LMFDB - Embedded newform 1512.2.cx.a.17.19

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			17.19
Character	$\chi$	$=$	1512.17
Dual form			1512.2.cx.a.89.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+1.81173 q^{5} +(1.69266 - 2.03345i) q^{7} -0.255864i q^{11} +(-5.77765 - 3.33573i) q^{13} +(1.99857 - 3.46163i) q^{17} +(1.24687 - 0.719882i) q^{19} -5.66665i q^{23} -1.71762 q^{25} +(4.18486 - 2.41613i) q^{29} +(-8.80648 + 5.08442i) q^{31} +(3.06665 - 3.68407i) q^{35} +(-1.65567 - 2.86771i) q^{37} +(5.10089 - 8.83499i) q^{41} +(1.12248 + 1.94419i) q^{43} +(-5.97092 + 10.3419i) q^{47} +(-1.26982 - 6.88386i) q^{49} +(3.97466 + 2.29477i) q^{53} -0.463558i q^{55} +(2.55575 + 4.42670i) q^{59} +(8.60220 + 4.96648i) q^{61} +(-10.4676 - 6.04346i) q^{65} +(-0.962135 - 1.66647i) q^{67} +7.31241i q^{71} +(-2.47807 - 1.43071i) q^{73} +(-0.520286 - 0.433090i) q^{77} +(1.83153 - 3.17231i) q^{79} +(-2.68261 - 4.64642i) q^{83} +(3.62089 - 6.27156i) q^{85} +(0.378446 + 0.655488i) q^{89} +(-16.5626 + 6.10230i) q^{91} +(2.25900 - 1.30424i) q^{95} +(4.21765 - 2.43506i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.81173			0.810232			0.405116	−	0.914265i	$-0.367231\pi$
$5$	1.81173			0.810232			0.405116	+	0.914265i	$0.367231\pi$
$6$		0			0
$7$	1.69266	−	2.03345i	0.639765	−	0.768571i
$7$	1.69266	−	2.03345i	0.639765	−	0.768571i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	0.255864i		−	0.0771459i	−0.999256	−	0.0385730i	$-0.987719\pi$
$11$		−	0.255864i		−	0.0771459i	0.999256	−	0.0385730i	$-0.0122812\pi$
$12$		0			0
$13$	−5.77765	−	3.33573i	−1.60243	−	0.925165i	−0.990999	−	0.133869i	$-0.957260\pi$
$13$	−5.77765	−	3.33573i	−1.60243	−	0.925165i	−0.611433	−	0.791296i	$-0.709407\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.99857	−	3.46163i	0.484725	−	0.839569i	−0.515121	−	0.857118i	$-0.672253\pi$
$17$	1.99857	−	3.46163i	0.484725	−	0.839569i	0.999846	+	0.0175487i	$0.00558621\pi$
$18$		0			0
$19$	1.24687	−	0.719882i	0.286052	−	0.165152i	−0.350108	−	0.936709i	$-0.613855\pi$
$19$	1.24687	−	0.719882i	0.286052	−	0.165152i	0.636160	+	0.771557i	$0.280522\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	5.66665i		−	1.18158i	−0.806826	−	0.590789i	$-0.798817\pi$
$23$		−	5.66665i		−	1.18158i	0.806826	−	0.590789i	$-0.201183\pi$
$24$		0			0
$25$	−1.71762			−0.343523
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.18486	−	2.41613i	0.777110	−	0.448665i	−0.0582952	−	0.998299i	$-0.518566\pi$
$29$	4.18486	−	2.41613i	0.777110	−	0.448665i	0.835405	+	0.549635i	$0.185233\pi$
$30$		0			0
$31$	−8.80648	+	5.08442i	−1.58169	+	0.913189i	−0.587077	+	0.809531i	$0.699722\pi$
$31$	−8.80648	+	5.08442i	−1.58169	+	0.913189i	−0.994613	+	0.103658i	$0.966945\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.06665	−	3.68407i	0.518358	−	0.622721i
$36$		0			0
$37$	−1.65567	−	2.86771i	−0.272191	−	0.471448i	0.697232	−	0.716846i	$-0.254415\pi$
$37$	−1.65567	−	2.86771i	−0.272191	−	0.471448i	−0.969423	+	0.245398i	$0.921082\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.10089	−	8.83499i	0.796624	−	1.37979i	−0.125178	−	0.992134i	$-0.539950\pi$
$41$	5.10089	−	8.83499i	0.796624	−	1.37979i	0.921803	−	0.387660i	$-0.126716\pi$
$42$		0			0
$43$	1.12248	+	1.94419i	0.171176	+	0.296486i	0.938831	−	0.344377i	$-0.111910\pi$
$43$	1.12248	+	1.94419i	0.171176	+	0.296486i	−0.767655	+	0.640863i	$0.778577\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.97092	+	10.3419i	−0.870948	+	1.50853i	−0.00993133	+	0.999951i	$0.503161\pi$
$47$	−5.97092	+	10.3419i	−0.870948	+	1.50853i	−0.861017	+	0.508576i	$0.830172\pi$
$48$		0			0
$49$	−1.26982	−	6.88386i	−0.181403	−	0.983409i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.97466	+	2.29477i	0.545962	+	0.315211i	0.747492	−	0.664271i	$-0.231258\pi$
$53$	3.97466	+	2.29477i	0.545962	+	0.315211i	−0.201530	+	0.979482i	$0.564591\pi$
$54$		0			0
$55$		−	0.463558i		−	0.0625061i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.55575	+	4.42670i	0.332731	+	0.576307i	0.983046	−	0.183358i	$-0.0586966\pi$
$59$	2.55575	+	4.42670i	0.332731	+	0.576307i	−0.650316	+	0.759664i	$0.725363\pi$
$60$		0			0
$61$	8.60220	+	4.96648i	1.10140	+	0.635893i	0.936588	−	0.350432i	$-0.113965\pi$
$61$	8.60220	+	4.96648i	1.10140	+	0.635893i	0.164811	+	0.986325i	$0.447299\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−10.4676	−	6.04346i	−1.29834	−	0.749598i
$66$		0			0
$67$	−0.962135	−	1.66647i	−0.117544	−	0.203591i	0.801250	−	0.598330i	$-0.204169\pi$
$67$	−0.962135	−	1.66647i	−0.117544	−	0.203591i	−0.918794	+	0.394738i	$0.870835\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			7.31241i			0.867823i	0.900955	+	0.433912i	$0.142867\pi$
$71$			7.31241i			0.867823i	−0.900955	+	0.433912i	$0.857133\pi$
$72$		0			0
$73$	−2.47807	−	1.43071i	−0.290036	−	0.167452i	0.347922	−	0.937523i	$-0.386887\pi$
$73$	−2.47807	−	1.43071i	−0.290036	−	0.167452i	−0.637958	+	0.770071i	$0.720221\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.520286	−	0.433090i	−0.0592921	−	0.0493552i
$78$		0			0
$79$	1.83153	−	3.17231i	0.206063	−	0.356912i	−0.744408	−	0.667725i	$-0.767268\pi$
$79$	1.83153	−	3.17231i	0.206063	−	0.356912i	0.950471	+	0.310813i	$0.100601\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.68261	−	4.64642i	−0.294455	−	0.510011i	0.680403	−	0.732838i	$-0.261805\pi$
$83$	−2.68261	−	4.64642i	−0.294455	−	0.510011i	−0.974858	+	0.222827i	$0.928471\pi$
$84$		0			0
$85$	3.62089	−	6.27156i	0.392740	−	0.680246i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.378446	+	0.655488i	0.0401152	+	0.0694815i	0.885386	−	0.464857i	$-0.153894\pi$
$89$	0.378446	+	0.655488i	0.0401152	+	0.0694815i	−0.845271	+	0.534338i	$0.820561\pi$
$90$		0			0
$91$	−16.5626	+	6.10230i	−1.73623	+	0.639695i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.25900	−	1.30424i	0.231769	−	0.133812i
$96$		0			0
$97$	4.21765	−	2.43506i	0.428237	−	0.247243i	−0.270358	−	0.962760i	$-0.587142\pi$
$97$	4.21765	−	2.43506i	0.428237	−	0.247243i	0.698595	+	0.715517i	$0.253809\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	16.4145			1.63330			0.816652	−	0.577131i	$-0.195828\pi$
$101$	16.4145			1.63330			0.816652	+	0.577131i	$0.195828\pi$
$102$		0			0
$103$		−	19.3989i		−	1.91143i	−0.294291	−	0.955716i	$-0.595084\pi$
$103$		−	19.3989i		−	1.91143i	0.294291	−	0.955716i	$-0.404916\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.47695	−	3.73947i	0.626150	−	0.361508i	−0.153109	−	0.988209i	$-0.548929\pi$
$107$	6.47695	−	3.73947i	0.626150	−	0.361508i	0.779260	+	0.626701i	$0.215595\pi$
$108$		0			0
$109$	4.26712	−	7.39087i	0.408716	−	0.707917i	−0.586030	−	0.810289i	$-0.699310\pi$
$109$	4.26712	−	7.39087i	0.408716	−	0.707917i	0.994746	+	0.102372i	$0.0326432\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.22966	−	0.709943i	−0.115676	−	0.0667858i	0.441045	−	0.897485i	$-0.354608\pi$
$113$	−1.22966	−	0.709943i	−0.115676	−	0.0667858i	−0.556722	+	0.830699i	$0.687941\pi$
$114$		0			0
$115$		−	10.2665i		−	0.957352i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.65614	−	9.92335i	−0.335158	−	0.909672i
$120$		0			0
$121$	10.9345			0.994049
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.1705			−1.08857
$126$		0			0
$127$	−5.17294			−0.459024			−0.229512	−	0.973306i	$-0.573713\pi$
$127$	−5.17294			−0.459024			−0.229512	+	0.973306i	$0.573713\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.36524			0.556133			0.278067	−	0.960562i	$-0.410306\pi$
$131$	6.36524			0.556133			0.278067	+	0.960562i	$0.410306\pi$
$132$		0			0
$133$	0.646686	−	3.75397i	0.0560748	−	0.325510i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	0.0486198i		−	0.00415387i	−0.999998	−	0.00207693i	$-0.999339\pi$
$137$		−	0.0486198i		−	0.00415387i	0.999998	−	0.00207693i	$-0.000661109\pi$
$138$		0			0
$139$	2.95962	+	1.70874i	0.251032	+	0.144933i	0.620237	−	0.784415i	$-0.287037\pi$
$139$	2.95962	+	1.70874i	0.251032	+	0.144933i	−0.369205	+	0.929348i	$0.620370\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.853493	+	1.47829i	−0.0713727	+	0.123621i
$144$		0			0
$145$	7.58186	−	4.37739i	0.629640	−	0.363523i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	9.89196i		−	0.810381i	−0.914232	−	0.405190i	$-0.867205\pi$
$149$		−	9.89196i		−	0.810381i	0.914232	−	0.405190i	$-0.132795\pi$
$150$		0			0
$151$	8.48564			0.690552			0.345276	−	0.938501i	$-0.387785\pi$
$151$	8.48564			0.690552			0.345276	+	0.938501i	$0.387785\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−15.9550	+	9.21163i	−1.28154	+	0.739896i
$156$		0			0
$157$	−16.0079	+	9.24219i	−1.27757	+	0.737607i	−0.976402	−	0.215963i	$-0.930711\pi$
$157$	−16.0079	+	9.24219i	−1.27757	+	0.737607i	−0.301171	+	0.953570i	$0.597378\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−11.5228	−	9.59169i	−0.908126	−	0.755931i
$162$		0			0
$163$	3.81360	+	6.60534i	0.298704	+	0.517370i	0.975840	−	0.218488i	$-0.0701124\pi$
$163$	3.81360	+	6.60534i	0.298704	+	0.517370i	−0.677136	+	0.735858i	$0.736779\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.86874	+	15.3611i	−0.686284	+	1.18868i	0.286748	+	0.958006i	$0.407426\pi$
$167$	−8.86874	+	15.3611i	−0.686284	+	1.18868i	−0.973032	+	0.230672i	$0.925908\pi$
$168$		0			0
$169$	15.7542	+	27.2870i	1.21186	+	2.09900i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.01266	−	12.1463i	0.533163	−	0.923465i	−0.466087	−	0.884739i	$-0.654337\pi$
$173$	7.01266	−	12.1463i	0.533163	−	0.923465i	0.999250	−	0.0387263i	$-0.0123300\pi$
$174$		0			0
$175$	−2.90734	+	3.49268i	−0.219774	+	0.264022i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	8.29501	+	4.78913i	0.619998	+	0.357956i	0.776868	−	0.629663i	$-0.216807\pi$
$179$	8.29501	+	4.78913i	0.619998	+	0.357956i	−0.156870	+	0.987619i	$0.550140\pi$
$180$		0			0
$181$			1.57861i			0.117337i	0.998278	+	0.0586687i	$0.0186856\pi$
$181$			1.57861i			0.117337i	−0.998278	+	0.0586687i	$0.981314\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.99964	−	5.19553i	−0.220538	−	0.381983i
$186$		0			0
$187$	−0.885707	−	0.511363i	−0.0647693	−	0.0373946i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	15.1037	+	8.72014i	1.09287	+	0.630967i	0.934338	−	0.356387i	$-0.115992\pi$
$191$	15.1037	+	8.72014i	1.09287	+	0.630967i	0.158529	+	0.987354i	$0.449325\pi$
$192$		0			0
$193$	−11.9263	−	20.6569i	−0.858472	−	1.48692i	−0.873386	−	0.487029i	$-0.838081\pi$
$193$	−11.9263	−	20.6569i	−0.858472	−	1.48692i	0.0149136	−	0.999889i	$-0.495253\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			19.1271i			1.36275i	0.731935	+	0.681374i	$0.238617\pi$
$197$			19.1271i			1.36275i	−0.731935	+	0.681374i	$0.761383\pi$
$198$		0			0
$199$	5.15196	+	2.97449i	0.365213	+	0.210856i	0.671365	−	0.741127i	$-0.265708\pi$
$199$	5.15196	+	2.97449i	0.365213	+	0.210856i	−0.306152	+	0.951983i	$0.599042\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.17047	−	12.5994i	0.152337	−	0.884304i
$204$		0			0
$205$	9.24145	−	16.0067i	0.645451	−	1.11795i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.184192	−	0.319030i	−0.0127408	−	0.0220678i
$210$		0			0
$211$	−5.86415	+	10.1570i	−0.403704	+	0.699237i	−0.994170	−	0.107826i	$-0.965611\pi$
$211$	−5.86415	+	10.1570i	−0.403704	+	0.699237i	0.590465	+	0.807063i	$0.298944\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.03363	+	3.52235i	0.138692	+	0.240222i
$216$		0			0
$217$	−4.56745	+	26.5137i	−0.310059	+	1.79987i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−23.0941	+	13.3334i	−1.55348	+	0.896902i
$222$		0			0
$223$	−16.0209	+	9.24969i	−1.07284	+	0.619405i	−0.928956	−	0.370189i	$-0.879293\pi$
$223$	−16.0209	+	9.24969i	−1.07284	+	0.619405i	−0.143885	+	0.989594i	$0.545960\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.677545			0.0449702			0.0224851	−	0.999747i	$-0.492842\pi$
$227$	0.677545			0.0449702			0.0224851	+	0.999747i	$0.492842\pi$
$228$		0			0
$229$		−	0.386469i		−	0.0255386i	−0.999918	−	0.0127693i	$-0.995935\pi$
$229$		−	0.386469i		−	0.0255386i	0.999918	−	0.0127693i	$-0.00406470\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.35520	−	1.93712i	0.219806	−	0.126905i	−0.386054	−	0.922476i	$-0.626162\pi$
$233$	3.35520	−	1.93712i	0.219806	−	0.126905i	0.605861	+	0.795571i	$0.292829\pi$
$234$		0			0
$235$	−10.8177	+	18.7368i	−0.705671	+	1.22226i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	9.97301	+	5.75792i	0.645100	+	0.372449i	0.786576	−	0.617493i	$-0.211852\pi$
$239$	9.97301	+	5.75792i	0.645100	+	0.372449i	−0.141476	+	0.989942i	$0.545185\pi$
$240$		0			0
$241$		−	11.7943i		−	0.759739i	−0.925040	−	0.379869i	$-0.875969\pi$
$241$		−	11.7943i		−	0.759739i	0.925040	−	0.379869i	$-0.124031\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.30057	−	12.4717i	−0.146978	−	0.796790i
$246$		0			0
$247$	−9.60533			−0.611173
$248$		0			0
$249$		0			0
$250$		0			0
$251$	9.76523			0.616376			0.308188	−	0.951326i	$-0.400277\pi$
$251$	9.76523			0.616376			0.308188	+	0.951326i	$0.400277\pi$
$252$		0			0
$253$	−1.44989			−0.0911539
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.1561			−0.883034			−0.441517	−	0.897253i	$-0.645560\pi$
$257$	−14.1561			−0.883034			−0.441517	+	0.897253i	$0.645560\pi$
$258$		0			0
$259$	−8.63382	−	1.48733i	−0.536479	−	0.0924180i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			10.2979i			0.634998i	0.948259	+	0.317499i	$0.102843\pi$
$263$			10.2979i			0.634998i	−0.948259	+	0.317499i	$0.897157\pi$
$264$		0			0
$265$	7.20104	+	4.15752i	0.442356	+	0.255395i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.95947	−	6.85801i	0.241413	−	0.418140i	−0.719704	−	0.694281i	$-0.755722\pi$
$269$	3.95947	−	6.85801i	0.241413	−	0.418140i	0.961117	+	0.276141i	$0.0890557\pi$
$270$		0			0
$271$	−9.45707	+	5.46004i	−0.574476	+	0.331674i	−0.758935	−	0.651166i	$-0.774280\pi$
$271$	−9.45707	+	5.46004i	−0.574476	+	0.331674i	0.184459	+	0.982840i	$0.440947\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			0.439477i			0.0265014i
$276$		0			0
$277$	12.8204			0.770304			0.385152	−	0.922853i	$-0.374149\pi$
$277$	12.8204			0.770304			0.385152	+	0.922853i	$0.374149\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	18.3380	−	10.5874i	1.09395	−	0.631593i	0.159326	−	0.987226i	$-0.449068\pi$
$281$	18.3380	−	10.5874i	1.09395	−	0.631593i	0.934626	+	0.355633i	$0.115735\pi$
$282$		0			0
$283$	22.2420	−	12.8415i	1.32215	−	0.763345i	0.338081	−	0.941117i	$-0.390222\pi$
$283$	22.2420	−	12.8415i	1.32215	−	0.763345i	0.984072	+	0.177772i	$0.0568890\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.33144	−	25.3270i	−0.550818	−	1.49501i
$288$		0			0
$289$	0.511404	+	0.885777i	0.0300826	+	0.0521046i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−14.4817	+	25.0831i	−0.846031	+	1.46537i	0.0386925	+	0.999251i	$0.487681\pi$
$293$	−14.4817	+	25.0831i	−0.846031	+	1.46537i	−0.884723	+	0.466117i	$0.845653\pi$
$294$		0			0
$295$	4.63035	+	8.02000i	0.269589	+	0.466942i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−18.9024	+	32.7399i	−1.09315	+	1.89340i
$300$		0			0
$301$	5.85337	+	1.00834i	0.337382	+	0.0581200i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	15.5849	+	8.99795i	0.892389	+	0.515221i
$306$		0			0
$307$			28.0634i			1.60167i	0.598888	+	0.800833i	$0.295609\pi$
$307$			28.0634i			1.60167i	−0.598888	+	0.800833i	$0.704391\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.95974	+	6.85847i	0.224536	+	0.388908i	0.956180	−	0.292779i	$-0.0945800\pi$
$311$	3.95974	+	6.85847i	0.224536	+	0.388908i	−0.731644	+	0.681687i	$0.761247\pi$
$312$		0			0
$313$	10.2043	+	5.89145i	0.576780	+	0.333004i	0.759853	−	0.650095i	$-0.225271\pi$
$313$	10.2043	+	5.89145i	0.576780	+	0.333004i	−0.183073	+	0.983099i	$0.558604\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	14.3671	+	8.29484i	0.806936	+	0.465884i	0.845891	−	0.533356i	$-0.179070\pi$
$317$	14.3671	+	8.29484i	0.806936	+	0.465884i	−0.0389550	+	0.999241i	$0.512403\pi$
$318$		0			0
$319$	−0.618202	−	1.07076i	−0.0346126	−	0.0599509i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	5.75495i		−	0.320214i
$324$		0			0
$325$	9.92379	+	5.72950i	0.550473	+	0.317816i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	10.9231	+	29.6469i	0.602208	+	1.63449i
$330$		0			0
$331$	−2.35856	+	4.08515i	−0.129638	+	0.224540i	−0.923536	−	0.383511i	$-0.874715\pi$
$331$	−2.35856	+	4.08515i	−0.129638	+	0.224540i	0.793898	+	0.608051i	$0.208048\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.74313	−	3.01920i	−0.0952376	−	0.164956i
$336$		0			0
$337$	1.79195	−	3.10375i	0.0976138	−	0.169072i	−0.813083	−	0.582148i	$-0.802212\pi$
$337$	1.79195	−	3.10375i	0.0976138	−	0.169072i	0.910697	+	0.413076i	$0.135546\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.30092	+	2.25326i	0.0704488	+	0.122021i
$342$		0			0
$343$	−16.1473	−	9.06992i	−0.871874	−	0.489729i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	15.7201	−	9.07599i	0.843898	−	0.487225i	−0.0146894	−	0.999892i	$-0.504676\pi$
$347$	15.7201	−	9.07599i	0.843898	−	0.487225i	0.858587	+	0.512667i	$0.171343\pi$
$348$		0			0
$349$	−28.1608	+	16.2586i	−1.50741	+	0.870304i	−0.507448	+	0.861683i	$0.669411\pi$
$349$	−28.1608	+	16.2586i	−1.50741	+	0.870304i	−0.999963	+	0.00862123i	$0.997256\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.212061			−0.0112869			−0.00564343	−	0.999984i	$-0.501796\pi$
$353$	−0.212061			−0.0112869			−0.00564343	+	0.999984i	$0.501796\pi$
$354$		0			0
$355$			13.2481i			0.703138i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−28.7469	+	16.5970i	−1.51720	+	0.875958i	−0.517408	+	0.855739i	$0.673103\pi$
$359$	−28.7469	+	16.5970i	−1.51720	+	0.875958i	−0.999796	+	0.0202187i	$0.993564\pi$
$360$		0			0
$361$	−8.46354	+	14.6593i	−0.445449	+	0.771541i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.48961	−	2.59208i	−0.234997	−	0.135675i
$366$		0			0
$367$			0.231688i			0.0120940i	0.999982	+	0.00604701i	$0.00192484\pi$
$367$			0.231688i			0.0120940i	−0.999982	+	0.00604701i	$0.998075\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	11.3941	−	4.19801i	0.591550	−	0.217950i
$372$		0			0
$373$	17.6955			0.916239			0.458119	−	0.888891i	$-0.348523\pi$
$373$	17.6955			0.916239			0.458119	+	0.888891i	$0.348523\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−32.2383			−1.66035
$378$		0			0
$379$	28.9131			1.48516			0.742582	−	0.669755i	$-0.233601\pi$
$379$	28.9131			1.48516			0.742582	+	0.669755i	$0.233601\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.35585			0.120378			0.0601891	−	0.998187i	$-0.480830\pi$
$383$	2.35585			0.120378			0.0601891	+	0.998187i	$0.480830\pi$
$384$		0			0
$385$	−0.942621	−	0.784645i	−0.0480404	−	0.0399892i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			11.1007i			0.562827i	0.959587	+	0.281413i	$0.0908032\pi$
$389$			11.1007i			0.562827i	−0.959587	+	0.281413i	$0.909197\pi$
$390$		0			0
$391$	−19.6158	−	11.3252i	−0.992016	−	0.572740i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	3.31825	−	5.74738i	0.166959	−	0.289182i
$396$		0			0
$397$	−4.59168	+	2.65101i	−0.230450	+	0.133050i	−0.610780	−	0.791801i	$-0.709144\pi$
$397$	−4.59168	+	2.65101i	−0.230450	+	0.133050i	0.380330	+	0.924851i	$0.375810\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	32.8070i		−	1.63830i	−0.573578	−	0.819151i	$-0.694445\pi$
$401$		−	32.8070i		−	1.63830i	0.573578	−	0.819151i	$-0.305555\pi$
$402$		0			0
$403$	67.8410			3.37940
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.733744	+	0.423627i	−0.0363703	+	0.0209984i
$408$		0			0
$409$	−13.1858	+	7.61284i	−0.651997	+	0.376431i	−0.789221	−	0.614109i	$-0.789515\pi$
$409$	−13.1858	+	7.61284i	−0.651997	+	0.376431i	0.137224	+	0.990540i	$0.456182\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	13.3275	+	2.29589i	0.655802	+	0.112973i
$414$		0			0
$415$	−4.86018	−	8.41808i	−0.238577	−	0.413227i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.32224	+	10.9504i	−0.308861	+	0.534964i	−0.978114	−	0.208072i	$-0.933281\pi$
$419$	−6.32224	+	10.9504i	−0.308861	+	0.534964i	0.669252	+	0.743035i	$0.266615\pi$
$420$		0			0
$421$	−14.4841	−	25.0872i	−0.705911	−	1.22267i	−0.966362	−	0.257187i	$-0.917204\pi$
$421$	−14.4841	−	25.0872i	−0.705911	−	1.22267i	0.260451	−	0.965487i	$-0.416129\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.43279	+	5.94576i	−0.166515	+	0.288412i
$426$		0			0
$427$	24.6597	−	9.08557i	1.19337	−	0.439682i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−31.6662	−	18.2825i	−1.52531	−	0.880638i	−0.999550	−	0.0300048i	$-0.990448\pi$
$431$	−31.6662	−	18.2825i	−1.52531	−	0.880638i	−0.525760	−	0.850633i	$-0.676219\pi$
$432$		0			0
$433$			29.3243i			1.40924i	0.709586	+	0.704619i	$0.248882\pi$
$433$			29.3243i			1.40924i	−0.709586	+	0.704619i	$0.751118\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.07932	−	7.06559i	−0.195140	−	0.337993i
$438$		0			0
$439$	−14.3630	−	8.29248i	−0.685508	−	0.395778i	0.116419	−	0.993200i	$-0.462859\pi$
$439$	−14.3630	−	8.29248i	−0.685508	−	0.395778i	−0.801927	+	0.597422i	$0.796192\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	13.2842	+	7.66961i	0.631149	+	0.364394i	0.781197	−	0.624285i	$-0.214609\pi$
$443$	13.2842	+	7.66961i	0.631149	+	0.364394i	−0.150048	+	0.988679i	$0.547943\pi$
$444$		0			0
$445$	0.685644	+	1.18757i	0.0325026	+	0.0562962i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			22.9580i			1.08346i	0.840554	+	0.541728i	$0.182230\pi$
$449$			22.9580i			1.08346i	−0.840554	+	0.541728i	$0.817770\pi$
$450$		0			0
$451$	−2.26056	−	1.30513i	−0.106445	−	0.0614563i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−30.0071	+	11.0558i	−1.40675	+	0.518302i
$456$		0			0
$457$	10.9126	−	18.9011i	0.510468	−	0.884156i	−0.489459	−	0.872026i	$-0.662806\pi$
$457$	10.9126	−	18.9011i	0.510468	−	0.884156i	0.999926	−	0.0121294i	$-0.00386099\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−16.9154	−	29.2984i	−0.787830	−	1.36456i	−0.927294	−	0.374335i	$-0.877871\pi$
$461$	−16.9154	−	29.2984i	−0.787830	−	1.36456i	0.139463	−	0.990227i	$-0.455462\pi$
$462$		0			0
$463$	−1.82082	+	3.15375i	−0.0846206	+	0.146567i	−0.905229	−	0.424923i	$-0.860301\pi$
$463$	−1.82082	+	3.15375i	−0.0846206	+	0.146567i	0.820609	+	0.571490i	$0.193634\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−12.1438	−	21.0337i	−0.561948	−	0.973322i	−0.997326	−	0.0730749i	$-0.976719\pi$
$467$	−12.1438	−	21.0337i	−0.561948	−	0.973322i	0.435378	−	0.900248i	$-0.356615\pi$
$468$		0			0
$469$	−5.01724	−	0.864307i	−0.231675	−	0.0399100i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.497447	−	0.287201i	0.0228727	−	0.0132055i
$474$		0			0
$475$	−2.14165	+	1.23648i	−0.0982657	+	0.0567337i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−30.2200			−1.38079			−0.690393	−	0.723434i	$-0.742563\pi$
$479$	−30.2200			−1.38079			−0.690393	+	0.723434i	$0.742563\pi$
$480$		0			0
$481$			22.0915i			1.00729i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.64126	−	4.41169i	0.346972	−	0.200324i
$486$		0			0
$487$	2.84999	−	4.93634i	0.129146	−	0.223687i	−0.794200	−	0.607656i	$-0.792110\pi$
$487$	2.84999	−	4.93634i	0.129146	−	0.223687i	0.923346	+	0.383969i	$0.125443\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	28.3275	+	16.3549i	1.27840	+	0.738086i	0.976555	−	0.215270i	$-0.0690631\pi$
$491$	28.3275	+	16.3549i	1.27840	+	0.738086i	0.301848	+	0.953356i	$0.402396\pi$
$492$		0			0
$493$		−	19.3153i		−	0.869916i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	14.8694	+	12.3774i	0.666984	+	0.555202i
$498$		0			0
$499$	7.47286			0.334531			0.167266	−	0.985912i	$-0.446506\pi$
$499$	7.47286			0.334531			0.167266	+	0.985912i	$0.446506\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−29.2765			−1.30537			−0.652686	−	0.757628i	$-0.726358\pi$
$503$	−29.2765			−1.30537			−0.652686	+	0.757628i	$0.726358\pi$
$504$		0			0
$505$	29.7387			1.32336
$506$		0			0
$507$		0			0
$508$		0			0
$509$	19.1385			0.848299			0.424150	−	0.905592i	$-0.360573\pi$
$509$	19.1385			0.848299			0.424150	+	0.905592i	$0.360573\pi$
$510$		0			0
$511$	−7.10381	+	2.61732i	−0.314254	+	0.115783i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	35.1457i		−	1.54870i
$516$		0			0
$517$	2.64613	+	1.52774i	0.116377	+	0.0671901i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−12.0228	+	20.8241i	−0.526727	+	0.912318i	0.472788	+	0.881176i	$0.343248\pi$
$521$	−12.0228	+	20.8241i	−0.526727	+	0.912318i	−0.999515	+	0.0311420i	$0.990086\pi$
$522$		0			0
$523$	22.2119	−	12.8241i	0.971259	−	0.560757i	0.0716394	−	0.997431i	$-0.477177\pi$
$523$	22.2119	−	12.8241i	0.971259	−	0.560757i	0.899620	+	0.436674i	$0.143844\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			40.6464i			1.77058i
$528$		0			0
$529$	−9.11087			−0.396125
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−58.9423	+	34.0303i	−2.55307	+	1.47402i
$534$		0			0
$535$	11.7345	−	6.77493i	0.507327	−	0.292906i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.76133	+	0.324901i	−0.0758660	+	0.0139945i
$540$		0			0
$541$	−10.4700	−	18.1346i	−0.450141	−	0.779667i	0.548254	−	0.836312i	$-0.315293\pi$
$541$	−10.4700	−	18.1346i	−0.450141	−	0.779667i	−0.998394	+	0.0566455i	$0.981960\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	7.73089	−	13.3903i	0.331155	−	0.573578i
$546$		0			0
$547$	6.53210	+	11.3139i	0.279292	+	0.483748i	0.971209	−	0.238229i	$-0.0765668\pi$
$547$	6.53210	+	11.3139i	0.279292	+	0.483748i	−0.691917	+	0.721977i	$0.743234\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.47866	−	6.02522i	0.148196	−	0.256683i
$552$		0			0
$553$	−3.35056	−	9.09395i	−0.142480	−	0.386714i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	32.5390	+	18.7864i	1.37872	+	0.796006i	0.992006	−	0.126193i	$-0.0402757\pi$
$557$	32.5390	+	18.7864i	1.37872	+	0.796006i	0.386717	+	0.922198i	$0.373609\pi$
$558$		0			0
$559$		−	14.9771i		−	0.633464i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−5.53671	−	9.58986i	−0.233344	−	0.404164i	0.725446	−	0.688279i	$-0.241634\pi$
$563$	−5.53671	−	9.58986i	−0.233344	−	0.404164i	−0.958790	+	0.284115i	$0.908300\pi$
$564$		0			0
$565$	−2.22781	−	1.28623i	−0.0937248	−	0.0541120i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	18.5956	+	10.7362i	0.779570	+	0.450085i	0.836278	−	0.548306i	$-0.184727\pi$
$569$	18.5956	+	10.7362i	0.779570	+	0.450085i	−0.0567078	+	0.998391i	$0.518060\pi$
$570$		0			0
$571$	7.45689	+	12.9157i	0.312061	+	0.540506i	0.978808	−	0.204778i	$-0.0656473\pi$
$571$	7.45689	+	12.9157i	0.312061	+	0.540506i	−0.666747	+	0.745284i	$0.732314\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			9.73313i			0.405899i
$576$		0			0
$577$	−28.0634	−	16.2024i	−1.16829	−	0.674515i	−0.215017	−	0.976610i	$-0.568981\pi$
$577$	−28.0634	−	16.2024i	−1.16829	−	0.674515i	−0.953278	+	0.302095i	$0.902314\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−13.9890	−	2.40985i	−0.580362	−	0.0999774i
$582$		0			0
$583$	0.587150	−	1.01697i	0.0243173	−	0.0421188i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.88731	−	17.1253i	−0.408093	−	0.706838i	0.586583	−	0.809889i	$-0.300473\pi$
$587$	−9.88731	−	17.1253i	−0.408093	−	0.706838i	−0.994676	+	0.103051i	$0.967139\pi$
$588$		0			0
$589$	−7.32037	+	12.6793i	−0.301631	+	0.522440i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	4.41904	+	7.65401i	0.181468	+	0.314312i	0.942381	−	0.334542i	$-0.108582\pi$
$593$	4.41904	+	7.65401i	0.181468	+	0.314312i	−0.760912	+	0.648855i	$0.775248\pi$
$594$		0			0
$595$	−6.62396	−	17.9785i	−0.271556	−	0.737046i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	32.7862	−	18.9291i	1.33961	−	0.773423i	0.352859	−	0.935676i	$-0.385209\pi$
$599$	32.7862	−	18.9291i	1.33961	−	0.773423i	0.986749	+	0.162253i	$0.0518761\pi$
$600$		0			0
$601$	−30.5662	+	17.6474i	−1.24682	+	0.719853i	−0.970474	−	0.241205i	$-0.922457\pi$
$601$	−30.5662	+	17.6474i	−1.24682	+	0.719853i	−0.276347	+	0.961058i	$0.589124\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	19.8105			0.805410
$606$		0			0
$607$		−	7.36587i		−	0.298971i	−0.988764	−	0.149486i	$-0.952238\pi$
$607$		−	7.36587i		−	0.298971i	0.988764	−	0.149486i	$-0.0477618\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	68.9958	−	39.8347i	2.79127	−	1.61154i
$612$		0			0
$613$	−9.39378	+	16.2705i	−0.379411	+	0.657159i	−0.990977	−	0.134034i	$-0.957207\pi$
$613$	−9.39378	+	16.2705i	−0.379411	+	0.657159i	0.611566	+	0.791194i	$0.290540\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.17209	−	1.83141i	−0.127703	−	0.0737296i	0.434787	−	0.900533i	$-0.356824\pi$
$617$	−3.17209	−	1.83141i	−0.127703	−	0.0737296i	−0.562491	+	0.826804i	$0.690157\pi$
$618$		0			0
$619$		−	4.61969i		−	0.185681i	−0.995681	−	0.0928405i	$-0.970405\pi$
$619$		−	4.61969i		−	0.185681i	0.995681	−	0.0928405i	$-0.0295947\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.97348	+	0.339966i	0.0790658	+	0.0136205i
$624$		0			0
$625$	−13.4617			−0.538468
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−13.2359			−0.527751
$630$		0			0
$631$	40.5302			1.61348			0.806740	−	0.590906i	$-0.201230\pi$
$631$	40.5302			1.61348			0.806740	+	0.590906i	$0.201230\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−9.37200			−0.371916
$636$		0			0
$637$	−15.6261	+	44.0083i	−0.619130	+	1.74367i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			15.6234i			0.617088i	0.951210	+	0.308544i	$0.0998416\pi$
$641$			15.6234i			0.617088i	−0.951210	+	0.308544i	$0.900158\pi$
$642$		0			0
$643$	13.9719	+	8.06670i	0.550999	+	0.318120i	0.749525	−	0.661976i	$-0.230282\pi$
$643$	13.9719	+	8.06670i	0.550999	+	0.318120i	−0.198526	+	0.980096i	$0.563615\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	17.2365	−	29.8545i	0.677637	−	1.17370i	−0.298054	−	0.954549i	$-0.596337\pi$
$647$	17.2365	−	29.8545i	0.677637	−	1.17370i	0.975691	−	0.219152i	$-0.0703292\pi$
$648$		0			0
$649$	1.13263	−	0.653926i	0.0444597	−	0.0256688i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	12.8990i		−	0.504777i	−0.967626	−	0.252388i	$-0.918784\pi$
$653$		−	12.8990i		−	0.504777i	0.967626	−	0.252388i	$-0.0812161\pi$
$654$		0			0
$655$	11.5321			0.450597
$656$		0			0
$657$		0			0
$658$		0			0
$659$	9.60396	−	5.54485i	0.374117	−	0.215997i	−0.301138	−	0.953580i	$-0.597367\pi$
$659$	9.60396	−	5.54485i	0.374117	−	0.215997i	0.675256	+	0.737584i	$0.264033\pi$
$660$		0			0
$661$	4.35683	−	2.51541i	0.169461	−	0.0978383i	−0.412871	−	0.910790i	$-0.635474\pi$
$661$	4.35683	−	2.51541i	0.169461	−	0.0978383i	0.582332	+	0.812951i	$0.302141\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.17162	−	6.80119i	0.0454336	−	0.263739i
$666$		0			0
$667$	−13.6914	−	23.7141i	−0.530132	−	0.918215i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.27074	−	2.20099i	0.0490566	−	0.0849685i
$672$		0			0
$673$	−2.50713	−	4.34248i	−0.0966428	−	0.167390i	0.813650	−	0.581355i	$-0.197477\pi$
$673$	−2.50713	−	4.34248i	−0.0966428	−	0.167390i	−0.910293	+	0.413964i	$0.864144\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.7728	−	32.5155i	0.721498	−	1.24967i	−0.238902	−	0.971044i	$-0.576787\pi$
$677$	18.7728	−	32.5155i	0.721498	−	1.24967i	0.960399	−	0.278627i	$-0.0898793\pi$
$678$		0			0
$679$	2.18747	−	12.6981i	0.0839474	−	0.487308i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	20.4810	+	11.8247i	0.783684	+	0.452460i	0.837734	−	0.546078i	$-0.183880\pi$
$683$	20.4810	+	11.8247i	0.783684	+	0.452460i	−0.0540503	+	0.998538i	$0.517213\pi$
$684$		0			0
$685$		−	0.0880862i		−	0.00336560i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−15.3095	−	26.5168i	−0.583245	−	1.01021i
$690$		0			0
$691$	−20.8588	−	12.0429i	−0.793508	−	0.458132i	0.0476881	−	0.998862i	$-0.484815\pi$
$691$	−20.8588	−	12.0429i	−0.793508	−	0.458132i	−0.841196	+	0.540730i	$0.818148\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	5.36205	+	3.09578i	0.203394	+	0.117430i
$696$		0			0
$697$	−20.3890	−	35.3148i	−0.772288	−	1.33764i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			15.6261i			0.590190i	0.955468	+	0.295095i	$0.0953513\pi$
$701$			15.6261i			0.590190i	−0.955468	+	0.295095i	$0.904649\pi$
$702$		0			0
$703$	−4.12883	−	2.38378i	−0.155722	−	0.0899059i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	27.7841	−	33.3780i	1.04493	−	1.25531i
$708$		0			0
$709$	−7.20504	+	12.4795i	−0.270591	+	0.468678i	−0.969013	−	0.247008i	$-0.920552\pi$
$709$	−7.20504	+	12.4795i	−0.270591	+	0.468678i	0.698422	+	0.715686i	$0.253886\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	28.8116	+	49.9032i	1.07900	+	1.86889i
$714$		0			0
$715$	−1.54630	+	2.67828i	−0.0578285	+	0.100162i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−7.49770	−	12.9864i	−0.279617	−	0.484311i	0.691673	−	0.722211i	$-0.256874\pi$
$719$	−7.49770	−	12.9864i	−0.279617	−	0.484311i	−0.971290	+	0.237900i	$0.923541\pi$
$720$		0			0
$721$	−39.4467	−	32.8357i	−1.46907	−	1.22287i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−7.18800	+	4.14999i	−0.266955	+	0.154127i
$726$		0			0
$727$	−17.9806	+	10.3811i	−0.666862	+	0.385013i	−0.794887	−	0.606758i	$-0.792470\pi$
$727$	−17.9806	+	10.3811i	−0.666862	+	0.385013i	0.128025	+	0.991771i	$0.459136\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	8.97341			0.331893
$732$		0			0
$733$			24.4072i			0.901502i	0.892650	+	0.450751i	$0.148844\pi$
$733$			24.4072i			0.901502i	−0.892650	+	0.450751i	$0.851156\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.426389	+	0.246176i	−0.0157062	+	0.00906800i
$738$		0			0
$739$	0.295124	−	0.511169i	0.0108563	−	0.0188037i	−0.860546	−	0.509372i	$-0.829878\pi$
$739$	0.295124	−	0.511169i	0.0108563	−	0.0188037i	0.871403	+	0.490569i	$0.163211\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−33.2573	−	19.2011i	−1.22009	−	0.704421i	−0.255155	−	0.966900i	$-0.582127\pi$
$743$	−33.2573	−	19.2011i	−1.22009	−	0.704421i	−0.964938	+	0.262479i	$0.915460\pi$
$744$		0			0
$745$		−	17.9216i		−	0.656597i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.35925	−	19.5002i	0.122744	−	0.712521i
$750$		0			0
$751$	−45.7173			−1.66825			−0.834124	−	0.551577i	$-0.814026\pi$
$751$	−45.7173			−1.66825			−0.834124	+	0.551577i	$0.814026\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	15.3737			0.559507
$756$		0			0
$757$	−7.42071			−0.269710			−0.134855	−	0.990865i	$-0.543057\pi$
$757$	−7.42071			−0.269710			−0.134855	+	0.990865i	$0.543057\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	47.3041			1.71477			0.857387	−	0.514672i	$-0.172086\pi$
$761$	47.3041			1.71477			0.857387	+	0.514672i	$0.172086\pi$
$762$		0			0
$763$	−7.80617	−	21.1872i	−0.282602	−	0.767028i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	34.1012i		−	1.23132i
$768$		0			0
$769$	42.3251	+	24.4364i	1.52628	+	0.881199i	0.999513	+	0.0311905i	$0.00992986\pi$
$769$	42.3251	+	24.4364i	1.52628	+	0.881199i	0.526769	+	0.850009i	$0.323403\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	11.4374	−	19.8101i	0.411374	−	0.712521i	−0.583666	−	0.811994i	$-0.698382\pi$
$773$	11.4374	−	19.8101i	0.411374	−	0.712521i	0.995040	+	0.0994731i	$0.0317157\pi$
$774$		0			0
$775$	15.1262	−	8.73309i	0.543348	−	0.313702i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	14.6882i		−	0.526258i
$780$		0			0
$781$	1.87098			0.0669490
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−29.0021	+	16.7444i	−1.03513	+	0.597633i
$786$		0			0
$787$	−22.8346	+	13.1836i	−0.813966	+	0.469943i	−0.848331	−	0.529466i	$-0.822392\pi$
$787$	−22.8346	+	13.1836i	−0.813966	+	0.469943i	0.0343656	+	0.999409i	$0.489059\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−3.52502	+	1.29875i	−0.125335	+	0.0461783i
$792$		0			0
$793$	−33.1337	−	57.3892i	−1.17661	−	2.03795i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	8.16906	−	14.1492i	0.289363	−	0.501191i	−0.684295	−	0.729205i	$-0.739890\pi$
$797$	8.16906	−	14.1492i	0.289363	−	0.501191i	0.973658	+	0.228014i	$0.0732232\pi$
$798$		0			0
$799$	23.8667	+	41.3383i	0.844342	+	1.46244i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.366068	+	0.634049i	−0.0129183	+	0.0223751i
$804$		0			0
$805$	−20.8763	−	17.3776i	−0.735793	−	0.612480i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−11.1321	−	6.42711i	−0.391383	−	0.225965i	0.291376	−	0.956609i	$-0.405887\pi$
$809$	−11.1321	−	6.42711i	−0.391383	−	0.225965i	−0.682759	+	0.730643i	$0.739220\pi$
$810$		0			0
$811$		−	38.3887i		−	1.34801i	−0.738727	−	0.674005i	$-0.764573\pi$
$811$		−	38.3887i		−	1.34801i	0.738727	−	0.674005i	$-0.235427\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.90922	+	11.9671i	0.242020	+	0.419190i
$816$		0			0
$817$	2.79917	+	1.61610i	0.0979306	+	0.0565402i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−19.2629	−	11.1215i	−0.672282	−	0.388142i	0.124659	−	0.992200i	$-0.460216\pi$
$821$	−19.2629	−	11.1215i	−0.672282	−	0.388142i	−0.796941	+	0.604058i	$0.793550\pi$
$822$		0			0
$823$	−17.5785	−	30.4469i	−0.612748	−	1.06131i	−0.990775	−	0.135516i	$-0.956731\pi$
$823$	−17.5785	−	30.4469i	−0.612748	−	1.06131i	0.378027	−	0.925795i	$-0.376603\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			42.3779i			1.47362i	0.676098	+	0.736812i	$0.263670\pi$
$827$			42.3779i			1.47362i	−0.676098	+	0.736812i	$0.736330\pi$
$828$		0			0
$829$	46.8574	+	27.0531i	1.62742	+	0.939593i	0.984858	+	0.173362i	$0.0554630\pi$
$829$	46.8574	+	27.0531i	1.62742	+	0.939593i	0.642565	+	0.766231i	$0.277870\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−26.3672	−	9.36227i	−0.913570	−	0.324383i
$834$		0			0
$835$	−16.0678	+	27.8303i	−0.556049	+	0.963106i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−20.1561	−	34.9114i	−0.695866	−	1.20528i	−0.969888	−	0.243552i	$-0.921687\pi$
$839$	−20.1561	−	34.9114i	−0.695866	−	1.20528i	0.274022	−	0.961724i	$-0.411646\pi$
$840$		0			0
$841$	−2.82461	+	4.89236i	−0.0974002	+	0.168702i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	28.5424	+	49.4369i	0.981888	+	1.70068i
$846$		0			0
$847$	18.5084	−	22.2348i	0.635957	−	0.763997i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−16.2503	+	9.38211i	−0.557053	+	0.321614i
$852$		0			0
$853$	−8.81155	+	5.08735i	−0.301702	+	0.174188i	−0.643207	−	0.765692i	$-0.722397\pi$
$853$	−8.81155	+	5.08735i	−0.301702	+	0.174188i	0.341505	+	0.939880i	$0.389063\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−14.4428			−0.493357			−0.246679	−	0.969097i	$-0.579339\pi$
$857$	−14.4428			−0.493357			−0.246679	+	0.969097i	$0.579339\pi$
$858$		0			0
$859$			17.3135i			0.590728i	0.955385	+	0.295364i	$0.0954409\pi$
$859$			17.3135i			0.590728i	−0.955385	+	0.295364i	$0.904559\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	24.1380	−	13.9361i	0.821667	−	0.474390i	−0.0293239	−	0.999570i	$-0.509335\pi$
$863$	24.1380	−	13.9361i	0.821667	−	0.474390i	0.850991	+	0.525180i	$0.176002\pi$
$864$		0			0
$865$	12.7051	−	22.0059i	0.431986	−	0.748221i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.811679	−	0.468623i	−0.0275343	−	0.0158970i
$870$		0			0
$871$			12.8377i			0.434988i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−20.6006	+	24.7482i	−0.696426	+	0.836640i
$876$		0			0
$877$	10.3087			0.348099			0.174049	−	0.984737i	$-0.444315\pi$
$877$	10.3087			0.348099			0.174049	+	0.984737i	$0.444315\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	2.48707			0.0837914			0.0418957	−	0.999122i	$-0.486660\pi$
$881$	2.48707			0.0837914			0.0418957	+	0.999122i	$0.486660\pi$
$882$		0			0
$883$	7.98895			0.268850			0.134425	−	0.990924i	$-0.457081\pi$
$883$	7.98895			0.268850			0.134425	+	0.990924i	$0.457081\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.61445			0.0542078			0.0271039	−	0.999633i	$-0.491371\pi$
$887$	1.61445			0.0542078			0.0271039	+	0.999633i	$0.491371\pi$
$888$		0			0
$889$	−8.75602	+	10.5189i	−0.293668	+	0.352793i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			17.1934i			0.575357i
$894$		0			0
$895$	15.0284	+	8.67663i	0.502343	+	0.290028i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−24.5693	+	42.5552i	−0.819431	+	1.41930i
$900$		0			0
$901$	15.8873	−	9.17255i	0.529283	−	0.305582i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			2.86003i			0.0950706i
$906$		0			0
$907$	1.61913			0.0537623			0.0268812	−	0.999639i	$-0.491442\pi$
$907$	1.61913			0.0537623			0.0268812	+	0.999639i	$0.491442\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	20.1759	−	11.6485i	0.668456	−	0.385933i	−0.127035	−	0.991898i	$-0.540546\pi$
$911$	20.1759	−	11.6485i	0.668456	−	0.385933i	0.795492	+	0.605965i	$0.207213\pi$
$912$		0			0
$913$	−1.18885	+	0.686384i	−0.0393453	+	0.0227160i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	10.7742	−	12.9434i	0.355794	−	0.427428i
$918$		0			0
$919$	−0.928631	−	1.60844i	−0.0306327	−	0.0530574i	0.850303	−	0.526294i	$-0.176419\pi$
$919$	−0.928631	−	1.60844i	−0.0306327	−	0.0530574i	−0.880935	+	0.473237i	$0.843086\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	24.3922	−	42.2485i	0.802879	−	1.39063i
$924$		0			0
$925$	2.84381	+	4.92562i	0.0935039	+	0.161954i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	23.0332	−	39.8947i	0.755695	−	1.30890i	−0.189332	−	0.981913i	$-0.560632\pi$
$929$	23.0332	−	39.8947i	0.755695	−	1.30890i	0.945028	−	0.326990i	$-0.106034\pi$
$930$		0			0
$931$	−6.53887	−	7.66918i	−0.214303	−	0.251347i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.60467	−	0.926455i	−0.0524782	−	0.0302983i
$936$		0			0
$937$		−	19.2806i		−	0.629871i	−0.949113	−	0.314935i	$-0.898017\pi$
$937$		−	19.2806i		−	0.629871i	0.949113	−	0.314935i	$-0.101983\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−8.31298	−	14.3985i	−0.270995	−	0.469378i	0.698122	−	0.715979i	$-0.254019\pi$
$941$	−8.31298	−	14.3985i	−0.270995	−	0.469378i	−0.969117	+	0.246601i	$0.920686\pi$
$942$		0			0
$943$	−50.0648	−	28.9049i	−1.63033	−	0.941273i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10.8861	+	6.28511i	0.353751	+	0.204238i	0.666336	−	0.745651i	$-0.267862\pi$
$947$	10.8861	+	6.28511i	0.353751	+	0.204238i	−0.312585	+	0.949890i	$0.601195\pi$
$948$		0			0
$949$	9.54495	+	16.5323i	0.309842	+	0.536662i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	47.3870i		−	1.53502i	−0.641040	−	0.767508i	$-0.721497\pi$
$953$		−	47.3870i		−	1.53502i	0.641040	−	0.767508i	$-0.278503\pi$
$954$		0			0
$955$	27.3639	+	15.7986i	0.885476	+	0.511230i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.0988658	−	0.0822967i	−0.00319254	−	0.00265750i
$960$		0			0
$961$	36.2027	−	62.7049i	1.16783	−	2.02274i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−21.6073	−	37.4249i	−0.695562	−	1.20475i
$966$		0			0
$967$	−11.6171	+	20.1215i	−0.373582	+	0.647063i	−0.990114	−	0.140267i	$-0.955204\pi$
$967$	−11.6171	+	20.1215i	−0.373582	+	0.647063i	0.616532	+	0.787330i	$0.288537\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−21.1024	−	36.5504i	−0.677208	−	1.17296i	−0.975818	−	0.218583i	$-0.929856\pi$
$971$	−21.1024	−	36.5504i	−0.677208	−	1.17296i	0.298610	−	0.954375i	$-0.403477\pi$
$972$		0			0
$973$	8.48426	−	3.12593i	0.271993	−	0.100213i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	25.7568	−	14.8707i	0.824031	−	0.475755i	−0.0277732	−	0.999614i	$-0.508842\pi$
$977$	25.7568	−	14.8707i	0.824031	−	0.475755i	0.851805	+	0.523859i	$0.175508\pi$
$978$		0			0
$979$	0.167716	−	0.0968307i	0.00536022	−	0.00309472i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	17.5969			0.561253			0.280626	−	0.959817i	$-0.409458\pi$
$983$	17.5969			0.561253			0.280626	+	0.959817i	$0.409458\pi$
$984$		0			0
$985$			34.6532i			1.10414i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	11.0170	−	6.36067i	0.350321	−	0.202258i
$990$		0			0
$991$	8.84717	−	15.3238i	0.281040	−	0.486775i	−0.690601	−	0.723236i	$-0.742654\pi$
$991$	8.84717	−	15.3238i	0.281040	−	0.486775i	0.971641	+	0.236461i	$0.0759874\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	9.33399	+	5.38898i	0.295907	+	0.170842i
$996$		0			0
$997$		−	36.4807i		−	1.15535i	−0.816265	−	0.577677i	$-0.803959\pi$
$997$		−	36.4807i		−	1.15535i	0.816265	−	0.577677i	$-0.196041\pi$
$998$		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.17.19		48
3.2	odd	2		504.2.cx.a.185.5	yes	48
4.3	odd	2		3024.2.df.e.17.19		48
7.5	odd	6		1512.2.bs.a.1097.19		48
9.2	odd	6		1512.2.bs.a.521.19		48
9.7	even	3		504.2.bs.a.353.4	yes	48
12.11	even	2		1008.2.df.e.689.20		48
21.5	even	6		504.2.bs.a.257.4	✓	48
28.19	even	6		3024.2.ca.e.2609.19		48
36.7	odd	6		1008.2.ca.e.353.21		48
36.11	even	6		3024.2.ca.e.2033.19		48
63.47	even	6	inner	1512.2.cx.a.89.19		48
63.61	odd	6		504.2.cx.a.425.5	yes	48
84.47	odd	6		1008.2.ca.e.257.21		48
252.47	odd	6		3024.2.df.e.1601.19		48
252.187	even	6		1008.2.df.e.929.20		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.4	✓	48	21.5	even	6
504.2.bs.a.353.4	yes	48	9.7	even	3
504.2.cx.a.185.5	yes	48	3.2	odd	2
504.2.cx.a.425.5	yes	48	63.61	odd	6
1008.2.ca.e.257.21		48	84.47	odd	6
1008.2.ca.e.353.21		48	36.7	odd	6
1008.2.df.e.689.20		48	12.11	even	2
1008.2.df.e.929.20		48	252.187	even	6
1512.2.bs.a.521.19		48	9.2	odd	6
1512.2.bs.a.1097.19		48	7.5	odd	6
1512.2.cx.a.17.19		48	1.1	even	1	trivial
1512.2.cx.a.89.19		48	63.47	even	6	inner
3024.2.ca.e.2033.19		48	36.11	even	6
3024.2.ca.e.2609.19		48	28.19	even	6
3024.2.df.e.17.19		48	4.3	odd	2
3024.2.df.e.1601.19		48	252.47	odd	6

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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)

\(f(q)\)	\(=\)	\(q+1.81173 q^{5} +(1.69266 - 2.03345i) q^{7} -0.255864i q^{11} +(-5.77765 - 3.33573i) q^{13} +(1.99857 - 3.46163i) q^{17} +(1.24687 - 0.719882i) q^{19} -5.66665i q^{23} -1.71762 q^{25} +(4.18486 - 2.41613i) q^{29} +(-8.80648 + 5.08442i) q^{31} +(3.06665 - 3.68407i) q^{35} +(-1.65567 - 2.86771i) q^{37} +(5.10089 - 8.83499i) q^{41} +(1.12248 + 1.94419i) q^{43} +(-5.97092 + 10.3419i) q^{47} +(-1.26982 - 6.88386i) q^{49} +(3.97466 + 2.29477i) q^{53} -0.463558i q^{55} +(2.55575 + 4.42670i) q^{59} +(8.60220 + 4.96648i) q^{61} +(-10.4676 - 6.04346i) q^{65} +(-0.962135 - 1.66647i) q^{67} +7.31241i q^{71} +(-2.47807 - 1.43071i) q^{73} +(-0.520286 - 0.433090i) q^{77} +(1.83153 - 3.17231i) q^{79} +(-2.68261 - 4.64642i) q^{83} +(3.62089 - 6.27156i) q^{85} +(0.378446 + 0.655488i) q^{89} +(-16.5626 + 6.10230i) q^{91} +(2.25900 - 1.30424i) q^{95} +(4.21765 - 2.43506i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{25} - 18 q^{29} + 18 q^{31} + 6 q^{41} - 6 q^{43} - 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} + 6 q^{79} + 18 q^{89} + 6 q^{91} + 54 q^{95}+O(q^{100}) \) 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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