−2.76568	+	4.79030i	−0.0887549	+	0.153728i	−0.906985	−	0.421163i	$-0.861622\pi$
$971$	−2.76568	+	4.79030i	−0.0887549	+	0.153728i	0.818230	+	0.574891i	$0.194955\pi$
$972$		0			0
$973$	2.40326	+	4.16257i	0.0770451	+	0.133446i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			15.1102i			0.483419i	0.970349	+	0.241709i	$0.0777081\pi$
$977$			15.1102i			0.483419i	−0.970349	+	0.241709i	$0.922292\pi$
$978$		0			0
$979$	7.08379	+	12.2695i	0.226399	+	0.392134i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−9.01709	+	15.6181i	−0.287601	+	0.498139i	−0.973237	−	0.229806i	$-0.926191\pi$
$983$	−9.01709	+	15.6181i	−0.287601	+	0.498139i	0.685636	+	0.727945i	$0.259524\pi$
$984$		0			0
$985$	4.38630	−	7.59730i	0.139759	−	0.242070i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	15.7142			0.499682
$990$		0			0
$991$	10.8741	−	18.8344i	0.345426	−	0.598295i	−0.640005	−	0.768370i	$-0.721068\pi$
$991$	10.8741	−	18.8344i	0.345426	−	0.598295i	0.985431	+	0.170076i	$0.0544012\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	64.4251i		−	2.04241i
$996$		0			0
$997$	−11.0995	−	19.2249i	−0.351525	−	0.608859i	0.634992	−	0.772519i	$-0.281003\pi$
$997$	−11.0995	−	19.2249i	−0.351525	−	0.608859i	−0.986517	+	0.163660i	$0.947670\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.bm.r.559.4		8
3.2	odd	2		912.2.bb.h.559.1	yes	8
4.3	odd	2		2736.2.bm.s.559.4		8
12.11	even	2		912.2.bb.g.559.1	yes	8
19.12	odd	6		2736.2.bm.s.1855.4		8
57.50	even	6		912.2.bb.g.31.1	✓	8
76.31	even	6	inner	2736.2.bm.r.1855.4		8
228.107	odd	6		912.2.bb.h.31.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.bb.g.31.1	✓	8	57.50	even	6
912.2.bb.g.559.1	yes	8	12.11	even	2
912.2.bb.h.31.1	yes	8	228.107	odd	6
912.2.bb.h.559.1	yes	8	3.2	odd	2
2736.2.bm.r.559.4		8	1.1	even	1	trivial
2736.2.bm.r.1855.4		8	76.31	even	6	inner
2736.2.bm.s.559.4		8	4.3	odd	2
2736.2.bm.s.1855.4		8	19.12	odd	6

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:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73843 - 3.01105i) q^{5} -3.36658i q^{7} +2.43134i q^{11} +(-5.02115 + 2.89896i) q^{13} +(-2.67711 + 4.63689i) q^{17} +(-2.84404 + 3.30325i) q^{19} +(-1.30585 + 0.753935i) q^{23} +(-3.54429 - 6.13888i) q^{25} +(4.21121 - 2.43134i) q^{29} -10.5654 q^{31} +(-10.1369 - 5.85256i) q^{35} -8.46521i q^{37} +(3.41146 + 1.96961i) q^{41} +(-9.02523 - 5.21072i) q^{43} +(-9.63084 + 5.56037i) q^{47} -4.33385 q^{49} +(4.41554 - 2.54931i) q^{53} +(7.32090 + 4.22672i) q^{55} +(-5.58247 + 9.66912i) q^{59} +(-2.80994 - 4.86695i) q^{61} +20.1586i q^{65} +(3.03818 + 5.26229i) q^{67} +(6.15397 - 10.6590i) q^{71} +(-3.97686 + 6.88813i) q^{73} +8.18531 q^{77} +(1.19415 - 2.06832i) q^{79} +5.59111i q^{83} +(9.30795 + 16.1218i) q^{85} +(5.04638 - 2.91353i) q^{89} +(9.75958 + 16.9041i) q^{91} +(5.00209 + 14.3060i) q^{95} +(2.47885 + 1.43117i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{5} - 4 q^{17} - 6 q^{23} - 12 q^{25} + 12 q^{29} - 28 q^{31} - 18 q^{35} + 12 q^{41} - 18 q^{43} - 12 q^{47} - 24 q^{49} + 6 q^{53} + 12 q^{55} - 10 q^{59} - 4 q^{61} + 6 q^{67} + 8 q^{71} - 8 q^{73}+ \cdots + 60 q^{97}+O(q^{100}) \) 8 * q + 2 * q^5 - 4 * q^17 - 6 * q^23 - 12 * q^25 + 12 * q^29 - 28 * q^31 - 18 * q^35 + 12 * q^41 - 18 * q^43 - 12 * q^47 - 24 * q^49 + 6 * q^53 + 12 * q^55 - 10 * q^59 - 4 * q^61 + 6 * q^67 + 8 * q^71 - 8 * q^73 - 28 * q^77 + 14 * q^79 - 8 * q^85 - 54 * q^89 + 26 * q^91 - 38 * q^95 + 60 * q^97

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