LMFDB - Embedded newform 1512.2.cx.a.17.7

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			17.7
Character	$\chi$	$=$	1512.17
Dual form			1512.2.cx.a.89.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20884 q^{5} +(2.16520 + 1.52049i) q^{7} +0.181913i q^{11} +(2.50424 + 1.44582i) q^{13} +(-1.98511 + 3.43832i) q^{17} +(0.867067 - 0.500601i) q^{19} -5.61313i q^{23} -0.121025 q^{25} +(-0.703311 + 0.406057i) q^{29} +(-6.89908 + 3.98319i) q^{31} +(-4.78259 - 3.35852i) q^{35} +(1.25614 + 2.17569i) q^{37} +(0.612906 - 1.06158i) q^{41} +(5.47716 + 9.48671i) q^{43} +(-3.57551 + 6.19296i) q^{47} +(2.37622 + 6.58434i) q^{49} +(1.75586 + 1.01374i) q^{53} -0.401817i q^{55} +(3.27911 + 5.67958i) q^{59} +(6.97275 + 4.02572i) q^{61} +(-5.53147 - 3.19359i) q^{65} +(-3.44505 - 5.96701i) q^{67} +11.4168i q^{71} +(-10.1861 - 5.88094i) q^{73} +(-0.276597 + 0.393879i) q^{77} +(-6.35501 + 11.0072i) q^{79} +(7.19085 + 12.4549i) q^{83} +(4.38480 - 7.59470i) q^{85} +(7.11375 + 12.3214i) q^{89} +(3.22383 + 6.93818i) q^{91} +(-1.91521 + 1.10575i) q^{95} +(-3.01040 + 1.73805i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{25} - 18 q^{29} + 18 q^{31} + 6 q^{41} - 6 q^{43} - 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} + 6 q^{79} + 18 q^{89} + 6 q^{91} + 54 q^{95}+O(q^{100}) $ 48 * q + 48 * q^25 - 18 * q^29 + 18 * q^31 + 6 * q^41 - 6 * q^43 - 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 + 6 * q^79 + 18 * q^89 + 6 * q^91 + 54 * q^95

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.20884			−0.987823			−0.493912	−	0.869512i	$-0.664433\pi$
$5$	−2.20884			−0.987823			−0.493912	+	0.869512i	$0.664433\pi$
$6$		0			0
$7$	2.16520	+	1.52049i	0.818370	+	0.574691i
$7$	2.16520	+	1.52049i	0.818370	+	0.574691i
$8$		0			0
$9$		0			0
$10$		0			0
$11$			0.181913i			0.0548488i	0.999624	+	0.0274244i	$0.00873056\pi$
$11$			0.181913i			0.0548488i	−0.999624	+	0.0274244i	$0.991269\pi$
$12$		0			0
$13$	2.50424	+	1.44582i	0.694551	+	0.400999i	0.805315	−	0.592847i	$-0.201996\pi$
$13$	2.50424	+	1.44582i	0.694551	+	0.400999i	−0.110763	+	0.993847i	$0.535330\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.98511	+	3.43832i	−0.481461	+	0.833915i	−0.999774	−	0.0212765i	$-0.993227\pi$
$17$	−1.98511	+	3.43832i	−0.481461	+	0.833915i	0.518313	+	0.855191i	$0.326560\pi$
$18$		0			0
$19$	0.867067	−	0.500601i	0.198919	−	0.114846i	−0.397232	−	0.917718i	$-0.630029\pi$
$19$	0.867067	−	0.500601i	0.198919	−	0.114846i	0.596151	+	0.802872i	$0.296696\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	5.61313i		−	1.17042i	−0.810882	−	0.585210i	$-0.801012\pi$
$23$		−	5.61313i		−	1.17042i	0.810882	−	0.585210i	$-0.198988\pi$
$24$		0			0
$25$	−0.121025			−0.0242050
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.703311	+	0.406057i	−0.130602	+	0.0754028i	−0.563877	−	0.825859i	$-0.690691\pi$
$29$	−0.703311	+	0.406057i	−0.130602	+	0.0754028i	0.433276	+	0.901261i	$0.357358\pi$
$30$		0			0
$31$	−6.89908	+	3.98319i	−1.23911	+	0.715401i	−0.968913	−	0.247403i	$-0.920423\pi$
$31$	−6.89908	+	3.98319i	−1.23911	+	0.715401i	−0.270199	+	0.962805i	$0.587089\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.78259	−	3.35852i	−0.808405	−	0.567693i
$36$		0			0
$37$	1.25614	+	2.17569i	0.206507	+	0.357681i	0.950612	−	0.310382i	$-0.100457\pi$
$37$	1.25614	+	2.17569i	0.206507	+	0.357681i	−0.744105	+	0.668063i	$0.767124\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.612906	−	1.06158i	0.0957198	−	0.165792i	−0.814189	−	0.580600i	$-0.802818\pi$
$41$	0.612906	−	1.06158i	0.0957198	−	0.165792i	0.909909	+	0.414808i	$0.136151\pi$
$42$		0			0
$43$	5.47716	+	9.48671i	0.835259	+	1.44671i	0.893820	+	0.448426i	$0.148015\pi$
$43$	5.47716	+	9.48671i	0.835259	+	1.44671i	−0.0585613	+	0.998284i	$0.518651\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.57551	+	6.19296i	−0.521542	+	0.903336i	0.478145	+	0.878281i	$0.341309\pi$
$47$	−3.57551	+	6.19296i	−0.521542	+	0.903336i	−0.999686	+	0.0250552i	$0.992024\pi$
$48$		0			0
$49$	2.37622	+	6.58434i	0.339460	+	0.940620i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.75586	+	1.01374i	0.241186	+	0.139249i	0.615722	−	0.787964i	$-0.288865\pi$
$53$	1.75586	+	1.01374i	0.241186	+	0.139249i	−0.374536	+	0.927212i	$0.622198\pi$
$54$		0			0
$55$		−	0.401817i		−	0.0541810i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.27911	+	5.67958i	0.426903	+	0.739418i	0.996596	−	0.0824396i	$-0.0262712\pi$
$59$	3.27911	+	5.67958i	0.426903	+	0.739418i	−0.569693	+	0.821858i	$0.692938\pi$
$60$		0			0
$61$	6.97275	+	4.02572i	0.892769	+	0.515440i	0.874847	−	0.484399i	$-0.160962\pi$
$61$	6.97275	+	4.02572i	0.892769	+	0.515440i	0.0179215	+	0.999839i	$0.494295\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.53147	−	3.19359i	−0.686094	−	0.396117i
$66$		0			0
$67$	−3.44505	−	5.96701i	−0.420880	−	0.728986i	0.575145	−	0.818051i	$-0.304945\pi$
$67$	−3.44505	−	5.96701i	−0.420880	−	0.728986i	−0.996026	+	0.0890650i	$0.971612\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			11.4168i			1.35492i	0.735560	+	0.677460i	$0.236919\pi$
$71$			11.4168i			1.35492i	−0.735560	+	0.677460i	$0.763081\pi$
$72$		0			0
$73$	−10.1861	−	5.88094i	−1.19219	−	0.688312i	−0.233388	−	0.972384i	$-0.574981\pi$
$73$	−10.1861	−	5.88094i	−1.19219	−	0.688312i	−0.958803	+	0.284072i	$0.908315\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.276597	+	0.393879i	−0.0315211	+	0.0448867i
$78$		0			0
$79$	−6.35501	+	11.0072i	−0.714994	+	1.23841i	0.247968	+	0.968768i	$0.420237\pi$
$79$	−6.35501	+	11.0072i	−0.714994	+	1.23841i	−0.962962	+	0.269638i	$0.913096\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.19085	+	12.4549i	0.789298	+	1.36710i	0.926397	+	0.376547i	$0.122889\pi$
$83$	7.19085	+	12.4549i	0.789298	+	1.36710i	−0.137099	+	0.990557i	$0.543778\pi$
$84$		0			0
$85$	4.38480	−	7.59470i	0.475598	−	0.823760i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.11375	+	12.3214i	0.754055	+	1.30606i	0.945843	+	0.324626i	$0.105238\pi$
$89$	7.11375	+	12.3214i	0.754055	+	1.30606i	−0.191787	+	0.981437i	$0.561428\pi$
$90$		0			0
$91$	3.22383	+	6.93818i	0.337949	+	0.727319i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.91521	+	1.10575i	−0.196497	+	0.113447i
$96$		0			0
$97$	−3.01040	+	1.73805i	−0.305659	+	0.176473i	−0.644982	−	0.764197i	$-0.723135\pi$
$97$	−3.01040	+	1.73805i	−0.305659	+	0.176473i	0.339323	+	0.940670i	$0.389802\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.50563			−0.945846			−0.472923	−	0.881104i	$-0.656801\pi$
$101$	−9.50563			−0.945846			−0.472923	+	0.881104i	$0.656801\pi$
$102$		0			0
$103$		−	8.38505i		−	0.826204i	−0.910685	−	0.413102i	$-0.864445\pi$
$103$		−	8.38505i		−	0.826204i	0.910685	−	0.413102i	$-0.135555\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.7310	+	7.35026i	−1.23075	+	0.710576i	−0.967187	−	0.254065i	$-0.918232\pi$
$107$	−12.7310	+	7.35026i	−1.23075	+	0.710576i	−0.263567	+	0.964641i	$0.584899\pi$
$108$		0			0
$109$	8.35648	−	14.4738i	0.800405	−	1.38634i	−0.118944	−	0.992901i	$-0.537951\pi$
$109$	8.35648	−	14.4738i	0.800405	−	1.38634i	0.919350	−	0.393442i	$-0.128716\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.19493	+	0.689894i	0.112410	+	0.0648998i	0.555151	−	0.831750i	$-0.312661\pi$
$113$	1.19493	+	0.689894i	0.112410	+	0.0648998i	−0.442741	+	0.896650i	$0.645994\pi$
$114$		0			0
$115$			12.3985i			1.15617i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−9.52611	+	4.42632i	−0.873257	+	0.405760i
$120$		0			0
$121$	10.9669			0.996992
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.3115			1.01173
$126$		0			0
$127$	−11.9684			−1.06202			−0.531012	−	0.847364i	$-0.678188\pi$
$127$	−11.9684			−1.06202			−0.531012	+	0.847364i	$0.678188\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.35396			0.642519			0.321259	−	0.946991i	$-0.395894\pi$
$131$	7.35396			0.642519			0.321259	+	0.946991i	$0.395894\pi$
$132$		0			0
$133$	2.63854	+	0.234462i	0.228790	+	0.0203305i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	16.4316i		−	1.40385i	−0.712251	−	0.701925i	$-0.752324\pi$
$137$		−	16.4316i		−	1.40385i	0.712251	−	0.701925i	$-0.247676\pi$
$138$		0			0
$139$	11.2110	+	6.47266i	0.950903	+	0.549004i	0.893361	−	0.449339i	$-0.148340\pi$
$139$	11.2110	+	6.47266i	0.950903	+	0.549004i	0.0575417	+	0.998343i	$0.481674\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.263014	+	0.455554i	−0.0219944	+	0.0380953i
$144$		0			0
$145$	1.55350	−	0.896914i	0.129011	−	0.0744847i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	15.2359i		−	1.24818i	−0.781354	−	0.624088i	$-0.785471\pi$
$149$		−	15.2359i		−	1.24818i	0.781354	−	0.624088i	$-0.214529\pi$
$150$		0			0
$151$	−13.6625			−1.11184			−0.555919	−	0.831236i	$-0.687634\pi$
$151$	−13.6625			−1.11184			−0.555919	+	0.831236i	$0.687634\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	15.2390	−	8.79822i	1.22402	−	0.706690i
$156$		0			0
$157$	10.2322	−	5.90757i	0.816619	−	0.471475i	−0.0326299	−	0.999468i	$-0.510388\pi$
$157$	10.2322	−	5.90757i	0.816619	−	0.471475i	0.849249	+	0.527992i	$0.177055\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	8.53471	−	12.1536i	0.672630	−	0.957836i
$162$		0			0
$163$	−4.35998	−	7.55170i	−0.341500	−	0.591495i	0.643212	−	0.765688i	$-0.277601\pi$
$163$	−4.35998	−	7.55170i	−0.341500	−	0.591495i	−0.984711	+	0.174194i	$0.944268\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.89862	+	15.4129i	−0.688596	+	1.19268i	0.283696	+	0.958914i	$0.408439\pi$
$167$	−8.89862	+	15.4129i	−0.688596	+	1.19268i	−0.972292	+	0.233769i	$0.924894\pi$
$168$		0			0
$169$	−2.31918	−	4.01695i	−0.178399	−	0.308996i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.56015	+	16.5587i	−0.726845	+	1.25893i	0.231366	+	0.972867i	$0.425681\pi$
$173$	−9.56015	+	16.5587i	−0.726845	+	1.25893i	−0.958210	+	0.286065i	$0.907653\pi$
$174$		0			0
$175$	−0.262044	−	0.184017i	−0.0198086	−	0.0139104i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	5.31891	+	3.07088i	0.397554	+	0.229528i	0.685428	−	0.728140i	$-0.259615\pi$
$179$	5.31891	+	3.07088i	0.397554	+	0.229528i	−0.287874	+	0.957668i	$0.592948\pi$
$180$		0			0
$181$			11.1208i			0.826604i	0.910594	+	0.413302i	$0.135625\pi$
$181$			11.1208i			0.826604i	−0.910594	+	0.413302i	$0.864375\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.77460	−	4.80575i	−0.203993	−	0.353326i
$186$		0			0
$187$	−0.625475	−	0.361118i	−0.0457393	−	0.0264076i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−12.9342	−	7.46759i	−0.935889	−	0.540336i	−0.0472195	−	0.998885i	$-0.515036\pi$
$191$	−12.9342	−	7.46759i	−0.935889	−	0.540336i	−0.888669	+	0.458549i	$0.848369\pi$
$192$		0			0
$193$	6.21387	+	10.7627i	0.447284	+	0.774719i	0.998208	−	0.0598363i	$-0.0190579\pi$
$193$	6.21387	+	10.7627i	0.447284	+	0.774719i	−0.550924	+	0.834556i	$0.685725\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	16.1512i		−	1.15073i	−0.817897	−	0.575364i	$-0.804860\pi$
$197$		−	16.1512i		−	1.15073i	0.817897	−	0.575364i	$-0.195140\pi$
$198$		0			0
$199$	−21.5762	−	12.4571i	−1.52950	−	0.883057i	−0.999383	−	0.0351325i	$-0.988815\pi$
$199$	−21.5762	−	12.4571i	−1.52950	−	0.883057i	−0.530117	−	0.847925i	$-0.677852\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.14022	−	0.190181i	−0.150214	−	0.0133481i
$204$		0			0
$205$	−1.35381	+	2.34487i	−0.0945542	+	0.163773i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.0910659	+	0.157731i	0.00629916	+	0.0109105i
$210$		0			0
$211$	5.78631	−	10.0222i	0.398346	−	0.689955i	−0.595176	−	0.803595i	$-0.702918\pi$
$211$	5.78631	−	10.0222i	0.398346	−	0.689955i	0.993522	+	0.113640i	$0.0362510\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−12.0982	−	20.9546i	−0.825088	−	1.42909i
$216$		0			0
$217$	−20.9943	−	1.86557i	−1.42519	−	0.126643i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−9.94241	+	5.74025i	−0.668799	+	0.386131i
$222$		0			0
$223$	13.9653	−	8.06285i	0.935183	−	0.539928i	0.0467358	−	0.998907i	$-0.485118\pi$
$223$	13.9653	−	8.06285i	0.935183	−	0.539928i	0.888447	+	0.458979i	$0.151785\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	19.8036			1.31441			0.657206	−	0.753711i	$-0.271738\pi$
$227$	19.8036			1.31441			0.657206	+	0.753711i	$0.271738\pi$
$228$		0			0
$229$		−	15.6001i		−	1.03088i	−0.856924	−	0.515442i	$-0.827628\pi$
$229$		−	15.6001i		−	1.03088i	0.856924	−	0.515442i	$-0.172372\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.6450	−	6.14590i	0.697378	−	0.402631i	−0.108992	−	0.994043i	$-0.534762\pi$
$233$	10.6450	−	6.14590i	0.697378	−	0.402631i	0.806370	+	0.591411i	$0.201429\pi$
$234$		0			0
$235$	7.89773	−	13.6793i	0.515191	−	0.892337i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	13.8058	+	7.97079i	0.893024	+	0.515588i	0.874930	−	0.484249i	$-0.160907\pi$
$239$	13.8058	+	7.97079i	0.893024	+	0.515588i	0.0180934	+	0.999836i	$0.494240\pi$
$240$		0			0
$241$			20.6872i			1.33258i	0.745693	+	0.666290i	$0.232119\pi$
$241$			20.6872i			1.33258i	−0.745693	+	0.666290i	$0.767881\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5.24869	−	14.5438i	−0.335327	−	0.929167i
$246$		0			0
$247$	2.89513			0.184212
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−7.66566			−0.483852			−0.241926	−	0.970295i	$-0.577779\pi$
$251$	−7.66566			−0.483852			−0.241926	+	0.970295i	$0.577779\pi$
$252$		0			0
$253$	1.02110			0.0641961
$254$		0			0
$255$		0			0
$256$		0			0
$257$	11.9297			0.744157			0.372078	−	0.928201i	$-0.378645\pi$
$257$	11.9297			0.744157			0.372078	+	0.928201i	$0.378645\pi$
$258$		0			0
$259$	−0.588325	+	6.62076i	−0.0365568	+	0.411394i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			7.72501i			0.476345i	0.971223	+	0.238172i	$0.0765483\pi$
$263$			7.72501i			0.476345i	−0.971223	+	0.238172i	$0.923452\pi$
$264$		0			0
$265$	−3.87841	−	2.23920i	−0.238249	−	0.137553i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.98739	−	8.63841i	0.304086	−	0.526693i	−0.672971	−	0.739669i	$-0.734982\pi$
$269$	4.98739	−	8.63841i	0.304086	−	0.526693i	0.977058	+	0.212976i	$0.0683155\pi$
$270$		0			0
$271$	3.61508	−	2.08717i	0.219600	−	0.126786i	−0.386165	−	0.922430i	$-0.626200\pi$
$271$	3.61508	−	2.08717i	0.219600	−	0.126786i	0.605765	+	0.795643i	$0.292867\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	0.0220160i		−	0.00132761i
$276$		0			0
$277$	4.45007			0.267379			0.133689	−	0.991023i	$-0.457318\pi$
$277$	4.45007			0.267379			0.133689	+	0.991023i	$0.457318\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	24.5472	−	14.1723i	1.46436	−	0.845451i	0.465155	−	0.885229i	$-0.345999\pi$
$281$	24.5472	−	14.1723i	1.46436	−	0.845451i	0.999209	+	0.0397785i	$0.0126652\pi$
$282$		0			0
$283$	−10.0427	+	5.79815i	−0.596976	+	0.344664i	−0.767851	−	0.640628i	$-0.778674\pi$
$283$	−10.0427	+	5.79815i	−0.596976	+	0.344664i	0.170875	+	0.985293i	$0.445341\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.94119	−	1.36663i	0.173613	−	0.0806696i
$288$		0			0
$289$	0.618645	+	1.07152i	0.0363909	+	0.0630308i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−14.4199	+	24.9760i	−0.842418	+	1.45911i	0.0454266	+	0.998968i	$0.485535\pi$
$293$	−14.4199	+	24.9760i	−0.842418	+	1.45911i	−0.887845	+	0.460143i	$0.847798\pi$
$294$		0			0
$295$	−7.24302	−	12.5453i	−0.421705	−	0.730414i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	8.11560	−	14.0566i	0.469337	−	0.812916i
$300$		0			0
$301$	−2.56529	+	28.8686i	−0.147861	+	1.66396i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−15.4017	−	8.89216i	−0.881898	−	0.509164i
$306$		0			0
$307$			10.8117i			0.617059i	0.951215	+	0.308529i	$0.0998368\pi$
$307$			10.8117i			0.617059i	−0.951215	+	0.308529i	$0.900163\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−8.59161	−	14.8811i	−0.487185	−	0.843830i	0.512706	−	0.858564i	$-0.328643\pi$
$311$	−8.59161	−	14.8811i	−0.487185	−	0.843830i	−0.999891	+	0.0147345i	$0.995310\pi$
$312$		0			0
$313$	−7.91893	−	4.57200i	−0.447604	−	0.258425i	0.259214	−	0.965820i	$-0.416537\pi$
$313$	−7.91893	−	4.57200i	−0.447604	−	0.258425i	−0.706818	+	0.707396i	$0.749870\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.984650	−	0.568488i	−0.0553034	−	0.0319295i	0.472093	−	0.881549i	$-0.343499\pi$
$317$	−0.984650	−	0.568488i	−0.0553034	−	0.0319295i	−0.527397	+	0.849619i	$0.676832\pi$
$318$		0			0
$319$	−0.0738670	−	0.127941i	−0.00413576	−	0.00716334i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			3.97500i			0.221175i
$324$		0			0
$325$	−0.303075	−	0.174981i	−0.0168116	−	0.00970618i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−17.1580	+	7.97250i	−0.945954	+	0.439538i
$330$		0			0
$331$	3.02394	−	5.23761i	0.166211	−	0.287885i	−0.770874	−	0.636988i	$-0.780180\pi$
$331$	3.02394	−	5.23761i	0.166211	−	0.287885i	0.937085	+	0.349102i	$0.113513\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	7.60957	+	13.1802i	0.415755	+	0.720110i
$336$		0			0
$337$	17.6873	−	30.6353i	0.963490	−	1.66881i	0.249871	−	0.968279i	$-0.419612\pi$
$337$	17.6873	−	30.6353i	0.963490	−	1.66881i	0.713619	−	0.700534i	$-0.247055\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.724593	−	1.25503i	−0.0392389	−	0.0679638i
$342$		0			0
$343$	−4.86643	+	17.8695i	−0.262762	+	0.964861i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	20.1007	−	11.6051i	1.07906	−	0.622995i	0.148417	−	0.988925i	$-0.452582\pi$
$347$	20.1007	−	11.6051i	1.07906	−	0.622995i	0.930643	+	0.365929i	$0.119249\pi$
$348$		0			0
$349$	12.7248	−	7.34667i	0.681144	−	0.393258i	−0.119142	−	0.992877i	$-0.538014\pi$
$349$	12.7248	−	7.34667i	0.681144	−	0.393258i	0.800286	+	0.599619i	$0.204681\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	13.4624			0.716533			0.358267	−	0.933619i	$-0.383368\pi$
$353$	13.4624			0.716533			0.358267	+	0.933619i	$0.383368\pi$
$354$		0			0
$355$		−	25.2178i		−	1.33842i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−13.5004	+	7.79444i	−0.712522	+	0.411375i	−0.811994	−	0.583666i	$-0.801618\pi$
$359$	−13.5004	+	7.79444i	−0.712522	+	0.411375i	0.0994721	+	0.995040i	$0.468285\pi$
$360$		0			0
$361$	−8.99880	+	15.5864i	−0.473621	+	0.820335i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	22.4994	+	12.9901i	1.17767	+	0.679930i
$366$		0			0
$367$		−	8.67003i		−	0.452572i	−0.974061	−	0.226286i	$-0.927342\pi$
$367$		−	8.67003i		−	0.452572i	0.974061	−	0.226286i	$-0.0726584\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.26040	+	4.86473i	0.117354	+	0.252564i
$372$		0			0
$373$	−24.0978			−1.24774			−0.623868	−	0.781530i	$-0.714440\pi$
$373$	−24.0978			−1.24774			−0.623868	+	0.781530i	$0.714440\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.34835			−0.120946
$378$		0			0
$379$	10.0778			0.517662			0.258831	−	0.965923i	$-0.416663\pi$
$379$	10.0778			0.517662			0.258831	+	0.965923i	$0.416663\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−4.70476			−0.240402			−0.120201	−	0.992750i	$-0.538354\pi$
$383$	−4.70476			−0.240402			−0.120201	+	0.992750i	$0.538354\pi$
$384$		0			0
$385$	0.610958	−	0.870015i	0.0311373	−	0.0443401i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	21.5003i		−	1.09011i	−0.838401	−	0.545055i	$-0.816509\pi$
$389$		−	21.5003i		−	1.09011i	0.838401	−	0.545055i	$-0.183491\pi$
$390$		0			0
$391$	19.2997	+	11.1427i	0.976030	+	0.563511i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	14.0372	−	24.3131i	0.706288	−	1.22333i
$396$		0			0
$397$	−23.7548	+	13.7148i	−1.19222	+	0.688327i	−0.958809	−	0.284052i	$-0.908321\pi$
$397$	−23.7548	+	13.7148i	−1.19222	+	0.688327i	−0.233408	+	0.972379i	$0.574988\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	29.2299i		−	1.45967i	−0.683622	−	0.729836i	$-0.739596\pi$
$401$		−	29.2299i		−	1.45967i	0.683622	−	0.729836i	$-0.260404\pi$
$402$		0			0
$403$	−23.0359			−1.14750
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.395786	+	0.228507i	−0.0196184	+	0.0113267i
$408$		0			0
$409$	27.3564	−	15.7942i	1.35269	−	0.780974i	0.364061	−	0.931375i	$-0.381390\pi$
$409$	27.3564	−	15.7942i	1.35269	−	0.780974i	0.988625	+	0.150401i	$0.0480565\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.53581	+	17.2833i	−0.0755721	+	0.850455i
$414$		0			0
$415$	−15.8834	−	27.5109i	−0.779687	−	1.35046i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6.80176	−	11.7810i	0.332288	−	0.575539i	−0.650672	−	0.759359i	$-0.725513\pi$
$419$	6.80176	−	11.7810i	0.332288	−	0.575539i	0.982960	+	0.183819i	$0.0588462\pi$
$420$		0			0
$421$	−14.8629	−	25.7432i	−0.724372	−	1.25465i	−0.959232	−	0.282620i	$-0.908797\pi$
$421$	−14.8629	−	25.7432i	−0.724372	−	1.25465i	0.234860	−	0.972029i	$-0.424537\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.240248	−	0.416122i	0.0116537	−	0.0201849i
$426$		0			0
$427$	8.97636	+	19.3185i	0.434396	+	0.934887i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	21.6467	+	12.4977i	1.04268	+	0.601994i	0.920592	−	0.390525i	$-0.127707\pi$
$431$	21.6467	+	12.4977i	1.04268	+	0.601994i	0.122091	+	0.992519i	$0.461040\pi$
$432$		0			0
$433$		−	18.7778i		−	0.902401i	−0.892423	−	0.451201i	$-0.850996\pi$
$433$		−	18.7778i		−	0.902401i	0.892423	−	0.451201i	$-0.149004\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.80994	−	4.86696i	−0.134418	−	0.232818i
$438$		0			0
$439$	−1.82363	−	1.05287i	−0.0870369	−	0.0502508i	0.455850	−	0.890057i	$-0.349335\pi$
$439$	−1.82363	−	1.05287i	−0.0870369	−	0.0502508i	−0.542887	+	0.839806i	$0.682669\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	11.6452	+	6.72337i	0.553281	+	0.319437i	0.750444	−	0.660934i	$-0.229840\pi$
$443$	11.6452	+	6.72337i	0.553281	+	0.319437i	−0.197163	+	0.980371i	$0.563173\pi$
$444$		0			0
$445$	−15.7131	−	27.2159i	−0.744874	−	1.29016i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			7.42429i			0.350374i	0.984535	+	0.175187i	$0.0560530\pi$
$449$			7.42429i			0.350374i	−0.984535	+	0.175187i	$0.943947\pi$
$450$		0			0
$451$	0.193116	+	0.111496i	0.00909347	+	0.00525012i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−7.12093	−	15.3253i	−0.333834	−	0.718462i
$456$		0			0
$457$	0.139009	−	0.240771i	0.00650257	−	0.0112628i	−0.862756	−	0.505621i	$-0.831263\pi$
$457$	0.139009	−	0.240771i	0.00650257	−	0.0112628i	0.869258	+	0.494358i	$0.164597\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.98573	+	6.90348i	0.185634	+	0.321527i	0.943790	−	0.330546i	$-0.107233\pi$
$461$	3.98573	+	6.90348i	0.185634	+	0.321527i	−0.758156	+	0.652073i	$0.773900\pi$
$462$		0			0
$463$	12.4572	−	21.5765i	0.578936	−	1.00275i	−0.416666	−	0.909060i	$-0.636801\pi$
$463$	12.4572	−	21.5765i	0.578936	−	1.00275i	0.995602	−	0.0936870i	$-0.0298653\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−18.4485	−	31.9538i	−0.853695	−	1.47864i	−0.877850	−	0.478935i	$-0.841023\pi$
$467$	−18.4485	−	31.9538i	−0.853695	−	1.47864i	0.0241548	−	0.999708i	$-0.492311\pi$
$468$		0			0
$469$	1.61353	−	18.1580i	0.0745059	−	0.838457i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.72576	+	0.996366i	−0.0793504	+	0.0458130i
$474$		0			0
$475$	−0.104937	+	0.0605852i	−0.00481483	+	0.00277984i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−3.41169			−0.155884			−0.0779420	−	0.996958i	$-0.524835\pi$
$479$	−3.41169			−0.155884			−0.0779420	+	0.996958i	$0.524835\pi$
$480$		0			0
$481$			7.26460i			0.331237i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	6.64948	−	3.83908i	0.301938	−	0.174324i
$486$		0			0
$487$	−1.17122	+	2.02861i	−0.0530729	+	0.0919249i	−0.891341	−	0.453333i	$-0.850235\pi$
$487$	−1.17122	+	2.02861i	−0.0530729	+	0.0919249i	0.838268	+	0.545258i	$0.183568\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−4.65365	−	2.68678i	−0.210016	−	0.121253i	0.391303	−	0.920262i	$-0.372025\pi$
$491$	−4.65365	−	2.68678i	−0.210016	−	0.121253i	−0.601319	+	0.799009i	$0.705358\pi$
$492$		0			0
$493$		−	3.22428i		−	0.145214i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17.3591	+	24.7196i	−0.778660	+	1.10883i
$498$		0			0
$499$	−33.3813			−1.49435			−0.747175	−	0.664627i	$-0.768591\pi$
$499$	−33.3813			−1.49435			−0.747175	+	0.664627i	$0.768591\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−6.01630			−0.268254			−0.134127	−	0.990964i	$-0.542823\pi$
$503$	−6.01630			−0.268254			−0.134127	+	0.990964i	$0.542823\pi$
$504$		0			0
$505$	20.9964			0.934328
$506$		0			0
$507$		0			0
$508$		0			0
$509$	10.0398			0.445007			0.222503	−	0.974932i	$-0.428577\pi$
$509$	10.0398			0.445007			0.222503	+	0.974932i	$0.428577\pi$
$510$		0			0
$511$	−13.1130	−	28.2213i	−0.580087	−	1.24844i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			18.5212i			0.816143i
$516$		0			0
$517$	−1.12658	−	0.650432i	−0.0495470	−	0.0286059i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−10.8007	+	18.7074i	−0.473188	+	0.819586i	−0.999529	−	0.0306875i	$-0.990230\pi$
$521$	−10.8007	+	18.7074i	−0.473188	+	0.819586i	0.526341	+	0.850274i	$0.323564\pi$
$522$		0			0
$523$	11.6105	−	6.70332i	0.507692	−	0.293116i	−0.224193	−	0.974545i	$-0.571974\pi$
$523$	11.6105	−	6.70332i	0.507692	−	0.293116i	0.731884	+	0.681429i	$0.238641\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	31.6283i		−	1.37775i
$528$		0			0
$529$	−8.50726			−0.369881
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3.06973	−	1.77231i	0.132965	−	0.0767672i
$534$		0			0
$535$	28.1208	−	16.2355i	1.21577	−	0.701924i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.19778	+	0.432265i	−0.0515919	+	0.0186190i
$540$		0			0
$541$	4.53805	+	7.86013i	0.195106	+	0.337933i	0.946935	−	0.321424i	$-0.104162\pi$
$541$	4.53805	+	7.86013i	0.195106	+	0.337933i	−0.751829	+	0.659358i	$0.770828\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−18.4581	+	31.9704i	−0.790659	+	1.36946i
$546$		0			0
$547$	13.5359	+	23.4448i	0.578752	+	1.00243i	0.995623	+	0.0934620i	$0.0297934\pi$
$547$	13.5359	+	23.4448i	0.578752	+	1.00243i	−0.416871	+	0.908966i	$0.636873\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.406545	+	0.704157i	−0.0173194	+	0.0299981i
$552$		0			0
$553$	−30.4962	+	14.1701i	−1.29683	+	0.602574i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	23.8690	+	13.7808i	1.01136	+	0.583911i	0.911591	−	0.411099i	$-0.134855\pi$
$557$	23.8690	+	13.7808i	1.01136	+	0.583911i	0.0997727	+	0.995010i	$0.468188\pi$
$558$		0			0
$559$			31.6760i			1.33975i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−6.92328	−	11.9915i	−0.291781	−	0.505380i	0.682450	−	0.730933i	$-0.260915\pi$
$563$	−6.92328	−	11.9915i	−0.291781	−	0.505380i	−0.974231	+	0.225552i	$0.927581\pi$
$564$		0			0
$565$	−2.63941	−	1.52387i	−0.111041	−	0.0641095i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	10.5219	+	6.07485i	0.441103	+	0.254671i	0.704065	−	0.710135i	$-0.251366\pi$
$569$	10.5219	+	6.07485i	0.441103	+	0.254671i	−0.262962	+	0.964806i	$0.584700\pi$
$570$		0			0
$571$	23.1505	+	40.0979i	0.968819	+	1.67804i	0.698985	+	0.715136i	$0.253635\pi$
$571$	23.1505	+	40.0979i	0.968819	+	1.67804i	0.269833	+	0.962907i	$0.413031\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			0.679329i			0.0283300i
$576$		0			0
$577$	−10.6284	−	6.13630i	−0.442465	−	0.255457i	0.262178	−	0.965020i	$-0.415559\pi$
$577$	−10.6284	−	6.13630i	−0.442465	−	0.255457i	−0.704643	+	0.709562i	$0.748893\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.36792	+	37.9011i	−0.139725	+	1.57240i
$582$		0			0
$583$	−0.184413	+	0.319413i	−0.00763762	+	0.0132287i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11.9875	−	20.7630i	−0.494778	−	0.856980i	0.505204	−	0.863000i	$-0.331417\pi$
$587$	−11.9875	−	20.7630i	−0.494778	−	0.856980i	−0.999982	+	0.00601986i	$0.998084\pi$
$588$		0			0
$589$	−3.98798	+	6.90738i	−0.164322	+	0.284614i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	15.4912	+	26.8315i	0.636146	+	1.10184i	0.986271	+	0.165134i	$0.0528056\pi$
$593$	15.4912	+	26.8315i	0.636146	+	1.10184i	−0.350125	+	0.936703i	$0.613861\pi$
$594$		0			0
$595$	21.0416	−	9.77702i	0.862623	−	0.400819i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	21.4392	−	12.3779i	0.875981	−	0.505748i	0.00665010	−	0.999978i	$-0.497883\pi$
$599$	21.4392	−	12.3779i	0.875981	−	0.505748i	0.869331	+	0.494230i	$0.164550\pi$
$600$		0			0
$601$	7.67329	−	4.43017i	0.313000	−	0.180711i	−0.335268	−	0.942123i	$-0.608827\pi$
$601$	7.67329	−	4.43017i	0.313000	−	0.180711i	0.648268	+	0.761412i	$0.275494\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−24.2241			−0.984852
$606$		0			0
$607$			13.0415i			0.529339i	0.964339	+	0.264670i	$0.0852629\pi$
$607$			13.0415i			0.529339i	−0.964339	+	0.264670i	$0.914737\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−17.9079	+	10.3391i	−0.724475	+	0.418276i
$612$		0			0
$613$	5.90775	−	10.2325i	0.238612	−	0.413288i	−0.721704	−	0.692201i	$-0.756641\pi$
$613$	5.90775	−	10.2325i	0.238612	−	0.413288i	0.960316	+	0.278914i	$0.0899743\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	13.7906	+	7.96200i	0.555188	+	0.320538i	0.751212	−	0.660061i	$-0.229470\pi$
$617$	13.7906	+	7.96200i	0.555188	+	0.320538i	−0.196024	+	0.980599i	$0.562803\pi$
$618$		0			0
$619$			30.9231i			1.24291i	0.783452	+	0.621453i	$0.213457\pi$
$619$			30.9231i			1.24291i	−0.783452	+	0.621453i	$0.786543\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.33180	+	37.4947i	−0.133486	+	1.50219i
$624$		0			0
$625$	−24.3802			−0.975209
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−9.97429			−0.397701
$630$		0			0
$631$	0.925450			0.0368416			0.0184208	−	0.999830i	$-0.494136\pi$
$631$	0.925450			0.0368416			0.0184208	+	0.999830i	$0.494136\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	26.4363			1.04909
$636$		0			0
$637$	−3.56917	+	19.9244i	−0.141416	+	0.789433i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	34.3482i		−	1.35667i	−0.734752	−	0.678336i	$-0.762702\pi$
$641$		−	34.3482i		−	1.35667i	0.734752	−	0.678336i	$-0.237298\pi$
$642$		0			0
$643$	11.8373	+	6.83426i	0.466817	+	0.269517i	0.714906	−	0.699220i	$-0.246469\pi$
$643$	11.8373	+	6.83426i	0.466817	+	0.269517i	−0.248089	+	0.968737i	$0.579803\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.1075	+	31.3630i	−0.711877	+	1.23301i	0.252274	+	0.967656i	$0.418822\pi$
$647$	−18.1075	+	31.3630i	−0.711877	+	1.23301i	−0.964152	+	0.265352i	$0.914512\pi$
$648$		0			0
$649$	−1.03319	+	0.596512i	−0.0405562	+	0.0234151i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			36.5270i			1.42941i	0.699426	+	0.714705i	$0.253439\pi$
$653$			36.5270i			1.42941i	−0.699426	+	0.714705i	$0.746561\pi$
$654$		0			0
$655$	−16.2437			−0.634695
$656$		0			0
$657$		0			0
$658$		0			0
$659$	19.5178	−	11.2686i	0.760305	−	0.438962i	−0.0691004	−	0.997610i	$-0.522013\pi$
$659$	19.5178	−	11.2686i	0.760305	−	0.438962i	0.829405	+	0.558648i	$0.188680\pi$
$660$		0			0
$661$	1.29595	−	0.748216i	0.0504065	−	0.0291022i	−0.474585	−	0.880210i	$-0.657402\pi$
$661$	1.29595	−	0.748216i	0.0504065	−	0.0291022i	0.524991	+	0.851107i	$0.324068\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−5.82811	−	0.517890i	−0.226004	−	0.0200829i
$666$		0			0
$667$	2.27925	+	3.94778i	0.0882529	+	0.152859i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.732330	+	1.26843i	−0.0282713	+	0.0489673i
$672$		0			0
$673$	13.9366	+	24.1389i	0.537215	+	0.930484i	0.999053	+	0.0435197i	$0.0138571\pi$
$673$	13.9366	+	24.1389i	0.537215	+	0.930484i	−0.461837	+	0.886965i	$0.652810\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	15.6344	−	27.0796i	0.600880	−	1.04075i	−0.391809	−	0.920047i	$-0.628150\pi$
$677$	15.6344	−	27.0796i	0.600880	−	1.04075i	0.992688	−	0.120707i	$-0.0385162\pi$
$678$		0			0
$679$	−9.16081	−	0.814037i	−0.351560	−	0.0312399i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−8.06769	−	4.65788i	−0.308701	−	0.178229i	0.337644	−	0.941274i	$-0.390370\pi$
$683$	−8.06769	−	4.65788i	−0.308701	−	0.178229i	−0.646345	+	0.763045i	$0.723703\pi$
$684$		0			0
$685$			36.2949i			1.38676i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.93139	+	5.07732i	0.111677	+	0.193431i
$690$		0			0
$691$	42.0468	+	24.2757i	1.59954	+	0.923493i	0.991576	+	0.129526i	$0.0413456\pi$
$691$	42.0468	+	24.2757i	1.59954	+	0.923493i	0.607961	+	0.793967i	$0.291988\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−24.7633	−	14.2971i	−0.939324	−	0.542319i
$696$		0			0
$697$	2.43338	+	4.21473i	0.0921707	+	0.159644i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	22.9812i		−	0.867987i	−0.900916	−	0.433994i	$-0.857104\pi$
$701$		−	22.9812i		−	0.867987i	0.900916	−	0.433994i	$-0.142896\pi$
$702$		0			0
$703$	2.17831	+	1.25765i	0.0821564	+	0.0474330i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−20.5816	−	14.4532i	−0.774052	−	0.543569i
$708$		0			0
$709$	−15.3433	+	26.5753i	−0.576228	+	0.998057i	0.419679	+	0.907673i	$0.362143\pi$
$709$	−15.3433	+	26.5753i	−0.576228	+	0.998057i	−0.995907	+	0.0903840i	$0.971191\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	22.3582	+	38.7255i	0.837319	+	1.45028i
$714$		0			0
$715$	0.580956	−	1.00625i	0.0217265	−	0.0376315i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−2.44166	−	4.22907i	−0.0910584	−	0.157718i	0.816898	−	0.576782i	$-0.195692\pi$
$719$	−2.44166	−	4.22907i	−0.0910584	−	0.157718i	−0.907957	+	0.419064i	$0.862358\pi$
$720$		0			0
$721$	12.7494	−	18.1554i	0.474812	−	0.676141i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.0851181	−	0.0491430i	0.00316121	−	0.00182512i
$726$		0			0
$727$	32.7779	−	18.9243i	1.21567	−	0.701865i	0.251678	−	0.967811i	$-0.419018\pi$
$727$	32.7779	−	18.9243i	1.21567	−	0.701865i	0.963988	+	0.265946i	$0.0856844\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−43.4911			−1.60858
$732$		0			0
$733$			46.3166i			1.71074i	0.518017	+	0.855370i	$0.326670\pi$
$733$			46.3166i			1.71074i	−0.518017	+	0.855370i	$0.673330\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.08548	−	0.626700i	0.0399840	−	0.0230848i
$738$		0			0
$739$	5.15606	−	8.93056i	0.189669	−	0.328516i	−0.755471	−	0.655182i	$-0.772592\pi$
$739$	5.15606	−	8.93056i	0.189669	−	0.328516i	0.945140	+	0.326666i	$0.105925\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−21.9984	−	12.7008i	−0.807042	−	0.465946i	0.0388856	−	0.999244i	$-0.487619\pi$
$743$	−21.9984	−	12.7008i	−0.807042	−	0.465946i	−0.845928	+	0.533298i	$0.820953\pi$
$744$		0			0
$745$			33.6537i			1.23298i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−38.7413	−	3.44258i	−1.41557	−	0.125789i
$750$		0			0
$751$	−53.7306			−1.96066			−0.980329	−	0.197369i	$-0.936760\pi$
$751$	−53.7306			−1.96066			−0.980329	+	0.197369i	$0.936760\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	30.1783			1.09830
$756$		0			0
$757$	28.3821			1.03157			0.515783	−	0.856719i	$-0.327501\pi$
$757$	28.3821			1.03157			0.515783	+	0.856719i	$0.327501\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−23.1184			−0.838041			−0.419021	−	0.907977i	$-0.637626\pi$
$761$	−23.1184			−0.838041			−0.419021	+	0.907977i	$0.637626\pi$
$762$		0			0
$763$	40.1008	−	18.6329i	1.45175	−	0.674556i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			18.9640i			0.684752i
$768$		0			0
$769$	−23.1698	−	13.3771i	−0.835524	−	0.482390i	0.0202163	−	0.999796i	$-0.493565\pi$
$769$	−23.1698	−	13.3771i	−0.835524	−	0.482390i	−0.855740	+	0.517406i	$0.826898\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.97203	−	6.87976i	0.142864	−	0.247448i	−0.785710	−	0.618595i	$-0.787702\pi$
$773$	3.97203	−	6.87976i	0.142864	−	0.247448i	0.928574	+	0.371147i	$0.121035\pi$
$774$		0			0
$775$	0.834960	−	0.482065i	0.0299927	−	0.0173163i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	1.22729i		−	0.0439721i
$780$		0			0
$781$	−2.07686			−0.0743158
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−22.6013	+	13.0489i	−0.806676	+	0.465734i
$786$		0			0
$787$	−10.5602	+	6.09696i	−0.376432	+	0.217333i	−0.676265	−	0.736659i	$-0.736402\pi$
$787$	−10.5602	+	6.09696i	−0.376432	+	0.217333i	0.299833	+	0.953992i	$0.403069\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.53829	+	3.31064i	0.0546954	+	0.117713i
$792$		0			0
$793$	11.6410	+	20.1627i	0.413382	+	0.715999i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	3.30173	−	5.71876i	0.116953	−	0.202569i	−0.801606	−	0.597853i	$-0.796021\pi$
$797$	3.30173	−	5.71876i	0.116953	−	0.202569i	0.918559	+	0.395284i	$0.129354\pi$
$798$		0			0
$799$	−14.1956	−	24.5875i	−0.502204	−	0.869842i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.06982	−	1.85298i	0.0377531	−	0.0653903i
$804$		0			0
$805$	−18.8518	+	26.8453i	−0.664439	+	0.946173i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−8.57462	−	4.95056i	−0.301468	−	0.174052i	0.341634	−	0.939833i	$-0.389020\pi$
$809$	−8.57462	−	4.95056i	−0.301468	−	0.174052i	−0.643102	+	0.765780i	$0.722353\pi$
$810$		0			0
$811$			33.1027i			1.16239i	0.813763	+	0.581197i	$0.197416\pi$
$811$			33.1027i			1.16239i	−0.813763	+	0.581197i	$0.802584\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	9.63049	+	16.6805i	0.337341	+	0.584292i
$816$		0			0
$817$	9.49812	+	5.48374i	0.332297	+	0.191852i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	9.90100	+	5.71634i	0.345547	+	0.199502i	0.662722	−	0.748865i	$-0.269401\pi$
$821$	9.90100	+	5.71634i	0.345547	+	0.199502i	−0.317175	+	0.948367i	$0.602734\pi$
$822$		0			0
$823$	19.4509	+	33.6900i	0.678017	+	1.17436i	0.975577	+	0.219656i	$0.0704936\pi$
$823$	19.4509	+	33.6900i	0.678017	+	1.17436i	−0.297561	+	0.954703i	$0.596173\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			8.05228i			0.280005i	0.990151	+	0.140003i	$0.0447111\pi$
$827$			8.05228i			0.280005i	−0.990151	+	0.140003i	$0.955289\pi$
$828$		0			0
$829$	−11.3389	−	6.54652i	−0.393816	−	0.227370i	0.289996	−	0.957028i	$-0.406346\pi$
$829$	−11.3389	−	6.54652i	−0.393816	−	0.227370i	−0.683812	+	0.729658i	$0.739679\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−27.3561	−	4.90047i	−0.947834	−	0.169791i
$834$		0			0
$835$	19.6556	−	34.0445i	0.680211	−	1.17816i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−5.51797	−	9.55740i	−0.190501	−	0.329958i	0.754915	−	0.655822i	$-0.227678\pi$
$839$	−5.51797	−	9.55740i	−0.190501	−	0.329958i	−0.945416	+	0.325864i	$0.894345\pi$
$840$		0			0
$841$	−14.1702	+	24.5436i	−0.488629	+	0.846330i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.12271	+	8.87279i	0.176227	+	0.305233i
$846$		0			0
$847$	23.7456	+	16.6751i	0.815908	+	0.572962i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	12.2124	−	7.05085i	0.418637	−	0.241700i
$852$		0			0
$853$	20.2134	−	11.6702i	0.692092	−	0.399580i	−0.112303	−	0.993674i	$-0.535823\pi$
$853$	20.2134	−	11.6702i	0.692092	−	0.399580i	0.804395	+	0.594094i	$0.202489\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−18.2121			−0.622115			−0.311057	−	0.950391i	$-0.600683\pi$
$857$	−18.2121			−0.622115			−0.311057	+	0.950391i	$0.600683\pi$
$858$		0			0
$859$		−	39.1597i		−	1.33611i	−0.744111	−	0.668057i	$-0.767126\pi$
$859$		−	39.1597i		−	1.33611i	0.744111	−	0.668057i	$-0.232874\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	22.7847	−	13.1548i	0.775601	−	0.447793i	−0.0592683	−	0.998242i	$-0.518877\pi$
$863$	22.7847	−	13.1548i	0.775601	−	0.447793i	0.834869	+	0.550449i	$0.185543\pi$
$864$		0			0
$865$	21.1168	−	36.5754i	0.717994	−	1.24360i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.00235	−	1.15606i	−0.0679252	−	0.0392166i
$870$		0			0
$871$		−	19.9238i		−	0.675091i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	24.4918	+	17.1991i	0.827973	+	0.581434i
$876$		0			0
$877$	7.19666			0.243014			0.121507	−	0.992591i	$-0.461227\pi$
$877$	7.19666			0.243014			0.121507	+	0.992591i	$0.461227\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−37.2133			−1.25375			−0.626874	−	0.779121i	$-0.715666\pi$
$881$	−37.2133			−1.25375			−0.626874	+	0.779121i	$0.715666\pi$
$882$		0			0
$883$	9.72629			0.327316			0.163658	−	0.986517i	$-0.447671\pi$
$883$	9.72629			0.327316			0.163658	+	0.986517i	$0.447671\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−20.6986			−0.694992			−0.347496	−	0.937681i	$-0.612968\pi$
$887$	−20.6986			−0.694992			−0.347496	+	0.937681i	$0.612968\pi$
$888$		0			0
$889$	−25.9140	−	18.1978i	−0.869129	−	0.610336i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			7.15962i			0.239587i
$894$		0			0
$895$	−11.7486	−	6.78307i	−0.392713	−	0.226733i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.23480	−	5.60284i	0.107887	−	0.186865i
$900$		0			0
$901$	−6.97115	+	4.02480i	−0.232243	+	0.134085i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	24.5641i		−	0.816539i
$906$		0			0
$907$	0.990928			0.0329032			0.0164516	−	0.999865i	$-0.494763\pi$
$907$	0.990928			0.0329032			0.0164516	+	0.999865i	$0.494763\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−15.2170	+	8.78552i	−0.504161	+	0.291077i	−0.730430	−	0.682987i	$-0.760680\pi$
$911$	−15.2170	+	8.78552i	−0.504161	+	0.291077i	0.226269	+	0.974065i	$0.427347\pi$
$912$		0			0
$913$	−2.26571	+	1.30811i	−0.0749841	+	0.0432921i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	15.9228	+	11.1816i	0.525818	+	0.369250i
$918$		0			0
$919$	−9.22417	−	15.9767i	−0.304277	−	0.527024i	0.672823	−	0.739804i	$-0.265082\pi$
$919$	−9.22417	−	15.9767i	−0.304277	−	0.527024i	−0.977100	+	0.212780i	$0.931748\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−16.5066	+	28.5903i	−0.543322	+	0.941061i
$924$		0			0
$925$	−0.152024	−	0.263313i	−0.00499851	−	0.00865767i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	10.4712	−	18.1367i	0.343550	−	0.595046i	−0.641539	−	0.767090i	$-0.721704\pi$
$929$	10.4712	−	18.1367i	0.343550	−	0.595046i	0.985089	+	0.172044i	$0.0550372\pi$
$930$		0			0
$931$	5.35647	+	4.51953i	0.175551	+	0.148122i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.38157	+	0.797652i	0.0451823	+	0.0260860i
$936$		0			0
$937$			27.1677i			0.887529i	0.896143	+	0.443764i	$0.146357\pi$
$937$			27.1677i			0.887529i	−0.896143	+	0.443764i	$0.853643\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.42576	+	2.46949i	0.0464785	+	0.0805031i	0.888329	−	0.459208i	$-0.151867\pi$
$941$	1.42576	+	2.46949i	0.0464785	+	0.0805031i	−0.841850	+	0.539711i	$0.818533\pi$
$942$		0			0
$943$	−5.95881	−	3.44032i	−0.194046	−	0.112032i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15.2662	−	8.81395i	−0.496085	−	0.286415i	0.231010	−	0.972951i	$-0.425797\pi$
$947$	−15.2662	−	8.81395i	−0.496085	−	0.286415i	−0.727095	+	0.686536i	$0.759130\pi$
$948$		0			0
$949$	−17.0056	−	29.4546i	−0.552025	−	0.956136i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			47.1766i			1.52820i	0.645097	+	0.764101i	$0.276817\pi$
$953$			47.1766i			1.52820i	−0.645097	+	0.764101i	$0.723183\pi$
$954$		0			0
$955$	28.5697	+	16.4947i	0.924493	+	0.533756i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	24.9842	−	35.5779i	0.806780	−	1.14887i
$960$		0			0
$961$	16.2315	−	28.1139i	0.523598	−	0.906899i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−13.7255	−	23.7732i	−0.441838	−	0.765286i
$966$		0			0
$967$	−3.62809	+	6.28404i	−0.116672	+	0.202081i	−0.918447	−	0.395545i	$-0.870556\pi$
$967$	−3.62809	+	6.28404i	−0.116672	+	0.202081i	0.801775	+	0.597626i	$0.203889\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	10.2653	+	17.7800i	0.329429	+	0.570588i	0.982399	−	0.186796i	$-0.0598104\pi$
$971$	10.2653	+	17.7800i	0.329429	+	0.570588i	−0.652970	+	0.757384i	$0.726477\pi$
$972$		0			0
$973$	14.4324	+	31.0608i	0.462683	+	0.995764i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−38.7545	+	22.3749i	−1.23987	+	0.715838i	−0.969067	−	0.246798i	$-0.920622\pi$
$977$	−38.7545	+	22.3749i	−1.23987	+	0.715838i	−0.270800	+	0.962636i	$0.587288\pi$
$978$		0			0
$979$	−2.24142	+	1.29408i	−0.0716360	+	0.0413591i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−26.9099			−0.858293			−0.429146	−	0.903235i	$-0.641186\pi$
$983$	−26.9099			−0.858293			−0.429146	+	0.903235i	$0.641186\pi$
$984$		0			0
$985$			35.6755i			1.13672i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	53.2502	−	30.7440i	1.69326	−	0.977602i
$990$		0			0
$991$	13.8668	−	24.0181i	0.440494	−	0.762959i	−0.557232	−	0.830357i	$-0.688136\pi$
$991$	13.8668	−	24.0181i	0.440494	−	0.762959i	0.997726	+	0.0673982i	$0.0214698\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	47.6585	+	27.5156i	1.51088	+	0.872304i
$996$		0			0
$997$			22.4382i			0.710624i	0.934748	+	0.355312i	$0.115625\pi$
$997$			22.4382i			0.710624i	−0.934748	+	0.355312i	$0.884375\pi$
$998$		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.17.7		48
3.2	odd	2		504.2.cx.a.185.8	yes	48
4.3	odd	2		3024.2.df.e.17.7		48
7.5	odd	6		1512.2.bs.a.1097.7		48
9.2	odd	6		1512.2.bs.a.521.7		48
9.7	even	3		504.2.bs.a.353.15	yes	48
12.11	even	2		1008.2.df.e.689.17		48
21.5	even	6		504.2.bs.a.257.15	✓	48
28.19	even	6		3024.2.ca.e.2609.7		48
36.7	odd	6		1008.2.ca.e.353.10		48
36.11	even	6		3024.2.ca.e.2033.7		48
63.47	even	6	inner	1512.2.cx.a.89.7		48
63.61	odd	6		504.2.cx.a.425.8	yes	48
84.47	odd	6		1008.2.ca.e.257.10		48
252.47	odd	6		3024.2.df.e.1601.7		48
252.187	even	6		1008.2.df.e.929.17		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.15	✓	48	21.5	even	6
504.2.bs.a.353.15	yes	48	9.7	even	3
504.2.cx.a.185.8	yes	48	3.2	odd	2
504.2.cx.a.425.8	yes	48	63.61	odd	6
1008.2.ca.e.257.10		48	84.47	odd	6
1008.2.ca.e.353.10		48	36.7	odd	6
1008.2.df.e.689.17		48	12.11	even	2
1008.2.df.e.929.17		48	252.187	even	6
1512.2.bs.a.521.7		48	9.2	odd	6
1512.2.bs.a.1097.7		48	7.5	odd	6
1512.2.cx.a.17.7		48	1.1	even	1	trivial
1512.2.cx.a.89.7		48	63.47	even	6	inner
3024.2.ca.e.2033.7		48	36.11	even	6
3024.2.ca.e.2609.7		48	28.19	even	6
3024.2.df.e.17.7		48	4.3	odd	2
3024.2.df.e.1601.7		48	252.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-2.20884 q^{5} +(2.16520 + 1.52049i) q^{7} +0.181913i q^{11} +(2.50424 + 1.44582i) q^{13} +(-1.98511 + 3.43832i) q^{17} +(0.867067 - 0.500601i) q^{19} -5.61313i q^{23} -0.121025 q^{25} +(-0.703311 + 0.406057i) q^{29} +(-6.89908 + 3.98319i) q^{31} +(-4.78259 - 3.35852i) q^{35} +(1.25614 + 2.17569i) q^{37} +(0.612906 - 1.06158i) q^{41} +(5.47716 + 9.48671i) q^{43} +(-3.57551 + 6.19296i) q^{47} +(2.37622 + 6.58434i) q^{49} +(1.75586 + 1.01374i) q^{53} -0.401817i q^{55} +(3.27911 + 5.67958i) q^{59} +(6.97275 + 4.02572i) q^{61} +(-5.53147 - 3.19359i) q^{65} +(-3.44505 - 5.96701i) q^{67} +11.4168i q^{71} +(-10.1861 - 5.88094i) q^{73} +(-0.276597 + 0.393879i) q^{77} +(-6.35501 + 11.0072i) q^{79} +(7.19085 + 12.4549i) q^{83} +(4.38480 - 7.59470i) q^{85} +(7.11375 + 12.3214i) q^{89} +(3.22383 + 6.93818i) q^{91} +(-1.91521 + 1.10575i) q^{95} +(-3.01040 + 1.73805i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{25} - 18 q^{29} + 18 q^{31} + 6 q^{41} - 6 q^{43} - 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} + 6 q^{79} + 18 q^{89} + 6 q^{91} + 54 q^{95}+O(q^{100}) \) 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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