LMFDB - Embedded newform 740.2.ce.b.247.1

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 = [12,0,0,0,0] 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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{36}]$

Embedding invariants

Embedding label			247.1
Root			$0.642788 + 0.766044i$ of defining polynomial
Character	$\chi$	$=$	740.247
Dual form			740.2.ce.b.3.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.123257 + 1.40883i) q^{2} +(-1.96962 - 0.347296i) q^{4} +(1.53737 + 1.62373i) q^{5} +(0.732051 - 2.73205i) q^{8} +(2.95442 - 0.520945i) q^{9} +(-2.47706 + 1.96575i) q^{10} +(4.43703 - 3.10684i) q^{13} +(3.75877 + 1.36808i) q^{16} +(1.28470 + 0.899557i) q^{17} +(0.369771 + 4.22650i) q^{18} +(-2.46410 - 3.73205i) q^{20} +(-0.273017 + 4.99254i) q^{25} +(3.83013 + 6.63397i) q^{26} +(-1.10137 - 1.90764i) q^{29} +(-2.39069 + 5.12685i) q^{32} +(-1.42567 + 1.69905i) q^{34} -6.00000 q^{36} +(-0.0570813 + 6.08249i) q^{37} +(5.56155 - 3.01150i) q^{40} +(0.711496 - 4.03509i) q^{41} +(5.38790 + 3.99631i) q^{45} +(4.49951 + 5.36231i) q^{49} +(-7.00000 - 1.00000i) q^{50} +(-9.81825 + 4.57832i) q^{52} +(-13.1942 + 6.15258i) q^{53} +(2.82329 - 1.31652i) q^{58} +(9.92806 + 1.75058i) q^{61} +(-6.92820 - 4.00000i) q^{64} +(11.8660 + 2.42820i) q^{65} +(-2.21795 - 2.21795i) q^{68} +(0.739541 - 8.45299i) q^{72} +(-7.02628 + 7.02628i) q^{73} +(-8.56218 - 0.830127i) q^{74} +(3.55721 + 8.20648i) q^{80} +(8.45723 - 3.07818i) q^{81} +(5.59707 + 1.49973i) q^{82} +(0.514414 + 3.46896i) q^{85} +(-13.9725 - 5.08558i) q^{89} +(-6.29423 + 7.09808i) q^{90} +(-0.976048 - 3.64266i) q^{97} +(-8.10919 + 5.67812i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{8} - 6 q^{17} + 12 q^{20} - 6 q^{26} - 30 q^{34} - 72 q^{36} + 24 q^{41} - 84 q^{50} - 18 q^{58} + 72 q^{61} + 132 q^{65} + 30 q^{73} - 30 q^{74} - 42 q^{85} - 60 q^{89} + 18 q^{90}+O(q^{100}) $ 12 * q - 12 * q^8 - 6 * q^17 + 12 * q^20 - 6 * q^26 - 30 * q^34 - 72 * q^36 + 24 * q^41 - 84 * q^50 - 18 * q^58 + 72 * q^61 + 132 * q^65 + 30 * q^73 - 30 * q^74 - 42 * q^85 - 60 * q^89 + 18 * q^90

Character values

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

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.123257	+	1.40883i	−0.0871557	+	0.996195i
$2$	−0.123257	+	1.40883i	−0.0871557	+	0.996195i
$3$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$3$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$4$	−1.96962	−	0.347296i	−0.984808	−	0.173648i
$5$	1.53737	+	1.62373i	0.687531	+	0.726155i
$5$	1.53737	+	1.62373i	0.687531	+	0.726155i
$6$		0			0
$7$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$7$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$8$	0.732051	−	2.73205i	0.258819	−	0.965926i
$9$	2.95442	−	0.520945i	0.984808	−	0.173648i
$10$	−2.47706	+	1.96575i	−0.783314	+	0.621626i
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$		0			0
$13$	4.43703	−	3.10684i	1.23061	−	0.861684i	0.236670	−	0.971590i	$-0.423944\pi$
$13$	4.43703	−	3.10684i	1.23061	−	0.861684i	0.993942	+	0.109907i	$0.0350552\pi$
$14$		0			0
$15$		0			0
$16$	3.75877	+	1.36808i	0.939693	+	0.342020i
$17$	1.28470	+	0.899557i	0.311586	+	0.218175i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	1.28470	+	0.899557i	0.311586	+	0.218175i	−0.407314	+	0.913288i	$0.633535\pi$
$18$	0.369771	+	4.22650i	0.0871557	+	0.996195i
$19$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$19$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$20$	−2.46410	−	3.73205i	−0.550990	−	0.834512i
$21$		0			0
$22$		0			0
$23$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$23$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$24$		0			0
$25$	−0.273017	+	4.99254i	−0.0546034	+	0.998508i
$26$	3.83013	+	6.63397i	0.751150	+	1.30103i
$27$		0			0
$28$		0			0
$29$	−1.10137	−	1.90764i	−0.204520	−	0.354239i	0.745460	−	0.666551i	$-0.232230\pi$
$29$	−1.10137	−	1.90764i	−0.204520	−	0.354239i	−0.949980	+	0.312312i	$0.898897\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−2.39069	+	5.12685i	−0.422618	+	0.906308i
$33$		0			0
$34$	−1.42567	+	1.69905i	−0.244501	+	0.291385i
$35$		0			0
$36$	−6.00000			−1.00000
$37$	−0.0570813	+	6.08249i	−0.00938411	+	0.999956i
$37$	−0.0570813	+	6.08249i	−0.00938411	+	0.999956i
$38$		0			0
$39$		0			0
$40$	5.56155	−	3.01150i	0.879358	−	0.476161i
$41$	0.711496	−	4.03509i	0.111117	−	0.630175i	−0.877483	−	0.479608i	$-0.840779\pi$
$41$	0.711496	−	4.03509i	0.111117	−	0.630175i	0.988600	−	0.150567i	$-0.0481100\pi$
$42$		0			0
$43$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$43$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$44$		0			0
$45$	5.38790	+	3.99631i	0.803181	+	0.595735i
$46$		0			0
$47$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$47$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$48$		0			0
$49$	4.49951	+	5.36231i	0.642788	+	0.766044i
$50$	−7.00000	−	1.00000i	−0.989949	−	0.141421i
$51$		0			0
$52$	−9.81825	+	4.57832i	−1.36155	+	0.634899i
$53$	−13.1942	+	6.15258i	−1.81237	+	0.845121i	−0.899211	+	0.437514i	$0.855859\pi$
$53$	−13.1942	+	6.15258i	−1.81237	+	0.845121i	−0.913157	+	0.407607i	$0.866363\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	2.82329	−	1.31652i	0.370716	−	0.172868i
$59$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$59$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$60$		0			0
$61$	9.92806	+	1.75058i	1.27116	+	0.224139i	0.768221	−	0.640184i	$-0.221142\pi$
$61$	9.92806	+	1.75058i	1.27116	+	0.224139i	0.502936	+	0.864324i	$0.332253\pi$
$62$		0			0
$63$		0			0
$64$	−6.92820	−	4.00000i	−0.866025	−	0.500000i
$65$	11.8660	+	2.42820i	1.47180	+	0.301182i
$66$		0			0
$67$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$67$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$68$	−2.21795	−	2.21795i	−0.268966	−	0.268966i
$69$		0			0
$70$		0			0
$71$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$71$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$72$	0.739541	−	8.45299i	0.0871557	−	0.996195i
$73$	−7.02628	+	7.02628i	−0.822364	+	0.822364i	−0.986447	−	0.164083i	$-0.947534\pi$
$73$	−7.02628	+	7.02628i	−0.822364	+	0.822364i	0.164083	+	0.986447i	$0.447534\pi$
$74$	−8.56218	−	0.830127i	−0.995333	−	0.0965003i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$79$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$80$	3.55721	+	8.20648i	0.397708	+	0.917512i
$81$	8.45723	−	3.07818i	0.939693	−	0.342020i
$82$	5.59707	+	1.49973i	0.618093	+	0.165618i
$83$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$83$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$84$		0			0
$85$	0.514414	+	3.46896i	0.0557960	+	0.376262i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−13.9725	−	5.08558i	−1.48108	−	0.539071i	−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−13.9725	−	5.08558i	−1.48108	−	0.539071i	−0.951086	+	0.308928i	$0.900030\pi$
$90$	−6.29423	+	7.09808i	−0.663470	+	0.748203i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.976048	−	3.64266i	−0.0991026	−	0.369856i	0.898507	−	0.438959i	$-0.144653\pi$
$97$	−0.976048	−	3.64266i	−0.0991026	−	0.369856i	−0.997610	+	0.0691034i	$0.977986\pi$
$98$	−8.10919	+	5.67812i	−0.819152	+	0.573576i
$99$		0			0
$100$	2.27163	−	9.73857i	0.227163	−	0.973857i
$101$	10.0217	−	17.3581i	0.997199	−	1.72720i	0.433826	−	0.900997i	$-0.357163\pi$
$101$	10.0217	−	17.3581i	0.997199	−	1.72720i	0.563373	−	0.826202i	$-0.309503\pi$
$102$		0			0
$103$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$103$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$104$	−5.23992	−	14.3966i	−0.513817	−	1.41170i
$105$		0			0
$106$	−7.04167	−	19.3468i	−0.683947	−	1.87913i
$107$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$107$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$108$		0			0
$109$	15.9689	−	13.3995i	1.52955	−	1.28344i	0.727764	−	0.685828i	$-0.240560\pi$
$109$	15.9689	−	13.3995i	1.52955	−	1.28344i	0.801784	−	0.597615i	$-0.203885\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−19.0057	−	1.66278i	−1.78790	−	0.156421i	−0.855491	−	0.517817i	$-0.826745\pi$
$113$	−19.0057	−	1.66278i	−1.78790	−	0.156421i	−0.932413	+	0.361396i	$0.882300\pi$
$114$		0			0
$115$		0			0
$116$	1.50677	+	4.13981i	0.139900	+	0.384372i
$117$	11.4904	−	11.4904i	1.06229	−	1.06229i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−5.50000	+	9.52628i	−0.500000	+	0.866025i
$122$	−3.68998	+	13.7712i	−0.334075	+	1.24679i
$123$		0			0
$124$		0			0
$125$	−8.52628	+	7.23205i	−0.762614	+	0.646854i
$126$		0			0
$127$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$127$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$128$	6.48928	−	9.26765i	0.573576	−	0.819152i
$129$		0			0
$130$	−4.88350	+	16.4179i	−0.428311	+	1.43995i
$131$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$131$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	3.39810	−	2.85135i	0.291385	−	0.244501i
$137$	2.55894	−	9.55009i	0.218625	−	0.815920i	−0.766234	−	0.642562i	$-0.777872\pi$
$137$	2.55894	−	9.55009i	0.218625	−	0.815920i	0.984859	−	0.173358i	$-0.0554617\pi$
$138$		0			0
$139$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$139$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	11.8177	+	2.08378i	0.984808	+	0.173648i
$145$	1.40428	−	4.72107i	0.116619	−	0.392064i
$146$	−9.03281	−	10.7649i	−0.747561	−	0.890908i
$147$		0			0
$148$	2.22486	−	11.9604i	0.182882	−	0.983135i
$149$		−	2.13113i		−	0.174589i	−0.996183	−	0.0872945i	$-0.972178\pi$
$149$		−	2.13113i		−	0.174589i	0.996183	−	0.0872945i	$-0.0278221\pi$
$150$		0			0
$151$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$151$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$152$		0			0
$153$	4.26417	+	1.98842i	0.344738	+	0.160754i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.905156	−	1.29270i	0.0722393	−	0.103168i	−0.781407	−	0.624022i	$-0.785497\pi$
$157$	0.905156	−	1.29270i	0.0722393	−	0.103168i	0.853646	+	0.520854i	$0.174386\pi$
$158$		0			0
$159$		0			0
$160$	−12.0000	+	4.00000i	−0.948683	+	0.316228i
$161$		0			0
$162$	3.29423	+	12.2942i	0.258819	+	0.965926i
$163$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$163$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$164$	−2.80275	+	7.70048i	−0.218858	+	0.601306i
$165$		0			0
$166$		0			0
$167$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$167$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$168$		0			0
$169$	5.58852	−	15.3543i	0.429886	−	1.18110i
$170$	−4.95059	+	0.297150i	−0.379693	+	0.0227903i
$171$		0			0
$172$		0			0
$173$	−2.28781	+	26.1498i	−0.173939	+	1.98813i	−0.0218819	+	0.999761i	$0.506966\pi$
$173$	−2.28781	+	26.1498i	−0.173939	+	1.98813i	−0.152057	+	0.988372i	$0.548590\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	8.88694	−	19.0581i	0.666104	−	1.42847i
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$	−9.22419	−	9.74240i	−0.687531	−	0.726155i
$181$	4.62678	−	26.2398i	0.343906	−	1.95039i	0.0346764	−	0.999399i	$-0.488960\pi$
$181$	4.62678	−	26.2398i	0.343906	−	1.95039i	0.309229	−	0.950988i	$-0.399929\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−9.96410	+	9.25833i	−0.732575	+	0.680686i
$186$		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
$193$	3.00996	−	11.2333i	0.216661	−	0.808591i	−0.768914	−	0.639353i	$-0.779202\pi$
$193$	3.00996	−	11.2333i	0.216661	−	0.808591i	0.985575	−	0.169239i	$-0.0541309\pi$
$194$	5.25220	−	0.926105i	0.377086	−	0.0664904i
$195$		0			0
$196$	−7.00000	−	12.1244i	−0.500000	−	0.866025i
$197$	13.5940	+	1.18932i	0.968532	+	0.0847356i	0.560431	−	0.828201i	$-0.310635\pi$
$197$	13.5940	+	1.18932i	0.968532	+	0.0847356i	0.408101	+	0.912937i	$0.366191\pi$
$198$		0			0
$199$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$199$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$200$	13.4400	+	4.40069i	0.950352	+	0.311176i
$201$		0			0
$202$	23.2195	+	16.2584i	1.63372	+	1.14394i
$203$		0			0
$204$		0			0
$205$	7.64574	−	5.04813i	0.534002	−	0.352577i
$206$		0			0
$207$		0			0
$208$	20.9282	−	5.60770i	1.45111	−	0.388824i
$209$		0			0
$210$		0			0
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$	28.1244	−	7.53590i	1.93159	−	0.517568i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	16.9094	+	24.1491i	1.14525	+	1.63559i
$219$		0			0
$220$		0			0
$221$	8.49505			0.571439
$222$		0			0
$223$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$223$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$224$		0			0
$225$	1.79423	+	14.8923i	0.119615	+	0.992820i
$226$	4.68516	−	26.5709i	0.311652	−	1.76747i
$227$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$227$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$228$		0			0
$229$	−9.86716	−	27.1098i	−0.652040	−	1.79147i	−0.610071	−	0.792347i	$-0.708859\pi$
$229$	−9.86716	−	27.1098i	−0.652040	−	1.79147i	−0.0419691	−	0.999119i	$-0.513363\pi$
$230$		0			0
$231$		0			0
$232$	−6.01802	+	1.61252i	−0.395103	+	0.105867i
$233$	13.2072	+	3.53885i	0.865230	+	0.231838i	0.664024	−	0.747711i	$-0.268847\pi$
$233$	13.2072	+	3.53885i	0.865230	+	0.231838i	0.201206	+	0.979549i	$0.435514\pi$
$234$	14.7717	+	17.6043i	0.965659	+	1.15083i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$239$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$240$		0			0
$241$	−14.0952	+	16.7980i	−0.907950	+	1.08205i	0.0883481	+	0.996090i	$0.471841\pi$
$241$	−14.0952	+	16.7980i	−0.907950	+	1.08205i	−0.996298	+	0.0859632i	$0.972603\pi$
$242$	−12.7430	−	8.92276i	−0.819152	−	0.573576i
$243$		0			0
$244$	−18.9465	−	6.89595i	−1.21292	−	0.441468i
$245$	−1.78957	+	15.5498i	−0.114331	+	0.993443i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−9.13782	−	12.9035i	−0.577927	−	0.816089i
$251$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$251$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	12.2567	+	10.2846i	0.766044	+	0.642788i
$257$	−1.45691	+	16.6525i	−0.0908794	+	1.03876i	0.804649	+	0.593751i	$0.202354\pi$
$257$	−1.45691	+	16.6525i	−0.0908794	+	1.03876i	−0.895528	+	0.445005i	$0.853202\pi$
$258$		0			0
$259$		0			0
$260$	−22.5282	−	8.90365i	−1.39714	−	0.552181i
$261$	−4.24770	−	5.06221i	−0.262926	−	0.313343i
$262$		0			0
$263$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$263$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$264$		0			0
$265$	−30.2745	−	11.9652i	−1.85975	−	0.735015i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−26.2583	−	15.1603i	−1.60100	−	0.924337i	−0.991288	−	0.131713i	$-0.957952\pi$
$269$	−26.2583	−	15.1603i	−1.60100	−	0.924337i	−0.609711	−	0.792624i	$-0.708714\pi$
$270$		0			0
$271$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$271$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$272$	3.59823	+	5.13880i	0.218175	+	0.311586i
$273$		0			0
$274$	13.1391	+	4.78223i	0.793760	+	0.288905i
$275$		0			0
$276$		0			0
$277$	−29.3501	+	2.56780i	−1.76348	+	0.154284i	−0.922301	−	0.386473i	$-0.873693\pi$
$277$	−29.3501	+	2.56780i	−1.76348	+	0.154284i	−0.841178	+	0.540758i	$0.818138\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.65511	+	26.5272i	−0.575975	+	1.58248i	0.218926	+	0.975741i	$0.429745\pi$
$281$	−9.65511	+	26.5272i	−0.575975	+	1.58248i	−0.794902	+	0.606738i	$0.792478\pi$
$282$		0			0
$283$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$283$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−4.39230	+	16.3923i	−0.258819	+	0.965926i
$289$	−4.97309	−	13.6634i	−0.292535	−	0.803732i
$290$	6.47811	+	2.56030i	0.380408	+	0.150346i
$291$		0			0
$292$	16.2793	−	11.3989i	0.952672	−	0.667068i
$293$	−30.0308	+	2.62735i	−1.75442	+	0.153492i	−0.918514	−	0.395388i	$-0.870610\pi$
$293$	−30.0308	+	2.62735i	−1.75442	+	0.153492i	−0.835902	+	0.548879i	$0.815055\pi$
$294$		0			0
$295$		0			0
$296$	16.5759	+	4.60864i	0.963455	+	0.267872i
$297$		0			0
$298$	3.00240	+	0.262676i	0.173925	+	0.0152164i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	12.4206	+	18.8118i	0.711199	+	1.07716i
$306$	−3.32693	+	5.76241i	−0.190188	+	0.329415i
$307$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$307$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$311$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$312$		0			0
$313$	13.6565	−	19.5035i	0.771909	−	1.10240i	−0.220006	−	0.975499i	$-0.570608\pi$
$313$	13.6565	−	19.5035i	0.771909	−	1.10240i	0.991915	−	0.126902i	$-0.0405034\pi$
$314$	1.70963	+	1.43455i	0.0964798	+	0.0809562i
$315$		0			0
$316$		0			0
$317$	−14.6540	−	31.4255i	−0.823048	−	1.76503i	−0.617822	−	0.786318i	$-0.711985\pi$
$317$	−14.6540	−	31.4255i	−0.823048	−	1.76503i	−0.205227	−	0.978714i	$-0.565793\pi$
$318$		0			0
$319$		0			0
$320$	−4.15625	−	17.3990i	−0.232341	−	0.972634i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−17.7265	+	3.12567i	−0.984808	+	0.173648i
$325$	14.2997	+	23.0003i	0.793202	+	1.27583i
$326$		0			0
$327$		0			0
$328$	−10.5032	−	4.89773i	−0.579944	−	0.270432i
$329$		0			0
$330$		0			0
$331$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$331$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$332$		0			0
$333$	3.00000	+	18.0000i	0.164399	+	0.986394i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−13.0151	+	9.11326i	−0.708977	+	0.496431i	−0.871576	−	0.490261i	$-0.836901\pi$
$337$	−13.0151	+	9.11326i	−0.708977	+	0.496431i	0.162598	+	0.986692i	$0.448012\pi$
$338$	20.9429	+	9.76582i	1.13914	+	0.531190i
$339$		0			0
$340$	0.191560	−	7.01117i	0.0103888	−	0.380234i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−36.5587	−	6.44628i	−1.96541	−	0.346554i
$347$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$347$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$348$		0			0
$349$	1.23016	−	3.37983i	0.0658489	−	0.180918i	−0.902404	−	0.430891i	$-0.858199\pi$
$349$	1.23016	−	3.37983i	0.0658489	−	0.180918i	0.968253	+	0.249973i	$0.0804216\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−21.2386	+	30.3319i	−1.13042	+	1.61440i	−0.425797	+	0.904819i	$0.640006\pi$
$353$	−21.2386	+	30.3319i	−1.13042	+	1.61440i	−0.704620	+	0.709585i	$0.748883\pi$
$354$		0			0
$355$		0			0
$356$	25.7543	+	14.8692i	1.36497	+	0.788069i
$357$		0			0
$358$		0			0
$359$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$	14.8623	−	11.7945i	0.783314	−	0.621626i
$361$	3.29932	+	18.7113i	0.173648	+	0.984808i
$362$	36.3971	+	9.75258i	1.91299	+	0.512584i
$363$		0			0
$364$		0			0
$365$	−22.2108	−	0.606844i	−1.16256	−	0.0317637i
$366$		0			0
$367$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$367$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$368$		0			0
$369$		−	12.2920i		−	0.639897i
$370$	−11.8153	−	15.1789i	−0.614248	−	0.789113i
$371$		0			0
$372$		0			0
$373$	−27.7964	+	2.43187i	−1.43924	+	0.125917i	−0.779890	−	0.625917i	$-0.784725\pi$
$373$	−27.7964	+	2.43187i	−1.43924	+	0.125917i	−0.659352	+	0.751834i	$0.729169\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.8136	−	5.04245i	−0.556927	−	0.259699i
$378$		0			0
$379$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$379$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$383$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$384$		0			0
$385$		0			0
$386$	15.4549	+	5.62511i	0.786631	+	0.286310i
$387$		0			0
$388$	0.657356	+	7.51362i	0.0333722	+	0.381446i
$389$	−5.00525	−	4.19990i	−0.253776	−	0.212944i	0.507020	−	0.861934i	$-0.330747\pi$
$389$	−5.00525	−	4.19990i	−0.253776	−	0.212944i	−0.760796	+	0.648991i	$0.775191\pi$
$390$		0			0
$391$		0			0
$392$	17.9440	−	8.36741i	0.906308	−	0.422618i
$393$		0			0
$394$	−3.35111	+	19.0051i	−0.168826	+	0.957462i
$395$		0			0
$396$		0			0
$397$	37.5757	−	10.0684i	1.88587	−	0.505318i	0.886805	−	0.462144i	$-0.152920\pi$
$397$	37.5757	−	10.0684i	1.88587	−	0.505318i	0.999068	−	0.0431736i	$-0.0137468\pi$
$398$		0			0
$399$		0			0
$400$	−7.85641	+	18.3923i	−0.392820	+	0.919615i
$401$			18.2679i			0.912258i	0.889914	+	0.456129i	$0.150764\pi$
$401$			18.2679i			0.912258i	−0.889914	+	0.456129i	$0.849236\pi$
$402$		0			0
$403$		0			0
$404$	−25.7674	+	30.7083i	−1.28197	+	1.52780i
$405$	18.0000	+	9.00000i	0.894427	+	0.447214i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−26.4274	+	22.1752i	−1.30675	+	1.09649i	−0.317814	+	0.948153i	$0.602949\pi$
$409$	−26.4274	+	22.1752i	−1.30675	+	1.09649i	−0.988936	+	0.148340i	$0.952607\pi$
$410$	6.16958	+	11.3938i	0.304694	+	0.562699i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	5.32076	+	30.1755i	0.260872	+	1.47948i
$417$		0			0
$418$		0			0
$419$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$419$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$420$		0			0
$421$	16.1204	+	9.30711i	0.785659	+	0.453601i	0.838432	−	0.545006i	$-0.183473\pi$
$421$	16.1204	+	9.30711i	0.785659	+	0.453601i	−0.0527728	+	0.998607i	$0.516806\pi$
$422$		0			0
$423$		0			0
$424$	7.15030	+	40.5513i	0.347249	+	1.96935i
$425$	−4.84182	+	6.16833i	−0.234863	+	0.299208i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$431$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$432$		0			0
$433$	7.13082	+	1.91070i	0.342685	+	0.0918222i	0.426057	−	0.904696i	$-0.359902\pi$
$433$	7.13082	+	1.91070i	0.342685	+	0.0918222i	−0.0833719	+	0.996519i	$0.526569\pi$
$434$		0			0
$435$		0			0
$436$	−36.1063	+	20.8460i	−1.72918	+	0.998341i
$437$		0			0
$438$		0			0
$439$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$439$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$440$		0			0
$441$	16.0869	+	13.4985i	0.766044	+	0.642788i
$442$	−1.04707	+	11.9681i	−0.0498042	+	0.569264i
$443$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$443$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$444$		0			0
$445$	−13.2232	−	30.5060i	−0.626842	−	1.44613i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	7.40068	−	2.69363i	0.349260	−	0.127120i	−0.161432	−	0.986884i	$-0.551611\pi$
$449$	7.40068	−	2.69363i	0.349260	−	0.127120i	0.510692	+	0.859764i	$0.329389\pi$
$450$	−21.2019	+	0.692188i	−0.999467	+	0.0326301i
$451$		0			0
$452$	36.8564	+	9.87564i	1.73358	+	0.464511i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−19.8939	−	28.4115i	−0.930598	−	1.32903i	−0.944286	−	0.329125i	$-0.893246\pi$
$457$	−19.8939	−	28.4115i	−0.930598	−	1.32903i	0.0136882	−	0.999906i	$-0.495643\pi$
$458$	39.4093	−	10.5597i	1.84148	−	0.493422i
$459$		0			0
$460$		0			0
$461$	22.5609	−	3.97810i	1.05077	−	0.185279i	0.378511	−	0.925597i	$-0.376436\pi$
$461$	22.5609	−	3.97810i	1.05077	−	0.185279i	0.672256	+	0.740318i	$0.265325\pi$
$462$		0			0
$463$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$463$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$464$	−1.53001	−	8.67714i	−0.0710291	−	0.402826i
$465$		0			0
$466$	−6.61352	+	18.1705i	−0.306365	+	0.841732i
$467$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$467$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$468$	−26.6222	+	18.6411i	−1.23061	+	0.861684i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−35.7762	+	25.0508i	−1.63808	+	1.14700i
$478$		0			0
$479$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$479$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$480$		0			0
$481$	18.6441	+	27.1656i	0.850097	+	1.23864i
$482$	−21.9282	−	21.9282i	−0.998802	−	0.998802i
$483$		0			0
$484$	14.1413	−	16.8530i	0.642788	−	0.766044i
$485$	4.41417	−	7.18494i	0.200437	−	0.326251i
$486$		0			0
$487$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$487$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$488$	12.0505	−	25.8424i	0.545502	−	1.16983i
$489$		0			0
$490$	−21.6865	−	4.43782i	−0.979698	−	0.200480i
$491$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$491$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$492$		0			0
$493$	0.301092	−	3.44149i	0.0135605	−	0.154997i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$499$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$500$	19.3052	−	11.2832i	0.863353	−	0.504601i
$501$		0			0
$502$		0			0
$503$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$503$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$504$		0			0
$505$	43.5920	−	10.4132i	1.93982	−	0.463381i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	26.8637	−	4.73679i	1.19071	−	0.209954i	0.457032	−	0.889450i	$-0.348913\pi$
$509$	26.8637	−	4.73679i	1.19071	−	0.209954i	0.733679	+	0.679496i	$0.237801\pi$
$510$		0			0
$511$		0			0
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$		0			0
$514$	−23.2810	−	4.10508i	−1.02688	−	0.181067i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	15.3205	−	30.6410i	0.671849	−	1.34370i
$521$	−18.1101	−	15.1962i	−0.793417	−	0.665756i	0.153172	−	0.988200i	$-0.451051\pi$
$521$	−18.1101	−	15.1962i	−0.793417	−	0.665756i	−0.946589	+	0.322444i	$0.895496\pi$
$522$	7.65536	−	5.36034i	0.335066	−	0.234616i
$523$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$523$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	19.9186	−	11.5000i	0.866025	−	0.500000i
$530$	20.5885	−	41.1769i	0.894305	−	1.78861i
$531$		0			0
$532$		0			0
$533$	−9.37947	−	20.1143i	−0.406270	−	0.871249i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	24.5948	−	35.1250i	1.06036	−	1.51435i
$539$		0			0
$540$		0			0
$541$	−3.83563	−	2.21450i	−0.164907	−	0.0952089i	0.415275	−	0.909696i	$-0.363685\pi$
$541$	−3.83563	−	2.21450i	−0.164907	−	0.0952089i	−0.580182	+	0.814487i	$0.697019\pi$
$542$		0			0
$543$		0			0
$544$	−7.68322	+	4.43591i	−0.329415	+	0.190188i
$545$	46.3074	+	5.32932i	1.98359	+	0.228283i
$546$		0			0
$547$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$547$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$548$	−8.35684	+	17.9213i	−0.356987	+	0.765560i
$549$	30.2436			1.29077
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		−	41.6659i		−	1.77022i
$555$		0			0
$556$		0			0
$557$	4.03296	−	46.0969i	0.170882	−	1.95319i	−0.111198	−	0.993798i	$-0.535469\pi$
$557$	4.03296	−	46.0969i	0.170882	−	1.95319i	0.282079	−	0.959391i	$-0.408976\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−36.1823	−	16.8721i	−1.52626	−	0.711706i
$563$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$563$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$564$		0			0
$565$	−26.5188	−	33.4165i	−1.11565	−	1.40584i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−16.2755	+	28.1899i	−0.682303	+	1.18178i	0.291973	+	0.956426i	$0.405688\pi$
$569$	−16.2755	+	28.1899i	−0.682303	+	1.18178i	−0.974276	+	0.225357i	$0.927645\pi$
$570$		0			0
$571$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$571$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−22.5526	−	8.20848i	−0.939693	−	0.342020i
$577$	13.0102	−	6.06676i	0.541622	−	0.252562i	−0.132500	−	0.991183i	$-0.542300\pi$
$577$	13.0102	−	6.06676i	0.541622	−	0.252562i	0.674121	+	0.738621i	$0.264523\pi$
$578$	19.8625	−	5.32213i	0.826170	−	0.221372i
$579$		0			0
$580$	−4.40550	+	8.81100i	−0.182928	+	0.365857i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	14.0526	+	24.3397i	0.581499	+	1.00719i
$585$	36.3222	+	0.992399i	1.50174	+	0.0410307i
$586$		−	42.6321i		−	1.76112i
$587$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$587$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−8.53590	+	22.7846i	−0.350823	+	0.936442i
$593$	−33.1338	+	33.1338i	−1.36064	+	1.36064i	−0.487540	+	0.873101i	$0.662106\pi$
$593$	−33.1338	+	33.1338i	−1.36064	+	1.36064i	−0.873101	+	0.487540i	$0.837894\pi$
$594$		0			0
$595$		0			0
$596$	−0.740134	+	4.19751i	−0.0303171	+	0.171937i
$597$		0			0
$598$		0			0
$599$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$599$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$600$		0			0
$601$	3.15748	+	17.9069i	0.128796	+	0.730440i	0.978980	+	0.203954i	$0.0653794\pi$
$601$	3.15748	+	17.9069i	0.128796	+	0.730440i	−0.850184	+	0.526485i	$0.823510\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−23.9236	+	5.71484i	−0.972634	+	0.232341i
$606$		0			0
$607$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$607$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$608$		0			0
$609$		0			0
$610$	−28.0336	+	15.1798i	−1.13505	+	0.614612i
$611$		0			0
$612$	−7.70821	−	5.39734i	−0.311586	−	0.218175i
$613$	35.1886	−	16.4087i	1.42125	−	0.662741i	0.448330	−	0.893868i	$-0.352019\pi$
$613$	35.1886	−	16.4087i	1.42125	−	0.662741i	0.972924	+	0.231127i	$0.0742412\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−20.9943	−	1.83676i	−0.845199	−	0.0739453i	−0.343675	−	0.939089i	$-0.611672\pi$
$617$	−20.9943	−	1.83676i	−0.845199	−	0.0739453i	−0.501524	+	0.865143i	$0.667227\pi$
$618$		0			0
$619$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$619$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−24.8509	−	2.72610i	−0.994037	−	0.109044i
$626$	25.7938	+	21.6436i	1.03093	+	0.865052i
$627$		0			0
$628$	−2.23176	+	2.23176i	−0.0890569	+	0.0890569i
$629$	−5.54489	+	7.76284i	−0.221089	+	0.309525i
$630$		0			0
$631$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$631$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$632$		0			0
$633$		0			0
$634$	46.0795	−	16.7716i	1.83005	−	0.666084i
$635$		0			0
$636$		0			0
$637$	36.6244	+	9.81347i	1.45111	+	0.388824i
$638$		0			0
$639$		0			0
$640$	25.0246	−	3.71091i	0.989183	−	0.146686i
$641$	29.3148	−	24.5980i	1.15786	−	0.971564i	0.157991	−	0.987441i	$-0.449498\pi$
$641$	29.3148	−	24.5980i	1.15786	−	0.971564i	0.999874	+	0.0158770i	$0.00505402\pi$
$642$		0			0
$643$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$643$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$647$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$648$	−2.21862	−	25.3590i	−0.0871557	−	0.996195i
$649$		0			0
$650$	−34.1661	+	17.3109i	−1.34010	+	0.678988i
$651$		0			0
$652$		0			0
$653$	−23.6649	+	16.5703i	−0.926078	+	0.648447i	−0.936187	−	0.351502i	$-0.885671\pi$
$653$	−23.6649	+	16.5703i	−0.926078	+	0.648447i	0.0101092	+	0.999949i	$0.496782\pi$
$654$		0			0
$655$		0			0
$656$	8.19468	−	14.1936i	0.319948	−	0.554167i
$657$	−17.0983	+	24.4189i	−0.667068	+	0.952672i
$658$		0			0
$659$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$659$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$660$		0			0
$661$	−15.7383	−	43.2406i	−0.612148	−	1.68186i	−0.725426	−	0.688301i	$-0.758357\pi$
$661$	−15.7383	−	43.2406i	−0.612148	−	1.68186i	0.113277	−	0.993563i	$-0.463865\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−25.7287	+	2.00787i	−0.996969	+	0.0778035i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−4.76567	+	10.2200i	−0.183703	+	0.393953i	−0.976495	−	0.215540i	$-0.930849\pi$
$673$	−4.76567	+	10.2200i	−0.183703	+	0.393953i	0.792792	+	0.609492i	$0.208627\pi$
$674$	−11.2349	−	19.4593i	−0.432751	−	0.749546i
$675$		0			0
$676$	−16.3397	+	28.3013i	−0.628452	+	1.08851i
$677$	11.3215	−	42.2526i	0.435122	−	1.62390i	−0.305652	−	0.952143i	$-0.598874\pi$
$677$	11.3215	−	42.2526i	0.435122	−	1.62390i	0.740774	−	0.671754i	$-0.234459\pi$
$678$		0			0
$679$		0			0
$680$	9.85395	+	1.13405i	0.377882	+	0.0434888i
$681$		0			0
$682$		0			0
$683$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$683$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$684$		0			0
$685$	19.4408	−	10.5269i	0.742796	−	0.402214i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−39.4282	+	68.2917i	−1.50209	+	2.60170i
$690$		0			0
$691$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$691$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$692$	13.5878	−	50.7105i	0.516532	−	1.92772i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	4.54386	−	4.54386i	0.172111	−	0.172111i
$698$	4.60999	+	2.14967i	0.174491	+	0.0813664i
$699$		0			0
$700$		0			0
$701$	−32.1608	−	38.3277i	−1.21470	−	1.44762i	−0.858195	−	0.513324i	$-0.828414\pi$
$701$	−32.1608	−	38.3277i	−1.21470	−	1.44762i	−0.356502	−	0.934295i	$-0.616031\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−40.1147	−	33.6603i	−1.50974	−	1.26682i
$707$		0			0
$708$		0			0
$709$	30.0000			1.12667			0.563337	−	0.826227i	$-0.309517\pi$
$709$	30.0000			1.12667			0.563337	+	0.826227i	$0.309517\pi$
$710$		0			0
$711$		0			0
$712$	−24.1227	+	34.4507i	−0.904035	+	1.29110i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$719$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$720$	14.7846	+	22.3923i	0.550990	+	0.834512i
$721$		0			0
$722$	−26.7678	+	2.34188i	−0.996195	+	0.0871557i
$723$		0			0
$724$	−18.2259	+	50.0754i	−0.677362	+	1.86104i
$725$	9.82465	−	4.97784i	0.364878	−	0.184872i
$726$		0			0
$727$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$727$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$728$		0			0
$729$	23.3827	−	13.5000i	0.866025	−	0.500000i
$730$	3.59257	−	31.2164i	0.132967	−	1.15537i
$731$		0			0
$732$		0			0
$733$	7.53948	−	16.1685i	0.278477	−	0.597196i	−0.716468	−	0.697620i	$-0.754242\pi$
$733$	7.53948	−	16.1685i	0.278477	−	0.597196i	0.994945	+	0.100424i	$0.0320200\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	17.3174	+	1.51508i	0.637462	+	0.0557707i
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$	22.8408	−	14.7749i	0.839646	−	0.543134i
$741$		0			0
$742$		0			0
$743$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$743$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$744$		0			0
$745$	3.46039	−	3.27632i	0.126779	−	0.120035i
$746$		−	39.4602i		−	1.44474i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$		0			0
$753$		0			0
$754$	8.43681	−	14.6130i	0.307250	−	0.532173i
$755$		0			0
$756$		0			0
$757$	36.5102	+	25.5647i	1.32699	+	0.929165i	0.999875	−	0.0158209i	$-0.00503616\pi$
$757$	36.5102	+	25.5647i	1.32699	+	0.929165i	0.327111	+	0.944986i	$0.393925\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	3.19325	+	1.16225i	0.115755	+	0.0421314i	0.399248	−	0.916843i	$-0.369271\pi$
$761$	3.19325	+	1.16225i	0.115755	+	0.0421314i	−0.283493	+	0.958974i	$0.591493\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	3.32693	+	9.98079i	0.120285	+	0.360856i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.825518	+	0.564376i	$0.190883\pi$
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.0760054	+	0.997107i	$0.475783\pi$
$770$		0			0
$771$		0			0
$772$	−9.82974	+	21.0800i	−0.353780	+	0.758684i
$773$	−30.4503	−	43.4876i	−1.09522	−	1.56414i	−0.791285	−	0.611448i	$-0.790588\pi$
$773$	−30.4503	−	43.4876i	−1.09522	−	1.56414i	−0.303937	−	0.952692i	$-0.598301\pi$
$774$		0			0
$775$		0			0
$776$	−10.6664			−0.382903
$777$		0			0
$778$	6.53389	−	6.53389i	0.234251	−	0.234251i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	9.57656	+	26.3114i	0.342020	+	0.939693i
$785$	3.49055	−	0.517615i	0.124583	−	0.0184745i
$786$		0			0
$787$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$787$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$788$	−26.3619	−	7.06365i	−0.939104	−	0.251632i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	49.4899	−	23.0775i	1.75744	−	0.819507i
$794$	9.55320	+	54.1789i	0.339030	+	1.92274i
$795$		0			0
$796$		0			0
$797$	42.8629	+	30.0129i	1.51828	+	1.06311i	0.974636	+	0.223796i	$0.0718450\pi$
$797$	42.8629	+	30.0129i	1.51828	+	1.06311i	0.543645	+	0.839315i	$0.317044\pi$
$798$		0			0
$799$		0			0
$800$	−24.9433	−	13.3353i	−0.881879	−	0.471475i
$801$	−43.9301	−	7.74605i	−1.55219	−	0.273693i
$802$	−25.7365	−	2.25165i	−0.908786	−	0.0795085i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−40.0869	−	40.0869i	−1.41025	−	1.41025i
$809$	40.8742	−	14.8770i	1.43706	−	0.523047i	0.498114	−	0.867111i	$-0.334026\pi$
$809$	40.8742	−	14.8770i	1.43706	−	0.523047i	0.938946	+	0.344064i	$0.111804\pi$
$810$	−14.8981	+	24.2497i	−0.523466	+	0.852046i
$811$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$811$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−27.9838	−	39.9650i	−0.978430	−	1.39734i
$819$		0			0
$820$	−16.8124	+	7.28754i	−0.587113	+	0.254492i
$821$	−53.8456	+	19.5982i	−1.87922	+	0.683981i	−0.935128	+	0.354310i	$0.884716\pi$
$821$	−53.8456	+	19.5982i	−1.87922	+	0.683981i	−0.944096	+	0.329671i	$0.893062\pi$
$822$		0			0
$823$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$823$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$827$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$828$		0			0
$829$	18.7939	+	6.84040i	0.652737	+	0.237577i	0.647098	−	0.762407i	$-0.275983\pi$
$829$	18.7939	+	6.84040i	0.652737	+	0.237577i	0.00563977	+	0.999984i	$0.498205\pi$
$830$		0			0
$831$		0			0
$832$	−43.1680	+	3.77671i	−1.49658	+	0.130934i
$833$	0.956823	+	10.9365i	0.0331520	+	0.378929i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$839$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$840$		0			0
$841$	12.0739	−	20.9127i	0.416343	−	0.721127i
$842$	−15.0991	+	21.5637i	−0.520349	+	0.743136i
$843$		0			0
$844$		0			0
$845$	33.5229	−	14.5310i	1.15322	−	0.499880i
$846$		0			0
$847$		0			0
$848$	−58.0114	+	5.07534i	−1.99212	+	0.174288i
$849$		0			0
$850$	−8.09335	−	7.58160i	−0.277600	−	0.260047i
$851$		0			0
$852$		0			0
$853$	51.8694	+	4.53798i	1.77597	+	0.155378i	0.927491	−	0.373845i	$-0.121961\pi$
$853$	51.8694	+	4.53798i	1.77597	+	0.155378i	0.848483	+	0.529223i	$0.177516\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	9.20978	−	9.20978i	0.314600	−	0.314600i	−0.532089	−	0.846689i	$-0.678593\pi$
$857$	9.20978	−	9.20978i	0.314600	−	0.314600i	0.846689	+	0.532089i	$0.178593\pi$
$858$		0			0
$859$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$859$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$863$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$864$		0			0
$865$	−45.9775	+	36.4870i	−1.56328	+	1.24059i
$866$	−3.57077	+	9.81062i	−0.121340	+	0.333378i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−24.9181	−	53.4371i	−0.843834	−	1.80961i
$873$	−4.78128	−	10.2535i	−0.161822	−	0.347028i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	10.5153	−	39.2435i	0.355076	−	1.32516i	−0.525314	−	0.850909i	$-0.676052\pi$
$877$	10.5153	−	39.2435i	0.355076	−	1.32516i	0.880389	−	0.474252i	$-0.157281\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−41.0492	+	14.9407i	−1.38298	+	0.503365i	−0.923081	−	0.384605i	$-0.874338\pi$
$881$	−41.0492	+	14.9407i	−1.38298	+	0.503365i	−0.459902	+	0.887970i	$0.652115\pi$
$882$	−21.0000	+	21.0000i	−0.707107	+	0.707107i
$883$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$883$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$884$	−16.7320	−	2.95030i	−0.562757	−	0.0992293i
$885$		0			0
$886$		0			0
$887$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$887$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$888$		0			0
$889$		0			0
$890$	44.6077	−	14.8692i	1.49526	−	0.498418i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	2.88269	+	10.7583i	0.0961965	+	0.359010i
$899$		0			0
$900$	1.63810	−	29.9552i	0.0546034	−	0.998508i
$901$	−22.4853	−	3.96476i	−0.749093	−	0.132085i
$902$		0			0
$903$		0			0
$904$	−18.4559	+	50.7072i	−0.613835	+	1.68650i
$905$	49.7194	−	32.8274i	1.65273	−	1.09122i
$906$		0			0
$907$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$907$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$908$		0			0
$909$	20.5658	−	56.5041i	0.682124	−	1.87412i
$910$		0			0
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$		0			0
$913$		0			0
$914$	42.4790	−	24.5253i	1.40508	−	0.811224i
$915$		0			0
$916$	10.0194	+	56.8227i	0.331049	+	1.87747i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	2.82369	+	32.2749i	0.0929932	+	1.06292i
$923$		0			0
$924$		0			0
$925$	−30.3515	−	1.94561i	−0.997952	−	0.0639711i
$926$		0			0
$927$		0			0
$928$	12.4132	−	1.08602i	0.407484	−	0.0356502i
$929$	60.0236	+	10.5838i	1.96931	+	0.347242i	0.987713	+	0.156278i	$0.0499495\pi$
$929$	60.0236	+	10.5838i	1.96931	+	0.347242i	0.981597	+	0.190965i	$0.0611616\pi$
$930$		0			0
$931$		0			0
$932$	−24.7840	−	11.5570i	−0.811827	−	0.378561i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−22.9808	−	39.8038i	−0.751150	−	1.30103i
$937$	−58.4362	−	5.11251i	−1.90903	−	0.167018i	−0.929567	−	0.368652i	$-0.879819\pi$
$937$	−58.4362	−	5.11251i	−1.90903	−	0.167018i	−0.979461	+	0.201634i	$0.935375\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	57.6432	+	20.9804i	1.87911	+	0.683941i	0.945373	+	0.325991i	$0.105698\pi$
$941$	57.6432	+	20.9804i	1.87911	+	0.683941i	0.933740	+	0.357951i	$0.116524\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$947$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$948$		0			0
$949$	−9.34628	+	53.0054i	−0.303393	+	1.72063i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−49.8218	−	34.8856i	−1.61389	−	1.13005i	−0.905604	−	0.424124i	$-0.860582\pi$
$953$	−49.8218	−	34.8856i	−1.61389	−	1.13005i	−0.708281	−	0.705931i	$-0.750529\pi$
$954$	−30.8827	−	53.4904i	−0.999864	−	1.73182i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−31.0000			−1.00000
$962$	−40.5697	+	22.9181i	−1.30802	+	0.738908i
$963$		0			0
$964$	33.5960	−	28.1904i	1.08205	−	0.907950i
$965$	22.8673	−	12.3823i	0.736124	−	0.398601i
$966$		0			0
$967$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$967$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$968$	22.0000	+	22.0000i	0.707107	+	0.707107i
$969$		0			0
$970$	9.57830	+	7.10441i	0.307541	+	0.228109i
$971$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$971$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	34.9223	+	20.1624i	1.11784	+	0.645383i
$977$	−56.1530	+	26.1846i	−1.79649	+	0.837718i	−0.842004	+	0.539471i	$0.818624\pi$
$977$	−56.1530	+	26.1846i	−1.79649	+	0.837718i	−0.954489	+	0.298248i	$0.903598\pi$
$978$		0			0
$979$		0			0
$980$	8.92516	−	30.0057i	0.285104	−	0.958497i
$981$	40.1986	−	47.9068i	1.28344	−	1.52955i
$982$		0			0
$983$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$983$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$984$		0			0
$985$	18.9678	+	23.9014i	0.604364	+	0.761563i
$986$	4.81137	+	0.848375i	0.153225	+	0.0270178i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$991$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−4.56050	+	52.1268i	−0.144433	+	1.65087i	0.485511	+	0.874231i	$0.338634\pi$
$997$	−4.56050	+	52.1268i	−0.144433	+	1.65087i	−0.629943	+	0.776641i	$0.716922\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.ce.b.247.1	yes	12
4.3	odd	2	CM	740.2.ce.b.247.1	yes	12
5.3	odd	4		740.2.ce.a.543.1	yes	12
20.3	even	4		740.2.ce.a.543.1	yes	12
37.3	even	18		740.2.ce.a.447.1	✓	12
148.3	odd	18		740.2.ce.a.447.1	✓	12
185.3	odd	36	inner	740.2.ce.b.3.1	yes	12
740.3	even	36	inner	740.2.ce.b.3.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.ce.a.447.1	✓	12	37.3	even	18
740.2.ce.a.447.1	✓	12	148.3	odd	18
740.2.ce.a.543.1	yes	12	5.3	odd	4
740.2.ce.a.543.1	yes	12	20.3	even	4
740.2.ce.b.3.1	yes	12	185.3	odd	36	inner
740.2.ce.b.3.1	yes	12	740.3	even	36	inner
740.2.ce.b.247.1	yes	12	1.1	even	1	trivial
740.2.ce.b.247.1	yes	12	4.3	odd	2	CM

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)

\(f(q)\)	\(=\)	\(q+(-0.123257 + 1.40883i) q^{2} +(-1.96962 - 0.347296i) q^{4} +(1.53737 + 1.62373i) q^{5} +(0.732051 - 2.73205i) q^{8} +(2.95442 - 0.520945i) q^{9} +(-2.47706 + 1.96575i) q^{10} +(4.43703 - 3.10684i) q^{13} +(3.75877 + 1.36808i) q^{16} +(1.28470 + 0.899557i) q^{17} +(0.369771 + 4.22650i) q^{18} +(-2.46410 - 3.73205i) q^{20} +(-0.273017 + 4.99254i) q^{25} +(3.83013 + 6.63397i) q^{26} +(-1.10137 - 1.90764i) q^{29} +(-2.39069 + 5.12685i) q^{32} +(-1.42567 + 1.69905i) q^{34} -6.00000 q^{36} +(-0.0570813 + 6.08249i) q^{37} +(5.56155 - 3.01150i) q^{40} +(0.711496 - 4.03509i) q^{41} +(5.38790 + 3.99631i) q^{45} +(4.49951 + 5.36231i) q^{49} +(-7.00000 - 1.00000i) q^{50} +(-9.81825 + 4.57832i) q^{52} +(-13.1942 + 6.15258i) q^{53} +(2.82329 - 1.31652i) q^{58} +(9.92806 + 1.75058i) q^{61} +(-6.92820 - 4.00000i) q^{64} +(11.8660 + 2.42820i) q^{65} +(-2.21795 - 2.21795i) q^{68} +(0.739541 - 8.45299i) q^{72} +(-7.02628 + 7.02628i) q^{73} +(-8.56218 - 0.830127i) q^{74} +(3.55721 + 8.20648i) q^{80} +(8.45723 - 3.07818i) q^{81} +(5.59707 + 1.49973i) q^{82} +(0.514414 + 3.46896i) q^{85} +(-13.9725 - 5.08558i) q^{89} +(-6.29423 + 7.09808i) q^{90} +(-0.976048 - 3.64266i) q^{97} +(-8.10919 + 5.67812i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{8} - 6 q^{17} + 12 q^{20} - 6 q^{26} - 30 q^{34} - 72 q^{36} + 24 q^{41} - 84 q^{50} - 18 q^{58} + 72 q^{61} + 132 q^{65} + 30 q^{73} - 30 q^{74} - 42 q^{85} - 60 q^{89} + 18 q^{90}+O(q^{100}) \) 12 * q - 12 * q^8 - 6 * q^17 + 12 * q^20 - 6 * q^26 - 30 * q^34 - 72 * q^36 + 24 * q^41 - 84 * q^50 - 18 * q^58 + 72 * q^61 + 132 * q^65 + 30 * q^73 - 30 * q^74 - 42 * q^85 - 60 * q^89 + 18 * q^90

Introduction

L-functions

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