LMFDB - Embedded newform 1512.2.cx.a.89.12

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			89.12
Character	$\chi$	$=$	1512.89
Dual form			1512.2.cx.a.17.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+0.207028 q^{5} +(-1.37075 - 2.26297i) q^{7} +1.51705i q^{11} +(-3.39130 + 1.95797i) q^{13} +(0.873421 + 1.51281i) q^{17} +(-0.968573 - 0.559206i) q^{19} -1.44570i q^{23} -4.95714 q^{25} +(-1.99711 - 1.15303i) q^{29} +(-5.15733 - 2.97759i) q^{31} +(-0.283783 - 0.468499i) q^{35} +(-2.13573 + 3.69920i) q^{37} +(2.91134 + 5.04260i) q^{41} +(-0.213489 + 0.369774i) q^{43} +(4.13407 + 7.16042i) q^{47} +(-3.24210 + 6.20393i) q^{49} +(-8.16638 + 4.71486i) q^{53} +0.314071i q^{55} +(-1.63405 + 2.83025i) q^{59} +(-10.5244 + 6.07629i) q^{61} +(-0.702095 + 0.405354i) q^{65} +(3.24491 - 5.62035i) q^{67} -7.10884i q^{71} +(10.6188 - 6.13075i) q^{73} +(3.43304 - 2.07949i) q^{77} +(-2.57806 - 4.46533i) q^{79} +(-8.36457 + 14.4879i) q^{83} +(0.180823 + 0.313194i) q^{85} +(-1.96290 + 3.39984i) q^{89} +(9.07945 + 4.99055i) q^{91} +(-0.200522 - 0.115771i) q^{95} +(-13.1184 - 7.57392i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

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

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
$5$	0.207028			0.0925858			0.0462929	−	0.998928i	$-0.485259\pi$
$5$	0.207028			0.0925858			0.0462929	+	0.998928i	$0.485259\pi$
$6$		0			0
$7$	−1.37075	−	2.26297i	−0.518094	−	0.855324i
$7$	−1.37075	−	2.26297i	−0.518094	−	0.855324i
$8$		0			0
$9$		0			0
$10$		0			0
$11$			1.51705i			0.457407i	0.973496	+	0.228703i	$0.0734486\pi$
$11$			1.51705i			0.457407i	−0.973496	+	0.228703i	$0.926551\pi$
$12$		0			0
$13$	−3.39130	+	1.95797i	−0.940578	+	0.543043i	−0.890141	−	0.455684i	$-0.849395\pi$
$13$	−3.39130	+	1.95797i	−0.940578	+	0.543043i	−0.0504364	+	0.998727i	$0.516061\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.873421	+	1.51281i	0.211836	+	0.366910i	0.952289	−	0.305198i	$-0.0987225\pi$
$17$	0.873421	+	1.51281i	0.211836	+	0.366910i	−0.740453	+	0.672108i	$0.765389\pi$
$18$		0			0
$19$	−0.968573	−	0.559206i	−0.222206	−	0.128291i	0.384765	−	0.923014i	$-0.374282\pi$
$19$	−0.968573	−	0.559206i	−0.222206	−	0.128291i	−0.606971	+	0.794724i	$0.707616\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	1.44570i		−	0.301450i	−0.988576	−	0.150725i	$-0.951839\pi$
$23$		−	1.44570i		−	0.301450i	0.988576	−	0.150725i	$-0.0481608\pi$
$24$		0			0
$25$	−4.95714			−0.991428
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.99711	−	1.15303i	−0.370853	−	0.214112i	0.302978	−	0.952998i	$-0.402019\pi$
$29$	−1.99711	−	1.15303i	−0.370853	−	0.214112i	−0.673831	+	0.738885i	$0.735352\pi$
$30$		0			0
$31$	−5.15733	−	2.97759i	−0.926285	−	0.534791i	−0.0406501	−	0.999173i	$-0.512943\pi$
$31$	−5.15733	−	2.97759i	−0.926285	−	0.534791i	−0.885635	+	0.464383i	$0.846276\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.283783	−	0.468499i	−0.0479681	−	0.0791908i
$36$		0			0
$37$	−2.13573	+	3.69920i	−0.351113	+	0.608145i	−0.986445	−	0.164094i	$-0.947530\pi$
$37$	−2.13573	+	3.69920i	−0.351113	+	0.608145i	0.635332	+	0.772239i	$0.280863\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.91134	+	5.04260i	0.454676	+	0.787521i	0.998669	−	0.0515680i	$-0.0164219\pi$
$41$	2.91134	+	5.04260i	0.454676	+	0.787521i	−0.543994	+	0.839089i	$0.683089\pi$
$42$		0			0
$43$	−0.213489	+	0.369774i	−0.0325568	+	0.0563900i	−0.881845	−	0.471540i	$-0.843698\pi$
$43$	−0.213489	+	0.369774i	−0.0325568	+	0.0563900i	0.849288	+	0.527930i	$0.177032\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.13407	+	7.16042i	0.603016	+	1.04445i	0.992362	+	0.123363i	$0.0393678\pi$
$47$	4.13407	+	7.16042i	0.603016	+	1.04445i	−0.389346	+	0.921092i	$0.627299\pi$
$48$		0			0
$49$	−3.24210	+	6.20393i	−0.463158	+	0.886276i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−8.16638	+	4.71486i	−1.12174	+	0.647636i	−0.941844	−	0.336050i	$-0.890909\pi$
$53$	−8.16638	+	4.71486i	−1.12174	+	0.647636i	−0.179894	+	0.983686i	$0.557576\pi$
$54$		0			0
$55$			0.314071i			0.0423494i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.63405	+	2.83025i	−0.212735	+	0.368467i	−0.952569	−	0.304321i	$-0.901570\pi$
$59$	−1.63405	+	2.83025i	−0.212735	+	0.368467i	0.739835	+	0.672789i	$0.234904\pi$
$60$		0			0
$61$	−10.5244	+	6.07629i	−1.34752	+	0.777990i	−0.987897	−	0.155109i	$-0.950427\pi$
$61$	−10.5244	+	6.07629i	−1.34752	+	0.777990i	−0.359620	+	0.933099i	$0.617094\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.702095	+	0.405354i	−0.0870841	+	0.0502780i
$66$		0			0
$67$	3.24491	−	5.62035i	0.396429	−	0.686635i	−0.596854	−	0.802350i	$-0.703583\pi$
$67$	3.24491	−	5.62035i	0.396429	−	0.686635i	0.993282	+	0.115715i	$0.0369160\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	7.10884i		−	0.843665i	−0.906674	−	0.421832i	$-0.861387\pi$
$71$		−	7.10884i		−	0.843665i	0.906674	−	0.421832i	$-0.138613\pi$
$72$		0			0
$73$	10.6188	−	6.13075i	1.24283	−	0.717549i	0.273162	−	0.961968i	$-0.411930\pi$
$73$	10.6188	−	6.13075i	1.24283	−	0.717549i	0.969670	+	0.244419i	$0.0785971\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.43304	−	2.07949i	0.391231	−	0.236980i
$78$		0			0
$79$	−2.57806	−	4.46533i	−0.290054	−	0.502389i	0.683768	−	0.729700i	$-0.260340\pi$
$79$	−2.57806	−	4.46533i	−0.290054	−	0.502389i	−0.973822	+	0.227311i	$0.927007\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.36457	+	14.4879i	−0.918131	+	1.59025i	−0.115879	+	0.993263i	$0.536969\pi$
$83$	−8.36457	+	14.4879i	−0.918131	+	1.59025i	−0.802252	+	0.596986i	$0.796365\pi$
$84$		0			0
$85$	0.180823	+	0.313194i	0.0196130	+	0.0339707i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.96290	+	3.39984i	−0.208067	+	0.360382i	−0.951105	−	0.308866i	$-0.900050\pi$
$89$	−1.96290	+	3.39984i	−0.208067	+	0.360382i	0.743039	+	0.669248i	$0.233384\pi$
$90$		0			0
$91$	9.07945	+	4.99055i	0.951785	+	0.523151i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.200522	−	0.115771i	−0.0205731	−	0.0118779i
$96$		0			0
$97$	−13.1184	−	7.57392i	−1.33197	−	0.769016i	−0.346372	−	0.938097i	$-0.612586\pi$
$97$	−13.1184	−	7.57392i	−1.33197	−	0.769016i	−0.985602	+	0.169082i	$0.945920\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−10.2663			−1.02153			−0.510767	−	0.859719i	$-0.670639\pi$
$101$	−10.2663			−1.02153			−0.510767	+	0.859719i	$0.670639\pi$
$102$		0			0
$103$		−	11.2576i		−	1.10924i	−0.832103	−	0.554621i	$-0.812863\pi$
$103$		−	11.2576i		−	1.10924i	0.832103	−	0.554621i	$-0.187137\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.87450	−	5.70104i	−0.954604	−	0.551141i	−0.0600957	−	0.998193i	$-0.519141\pi$
$107$	−9.87450	−	5.70104i	−0.954604	−	0.551141i	−0.894508	+	0.447052i	$0.852474\pi$
$108$		0			0
$109$	1.50422	+	2.60538i	0.144078	+	0.249550i	0.929029	−	0.370008i	$-0.120645\pi$
$109$	1.50422	+	2.60538i	0.144078	+	0.249550i	−0.784951	+	0.619558i	$0.787312\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−14.2634	+	8.23500i	−1.34179	+	0.774683i	−0.987070	−	0.160289i	$-0.948757\pi$
$113$	−14.2634	+	8.23500i	−1.34179	+	0.774683i	−0.354721	+	0.934972i	$0.615424\pi$
$114$		0			0
$115$		−	0.299301i		−	0.0279100i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.22621	−	4.05021i	0.204076	−	0.371282i
$120$		0			0
$121$	8.69857			0.790779
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−2.06141			−0.184378
$126$		0			0
$127$	−8.52680			−0.756631			−0.378316	−	0.925677i	$-0.623497\pi$
$127$	−8.52680			−0.756631			−0.378316	+	0.925677i	$0.623497\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	14.5546			1.27164			0.635821	−	0.771837i	$-0.280662\pi$
$131$	14.5546			1.27164			0.635821	+	0.771837i	$0.280662\pi$
$132$		0			0
$133$	0.0622005	+	2.95838i	0.00539347	+	0.256524i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			10.6840i			0.912797i	0.889776	+	0.456398i	$0.150861\pi$
$137$			10.6840i			0.912797i	−0.889776	+	0.456398i	$0.849139\pi$
$138$		0			0
$139$	7.46448	−	4.30962i	0.633129	−	0.365537i	−0.148834	−	0.988862i	$-0.547552\pi$
$139$	7.46448	−	4.30962i	0.633129	−	0.365537i	0.781963	+	0.623325i	$0.214219\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.97033	−	5.14476i	−0.248391	−	0.430227i
$144$		0			0
$145$	−0.413457	−	0.238709i	−0.0343357	−	0.0198237i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	22.0491i		−	1.80633i	−0.429292	−	0.903166i	$-0.641237\pi$
$149$		−	22.0491i		−	1.80633i	0.429292	−	0.903166i	$-0.358763\pi$
$150$		0			0
$151$	−8.80127			−0.716237			−0.358119	−	0.933676i	$-0.616582\pi$
$151$	−8.80127			−0.716237			−0.358119	+	0.933676i	$0.616582\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.06771	−	0.616444i	−0.0857608	−	0.0495140i
$156$		0			0
$157$	9.13924	+	5.27654i	0.729391	+	0.421114i	0.818199	−	0.574935i	$-0.194973\pi$
$157$	9.13924	+	5.27654i	0.729391	+	0.421114i	−0.0888086	+	0.996049i	$0.528306\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.27159	+	1.98169i	−0.257837	+	0.156179i
$162$		0			0
$163$	−4.64731	+	8.04937i	−0.364005	+	0.630475i	−0.988616	−	0.150461i	$-0.951924\pi$
$163$	−4.64731	+	8.04937i	−0.364005	+	0.630475i	0.624611	+	0.780936i	$0.285258\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.44458	+	7.69824i	0.343932	+	0.595707i	0.985159	−	0.171644i	$-0.0549078\pi$
$167$	4.44458	+	7.69824i	0.343932	+	0.595707i	−0.641227	+	0.767351i	$0.721574\pi$
$168$		0			0
$169$	1.16728	−	2.02179i	0.0897910	−	0.155523i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−4.89970	−	8.48653i	−0.372517	−	0.645219i	0.617435	−	0.786622i	$-0.288172\pi$
$173$	−4.89970	−	8.48653i	−0.372517	−	0.645219i	−0.989952	+	0.141403i	$0.954839\pi$
$174$		0			0
$175$	6.79499	+	11.2179i	0.513653	+	0.847992i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	14.3141	−	8.26425i	1.06989	−	0.617699i	0.141735	−	0.989905i	$-0.454732\pi$
$179$	14.3141	−	8.26425i	1.06989	−	0.617699i	0.928150	+	0.372206i	$0.121398\pi$
$180$		0			0
$181$			23.8542i			1.77307i	0.462664	+	0.886534i	$0.346894\pi$
$181$			23.8542i			1.77307i	−0.462664	+	0.886534i	$0.653106\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.442157	+	0.765838i	−0.0325080	+	0.0563056i
$186$		0			0
$187$	−2.29500	+	1.32502i	−0.167827	+	0.0968951i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	19.3644	−	11.1800i	1.40116	−	0.808960i	0.406648	−	0.913585i	$-0.366698\pi$
$191$	19.3644	−	11.1800i	1.40116	−	0.808960i	0.994512	+	0.104625i	$0.0333642\pi$
$192$		0			0
$193$	4.32850	−	7.49719i	0.311572	−	0.539659i	−0.667131	−	0.744941i	$-0.732478\pi$
$193$	4.32850	−	7.49719i	0.311572	−	0.539659i	0.978703	+	0.205282i	$0.0658110\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			23.2821i			1.65878i	0.558668	+	0.829391i	$0.311313\pi$
$197$			23.2821i			1.65878i	−0.558668	+	0.829391i	$0.688687\pi$
$198$		0			0
$199$	8.80893	−	5.08584i	0.624449	−	0.360526i	−0.154150	−	0.988047i	$-0.549264\pi$
$199$	8.80893	−	5.08584i	0.624449	−	0.360526i	0.778599	+	0.627522i	$0.215931\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.128252	+	6.09991i	0.00900150	+	0.428130i
$204$		0			0
$205$	0.602730	+	1.04396i	0.0420965	+	0.0729132i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.848341	−	1.46937i	0.0586810	−	0.101638i
$210$		0			0
$211$	−13.2184	−	22.8949i	−0.909991	−	1.57615i	−0.814073	−	0.580762i	$-0.802755\pi$
$211$	−13.2184	−	22.8949i	−0.909991	−	1.57615i	−0.0959178	−	0.995389i	$-0.530579\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.0441983	+	0.0765537i	−0.00301430	+	0.00522092i
$216$		0			0
$217$	0.331198	+	15.7524i	0.0224832	+	1.06935i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−5.92407	−	3.42026i	−0.398496	−	0.230072i
$222$		0			0
$223$	−14.4887	−	8.36504i	−0.970233	−	0.560164i	−0.0709258	−	0.997482i	$-0.522595\pi$
$223$	−14.4887	−	8.36504i	−0.970233	−	0.560164i	−0.899307	+	0.437317i	$0.855929\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.88921			0.589998			0.294999	−	0.955498i	$-0.404681\pi$
$227$	8.88921			0.589998			0.294999	+	0.955498i	$0.404681\pi$
$228$		0			0
$229$		−	16.9536i		−	1.12032i	−0.828383	−	0.560162i	$-0.810739\pi$
$229$		−	16.9536i		−	1.12032i	0.828383	−	0.560162i	$-0.189261\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	17.3861	+	10.0379i	1.13900	+	0.657602i	0.946183	−	0.323633i	$-0.104904\pi$
$233$	17.3861	+	10.0379i	1.13900	+	0.657602i	0.192817	+	0.981235i	$0.438238\pi$
$234$		0			0
$235$	0.855868	+	1.48241i	0.0558307	+	0.0967016i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−11.5629	+	6.67585i	−0.747943	+	0.431825i	−0.824950	−	0.565206i	$-0.808797\pi$
$239$	−11.5629	+	6.67585i	−0.747943	+	0.431825i	0.0770074	+	0.997031i	$0.475464\pi$
$240$		0			0
$241$			12.7673i			0.822417i	0.911541	+	0.411209i	$0.134893\pi$
$241$			12.7673i			0.822417i	−0.911541	+	0.411209i	$0.865107\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.671206	+	1.28439i	−0.0428818	+	0.0820565i
$246$		0			0
$247$	4.37963			0.278669
$248$		0			0
$249$		0			0
$250$		0			0
$251$	17.8367			1.12584			0.562921	−	0.826511i	$-0.309678\pi$
$251$	17.8367			1.12584			0.562921	+	0.826511i	$0.309678\pi$
$252$		0			0
$253$	2.19320			0.137885
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.63718			−0.102124			−0.0510621	−	0.998695i	$-0.516261\pi$
$257$	−1.63718			−0.102124			−0.0510621	+	0.998695i	$0.516261\pi$
$258$		0			0
$259$	11.2987	−	0.237558i	0.702070	−	0.0147611i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	30.7251i		−	1.89459i	−0.320359	−	0.947296i	$-0.603803\pi$
$263$		−	30.7251i		−	1.89459i	0.320359	−	0.947296i	$-0.396197\pi$
$264$		0			0
$265$	−1.69067	+	0.976108i	−0.103857	+	0.0599619i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.491194	−	0.850773i	−0.0299486	−	0.0518726i	0.850663	−	0.525712i	$-0.176201\pi$
$269$	−0.491194	−	0.850773i	−0.0299486	−	0.0518726i	−0.880611	+	0.473839i	$0.842868\pi$
$270$		0			0
$271$	−0.707412	−	0.408425i	−0.0429722	−	0.0248100i	0.478360	−	0.878164i	$-0.341231\pi$
$271$	−0.707412	−	0.408425i	−0.0429722	−	0.0248100i	−0.521332	+	0.853354i	$0.674565\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	7.52021i		−	0.453486i
$276$		0			0
$277$	10.6038			0.637118			0.318559	−	0.947903i	$-0.396801\pi$
$277$	10.6038			0.637118			0.318559	+	0.947903i	$0.396801\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−14.1764	−	8.18477i	−0.845695	−	0.488262i	0.0135009	−	0.999909i	$-0.495702\pi$
$281$	−14.1764	−	8.18477i	−0.845695	−	0.488262i	−0.859196	+	0.511647i	$0.829036\pi$
$282$		0			0
$283$	−5.67689	−	3.27755i	−0.337456	−	0.194830i	0.321691	−	0.946845i	$-0.395749\pi$
$283$	−5.67689	−	3.27755i	−0.337456	−	0.194830i	−0.659146	+	0.752015i	$0.729082\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7.42055	−	13.5004i	0.438021	−	0.796905i
$288$		0			0
$289$	6.97427	−	12.0798i	0.410251	−	0.710576i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	7.02441	+	12.1666i	0.410370	+	0.710782i	0.994930	−	0.100568i	$-0.0320662\pi$
$293$	7.02441	+	12.1666i	0.410370	+	0.710782i	−0.584560	+	0.811351i	$0.698733\pi$
$294$		0			0
$295$	−0.338293	+	0.585941i	−0.0196962	+	0.0341148i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.83064	+	4.90281i	0.163700	+	0.283537i
$300$		0			0
$301$	1.12943	−	0.0237464i	0.0650992	−	0.00136872i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.17886	+	1.25796i	−0.124761	+	0.0720308i
$306$		0			0
$307$			17.4335i			0.994982i	0.867469	+	0.497491i	$0.165745\pi$
$307$			17.4335i			0.994982i	−0.867469	+	0.497491i	$0.834255\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	7.79813	−	13.5068i	0.442191	−	0.765898i	−0.555661	−	0.831409i	$-0.687535\pi$
$311$	7.79813	−	13.5068i	0.442191	−	0.765898i	0.997852	+	0.0655116i	$0.0208679\pi$
$312$		0			0
$313$	−1.93111	+	1.11493i	−0.109153	+	0.0630193i	−0.553582	−	0.832794i	$-0.686740\pi$
$313$	−1.93111	+	1.11493i	−0.109153	+	0.0630193i	0.444430	+	0.895814i	$0.353406\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	29.7264	−	17.1625i	1.66960	−	0.963943i	0.701745	−	0.712428i	$-0.252405\pi$
$317$	29.7264	−	17.1625i	1.66960	−	0.963943i	0.967853	−	0.251515i	$-0.0809287\pi$
$318$		0			0
$319$	1.74920	−	3.02970i	0.0979364	−	0.169631i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	1.95369i		−	0.108706i
$324$		0			0
$325$	16.8112	−	9.70592i	0.932515	−	0.538388i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	10.5371	−	19.1704i	0.580928	−	1.05690i
$330$		0			0
$331$	11.2701	+	19.5205i	0.619463	+	1.07294i	0.989584	+	0.143958i	$0.0459829\pi$
$331$	11.2701	+	19.5205i	0.619463	+	1.07294i	−0.370121	+	0.928984i	$0.620684\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.671787	−	1.16357i	0.0367037	−	0.0635726i
$336$		0			0
$337$	−11.3776	−	19.7065i	−0.619776	−	1.07348i	−0.989526	−	0.144353i	$-0.953890\pi$
$337$	−11.3776	−	19.7065i	−0.619776	−	1.07348i	0.369750	−	0.929131i	$-0.379443\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	4.51714	−	7.82392i	0.244617	−	0.423689i
$342$		0			0
$343$	18.4834	−	1.16723i	0.998012	−	0.0630244i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.46927	−	3.73504i	−0.347289	−	0.200507i	0.316202	−	0.948692i	$-0.397592\pi$
$347$	−6.46927	−	3.73504i	−0.347289	−	0.200507i	−0.663491	+	0.748185i	$0.730926\pi$
$348$		0			0
$349$	7.60969	+	4.39346i	0.407337	+	0.235176i	0.689645	−	0.724148i	$-0.257767\pi$
$349$	7.60969	+	4.39346i	0.407337	+	0.235176i	−0.282308	+	0.959324i	$0.591100\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−7.32610			−0.389929			−0.194965	−	0.980810i	$-0.562459\pi$
$353$	−7.32610			−0.389929			−0.194965	+	0.980810i	$0.562459\pi$
$354$		0			0
$355$		−	1.47173i		−	0.0781113i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−11.0036	−	6.35295i	−0.580749	−	0.335296i	0.180682	−	0.983542i	$-0.442170\pi$
$359$	−11.0036	−	6.35295i	−0.580749	−	0.335296i	−0.761431	+	0.648246i	$0.775503\pi$
$360$		0			0
$361$	−8.87458	−	15.3712i	−0.467083	−	0.809012i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.19838	−	1.26924i	0.115069	−	0.0664349i
$366$		0			0
$367$			16.2728i			0.849435i	0.905326	+	0.424717i	$0.139626\pi$
$367$			16.2728i			0.849435i	−0.905326	+	0.424717i	$0.860374\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	21.8636	+	12.0174i	1.13510	+	0.623913i
$372$		0			0
$373$	15.8803			0.822251			0.411126	−	0.911579i	$-0.365136\pi$
$373$	15.8803			0.822251			0.411126	+	0.911579i	$0.365136\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	9.03038			0.465088
$378$		0			0
$379$	−0.0882488			−0.00453304			−0.00226652	−	0.999997i	$-0.500721\pi$
$379$	−0.0882488			−0.00453304			−0.00226652	+	0.999997i	$0.500721\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−33.9273			−1.73360			−0.866802	−	0.498652i	$-0.833828\pi$
$383$	−33.9273			−1.73360			−0.866802	+	0.498652i	$0.833828\pi$
$384$		0			0
$385$	0.710735	−	0.430512i	0.0362224	−	0.0219409i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	11.3976i		−	0.577881i	−0.957347	−	0.288940i	$-0.906697\pi$
$389$		−	11.3976i		−	0.577881i	0.957347	−	0.288940i	$-0.0933029\pi$
$390$		0			0
$391$	2.18707	−	1.26271i	0.110605	−	0.0638578i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.533731	−	0.924449i	−0.0268549	−	0.0465141i
$396$		0			0
$397$	−3.81168	−	2.20068i	−0.191303	−	0.110449i	0.401289	−	0.915951i	$-0.368562\pi$
$397$	−3.81168	−	2.20068i	−0.191303	−	0.110449i	−0.592592	+	0.805503i	$0.701895\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	8.48250i		−	0.423596i	−0.977313	−	0.211798i	$-0.932068\pi$
$401$		−	8.48250i		−	0.423596i	0.977313	−	0.211798i	$-0.0679318\pi$
$402$		0			0
$403$	23.3201			1.16166
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.61186	−	3.24001i	−0.278170	−	0.160601i
$408$		0			0
$409$	10.0254	+	5.78819i	0.495726	+	0.286207i	0.726947	−	0.686694i	$-0.240939\pi$
$409$	10.0254	+	5.78819i	0.495726	+	0.286207i	−0.231221	+	0.972901i	$0.574272\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	8.64465	−	0.181755i	0.425375	−	0.00894359i
$414$		0			0
$415$	−1.73170	+	2.99939i	−0.0850059	+	0.147234i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	11.3173	+	19.6021i	0.552885	+	0.957625i	0.998065	+	0.0621839i	$0.0198065\pi$
$419$	11.3173	+	19.6021i	0.552885	+	0.957625i	−0.445180	+	0.895441i	$0.646860\pi$
$420$		0			0
$421$	−3.51429	+	6.08693i	−0.171276	+	0.296659i	−0.938866	−	0.344282i	$-0.888122\pi$
$421$	−3.51429	+	6.08693i	−0.171276	+	0.296659i	0.767590	+	0.640941i	$0.221456\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.32967	−	7.49921i	−0.210020	−	0.363765i
$426$		0			0
$427$	28.1769	+	15.4875i	1.36357	+	0.749492i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.267173	+	0.154252i	−0.0128693	+	0.00743007i	−0.506421	−	0.862286i	$-0.669032\pi$
$431$	−0.267173	+	0.154252i	−0.0128693	+	0.00743007i	0.493552	+	0.869717i	$0.335698\pi$
$432$		0			0
$433$			32.8376i			1.57807i	0.614347	+	0.789036i	$0.289420\pi$
$433$			32.8376i			1.57807i	−0.614347	+	0.789036i	$0.710580\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.808445	+	1.40027i	−0.0386732	+	0.0669839i
$438$		0			0
$439$	2.91256	−	1.68157i	0.139009	−	0.0802568i	−0.428883	−	0.903360i	$-0.641093\pi$
$439$	2.91256	−	1.68157i	0.139009	−	0.0802568i	0.567891	+	0.823103i	$0.307759\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−31.0997	+	17.9554i	−1.47759	+	0.853087i	−0.999679	−	0.0253206i	$-0.991939\pi$
$443$	−31.0997	+	17.9554i	−1.47759	+	0.853087i	−0.477911	+	0.878408i	$0.658606\pi$
$444$		0			0
$445$	−0.406375	+	0.703862i	−0.0192640	+	0.0333662i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	13.9993i		−	0.660668i	−0.943864	−	0.330334i	$-0.892839\pi$
$449$		−	13.9993i		−	0.660668i	0.943864	−	0.330334i	$-0.107161\pi$
$450$		0			0
$451$	−7.64985	+	4.41664i	−0.360217	+	0.207972i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.87970	+	1.03318i	0.0881217	+	0.0484364i
$456$		0			0
$457$	−3.97051	−	6.87713i	−0.185733	−	0.321699i	0.758090	−	0.652149i	$-0.226133\pi$
$457$	−3.97051	−	6.87713i	−0.185733	−	0.321699i	−0.943823	+	0.330451i	$0.892799\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.12627	+	3.68281i	−0.0990304	+	0.171526i	−0.911284	−	0.411779i	$-0.864907\pi$
$461$	−2.12627	+	3.68281i	−0.0990304	+	0.171526i	0.812253	+	0.583305i	$0.198241\pi$
$462$		0			0
$463$	−10.2557	−	17.7634i	−0.476622	−	0.825534i	0.523019	−	0.852321i	$-0.324806\pi$
$463$	−10.2557	−	17.7634i	−0.476622	−	0.825534i	−0.999641	+	0.0267869i	$0.991472\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.8842	+	24.0481i	−0.642484	+	1.11281i	0.342393	+	0.939557i	$0.388763\pi$
$467$	−13.8842	+	24.0481i	−0.642484	+	1.11281i	−0.984877	+	0.173257i	$0.944571\pi$
$468$		0			0
$469$	−17.1667	+	0.360932i	−0.792682	+	0.0166663i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.560965	−	0.323873i	−0.0257932	−	0.0148917i
$474$		0			0
$475$	4.80135	+	2.77206i	0.220301	+	0.127191i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	31.4128			1.43529			0.717643	−	0.696411i	$-0.245221\pi$
$479$	31.4128			1.43529			0.717643	+	0.696411i	$0.245221\pi$
$480$		0			0
$481$		−	16.7268i		−	0.762677i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.71588	−	1.56801i	−0.123322	−	0.0711999i
$486$		0			0
$487$	−16.1798	−	28.0242i	−0.733176	−	1.26990i	−0.955519	−	0.294929i	$-0.904704\pi$
$487$	−16.1798	−	28.0242i	−0.733176	−	1.26990i	0.222343	−	0.974968i	$-0.428629\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−33.6617	+	19.4346i	−1.51913	+	0.877071i	−0.519385	+	0.854540i	$0.673839\pi$
$491$	−33.6617	+	19.4346i	−1.51913	+	0.877071i	−0.999746	+	0.0225309i	$0.992828\pi$
$492$		0			0
$493$		−	4.02832i		−	0.181426i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−16.0871	+	9.74443i	−0.721606	+	0.437097i
$498$		0			0
$499$	39.7540			1.77963			0.889816	−	0.456319i	$-0.150832\pi$
$499$	39.7540			1.77963			0.889816	+	0.456319i	$0.150832\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	4.45463			0.198622			0.0993110	−	0.995056i	$-0.468336\pi$
$503$	4.45463			0.198622			0.0993110	+	0.995056i	$0.468336\pi$
$504$		0			0
$505$	−2.12541			−0.0945796
$506$		0			0
$507$		0			0
$508$		0			0
$509$	19.8433			0.879539			0.439769	−	0.898111i	$-0.355060\pi$
$509$	19.8433			0.879539			0.439769	+	0.898111i	$0.355060\pi$
$510$		0			0
$511$	−28.4294	−	15.6263i	−1.25764	−	0.691266i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	2.33064i		−	0.102700i
$516$		0			0
$517$	−10.8627	+	6.27157i	−0.477740	+	0.275824i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	6.51527	+	11.2848i	0.285439	+	0.494395i	0.972716	−	0.232001i	$-0.0745273\pi$
$521$	6.51527	+	11.2848i	0.285439	+	0.494395i	−0.687277	+	0.726396i	$0.741194\pi$
$522$		0			0
$523$	28.6981	+	16.5688i	1.25488	+	0.724505i	0.972075	−	0.234672i	$-0.0754017\pi$
$523$	28.6981	+	16.5688i	1.25488	+	0.724505i	0.282805	+	0.959177i	$0.408735\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	10.4028i		−	0.453151i
$528$		0			0
$529$	20.9099			0.909128
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−19.7465	−	11.4006i	−0.855315	−	0.493817i
$534$		0			0
$535$	−2.04430	−	1.18028i	−0.0883827	−	0.0510278i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−9.41165	−	4.91842i	−0.405389	−	0.211851i
$540$		0			0
$541$	13.3022	−	23.0402i	0.571908	−	0.990574i	−0.424462	−	0.905446i	$-0.639537\pi$
$541$	13.3022	−	23.0402i	0.571908	−	0.990574i	0.996370	−	0.0851281i	$-0.0271300\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.311415	+	0.539387i	0.0133396	+	0.0231048i
$546$		0			0
$547$	−4.32361	+	7.48870i	−0.184864	+	0.320194i	−0.943531	−	0.331285i	$-0.892518\pi$
$547$	−4.32361	+	7.48870i	−0.184864	+	0.320194i	0.758667	+	0.651479i	$0.225851\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.28956	+	2.23359i	0.0549372	+	0.0951539i
$552$		0			0
$553$	−6.57106	+	11.9549i	−0.279430	+	0.508375i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−19.1707	+	11.0682i	−0.812289	+	0.468975i	−0.847750	−	0.530396i	$-0.822043\pi$
$557$	−19.1707	+	11.0682i	−0.812289	+	0.468975i	0.0354610	+	0.999371i	$0.488710\pi$
$558$		0			0
$559$		−	1.67202i		−	0.0707190i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−6.10275	+	10.5703i	−0.257200	+	0.445484i	−0.965491	−	0.260437i	$-0.916133\pi$
$563$	−6.10275	+	10.5703i	−0.257200	+	0.445484i	0.708291	+	0.705921i	$0.249467\pi$
$564$		0			0
$565$	−2.95293	+	1.70488i	−0.124231	+	0.0717247i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.16135	−	4.71196i	0.342142	−	0.197536i	−0.319077	−	0.947729i	$-0.603373\pi$
$569$	8.16135	−	4.71196i	0.342142	−	0.197536i	0.661219	+	0.750193i	$0.270040\pi$
$570$		0			0
$571$	−7.73579	+	13.3988i	−0.323733	+	0.560721i	−0.981255	−	0.192714i	$-0.938271\pi$
$571$	−7.73579	+	13.3988i	−0.323733	+	0.560721i	0.657522	+	0.753435i	$0.271604\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			7.16655i			0.298866i
$576$		0			0
$577$	−8.48608	+	4.89944i	−0.353280	+	0.203966i	−0.666129	−	0.745836i	$-0.732050\pi$
$577$	−8.48608	+	4.89944i	−0.353280	+	0.203966i	0.312849	+	0.949803i	$0.398717\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	44.2514	−	0.930392i	1.83586	−	0.0385992i
$582$		0			0
$583$	−7.15266	−	12.3888i	−0.296233	−	0.513091i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.4297	+	21.5289i	−0.513028	+	0.888591i	0.486858	+	0.873481i	$0.338143\pi$
$587$	−12.4297	+	21.5289i	−0.513028	+	0.888591i	−0.999886	+	0.0151097i	$0.995190\pi$
$588$		0			0
$589$	3.33017	+	5.76802i	0.137217	+	0.237667i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	20.9831	−	36.3438i	0.861673	−	1.49246i	−0.00863918	−	0.999963i	$-0.502750\pi$
$593$	20.9831	−	36.3438i	0.861673	−	1.49246i	0.870313	−	0.492500i	$-0.163917\pi$
$594$		0			0
$595$	0.460888	−	0.838507i	0.0188946	−	0.0343754i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−26.2575	−	15.1598i	−1.07285	−	0.619412i	−0.143894	−	0.989593i	$-0.545962\pi$
$599$	−26.2575	−	15.1598i	−1.07285	−	0.619412i	−0.928960	+	0.370181i	$0.879296\pi$
$600$		0			0
$601$	−2.71173	−	1.56562i	−0.110614	−	0.0638628i	0.443673	−	0.896189i	$-0.353675\pi$
$601$	−2.71173	−	1.56562i	−0.110614	−	0.0638628i	−0.554286	+	0.832326i	$0.687009\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.80085			0.0732149
$606$		0			0
$607$			14.3866i			0.583934i	0.956428	+	0.291967i	$0.0943097\pi$
$607$			14.3866i			0.583934i	−0.956428	+	0.291967i	$0.905690\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−28.0397	−	16.1888i	−1.13437	−	0.654927i
$612$		0			0
$613$	−4.36863	−	7.56669i	−0.176447	−	0.305616i	0.764214	−	0.644963i	$-0.223127\pi$
$613$	−4.36863	−	7.56669i	−0.176447	−	0.305616i	−0.940661	+	0.339347i	$0.889794\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	25.9444	−	14.9790i	1.04448	−	0.603033i	0.123384	−	0.992359i	$-0.460625\pi$
$617$	25.9444	−	14.9790i	1.04448	−	0.603033i	0.921100	+	0.389326i	$0.127292\pi$
$618$		0			0
$619$			2.63070i			0.105737i	0.998601	+	0.0528683i	$0.0168363\pi$
$619$			2.63070i			0.105737i	−0.998601	+	0.0528683i	$0.983164\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	10.3844	−	0.218333i	0.416041	−	0.00874734i
$624$		0			0
$625$	24.3589			0.974357
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−7.46158			−0.297513
$630$		0			0
$631$	−18.0872			−0.720039			−0.360019	−	0.932945i	$-0.617230\pi$
$631$	−18.0872			−0.720039			−0.360019	+	0.932945i	$0.617230\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.76529			−0.0700533
$636$		0			0
$637$	−1.15216	−	27.3873i	−0.0456501	−	1.08513i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			41.1733i			1.62625i	0.582091	+	0.813124i	$0.302235\pi$
$641$			41.1733i			1.62625i	−0.582091	+	0.813124i	$0.697765\pi$
$642$		0			0
$643$	−31.3046	+	18.0737i	−1.23453	+	0.712758i	−0.967971	−	0.251060i	$-0.919221\pi$
$643$	−31.3046	+	18.0737i	−1.23453	+	0.712758i	−0.266561	+	0.963818i	$0.585887\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.09812	−	7.09815i	−0.161114	−	0.279057i	0.774155	−	0.632996i	$-0.218175\pi$
$647$	−4.09812	−	7.09815i	−0.161114	−	0.279057i	−0.935268	+	0.353939i	$0.884842\pi$
$648$		0			0
$649$	−4.29362	−	2.47892i	−0.168539	−	0.0973063i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			26.9751i			1.05562i	0.849364	+	0.527808i	$0.176986\pi$
$653$			26.9751i			1.05562i	−0.849364	+	0.527808i	$0.823014\pi$
$654$		0			0
$655$	3.01321			0.117736
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.60125	+	1.50183i	0.101330	+	0.0585032i	0.549809	−	0.835291i	$-0.314701\pi$
$659$	2.60125	+	1.50183i	0.101330	+	0.0585032i	−0.448478	+	0.893794i	$0.648034\pi$
$660$		0			0
$661$	−31.2423	−	18.0377i	−1.21518	−	0.701586i	−0.251299	−	0.967909i	$-0.580858\pi$
$661$	−31.2423	−	18.0377i	−1.21518	−	0.701586i	−0.963884	+	0.266323i	$0.914191\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.0128773	+	0.612469i	0.000499359	+	0.0237505i
$666$		0			0
$667$	−1.66694	+	2.88722i	−0.0645441	+	0.111794i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−9.21802	−	15.9661i	−0.355858	−	0.616364i
$672$		0			0
$673$	3.20540	−	5.55191i	0.123559	−	0.214010i	−0.797610	−	0.603174i	$-0.793903\pi$
$673$	3.20540	−	5.55191i	0.123559	−	0.214010i	0.921169	+	0.389163i	$0.127236\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−17.2249	−	29.8344i	−0.662007	−	1.14663i	−0.980088	−	0.198566i	$-0.936372\pi$
$677$	−17.2249	−	29.8344i	−0.662007	−	1.14663i	0.318081	−	0.948064i	$-0.396962\pi$
$678$		0			0
$679$	0.842449	+	40.0686i	0.0323302	+	1.53769i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−2.53802	+	1.46533i	−0.0971148	+	0.0560693i	−0.547771	−	0.836628i	$-0.684523\pi$
$683$	−2.53802	+	1.46533i	−0.0971148	+	0.0560693i	0.450656	+	0.892698i	$0.351190\pi$
$684$		0			0
$685$			2.21189i			0.0845120i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	18.4631	−	31.9790i	0.703388	−	1.21830i
$690$		0			0
$691$	−3.29381	+	1.90168i	−0.125303	+	0.0723434i	−0.561341	−	0.827585i	$-0.689714\pi$
$691$	−3.29381	+	1.90168i	−0.125303	+	0.0723434i	0.436039	+	0.899928i	$0.356381\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.54536	−	0.892213i	0.0586188	−	0.0338436i
$696$		0			0
$697$	−5.08566	+	8.80862i	−0.192633	+	0.333650i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			36.7042i			1.38630i	0.720795	+	0.693149i	$0.243777\pi$
$701$			36.7042i			1.38630i	−0.720795	+	0.693149i	$0.756223\pi$
$702$		0			0
$703$	4.13723	−	2.38863i	0.156039	−	0.0900889i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	14.0725	+	23.2324i	0.529251	+	0.873743i
$708$		0			0
$709$	−10.4040	−	18.0202i	−0.390730	−	0.676764i	0.601816	−	0.798635i	$-0.294444\pi$
$709$	−10.4040	−	18.0202i	−0.390730	−	0.676764i	−0.992546	+	0.121870i	$0.961111\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−4.30471	+	7.45597i	−0.161213	+	0.279228i
$714$		0			0
$715$	−0.614942	−	1.06511i	−0.0229975	−	0.0398329i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−15.1577	+	26.2540i	−0.565288	+	0.979108i	0.431734	+	0.902001i	$0.357902\pi$
$719$	−15.1577	+	26.2540i	−0.565288	+	0.979108i	−0.997023	+	0.0771074i	$0.975432\pi$
$720$		0			0
$721$	−25.4756	+	15.4313i	−0.948761	+	0.574692i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	9.89993	+	5.71573i	0.367674	+	0.212277i
$726$		0			0
$727$	−29.7259	−	17.1622i	−1.10247	−	0.636512i	−0.165602	−	0.986193i	$-0.552957\pi$
$727$	−29.7259	−	17.1622i	−1.10247	−	0.636512i	−0.936869	+	0.349680i	$0.886290\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.745864			−0.0275868
$732$		0			0
$733$		−	6.18213i		−	0.228342i	−0.993461	−	0.114171i	$-0.963579\pi$
$733$		−	6.18213i		−	0.228342i	0.993461	−	0.114171i	$-0.0364212\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.52633	+	4.92268i	0.314071	+	0.181329i
$738$		0			0
$739$	−13.5892	−	23.5372i	−0.499887	−	0.865829i	0.500113	−	0.865960i	$-0.333292\pi$
$739$	−13.5892	−	23.5372i	−0.499887	−	0.865829i	−1.00000		0.000131035i	$0.999958\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−24.3213	+	14.0419i	−0.892262	+	0.515148i	−0.874682	−	0.484698i	$-0.838930\pi$
$743$	−24.3213	+	14.0419i	−0.892262	+	0.515148i	−0.0175804	+	0.999845i	$0.505596\pi$
$744$		0			0
$745$		−	4.56478i		−	0.167241i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.634128	+	30.1604i	0.0231705	+	1.10204i
$750$		0			0
$751$	−42.1842			−1.53932			−0.769661	−	0.638453i	$-0.779575\pi$
$751$	−42.1842			−1.53932			−0.769661	+	0.638453i	$0.779575\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−1.82211			−0.0663134
$756$		0			0
$757$	−32.6771			−1.18767			−0.593835	−	0.804587i	$-0.702387\pi$
$757$	−32.6771			−1.18767			−0.593835	+	0.804587i	$0.702387\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−31.7567			−1.15118			−0.575589	−	0.817739i	$-0.695227\pi$
$761$	−31.7567			−1.15118			−0.575589	+	0.817739i	$0.695227\pi$
$762$		0			0
$763$	3.83401	−	6.97532i	0.138800	−	0.252524i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	12.7976i		−	0.462096i
$768$		0			0
$769$	−30.8593	+	17.8166i	−1.11281	+	0.642484i	−0.939557	−	0.342393i	$-0.888763\pi$
$769$	−30.8593	+	17.8166i	−1.11281	+	0.642484i	−0.173258	+	0.984877i	$0.555429\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−6.44721	−	11.1669i	−0.231890	−	0.401645i	0.726474	−	0.687194i	$-0.241158\pi$
$773$	−6.44721	−	11.1669i	−0.231890	−	0.401645i	−0.958364	+	0.285548i	$0.907824\pi$
$774$		0			0
$775$	25.5656	+	14.7603i	0.918344	+	0.530206i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	6.51216i		−	0.233322i
$780$		0			0
$781$	10.7844			0.385898
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.89208	+	1.09239i	0.0675312	+	0.0389892i
$786$		0			0
$787$	−15.3158	−	8.84260i	−0.545950	−	0.315205i	0.201537	−	0.979481i	$-0.435406\pi$
$787$	−15.3158	−	8.84260i	−0.545950	−	0.315205i	−0.747487	+	0.664276i	$0.768740\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	38.1871	+	20.9897i	1.35778	+	0.746307i
$792$		0			0
$793$	23.7944	−	41.2131i	0.844963	−	1.46352i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	22.8391	+	39.5585i	0.809003	+	1.40123i	0.913555	+	0.406714i	$0.133326\pi$
$797$	22.8391	+	39.5585i	0.809003	+	1.40123i	−0.104553	+	0.994519i	$0.533341\pi$
$798$		0			0
$799$	−7.22156	+	12.5081i	−0.255481	+	0.442505i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	9.30063	+	16.1092i	0.328212	+	0.568480i
$804$		0			0
$805$	−0.677310	+	0.410266i	−0.0238721	+	0.0144600i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	10.8291	−	6.25218i	0.380731	−	0.219815i	−0.297405	−	0.954751i	$-0.596121\pi$
$809$	10.8291	−	6.25218i	0.380731	−	0.219815i	0.678136	+	0.734936i	$0.262788\pi$
$810$		0			0
$811$			9.57778i			0.336322i	0.985760	+	0.168161i	$0.0537828\pi$
$811$			9.57778i			0.336322i	−0.985760	+	0.168161i	$0.946217\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.962123	+	1.66645i	−0.0337017	+	0.0583730i
$816$		0			0
$817$	0.413560	−	0.238769i	0.0144686	−	0.00835346i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−24.1379	+	13.9360i	−0.842420	+	0.486371i	−0.858086	−	0.513506i	$-0.828346\pi$
$821$	−24.1379	+	13.9360i	−0.842420	+	0.486371i	0.0156664	+	0.999877i	$0.495013\pi$
$822$		0			0
$823$	−23.6383	+	40.9428i	−0.823980	+	1.42717i	0.0787167	+	0.996897i	$0.474918\pi$
$823$	−23.6383	+	40.9428i	−0.823980	+	1.42717i	−0.902697	+	0.430278i	$0.858416\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	24.1672i		−	0.840377i	−0.907437	−	0.420188i	$-0.861964\pi$
$827$		−	24.1672i		−	0.840377i	0.907437	−	0.420188i	$-0.138036\pi$
$828$		0			0
$829$	23.0216	−	13.2915i	0.799572	−	0.461633i	−0.0437494	−	0.999043i	$-0.513930\pi$
$829$	23.0216	−	13.2915i	0.799572	−	0.461633i	0.843322	+	0.537409i	$0.180597\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−12.2171	+	0.513960i	−0.423297	+	0.0178076i
$834$		0			0
$835$	0.920152	+	1.59375i	0.0318432	+	0.0551540i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−4.03255	+	6.98459i	−0.139219	+	0.241135i	−0.927201	−	0.374563i	$-0.877793\pi$
$839$	−4.03255	+	6.98459i	−0.139219	+	0.241135i	0.787982	+	0.615698i	$0.211126\pi$
$840$		0			0
$841$	−11.8410	−	20.5093i	−0.408312	−	0.707217i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.241660	−	0.418568i	0.00831337	−	0.0143992i
$846$		0			0
$847$	−11.9235	−	19.6846i	−0.409698	−	0.676372i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	5.34794	+	3.08764i	0.183325	+	0.105843i
$852$		0			0
$853$	−11.6046	−	6.69994i	−0.397335	−	0.229402i	0.287998	−	0.957631i	$-0.407010\pi$
$853$	−11.6046	−	6.69994i	−0.397335	−	0.229402i	−0.685334	+	0.728229i	$0.740344\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	44.6679			1.52583			0.762914	−	0.646500i	$-0.223768\pi$
$857$	44.6679			1.52583			0.762914	+	0.646500i	$0.223768\pi$
$858$		0			0
$859$			50.5104i			1.72339i	0.507425	+	0.861696i	$0.330597\pi$
$859$			50.5104i			1.72339i	−0.507425	+	0.861696i	$0.669403\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.227203	−	0.131176i	−0.00773408	−	0.00446528i	0.496128	−	0.868249i	$-0.334755\pi$
$863$	−0.227203	−	0.131176i	−0.00773408	−	0.00446528i	−0.503862	+	0.863784i	$0.668088\pi$
$864$		0			0
$865$	−1.01438	−	1.75695i	−0.0344898	−	0.0597381i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	6.77412	−	3.91104i	0.229796	−	0.132673i
$870$		0			0
$871$			25.4137i			0.861111i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.82567	+	4.66491i	0.0955250	+	0.157703i
$876$		0			0
$877$	−9.26607			−0.312893			−0.156446	−	0.987686i	$-0.550004\pi$
$877$	−9.26607			−0.312893			−0.156446	+	0.987686i	$0.550004\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−41.5555			−1.40004			−0.700021	−	0.714122i	$-0.746826\pi$
$881$	−41.5555			−1.40004			−0.700021	+	0.714122i	$0.746826\pi$
$882$		0			0
$883$	−29.4547			−0.991231			−0.495615	−	0.868542i	$-0.665057\pi$
$883$	−29.4547			−0.991231			−0.495615	+	0.868542i	$0.665057\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−15.5824			−0.523207			−0.261603	−	0.965175i	$-0.584251\pi$
$887$	−15.5824			−0.523207			−0.261603	+	0.965175i	$0.584251\pi$
$888$		0			0
$889$	11.6881	+	19.2959i	0.392006	+	0.647165i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	9.24718i		−	0.309445i
$894$		0			0
$895$	2.96342	−	1.71093i	0.0990562	−	0.0571901i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	6.86649	+	11.8931i	0.229010	+	0.396658i
$900$		0			0
$901$	−14.2654	−	8.23612i	−0.475248	−	0.274385i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			4.93849i			0.164161i
$906$		0			0
$907$	20.5208			0.681383			0.340692	−	0.940175i	$-0.389339\pi$
$907$	20.5208			0.681383			0.340692	+	0.940175i	$0.389339\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	15.0554	+	8.69226i	0.498809	+	0.287987i	0.728222	−	0.685342i	$-0.240347\pi$
$911$	15.0554	+	8.69226i	0.498809	+	0.287987i	−0.229413	+	0.973329i	$0.573681\pi$
$912$		0			0
$913$	−21.9788	−	12.6894i	−0.727391	−	0.419959i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−19.9507	−	32.9367i	−0.658830	−	1.08767i
$918$		0			0
$919$	17.1002	−	29.6183i	0.564082	−	0.977019i	−0.433052	−	0.901369i	$-0.642563\pi$
$919$	17.1002	−	29.6183i	0.564082	−	0.977019i	0.997134	−	0.0756501i	$-0.0241032\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	13.9189	+	24.1082i	0.458146	+	0.793532i
$924$		0			0
$925$	10.5871	−	18.3375i	0.348103	−	0.602932i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.49596	+	2.59108i	0.0490808	+	0.0850105i	0.889522	−	0.456892i	$-0.151037\pi$
$929$	1.49596	+	2.59108i	0.0490808	+	0.0850105i	−0.840441	+	0.541903i	$0.817704\pi$
$930$		0			0
$931$	6.60949	−	4.19596i	0.216617	−	0.137517i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.475130	+	0.274316i	−0.0155384	+	0.00897110i
$936$		0			0
$937$			10.9928i			0.359120i	0.983747	+	0.179560i	$0.0574674\pi$
$937$			10.9928i			0.359120i	−0.983747	+	0.179560i	$0.942533\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	4.95300	−	8.57884i	0.161463	−	0.279662i	−0.773931	−	0.633271i	$-0.781712\pi$
$941$	4.95300	−	8.57884i	0.161463	−	0.279662i	0.935394	+	0.353608i	$0.115045\pi$
$942$		0			0
$943$	7.29009	−	4.20894i	0.237398	−	0.137062i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−23.4219	+	13.5227i	−0.761110	+	0.439427i	−0.829694	−	0.558218i	$-0.811485\pi$
$947$	−23.4219	+	13.5227i	−0.761110	+	0.439427i	0.0685840	+	0.997645i	$0.478152\pi$
$948$		0			0
$949$	−24.0076	+	41.5824i	−0.779320	+	1.34982i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			51.9958i			1.68431i	0.539236	+	0.842155i	$0.318713\pi$
$953$			51.9958i			1.68431i	−0.539236	+	0.842155i	$0.681287\pi$
$954$		0			0
$955$	4.00898	−	2.31458i	0.129727	−	0.0748982i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	24.1776	−	14.6451i	0.780737	−	0.472914i
$960$		0			0
$961$	2.23207	+	3.86605i	0.0720022	+	0.124711i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.896121	−	1.55213i	0.0288472	−	0.0499648i
$966$		0			0
$967$	8.23005	+	14.2549i	0.264660	+	0.458405i	0.967475	−	0.252968i	$-0.0814068\pi$
$967$	8.23005	+	14.2549i	0.264660	+	0.458405i	−0.702814	+	0.711374i	$0.748073\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	6.09724	−	10.5607i	0.195670	−	0.338910i	−0.751450	−	0.659790i	$-0.770645\pi$
$971$	6.09724	−	10.5607i	0.195670	−	0.338910i	0.947120	+	0.320880i	$0.103979\pi$
$972$		0			0
$973$	−19.9845	−	10.9845i	−0.640673	−	0.352148i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−18.8425	−	10.8787i	−0.602824	−	0.348040i	0.167328	−	0.985901i	$-0.446486\pi$
$977$	−18.8425	−	10.8787i	−0.602824	−	0.348040i	−0.770152	+	0.637861i	$0.779819\pi$
$978$		0			0
$979$	−5.15771	−	2.97781i	−0.164841	−	0.0951711i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−62.4746			−1.99263			−0.996316	−	0.0857622i	$-0.972667\pi$
$983$	−62.4746			−1.99263			−0.996316	+	0.0857622i	$0.972667\pi$
$984$		0			0
$985$			4.82005i			0.153580i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.534583	+	0.308642i	0.0169988	+	0.00981424i
$990$		0			0
$991$	−27.5362	−	47.6942i	−0.874717	−	1.51505i	−0.857064	−	0.515210i	$-0.827714\pi$
$991$	−27.5362	−	47.6942i	−0.874717	−	1.51505i	−0.0176535	−	0.999844i	$-0.505620\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.82370	−	1.05291i	0.0578151	−	0.0333795i
$996$		0			0
$997$			23.8706i			0.755990i	0.925808	+	0.377995i	$0.123386\pi$
$997$			23.8706i			0.755990i	−0.925808	+	0.377995i	$0.876614\pi$
$998$		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.89.12		48
3.2	odd	2		504.2.cx.a.425.10	yes	48
4.3	odd	2		3024.2.df.e.1601.12		48
7.3	odd	6		1512.2.bs.a.521.12		48
9.4	even	3		504.2.bs.a.257.19	✓	48
9.5	odd	6		1512.2.bs.a.1097.12		48
12.11	even	2		1008.2.df.e.929.15		48
21.17	even	6		504.2.bs.a.353.19	yes	48
28.3	even	6		3024.2.ca.e.2033.12		48
36.23	even	6		3024.2.ca.e.2609.12		48
36.31	odd	6		1008.2.ca.e.257.6		48
63.31	odd	6		504.2.cx.a.185.10	yes	48
63.59	even	6	inner	1512.2.cx.a.17.12		48
84.59	odd	6		1008.2.ca.e.353.6		48
252.31	even	6		1008.2.df.e.689.15		48
252.59	odd	6		3024.2.df.e.17.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.19	✓	48	9.4	even	3
504.2.bs.a.353.19	yes	48	21.17	even	6
504.2.cx.a.185.10	yes	48	63.31	odd	6
504.2.cx.a.425.10	yes	48	3.2	odd	2
1008.2.ca.e.257.6		48	36.31	odd	6
1008.2.ca.e.353.6		48	84.59	odd	6
1008.2.df.e.689.15		48	252.31	even	6
1008.2.df.e.929.15		48	12.11	even	2
1512.2.bs.a.521.12		48	7.3	odd	6
1512.2.bs.a.1097.12		48	9.5	odd	6
1512.2.cx.a.17.12		48	63.59	even	6	inner
1512.2.cx.a.89.12		48	1.1	even	1	trivial
3024.2.ca.e.2033.12		48	28.3	even	6
3024.2.ca.e.2609.12		48	36.23	even	6
3024.2.df.e.17.12		48	252.59	odd	6
3024.2.df.e.1601.12		48	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+0.207028 q^{5} +(-1.37075 - 2.26297i) q^{7} +1.51705i q^{11} +(-3.39130 + 1.95797i) q^{13} +(0.873421 + 1.51281i) q^{17} +(-0.968573 - 0.559206i) q^{19} -1.44570i q^{23} -4.95714 q^{25} +(-1.99711 - 1.15303i) q^{29} +(-5.15733 - 2.97759i) q^{31} +(-0.283783 - 0.468499i) q^{35} +(-2.13573 + 3.69920i) q^{37} +(2.91134 + 5.04260i) q^{41} +(-0.213489 + 0.369774i) q^{43} +(4.13407 + 7.16042i) q^{47} +(-3.24210 + 6.20393i) q^{49} +(-8.16638 + 4.71486i) q^{53} +0.314071i q^{55} +(-1.63405 + 2.83025i) q^{59} +(-10.5244 + 6.07629i) q^{61} +(-0.702095 + 0.405354i) q^{65} +(3.24491 - 5.62035i) q^{67} -7.10884i q^{71} +(10.6188 - 6.13075i) q^{73} +(3.43304 - 2.07949i) q^{77} +(-2.57806 - 4.46533i) q^{79} +(-8.36457 + 14.4879i) q^{83} +(0.180823 + 0.313194i) q^{85} +(-1.96290 + 3.39984i) q^{89} +(9.07945 + 4.99055i) q^{91} +(-0.200522 - 0.115771i) q^{95} +(-13.1184 - 7.57392i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{25} - 18 q^{29} + 18 q^{31} + 6 q^{41} - 6 q^{43} - 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} + 6 q^{79} + 18 q^{89} + 6 q^{91} + 54 q^{95}+O(q^{100}) \) 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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