LMFDB - Embedded newform 1512.2.cx.a.17.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1512,2,Mod(17,1512)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1512, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1512.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.cx (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	1512.17
Dual form			1512.2.cx.a.89.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76937 q^{5} +(-1.21939 - 2.34800i) q^{7} +2.41924i q^{11} +(0.0461613 + 0.0266512i) q^{13} +(1.79727 - 3.11297i) q^{17} +(3.96978 - 2.29195i) q^{19} -0.106917i q^{23} +2.66939 q^{25} +(-6.57376 + 3.79536i) q^{29} +(-5.90251 + 3.40781i) q^{31} +(3.37694 + 6.50246i) q^{35} +(2.06198 + 3.57146i) q^{37} +(-0.838974 + 1.45315i) q^{41} +(1.74347 + 3.01978i) q^{43} +(-6.59698 + 11.4263i) q^{47} +(-4.02618 + 5.72625i) q^{49} +(5.27512 + 3.04559i) q^{53} -6.69977i q^{55} +(4.72417 + 8.18250i) q^{59} +(2.29928 + 1.32749i) q^{61} +(-0.127838 - 0.0738070i) q^{65} +(7.09356 + 12.2864i) q^{67} +1.40262i q^{71} +(5.54168 + 3.19949i) q^{73} +(5.68038 - 2.95000i) q^{77} +(-2.11067 + 3.65578i) q^{79} +(-6.86670 - 11.8935i) q^{83} +(-4.97731 + 8.62095i) q^{85} +(-5.71724 - 9.90254i) q^{89} +(0.00628839 - 0.140885i) q^{91} +(-10.9938 + 6.34726i) q^{95} +(14.3549 - 8.28778i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{25} - 18 q^{29} + 18 q^{31} + 6 q^{41} - 6 q^{43} - 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} + 6 q^{79} + 18 q^{89} + 6 q^{91} + 54 q^{95}+O(q^{100}) $ 48 * q + 48 * q^25 - 18 * q^29 + 18 * q^31 + 6 * q^41 - 6 * q^43 - 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 + 6 * q^79 + 18 * q^89 + 6 * q^91 + 54 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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
$5$	−2.76937			−1.23850			−0.619249	−	0.785195i	$-0.712563\pi$
$5$	−2.76937			−1.23850			−0.619249	+	0.785195i	$0.712563\pi$
$6$		0			0
$7$	−1.21939	−	2.34800i	−0.460886	−	0.887459i
$7$	−1.21939	−	2.34800i	−0.460886	−	0.887459i
$8$		0			0
$9$		0			0
$10$		0			0
$11$			2.41924i			0.729429i	0.931119	+	0.364715i	$0.118833\pi$
$11$			2.41924i			0.729429i	−0.931119	+	0.364715i	$0.881167\pi$
$12$		0			0
$13$	0.0461613	+	0.0266512i	0.0128028	+	0.00739172i	0.506388	−	0.862306i	$-0.330980\pi$
$13$	0.0461613	+	0.0266512i	0.0128028	+	0.00739172i	−0.493585	+	0.869698i	$0.664314\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.79727	−	3.11297i	0.435903	−	0.755006i	−0.561466	−	0.827500i	$-0.689762\pi$
$17$	1.79727	−	3.11297i	0.435903	−	0.755006i	0.997369	+	0.0724940i	$0.0230958\pi$
$18$		0			0
$19$	3.96978	−	2.29195i	0.910730	−	0.525810i	0.0300639	−	0.999548i	$-0.490429\pi$
$19$	3.96978	−	2.29195i	0.910730	−	0.525810i	0.880666	+	0.473738i	$0.157096\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	0.106917i		−	0.0222937i	−0.999938	−	0.0111469i	$-0.996452\pi$
$23$		−	0.106917i		−	0.0222937i	0.999938	−	0.0111469i	$-0.00354823\pi$
$24$		0			0
$25$	2.66939			0.533877
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.57376	+	3.79536i	−1.22072	+	0.704781i	−0.965071	−	0.261989i	$-0.915622\pi$
$29$	−6.57376	+	3.79536i	−1.22072	+	0.704781i	−0.255646	+	0.966770i	$0.582288\pi$
$30$		0			0
$31$	−5.90251	+	3.40781i	−1.06012	+	0.612062i	−0.925466	−	0.378831i	$-0.876326\pi$
$31$	−5.90251	+	3.40781i	−1.06012	+	0.612062i	−0.134656	+	0.990892i	$0.542993\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.37694	+	6.50246i	0.570807	+	1.09912i
$36$		0			0
$37$	2.06198	+	3.57146i	0.338988	+	0.587144i	0.984243	−	0.176823i	$-0.0565821\pi$
$37$	2.06198	+	3.57146i	0.338988	+	0.587144i	−0.645255	+	0.763967i	$0.723249\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.838974	+	1.45315i	−0.131026	+	0.226943i	−0.924072	−	0.382218i	$-0.875160\pi$
$41$	−0.838974	+	1.45315i	−0.131026	+	0.226943i	0.793047	+	0.609161i	$0.208494\pi$
$42$		0			0
$43$	1.74347	+	3.01978i	0.265877	+	0.460513i	0.967793	−	0.251747i	$-0.0810051\pi$
$43$	1.74347	+	3.01978i	0.265877	+	0.460513i	−0.701916	+	0.712260i	$0.747672\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.59698	+	11.4263i	−0.962268	+	1.66670i	−0.245484	+	0.969401i	$0.578947\pi$
$47$	−6.59698	+	11.4263i	−0.962268	+	1.66670i	−0.716783	+	0.697296i	$0.754386\pi$
$48$		0			0
$49$	−4.02618	+	5.72625i	−0.575168	+	0.818035i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	5.27512	+	3.04559i	0.724593	+	0.418344i	0.816441	−	0.577429i	$-0.195944\pi$
$53$	5.27512	+	3.04559i	0.724593	+	0.418344i	−0.0918477	+	0.995773i	$0.529277\pi$
$54$		0			0
$55$		−	6.69977i		−	0.903397i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.72417	+	8.18250i	0.615034	+	1.06527i	0.990379	+	0.138385i	$0.0441911\pi$
$59$	4.72417	+	8.18250i	0.615034	+	1.06527i	−0.375344	+	0.926885i	$0.622476\pi$
$60$		0			0
$61$	2.29928	+	1.32749i	0.294392	+	0.169967i	0.639921	−	0.768441i	$-0.278967\pi$
$61$	2.29928	+	1.32749i	0.294392	+	0.169967i	−0.345529	+	0.938408i	$0.612300\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.127838	−	0.0738070i	−0.0158563	−	0.00915464i
$66$		0			0
$67$	7.09356	+	12.2864i	0.866616	+	1.50102i	0.865433	+	0.501024i	$0.167043\pi$
$67$	7.09356	+	12.2864i	0.866616	+	1.50102i	0.00118266	+	0.999999i	$0.499624\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			1.40262i			0.166460i	0.996530	+	0.0832300i	$0.0265236\pi$
$71$			1.40262i			0.166460i	−0.996530	+	0.0832300i	$0.973476\pi$
$72$		0			0
$73$	5.54168	+	3.19949i	0.648605	+	0.374472i	0.787921	−	0.615776i	$-0.211157\pi$
$73$	5.54168	+	3.19949i	0.648605	+	0.374472i	−0.139317	+	0.990248i	$0.544491\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.68038	−	2.95000i	0.647339	−	0.336184i
$78$		0			0
$79$	−2.11067	+	3.65578i	−0.237469	+	0.411308i	−0.959987	−	0.280044i	$-0.909651\pi$
$79$	−2.11067	+	3.65578i	−0.237469	+	0.411308i	0.722519	+	0.691351i	$0.242984\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−6.86670	−	11.8935i	−0.753719	−	1.30548i	−0.946009	−	0.324141i	$-0.894925\pi$
$83$	−6.86670	−	11.8935i	−0.753719	−	1.30548i	0.192290	−	0.981338i	$-0.438409\pi$
$84$		0			0
$85$	−4.97731	+	8.62095i	−0.539865	+	0.935073i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.71724	−	9.90254i	−0.606026	−	1.04967i	−0.991888	−	0.127111i	$-0.959429\pi$
$89$	−5.71724	−	9.90254i	−0.606026	−	1.04967i	0.385863	−	0.922556i	$-0.373904\pi$
$90$		0			0
$91$	0.00628839	−	0.140885i	0.000659203	−	0.0147687i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−10.9938	+	6.34726i	−1.12794	+	0.651215i
$96$		0			0
$97$	14.3549	−	8.28778i	1.45751	−	0.841496i	0.458626	−	0.888630i	$-0.348342\pi$
$97$	14.3549	−	8.28778i	1.45751	−	0.841496i	0.998889	+	0.0471333i	$0.0150086\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	10.5000			1.04479			0.522394	−	0.852704i	$-0.325039\pi$
$101$	10.5000			1.04479			0.522394	+	0.852704i	$0.325039\pi$
$102$		0			0
$103$			15.4270i			1.52007i	0.649884	+	0.760033i	$0.274817\pi$
$103$			15.4270i			1.52007i	−0.649884	+	0.760033i	$0.725183\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.76426	+	5.63740i	−0.943946	+	0.544988i	−0.891195	−	0.453620i	$-0.850132\pi$
$107$	−9.76426	+	5.63740i	−0.943946	+	0.544988i	−0.0527511	+	0.998608i	$0.516799\pi$
$108$		0			0
$109$	−8.06307	+	13.9657i	−0.772302	+	1.33767i	0.163996	+	0.986461i	$0.447562\pi$
$109$	−8.06307	+	13.9657i	−0.772302	+	1.33767i	−0.936298	+	0.351206i	$0.885772\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−11.7542	−	6.78629i	−1.10574	−	0.638400i	−0.168018	−	0.985784i	$-0.553737\pi$
$113$	−11.7542	−	6.78629i	−1.10574	−	0.638400i	−0.937723	+	0.347384i	$0.887070\pi$
$114$		0			0
$115$			0.296092i			0.0276107i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−9.50082	−	0.424069i	−0.870938	−	0.0388743i
$120$		0			0
$121$	5.14726			0.467933
$122$		0			0
$123$		0			0
$124$		0			0
$125$	6.45432			0.577292
$126$		0			0
$127$	−9.23056			−0.819080			−0.409540	−	0.912292i	$-0.634311\pi$
$127$	−9.23056			−0.819080			−0.409540	+	0.912292i	$0.634311\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.18879			0.278606			0.139303	−	0.990250i	$-0.455514\pi$
$131$	3.18879			0.278606			0.139303	+	0.990250i	$0.455514\pi$
$132$		0			0
$133$	−10.2222	−	6.52624i	−0.886378	−	0.565897i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			5.62925i			0.480939i	0.970657	+	0.240470i	$0.0773014\pi$
$137$			5.62925i			0.480939i	−0.970657	+	0.240470i	$0.922699\pi$
$138$		0			0
$139$	−18.6739	−	10.7814i	−1.58390	−	0.914467i	−0.994282	−	0.106786i	$-0.965944\pi$
$139$	−18.6739	−	10.7814i	−1.58390	−	0.914467i	−0.589620	−	0.807680i	$-0.700723\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.0644758	+	0.111675i	−0.00539174	+	0.00933877i
$144$		0			0
$145$	18.2052	−	10.5107i	1.51186	−	0.872870i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	19.1303i		−	1.56722i	−0.621254	−	0.783609i	$-0.713377\pi$
$149$		−	19.1303i		−	1.56722i	0.621254	−	0.783609i	$-0.286623\pi$
$150$		0			0
$151$	−7.88100			−0.641347			−0.320673	−	0.947190i	$-0.603909\pi$
$151$	−7.88100			−0.641347			−0.320673	+	0.947190i	$0.603909\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	16.3462	−	9.43748i	1.31296	−	0.758037i
$156$		0			0
$157$	17.2853	−	9.97966i	1.37952	−	0.796463i	0.387414	−	0.921906i	$-0.373368\pi$
$157$	17.2853	−	9.97966i	1.37952	−	0.796463i	0.992101	+	0.125442i	$0.0400350\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.251041	+	0.130373i	−0.0197848	+	0.0102749i
$162$		0			0
$163$	12.0423	+	20.8578i	0.943223	+	1.63371i	0.759271	+	0.650774i	$0.225556\pi$
$163$	12.0423	+	20.8578i	0.943223	+	1.63371i	0.183951	+	0.982935i	$0.441111\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.793686	+	1.37470i	−0.0614172	+	0.106378i	−0.895099	−	0.445867i	$-0.852895\pi$
$167$	−0.793686	+	1.37470i	−0.0614172	+	0.106378i	0.833682	+	0.552245i	$0.186229\pi$
$168$		0			0
$169$	−6.49858	−	11.2559i	−0.499891	−	0.865836i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.11856	+	3.66945i	−0.161071	+	0.278983i	−0.935253	−	0.353980i	$-0.884828\pi$
$173$	−2.11856	+	3.66945i	−0.161071	+	0.278983i	0.774182	+	0.632963i	$0.218161\pi$
$174$		0			0
$175$	−3.25502	−	6.26771i	−0.246057	−	0.473794i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.38034	+	1.95164i	0.252658	+	0.145872i	0.620981	−	0.783826i	$-0.286734\pi$
$179$	3.38034	+	1.95164i	0.252658	+	0.145872i	−0.368323	+	0.929698i	$0.620068\pi$
$180$		0			0
$181$		−	15.3685i		−	1.14233i	−0.820835	−	0.571166i	$-0.806491\pi$
$181$		−	15.3685i		−	1.14233i	0.820835	−	0.571166i	$-0.193509\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−5.71038	−	9.89067i	−0.419836	−	0.727177i
$186$		0			0
$187$	7.53103	+	4.34804i	0.550723	+	0.317960i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.28415	+	1.31876i	0.165276	+	0.0954219i	0.580356	−	0.814363i	$-0.302913\pi$
$191$	2.28415	+	1.31876i	0.165276	+	0.0954219i	−0.415081	+	0.909785i	$0.636247\pi$
$192$		0			0
$193$	3.72965	+	6.45994i	0.268466	+	0.464997i	0.968466	−	0.249146i	$-0.0801499\pi$
$193$	3.72965	+	6.45994i	0.268466	+	0.464997i	−0.700000	+	0.714143i	$0.746817\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			2.77770i			0.197903i	0.995092	+	0.0989515i	$0.0315489\pi$
$197$			2.77770i			0.197903i	−0.995092	+	0.0989515i	$0.968451\pi$
$198$		0			0
$199$	−3.49892	−	2.02010i	−0.248032	−	0.143201i	0.370831	−	0.928700i	$-0.379073\pi$
$199$	−3.49892	−	2.02010i	−0.248032	−	0.143201i	−0.618863	+	0.785499i	$0.712406\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	16.9275	+	10.8071i	1.18808	+	0.758513i
$204$		0			0
$205$	2.32343	−	4.02429i	0.162275	−	0.281069i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	5.54479	+	9.60386i	0.383541	+	0.664313i
$210$		0			0
$211$	−10.4855	+	18.1614i	−0.721849	+	1.25028i	0.238409	+	0.971165i	$0.423374\pi$
$211$	−10.4855	+	18.1614i	−0.721849	+	1.25028i	−0.960258	+	0.279115i	$0.909959\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.82831	−	8.36289i	−0.329288	−	0.570344i
$216$		0			0
$217$	15.1990	+	9.70361i	1.03178	+	0.658724i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.165929	−	0.0957991i	0.0111616	−	0.00644415i
$222$		0			0
$223$	−8.82344	+	5.09421i	−0.590861	+	0.341134i	−0.765438	−	0.643510i	$-0.777478\pi$
$223$	−8.82344	+	5.09421i	−0.590861	+	0.341134i	0.174577	+	0.984644i	$0.444144\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.0630			0.667906			0.333953	−	0.942590i	$-0.391617\pi$
$227$	10.0630			0.667906			0.333953	+	0.942590i	$0.391617\pi$
$228$		0			0
$229$		−	14.9555i		−	0.988287i	−0.869380	−	0.494144i	$-0.835482\pi$
$229$		−	14.9555i		−	0.988287i	0.869380	−	0.494144i	$-0.164518\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−14.3200	+	8.26764i	−0.938133	+	0.541631i	−0.889374	−	0.457180i	$-0.848860\pi$
$233$	−14.3200	+	8.26764i	−0.938133	+	0.541631i	−0.0487581	+	0.998811i	$0.515526\pi$
$234$		0			0
$235$	18.2694	−	31.6436i	1.19177	−	2.06420i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−9.02155	−	5.20859i	−0.583555	−	0.336916i	0.178990	−	0.983851i	$-0.442717\pi$
$239$	−9.02155	−	5.20859i	−0.583555	−	0.336916i	−0.762545	+	0.646935i	$0.776050\pi$
$240$		0			0
$241$		−	10.3654i		−	0.667693i	−0.942627	−	0.333846i	$-0.891653\pi$
$241$		−	10.3654i		−	0.667693i	0.942627	−	0.333846i	$-0.108347\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	11.1500	−	15.8581i	0.712344	−	1.01314i
$246$		0			0
$247$	0.244334			0.0155466
$248$		0			0
$249$		0			0
$250$		0			0
$251$	13.1006			0.826903			0.413452	−	0.910526i	$-0.364323\pi$
$251$	13.1006			0.826903			0.413452	+	0.910526i	$0.364323\pi$
$252$		0			0
$253$	0.258658			0.0162617
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.886831			−0.0553190			−0.0276595	−	0.999617i	$-0.508805\pi$
$257$	−0.886831			−0.0553190			−0.0276595	+	0.999617i	$0.508805\pi$
$258$		0			0
$259$	5.87141	−	9.19653i	0.364832	−	0.571444i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			7.12492i			0.439342i	0.975574	+	0.219671i	$0.0704983\pi$
$263$			7.12492i			0.439342i	−0.975574	+	0.219671i	$0.929502\pi$
$264$		0			0
$265$	−14.6087	−	8.43436i	−0.897407	−	0.518118i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−15.7987	+	27.3641i	−0.963261	+	1.66842i	−0.249045	+	0.968492i	$0.580117\pi$
$269$	−15.7987	+	27.3641i	−0.963261	+	1.66842i	−0.714216	+	0.699925i	$0.753217\pi$
$270$		0			0
$271$	−15.8215	+	9.13455i	−0.961088	+	0.554884i	−0.896508	−	0.443028i	$-0.853904\pi$
$271$	−15.8215	+	9.13455i	−0.961088	+	0.554884i	−0.0645803	+	0.997913i	$0.520571\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			6.45790i			0.389426i
$276$		0			0
$277$	−30.5690			−1.83671			−0.918357	−	0.395753i	$-0.870484\pi$
$277$	−30.5690			−1.83671			−0.918357	+	0.395753i	$0.870484\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.92237	+	2.26458i	−0.233989	+	0.135094i	−0.612411	−	0.790540i	$-0.709800\pi$
$281$	−3.92237	+	2.26458i	−0.233989	+	0.135094i	0.378422	+	0.925633i	$0.376467\pi$
$282$		0			0
$283$	−8.10730	+	4.68075i	−0.481929	+	0.278242i	−0.721220	−	0.692706i	$-0.756418\pi$
$283$	−8.10730	+	4.68075i	−0.481929	+	0.278242i	0.239291	+	0.970948i	$0.423085\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.43502	+	0.197957i	0.261791	+	0.0116850i
$288$		0			0
$289$	2.03962	+	3.53272i	0.119977	+	0.207807i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8.17267	−	14.1555i	0.477452	−	0.826972i	−0.522214	−	0.852815i	$-0.674894\pi$
$293$	8.17267	−	14.1555i	0.477452	−	0.826972i	0.999666	+	0.0258430i	$0.00822701\pi$
$294$		0			0
$295$	−13.0829	−	22.6603i	−0.761719	−	1.31934i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.00284947	−	0.00493542i	0.000164789	−	0.000285423i
$300$		0			0
$301$	4.96447	−	7.77596i	0.286147	−	0.448199i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.36754	−	3.67630i	−0.364604	−	0.210504i
$306$		0			0
$307$		−	0.985041i		−	0.0562193i	−0.999605	−	0.0281096i	$-0.991051\pi$
$307$		−	0.985041i		−	0.0562193i	0.999605	−	0.0281096i	$-0.00894875\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	13.1302	+	22.7422i	0.744545	+	1.28959i	0.950407	+	0.311008i	$0.100667\pi$
$311$	13.1302	+	22.7422i	0.744545	+	1.28959i	−0.205863	+	0.978581i	$0.566000\pi$
$312$		0			0
$313$	−12.5858	−	7.26643i	−0.711393	−	0.410723i	0.100184	−	0.994969i	$-0.468057\pi$
$313$	−12.5858	−	7.26643i	−0.711393	−	0.410723i	−0.811576	+	0.584246i	$0.801390\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	25.5148	+	14.7310i	1.43306	+	0.827375i	0.997353	−	0.0727147i	$-0.0231663\pi$
$317$	25.5148	+	14.7310i	1.43306	+	0.827375i	0.435704	+	0.900090i	$0.356500\pi$
$318$		0			0
$319$	−9.18191	−	15.9035i	−0.514088	−	0.890427i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	16.4771i		−	0.916808i
$324$		0			0
$325$	0.123222	+	0.0711425i	0.00683515	+	0.00394627i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	34.8732	+	1.55656i	1.92262	+	0.0858162i
$330$		0			0
$331$	2.91015	−	5.04053i	0.159956	−	0.277052i	−0.774896	−	0.632088i	$-0.782198\pi$
$331$	2.91015	−	5.04053i	0.159956	−	0.277052i	0.934853	+	0.355036i	$0.115531\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−19.6447	−	34.0255i	−1.07330	−	1.85901i
$336$		0			0
$337$	−11.4909	+	19.9028i	−0.625950	+	1.08418i	0.362407	+	0.932020i	$0.381955\pi$
$337$	−11.4909	+	19.9028i	−0.625950	+	1.08418i	−0.988356	+	0.152157i	$0.951378\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−8.24433	−	14.2796i	−0.446456	−	0.773284i
$342$		0			0
$343$	18.3547	+	2.47092i	0.991060	+	0.133417i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.9435	+	7.47293i	−0.694843	+	0.401168i	−0.805424	−	0.592699i	$-0.798062\pi$
$347$	−12.9435	+	7.47293i	−0.694843	+	0.401168i	0.110581	+	0.993867i	$0.464729\pi$
$348$		0			0
$349$	−0.768588	+	0.443744i	−0.0411416	+	0.0237531i	−0.520430	−	0.853905i	$-0.674228\pi$
$349$	−0.768588	+	0.443744i	−0.0411416	+	0.0237531i	0.479288	+	0.877658i	$0.340895\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.04996			−0.268782			−0.134391	−	0.990928i	$-0.542908\pi$
$353$	−5.04996			−0.268782			−0.134391	+	0.990928i	$0.542908\pi$
$354$		0			0
$355$		−	3.88436i		−	0.206160i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	30.2467	−	17.4629i	1.59636	−	0.921659i	0.604179	−	0.796848i	$-0.293501\pi$
$359$	30.2467	−	17.4629i	1.59636	−	0.921659i	0.992181	−	0.124810i	$-0.0398322\pi$
$360$		0			0
$361$	1.00610	−	1.74261i	0.0529524	−	0.0917163i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−15.3469	−	8.86056i	−0.803296	−	0.463783i
$366$		0			0
$367$		−	23.0893i		−	1.20525i	−0.798025	−	0.602625i	$-0.794122\pi$
$367$		−	23.0893i		−	1.20525i	0.798025	−	0.602625i	$-0.205878\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.718611	−	16.0997i	0.0373084	−	0.835856i
$372$		0			0
$373$	1.79851			0.0931235			0.0465617	−	0.998915i	$-0.485174\pi$
$373$	1.79851			0.0931235			0.0465617	+	0.998915i	$0.485174\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.404605			−0.0208382
$378$		0			0
$379$	−3.34605			−0.171875			−0.0859375	−	0.996301i	$-0.527389\pi$
$379$	−3.34605			−0.171875			−0.0859375	+	0.996301i	$0.527389\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.97833			−0.101088			−0.0505439	−	0.998722i	$-0.516095\pi$
$383$	−1.97833			−0.101088			−0.0505439	+	0.998722i	$0.516095\pi$
$384$		0			0
$385$	−15.7310	+	8.16963i	−0.801728	+	0.416363i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	34.9095i		−	1.76998i	−0.465609	−	0.884990i	$-0.654165\pi$
$389$		−	34.9095i		−	1.76998i	0.465609	−	0.884990i	$-0.345835\pi$
$390$		0			0
$391$	−0.332829	−	0.192159i	−0.0168319	−	0.00971789i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	5.84521	−	10.1242i	0.294104	−	0.509404i
$396$		0			0
$397$	2.73751	−	1.58050i	0.137392	−	0.0793231i	−0.429729	−	0.902958i	$-0.641391\pi$
$397$	2.73751	−	1.58050i	0.137392	−	0.0793231i	0.567120	+	0.823635i	$0.308057\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			33.0291i			1.64940i	0.565573	+	0.824698i	$0.308655\pi$
$401$			33.0291i			1.64940i	−0.565573	+	0.824698i	$0.691345\pi$
$402$		0			0
$403$	−0.363290			−0.0180968
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−8.64023	+	4.98844i	−0.428280	+	0.247268i
$408$		0			0
$409$	0.933684	−	0.539063i	0.0461677	−	0.0266549i	−0.476739	−	0.879045i	$-0.658181\pi$
$409$	0.933684	−	0.539063i	0.0461677	−	0.0266549i	0.522906	+	0.852390i	$0.324848\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	13.4519	−	21.0700i	0.661923	−	1.03679i
$414$		0			0
$415$	19.0164	+	32.9374i	0.933479	+	1.61683i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	13.2799	−	23.0015i	0.648768	−	1.12370i	−0.334650	−	0.942343i	$-0.608618\pi$
$419$	13.2799	−	23.0015i	0.648768	−	1.12370i	0.983418	−	0.181356i	$-0.0580486\pi$
$420$		0			0
$421$	3.32791	+	5.76411i	0.162192	+	0.280925i	0.935655	−	0.352917i	$-0.114810\pi$
$421$	3.32791	+	5.76411i	0.162192	+	0.280925i	−0.773462	+	0.633842i	$0.781477\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	4.79762	−	8.30972i	0.232719	−	0.403081i
$426$		0			0
$427$	0.313223	−	7.01742i	0.0151579	−	0.339597i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−13.2930	−	7.67471i	−0.640300	−	0.369678i	0.144430	−	0.989515i	$-0.453865\pi$
$431$	−13.2930	−	7.67471i	−0.640300	−	0.369678i	−0.784730	+	0.619837i	$0.787199\pi$
$432$		0			0
$433$			15.9407i			0.766060i	0.923736	+	0.383030i	$0.125119\pi$
$433$			15.9407i			0.766060i	−0.923736	+	0.383030i	$0.874881\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.245049	−	0.424436i	−0.0117223	−	0.0203036i
$438$		0			0
$439$	−17.8768	−	10.3212i	−0.853214	−	0.492603i	0.00852006	−	0.999964i	$-0.497288\pi$
$439$	−17.8768	−	10.3212i	−0.853214	−	0.492603i	−0.861734	+	0.507360i	$0.830621\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.25880	−	0.726768i	−0.0598073	−	0.0345298i	0.469798	−	0.882774i	$-0.344327\pi$
$443$	−1.25880	−	0.726768i	−0.0598073	−	0.0345298i	−0.529605	+	0.848244i	$0.677660\pi$
$444$		0			0
$445$	15.8331	+	27.4238i	0.750562	+	1.30001i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	9.09933i		−	0.429424i	−0.976677	−	0.214712i	$-0.931119\pi$
$449$		−	9.09933i		−	0.429424i	0.976677	−	0.214712i	$-0.0688813\pi$
$450$		0			0
$451$	−3.51551	−	2.02968i	−0.165539	−	0.0955740i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.0174149	+	0.390162i	−0.000816421	+	0.0182911i
$456$		0			0
$457$	7.23209	−	12.5264i	0.338303	−	0.585958i	−0.645811	−	0.763498i	$-0.723480\pi$
$457$	7.23209	−	12.5264i	0.338303	−	0.585958i	0.984114	+	0.177540i	$0.0568138\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	13.2769	+	22.9963i	0.618369	+	1.07105i	0.989783	+	0.142579i	$0.0455395\pi$
$461$	13.2769	+	22.9963i	0.618369	+	1.07105i	−0.371415	+	0.928467i	$0.621127\pi$
$462$		0			0
$463$	15.4968	−	26.8412i	0.720196	−	1.24742i	−0.240725	−	0.970593i	$-0.577385\pi$
$463$	15.4968	−	26.8412i	0.720196	−	1.24742i	0.960921	−	0.276823i	$-0.0892816\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.1348	+	17.5541i	0.468985	+	0.812306i	0.999371	−	0.0354503i	$-0.0112865\pi$
$467$	10.1348	+	17.5541i	0.468985	+	0.812306i	−0.530387	+	0.847756i	$0.677953\pi$
$468$		0			0
$469$	20.1986	−	31.6376i	0.932686	−	1.46089i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−7.30559	+	4.21789i	−0.335911	+	0.193939i
$474$		0			0
$475$	10.5969	−	6.11811i	0.486218	−	0.280718i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−16.0258			−0.732236			−0.366118	−	0.930568i	$-0.619313\pi$
$479$	−16.0258			−0.732236			−0.366118	+	0.930568i	$0.619313\pi$
$480$		0			0
$481$			0.219817i			0.0100228i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−39.7538	+	22.9519i	−1.80513	+	1.04219i
$486$		0			0
$487$	8.54048	−	14.7925i	0.387006	−	0.670314i	−0.605039	−	0.796196i	$-0.706843\pi$
$487$	8.54048	−	14.7925i	0.387006	−	0.670314i	0.992045	+	0.125881i	$0.0401759\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−12.9745	−	7.49082i	−0.585530	−	0.338056i	0.177798	−	0.984067i	$-0.443103\pi$
$491$	−12.9745	−	7.49082i	−0.585530	−	0.338056i	−0.763328	+	0.646011i	$0.776436\pi$
$492$		0			0
$493$			27.2852i			1.22886i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.29334	−	1.71034i	0.147726	−	0.0767191i
$498$		0			0
$499$	25.3276			1.13382			0.566910	−	0.823780i	$-0.308139\pi$
$499$	25.3276			1.13382			0.566910	+	0.823780i	$0.308139\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	9.95401			0.443827			0.221914	−	0.975066i	$-0.428770\pi$
$503$	9.95401			0.443827			0.221914	+	0.975066i	$0.428770\pi$
$504$		0			0
$505$	−29.0783			−1.29397
$506$		0			0
$507$		0			0
$508$		0			0
$509$	11.6595			0.516800			0.258400	−	0.966038i	$-0.416805\pi$
$509$	11.6595			0.516800			0.258400	+	0.966038i	$0.416805\pi$
$510$		0			0
$511$	0.754924	−	16.9133i	0.0333959	−	0.748199i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	42.7230i		−	1.88260i
$516$		0			0
$517$	−27.6430	−	15.9597i	−1.21574	−	0.701906i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	8.59307	−	14.8836i	0.376469	−	0.652064i	−0.614077	−	0.789246i	$-0.710471\pi$
$521$	8.59307	−	14.8836i	0.376469	−	0.652064i	0.990546	+	0.137183i	$0.0438048\pi$
$522$		0			0
$523$	−38.1175	+	22.0071i	−1.66676	+	0.962305i	−0.697394	+	0.716688i	$0.745657\pi$
$523$	−38.1175	+	22.0071i	−1.66676	+	0.962305i	−0.969367	+	0.245616i	$0.921010\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			24.4991i			1.06720i
$528$		0			0
$529$	22.9886			0.999503
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.0774562	+	0.0447194i	−0.00335500	+	0.00193701i
$534$		0			0
$535$	27.0408	−	15.6120i	1.16908	−	0.674966i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−13.8532	−	9.74030i	−0.596699	−	0.419544i
$540$		0			0
$541$	−5.06580	−	8.77423i	−0.217796	−	0.377234i	0.736338	−	0.676614i	$-0.236553\pi$
$541$	−5.06580	−	8.77423i	−0.217796	−	0.377234i	−0.954134	+	0.299380i	$0.903220\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	22.3296	−	38.6760i	0.956495	−	1.65670i
$546$		0			0
$547$	17.0000	+	29.4449i	0.726869	+	1.25897i	0.958200	+	0.286099i	$0.0923585\pi$
$547$	17.0000	+	29.4449i	0.726869	+	1.25897i	−0.231331	+	0.972875i	$0.574308\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−17.3976	+	30.1335i	−0.741162	+	1.28373i
$552$		0			0
$553$	11.1575	+	0.498014i	0.474465	+	0.0211777i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.88366	−	1.08753i	−0.0798133	−	0.0460802i	0.459562	−	0.888146i	$-0.348006\pi$
$557$	−1.88366	−	1.08753i	−0.0798133	−	0.0460802i	−0.539376	+	0.842065i	$0.681340\pi$
$558$		0			0
$559$			0.185863i			0.00786116i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.24777	+	3.89326i	0.0947324	+	0.164081i	0.909497	−	0.415711i	$-0.136467\pi$
$563$	2.24777	+	3.89326i	0.0947324	+	0.164081i	−0.814765	+	0.579792i	$0.803134\pi$
$564$		0			0
$565$	32.5517	+	18.7937i	1.36946	+	0.790657i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.30272	−	3.06153i	−0.222302	−	0.128346i	0.384714	−	0.923036i	$-0.374300\pi$
$569$	−5.30272	−	3.06153i	−0.222302	−	0.128346i	−0.607016	+	0.794690i	$0.707633\pi$
$570$		0			0
$571$	16.1829	+	28.0296i	0.677233	+	1.17300i	0.975811	+	0.218616i	$0.0701543\pi$
$571$	16.1829	+	28.0296i	0.677233	+	1.17300i	−0.298578	+	0.954385i	$0.596512\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	0.285403i		−	0.0119021i
$576$		0			0
$577$	−34.2034	−	19.7473i	−1.42390	−	0.822092i	−0.427274	−	0.904122i	$-0.640526\pi$
$577$	−34.2034	−	19.7473i	−1.42390	−	0.822092i	−0.996630	+	0.0820304i	$0.973860\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−19.5527	+	30.6258i	−0.811181	+	1.27057i
$582$		0			0
$583$	−7.36803	+	12.7618i	−0.305152	+	0.528540i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.129711	−	0.224667i	−0.00535376	−	0.00927298i	0.863336	−	0.504629i	$-0.168371\pi$
$587$	−0.129711	−	0.224667i	−0.00535376	−	0.00927298i	−0.868690	+	0.495356i	$0.835037\pi$
$588$		0			0
$589$	−15.6211	+	27.0565i	−0.643656	+	1.11485i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.13549	−	5.43083i	−0.128759	−	0.223017i	0.794437	−	0.607347i	$-0.207766\pi$
$593$	−3.13549	−	5.43083i	−0.128759	−	0.223017i	−0.923196	+	0.384329i	$0.874433\pi$
$594$		0			0
$595$	26.3112	+	1.17440i	1.07866	+	0.0481458i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−5.52001	+	3.18698i	−0.225542	+	0.130217i	−0.608514	−	0.793543i	$-0.708234\pi$
$599$	−5.52001	+	3.18698i	−0.225542	+	0.130217i	0.382972	+	0.923760i	$0.374901\pi$
$600$		0			0
$601$	−15.0862	+	8.71001i	−0.615378	+	0.355289i	−0.775067	−	0.631879i	$-0.782284\pi$
$601$	−15.0862	+	8.71001i	−0.615378	+	0.355289i	0.159689	+	0.987167i	$0.448951\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−14.2546			−0.579534
$606$		0			0
$607$		−	1.80344i		−	0.0731996i	−0.999330	−	0.0365998i	$-0.988347\pi$
$607$		−	1.80344i		−	0.0731996i	0.999330	−	0.0365998i	$-0.0116527\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.609050	+	0.351635i	−0.0246395	+	0.0142256i
$612$		0			0
$613$	−17.6290	+	30.5343i	−0.712028	+	1.23327i	0.252066	+	0.967710i	$0.418890\pi$
$613$	−17.6290	+	30.5343i	−0.712028	+	1.23327i	−0.964095	+	0.265559i	$0.914443\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.73458	+	4.46556i	0.311383	+	0.179777i	0.647545	−	0.762027i	$-0.275796\pi$
$617$	7.73458	+	4.46556i	0.311383	+	0.179777i	−0.336162	+	0.941804i	$0.609129\pi$
$618$		0			0
$619$			38.5146i			1.54803i	0.633166	+	0.774016i	$0.281755\pi$
$619$			38.5146i			1.54803i	−0.633166	+	0.774016i	$0.718245\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−16.2796	+	25.4991i	−0.652228	+	1.02160i
$624$		0			0
$625$	−31.2213			−1.24885
$626$		0			0
$627$		0			0
$628$		0			0
$629$	14.8238			0.591063
$630$		0			0
$631$	−24.5826			−0.978616			−0.489308	−	0.872111i	$-0.662751\pi$
$631$	−24.5826			−0.978616			−0.489308	+	0.872111i	$0.662751\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	25.5628			1.01443
$636$		0			0
$637$	−0.338465	+	0.157028i	−0.0134105	+	0.00622169i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			33.6752i			1.33009i	0.746804	+	0.665044i	$0.231587\pi$
$641$			33.6752i			1.33009i	−0.746804	+	0.665044i	$0.768413\pi$
$642$		0			0
$643$	2.02496	+	1.16911i	0.0798567	+	0.0461053i	0.539397	−	0.842052i	$-0.318652\pi$
$643$	2.02496	+	1.16911i	0.0798567	+	0.0461053i	−0.459540	+	0.888157i	$0.651986\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.89769	+	3.28689i	−0.0746059	+	0.129221i	−0.900915	−	0.433996i	$-0.857103\pi$
$647$	−1.89769	+	3.28689i	−0.0746059	+	0.129221i	0.826309	+	0.563217i	$0.190437\pi$
$648$		0			0
$649$	−19.7955	+	11.4289i	−0.777040	+	0.448624i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	11.7151i		−	0.458447i	−0.973374	−	0.229224i	$-0.926381\pi$
$653$		−	11.7151i		−	0.458447i	0.973374	−	0.229224i	$-0.0736187\pi$
$654$		0			0
$655$	−8.83094			−0.345053
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−22.4962	+	12.9882i	−0.876329	+	0.505949i	−0.869446	−	0.494028i	$-0.835524\pi$
$659$	−22.4962	+	12.9882i	−0.876329	+	0.505949i	−0.00688257	+	0.999976i	$0.502191\pi$
$660$		0			0
$661$	5.94177	−	3.43048i	0.231108	−	0.133430i	−0.379975	−	0.924997i	$-0.624067\pi$
$661$	5.94177	−	3.43048i	0.231108	−	0.133430i	0.611083	+	0.791566i	$0.290734\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	28.3090	+	18.0736i	1.09778	+	0.700862i
$666$		0			0
$667$	0.405789	+	0.702846i	0.0157122	+	0.0272143i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.21152	+	5.56251i	−0.123979	+	0.214738i
$672$		0			0
$673$	−0.652179	−	1.12961i	−0.0251397	−	0.0435432i	0.853182	−	0.521614i	$-0.174670\pi$
$673$	−0.652179	−	1.12961i	−0.0251397	−	0.0435432i	−0.878322	+	0.478070i	$0.841336\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.61516	−	11.4578i	0.254241	−	0.440359i	−0.710448	−	0.703750i	$-0.751508\pi$
$677$	6.61516	−	11.4578i	0.254241	−	0.440359i	0.964689	+	0.263391i	$0.0848409\pi$
$678$		0			0
$679$	−36.9638	−	23.5991i	−1.41854	−	0.905651i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.49949	+	0.865733i	0.0573765	+	0.0331264i	0.528414	−	0.848987i	$-0.322787\pi$
$683$	1.49949	+	0.865733i	0.0573765	+	0.0331264i	−0.471037	+	0.882113i	$0.656120\pi$
$684$		0			0
$685$		−	15.5894i		−	0.595642i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.162338	+	0.281177i	0.00618457	+	0.0107120i
$690$		0			0
$691$	−7.27541	−	4.20046i	−0.276770	−	0.159793i	0.355190	−	0.934794i	$-0.384416\pi$
$691$	−7.27541	−	4.20046i	−0.276770	−	0.159793i	−0.631960	+	0.775001i	$0.717749\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	51.7150	+	29.8576i	1.96166	+	1.13256i
$696$		0			0
$697$	3.01573	+	5.22340i	0.114229	+	0.197850i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			21.3493i			0.806353i	0.915122	+	0.403176i	$0.132094\pi$
$701$			21.3493i			0.806353i	−0.915122	+	0.403176i	$0.867906\pi$
$702$		0			0
$703$	16.3712	+	9.45193i	0.617452	+	0.356486i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−12.8036	−	24.6539i	−0.481528	−	0.927207i
$708$		0			0
$709$	9.63087	−	16.6812i	0.361695	−	0.626474i	−0.626545	−	0.779385i	$-0.715532\pi$
$709$	9.63087	−	16.6812i	0.361695	−	0.626474i	0.988240	+	0.152911i	$0.0488648\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.364353	+	0.631078i	0.0136451	+	0.0236341i
$714$		0			0
$715$	0.178557	−	0.309270i	0.00667766	−	0.0115660i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	5.39920	+	9.35168i	0.201356	+	0.348759i	0.948966	−	0.315380i	$-0.102132\pi$
$719$	5.39920	+	9.35168i	0.201356	+	0.348759i	−0.747610	+	0.664138i	$0.768799\pi$
$720$		0			0
$721$	36.2225	−	18.8115i	1.34900	−	0.700577i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−17.5479	+	10.1313i	−0.651713	+	0.376267i
$726$		0			0
$727$	25.9316	−	14.9716i	0.961751	−	0.555267i	0.0650393	−	0.997883i	$-0.479283\pi$
$727$	25.9316	−	14.9716i	0.961751	−	0.555267i	0.896711	+	0.442616i	$0.145949\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	12.5340			0.463586
$732$		0			0
$733$			16.0355i			0.592286i	0.955144	+	0.296143i	$0.0957004\pi$
$733$			16.0355i			0.592286i	−0.955144	+	0.296143i	$0.904300\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−29.7238	+	17.1610i	−1.09489	+	0.632135i
$738$		0			0
$739$	11.5186	−	19.9508i	0.423719	−	0.733903i	−0.572581	−	0.819848i	$-0.694058\pi$
$739$	11.5186	−	19.9508i	0.423719	−	0.733903i	0.996300	+	0.0859453i	$0.0273910\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−37.2352	−	21.4978i	−1.36603	−	0.788676i	−0.375609	−	0.926778i	$-0.622567\pi$
$743$	−37.2352	−	21.4978i	−1.36603	−	0.788676i	−0.990418	+	0.138102i	$0.955900\pi$
$744$		0			0
$745$			52.9789i			1.94100i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	25.1430	+	16.0523i	0.918706	+	0.586537i
$750$		0			0
$751$	35.3800			1.29104			0.645518	−	0.763745i	$-0.276642\pi$
$751$	35.3800			1.29104			0.645518	+	0.763745i	$0.276642\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	21.8254			0.794307
$756$		0			0
$757$	−24.6138			−0.894604			−0.447302	−	0.894383i	$-0.647615\pi$
$757$	−24.6138			−0.894604			−0.447302	+	0.894383i	$0.647615\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−13.7853			−0.499716			−0.249858	−	0.968283i	$-0.580384\pi$
$761$	−13.7853			−0.499716			−0.249858	+	0.968283i	$0.580384\pi$
$762$		0			0
$763$	42.6233	+	1.90249i	1.54307	+	0.0688748i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			0.503620i			0.0181847i
$768$		0			0
$769$	−20.0352	−	11.5673i	−0.722486	−	0.417128i	0.0931808	−	0.995649i	$-0.470297\pi$
$769$	−20.0352	−	11.5673i	−0.722486	−	0.417128i	−0.815667	+	0.578522i	$0.803630\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−26.5072	+	45.9118i	−0.953398	+	1.65133i	−0.215405	+	0.976525i	$0.569107\pi$
$773$	−26.5072	+	45.9118i	−0.953398	+	1.65133i	−0.737993	+	0.674808i	$0.764226\pi$
$774$		0			0
$775$	−15.7561	+	9.09678i	−0.565975	+	0.326766i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			7.69155i			0.275578i
$780$		0			0
$781$	−3.39327			−0.121421
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−47.8693	+	27.6373i	−1.70853	+	0.986418i
$786$		0			0
$787$	5.16436	−	2.98164i	0.184089	−	0.106284i	−0.405123	−	0.914262i	$-0.632771\pi$
$787$	5.16436	−	2.98164i	0.184089	−	0.106284i	0.589213	+	0.807978i	$0.299438\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.60123	+	35.8739i	−0.0569333	+	1.27553i
$792$		0			0
$793$	0.0707584	+	0.122557i	0.00251271	+	0.00435213i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−5.28758	+	9.15836i	−0.187296	+	0.324406i	−0.944348	−	0.328949i	$-0.893306\pi$
$797$	−5.28758	+	9.15836i	−0.187296	+	0.324406i	0.757052	+	0.653355i	$0.226639\pi$
$798$		0			0
$799$	23.7131	+	41.0724i	0.838910	+	1.45304i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−7.74035	+	13.4067i	−0.273151	+	0.473111i
$804$		0			0
$805$	0.695223	−	0.361052i	0.0245034	−	0.0127254i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	32.1452	+	18.5591i	1.13017	+	0.652501i	0.943977	−	0.330012i	$-0.107053\pi$
$809$	32.1452	+	18.5591i	1.13017	+	0.652501i	0.186189	+	0.982514i	$0.440386\pi$
$810$		0			0
$811$		−	7.02945i		−	0.246837i	−0.992355	−	0.123419i	$-0.960614\pi$
$811$		−	7.02945i		−	0.246837i	0.992355	−	0.123419i	$-0.0393858\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−33.3494	−	57.7629i	−1.16818	−	2.02335i
$816$		0			0
$817$	13.8424	+	7.99192i	0.484284	+	0.279602i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−18.5657	−	10.7189i	−0.647947	−	0.374092i	0.139722	−	0.990191i	$-0.455379\pi$
$821$	−18.5657	−	10.7189i	−0.647947	−	0.374092i	−0.787669	+	0.616099i	$0.788712\pi$
$822$		0			0
$823$	9.72455	+	16.8434i	0.338977	+	0.587125i	0.984240	−	0.176835i	$-0.0565859\pi$
$823$	9.72455	+	16.8434i	0.338977	+	0.587125i	−0.645264	+	0.763960i	$0.723253\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	16.3789i		−	0.569549i	−0.958595	−	0.284774i	$-0.908081\pi$
$827$		−	16.3789i		−	0.569549i	0.958595	−	0.284774i	$-0.0919187\pi$
$828$		0			0
$829$	−13.5517	−	7.82408i	−0.470670	−	0.271741i	0.245850	−	0.969308i	$-0.420933\pi$
$829$	−13.5517	−	7.82408i	−0.470670	−	0.271741i	−0.716520	+	0.697566i	$0.754266\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	10.5895	+	22.8250i	0.366904	+	0.790839i
$834$		0			0
$835$	2.19801	−	3.80706i	0.0760651	−	0.131749i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.260756	−	0.451642i	−0.00900229	−	0.0155924i	0.861489	−	0.507776i	$-0.169532\pi$
$839$	−0.260756	−	0.451642i	−0.00900229	−	0.0155924i	−0.870491	+	0.492184i	$0.836199\pi$
$840$		0			0
$841$	14.3096	−	24.7849i	0.493433	−	0.854652i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	17.9969	+	31.1716i	0.619114	+	1.07234i
$846$		0			0
$847$	−6.27652	−	12.0858i	−0.215664	−	0.415271i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.381849	−	0.220461i	0.0130896	−	0.00755730i
$852$		0			0
$853$	15.3460	−	8.85999i	0.525436	−	0.303360i	−0.213720	−	0.976895i	$-0.568558\pi$
$853$	15.3460	−	8.85999i	0.525436	−	0.303360i	0.739156	+	0.673535i	$0.235225\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	2.82727			0.0965777			0.0482888	−	0.998833i	$-0.484623\pi$
$857$	2.82727			0.0965777			0.0482888	+	0.998833i	$0.484623\pi$
$858$		0			0
$859$		−	9.21152i		−	0.314293i	−0.987575	−	0.157147i	$-0.949770\pi$
$859$		−	9.21152i		−	0.314293i	0.987575	−	0.157147i	$-0.0502295\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	15.7016	−	9.06534i	0.534490	−	0.308588i	−0.208353	−	0.978054i	$-0.566810\pi$
$863$	15.7016	−	9.06534i	0.534490	−	0.308588i	0.742843	+	0.669466i	$0.233477\pi$
$864$		0			0
$865$	5.86705	−	10.1620i	0.199486	−	0.345520i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−8.84423	−	5.10622i	−0.300020	−	0.173217i
$870$		0			0
$871$			0.756208i			0.0256231i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−7.87033	−	15.1547i	−0.266066	−	0.512323i
$876$		0			0
$877$	14.2086			0.479792			0.239896	−	0.970799i	$-0.422887\pi$
$877$	14.2086			0.479792			0.239896	+	0.970799i	$0.422887\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−46.0649			−1.55197			−0.775984	−	0.630753i	$-0.782746\pi$
$881$	−46.0649			−1.55197			−0.775984	+	0.630753i	$0.782746\pi$
$882$		0			0
$883$	8.16154			0.274658			0.137329	−	0.990526i	$-0.456148\pi$
$883$	8.16154			0.274658			0.137329	+	0.990526i	$0.456148\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−27.1287			−0.910893			−0.455446	−	0.890263i	$-0.650520\pi$
$887$	−27.1287			−0.910893			−0.455446	+	0.890263i	$0.650520\pi$
$888$		0			0
$889$	11.2557	+	21.6733i	0.377503	+	0.726900i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			60.4798i			2.02388i
$894$		0			0
$895$	−9.36139	−	5.40480i	−0.312917	−	0.180662i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	25.8678	−	44.8043i	0.862739	−	1.49431i
$900$		0			0
$901$	18.9617	−	10.9475i	0.631704	−	0.364715i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			42.5610i			1.41478i
$906$		0			0
$907$	−25.5851			−0.849541			−0.424770	−	0.905301i	$-0.639645\pi$
$907$	−25.5851			−0.849541			−0.424770	+	0.905301i	$0.639645\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−4.57426	+	2.64095i	−0.151552	+	0.0874986i	−0.573858	−	0.818955i	$-0.694554\pi$
$911$	−4.57426	+	2.64095i	−0.151552	+	0.0874986i	0.422306	+	0.906453i	$0.361221\pi$
$912$		0			0
$913$	28.7732	−	16.6122i	0.952255	−	0.549785i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−3.88838	−	7.48728i	−0.128406	−	0.247252i
$918$		0			0
$919$	−27.7214	−	48.0149i	−0.914445	−	1.58387i	−0.807712	−	0.589578i	$-0.799294\pi$
$919$	−27.7214	−	48.0149i	−0.914445	−	1.58387i	−0.106733	−	0.994288i	$-0.534039\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.0373815	+	0.0647466i	−0.00123043	+	0.00213116i
$924$		0			0
$925$	5.50423	+	9.53360i	0.180978	+	0.313463i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	17.6004	−	30.4849i	0.577452	−	1.00018i	−0.418319	−	0.908300i	$-0.637380\pi$
$929$	17.6004	−	30.4849i	0.577452	−	1.00018i	0.995770	−	0.0918756i	$-0.0292862\pi$
$930$		0			0
$931$	−2.85874	+	31.9597i	−0.0936914	+	1.04744i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−20.8562	−	12.0413i	−0.682070	−	0.393793i
$936$		0			0
$937$			47.6315i			1.55605i	0.628231	+	0.778027i	$0.283779\pi$
$937$			47.6315i			1.55605i	−0.628231	+	0.778027i	$0.716221\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−10.3802	−	17.9790i	−0.338384	−	0.586098i	0.645745	−	0.763553i	$-0.276547\pi$
$941$	−10.3802	−	17.9790i	−0.338384	−	0.586098i	−0.984129	+	0.177455i	$0.943213\pi$
$942$		0			0
$943$	0.155366	+	0.0897005i	0.00505941	+	0.00292105i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.50667	+	3.75663i	0.211438	+	0.122074i	0.601980	−	0.798511i	$-0.294379\pi$
$947$	6.50667	+	3.75663i	0.211438	+	0.122074i	−0.390541	+	0.920585i	$0.627712\pi$
$948$		0			0
$949$	0.170541	+	0.295385i	0.00553599	+	0.00958861i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	53.6047i		−	1.73643i	−0.496192	−	0.868213i	$-0.665269\pi$
$953$		−	53.6047i		−	1.73643i	0.496192	−	0.868213i	$-0.334731\pi$
$954$		0			0
$955$	−6.32566	−	3.65212i	−0.204694	−	0.118180i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	13.2175	−	6.86425i	0.426814	−	0.221658i
$960$		0			0
$961$	7.72640	−	13.3825i	0.249239	−	0.431694i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−10.3288	−	17.8899i	−0.332495	−	0.575898i
$966$		0			0
$967$	−5.72860	+	9.92223i	−0.184220	+	0.319078i	−0.943313	−	0.331904i	$-0.892309\pi$
$967$	−5.72860	+	9.92223i	−0.184220	+	0.319078i	0.759094	+	0.650981i	$0.225642\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	4.02601	+	6.97326i	0.129201	+	0.223782i	0.923367	−	0.383918i	$-0.125425\pi$
$971$	4.02601	+	6.97326i	0.129201	+	0.223782i	−0.794166	+	0.607700i	$0.792092\pi$
$972$		0			0
$973$	−2.54388	+	56.9931i	−0.0815532	+	1.82711i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	41.4615	−	23.9378i	1.32647	−	0.765838i	0.341718	−	0.939802i	$-0.388991\pi$
$977$	41.4615	−	23.9378i	1.32647	−	0.765838i	0.984752	+	0.173965i	$0.0556578\pi$
$978$		0			0
$979$	23.9567	−	13.8314i	0.765658	−	0.442053i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−2.36180			−0.0753297			−0.0376648	−	0.999290i	$-0.511992\pi$
$983$	−2.36180			−0.0753297			−0.0376648	+	0.999290i	$0.511992\pi$
$984$		0			0
$985$		−	7.69247i		−	0.245102i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.322866	−	0.186407i	0.0102665	−	0.00592739i
$990$		0			0
$991$	−11.8241	+	20.4800i	−0.375606	+	0.650568i	−0.990417	−	0.138106i	$-0.955899\pi$
$991$	−11.8241	+	20.4800i	−0.375606	+	0.650568i	0.614812	+	0.788674i	$0.289232\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	9.68979	+	5.59440i	0.307187	+	0.177355i
$996$		0			0
$997$			42.4290i			1.34374i	0.740670	+	0.671869i	$0.234508\pi$
$997$			42.4290i			1.34374i	−0.740670	+	0.671869i	$0.765492\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.cx.a.17.4		48
3.2	odd	2		504.2.cx.a.185.14	yes	48
4.3	odd	2		3024.2.df.e.17.4		48
7.5	odd	6		1512.2.bs.a.1097.4		48
9.2	odd	6		1512.2.bs.a.521.4		48
9.7	even	3		504.2.bs.a.353.6	yes	48
12.11	even	2		1008.2.df.e.689.11		48
21.5	even	6		504.2.bs.a.257.6	✓	48
28.19	even	6		3024.2.ca.e.2609.4		48
36.7	odd	6		1008.2.ca.e.353.19		48
36.11	even	6		3024.2.ca.e.2033.4		48
63.47	even	6	inner	1512.2.cx.a.89.4		48
63.61	odd	6		504.2.cx.a.425.14	yes	48
84.47	odd	6		1008.2.ca.e.257.19		48
252.47	odd	6		3024.2.df.e.1601.4		48
252.187	even	6		1008.2.df.e.929.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.6	✓	48	21.5	even	6
504.2.bs.a.353.6	yes	48	9.7	even	3
504.2.cx.a.185.14	yes	48	3.2	odd	2
504.2.cx.a.425.14	yes	48	63.61	odd	6
1008.2.ca.e.257.19		48	84.47	odd	6
1008.2.ca.e.353.19		48	36.7	odd	6
1008.2.df.e.689.11		48	12.11	even	2
1008.2.df.e.929.11		48	252.187	even	6
1512.2.bs.a.521.4		48	9.2	odd	6
1512.2.bs.a.1097.4		48	7.5	odd	6
1512.2.cx.a.17.4		48	1.1	even	1	trivial
1512.2.cx.a.89.4		48	63.47	even	6	inner
3024.2.ca.e.2033.4		48	36.11	even	6
3024.2.ca.e.2609.4		48	28.19	even	6
3024.2.df.e.17.4		48	4.3	odd	2
3024.2.df.e.1601.4		48	252.47	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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.cx (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.76937 q^{5} +(-1.21939 - 2.34800i) q^{7} +2.41924i q^{11} +(0.0461613 + 0.0266512i) q^{13} +(1.79727 - 3.11297i) q^{17} +(3.96978 - 2.29195i) q^{19} -0.106917i q^{23} +2.66939 q^{25} +(-6.57376 + 3.79536i) q^{29} +(-5.90251 + 3.40781i) q^{31} +(3.37694 + 6.50246i) q^{35} +(2.06198 + 3.57146i) q^{37} +(-0.838974 + 1.45315i) q^{41} +(1.74347 + 3.01978i) q^{43} +(-6.59698 + 11.4263i) q^{47} +(-4.02618 + 5.72625i) q^{49} +(5.27512 + 3.04559i) q^{53} -6.69977i q^{55} +(4.72417 + 8.18250i) q^{59} +(2.29928 + 1.32749i) q^{61} +(-0.127838 - 0.0738070i) q^{65} +(7.09356 + 12.2864i) q^{67} +1.40262i q^{71} +(5.54168 + 3.19949i) q^{73} +(5.68038 - 2.95000i) q^{77} +(-2.11067 + 3.65578i) q^{79} +(-6.86670 - 11.8935i) q^{83} +(-4.97731 + 8.62095i) q^{85} +(-5.71724 - 9.90254i) q^{89} +(0.00628839 - 0.140885i) q^{91} +(-10.9938 + 6.34726i) q^{95} +(14.3549 - 8.28778i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{25} - 18 q^{29} + 18 q^{31} + 6 q^{41} - 6 q^{43} - 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} + 6 q^{79} + 18 q^{89} + 6 q^{91} + 54 q^{95}+O(q^{100}) \) 48 * q + 48 * q^25 - 18 * q^29 + 18 * q^31 + 6 * q^41 - 6 * q^43 - 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 + 6 * q^79 + 18 * q^89 + 6 * q^91 + 54 * q^95

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