LMFDB - Embedded newform 740.2.ce.a.263.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(3,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([18, 27, 26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.3"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.ce (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\Q(\zeta_{36})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{36}]$

Embedding invariants

Embedding label			263.1
Root			$-0.984808 - 0.173648i$ of defining polynomial
Character	$\chi$	$=$	740.263
Dual form			740.2.ce.a.287.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.15846 - 0.811160i) q^{2} +(0.684040 - 1.87939i) q^{4} +(-1.86603 - 1.23205i) q^{5} +(-0.732051 - 2.73205i) q^{8} +(-1.02606 - 2.81908i) q^{9} +(-3.16110 + 0.0863678i) q^{10} +(-6.19084 + 2.88683i) q^{13} +(-3.06418 - 2.57115i) q^{16} +(1.17380 + 0.547351i) q^{17} +(-3.47537 - 2.43348i) q^{18} +(-3.59193 + 2.66421i) q^{20} +(1.96410 + 4.59808i) q^{25} +(-4.83013 + 8.36603i) q^{26} +(5.38250 - 9.32277i) q^{29} +(-5.63533 - 0.493027i) q^{32} +(1.80378 - 0.318056i) q^{34} -6.00000 q^{36} +(1.11243 - 5.98018i) q^{37} +(-2.00000 + 6.00000i) q^{40} +(-0.281457 - 0.102442i) q^{41} +(-1.55859 + 6.52463i) q^{45} +(-6.89365 - 1.21554i) q^{49} +(6.00510 + 3.73347i) q^{50} +(1.19069 + 13.6097i) q^{52} +(-0.652550 - 7.45868i) q^{53} +(-1.32686 - 15.1661i) q^{58} +(4.61767 - 12.6869i) q^{61} +(-6.92820 + 4.00000i) q^{64} +(15.1090 + 2.24052i) q^{65} +(1.83161 - 1.83161i) q^{68} +(-6.95074 + 4.86696i) q^{72} +(12.0263 + 12.0263i) q^{73} +(-3.56218 - 7.83013i) q^{74} +(2.55005 + 8.57305i) q^{80} +(-6.89440 + 5.78509i) q^{81} +(-0.409153 + 0.109632i) q^{82} +(-1.51597 - 2.46755i) q^{85} +(13.7467 + 11.5349i) q^{89} +(3.48696 + 8.82276i) q^{90} +(5.09731 - 19.0234i) q^{97} +(-8.97199 + 4.18371i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{5} + 12 q^{8} - 24 q^{17} - 18 q^{25} - 6 q^{26} + 30 q^{34} - 72 q^{36} - 24 q^{40} + 24 q^{41} - 42 q^{58} + 72 q^{61} + 30 q^{73} + 30 q^{74} + 84 q^{85} + 60 q^{89}+O(q^{100}) $ 12 * q - 12 * q^5 + 12 * q^8 - 24 * q^17 - 18 * q^25 - 6 * q^26 + 30 * q^34 - 72 * q^36 - 24 * q^40 + 24 * q^41 - 42 * q^58 + 72 * q^61 + 30 * q^73 + 30 * q^74 + 84 * q^85 + 60 * q^89

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	1.15846	−	0.811160i	0.819152	−	0.573576i
$2$	1.15846	−	0.811160i	0.819152	−	0.573576i
$3$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$3$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$4$	0.684040	−	1.87939i	0.342020	−	0.939693i
$5$	−1.86603	−	1.23205i	−0.834512	−	0.550990i
$5$	−1.86603	−	1.23205i	−0.834512	−	0.550990i
$6$		0			0
$7$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$7$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$8$	−0.732051	−	2.73205i	−0.258819	−	0.965926i
$9$	−1.02606	−	2.81908i	−0.342020	−	0.939693i
$10$	−3.16110	+	0.0863678i	−0.999627	+	0.0273119i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$		0			0
$13$	−6.19084	+	2.88683i	−1.71703	+	0.800664i	−0.723087	+	0.690757i	$0.757277\pi$
$13$	−6.19084	+	2.88683i	−1.71703	+	0.800664i	−0.993942	+	0.109907i	$0.964945\pi$
$14$		0			0
$15$		0			0
$16$	−3.06418	−	2.57115i	−0.766044	−	0.642788i
$17$	1.17380	+	0.547351i	0.284688	+	0.132752i	0.559717	−	0.828684i	$-0.310910\pi$
$17$	1.17380	+	0.547351i	0.284688	+	0.132752i	−0.275029	+	0.961436i	$0.588688\pi$
$18$	−3.47537	−	2.43348i	−0.819152	−	0.573576i
$19$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$19$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$20$	−3.59193	+	2.66421i	−0.803181	+	0.595735i
$21$		0			0
$22$		0			0
$23$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$23$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$24$		0			0
$25$	1.96410	+	4.59808i	0.392820	+	0.919615i
$26$	−4.83013	+	8.36603i	−0.947266	+	1.64071i
$27$		0			0
$28$		0			0
$29$	5.38250	−	9.32277i	0.999506	−	1.73119i	0.472529	−	0.881315i	$-0.343341\pi$
$29$	5.38250	−	9.32277i	0.999506	−	1.73119i	0.526977	−	0.849880i	$-0.323326\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−5.63533	−	0.493027i	−0.996195	−	0.0871557i
$33$		0			0
$34$	1.80378	−	0.318056i	0.309346	−	0.0545461i
$35$		0			0
$36$	−6.00000			−1.00000
$37$	1.11243	−	5.98018i	0.182882	−	0.983135i
$37$	1.11243	−	5.98018i	0.182882	−	0.983135i
$38$		0			0
$39$		0			0
$40$	−2.00000	+	6.00000i	−0.316228	+	0.948683i
$41$	−0.281457	−	0.102442i	−0.0439562	−	0.0159988i	0.319948	−	0.947435i	$-0.396334\pi$
$41$	−0.281457	−	0.102442i	−0.0439562	−	0.0159988i	−0.363905	+	0.931436i	$0.618557\pi$
$42$		0			0
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$		0			0
$45$	−1.55859	+	6.52463i	−0.232341	+	0.972634i
$46$		0			0
$47$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$47$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$48$		0			0
$49$	−6.89365	−	1.21554i	−0.984808	−	0.173648i
$50$	6.00510	+	3.73347i	0.849249	+	0.527992i
$51$		0			0
$52$	1.19069	+	13.6097i	0.165119	+	1.88732i
$53$	−0.652550	−	7.45868i	−0.0896346	−	1.02453i	−0.899211	−	0.437514i	$-0.855859\pi$
$53$	−0.652550	−	7.45868i	−0.0896346	−	1.02453i	0.809577	−	0.587014i	$-0.199697\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−1.32686	−	15.1661i	−0.174225	−	1.99140i
$59$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$59$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$60$		0			0
$61$	4.61767	−	12.6869i	0.591232	−	1.62440i	−0.176989	−	0.984213i	$-0.556636\pi$
$61$	4.61767	−	12.6869i	0.591232	−	1.62440i	0.768221	−	0.640184i	$-0.221142\pi$
$62$		0			0
$63$		0			0
$64$	−6.92820	+	4.00000i	−0.866025	+	0.500000i
$65$	15.1090	+	2.24052i	1.87404	+	0.277902i
$66$		0			0
$67$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$67$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$68$	1.83161	−	1.83161i	0.222115	−	0.222115i
$69$		0			0
$70$		0			0
$71$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$71$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$72$	−6.95074	+	4.86696i	−0.819152	+	0.573576i
$73$	12.0263	+	12.0263i	1.40757	+	1.40757i	0.772246	+	0.635323i	$0.219133\pi$
$73$	12.0263	+	12.0263i	1.40757	+	1.40757i	0.635323	+	0.772246i	$0.280867\pi$
$74$	−3.56218	−	7.83013i	−0.414095	−	0.910234i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$79$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$80$	2.55005	+	8.57305i	0.285104	+	0.958497i
$81$	−6.89440	+	5.78509i	−0.766044	+	0.642788i
$82$	−0.409153	+	0.109632i	−0.0451834	+	0.0121068i
$83$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$83$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$84$		0			0
$85$	−1.51597	−	2.46755i	−0.164430	−	0.267643i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	13.7467	+	11.5349i	1.45715	+	1.22269i	0.927149	+	0.374694i	$0.122252\pi$
$89$	13.7467	+	11.5349i	1.45715	+	1.22269i	0.529999	+	0.847998i	$0.322192\pi$
$90$	3.48696	+	8.82276i	0.367557	+	0.930001i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	5.09731	−	19.0234i	0.517553	−	1.93153i	0.241287	−	0.970454i	$-0.422431\pi$
$97$	5.09731	−	19.0234i	0.517553	−	1.93153i	0.276267	−	0.961081i	$-0.410903\pi$
$98$	−8.97199	+	4.18371i	−0.906308	+	0.422618i
$99$		0			0
$100$	9.98508	−	0.546034i	0.998508	−	0.0546034i
$101$	2.48051	+	4.29637i	0.246820	+	0.427505i	0.962642	−	0.270778i	$-0.0872811\pi$
$101$	2.48051	+	4.29637i	0.246820	+	0.427505i	−0.715822	+	0.698283i	$0.753948\pi$
$102$		0			0
$103$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$103$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$104$	12.4190	+	14.8004i	1.21778	+	1.45130i
$105$		0			0
$106$	−6.80613	−	8.11123i	−0.661070	−	0.787832i
$107$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$107$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$108$		0			0
$109$	3.33016	−	18.8863i	0.318971	−	1.80898i	−0.230063	−	0.973176i	$-0.573893\pi$
$109$	3.33016	−	18.8863i	0.318971	−	1.80898i	0.549034	−	0.835800i	$-0.314996\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	10.1317	+	14.4696i	0.953109	+	1.36118i	0.932413	+	0.361396i	$0.117700\pi$
$113$	10.1317	+	14.4696i	0.953109	+	1.36118i	0.0206968	+	0.999786i	$0.493412\pi$
$114$		0			0
$115$		0			0
$116$	−13.8392	−	16.4929i	−1.28494	−	1.53133i
$117$	14.4904	+	14.4904i	1.33964	+	1.33964i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−5.50000	−	9.52628i	−0.500000	−	0.866025i
$122$	−4.94177	−	18.4429i	−0.447407	−	1.66975i
$123$		0			0
$124$		0			0
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$		0			0
$127$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$127$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$128$	−4.78138	+	10.2537i	−0.422618	+	0.906308i
$129$		0			0
$130$	19.3205	−	9.66025i	1.69452	−	0.847260i
$131$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$131$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.636111	−	3.60757i	0.0545461	−	0.309346i
$137$	−1.56986	−	5.85879i	−0.134122	−	0.500550i	−1.00000		0.000294847i	$-0.999906\pi$
$137$	−1.56986	−	5.85879i	−0.134122	−	0.500550i	0.865878	−	0.500255i	$-0.166761\pi$
$138$		0			0
$139$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$139$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−4.10424	+	11.2763i	−0.342020	+	0.939693i
$145$	−21.5300	+	10.7650i	−1.78797	+	0.893985i
$146$	23.6871	+	4.17668i	1.96036	+	0.345665i
$147$		0			0
$148$	−10.4781	−	6.18136i	−0.861295	−	0.508105i
$149$			17.2651i			1.41441i	0.707008	+	0.707205i	$0.250044\pi$
$149$			17.2651i			1.41441i	−0.707008	+	0.707205i	$0.749956\pi$
$150$		0			0
$151$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$151$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$152$		0			0
$153$	0.338638	−	3.87065i	0.0273772	−	0.312923i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−4.24178	+	9.09653i	−0.338531	+	0.725982i	−0.999706	−	0.0242497i	$-0.992280\pi$
$157$	−4.24178	+	9.09653i	−0.338531	+	0.725982i	0.661175	+	0.750232i	$0.270058\pi$
$158$		0			0
$159$		0			0
$160$	9.90823	+	7.86301i	0.783314	+	0.621626i
$161$		0			0
$162$	−3.29423	+	12.2942i	−0.258819	+	0.965926i
$163$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$163$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$164$	−0.385056	+	0.458892i	−0.0300678	+	0.0358335i
$165$		0			0
$166$		0			0
$167$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$167$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$168$		0			0
$169$	21.6364	−	25.7853i	1.66434	−	1.98348i
$170$	−3.75777	−	1.62885i	−0.288207	−	0.124927i
$171$		0			0
$172$		0			0
$173$	−15.5669	+	10.9000i	−1.18353	+	0.828715i	−0.988372	−	0.152057i	$-0.951410\pi$
$173$	−15.5669	+	10.9000i	−1.18353	+	0.828715i	−0.195156	+	0.980772i	$0.562521\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	25.2816	+	2.21185i	1.89493	+	0.165785i
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$	11.1962	+	7.39230i	0.834512	+	0.550990i
$181$	−21.4455	−	7.80552i	−1.59403	−	0.580180i	−0.615837	−	0.787873i	$-0.711182\pi$
$181$	−21.4455	−	7.80552i	−1.59403	−	0.580180i	−0.978194	+	0.207693i	$0.933404\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−9.44370	+	9.78859i	−0.694315	+	0.719672i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		0			0
$193$	5.90914	+	22.0532i	0.425349	+	1.58742i	0.763160	+	0.646210i	$0.223647\pi$
$193$	5.90914	+	22.0532i	0.425349	+	1.58742i	−0.337811	+	0.941214i	$0.609686\pi$
$194$	−9.52602	−	26.1725i	−0.683928	−	1.87908i
$195$		0			0
$196$	−7.00000	+	12.1244i	−0.500000	+	0.866025i
$197$	2.54252	+	3.63110i	0.181147	+	0.258705i	0.899448	−	0.437028i	$-0.143969\pi$
$197$	2.54252	+	3.63110i	0.181147	+	0.258705i	−0.718301	+	0.695733i	$0.755080\pi$
$198$		0			0
$199$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$199$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$200$	11.1244	−	8.73205i	0.786611	−	0.617449i
$201$		0			0
$202$	6.35860	+	2.96506i	0.447390	+	0.208621i
$203$		0			0
$204$		0			0
$205$	0.398993	+	0.537929i	0.0278668	+	0.0375706i
$206$		0			0
$207$		0			0
$208$	26.3923	+	7.07180i	1.82998	+	0.490341i
$209$		0			0
$210$		0			0
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$	−14.4641	−	3.87564i	−0.993399	−	0.266180i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−11.4619	−	24.5802i	−0.776300	−	1.66478i
$219$		0			0
$220$		0			0
$221$	−8.84691			−0.595107
$222$		0			0
$223$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$223$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$224$		0			0
$225$	10.9470	−	10.2549i	0.729803	−	0.683657i
$226$	23.4742	+	8.54392i	1.56148	+	0.568333i
$227$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$227$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$228$		0			0
$229$	−9.01148	−	10.7395i	−0.595495	−	0.709684i	0.381157	−	0.924510i	$-0.375526\pi$
$229$	−9.01148	−	10.7395i	−0.595495	−	0.709684i	−0.976652	+	0.214827i	$0.931081\pi$
$230$		0			0
$231$		0			0
$232$	−29.4105	−	7.88053i	−1.93090	−	0.517382i
$233$	27.0647	−	7.25196i	1.77307	−	0.475092i	0.783775	−	0.621045i	$-0.213292\pi$
$233$	27.0647	−	7.25196i	1.77307	−	0.475092i	0.989291	+	0.145953i	$0.0466250\pi$
$234$	28.5405	+	5.03246i	1.86575	+	0.328982i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$239$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$240$		0			0
$241$	−7.94917	+	1.40165i	−0.512051	+	0.0902884i	−0.423703	−	0.905801i	$-0.639270\pi$
$241$	−7.94917	+	1.40165i	−0.512051	+	0.0902884i	−0.0883481	+	0.996090i	$0.528159\pi$
$242$	−14.0988	−	6.57440i	−0.906308	−	0.422618i
$243$		0			0
$244$	−20.6850	−	17.3568i	−1.32422	−	1.11115i
$245$	11.3661	+	10.7616i	0.726155	+	0.687531i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−6.60584	−	14.3653i	−0.417790	−	0.908544i
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	2.77837	+	15.7569i	0.173648	+	0.984808i
$257$	24.4493	−	17.1196i	1.52511	−	1.06789i	0.553047	−	0.833150i	$-0.313465\pi$
$257$	24.4493	−	17.1196i	1.52511	−	1.06789i	0.972058	−	0.234741i	$-0.0754241\pi$
$258$		0			0
$259$		0			0
$260$	14.5459	−	26.8630i	0.902101	−	1.66597i
$261$	−31.8044	−	5.60797i	−1.96864	−	0.347125i
$262$		0			0
$263$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$263$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$264$		0			0
$265$	−7.97180	+	14.7221i	−0.489704	+	0.904369i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.74167	−	2.16025i	0.228134	−	0.131713i	−0.381577	−	0.924337i	$-0.624619\pi$
$269$	3.74167	−	2.16025i	0.228134	−	0.131713i	0.609711	+	0.792624i	$0.291286\pi$
$270$		0			0
$271$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$271$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$272$	−2.18941	−	4.69519i	−0.132752	−	0.284688i
$273$		0			0
$274$	−6.57102	−	5.51374i	−0.396970	−	0.333097i
$275$		0			0
$276$		0			0
$277$	−7.23388	+	10.3310i	−0.434642	+	0.620733i	−0.975399	−	0.220446i	$-0.929249\pi$
$277$	−7.23388	+	10.3310i	−0.434642	+	0.620733i	0.540758	+	0.841178i	$0.318138\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	21.3729	−	25.4712i	1.27500	−	1.51949i	0.539447	−	0.842020i	$-0.318633\pi$
$281$	21.3729	−	25.4712i	1.27500	−	1.51949i	0.735554	−	0.677466i	$-0.236922\pi$
$282$		0			0
$283$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$283$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	4.39230	+	16.3923i	0.258819	+	0.965926i
$289$	−9.84918	−	11.7378i	−0.579364	−	0.690459i
$290$	−16.2094	+	29.9351i	−0.951851	+	1.75785i
$291$		0			0
$292$	30.8285	−	14.3756i	1.80410	−	0.841266i
$293$	−6.16238	+	8.80080i	−0.360010	+	0.514148i	−0.957773	−	0.287525i	$-0.907168\pi$
$293$	−6.16238	+	8.80080i	−0.360010	+	0.514148i	0.597763	+	0.801673i	$0.296056\pi$
$294$		0			0
$295$		0			0
$296$	−17.1525	+	1.33858i	−0.996969	+	0.0778035i
$297$		0			0
$298$	14.0047	+	20.0008i	0.811273	+	1.15862i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−24.2477	+	17.9850i	−1.38842	+	1.02982i
$306$	−2.74741	−	4.75866i	−0.157059	−	0.272035i
$307$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$307$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$311$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$312$		0			0
$313$	−14.8186	+	31.7786i	−0.837597	+	1.79623i	−0.297218	+	0.954810i	$0.596059\pi$
$313$	−14.8186	+	31.7786i	−0.837597	+	1.79623i	−0.540378	+	0.841422i	$0.681719\pi$
$314$	2.46482	+	13.9787i	0.139098	+	0.788863i
$315$		0			0
$316$		0			0
$317$	−29.6974	+	2.59819i	−1.66797	+	0.145929i	−0.881656	−	0.471893i	$-0.843571\pi$
$317$	−29.6974	+	2.59819i	−1.66797	+	0.145929i	−0.786318	+	0.617822i	$0.788015\pi$
$318$		0			0
$319$		0			0
$320$	17.8564	+	1.07180i	0.998203	+	0.0599153i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	6.15636	+	16.9145i	0.342020	+	0.939693i
$325$	−25.4333	−	22.7959i	−1.41079	−	1.26449i
$326$		0			0
$327$		0			0
$328$	−0.0738359	+	0.843948i	−0.00407691	+	0.0465992i
$329$		0			0
$330$		0			0
$331$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$331$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$332$		0			0
$333$	−18.0000	+	3.00000i	−0.986394	+	0.164399i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−27.0418	+	12.6098i	−1.47306	+	0.686899i	−0.982799	−	0.184676i	$-0.940876\pi$
$337$	−27.0418	+	12.6098i	−1.47306	+	0.686899i	−0.490261	+	0.871576i	$0.663099\pi$
$338$	4.14886	−	47.4216i	0.225668	−	2.57940i
$339$		0			0
$340$	−5.67447	+	1.16119i	−0.307741	+	0.0629746i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−9.19187	+	25.2544i	−0.494158	+	1.35769i
$347$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$347$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$348$		0			0
$349$	23.9433	−	28.5345i	1.28165	−	1.52742i	0.581045	−	0.813871i	$-0.302644\pi$
$349$	23.9433	−	28.5345i	1.28165	−	1.52742i	0.700609	−	0.713545i	$-0.252912\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.0557449	−	0.119545i	0.00296700	−	0.00636276i	−0.904819	−	0.425797i	$-0.859994\pi$
$353$	0.0557449	−	0.119545i	0.00296700	−	0.00636276i	0.907786	+	0.419434i	$0.137772\pi$
$354$		0			0
$355$		0			0
$356$	31.0817	−	17.9450i	1.64733	−	0.951086i
$357$		0			0
$358$		0			0
$359$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$359$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$360$	18.9666	−	0.518207i	0.999627	−	0.0273119i
$361$	−17.8542	+	6.49838i	−0.939693	+	0.342020i
$362$	−31.1752	+	8.35337i	−1.63853	+	0.439043i
$363$		0			0
$364$		0			0
$365$	−7.62436	−	37.2583i	−0.399077	−	1.95019i
$366$		0			0
$367$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$367$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$368$		0			0
$369$			0.898562i			0.0467773i
$370$	−3.00000	+	19.0000i	−0.155963	+	0.987763i
$371$		0			0
$372$		0			0
$373$	−9.79917	+	13.9947i	−0.507382	+	0.724616i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−9.79917	+	13.9947i	−0.507382	+	0.724616i	0.480981	+	0.876731i	$0.340281\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−6.40891	+	73.2541i	−0.330075	+	3.77278i
$378$		0			0
$379$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$379$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$383$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$384$		0			0
$385$		0			0
$386$	24.7341	+	20.7544i	1.25893	+	1.05637i
$387$		0			0
$388$	−32.2656	−	22.5926i	−1.63804	−	1.14696i
$389$	5.21127	+	29.5546i	0.264222	+	1.49848i	0.771242	+	0.636542i	$0.219636\pi$
$389$	5.21127	+	29.5546i	0.264222	+	1.49848i	−0.507020	+	0.861934i	$0.669253\pi$
$390$		0			0
$391$		0			0
$392$	1.72560	+	19.7236i	0.0871557	+	0.996195i
$393$		0			0
$394$	5.89080	+	2.14407i	0.296774	+	0.108017i
$395$		0			0
$396$		0			0
$397$	23.4187	+	6.27503i	1.17535	+	0.314935i	0.793082	−	0.609115i	$-0.208475\pi$
$397$	23.4187	+	6.27503i	1.17535	+	0.314935i	0.382271	+	0.924050i	$0.375142\pi$
$398$		0			0
$399$		0			0
$400$	5.80399	−	19.1393i	0.290199	−	0.956966i
$401$			21.7321i			1.08525i	0.839976	+	0.542623i	$0.182569\pi$
$401$			21.7321i			1.08525i	−0.839976	+	0.542623i	$0.817431\pi$
$402$		0			0
$403$		0			0
$404$	9.77130	−	1.72294i	0.486140	−	0.0857196i
$405$	19.9926	−	2.30087i	0.993443	−	0.114331i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	2.23221	−	12.6595i	0.110376	−	0.625971i	−0.878561	−	0.477631i	$-0.841496\pi$
$409$	2.23221	−	12.6595i	0.110376	−	0.625971i	0.988936	−	0.148340i	$-0.0473931\pi$
$410$	0.898562	+	0.299521i	0.0443768	+	0.0147923i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	36.3107	−	13.2160i	1.78028	−	0.647968i
$417$		0			0
$418$		0			0
$419$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$419$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$420$		0			0
$421$	4.31565	−	2.49164i	0.210332	−	0.121435i	−0.391134	−	0.920334i	$-0.627917\pi$
$421$	4.31565	−	2.49164i	0.210332	−	0.121435i	0.601466	+	0.798899i	$0.294584\pi$
$422$		0			0
$423$		0			0
$424$	−19.8998	+	7.24293i	−0.966419	+	0.351748i
$425$	−0.211303	+	6.47227i	−0.0102497	+	0.313951i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$431$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$432$		0			0
$433$	−20.2317	+	5.42106i	−0.972273	+	0.260520i	−0.709787	−	0.704416i	$-0.751209\pi$
$433$	−20.2317	+	5.42106i	−0.972273	+	0.260520i	−0.262485	+	0.964936i	$0.584542\pi$
$434$		0			0
$435$		0			0
$436$	−33.2166	−	19.1776i	−1.59079	−	0.918441i
$437$		0			0
$438$		0			0
$439$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$439$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$440$		0			0
$441$	3.64661	+	20.6810i	0.173648	+	0.984808i
$442$	−10.2488	+	7.17625i	−0.487483	+	0.341340i
$443$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$443$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$444$		0			0
$445$	−11.4402	−	38.4610i	−0.542316	−	1.82322i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	24.6087	−	20.6491i	1.16136	−	0.974493i	0.161432	−	0.986884i	$-0.448389\pi$
$449$	24.6087	−	20.6491i	1.16136	−	0.974493i	0.999923	+	0.0123907i	$0.00394419\pi$
$450$	4.36335	−	20.7596i	0.205690	−	0.978617i
$451$		0			0
$452$	34.1244	−	9.14359i	1.60507	−	0.430078i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−17.3878	−	37.2882i	−0.813365	−	1.74427i	−0.653213	−	0.757174i	$-0.726579\pi$
$457$	−17.3878	−	37.2882i	−0.813365	−	1.74427i	−0.160152	−	0.987092i	$-0.551198\pi$
$458$	−19.1508	−	5.13145i	−0.894859	−	0.239777i
$459$		0			0
$460$		0			0
$461$	−14.6757	−	40.3212i	−0.683517	−	1.87795i	−0.378511	−	0.925597i	$-0.623564\pi$
$461$	−14.6757	−	40.3212i	−0.683517	−	1.87795i	−0.305006	−	0.952350i	$-0.598659\pi$
$462$		0			0
$463$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$463$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$464$	−40.4632	+	14.7274i	−1.87846	+	0.683702i
$465$		0			0
$466$	25.4707	−	30.3549i	1.17991	−	1.40616i
$467$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$467$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$468$	37.1450	−	17.3210i	1.71703	−	0.800664i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−20.3570	+	9.49264i	−0.932085	+	0.434638i
$478$		0			0
$479$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$479$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$480$		0			0
$481$	10.3769	+	40.2337i	0.473147	+	1.83450i
$482$	−8.07180	+	8.07180i	−0.367660	+	0.367660i
$483$		0			0
$484$	−21.6658	+	3.82026i	−0.984808	+	0.173648i
$485$	−32.9495	+	29.2180i	−1.49616	+	1.32672i
$486$		0			0
$487$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$487$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$488$	−38.0418	−	3.32822i	−1.72207	−	0.150662i
$489$		0			0
$490$	21.8965	+	3.24704i	0.989183	+	0.146686i
$491$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$491$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$492$		0			0
$493$	11.4208	−	7.99693i	0.514367	−	0.360164i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$499$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$500$	−19.3052	−	11.2832i	−0.863353	−	0.504601i
$501$		0			0
$502$		0			0
$503$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$503$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$504$		0			0
$505$	0.664650	−	11.0732i	0.0295766	−	0.492753i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	0.755029	+	2.07443i	0.0334661	+	0.0919473i	0.955300	−	0.295637i	$-0.0955319\pi$
$509$	0.755029	+	2.07443i	0.0334661	+	0.0919473i	−0.921834	+	0.387584i	$0.873310\pi$
$510$		0			0
$511$		0			0
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$		0			0
$514$	14.4367	−	39.6646i	0.636777	−	1.74953i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−4.93933	−	42.9187i	−0.216604	−	1.88211i
$521$	7.92548	+	44.9476i	0.347222	+	1.96919i	0.194050	+	0.980992i	$0.437838\pi$
$521$	7.92548	+	44.9476i	0.347222	+	1.96919i	0.153172	+	0.988200i	$0.451051\pi$
$522$	−41.3929	+	19.3018i	−1.81172	+	0.844819i
$523$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$523$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	19.9186	+	11.5000i	0.866025	+	0.500000i
$530$	2.70696	+	23.5213i	0.117583	+	1.02170i
$531$		0			0
$532$		0			0
$533$	2.03819	−	0.178318i	0.0882838	−	0.00772383i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	2.58225	−	5.53765i	0.111329	−	0.238745i
$539$		0			0
$540$		0			0
$541$	10.1119	−	5.83810i	0.434744	−	0.250999i	−0.266622	−	0.963801i	$-0.585907\pi$
$541$	10.1119	−	5.83810i	0.434744	−	0.250999i	0.701365	+	0.712802i	$0.252574\pi$
$542$		0			0
$543$		0			0
$544$	−6.34488	−	3.66322i	−0.272035	−	0.157059i
$545$	−29.4830	+	31.1393i	−1.26291	+	1.33386i
$546$		0			0
$547$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$547$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$548$	−12.0848	−	1.05728i	−0.516236	−	0.0451648i
$549$	−40.5035			−1.72865
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$			17.8359i			0.757775i
$555$		0			0
$556$		0			0
$557$	33.0084	−	23.1127i	1.39861	−	0.979316i	0.400599	−	0.916253i	$-0.368802\pi$
$557$	33.0084	−	23.1127i	1.39861	−	0.979316i	0.998010	−	0.0630631i	$-0.0200869\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	4.09833	−	46.8441i	0.172878	−	1.97600i
$563$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$563$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$564$		0			0
$565$	−1.07877	−	39.4833i	−0.0453841	−	1.66108i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.3476	−	24.8508i	−0.601482	−	1.04180i	−0.992597	−	0.121456i	$-0.961244\pi$
$569$	−14.3476	−	24.8508i	−0.601482	−	1.04180i	0.391115	−	0.920342i	$-0.372090\pi$
$570$		0			0
$571$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$571$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	18.3851	+	15.4269i	0.766044	+	0.642788i
$577$	−4.08604	−	46.7037i	−0.170104	−	1.94430i	−0.302604	−	0.953116i	$-0.597856\pi$
$577$	−4.08604	−	46.7037i	−0.170104	−	1.94430i	0.132500	−	0.991183i	$-0.457700\pi$
$578$	−20.9311	−	5.60846i	−0.870618	−	0.233281i
$579$		0			0
$580$	5.50420	+	47.8269i	0.228549	+	1.98590i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	24.0526	−	41.6603i	0.995302	−	1.72391i
$585$	−9.18653	−	44.8923i	−0.379816	−	1.85607i
$586$			15.1940i			0.627659i
$587$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$587$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−18.7846	+	15.4641i	−0.772043	+	0.635571i
$593$	3.49276	+	3.49276i	0.143431	+	0.143431i	0.775176	−	0.631745i	$-0.217661\pi$
$593$	3.49276	+	3.49276i	0.143431	+	0.143431i	−0.631745	+	0.775176i	$0.717661\pi$
$594$		0			0
$595$		0			0
$596$	32.4477	+	11.8100i	1.32911	+	0.483757i
$597$		0			0
$598$		0			0
$599$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$599$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$600$		0			0
$601$	39.1711	−	14.2571i	1.59782	−	0.581560i	0.618843	−	0.785515i	$-0.287602\pi$
$601$	39.1711	−	14.2571i	1.59782	−	0.581560i	0.978980	+	0.203954i	$0.0653794\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.47372	+	24.5526i	−0.0599153	+	0.998203i
$606$		0			0
$607$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$607$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$608$		0			0
$609$		0			0
$610$	−13.5012	+	40.5035i	−0.546646	+	1.63994i
$611$		0			0
$612$	−7.04279	−	3.28411i	−0.284688	−	0.132752i
$613$	−0.870501	−	9.94987i	−0.0351592	−	0.401871i	−0.993299	−	0.115571i	$-0.963130\pi$
$613$	−0.870501	−	9.94987i	−0.0351592	−	0.401871i	0.958140	−	0.286300i	$-0.0924254\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	16.3027	+	23.2827i	0.656324	+	0.937328i	0.999998	−	0.00176117i	$-0.000560597\pi$
$617$	16.3027	+	23.2827i	0.656324	+	0.937328i	−0.343675	+	0.939089i	$0.611672\pi$
$618$		0			0
$619$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$619$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	8.61081	+	48.8343i	0.344157	+	1.95181i
$627$		0			0
$628$	14.1943	+	14.1943i	0.566416	+	0.566416i
$629$	4.57902	−	6.41063i	0.182578	−	0.255609i
$630$		0			0
$631$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$631$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$632$		0			0
$633$		0			0
$634$	−32.2956	+	27.0992i	−1.28262	+	1.07625i
$635$		0			0
$636$		0			0
$637$	46.1865	−	12.3756i	1.82998	−	0.490341i
$638$		0			0
$639$		0			0
$640$	21.5553	−	13.2428i	0.852046	−	0.523466i
$641$	8.79173	−	49.8604i	0.347253	−	1.96937i	0.157991	−	0.987441i	$-0.449498\pi$
$641$	8.79173	−	49.8604i	0.347253	−	1.96937i	0.189262	−	0.981927i	$-0.439390\pi$
$642$		0			0
$643$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$643$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$647$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$648$	20.8522	+	14.6009i	0.819152	+	0.573576i
$649$		0			0
$650$	−47.9545	−	5.77757i	−1.88093	−	0.226615i
$651$		0			0
$652$		0			0
$653$	37.6721	−	17.5668i	1.47422	−	0.687441i	0.491220	−	0.871036i	$-0.336551\pi$
$653$	37.6721	−	17.5668i	1.47422	−	0.687441i	0.983002	+	0.183595i	$0.0587735\pi$
$654$		0			0
$655$		0			0
$656$	0.599041	+	1.03757i	0.0233886	+	0.0405103i
$657$	21.5633	−	46.2427i	0.841266	−	1.80410i
$658$		0			0
$659$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$659$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$660$		0			0
$661$	13.1772	+	15.7040i	0.512534	+	0.610814i	0.958799	−	0.284087i	$-0.0916904\pi$
$661$	13.1772	+	15.7040i	0.512534	+	0.610814i	−0.446264	+	0.894901i	$0.647246\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−18.4187	+	18.0762i	−0.713711	+	0.700440i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	38.0755	+	3.33117i	1.46770	+	0.128407i	0.792792	−	0.609492i	$-0.208627\pi$
$673$	38.0755	+	3.33117i	1.46770	+	0.128407i	0.674910	+	0.737900i	$0.264182\pi$
$674$	−21.0982	+	36.5431i	−0.812671	+	1.40759i
$675$		0			0
$676$	−33.6603	−	58.3013i	−1.29463	−	2.24236i
$677$	−5.21871	−	19.4765i	−0.200571	−	0.748542i	−0.990754	−	0.135671i	$-0.956681\pi$
$677$	−5.21871	−	19.4765i	−0.200571	−	0.748542i	0.790183	−	0.612871i	$-0.209986\pi$
$678$		0			0
$679$		0			0
$680$	−5.63170	+	5.94809i	−0.215966	+	0.228099i
$681$		0			0
$682$		0			0
$683$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$683$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$684$		0			0
$685$	−4.28893	+	12.8668i	−0.163872	+	0.491615i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	25.5718	+	44.2917i	0.974208	+	1.68738i
$690$		0			0
$691$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$691$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$692$	9.83701	+	36.7122i	0.373947	+	1.39559i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.274302	−	0.274302i	−0.0103899	−	0.0103899i
$698$	4.59121	−	52.4778i	0.173780	−	1.98631i
$699$		0			0
$700$		0			0
$701$	39.4251	+	6.95171i	1.48907	+	0.262563i	0.858195	−	0.513324i	$-0.171586\pi$
$701$	39.4251	+	6.95171i	1.48907	+	0.262563i	0.630872	+	0.775887i	$0.282697\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.0323923	−	0.183706i	−0.00121910	−	0.00691387i
$707$		0			0
$708$		0			0
$709$	−30.0000			−1.12667			−0.563337	−	0.826227i	$-0.690483\pi$
$709$	−30.0000			−1.12667			−0.563337	+	0.826227i	$0.690483\pi$
$710$		0			0
$711$		0			0
$712$	21.4505	−	46.0008i	0.803892	−	1.72395i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$719$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$720$	21.5516	−	15.9852i	0.803181	−	0.595735i
$721$		0			0
$722$	−15.4120	+	22.0107i	−0.573576	+	0.819152i
$723$		0			0
$724$	−29.3392	+	34.9651i	−1.09038	+	1.29947i
$725$	53.4386	+	6.43829i	1.98466	+	0.239112i
$726$		0			0
$727$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$727$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$728$		0			0
$729$	23.3827	+	13.5000i	0.866025	+	0.500000i
$730$	−39.0549	−	36.9776i	−1.44549	−	1.36860i
$731$		0			0
$732$		0			0
$733$	52.9928	+	4.63627i	1.95734	+	0.171245i	0.994945	−	0.100424i	$-0.0320200\pi$
$733$	52.9928	+	4.63627i	1.95734	+	0.171245i	0.962391	+	0.271669i	$0.0875756\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	0.728877	+	1.04094i	0.0268303	+	0.0383177i
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$	11.9367	+	24.4441i	0.438801	+	0.898585i
$741$		0			0
$742$		0			0
$743$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$743$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$744$		0			0
$745$	21.2715	−	32.2171i	0.779326	−	1.18034i
$746$			24.1609i			0.884593i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$		0			0
$753$		0			0
$754$	51.9964	+	90.0603i	1.89360	+	3.27980i
$755$		0			0
$756$		0			0
$757$	35.8181	+	16.7022i	1.30183	+	0.607053i	0.944986	−	0.327111i	$-0.106075\pi$
$757$	35.8181	+	16.7022i	1.30183	+	0.607053i	0.356844	+	0.934164i	$0.383853\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	25.1214	+	21.0794i	0.910651	+	0.764127i	0.972243	−	0.233975i	$-0.0751733\pi$
$761$	25.1214	+	21.0794i	0.910651	+	0.764127i	−0.0615920	+	0.998101i	$0.519618\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−5.40074	+	6.80550i	−0.195264	+	0.246053i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−25.0000	+	43.3013i	−0.901523	+	1.56148i	−0.0760054	+	0.997107i	$0.524217\pi$
$769$	−25.0000	+	43.3013i	−0.901523	+	1.56148i	−0.825518	+	0.564376i	$0.809117\pi$
$770$		0			0
$771$		0			0
$772$	45.4885	+	3.97973i	1.63717	+	0.143234i
$773$	−10.7804	−	23.1186i	−0.387743	−	0.831517i	−0.999190	−	0.0402322i	$-0.987190\pi$
$773$	−10.7804	−	23.1186i	−0.387743	−	0.831517i	0.611448	−	0.791285i	$-0.290588\pi$
$774$		0			0
$775$		0			0
$776$	−55.7044			−1.99967
$777$		0			0
$778$	30.0105	+	30.0105i	1.07593	+	1.07593i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	17.9981	+	21.4492i	0.642788	+	0.766044i
$785$	19.1227	−	11.7483i	0.682517	−	0.419314i
$786$		0			0
$787$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$787$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$788$	8.56342	−	2.29456i	0.305059	−	0.0817403i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	8.03787	+	91.8733i	0.285433	+	3.26252i
$794$	32.2196	−	11.7270i	1.14343	−	0.416175i
$795$		0			0
$796$		0			0
$797$	47.4234	+	22.1139i	1.67982	+	0.783314i	0.998691	+	0.0511525i	$0.0162894\pi$
$797$	47.4234	+	22.1139i	1.67982	+	0.783314i	0.681131	+	0.732161i	$0.261488\pi$
$798$		0			0
$799$		0			0
$800$	−8.80138	−	26.8800i	−0.311176	−	0.950352i
$801$	18.4127	−	50.5885i	0.650581	−	1.78746i
$802$	17.6282	+	25.1756i	0.622472	+	0.888982i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	9.92204	−	9.92204i	0.349056	−	0.349056i
$809$	−40.9814	+	34.3875i	−1.44083	+	1.20900i	−0.501883	+	0.864935i	$0.667359\pi$
$809$	−40.9814	+	34.3875i	−1.44083	+	1.20900i	−0.938946	+	0.344064i	$0.888196\pi$
$810$	21.2942	−	18.8827i	0.748203	−	0.663470i
$811$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$811$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−7.68294	−	16.4761i	−0.268628	−	0.576074i
$819$		0			0
$820$	1.28390	−	0.381896i	0.0448358	−	0.0133364i
$821$	−22.4461	+	18.8345i	−0.783373	+	0.657328i	−0.944096	−	0.329671i	$-0.893062\pi$
$821$	−22.4461	+	18.8345i	−0.783373	+	0.657328i	0.160722	+	0.987000i	$0.448618\pi$
$822$		0			0
$823$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$823$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$827$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$828$		0			0
$829$	15.3209	+	12.8558i	0.532116	+	0.446499i	0.868832	−	0.495108i	$-0.164871\pi$
$829$	15.3209	+	12.8558i	0.532116	+	0.446499i	−0.336715	+	0.941607i	$0.609316\pi$
$830$		0			0
$831$		0			0
$832$	31.3440	−	44.7639i	1.08666	−	1.55191i
$833$	−7.42644	−	5.20005i	−0.257311	−	0.180171i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$839$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$840$		0			0
$841$	−43.4427	−	75.2449i	−1.49802	−	2.59465i
$842$	2.97837	−	6.38713i	0.102641	−	0.220115i
$843$		0			0
$844$		0			0
$845$	−72.1428	+	21.4588i	−2.48179	+	0.738205i
$846$		0			0
$847$		0			0
$848$	−17.1779	+	24.5325i	−0.589890	+	0.842450i
$849$		0			0
$850$	5.00526	+	7.66924i	0.171679	+	0.263053i
$851$		0			0
$852$		0			0
$853$	−22.8697	−	32.6614i	−0.783045	−	1.11830i	−0.990153	−	0.139986i	$-0.955294\pi$
$853$	−22.8697	−	32.6614i	−0.783045	−	1.11830i	0.207109	−	0.978318i	$-0.433595\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	18.8898	+	18.8898i	0.645263	+	0.645263i	0.951845	−	0.306581i	$-0.0991851\pi$
$857$	18.8898	+	18.8898i	0.645263	+	0.645263i	−0.306581	+	0.951845i	$0.599185\pi$
$858$		0			0
$859$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$859$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$863$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$864$		0			0
$865$	42.4776	−	1.16058i	1.44428	−	0.0394608i
$866$	−19.0402	+	22.6912i	−0.647011	+	0.771078i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−54.0361	+	4.72754i	−1.82989	+	0.160095i
$873$	−58.8586	+	5.14946i	−1.99206	+	0.174283i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−9.15897	−	34.1818i	−0.309277	−	1.15424i	−0.929201	−	0.369574i	$-0.879504\pi$
$877$	−9.15897	−	34.1818i	−0.309277	−	1.15424i	0.619925	−	0.784661i	$-0.287163\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	36.1352	−	30.3210i	1.21743	−	1.02154i	0.218471	−	0.975843i	$-0.429893\pi$
$881$	36.1352	−	30.3210i	1.21743	−	1.02154i	0.998955	−	0.0456985i	$-0.0145514\pi$
$882$	21.0000	+	21.0000i	0.707107	+	0.707107i
$883$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$883$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$884$	−6.05164	+	16.6267i	−0.203539	+	0.559218i
$885$		0			0
$886$		0			0
$887$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$887$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$888$		0			0
$889$		0			0
$890$	−44.4509	−	35.2755i	−1.49000	−	1.18244i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	11.7583	−	43.8827i	0.392381	−	1.46438i
$899$		0			0
$900$	−11.7846	−	27.5885i	−0.392820	−	0.919615i
$901$	3.31656	−	9.11216i	0.110490	−	0.303570i
$902$		0			0
$903$		0			0
$904$	32.1146	−	38.2727i	1.06812	−	1.27293i
$905$	30.4010	+	40.9872i	1.01056	+	1.36246i
$906$		0			0
$907$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$907$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$908$		0			0
$909$	9.56664	−	11.4011i	0.317305	−	0.378150i
$910$		0			0
$911$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$911$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$912$		0			0
$913$		0			0
$914$	−50.3896	−	29.0924i	−1.66674	−	0.962293i
$915$		0			0
$916$	−26.3478	+	9.58982i	−0.870556	+	0.316856i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	−49.7081	−	34.8060i	−1.63705	−	1.14628i
$923$		0			0
$924$		0			0
$925$	29.6822	−	6.63064i	0.975946	−	0.218014i
$926$		0			0
$927$		0			0
$928$	−34.9286	+	49.8831i	−1.14659	+	1.63749i
$929$	−16.2050	+	44.5228i	−0.531667	+	1.46074i	0.325418	+	0.945570i	$0.394495\pi$
$929$	−16.2050	+	44.5228i	−0.531667	+	1.46074i	−0.857086	+	0.515174i	$0.827727\pi$
$930$		0			0
$931$		0			0
$932$	4.88411	−	55.8256i	0.159984	−	1.82863i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	28.9808	−	50.1962i	0.947266	−	1.64071i
$937$	15.7408	+	22.4802i	0.514230	+	0.734397i	0.989355	−	0.145522i	$-0.0464860\pi$
$937$	15.7408	+	22.4802i	0.514230	+	0.734397i	−0.475125	+	0.879918i	$0.657597\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	43.8839	+	36.8229i	1.43057	+	1.20039i	0.945373	+	0.325991i	$0.105698\pi$
$941$	43.8839	+	36.8229i	1.43057	+	1.20039i	0.485200	+	0.874403i	$0.338747\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$947$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$948$		0			0
$949$	−109.171	−	39.7348i	−3.54383	−	1.28985i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−35.8970	−	16.7390i	−1.16282	−	0.542231i	−0.257213	−	0.966355i	$-0.582804\pi$
$953$	−35.8970	−	16.7390i	−1.16282	−	0.542231i	−0.905604	+	0.424124i	$0.860582\pi$
$954$	−15.8827	+	27.5096i	−0.514221	+	0.890657i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−31.0000			−1.00000
$962$	44.6571	+	38.1916i	1.43980	+	1.23135i
$963$		0			0
$964$	−2.80331	+	15.8983i	−0.0902884	+	0.512051i
$965$	16.1441	−	48.4322i	0.519696	−	1.55909i
$966$		0			0
$967$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$967$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$968$	−22.0000	+	22.0000i	−0.707107	+	0.707107i
$969$		0			0
$970$	−14.4701	+	60.5751i	−0.464606	+	1.94495i
$971$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$971$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−46.7694	+	27.0023i	−1.49705	+	0.864324i
$977$	2.07206	+	23.6837i	0.0662910	+	0.757709i	0.954489	+	0.298248i	$0.0964021\pi$
$977$	2.07206	+	23.6837i	0.0662910	+	0.757709i	−0.888198	+	0.459462i	$0.848042\pi$
$978$		0			0
$979$		0			0
$980$	28.0000	−	14.0000i	0.894427	−	0.447214i
$981$	−56.6588	+	9.99047i	−1.80898	+	0.318971i
$982$		0			0
$983$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$983$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$984$		0			0
$985$	−0.270714	−	9.90823i	−0.00862565	−	0.315703i
$986$	6.74371	−	18.5282i	0.214763	−	0.590058i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$991$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	42.8629	−	30.0129i	1.35748	−	0.950518i	0.357619	−	0.933867i	$-0.383589\pi$
$997$	42.8629	−	30.0129i	1.35748	−	0.950518i	0.999861	−	0.0166508i	$-0.00530035\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.ce.a.263.1	✓	12
4.3	odd	2	CM	740.2.ce.a.263.1	✓	12
5.2	odd	4		740.2.ce.b.707.1	yes	12
20.7	even	4		740.2.ce.b.707.1	yes	12
37.28	even	18		740.2.ce.b.583.1	yes	12
148.139	odd	18		740.2.ce.b.583.1	yes	12
185.102	odd	36	inner	740.2.ce.a.287.1	yes	12
740.287	even	36	inner	740.2.ce.a.287.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.ce.a.263.1	✓	12	1.1	even	1	trivial
740.2.ce.a.263.1	✓	12	4.3	odd	2	CM
740.2.ce.a.287.1	yes	12	185.102	odd	36	inner
740.2.ce.a.287.1	yes	12	740.287	even	36	inner
740.2.ce.b.583.1	yes	12	37.28	even	18
740.2.ce.b.583.1	yes	12	148.139	odd	18
740.2.ce.b.707.1	yes	12	5.2	odd	4
740.2.ce.b.707.1	yes	12	20.7	even	4

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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.ce (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15846 - 0.811160i) q^{2} +(0.684040 - 1.87939i) q^{4} +(-1.86603 - 1.23205i) q^{5} +(-0.732051 - 2.73205i) q^{8} +(-1.02606 - 2.81908i) q^{9} +(-3.16110 + 0.0863678i) q^{10} +(-6.19084 + 2.88683i) q^{13} +(-3.06418 - 2.57115i) q^{16} +(1.17380 + 0.547351i) q^{17} +(-3.47537 - 2.43348i) q^{18} +(-3.59193 + 2.66421i) q^{20} +(1.96410 + 4.59808i) q^{25} +(-4.83013 + 8.36603i) q^{26} +(5.38250 - 9.32277i) q^{29} +(-5.63533 - 0.493027i) q^{32} +(1.80378 - 0.318056i) q^{34} -6.00000 q^{36} +(1.11243 - 5.98018i) q^{37} +(-2.00000 + 6.00000i) q^{40} +(-0.281457 - 0.102442i) q^{41} +(-1.55859 + 6.52463i) q^{45} +(-6.89365 - 1.21554i) q^{49} +(6.00510 + 3.73347i) q^{50} +(1.19069 + 13.6097i) q^{52} +(-0.652550 - 7.45868i) q^{53} +(-1.32686 - 15.1661i) q^{58} +(4.61767 - 12.6869i) q^{61} +(-6.92820 + 4.00000i) q^{64} +(15.1090 + 2.24052i) q^{65} +(1.83161 - 1.83161i) q^{68} +(-6.95074 + 4.86696i) q^{72} +(12.0263 + 12.0263i) q^{73} +(-3.56218 - 7.83013i) q^{74} +(2.55005 + 8.57305i) q^{80} +(-6.89440 + 5.78509i) q^{81} +(-0.409153 + 0.109632i) q^{82} +(-1.51597 - 2.46755i) q^{85} +(13.7467 + 11.5349i) q^{89} +(3.48696 + 8.82276i) q^{90} +(5.09731 - 19.0234i) q^{97} +(-8.97199 + 4.18371i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{5} + 12 q^{8} - 24 q^{17} - 18 q^{25} - 6 q^{26} + 30 q^{34} - 72 q^{36} - 24 q^{40} + 24 q^{41} - 42 q^{58} + 72 q^{61} + 30 q^{73} + 30 q^{74} + 84 q^{85} + 60 q^{89}+O(q^{100}) \) 12 * q - 12 * q^5 + 12 * q^8 - 24 * q^17 - 18 * q^25 - 6 * q^26 + 30 * q^34 - 72 * q^36 - 24 * q^40 + 24 * q^41 - 42 * q^58 + 72 * q^61 + 30 * q^73 + 30 * q^74 + 84 * q^85 + 60 * q^89

Introduction

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