LMFDB - Embedded newform 2240.2.e.f.2239.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2240,2,Mod(2239,2240)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2240.2239"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2240, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2240 = 2^{6} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2240.e (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$17.8864900528$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 28x^{12} + 16x^{10} - 40x^{8} + 610x^{6} + 1625x^{4} - 524x^{2} + 1444 $ x^16 - 6x^14 + 28x^12 + 16x^10 - 40x^8 + 610x^6 + 1625x^4 - 524*x^2 + 1444
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2239.3
Root			$-0.328458 - 1.49331i$ of defining polynomial
Character	$\chi$	$=$	2240.2239
Dual form			2240.2.e.f.2239.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.13578i q^{3} +(1.94442 - 1.10418i) q^{5} +(-2.35829 + 1.19935i) q^{7} -1.56155 q^{9} -2.33205i q^{11} +1.09190 q^{13} +(-2.35829 - 4.15286i) q^{15} +4.98074 q^{17} +2.57501 q^{19} +(2.56155 + 5.03680i) q^{21} +6.04090 q^{23} +(2.56155 - 4.29400i) q^{25} -3.07221i q^{27} -0.561553 q^{29} -6.59603 q^{31} -4.98074 q^{33} +(-3.26121 + 4.93604i) q^{35} -5.49966i q^{37} -2.33205i q^{39} +8.48528i q^{41} +1.32431 q^{43} +(-3.03632 + 1.72424i) q^{45} -9.74247i q^{47} +(4.12311 - 5.65685i) q^{49} -10.6378i q^{51} -8.58800i q^{53} +(-2.57501 - 4.53448i) q^{55} -5.49966i q^{57} -14.3211 q^{59} -0.620058i q^{61} +(3.68260 - 1.87285i) q^{63} +(2.12311 - 1.20565i) q^{65} -4.71659 q^{67} -12.9020i q^{69} +11.9473i q^{71} +9.96148 q^{73} +(-9.17104 - 5.47091i) q^{75} +(2.79695 + 5.49966i) q^{77} -10.6378i q^{79} -11.2462 q^{81} +3.86098i q^{83} +(9.68466 - 5.49966i) q^{85} +1.19935i q^{87} -2.82843i q^{89} +(-2.57501 + 1.30957i) q^{91} +14.0877i q^{93} +(5.00691 - 2.84329i) q^{95} -14.9422 q^{97} +3.64162i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{9} + 8 q^{21} + 8 q^{25} + 24 q^{29} - 32 q^{65} - 48 q^{81} + 56 q^{85}+O(q^{100}) $ 16 * q + 8 * q^9 + 8 * q^21 + 8 * q^25 + 24 * q^29 - 32 * q^65 - 48 * q^81 + 56 * q^85

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times$.

$n$	$897$	$1471$	$1541$	$1921$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	2.13578i		−	1.23309i	−0.787319	−	0.616546i	$-0.788531\pi$
$3$		−	2.13578i		−	1.23309i	0.787319	−	0.616546i	$-0.211469\pi$
$4$		0			0
$5$	1.94442	−	1.10418i	0.869572	−	0.493806i
$5$	1.94442	−	1.10418i	0.869572	−	0.493806i
$6$		0			0
$7$	−2.35829	+	1.19935i	−0.891352	+	0.453313i
$7$	−2.35829	+	1.19935i	−0.891352	+	0.453313i
$8$		0			0
$9$	−1.56155			−0.520518
$10$		0			0
$11$		−	2.33205i		−	0.703139i	−0.936162	−	0.351569i	$-0.885648\pi$
$11$		−	2.33205i		−	0.703139i	0.936162	−	0.351569i	$-0.114352\pi$
$12$		0			0
$13$	1.09190			0.302837			0.151419	−	0.988470i	$-0.451616\pi$
$13$	1.09190			0.302837			0.151419	+	0.988470i	$0.451616\pi$
$14$		0			0
$15$	−2.35829	−	4.15286i	−0.608909	−	1.07226i
$16$		0			0
$17$	4.98074			1.20801			0.604003	−	0.796982i	$-0.293571\pi$
$17$	4.98074			1.20801			0.604003	+	0.796982i	$0.293571\pi$
$18$		0			0
$19$	2.57501			0.590748			0.295374	−	0.955382i	$-0.404556\pi$
$19$	2.57501			0.590748			0.295374	+	0.955382i	$0.404556\pi$
$20$		0			0
$21$	2.56155	+	5.03680i	0.558977	+	1.09912i
$22$		0			0
$23$	6.04090			1.25961			0.629807	−	0.776752i	$-0.283134\pi$
$23$	6.04090			1.25961			0.629807	+	0.776752i	$0.283134\pi$
$24$		0			0
$25$	2.56155	−	4.29400i	0.512311	−	0.858800i
$26$		0			0
$27$		−	3.07221i		−	0.591246i
$28$		0			0
$29$	−0.561553			−0.104278			−0.0521389	−	0.998640i	$-0.516604\pi$
$29$	−0.561553			−0.104278			−0.0521389	+	0.998640i	$0.516604\pi$
$30$		0			0
$31$	−6.59603			−1.18468			−0.592341	−	0.805688i	$-0.701796\pi$
$31$	−6.59603			−1.18468			−0.592341	+	0.805688i	$0.701796\pi$
$32$		0			0
$33$	−4.98074			−0.867035
$34$		0			0
$35$	−3.26121	+	4.93604i	−0.551246	+	0.834343i
$36$		0			0
$37$		−	5.49966i		−	0.904138i	−0.891983	−	0.452069i	$-0.850686\pi$
$37$		−	5.49966i		−	0.904138i	0.891983	−	0.452069i	$-0.149314\pi$
$38$		0			0
$39$		−	2.33205i		−	0.373427i
$40$		0			0
$41$			8.48528i			1.32518i	0.748983	+	0.662589i	$0.230542\pi$
$41$			8.48528i			1.32518i	−0.748983	+	0.662589i	$0.769458\pi$
$42$		0			0
$43$	1.32431			0.201955			0.100977	−	0.994889i	$-0.467803\pi$
$43$	1.32431			0.201955			0.100977	+	0.994889i	$0.467803\pi$
$44$		0			0
$45$	−3.03632	+	1.72424i	−0.452627	+	0.257035i
$46$		0			0
$47$		−	9.74247i		−	1.42109i	−0.703654	−	0.710543i	$-0.748450\pi$
$47$		−	9.74247i		−	1.42109i	0.703654	−	0.710543i	$-0.251550\pi$
$48$		0			0
$49$	4.12311	−	5.65685i	0.589015	−	0.808122i
$50$		0			0
$51$		−	10.6378i		−	1.48958i
$52$		0			0
$53$		−	8.58800i		−	1.17965i	−0.807530	−	0.589826i	$-0.799196\pi$
$53$		−	8.58800i		−	1.17965i	0.807530	−	0.589826i	$-0.200804\pi$
$54$		0			0
$55$	−2.57501	−	4.53448i	−0.347214	−	0.611430i
$56$		0			0
$57$		−	5.49966i		−	0.728447i
$58$		0			0
$59$	−14.3211			−1.86444			−0.932222	−	0.361888i	$-0.882132\pi$
$59$	−14.3211			−1.86444			−0.932222	+	0.361888i	$0.882132\pi$
$60$		0			0
$61$		−	0.620058i		−	0.0793903i	−0.999212	−	0.0396951i	$-0.987361\pi$
$61$		−	0.620058i		−	0.0793903i	0.999212	−	0.0396951i	$-0.0126387\pi$
$62$		0			0
$63$	3.68260	−	1.87285i	0.463964	−	0.235957i
$64$		0			0
$65$	2.12311	−	1.20565i	0.263339	−	0.149543i
$66$		0			0
$67$	−4.71659			−0.576223			−0.288112	−	0.957597i	$-0.593027\pi$
$67$	−4.71659			−0.576223			−0.288112	+	0.957597i	$0.593027\pi$
$68$		0			0
$69$		−	12.9020i		−	1.55322i
$70$		0			0
$71$			11.9473i			1.41789i	0.705265	+	0.708943i	$0.250828\pi$
$71$			11.9473i			1.41789i	−0.705265	+	0.708943i	$0.749172\pi$
$72$		0			0
$73$	9.96148			1.16590			0.582951	−	0.812507i	$-0.301898\pi$
$73$	9.96148			1.16590			0.582951	+	0.812507i	$0.301898\pi$
$74$		0			0
$75$	−9.17104	−	5.47091i	−1.05898	−	0.631726i
$76$		0			0
$77$	2.79695	+	5.49966i	0.318742	+	0.626744i
$78$		0			0
$79$		−	10.6378i		−	1.19684i	−0.801182	−	0.598421i	$-0.795795\pi$
$79$		−	10.6378i		−	1.19684i	0.801182	−	0.598421i	$-0.204205\pi$
$80$		0			0
$81$	−11.2462			−1.24958
$82$		0			0
$83$			3.86098i			0.423798i	0.977292	+	0.211899i	$0.0679648\pi$
$83$			3.86098i			0.423798i	−0.977292	+	0.211899i	$0.932035\pi$
$84$		0			0
$85$	9.68466	−	5.49966i	1.05045	−	0.596521i
$86$		0			0
$87$			1.19935i			0.128584i
$88$		0			0
$89$		−	2.82843i		−	0.299813i	−0.988700	−	0.149906i	$-0.952103\pi$
$89$		−	2.82843i		−	0.299813i	0.988700	−	0.149906i	$-0.0478972\pi$
$90$		0			0
$91$	−2.57501	+	1.30957i	−0.269935	+	0.137280i
$92$		0			0
$93$			14.0877i			1.46082i
$94$		0			0
$95$	5.00691	−	2.84329i	0.513698	−	0.291715i
$96$		0			0
$97$	−14.9422			−1.51715			−0.758576	−	0.651584i	$-0.774105\pi$
$97$	−14.9422			−1.51715			−0.758576	+	0.651584i	$0.774105\pi$
$98$		0			0
$99$			3.64162i			0.365996i
$100$		0			0
$101$			15.1104i			1.50354i	0.659425	+	0.751770i	$0.270800\pi$
$101$			15.1104i			1.50354i	−0.659425	+	0.751770i	$0.729200\pi$
$102$		0			0
$103$			5.47091i			0.539065i	0.962991	+	0.269532i	$0.0868691\pi$
$103$			5.47091i			0.539065i	−0.962991	+	0.269532i	$0.913131\pi$
$104$		0			0
$105$	10.5423	+	6.96523i	1.02882	+	0.679737i
$106$		0			0
$107$	10.0138			0.968072			0.484036	−	0.875048i	$-0.339170\pi$
$107$	10.0138			0.968072			0.484036	+	0.875048i	$0.339170\pi$
$108$		0			0
$109$	−4.56155			−0.436918			−0.218459	−	0.975846i	$-0.570103\pi$
$109$	−4.56155			−0.436918			−0.218459	+	0.975846i	$0.570103\pi$
$110$		0			0
$111$	−11.7460			−1.11489
$112$		0			0
$113$			5.49966i			0.517364i	0.965963	+	0.258682i	$0.0832882\pi$
$113$			5.49966i			0.517364i	−0.965963	+	0.258682i	$0.916712\pi$
$114$		0			0
$115$	11.7460	−	6.67026i	1.09532	−	0.622005i
$116$		0			0
$117$	−1.70505			−0.157632
$118$		0			0
$119$	−11.7460	+	5.97366i	−1.07676	+	0.547605i
$120$		0			0
$121$	5.56155			0.505596
$122$		0			0
$123$	18.1227			1.63407
$124$		0			0
$125$	0.239369	−	11.1778i	0.0214098	−	0.999771i
$126$		0			0
$127$	5.29723			0.470053			0.235026	−	0.971989i	$-0.424482\pi$
$127$	5.29723			0.470053			0.235026	+	0.971989i	$0.424482\pi$
$128$		0			0
$129$		−	2.82843i		−	0.249029i
$130$		0			0
$131$	−2.57501			−0.224980			−0.112490	−	0.993653i	$-0.535883\pi$
$131$	−2.57501			−0.224980			−0.112490	+	0.993653i	$0.535883\pi$
$132$		0			0
$133$	−6.07263	+	3.08835i	−0.526564	+	0.267794i
$134$		0			0
$135$	−3.39228	−	5.97366i	−0.291961	−	0.514131i
$136$		0			0
$137$		−	3.08835i		−	0.263855i	−0.991259	−	0.131928i	$-0.957883\pi$
$137$		−	3.08835i		−	0.263855i	0.991259	−	0.131928i	$-0.0421167\pi$
$138$		0			0
$139$	−4.02102			−0.341058			−0.170529	−	0.985353i	$-0.554548\pi$
$139$	−4.02102			−0.341058			−0.170529	+	0.985353i	$0.554548\pi$
$140$		0			0
$141$	−20.8078			−1.75233
$142$		0			0
$143$		−	2.54635i		−	0.212937i
$144$		0			0
$145$	−1.09190	+	0.620058i	−0.0906770	+	0.0514930i
$146$		0			0
$147$	−12.0818	−	8.80604i	−0.996489	−	0.726310i
$148$		0			0
$149$	2.00000			0.163846			0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000			0.163846			0.0819232	+	0.996639i	$0.473894\pi$
$150$		0			0
$151$		−	4.95118i		−	0.402922i	−0.979497	−	0.201461i	$-0.935431\pi$
$151$		−	4.95118i		−	0.402922i	0.979497	−	0.201461i	$-0.0645689\pi$
$152$		0			0
$153$	−7.77769			−0.628789
$154$		0			0
$155$	−12.8255	+	7.28323i	−1.03017	+	0.585003i
$156$		0			0
$157$	3.88884			0.310364			0.155182	−	0.987886i	$-0.450404\pi$
$157$	3.88884			0.310364			0.155182	+	0.987886i	$0.450404\pi$
$158$		0			0
$159$	−18.3421			−1.45462
$160$		0			0
$161$	−14.2462	+	7.24517i	−1.12276	+	0.570999i
$162$		0			0
$163$	11.5012			0.900840			0.450420	−	0.892817i	$-0.351274\pi$
$163$	11.5012			0.900840			0.450420	+	0.892817i	$0.351274\pi$
$164$		0			0
$165$	−9.68466	+	5.49966i	−0.753950	+	0.428148i
$166$		0			0
$167$			0.673500i			0.0521170i	0.999660	+	0.0260585i	$0.00829562\pi$
$167$			0.673500i			0.0521170i	−0.999660	+	0.0260585i	$0.991704\pi$
$168$		0			0
$169$	−11.8078			−0.908290
$170$		0			0
$171$	−4.02102			−0.307495
$172$		0			0
$173$	−11.0534			−0.840372			−0.420186	−	0.907438i	$-0.638035\pi$
$173$	−11.0534			−0.840372			−0.420186	+	0.907438i	$0.638035\pi$
$174$		0			0
$175$	−0.890873	+	13.1987i	−0.0673437	+	0.997730i
$176$		0			0
$177$			30.5866i			2.29903i
$178$		0			0
$179$		−	8.30571i		−	0.620798i	−0.950606	−	0.310399i	$-0.899537\pi$
$179$		−	8.30571i		−	0.620798i	0.950606	−	0.310399i	$-0.100463\pi$
$180$		0			0
$181$			3.44849i			0.256324i	0.991753	+	0.128162i	$0.0409077\pi$
$181$			3.44849i			0.256324i	−0.991753	+	0.128162i	$0.959092\pi$
$182$		0			0
$183$	−1.32431			−0.0978956
$184$		0			0
$185$	−6.07263	−	10.6937i	−0.446469	−	0.786213i
$186$		0			0
$187$		−	11.6153i		−	0.849396i
$188$		0			0
$189$	3.68466	+	7.24517i	0.268019	+	0.527008i
$190$		0			0
$191$		−	19.9660i		−	1.44469i	−0.691535	−	0.722343i	$-0.743065\pi$
$191$		−	19.9660i		−	1.44469i	0.691535	−	0.722343i	$-0.256935\pi$
$192$		0			0
$193$		−	5.49966i		−	0.395874i	−0.980215	−	0.197937i	$-0.936576\pi$
$193$		−	5.49966i		−	0.395874i	0.980215	−	0.197937i	$-0.0634241\pi$
$194$		0			0
$195$	−2.57501	−	4.53448i	−0.184400	−	0.324721i
$196$		0			0
$197$			16.4990i			1.17550i	0.809042	+	0.587751i	$0.199987\pi$
$197$			16.4990i			1.17550i	−0.809042	+	0.587751i	$0.800013\pi$
$198$		0			0
$199$	18.3421			1.30024			0.650118	−	0.759834i	$-0.274720\pi$
$199$	18.3421			1.30024			0.650118	+	0.759834i	$0.274720\pi$
$200$		0			0
$201$			10.0736i			0.710536i
$202$		0			0
$203$	1.32431	−	0.673500i	0.0929481	−	0.0472704i
$204$		0			0
$205$	9.36932	+	16.4990i	0.654381	+	1.15234i
$206$		0			0
$207$	−9.43318			−0.655651
$208$		0			0
$209$		−	6.00505i		−	0.415378i
$210$		0			0
$211$		−	0.287088i		−	0.0197640i	−0.999951	−	0.00988198i	$-0.996854\pi$
$211$		−	0.287088i		−	0.0197640i	0.999951	−	0.00988198i	$-0.00314558\pi$
$212$		0			0
$213$	25.5169			1.74839
$214$		0			0
$215$	2.57501	−	1.46228i	0.175614	−	0.0997266i
$216$		0			0
$217$	15.5554	−	7.91096i	1.05597	−	0.537031i
$218$		0			0
$219$		−	21.2755i		−	1.43767i
$220$		0			0
$221$	5.43845			0.365830
$222$		0			0
$223$		−	0.147647i		−	0.00988718i	−0.999988	−	0.00494359i	$-0.998426\pi$
$223$		−	0.147647i		−	0.00988718i	0.999988	−	0.00494359i	$-0.00157360\pi$
$224$		0			0
$225$	−4.00000	+	6.70531i	−0.266667	+	0.447021i
$226$		0			0
$227$			10.1530i			0.673881i	0.941526	+	0.336941i	$0.109392\pi$
$227$			10.1530i			0.673881i	−0.941526	+	0.336941i	$0.890608\pi$
$228$		0			0
$229$		−	9.45353i		−	0.624707i	−0.949966	−	0.312354i	$-0.898883\pi$
$229$		−	9.45353i		−	0.624707i	0.949966	−	0.312354i	$-0.101117\pi$
$230$		0			0
$231$	11.7460	−	5.97366i	0.772833	−	0.393038i
$232$		0			0
$233$		−	10.9993i		−	0.720589i	−0.932839	−	0.360294i	$-0.882676\pi$
$233$		−	10.9993i		−	0.720589i	0.932839	−	0.360294i	$-0.117324\pi$
$234$		0			0
$235$	−10.7575	−	18.9435i	−0.701741	−	1.23574i
$236$		0			0
$237$	−22.7199			−1.47582
$238$		0			0
$239$			2.33205i			0.150848i	0.997152	+	0.0754238i	$0.0240310\pi$
$239$			2.33205i			0.150848i	−0.997152	+	0.0754238i	$0.975969\pi$
$240$		0			0
$241$			16.0786i			1.03572i	0.855466	+	0.517858i	$0.173271\pi$
$241$			16.0786i			1.03572i	−0.855466	+	0.517858i	$0.826729\pi$
$242$		0			0
$243$			14.8028i			0.949601i
$244$		0			0
$245$	1.77085	−	15.5520i	0.113135	−	0.993580i
$246$		0			0
$247$	2.81164			0.178901
$248$		0			0
$249$	8.24621			0.522582
$250$		0			0
$251$	−9.17104			−0.578871			−0.289435	−	0.957198i	$-0.593468\pi$
$251$	−9.17104			−0.578871			−0.289435	+	0.957198i	$0.593468\pi$
$252$		0			0
$253$		−	14.0877i		−	0.885683i
$254$		0			0
$255$	−11.7460	−	20.6843i	−0.735566	−	1.29530i
$256$		0			0
$257$	6.55137			0.408663			0.204332	−	0.978902i	$-0.434498\pi$
$257$	6.55137			0.408663			0.204332	+	0.978902i	$0.434498\pi$
$258$		0			0
$259$	6.59603	+	12.9698i	0.409857	+	0.805905i
$260$		0			0
$261$	0.876894			0.0542784
$262$		0			0
$263$	23.5829			1.45419			0.727093	−	0.686539i	$-0.240871\pi$
$263$	23.5829			1.45419			0.727093	+	0.686539i	$0.240871\pi$
$264$		0			0
$265$	−9.48274	−	16.6987i	−0.582520	−	1.02579i
$266$		0			0
$267$	−6.04090			−0.369697
$268$		0			0
$269$			0.968253i			0.0590354i	0.999564	+	0.0295177i	$0.00939715\pi$
$269$			0.968253i			0.0590354i	−0.999564	+	0.0295177i	$0.990603\pi$
$270$		0			0
$271$	6.59603			0.400680			0.200340	−	0.979726i	$-0.435795\pi$
$271$	6.59603			0.400680			0.200340	+	0.979726i	$0.435795\pi$
$272$		0			0
$273$	2.79695	+	5.49966i	0.169279	+	0.332854i
$274$		0			0
$275$	−10.0138	−	5.97366i	−0.603856	−	0.360225i
$276$		0			0
$277$		−	19.5873i		−	1.17689i	−0.808538	−	0.588444i	$-0.799741\pi$
$277$		−	19.5873i		−	1.17689i	0.808538	−	0.588444i	$-0.200259\pi$
$278$		0			0
$279$	10.3000			0.616648
$280$		0			0
$281$	17.0540			1.01735			0.508677	−	0.860957i	$-0.330135\pi$
$281$	17.0540			1.01735			0.508677	+	0.860957i	$0.330135\pi$
$282$		0			0
$283$			7.45904i			0.443394i	0.975116	+	0.221697i	$0.0711596\pi$
$283$			7.45904i			0.443394i	−0.975116	+	0.221697i	$0.928840\pi$
$284$		0			0
$285$	−6.07263	−	10.6937i	−0.359712	−	0.633437i
$286$		0			0
$287$	−10.1768	−	20.0108i	−0.600720	−	1.18120i
$288$		0			0
$289$	7.80776			0.459280
$290$		0			0
$291$			31.9133i			1.87079i
$292$		0			0
$293$	−14.4635			−0.844965			−0.422483	−	0.906371i	$-0.638841\pi$
$293$	−14.4635			−0.844965			−0.422483	+	0.906371i	$0.638841\pi$
$294$		0			0
$295$	−27.8462	+	15.8131i	−1.62127	+	0.920674i
$296$		0			0
$297$	−7.16453			−0.415728
$298$		0			0
$299$	6.59603			0.381458
$300$		0			0
$301$	−3.12311	+	1.58831i	−0.180013	+	0.0915487i
$302$		0			0
$303$	32.2725			1.85400
$304$		0			0
$305$	−0.684658	−	1.20565i	−0.0392034	−	0.0690356i
$306$		0			0
$307$			13.8987i			0.793243i	0.917982	+	0.396622i	$0.129818\pi$
$307$			13.8987i			0.793243i	−0.917982	+	0.396622i	$0.870182\pi$
$308$		0			0
$309$	11.6847			0.664717
$310$		0			0
$311$	1.44600			0.0819954			0.0409977	−	0.999159i	$-0.486946\pi$
$311$	1.44600			0.0819954			0.0409977	+	0.999159i	$0.486946\pi$
$312$		0			0
$313$	−7.16453			−0.404963			−0.202482	−	0.979286i	$-0.564901\pi$
$313$	−7.16453			−0.404963			−0.202482	+	0.979286i	$0.564901\pi$
$314$		0			0
$315$	5.09256	−	7.70789i	0.286933	−	0.434290i
$316$		0			0
$317$		−	24.4099i		−	1.37100i	−0.728073	−	0.685499i	$-0.759584\pi$
$317$		−	24.4099i		−	1.37100i	0.728073	−	0.685499i	$-0.240416\pi$
$318$		0			0
$319$			1.30957i			0.0733217i
$320$		0			0
$321$		−	21.3873i		−	1.19372i
$322$		0			0
$323$	12.8255			0.713628
$324$		0			0
$325$	2.79695	−	4.68860i	0.155147	−	0.260077i
$326$		0			0
$327$			9.74247i			0.538760i
$328$		0			0
$329$	11.6847	+	22.9756i	0.644196	+	1.26669i
$330$		0			0
$331$		−	8.30571i		−	0.456523i	−0.973600	−	0.228262i	$-0.926696\pi$
$331$		−	8.30571i		−	0.456523i	0.973600	−	0.228262i	$-0.0733041\pi$
$332$		0			0
$333$			8.58800i			0.470620i
$334$		0			0
$335$	−9.17104	+	5.20798i	−0.501067	+	0.284543i
$336$		0			0
$337$		−	30.5866i		−	1.66616i	−0.553153	−	0.833080i	$-0.686575\pi$
$337$		−	30.5866i		−	1.66616i	0.553153	−	0.833080i	$-0.313425\pi$
$338$		0			0
$339$	11.7460			0.637958
$340$		0			0
$341$			15.3823i			0.832996i
$342$		0			0
$343$	−2.93893	+	18.2856i	−0.158687	+	0.987329i
$344$		0			0
$345$	−14.2462	−	25.0870i	−0.766990	−	1.35064i
$346$		0			0
$347$	1.32431			0.0710925			0.0355463	−	0.999368i	$-0.488683\pi$
$347$	1.32431			0.0710925			0.0355463	+	0.999368i	$0.488683\pi$
$348$		0			0
$349$			18.8307i			1.00799i	0.863708	+	0.503993i	$0.168136\pi$
$349$			18.8307i			1.00799i	−0.863708	+	0.503993i	$0.831864\pi$
$350$		0			0
$351$		−	3.35453i		−	0.179051i
$352$		0			0
$353$	16.1685			0.860564			0.430282	−	0.902694i	$-0.358414\pi$
$353$	16.1685			0.860564			0.430282	+	0.902694i	$0.358414\pi$
$354$		0			0
$355$	13.1921	+	23.2306i	0.700162	+	1.23295i
$356$		0			0
$357$	12.7584	+	25.0870i	0.675248	+	1.32774i
$358$		0			0
$359$			10.3507i			0.546288i	0.961973	+	0.273144i	$0.0880635\pi$
$359$			10.3507i			0.546288i	−0.961973	+	0.273144i	$0.911937\pi$
$360$		0			0
$361$	−12.3693			−0.651017
$362$		0			0
$363$		−	11.8782i		−	0.623446i
$364$		0			0
$365$	19.3693	−	10.9993i	1.01384	−	0.575730i
$366$		0			0
$367$			23.3783i			1.22034i	0.792272	+	0.610168i	$0.208898\pi$
$367$			23.3783i			1.22034i	−0.792272	+	0.610168i	$0.791102\pi$
$368$		0			0
$369$		−	13.2502i		−	0.689779i
$370$		0			0
$371$	10.3000	+	20.2530i	0.534752	+	1.05149i
$372$		0			0
$373$		−	11.6763i		−	0.604578i	−0.953216	−	0.302289i	$-0.902249\pi$
$373$		−	11.6763i		−	0.604578i	0.953216	−	0.302289i	$-0.0977508\pi$
$374$		0			0
$375$	−23.8733	−	0.511240i	−1.23281	−	0.0264003i
$376$		0			0
$377$	−0.613157			−0.0315792
$378$		0			0
$379$			24.9171i			1.27991i	0.768414	+	0.639954i	$0.221046\pi$
$379$			24.9171i			1.27991i	−0.768414	+	0.639954i	$0.778954\pi$
$380$		0			0
$381$		−	11.3137i		−	0.579619i
$382$		0			0
$383$			18.6638i			0.953675i	0.878991	+	0.476838i	$0.158217\pi$
$383$			18.6638i			0.953675i	−0.878991	+	0.476838i	$0.841783\pi$
$384$		0			0
$385$	11.5111	+	7.60530i	0.586659	+	0.387602i
$386$		0			0
$387$	−2.06798			−0.105121
$388$		0			0
$389$	11.9309			0.604919			0.302460	−	0.953162i	$-0.402192\pi$
$389$	11.9309			0.604919			0.302460	+	0.953162i	$0.402192\pi$
$390$		0			0
$391$	30.0881			1.52162
$392$		0			0
$393$			5.49966i			0.277421i
$394$		0			0
$395$	−11.7460	−	20.6843i	−0.591008	−	1.04074i
$396$		0			0
$397$	21.0149			1.05471			0.527353	−	0.849647i	$-0.323185\pi$
$397$	21.0149			1.05471			0.527353	+	0.849647i	$0.323185\pi$
$398$		0			0
$399$	6.59603	+	12.9698i	0.330214	+	0.649303i
$400$		0			0
$401$	13.4384			0.671084			0.335542	−	0.942025i	$-0.391081\pi$
$401$	13.4384			0.671084			0.335542	+	0.942025i	$0.391081\pi$
$402$		0			0
$403$	−7.20217			−0.358766
$404$		0			0
$405$	−21.8674	+	12.4179i	−1.08660	+	0.617050i
$406$		0			0
$407$	−12.8255			−0.635734
$408$		0			0
$409$			30.2208i			1.49432i	0.664643	+	0.747161i	$0.268583\pi$
$409$			30.2208i			1.49432i	−0.664643	+	0.747161i	$0.731417\pi$
$410$		0			0
$411$	−6.59603			−0.325358
$412$		0			0
$413$	33.7733	−	17.1760i	1.66187	−	0.845176i
$414$		0			0
$415$	4.26324	+	7.50738i	0.209274	+	0.368523i
$416$		0			0
$417$			8.58800i			0.420556i
$418$		0			0
$419$	22.3631			1.09251			0.546254	−	0.837619i	$-0.316053\pi$
$419$	22.3631			1.09251			0.546254	+	0.837619i	$0.316053\pi$
$420$		0			0
$421$	−12.5616			−0.612213			−0.306106	−	0.951997i	$-0.599026\pi$
$421$	−12.5616			−0.612213			−0.306106	+	0.951997i	$0.599026\pi$
$422$		0			0
$423$			15.2134i			0.739700i
$424$		0			0
$425$	12.7584	−	21.3873i	0.618875	−	1.03744i
$426$		0			0
$427$	0.743668	+	1.46228i	0.0359886	+	0.0707647i
$428$		0			0
$429$	−5.43845			−0.262571
$430$		0			0
$431$			11.6602i			0.561654i	0.959758	+	0.280827i	$0.0906087\pi$
$431$			11.6602i			0.561654i	−0.959758	+	0.280827i	$0.909391\pi$
$432$		0			0
$433$	−9.00400			−0.432705			−0.216352	−	0.976315i	$-0.569416\pi$
$433$	−9.00400			−0.432705			−0.216352	+	0.976315i	$0.569416\pi$
$434$		0			0
$435$	1.32431	+	2.33205i	0.0634957	+	0.111813i
$436$		0			0
$437$	15.5554			0.744114
$438$		0			0
$439$	31.5341			1.50504			0.752521	−	0.658568i	$-0.228838\pi$
$439$	31.5341			1.50504			0.752521	+	0.658568i	$0.228838\pi$
$440$		0			0
$441$	−6.43845	+	8.83348i	−0.306593	+	0.420642i
$442$		0			0
$443$	17.5420			0.833448			0.416724	−	0.909033i	$-0.363178\pi$
$443$	17.5420			0.833448			0.416724	+	0.909033i	$0.363178\pi$
$444$		0			0
$445$	−3.12311	−	5.49966i	−0.148049	−	0.260709i
$446$		0			0
$447$		−	4.27156i		−	0.202038i
$448$		0			0
$449$	6.31534			0.298039			0.149020	−	0.988834i	$-0.452388\pi$
$449$	6.31534			0.298039			0.149020	+	0.988834i	$0.452388\pi$
$450$		0			0
$451$	19.7881			0.931784
$452$		0			0
$453$	−10.5746			−0.496840
$454$		0			0
$455$	−3.56090	+	5.38964i	−0.166938	+	0.252670i
$456$		0			0
$457$			10.3223i			0.482856i	0.970419	+	0.241428i	$0.0776157\pi$
$457$			10.3223i			0.482856i	−0.970419	+	0.241428i	$0.922384\pi$
$458$		0			0
$459$		−	15.3019i		−	0.714229i
$460$		0			0
$461$		−	21.1154i		−	0.983444i	−0.870752	−	0.491722i	$-0.836368\pi$
$461$		−	21.1154i		−	0.983444i	0.870752	−	0.491722i	$-0.163632\pi$
$462$		0			0
$463$	24.3266			1.13055			0.565277	−	0.824901i	$-0.308769\pi$
$463$	24.3266			1.13055			0.565277	+	0.824901i	$0.308769\pi$
$464$		0			0
$465$	15.5554	+	27.3924i	0.721363	+	1.27029i
$466$		0			0
$467$		−	23.1983i		−	1.07349i	−0.843745	−	0.536744i	$-0.819654\pi$
$467$		−	23.1983i		−	1.07349i	0.843745	−	0.536744i	$-0.180346\pi$
$468$		0			0
$469$	11.1231	−	5.65685i	0.513617	−	0.261209i
$470$		0			0
$471$		−	8.30571i		−	0.382707i
$472$		0			0
$473$		−	3.08835i		−	0.142002i
$474$		0			0
$475$	6.59603	−	11.0571i	0.302646	−	0.507335i
$476$		0			0
$477$			13.4106i			0.614030i
$478$		0			0
$479$	−30.0881			−1.37476			−0.687381	−	0.726297i	$-0.741240\pi$
$479$	−30.0881			−1.37476			−0.687381	+	0.726297i	$0.741240\pi$
$480$		0			0
$481$		−	6.00505i		−	0.273807i
$482$		0			0
$483$	15.4741	+	30.4268i	0.704095	+	1.38447i
$484$		0			0
$485$	−29.0540	+	16.4990i	−1.31927	+	0.749179i
$486$		0			0
$487$	−1.16128			−0.0526225			−0.0263112	−	0.999654i	$-0.508376\pi$
$487$	−1.16128			−0.0526225			−0.0263112	+	0.999654i	$0.508376\pi$
$488$		0			0
$489$		−	24.5639i		−	1.11082i
$490$		0			0
$491$			14.2794i			0.644419i	0.946668	+	0.322210i	$0.104426\pi$
$491$			14.2794i			0.644419i	−0.946668	+	0.322210i	$0.895574\pi$
$492$		0			0
$493$	−2.79695			−0.125968
$494$		0			0
$495$	4.02102	+	7.08084i	0.180731	+	0.318260i
$496$		0			0
$497$	−14.3291	−	28.1753i	−0.642746	−	1.26384i
$498$		0			0
$499$			25.6525i			1.14836i	0.818727	+	0.574182i	$0.194680\pi$
$499$			25.6525i			1.14836i	−0.818727	+	0.574182i	$0.805320\pi$
$500$		0			0
$501$	1.43845			0.0642651
$502$		0			0
$503$			18.8114i			0.838761i	0.907811	+	0.419380i	$0.137753\pi$
$503$			18.8114i			0.838761i	−0.907811	+	0.419380i	$0.862247\pi$
$504$		0			0
$505$	16.6847	+	29.3810i	0.742458	+	1.30744i
$506$		0			0
$507$			25.2188i			1.12001i
$508$		0			0
$509$			28.0124i			1.24163i	0.783958	+	0.620814i	$0.213198\pi$
$509$			28.0124i			1.24163i	−0.783958	+	0.620814i	$0.786802\pi$
$510$		0			0
$511$	−23.4921	+	11.9473i	−1.03923	+	0.528519i
$512$		0			0
$513$		−	7.91096i		−	0.349278i
$514$		0			0
$515$	6.04090	+	10.6378i	0.266194	+	0.468756i
$516$		0			0
$517$	−22.7199			−0.999220
$518$		0			0
$519$			23.6076i			1.03626i
$520$		0			0
$521$			2.82843i			0.123916i	0.998079	+	0.0619578i	$0.0197344\pi$
$521$			2.82843i			0.123916i	−0.998079	+	0.0619578i	$0.980266\pi$
$522$		0			0
$523$			20.9472i			0.915958i	0.888963	+	0.457979i	$0.151426\pi$
$523$			20.9472i			0.915958i	−0.888963	+	0.457979i	$0.848574\pi$
$524$		0			0
$525$	28.1896	+	1.90271i	1.23029	+	0.0830410i
$526$		0			0
$527$	−32.8531			−1.43110
$528$		0			0
$529$	13.4924			0.586627
$530$		0			0
$531$	22.3631			0.970476
$532$		0			0
$533$			9.26504i			0.401313i
$534$		0			0
$535$	19.4711	−	11.0571i	0.841808	−	0.478040i
$536$		0			0
$537$	−17.7392			−0.765502
$538$		0			0
$539$	−13.1921	−	9.61528i	−0.568222	−	0.414159i
$540$		0			0
$541$	19.4384			0.835724			0.417862	−	0.908510i	$-0.362780\pi$
$541$	19.4384			0.835724			0.417862	+	0.908510i	$0.362780\pi$
$542$		0			0
$543$	7.36520			0.316071
$544$		0			0
$545$	−8.86958	+	5.03680i	−0.379931	+	0.215753i
$546$		0			0
$547$	−33.4337			−1.42952			−0.714762	−	0.699368i	$-0.753465\pi$
$547$	−33.4337			−1.42952			−0.714762	+	0.699368i	$0.753465\pi$
$548$		0			0
$549$			0.968253i			0.0413240i
$550$		0			0
$551$	−1.44600			−0.0616019
$552$		0			0
$553$	12.7584	+	25.0870i	0.542543	+	1.06681i
$554$		0			0
$555$	−22.8393	+	12.9698i	−0.969473	+	0.550538i
$556$		0			0
$557$			8.58800i			0.363885i	0.983309	+	0.181943i	$0.0582385\pi$
$557$			8.58800i			0.363885i	−0.983309	+	0.181943i	$0.941761\pi$
$558$		0			0
$559$	1.44600			0.0611595
$560$		0			0
$561$	−24.8078			−1.04738
$562$		0			0
$563$			6.78554i			0.285977i	0.989724	+	0.142988i	$0.0456711\pi$
$563$			6.78554i			0.285977i	−0.989724	+	0.142988i	$0.954329\pi$
$564$		0			0
$565$	6.07263	+	10.6937i	0.255478	+	0.449885i
$566$		0			0
$567$	26.5219	−	13.4882i	1.11381	−	0.566450i
$568$		0			0
$569$	−43.8617			−1.83878			−0.919390	−	0.393347i	$-0.871317\pi$
$569$	−43.8617			−1.83878			−0.919390	+	0.393347i	$0.871317\pi$
$570$		0			0
$571$		−	15.5889i		−	0.652377i	−0.945305	−	0.326188i	$-0.894236\pi$
$571$		−	15.5889i		−	0.652377i	0.945305	−	0.326188i	$-0.105764\pi$
$572$		0			0
$573$	−42.6429			−1.78143
$574$		0			0
$575$	15.4741	−	25.9396i	0.645313	−	1.08176i
$576$		0			0
$577$	36.0915			1.50251			0.751254	−	0.660013i	$-0.229449\pi$
$577$	36.0915			1.50251			0.751254	+	0.660013i	$0.229449\pi$
$578$		0			0
$579$	−11.7460			−0.488149
$580$		0			0
$581$	−4.63068	−	9.10534i	−0.192113	−	0.377753i
$582$		0			0
$583$	−20.0276			−0.829460
$584$		0			0
$585$	−3.31534	+	1.88269i	−0.137073	+	0.0778398i
$586$		0			0
$587$		−	2.80928i		−	0.115951i	−0.998318	−	0.0579757i	$-0.981535\pi$
$587$		−	2.80928i		−	0.115951i	0.998318	−	0.0579757i	$-0.0184646\pi$
$588$		0			0
$589$	−16.9848			−0.699848
$590$		0			0
$591$	35.2381			1.44950
$592$		0			0
$593$	−6.20705			−0.254893			−0.127447	−	0.991845i	$-0.540678\pi$
$593$	−6.20705			−0.254893			−0.127447	+	0.991845i	$0.540678\pi$
$594$		0			0
$595$	−16.2432	+	24.5851i	−0.665908	+	1.00789i
$596$		0			0
$597$		−	39.1746i		−	1.60331i
$598$		0			0
$599$		−	17.9210i		−	0.732232i	−0.930569	−	0.366116i	$-0.880687\pi$
$599$		−	17.9210i		−	0.732232i	0.930569	−	0.366116i	$-0.119313\pi$
$600$		0			0
$601$		−	42.2309i		−	1.72263i	−0.508068	−	0.861317i	$-0.669640\pi$
$601$		−	42.2309i		−	1.72263i	0.508068	−	0.861317i	$-0.330360\pi$
$602$		0			0
$603$	7.36520			0.299934
$604$		0			0
$605$	10.8140	−	6.14098i	0.439652	−	0.249666i
$606$		0			0
$607$		−	44.9666i		−	1.82514i	−0.408921	−	0.912570i	$-0.634095\pi$
$607$		−	44.9666i		−	1.82514i	0.408921	−	0.912570i	$-0.365905\pi$
$608$		0			0
$609$	−1.43845	−	2.82843i	−0.0582888	−	0.114614i
$610$		0			0
$611$		−	10.6378i		−	0.430358i
$612$		0			0
$613$			47.7626i			1.92911i	0.263874	+	0.964557i	$0.415000\pi$
$613$			47.7626i			1.92911i	−0.263874	+	0.964557i	$0.585000\pi$
$614$		0			0
$615$	35.2381	−	20.0108i	1.42094	−	0.806913i
$616$		0			0
$617$			14.7647i			0.594404i	0.954815	+	0.297202i	$0.0960535\pi$
$617$			14.7647i			0.594404i	−0.954815	+	0.297202i	$0.903946\pi$
$618$		0			0
$619$	26.0671			1.04773			0.523863	−	0.851803i	$-0.324490\pi$
$619$	26.0671			1.04773			0.523863	+	0.851803i	$0.324490\pi$
$620$		0			0
$621$		−	18.5589i		−	0.744742i
$622$		0			0
$623$	3.39228	+	6.67026i	0.135909	+	0.267238i
$624$		0			0
$625$	−11.8769	−	21.9986i	−0.475076	−	0.879945i
$626$		0			0
$627$	−12.8255			−0.512200
$628$		0			0
$629$		−	27.3924i		−	1.09220i
$630$		0			0
$631$			33.9582i			1.35186i	0.736968	+	0.675928i	$0.236257\pi$
$631$			33.9582i			1.35186i	−0.736968	+	0.675928i	$0.763743\pi$
$632$		0			0
$633$	−0.613157			−0.0243708
$634$		0			0
$635$	10.3000	−	5.84912i	0.408745	−	0.232115i
$636$		0			0
$637$	4.50200	−	6.17669i	0.178376	−	0.244730i
$638$		0			0
$639$		−	18.6564i		−	0.738035i
$640$		0			0
$641$	39.8617			1.57444			0.787222	−	0.616670i	$-0.211519\pi$
$641$	39.8617			1.57444			0.787222	+	0.616670i	$0.211519\pi$
$642$		0			0
$643$			36.8341i			1.45260i	0.687380	+	0.726298i	$0.258761\pi$
$643$			36.8341i			1.45260i	−0.687380	+	0.726298i	$0.741239\pi$
$644$		0			0
$645$	−3.12311	−	5.49966i	−0.122972	−	0.216549i
$646$		0			0
$647$			36.5712i			1.43776i	0.695134	+	0.718881i	$0.255345\pi$
$647$			36.5712i			1.43776i	−0.695134	+	0.718881i	$0.744655\pi$
$648$		0			0
$649$			33.3974i			1.31096i
$650$		0			0
$651$	−16.8961	−	33.2228i	−0.662209	−	1.30211i
$652$		0			0
$653$			16.4990i			0.645654i	0.946458	+	0.322827i	$0.104633\pi$
$653$			16.4990i			0.645654i	−0.946458	+	0.322827i	$0.895367\pi$
$654$		0			0
$655$	−5.00691	+	2.84329i	−0.195636	+	0.111096i
$656$		0			0
$657$	−15.5554			−0.606873
$658$		0			0
$659$		−	42.8381i		−	1.66874i	−0.551207	−	0.834368i	$-0.685833\pi$
$659$		−	42.8381i		−	1.66874i	0.551207	−	0.834368i	$-0.314167\pi$
$660$		0			0
$661$		−	1.51198i		−	0.0588092i	−0.999568	−	0.0294046i	$-0.990639\pi$
$661$		−	1.51198i		−	0.0588092i	0.999568	−	0.0294046i	$-0.00936112\pi$
$662$		0			0
$663$		−	11.6153i		−	0.451102i
$664$		0			0
$665$	−8.39766	+	12.7104i	−0.325647	+	0.492887i
$666$		0			0
$667$	−3.39228			−0.131350
$668$		0			0
$669$	−0.315342			−0.0121918
$670$		0			0
$671$	−1.44600			−0.0558224
$672$		0			0
$673$		−	14.0877i		−	0.543039i	−0.962433	−	0.271520i	$-0.912474\pi$
$673$		−	14.0877i		−	0.543039i	0.962433	−	0.271520i	$-0.0875262\pi$
$674$		0			0
$675$	−13.1921	−	7.86962i	−0.507762	−	0.302902i
$676$		0			0
$677$	−46.5317			−1.78836			−0.894179	−	0.447709i	$-0.852240\pi$
$677$	−46.5317			−1.78836			−0.894179	+	0.447709i	$0.852240\pi$
$678$		0			0
$679$	35.2381	−	17.9210i	1.35232	−	0.687745i
$680$		0			0
$681$	21.6847			0.830958
$682$		0			0
$683$	20.1907			0.772574			0.386287	−	0.922379i	$-0.373757\pi$
$683$	20.1907			0.772574			0.386287	+	0.922379i	$0.373757\pi$
$684$		0			0
$685$	−3.41011	−	6.00505i	−0.130293	−	0.229441i
$686$		0			0
$687$	−20.1907			−0.770322
$688$		0			0
$689$		−	9.37720i		−	0.357243i
$690$		0			0
$691$	37.8132			1.43848			0.719240	−	0.694761i	$-0.244490\pi$
$691$	37.8132			1.43848			0.719240	+	0.694761i	$0.244490\pi$
$692$		0			0
$693$	−4.36758	−	8.58800i	−0.165911	−	0.326231i
$694$		0			0
$695$	−7.81855	+	4.43994i	−0.296575	+	0.168417i
$696$		0			0
$697$			42.2630i			1.60082i
$698$		0			0
$699$	−23.4921			−0.888553
$700$		0			0
$701$	30.6695			1.15837			0.579186	−	0.815196i	$-0.303371\pi$
$701$	30.6695			1.15837			0.579186	+	0.815196i	$0.303371\pi$
$702$		0			0
$703$		−	14.1617i		−	0.534118i
$704$		0			0
$705$	−40.4591	+	22.9756i	−1.52378	+	0.865312i
$706$		0			0
$707$	−18.1227	−	35.6347i	−0.681574	−	1.34018i
$708$		0			0
$709$	−30.8078			−1.15701			−0.578505	−	0.815679i	$-0.696364\pi$
$709$	−30.8078			−1.15701			−0.578505	+	0.815679i	$0.696364\pi$
$710$		0			0
$711$			16.6114i			0.622977i
$712$		0			0
$713$	−39.8459			−1.49224
$714$		0			0
$715$	−2.81164	−	4.95118i	−0.105150	−	0.185164i
$716$		0			0
$717$	4.98074			0.186009
$718$		0			0
$719$	27.1961			1.01424			0.507122	−	0.861874i	$-0.330709\pi$
$719$	27.1961			1.01424			0.507122	+	0.861874i	$0.330709\pi$
$720$		0			0
$721$	−6.56155	−	12.9020i	−0.244365	−	0.480496i
$722$		0			0
$723$	34.3404			1.27713
$724$		0			0
$725$	−1.43845	+	2.41131i	−0.0534226	+	0.0895537i
$726$		0			0
$727$			32.8255i			1.21743i	0.793389	+	0.608715i	$0.208315\pi$
$727$			32.8255i			1.21743i	−0.793389	+	0.608715i	$0.791685\pi$
$728$		0			0
$729$	−2.12311			−0.0786335
$730$		0			0
$731$	6.59603			0.243963
$732$		0			0
$733$	24.4250			0.902156			0.451078	−	0.892484i	$-0.351040\pi$
$733$	24.4250			0.902156			0.451078	+	0.892484i	$0.351040\pi$
$734$		0			0
$735$	−33.2156	−	3.78213i	−1.22518	−	0.139506i
$736$		0			0
$737$			10.9993i			0.405165i
$738$		0			0
$739$			49.5472i			1.82262i	0.411718	+	0.911311i	$0.364929\pi$
$739$			49.5472i			1.82262i	−0.411718	+	0.911311i	$0.635071\pi$
$740$		0			0
$741$		−	6.00505i		−	0.220601i
$742$		0			0
$743$	9.43318			0.346070			0.173035	−	0.984916i	$-0.444643\pi$
$743$	9.43318			0.346070			0.173035	+	0.984916i	$0.444643\pi$
$744$		0			0
$745$	3.88884	−	2.20837i	0.142476	−	0.0809084i
$746$		0			0
$747$		−	6.02913i		−	0.220594i
$748$		0			0
$749$	−23.6155	+	12.0101i	−0.862893	+	0.438839i
$750$		0			0
$751$			37.5999i			1.37204i	0.727584	+	0.686019i	$0.240643\pi$
$751$			37.5999i			1.37204i	−0.727584	+	0.686019i	$0.759357\pi$
$752$		0			0
$753$			19.5873i			0.713801i
$754$		0			0
$755$	−5.46702	−	9.62719i	−0.198965	−	0.350369i
$756$		0			0
$757$			25.7640i			0.936409i	0.883620	+	0.468204i	$0.155099\pi$
$757$			25.7640i			0.936409i	−0.883620	+	0.468204i	$0.844901\pi$
$758$		0			0
$759$	−30.0881			−1.09213
$760$		0			0
$761$		−	43.1228i		−	1.56320i	−0.623780	−	0.781600i	$-0.714404\pi$
$761$		−	43.1228i		−	1.56320i	0.623780	−	0.781600i	$-0.285596\pi$
$762$		0			0
$763$	10.7575	−	5.47091i	0.389447	−	0.198060i
$764$		0			0
$765$	−15.1231	+	8.58800i	−0.546777	+	0.310500i
$766$		0			0
$767$	−15.6371			−0.564623
$768$		0			0
$769$		−	14.4903i		−	0.522535i	−0.965266	−	0.261267i	$-0.915860\pi$
$769$		−	14.4903i		−	0.522535i	0.965266	−	0.261267i	$-0.0841404\pi$
$770$		0			0
$771$		−	13.9923i		−	0.503920i
$772$		0			0
$773$	15.6898			0.564323			0.282161	−	0.959367i	$-0.408949\pi$
$773$	15.6898			0.564323			0.282161	+	0.959367i	$0.408949\pi$
$774$		0			0
$775$	−16.8961	+	28.3234i	−0.606925	+	1.01740i
$776$		0			0
$777$	27.7006	−	14.0877i	0.993755	−	0.505392i
$778$		0			0
$779$			21.8497i			0.782847i
$780$		0			0
$781$	27.8617			0.996971
$782$		0			0
$783$			1.72521i			0.0616538i
$784$		0			0
$785$	7.56155	−	4.29400i	0.269883	−	0.153259i
$786$		0			0
$787$			32.8578i			1.17126i	0.810580	+	0.585628i	$0.199152\pi$
$787$			32.8578i			1.17126i	−0.810580	+	0.585628i	$0.800848\pi$
$788$		0			0
$789$		−	50.3680i		−	1.79315i
$790$		0			0
$791$	−6.59603	−	12.9698i	−0.234528	−	0.461153i
$792$		0			0
$793$		−	0.677039i		−	0.0240423i
$794$		0			0
$795$	−35.6647	+	20.2530i	−1.26490	+	0.718301i
$796$		0			0
$797$	2.04937			0.0725925			0.0362963	−	0.999341i	$-0.488444\pi$
$797$	2.04937			0.0725925			0.0362963	+	0.999341i	$0.488444\pi$
$798$		0			0
$799$		−	48.5247i		−	1.71668i
$800$		0			0
$801$			4.41674i			0.156058i
$802$		0			0
$803$		−	23.2306i		−	0.819792i
$804$		0			0
$805$	−19.7006	+	29.8181i	−0.694356	+	1.05095i
$806$		0			0
$807$	2.06798			0.0727962
$808$		0			0
$809$	−27.0540			−0.951167			−0.475584	−	0.879671i	$-0.657763\pi$
$809$	−27.0540			−0.951167			−0.475584	+	0.879671i	$0.657763\pi$
$810$		0			0
$811$	9.17104			0.322039			0.161019	−	0.986951i	$-0.448522\pi$
$811$	9.17104			0.322039			0.161019	+	0.986951i	$0.448522\pi$
$812$		0			0
$813$		−	14.0877i		−	0.494076i
$814$		0			0
$815$	22.3631	−	12.6994i	0.783345	−	0.444840i
$816$		0			0
$817$	3.41011			0.119304
$818$		0			0
$819$	4.02102	−	2.04496i	0.140506	−	0.0714567i
$820$		0			0
$821$	35.9309			1.25400			0.626998	−	0.779021i	$-0.284283\pi$
$821$	35.9309			1.25400			0.626998	+	0.779021i	$0.284283\pi$
$822$		0			0
$823$	22.8393			0.796127			0.398064	−	0.917358i	$-0.369682\pi$
$823$	22.8393			0.796127			0.398064	+	0.917358i	$0.369682\pi$
$824$		0			0
$825$	−12.7584	+	21.3873i	−0.444191	+	0.744610i
$826$		0			0
$827$	−4.71659			−0.164012			−0.0820059	−	0.996632i	$-0.526133\pi$
$827$	−4.71659			−0.164012			−0.0820059	+	0.996632i	$0.526133\pi$
$828$		0			0
$829$			43.3947i			1.50716i	0.657357	+	0.753579i	$0.271674\pi$
$829$			43.3947i			1.50716i	−0.657357	+	0.753579i	$0.728326\pi$
$830$		0			0
$831$	−41.8342			−1.45121
$832$		0			0
$833$	20.5361	−	28.1753i	0.711534	−	0.976217i
$834$		0			0
$835$	0.743668	+	1.30957i	0.0257357	+	0.0453195i
$836$		0			0
$837$			20.2644i			0.700438i
$838$		0			0
$839$	−32.3461			−1.11671			−0.558356	−	0.829601i	$-0.688568\pi$
$839$	−32.3461			−1.11671			−0.558356	+	0.829601i	$0.688568\pi$
$840$		0			0
$841$	−28.6847			−0.989126
$842$		0			0
$843$		−	36.4235i		−	1.25449i
$844$		0			0
$845$	−22.9593	+	13.0380i	−0.789823	+	0.448519i
$846$		0			0
$847$	−13.1158	+	6.67026i	−0.450664	+	0.229193i
$848$		0			0
$849$	15.9309			0.546746
$850$		0			0
$851$		−	33.2228i		−	1.13886i
$852$		0			0
$853$	−2.93137			−0.100368			−0.0501840	−	0.998740i	$-0.515981\pi$
$853$	−2.93137			−0.100368			−0.0501840	+	0.998740i	$0.515981\pi$
$854$		0			0
$855$	−7.81855	+	4.43994i	−0.267389	+	0.151843i
$856$		0			0
$857$	−5.59390			−0.191084			−0.0955419	−	0.995425i	$-0.530458\pi$
$857$	−5.59390			−0.191084			−0.0955419	+	0.995425i	$0.530458\pi$
$858$		0			0
$859$	−9.17104			−0.312912			−0.156456	−	0.987685i	$-0.550007\pi$
$859$	−9.17104			−0.312912			−0.156456	+	0.987685i	$0.550007\pi$
$860$		0			0
$861$	−42.7386	+	21.7355i	−1.45653	+	0.740744i
$862$		0			0
$863$	30.7851			1.04794			0.523969	−	0.851737i	$-0.324451\pi$
$863$	30.7851			1.04794			0.523969	+	0.851737i	$0.324451\pi$
$864$		0			0
$865$	−21.4924	+	12.2050i	−0.730764	+	0.414981i
$866$		0			0
$867$		−	16.6757i		−	0.566335i
$868$		0			0
$869$	−24.8078			−0.841546
$870$		0			0
$871$	−5.15002			−0.174502
$872$		0			0
$873$	23.3331			0.789705
$874$		0			0
$875$	12.8416	+	26.6476i	0.434125	+	0.900853i
$876$		0			0
$877$			5.49966i			0.185710i	0.995680	+	0.0928551i	$0.0295993\pi$
$877$			5.49966i			0.185710i	−0.995680	+	0.0928551i	$0.970401\pi$
$878$		0			0
$879$			30.8908i			1.04192i
$880$		0			0
$881$			30.7645i			1.03648i	0.855234	+	0.518241i	$0.173413\pi$
$881$			30.7645i			1.03648i	−0.855234	+	0.518241i	$0.826587\pi$
$882$		0			0
$883$	48.4902			1.63183			0.815913	−	0.578175i	$-0.196235\pi$
$883$	48.4902			1.63183			0.815913	+	0.578175i	$0.196235\pi$
$884$		0			0
$885$	33.7733	+	59.4733i	1.13528	+	1.99917i
$886$		0			0
$887$		−	31.7738i		−	1.06686i	−0.845845	−	0.533429i	$-0.820903\pi$
$887$		−	31.7738i		−	1.06686i	0.845845	−	0.533429i	$-0.179097\pi$
$888$		0			0
$889$	−12.4924	+	6.35324i	−0.418982	+	0.213081i
$890$		0			0
$891$			26.2267i			0.878628i
$892$		0			0
$893$		−	25.0870i		−	0.839503i
$894$		0			0
$895$	−9.17104	−	16.1498i	−0.306554	−	0.539829i
$896$		0			0
$897$		−	14.0877i		−	0.470373i
$898$		0			0
$899$	3.70402			0.123536
$900$		0			0
$901$		−	42.7746i		−	1.42503i
$902$		0			0
$903$	3.39228	+	6.67026i	0.112888	+	0.221972i
$904$		0			0
$905$	3.80776	+	6.70531i	0.126574	+	0.222892i
$906$		0			0
$907$	53.7874			1.78598			0.892991	−	0.450074i	$-0.148603\pi$
$907$	53.7874			1.78598			0.892991	+	0.450074i	$0.148603\pi$
$908$		0			0
$909$		−	23.5957i		−	0.782619i
$910$		0			0
$911$		−	56.0950i		−	1.85851i	−0.369438	−	0.929255i	$-0.620450\pi$
$911$		−	56.0950i		−	1.85851i	0.369438	−	0.929255i	$-0.379550\pi$
$912$		0			0
$913$	9.00400			0.297989
$914$		0			0
$915$	−2.57501	+	1.46228i	−0.0851272	+	0.0483415i
$916$		0			0
$917$	6.07263	−	3.08835i	0.200536	−	0.101986i
$918$		0			0
$919$			39.1965i			1.29297i	0.762925	+	0.646487i	$0.223762\pi$
$919$			39.1965i			1.29297i	−0.762925	+	0.646487i	$0.776238\pi$
$920$		0			0
$921$	29.6847			0.978143
$922$		0			0
$923$			13.0452i			0.429389i
$924$		0			0
$925$	−23.6155	−	14.0877i	−0.776474	−	0.463199i
$926$		0			0
$927$		−	8.54312i		−	0.280593i
$928$		0			0
$929$		−	28.9807i		−	0.950825i	−0.879763	−	0.475412i	$-0.842299\pi$
$929$		−	28.9807i		−	0.950825i	0.879763	−	0.475412i	$-0.157701\pi$
$930$		0			0
$931$	10.6170	−	14.5665i	0.347960	−	0.477397i
$932$		0			0
$933$		−	3.08835i		−	0.101108i
$934$		0			0
$935$	−12.8255	−	22.5851i	−0.419437	−	0.738611i
$936$		0			0
$937$	−49.4631			−1.61589			−0.807944	−	0.589259i	$-0.799420\pi$
$937$	−49.4631			−1.61589			−0.807944	+	0.589259i	$0.799420\pi$
$938$		0			0
$939$			15.3019i			0.499357i
$940$		0			0
$941$			8.75714i			0.285475i	0.989761	+	0.142737i	$0.0455904\pi$
$941$			8.75714i			0.285475i	−0.989761	+	0.142737i	$0.954410\pi$
$942$		0			0
$943$			51.2587i			1.66921i
$944$		0			0
$945$	15.1645	+	10.0191i	0.493302	+	0.325922i
$946$		0			0
$947$	−52.6261			−1.71012			−0.855060	−	0.518529i	$-0.826480\pi$
$947$	−52.6261			−1.71012			−0.855060	+	0.518529i	$0.826480\pi$
$948$		0			0
$949$	10.8769			0.353079
$950$		0			0
$951$	−52.1342			−1.69057
$952$		0			0
$953$			31.2637i			1.01273i	0.862319	+	0.506365i	$0.169011\pi$
$953$			31.2637i			1.01273i	−0.862319	+	0.506365i	$0.830989\pi$
$954$		0			0
$955$	−22.0461	−	38.8222i	−0.713395	−	1.25626i
$956$		0			0
$957$	2.79695			0.0904125
$958$		0			0
$959$	3.70402	+	7.28323i	0.119609	+	0.235188i
$960$		0			0
$961$	12.5076			0.403470
$962$		0			0
$963$	−15.6371			−0.503899
$964$		0			0
$965$	−6.07263	−	10.6937i	−0.195485	−	0.344241i
$966$		0			0
$967$	16.2177			0.521527			0.260764	−	0.965403i	$-0.416026\pi$
$967$	16.2177			0.521527			0.260764	+	0.965403i	$0.416026\pi$
$968$		0			0
$969$		−	27.3924i		−	0.879969i
$970$		0			0
$971$	−36.3672			−1.16708			−0.583539	−	0.812085i	$-0.698332\pi$
$971$	−36.3672			−1.16708			−0.583539	+	0.812085i	$0.698332\pi$
$972$		0			0
$973$	9.48274	−	4.82262i	0.304003	−	0.154606i
$974$		0			0
$975$	−10.0138	−	5.97366i	−0.320699	−	0.191310i
$976$		0			0
$977$		−	14.0877i		−	0.450704i	−0.974277	−	0.225352i	$-0.927647\pi$
$977$		−	14.0877i		−	0.450704i	0.974277	−	0.225352i	$-0.0723532\pi$
$978$		0			0
$979$	−6.59603			−0.210810
$980$		0			0
$981$	7.12311			0.227423
$982$		0			0
$983$		−	44.7361i		−	1.42686i	−0.700727	−	0.713430i	$-0.747141\pi$
$983$		−	44.7361i		−	1.42686i	0.700727	−	0.713430i	$-0.252859\pi$
$984$		0			0
$985$	18.2179	+	32.0810i	0.580471	+	1.02218i
$986$		0			0
$987$	49.0708	−	24.9559i	1.56194	−	0.794353i
$988$		0			0
$989$	8.00000			0.254385
$990$		0			0
$991$			0.574176i			0.0182393i	0.999958	+	0.00911966i	$0.00290292\pi$
$991$			0.574176i			0.0182393i	−0.999958	+	0.00911966i	$0.997097\pi$
$992$		0			0
$993$	−17.7392			−0.562935
$994$		0			0
$995$	35.6647	−	20.2530i	1.13065	−	0.642065i
$996$		0			0
$997$	47.7580			1.51251			0.756256	−	0.654276i	$-0.227027\pi$
$997$	47.7580			1.51251			0.756256	+	0.654276i	$0.227027\pi$
$998$		0			0
$999$	−16.8961			−0.534568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.e.f.2239.3		16
4.3	odd	2	inner	2240.2.e.f.2239.15		16
5.4	even	2	inner	2240.2.e.f.2239.13		16
7.6	odd	2	inner	2240.2.e.f.2239.14		16
8.3	odd	2		140.2.c.b.139.9	yes	16
8.5	even	2		140.2.c.b.139.6	yes	16
20.19	odd	2	inner	2240.2.e.f.2239.1		16
28.27	even	2	inner	2240.2.e.f.2239.2		16
35.34	odd	2	inner	2240.2.e.f.2239.4		16
40.3	even	4		700.2.g.l.251.2		16
40.13	odd	4		700.2.g.l.251.3		16
40.19	odd	2		140.2.c.b.139.8	yes	16
40.27	even	4		700.2.g.l.251.15		16
40.29	even	2		140.2.c.b.139.11	yes	16
40.37	odd	4		700.2.g.l.251.14		16
56.3	even	6		980.2.s.f.19.12		32
56.5	odd	6		980.2.s.f.619.6		32
56.11	odd	6		980.2.s.f.19.11		32
56.13	odd	2		140.2.c.b.139.5	✓	16
56.19	even	6		980.2.s.f.619.1		32
56.27	even	2		140.2.c.b.139.10	yes	16
56.37	even	6		980.2.s.f.619.5		32
56.45	odd	6		980.2.s.f.19.15		32
56.51	odd	6		980.2.s.f.619.2		32
56.53	even	6		980.2.s.f.19.16		32
140.139	even	2	inner	2240.2.e.f.2239.16		16
280.13	even	4		700.2.g.l.251.4		16
280.19	even	6		980.2.s.f.619.16		32
280.27	odd	4		700.2.g.l.251.16		16
280.59	even	6		980.2.s.f.19.5		32
280.69	odd	2		140.2.c.b.139.12	yes	16
280.83	odd	4		700.2.g.l.251.1		16
280.109	even	6		980.2.s.f.19.1		32
280.139	even	2		140.2.c.b.139.7	yes	16
280.149	even	6		980.2.s.f.619.12		32
280.179	odd	6		980.2.s.f.19.6		32
280.219	odd	6		980.2.s.f.619.15		32
280.229	odd	6		980.2.s.f.619.11		32
280.237	even	4		700.2.g.l.251.13		16
280.269	odd	6		980.2.s.f.19.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.c.b.139.5	✓	16	56.13	odd	2
140.2.c.b.139.6	yes	16	8.5	even	2
140.2.c.b.139.7	yes	16	280.139	even	2
140.2.c.b.139.8	yes	16	40.19	odd	2
140.2.c.b.139.9	yes	16	8.3	odd	2
140.2.c.b.139.10	yes	16	56.27	even	2
140.2.c.b.139.11	yes	16	40.29	even	2
140.2.c.b.139.12	yes	16	280.69	odd	2
700.2.g.l.251.1		16	280.83	odd	4
700.2.g.l.251.2		16	40.3	even	4
700.2.g.l.251.3		16	40.13	odd	4
700.2.g.l.251.4		16	280.13	even	4
700.2.g.l.251.13		16	280.237	even	4
700.2.g.l.251.14		16	40.37	odd	4
700.2.g.l.251.15		16	40.27	even	4
700.2.g.l.251.16		16	280.27	odd	4
980.2.s.f.19.1		32	280.109	even	6
980.2.s.f.19.2		32	280.269	odd	6
980.2.s.f.19.5		32	280.59	even	6
980.2.s.f.19.6		32	280.179	odd	6
980.2.s.f.19.11		32	56.11	odd	6
980.2.s.f.19.12		32	56.3	even	6
980.2.s.f.19.15		32	56.45	odd	6
980.2.s.f.19.16		32	56.53	even	6
980.2.s.f.619.1		32	56.19	even	6
980.2.s.f.619.2		32	56.51	odd	6
980.2.s.f.619.5		32	56.37	even	6
980.2.s.f.619.6		32	56.5	odd	6
980.2.s.f.619.11		32	280.229	odd	6
980.2.s.f.619.12		32	280.149	even	6
980.2.s.f.619.15		32	280.219	odd	6
980.2.s.f.619.16		32	280.19	even	6
2240.2.e.f.2239.1		16	20.19	odd	2	inner
2240.2.e.f.2239.2		16	28.27	even	2	inner
2240.2.e.f.2239.3		16	1.1	even	1	trivial
2240.2.e.f.2239.4		16	35.34	odd	2	inner
2240.2.e.f.2239.13		16	5.4	even	2	inner
2240.2.e.f.2239.14		16	7.6	odd	2	inner
2240.2.e.f.2239.15		16	4.3	odd	2	inner
2240.2.e.f.2239.16		16	140.139	even	2	inner

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:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2240.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.13578i q^{3} +(1.94442 - 1.10418i) q^{5} +(-2.35829 + 1.19935i) q^{7} -1.56155 q^{9} -2.33205i q^{11} +1.09190 q^{13} +(-2.35829 - 4.15286i) q^{15} +4.98074 q^{17} +2.57501 q^{19} +(2.56155 + 5.03680i) q^{21} +6.04090 q^{23} +(2.56155 - 4.29400i) q^{25} -3.07221i q^{27} -0.561553 q^{29} -6.59603 q^{31} -4.98074 q^{33} +(-3.26121 + 4.93604i) q^{35} -5.49966i q^{37} -2.33205i q^{39} +8.48528i q^{41} +1.32431 q^{43} +(-3.03632 + 1.72424i) q^{45} -9.74247i q^{47} +(4.12311 - 5.65685i) q^{49} -10.6378i q^{51} -8.58800i q^{53} +(-2.57501 - 4.53448i) q^{55} -5.49966i q^{57} -14.3211 q^{59} -0.620058i q^{61} +(3.68260 - 1.87285i) q^{63} +(2.12311 - 1.20565i) q^{65} -4.71659 q^{67} -12.9020i q^{69} +11.9473i q^{71} +9.96148 q^{73} +(-9.17104 - 5.47091i) q^{75} +(2.79695 + 5.49966i) q^{77} -10.6378i q^{79} -11.2462 q^{81} +3.86098i q^{83} +(9.68466 - 5.49966i) q^{85} +1.19935i q^{87} -2.82843i q^{89} +(-2.57501 + 1.30957i) q^{91} +14.0877i q^{93} +(5.00691 - 2.84329i) q^{95} -14.9422 q^{97} +3.64162i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{9} + 8 q^{21} + 8 q^{25} + 24 q^{29} - 32 q^{65} - 48 q^{81} + 56 q^{85}+O(q^{100}) \) 16 * q + 8 * q^9 + 8 * q^21 + 8 * q^25 + 24 * q^29 - 32 * q^65 - 48 * q^81 + 56 * q^85

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more