LMFDB - Embedded newform 5292.2.l.i.3313.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5292,2,Mod(361,5292)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5292, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5292.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5292.l (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,0,4] 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:	$42.2568327497$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{8} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3313.3
Root			$1.13119 - 1.31165i$ of defining polynomial
Character	$\chi$	$=$	5292.3313
Dual form			5292.2.l.i.361.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-1.52940 q^{5} -0.835636 q^{11} +(-1.81222 - 3.13886i) q^{13} +(0.301057 + 0.521446i) q^{17} +(-0.846884 + 1.46685i) q^{19} +6.14405 q^{23} -2.66092 q^{25} +(-4.99671 + 8.65455i) q^{29} +(-1.65421 + 2.86517i) q^{31} +(4.39846 - 7.61835i) q^{37} +(3.51718 + 6.09194i) q^{41} +(0.846884 - 1.46685i) q^{43} +(-4.23200 - 7.33004i) q^{47} +(3.99616 + 6.92155i) q^{53} +1.27803 q^{55} +(-0.0652138 + 0.112954i) q^{59} +(-2.38343 - 4.12822i) q^{61} +(2.77162 + 4.80059i) q^{65} +(1.12166 - 1.94278i) q^{67} +9.39130 q^{71} +(2.25454 + 3.90498i) q^{73} +(-7.87120 - 13.6333i) q^{79} +(-3.16210 + 5.47692i) q^{83} +(-0.460438 - 0.797501i) q^{85} +(-0.531180 + 0.920030i) q^{89} +(1.29523 - 2.24340i) q^{95} +(7.76364 - 13.4470i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 4 q^{5} + 4 q^{11} - 2 q^{13} + 2 q^{17} - 7 q^{19} + 22 q^{23} + 18 q^{25} - q^{29} + q^{31} + 10 q^{37} - 33 q^{41} + 7 q^{43} - 3 q^{47} + 15 q^{53} + 28 q^{55} - 14 q^{59} + 10 q^{61} - 15 q^{65}+ \cdots + 18 q^{97}+O(q^{100}) $ 14 * q + 4 * q^5 + 4 * q^11 - 2 * q^13 + 2 * q^17 - 7 * q^19 + 22 * q^23 + 18 * q^25 - q^29 + q^31 + 10 * q^37 - 33 * q^41 + 7 * q^43 - 3 * q^47 + 15 * q^53 + 28 * q^55 - 14 * q^59 + 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 - 21 * q^73 - 10 * q^79 - 25 * q^83 + 8 * q^85 - 6 * q^89 + 28 * q^95 + 18 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$	$2647$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.52940			−0.683970			−0.341985	−	0.939705i	$-0.611099\pi$
$5$	−1.52940			−0.683970			−0.341985	+	0.939705i	$0.611099\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.835636			−0.251954			−0.125977	−	0.992033i	$-0.540207\pi$
$11$	−0.835636			−0.251954			−0.125977	+	0.992033i	$0.540207\pi$
$12$		0			0
$13$	−1.81222	−	3.13886i	−0.502620	−	0.870563i	−0.999995	−	0.00302796i	$-0.999036\pi$
$13$	−1.81222	−	3.13886i	−0.502620	−	0.870563i	0.497375	−	0.867535i	$-0.334297\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.301057	+	0.521446i	0.0730170	+	0.126469i	0.900222	−	0.435431i	$-0.143404\pi$
$17$	0.301057	+	0.521446i	0.0730170	+	0.126469i	−0.827205	+	0.561900i	$0.810071\pi$
$18$		0			0
$19$	−0.846884	+	1.46685i	−0.194289	+	0.336518i	−0.946667	−	0.322213i	$-0.895573\pi$
$19$	−0.846884	+	1.46685i	−0.194289	+	0.336518i	0.752379	+	0.658731i	$0.228906\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	6.14405			1.28112			0.640561	−	0.767907i	$-0.278702\pi$
$23$	6.14405			1.28112			0.640561	+	0.767907i	$0.278702\pi$
$24$		0			0
$25$	−2.66092			−0.532184
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.99671	+	8.65455i	−0.927865	+	1.60711i	−0.140977	+	0.990013i	$0.545024\pi$
$29$	−4.99671	+	8.65455i	−0.927865	+	1.60711i	−0.786888	+	0.617096i	$0.788309\pi$
$30$		0			0
$31$	−1.65421	+	2.86517i	−0.297104	+	0.514599i	−0.975472	−	0.220123i	$-0.929354\pi$
$31$	−1.65421	+	2.86517i	−0.297104	+	0.514599i	0.678368	+	0.734722i	$0.262688\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.39846	−	7.61835i	0.723102	−	1.25245i	−0.236649	−	0.971595i	$-0.576049\pi$
$37$	4.39846	−	7.61835i	0.723102	−	1.25245i	0.959751	−	0.280854i	$-0.0906177\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.51718	+	6.09194i	0.549291	+	0.951401i	0.998323	+	0.0578850i	$0.0184357\pi$
$41$	3.51718	+	6.09194i	0.549291	+	0.951401i	−0.449032	+	0.893516i	$0.648231\pi$
$42$		0			0
$43$	0.846884	−	1.46685i	0.129149	−	0.223692i	−0.794198	−	0.607659i	$-0.792109\pi$
$43$	0.846884	−	1.46685i	0.129149	−	0.223692i	0.923347	+	0.383967i	$0.125442\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.23200	−	7.33004i	−0.617301	−	1.06920i	−0.989976	−	0.141235i	$-0.954893\pi$
$47$	−4.23200	−	7.33004i	−0.617301	−	1.06920i	0.372675	−	0.927962i	$-0.378441\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.99616	+	6.92155i	0.548915	+	0.950748i	0.998349	+	0.0574350i	$0.0182922\pi$
$53$	3.99616	+	6.92155i	0.548915	+	0.950748i	−0.449434	+	0.893313i	$0.648374\pi$
$54$		0			0
$55$	1.27803			0.172329
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.0652138	+	0.112954i	−0.00849011	+	0.0147053i	−0.870239	−	0.492629i	$-0.836036\pi$
$59$	−0.0652138	+	0.112954i	−0.00849011	+	0.0147053i	0.861749	+	0.507335i	$0.169369\pi$
$60$		0			0
$61$	−2.38343	−	4.12822i	−0.305166	−	0.528564i	0.672132	−	0.740431i	$-0.265379\pi$
$61$	−2.38343	−	4.12822i	−0.305166	−	0.528564i	−0.977298	+	0.211868i	$0.932045\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.77162	+	4.80059i	0.343777	+	0.595440i
$66$		0			0
$67$	1.12166	−	1.94278i	0.137033	−	0.237348i	−0.789339	−	0.613957i	$-0.789577\pi$
$67$	1.12166	−	1.94278i	0.137033	−	0.237348i	0.926372	+	0.376609i	$0.122910\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	9.39130			1.11454			0.557271	−	0.830331i	$-0.311848\pi$
$71$	9.39130			1.11454			0.557271	+	0.830331i	$0.311848\pi$
$72$		0			0
$73$	2.25454	+	3.90498i	0.263874	+	0.457044i	0.967268	−	0.253757i	$-0.0816662\pi$
$73$	2.25454	+	3.90498i	0.263874	+	0.457044i	−0.703394	+	0.710800i	$0.748333\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−7.87120	−	13.6333i	−0.885580	−	1.53387i	−0.845048	−	0.534691i	$-0.820428\pi$
$79$	−7.87120	−	13.6333i	−0.885580	−	1.53387i	−0.0405317	−	0.999178i	$-0.512905\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.16210	+	5.47692i	−0.347085	+	0.601170i	−0.985730	−	0.168332i	$-0.946162\pi$
$83$	−3.16210	+	5.47692i	−0.347085	+	0.601170i	0.638645	+	0.769502i	$0.279495\pi$
$84$		0			0
$85$	−0.460438	−	0.797501i	−0.0499415	−	0.0865011i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.531180	+	0.920030i	−0.0563049	+	0.0975230i	−0.892804	−	0.450445i	$-0.851265\pi$
$89$	−0.531180	+	0.920030i	−0.0563049	+	0.0975230i	0.836499	+	0.547968i	$0.184599\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.29523	−	2.24340i	0.132888	−	0.230168i
$96$		0			0
$97$	7.76364	−	13.4470i	0.788279	−	1.36534i	−0.138742	−	0.990329i	$-0.544306\pi$
$97$	7.76364	−	13.4470i	0.788279	−	1.36534i	0.927021	−	0.375010i	$-0.122361\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	19.5151			1.94183			0.970914	−	0.239427i	$-0.0769597\pi$
$101$	19.5151			1.94183			0.970914	+	0.239427i	$0.0769597\pi$
$102$		0			0
$103$	1.82354			0.179679			0.0898394	−	0.995956i	$-0.471365\pi$
$103$	1.82354			0.179679			0.0898394	+	0.995956i	$0.471365\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.27078	−	9.12926i	0.509546	−	0.882559i	−0.490393	−	0.871501i	$-0.663147\pi$
$107$	5.27078	−	9.12926i	0.509546	−	0.882559i	0.999939	−	0.0110578i	$-0.00351989\pi$
$108$		0			0
$109$	6.30442	+	10.9196i	0.603854	+	1.04591i	0.992231	+	0.124406i	$0.0397025\pi$
$109$	6.30442	+	10.9196i	0.603854	+	1.04591i	−0.388377	+	0.921501i	$0.626964\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.76452	−	13.4485i	−0.730424	−	1.26513i	−0.956702	−	0.291069i	$-0.905989\pi$
$113$	−7.76452	−	13.4485i	−0.730424	−	1.26513i	0.226278	−	0.974063i	$-0.427344\pi$
$114$		0			0
$115$	−9.39673			−0.876250
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−10.3017			−0.936519
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.7166			1.04797
$126$		0			0
$127$	−10.8966			−0.966919			−0.483460	−	0.875367i	$-0.660620\pi$
$127$	−10.8966			−0.966919			−0.483460	+	0.875367i	$0.660620\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	19.4618			1.70038			0.850191	−	0.526474i	$-0.176486\pi$
$131$	19.4618			1.70038			0.850191	+	0.526474i	$0.176486\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12.2767			−1.04887			−0.524433	−	0.851452i	$-0.675723\pi$
$137$	−12.2767			−1.04887			−0.524433	+	0.851452i	$0.675723\pi$
$138$		0			0
$139$	6.44692	+	11.1664i	0.546821	+	0.947121i	0.998490	+	0.0549357i	$0.0174954\pi$
$139$	6.44692	+	11.1664i	0.546821	+	0.947121i	−0.451669	+	0.892185i	$0.649171\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.51436	+	2.62295i	0.126637	+	0.219342i
$144$		0			0
$145$	7.64198	−	13.2363i	0.634632	−	1.09922i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	18.0653			1.47997			0.739986	−	0.672623i	$-0.234832\pi$
$149$	18.0653			1.47997			0.739986	+	0.672623i	$0.234832\pi$
$150$		0			0
$151$	8.59782			0.699681			0.349840	−	0.936809i	$-0.386236\pi$
$151$	8.59782			0.699681			0.349840	+	0.936809i	$0.386236\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.52995	−	4.38200i	0.203210	−	0.351971i
$156$		0			0
$157$	1.59683	−	2.76579i	0.127441	−	0.220734i	−0.795244	−	0.606290i	$-0.792657\pi$
$157$	1.59683	−	2.76579i	0.127441	−	0.220734i	0.922684	+	0.385556i	$0.125990\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	2.04809	−	3.54740i	0.160419	−	0.277854i	−0.774600	−	0.632451i	$-0.782049\pi$
$163$	2.04809	−	3.54740i	0.160419	−	0.277854i	0.935019	+	0.354598i	$0.115382\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.24859	+	14.2870i	0.638295	+	1.10556i	0.985807	+	0.167883i	$0.0536932\pi$
$167$	8.24859	+	14.2870i	0.638295	+	1.10556i	−0.347512	+	0.937676i	$0.612973\pi$
$168$		0			0
$169$	−0.0682984	+	0.118296i	−0.00525372	+	0.00909971i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.41063	+	11.1035i	0.487391	+	0.844186i	0.999895	−	0.0144987i	$-0.00461525\pi$
$173$	6.41063	+	11.1035i	0.487391	+	0.844186i	−0.512504	+	0.858685i	$0.671282\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	11.8750	+	20.5680i	0.887576	+	1.53733i	0.842732	+	0.538333i	$0.180946\pi$
$179$	11.8750	+	20.5680i	0.887576	+	1.53733i	0.0448441	+	0.998994i	$0.485721\pi$
$180$		0			0
$181$	16.0244			1.19108			0.595542	−	0.803324i	$-0.296937\pi$
$181$	16.0244			1.19108			0.595542	+	0.803324i	$0.296937\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.72702	+	11.6515i	−0.494580	+	0.856638i
$186$		0			0
$187$	−0.251574	−	0.435739i	−0.0183969	−	0.0318644i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.40475	−	9.36130i	−0.391074	−	0.677360i	0.601517	−	0.798860i	$-0.294563\pi$
$191$	−5.40475	−	9.36130i	−0.391074	−	0.677360i	−0.992591	+	0.121500i	$0.961230\pi$
$192$		0			0
$193$	−0.375130	+	0.649745i	−0.0270025	+	0.0467696i	−0.879211	−	0.476433i	$-0.841930\pi$
$193$	−0.375130	+	0.649745i	−0.0270025	+	0.0467696i	0.852208	+	0.523203i	$0.175263\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.3186			−0.735169			−0.367584	−	0.929990i	$-0.619815\pi$
$197$	−10.3186			−0.735169			−0.367584	+	0.929990i	$0.619815\pi$
$198$		0			0
$199$	2.85430	+	4.94379i	0.202336	+	0.350456i	0.949281	−	0.314430i	$-0.101813\pi$
$199$	2.85430	+	4.94379i	0.202336	+	0.350456i	−0.746945	+	0.664886i	$0.768480\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−5.37919	−	9.31704i	−0.375699	−	0.650730i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.707687	−	1.22575i	0.0489517	−	0.0847869i
$210$		0			0
$211$	2.73050	+	4.72937i	0.187976	+	0.325583i	0.944575	−	0.328295i	$-0.106474\pi$
$211$	2.73050	+	4.72937i	0.187976	+	0.325583i	−0.756600	+	0.653878i	$0.773141\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.29523	+	2.24340i	−0.0883338	+	0.152999i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.09116	−	1.88995i	0.0733996	−	0.127132i
$222$		0			0
$223$	9.00530	−	15.5976i	0.603040	−	1.04450i	−0.389318	−	0.921103i	$-0.627289\pi$
$223$	9.00530	−	15.5976i	0.603040	−	1.04450i	0.992358	−	0.123392i	$-0.0393772\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−18.1740			−1.20625			−0.603125	−	0.797647i	$-0.706078\pi$
$227$	−18.1740			−1.20625			−0.603125	+	0.797647i	$0.706078\pi$
$228$		0			0
$229$	15.4278			1.01950			0.509750	−	0.860323i	$-0.329738\pi$
$229$	15.4278			1.01950			0.509750	+	0.860323i	$0.329738\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.20892	−	5.55801i	0.210223	−	0.364117i	−0.741561	−	0.670885i	$-0.765914\pi$
$233$	3.20892	−	5.55801i	0.210223	−	0.364117i	0.951784	+	0.306768i	$0.0992476\pi$
$234$		0			0
$235$	6.47244	+	11.2106i	0.422216	+	0.731299i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.33317	+	4.04118i	0.150920	+	0.261402i	0.931566	−	0.363572i	$-0.118443\pi$
$239$	2.33317	+	4.04118i	0.150920	+	0.261402i	−0.780646	+	0.624974i	$0.785110\pi$
$240$		0			0
$241$	18.8572			1.21470			0.607348	−	0.794436i	$-0.292233\pi$
$241$	18.8572			1.21470			0.607348	+	0.794436i	$0.292233\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	6.13897			0.390613
$248$		0			0
$249$		0			0
$250$		0			0
$251$	15.7016			0.991074			0.495537	−	0.868587i	$-0.334971\pi$
$251$	15.7016			0.991074			0.495537	+	0.868587i	$0.334971\pi$
$252$		0			0
$253$	−5.13419			−0.322784
$254$		0			0
$255$		0			0
$256$		0			0
$257$	9.21785			0.574993			0.287497	−	0.957782i	$-0.407177\pi$
$257$	9.21785			0.574993			0.287497	+	0.957782i	$0.407177\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.482621			−0.0297597			−0.0148799	−	0.999889i	$-0.504737\pi$
$263$	−0.482621			−0.0297597			−0.0148799	+	0.999889i	$0.504737\pi$
$264$		0			0
$265$	−6.11174	−	10.5859i	−0.375442	−	0.650284i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.94288	−	6.82927i	−0.240402	−	0.416388i	0.720427	−	0.693531i	$-0.243946\pi$
$269$	−3.94288	−	6.82927i	−0.240402	−	0.416388i	−0.960829	+	0.277143i	$0.910612\pi$
$270$		0			0
$271$	−12.7947	+	22.1610i	−0.777220	+	1.34618i	0.156318	+	0.987707i	$0.450037\pi$
$271$	−12.7947	+	22.1610i	−0.777220	+	1.34618i	−0.933538	+	0.358478i	$0.883296\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.22356			0.134086
$276$		0			0
$277$	8.36931			0.502863			0.251432	−	0.967875i	$-0.419099\pi$
$277$	8.36931			0.502863			0.251432	+	0.967875i	$0.419099\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.551848	−	0.955828i	0.0329205	−	0.0570199i	−0.849096	−	0.528239i	$-0.822853\pi$
$281$	0.551848	−	0.955828i	0.0329205	−	0.0570199i	0.882016	+	0.471219i	$0.156186\pi$
$282$		0			0
$283$	1.45369	−	2.51786i	0.0864128	−	0.149671i	−0.819580	−	0.572965i	$-0.805793\pi$
$283$	1.45369	−	2.51786i	0.0864128	−	0.149671i	0.905992	+	0.423294i	$0.139126\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.31873	−	14.4085i	0.489337	−	0.847557i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−12.4381	−	21.5434i	−0.726642	−	1.25858i	−0.958295	−	0.285782i	$-0.907747\pi$
$293$	−12.4381	−	21.5434i	−0.726642	−	1.25858i	0.231653	−	0.972798i	$-0.425587\pi$
$294$		0			0
$295$	0.0997383	−	0.172752i	0.00580699	−	0.0100580i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−11.1344	−	19.2853i	−0.643918	−	1.11530i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	3.64522	+	6.31371i	0.208725	+	0.361522i
$306$		0			0
$307$	23.7968			1.35816			0.679078	−	0.734066i	$-0.262380\pi$
$307$	23.7968			1.35816			0.679078	+	0.734066i	$0.262380\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.35677	+	16.2064i	−0.530574	+	0.918981i	0.468790	+	0.883310i	$0.344690\pi$
$311$	−9.35677	+	16.2064i	−0.530574	+	0.918981i	−0.999364	+	0.0356711i	$0.988643\pi$
$312$		0			0
$313$	−9.65797	−	16.7281i	−0.545901	−	0.945527i	−0.998550	−	0.0538387i	$-0.982854\pi$
$313$	−9.65797	−	16.7281i	−0.545901	−	0.945527i	0.452649	−	0.891689i	$-0.350479\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.897542	−	1.55459i	−0.0504110	−	0.0873144i	0.839719	−	0.543021i	$-0.182720\pi$
$317$	−0.897542	−	1.55459i	−0.0504110	−	0.0873144i	−0.890130	+	0.455707i	$0.849386\pi$
$318$		0			0
$319$	4.17543	−	7.23205i	0.233779	−	0.404917i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.01984			−0.0567455
$324$		0			0
$325$	4.82218	+	8.35226i	0.267487	+	0.463300i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	7.06833	+	12.2427i	0.388511	+	0.672920i	0.992249	−	0.124262i	$-0.0396563\pi$
$331$	7.06833	+	12.2427i	0.388511	+	0.672920i	−0.603739	+	0.797182i	$0.706323\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.71547	+	2.97129i	−0.0937264	+	0.162339i
$336$		0			0
$337$	−2.94072	−	5.09348i	−0.160191	−	0.277459i	0.774746	−	0.632273i	$-0.217878\pi$
$337$	−2.94072	−	5.09348i	−0.160191	−	0.277459i	−0.934937	+	0.354813i	$0.884544\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.38231	−	2.39424i	0.0748565	−	0.129655i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.17593	+	5.50087i	−0.170493	+	0.295302i	−0.938592	−	0.345028i	$-0.887869\pi$
$347$	−3.17593	+	5.50087i	−0.170493	+	0.295302i	0.768099	+	0.640331i	$0.221203\pi$
$348$		0			0
$349$	−10.4321	+	18.0689i	−0.558416	+	0.967205i	0.439213	+	0.898383i	$0.355257\pi$
$349$	−10.4321	+	18.0689i	−0.558416	+	0.967205i	−0.997629	+	0.0688222i	$0.978076\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2.14229			−0.114023			−0.0570114	−	0.998374i	$-0.518157\pi$
$353$	−2.14229			−0.114023			−0.0570114	+	0.998374i	$0.518157\pi$
$354$		0			0
$355$	−14.3631			−0.762314
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.6198	−	18.3940i	0.560492	−	0.970800i	−0.436962	−	0.899480i	$-0.643946\pi$
$359$	10.6198	−	18.3940i	0.560492	−	0.970800i	0.997454	−	0.0713198i	$-0.0227211\pi$
$360$		0			0
$361$	8.06557	+	13.9700i	0.424504	+	0.735262i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.44811	−	5.97230i	−0.180482	−	0.312605i
$366$		0			0
$367$	32.4107			1.69182			0.845912	−	0.533323i	$-0.179057\pi$
$367$	32.4107			1.69182			0.845912	+	0.533323i	$0.179057\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	33.6202			1.74079			0.870393	−	0.492358i	$-0.163865\pi$
$373$	33.6202			1.74079			0.870393	+	0.492358i	$0.163865\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	36.2206			1.86545
$378$		0			0
$379$	28.2829			1.45279			0.726396	−	0.687276i	$-0.241194\pi$
$379$	28.2829			1.45279			0.726396	+	0.687276i	$0.241194\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−10.1895			−0.520657			−0.260329	−	0.965520i	$-0.583831\pi$
$383$	−10.1895			−0.520657			−0.260329	+	0.965520i	$0.583831\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−10.4505			−0.529861			−0.264931	−	0.964267i	$-0.585349\pi$
$389$	−10.4505			−0.529861			−0.264931	+	0.964267i	$0.585349\pi$
$390$		0			0
$391$	1.84971	+	3.20379i	0.0935437	+	0.162022i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	12.0383	+	20.8509i	0.605710	+	1.04912i
$396$		0			0
$397$	7.25033	−	12.5579i	0.363884	−	0.630265i	−0.624713	−	0.780855i	$-0.714784\pi$
$397$	7.25033	−	12.5579i	0.363884	−	0.630265i	0.988596	+	0.150590i	$0.0481173\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	25.4142			1.26913			0.634563	−	0.772871i	$-0.281180\pi$
$401$	25.4142			1.26913			0.634563	+	0.772871i	$0.281180\pi$
$402$		0			0
$403$	11.9912			0.597322
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.67551	+	6.36617i	−0.182188	+	0.315559i
$408$		0			0
$409$	6.19535	−	10.7307i	0.306340	−	0.530597i	−0.671219	−	0.741259i	$-0.734229\pi$
$409$	6.19535	−	10.7307i	0.306340	−	0.530597i	0.977559	+	0.210663i	$0.0675622\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	4.83613	−	8.37642i	0.237396	−	0.411182i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−15.3596	−	26.6036i	−0.750365	−	1.29967i	−0.947646	−	0.319323i	$-0.896545\pi$
$419$	−15.3596	−	26.6036i	−0.750365	−	1.29967i	0.197281	−	0.980347i	$-0.436789\pi$
$420$		0			0
$421$	−2.88912	+	5.00410i	−0.140807	+	0.243885i	−0.927801	−	0.373076i	$-0.878303\pi$
$421$	−2.88912	+	5.00410i	−0.140807	+	0.243885i	0.786994	+	0.616961i	$0.211636\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.801089	−	1.38753i	−0.0388585	−	0.0673049i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.210278	+	0.364212i	0.0101287	+	0.0175435i	0.871045	−	0.491203i	$-0.163443\pi$
$431$	0.210278	+	0.364212i	0.0101287	+	0.0175435i	−0.860917	+	0.508746i	$0.830109\pi$
$432$		0			0
$433$	−30.8208			−1.48115			−0.740576	−	0.671972i	$-0.765447\pi$
$433$	−30.8208			−1.48115			−0.740576	+	0.671972i	$0.765447\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.20330	+	9.01237i	−0.248907	+	0.431120i
$438$		0			0
$439$	1.50590	+	2.60830i	0.0718729	+	0.124488i	0.899722	−	0.436463i	$-0.143769\pi$
$439$	1.50590	+	2.60830i	0.0718729	+	0.124488i	−0.827849	+	0.560951i	$0.810436\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−9.22141	−	15.9719i	−0.438122	−	0.758850i	0.559422	−	0.828883i	$-0.311023\pi$
$443$	−9.22141	−	15.9719i	−0.438122	−	0.758850i	−0.997545	+	0.0700326i	$0.977690\pi$
$444$		0			0
$445$	0.812388	−	1.40710i	0.0385109	−	0.0667028i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	6.80998			0.321383			0.160691	−	0.987005i	$-0.448628\pi$
$449$	6.80998			0.321383			0.160691	+	0.987005i	$0.448628\pi$
$450$		0			0
$451$	−2.93908	−	5.09064i	−0.138396	−	0.239709i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−6.18283	−	10.7090i	−0.289220	−	0.500944i	0.684403	−	0.729103i	$-0.260063\pi$
$457$	−6.18283	−	10.7090i	−0.289220	−	0.500944i	−0.973624	+	0.228159i	$0.926729\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−16.3651	+	28.3453i	−0.762201	+	1.32017i	0.179513	+	0.983756i	$0.442548\pi$
$461$	−16.3651	+	28.3453i	−0.762201	+	1.32017i	−0.941714	+	0.336415i	$0.890786\pi$
$462$		0			0
$463$	9.61023	+	16.6454i	0.446625	+	0.773577i	0.998164	−	0.0605719i	$-0.0192924\pi$
$463$	9.61023	+	16.6454i	0.446625	+	0.773577i	−0.551539	+	0.834149i	$0.685959\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.50855	−	2.61289i	0.0698075	−	0.120910i	−0.829009	−	0.559235i	$-0.811095\pi$
$467$	1.50855	−	2.61289i	0.0698075	−	0.120910i	0.898816	+	0.438325i	$0.144428\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.707687	+	1.22575i	−0.0325395	+	0.0563600i
$474$		0			0
$475$	2.25349	−	3.90316i	0.103397	−	0.179089i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−25.8972			−1.18327			−0.591635	−	0.806206i	$-0.701518\pi$
$479$	−25.8972			−1.18327			−0.591635	+	0.806206i	$0.701518\pi$
$480$		0			0
$481$	−31.8839			−1.45378
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−11.8738	+	20.5659i	−0.539159	+	0.933851i
$486$		0			0
$487$	−20.8841	−	36.1724i	−0.946350	−	1.63913i	−0.753025	−	0.657992i	$-0.771406\pi$
$487$	−20.8841	−	36.1724i	−0.946350	−	1.63913i	−0.193326	−	0.981135i	$-0.561927\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	13.9879	+	24.2278i	0.631265	+	1.09338i	0.987293	+	0.158908i	$0.0507974\pi$
$491$	13.9879	+	24.2278i	0.631265	+	1.09338i	−0.356028	+	0.934475i	$0.615869\pi$
$492$		0			0
$493$	−6.01717			−0.271000
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−24.9497			−1.11690			−0.558450	−	0.829538i	$-0.688604\pi$
$499$	−24.9497			−1.11690			−0.558450	+	0.829538i	$0.688604\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	34.1966			1.52475			0.762376	−	0.647135i	$-0.224033\pi$
$503$	34.1966			1.52475			0.762376	+	0.647135i	$0.224033\pi$
$504$		0			0
$505$	−29.8465			−1.32815
$506$		0			0
$507$		0			0
$508$		0			0
$509$	13.6868			0.606659			0.303329	−	0.952886i	$-0.401902\pi$
$509$	13.6868			0.606659			0.303329	+	0.952886i	$0.401902\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.78893			−0.122895
$516$		0			0
$517$	3.53641	+	6.12525i	0.155531	+	0.269388i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−13.3748	−	23.1658i	−0.585960	−	1.01491i	−0.994755	−	0.102286i	$-0.967384\pi$
$521$	−13.3748	−	23.1658i	−0.585960	−	1.01491i	0.408795	−	0.912626i	$-0.365949\pi$
$522$		0			0
$523$	10.6131	−	18.3824i	0.464079	−	0.803808i	−0.535081	−	0.844801i	$-0.679719\pi$
$523$	10.6131	−	18.3824i	0.464079	−	0.803808i	0.999159	+	0.0409928i	$0.0130521\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.99204			−0.0867746
$528$		0			0
$529$	14.7493			0.641275
$530$		0			0
$531$		0			0
$532$		0			0
$533$	12.7478	−	22.0799i	0.552170	−	0.956386i
$534$		0			0
$535$	−8.06116	+	13.9623i	−0.348514	+	0.603644i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	10.1269	−	17.5402i	0.435388	−	0.754114i	−0.561939	−	0.827178i	$-0.689945\pi$
$541$	10.1269	−	17.5402i	0.435388	−	0.754114i	0.997327	+	0.0730646i	$0.0232779\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−9.64201	−	16.7005i	−0.413019	−	0.715369i
$546$		0			0
$547$	−21.9668	+	38.0476i	−0.939233	+	1.62680i	−0.172327	+	0.985040i	$0.555129\pi$
$547$	−21.9668	+	38.0476i	−0.939233	+	1.62680i	−0.766906	+	0.641760i	$0.778205\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−8.46326	−	14.6588i	−0.360547	−	0.624486i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.45483	+	7.71599i	0.188757	+	0.326937i	0.944836	−	0.327544i	$-0.106221\pi$
$557$	4.45483	+	7.71599i	0.188757	+	0.326937i	−0.756079	+	0.654480i	$0.772887\pi$
$558$		0			0
$559$	−6.13897			−0.259651
$560$		0			0
$561$		0			0
$562$		0			0
$563$	14.2096	−	24.6118i	0.598865	−	1.03726i	−0.394124	−	0.919057i	$-0.628952\pi$
$563$	14.2096	−	24.6118i	0.598865	−	1.03726i	0.992989	−	0.118207i	$-0.0377146\pi$
$564$		0			0
$565$	11.8751	+	20.5683i	0.499589	+	0.865313i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−4.28948	−	7.42959i	−0.179824	−	0.311465i	0.761996	−	0.647582i	$-0.224220\pi$
$569$	−4.28948	−	7.42959i	−0.179824	−	0.311465i	−0.941820	+	0.336117i	$0.890886\pi$
$570$		0			0
$571$	−9.68861	+	16.7812i	−0.405456	+	0.702270i	−0.994374	−	0.105922i	$-0.966221\pi$
$571$	−9.68861	+	16.7812i	−0.405456	+	0.702270i	0.588919	+	0.808192i	$0.299554\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−16.3488			−0.681793
$576$		0			0
$577$	−0.584441	−	1.01228i	−0.0243306	−	0.0421418i	0.853604	−	0.520923i	$-0.174412\pi$
$577$	−0.584441	−	1.01228i	−0.0243306	−	0.0421418i	−0.877934	+	0.478781i	$0.841079\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−3.33934	−	5.78390i	−0.138301	−	0.239545i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−15.5863	+	26.9963i	−0.643316	+	1.11426i	0.341372	+	0.939928i	$0.389108\pi$
$587$	−15.5863	+	26.9963i	−0.643316	+	1.11426i	−0.984688	+	0.174327i	$0.944225\pi$
$588$		0			0
$589$	−2.80184	−	4.85293i	−0.115448	−	0.199962i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−15.1887	+	26.3075i	−0.623724	+	1.08032i	0.365062	+	0.930983i	$0.381048\pi$
$593$	−15.1887	+	26.3075i	−0.623724	+	1.08032i	−0.988786	+	0.149338i	$0.952286\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−3.65379	+	6.32855i	−0.149290	+	0.258577i	−0.930965	−	0.365108i	$-0.881032\pi$
$599$	−3.65379	+	6.32855i	−0.149290	+	0.258577i	0.781675	+	0.623685i	$0.214365\pi$
$600$		0			0
$601$	−4.61461	+	7.99274i	−0.188234	+	0.326031i	−0.944661	−	0.328047i	$-0.893610\pi$
$601$	−4.61461	+	7.99274i	−0.188234	+	0.326031i	0.756428	+	0.654077i	$0.226943\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	15.7555			0.640552
$606$		0			0
$607$	17.0674			0.692744			0.346372	−	0.938097i	$-0.387413\pi$
$607$	17.0674			0.692744			0.346372	+	0.938097i	$0.387413\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−15.3387	+	26.5673i	−0.620536	+	1.07480i
$612$		0			0
$613$	−0.393059	−	0.680797i	−0.0158755	−	0.0274972i	0.857979	−	0.513686i	$-0.171720\pi$
$613$	−0.393059	−	0.680797i	−0.0158755	−	0.0274972i	−0.873854	+	0.486188i	$0.838387\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−23.7960	−	41.2159i	−0.957991	−	1.65929i	−0.727370	−	0.686246i	$-0.759257\pi$
$617$	−23.7960	−	41.2159i	−0.957991	−	1.65929i	−0.230621	−	0.973044i	$-0.574076\pi$
$618$		0			0
$619$	−18.9743			−0.762643			−0.381321	−	0.924443i	$-0.624531\pi$
$619$	−18.9743			−0.762643			−0.381321	+	0.924443i	$0.624531\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−4.61488			−0.184595
$626$		0			0
$627$		0			0
$628$		0			0
$629$	5.29674			0.211195
$630$		0			0
$631$	0.300343			0.0119565			0.00597823	−	0.999982i	$-0.498097\pi$
$631$	0.300343			0.0119565			0.00597823	+	0.999982i	$0.498097\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	16.6653			0.661344
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−28.1096			−1.11026			−0.555131	−	0.831763i	$-0.687332\pi$
$641$	−28.1096			−1.11026			−0.555131	+	0.831763i	$0.687332\pi$
$642$		0			0
$643$	1.55289	+	2.68968i	0.0612399	+	0.106071i	0.895020	−	0.446026i	$-0.147161\pi$
$643$	1.55289	+	2.68968i	0.0612399	+	0.106071i	−0.833780	+	0.552097i	$0.813828\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	23.3556	+	40.4532i	0.918205	+	1.59038i	0.802140	+	0.597137i	$0.203695\pi$
$647$	23.3556	+	40.4532i	0.918205	+	1.59038i	0.116066	+	0.993242i	$0.462972\pi$
$648$		0			0
$649$	0.0544950	−	0.0943881i	0.00213912	−	0.00370506i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.99753			0.0781693			0.0390847	−	0.999236i	$-0.487556\pi$
$653$	1.99753			0.0781693			0.0390847	+	0.999236i	$0.487556\pi$
$654$		0			0
$655$	−29.7649			−1.16301
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−8.37284	+	14.5022i	−0.326160	+	0.564925i	−0.981746	−	0.190195i	$-0.939088\pi$
$659$	−8.37284	+	14.5022i	−0.326160	+	0.564925i	0.655587	+	0.755120i	$0.272421\pi$
$660$		0			0
$661$	6.28870	−	10.8924i	0.244602	−	0.423664i	−0.717417	−	0.696644i	$-0.754676\pi$
$661$	6.28870	−	10.8924i	0.244602	−	0.423664i	0.962020	+	0.272980i	$0.0880093\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−30.7000	+	53.1740i	−1.18871	+	2.05890i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.99168	+	3.44969i	0.0768878	+	0.133174i
$672$		0			0
$673$	23.8175	−	41.2531i	0.918096	−	1.59019i	0.115792	−	0.993273i	$-0.463059\pi$
$673$	23.8175	−	41.2531i	0.918096	−	1.59019i	0.802304	−	0.596916i	$-0.203607\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	4.54664	+	7.87500i	0.174741	+	0.302661i	0.940072	−	0.340977i	$-0.110758\pi$
$677$	4.54664	+	7.87500i	0.174741	+	0.302661i	−0.765330	+	0.643638i	$0.777424\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−2.41674	−	4.18592i	−0.0924741	−	0.160170i	0.816078	−	0.577942i	$-0.196144\pi$
$683$	−2.41674	−	4.18592i	−0.0924741	−	0.160170i	−0.908552	+	0.417773i	$0.862811\pi$
$684$		0			0
$685$	18.7760			0.717393
$686$		0			0
$687$		0			0
$688$		0			0
$689$	14.4839	−	25.0868i	0.551791	−	0.955730i
$690$		0			0
$691$	−5.39228	−	9.33969i	−0.205132	−	0.355299i	0.745043	−	0.667017i	$-0.232429\pi$
$691$	−5.39228	−	9.33969i	−0.205132	−	0.355299i	−0.950175	+	0.311718i	$0.899096\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−9.85995	−	17.0779i	−0.374009	−	0.647803i
$696$		0			0
$697$	−2.11774	+	3.66804i	−0.0802152	+	0.138937i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	31.8393			1.20255			0.601276	−	0.799041i	$-0.294659\pi$
$701$	31.8393			1.20255			0.601276	+	0.799041i	$0.294659\pi$
$702$		0			0
$703$	7.44997	+	12.9037i	0.280981	+	0.486673i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	13.6032	+	23.5614i	0.510879	+	0.884868i	0.999921	+	0.0126076i	$0.00401324\pi$
$709$	13.6032	+	23.5614i	0.510879	+	0.884868i	−0.489042	+	0.872260i	$0.662653\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−10.1635	+	17.6037i	−0.380627	+	0.659265i
$714$		0			0
$715$	−2.31607	−	4.01154i	−0.0866160	−	0.150023i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−14.4549	+	25.0366i	−0.539076	+	0.933707i	0.459878	+	0.887982i	$0.347893\pi$
$719$	−14.4549	+	25.0366i	−0.539076	+	0.933707i	−0.998954	+	0.0457252i	$0.985440\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	13.2958	−	23.0291i	0.493795	−	0.855278i
$726$		0			0
$727$	−4.29978	+	7.44744i	−0.159470	+	0.276210i	−0.934678	−	0.355496i	$-0.884312\pi$
$727$	−4.29978	+	7.44744i	−0.159470	+	0.276210i	0.775208	+	0.631706i	$0.217645\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.01984			0.0377202
$732$		0			0
$733$	45.5506			1.68245			0.841225	−	0.540685i	$-0.181835\pi$
$733$	45.5506			1.68245			0.841225	+	0.540685i	$0.181835\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.937301	+	1.62345i	−0.0345259	+	0.0598007i
$738$		0			0
$739$	6.34491	+	10.9897i	0.233401	+	0.404263i	0.958807	−	0.284059i	$-0.0916811\pi$
$739$	6.34491	+	10.9897i	0.233401	+	0.404263i	−0.725405	+	0.688322i	$0.758348\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5.04492	+	8.73806i	0.185080	+	0.320568i	0.943604	−	0.331078i	$-0.107412\pi$
$743$	5.04492	+	8.73806i	0.185080	+	0.320568i	−0.758523	+	0.651646i	$0.774079\pi$
$744$		0			0
$745$	−27.6292			−1.01226
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	5.00713			0.182713			0.0913565	−	0.995818i	$-0.470880\pi$
$751$	5.00713			0.182713			0.0913565	+	0.995818i	$0.470880\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−13.1495			−0.478561
$756$		0			0
$757$	6.83620			0.248466			0.124233	−	0.992253i	$-0.460353\pi$
$757$	6.83620			0.248466			0.124233	+	0.992253i	$0.460353\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	26.8753			0.974231			0.487115	−	0.873338i	$-0.338049\pi$
$761$	26.8753			0.974231			0.487115	+	0.873338i	$0.338049\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.472728			0.0170692
$768$		0			0
$769$	2.00631	+	3.47503i	0.0723493	+	0.125313i	0.899931	−	0.436033i	$-0.143617\pi$
$769$	2.00631	+	3.47503i	0.0723493	+	0.125313i	−0.827581	+	0.561346i	$0.810284\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−13.6861	−	23.7051i	−0.492256	−	0.852612i	0.507704	−	0.861531i	$-0.330494\pi$
$773$	−13.6861	−	23.7051i	−0.492256	−	0.852612i	−0.999960	+	0.00891927i	$0.997161\pi$
$774$		0			0
$775$	4.40171	−	7.62399i	0.158114	−	0.273862i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−11.9146			−0.426884
$780$		0			0
$781$	−7.84771			−0.280813
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.44220	+	4.23001i	−0.0871658	+	0.150976i
$786$		0			0
$787$	−6.43636	+	11.1481i	−0.229432	+	0.397387i	−0.957640	−	0.287969i	$-0.907020\pi$
$787$	−6.43636	+	11.1481i	−0.229432	+	0.397387i	0.728208	+	0.685356i	$0.240353\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−8.63860	+	14.9625i	−0.306766	+	0.531334i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.71139	−	15.0886i	−0.308573	−	0.534465i	0.669477	−	0.742833i	$-0.266518\pi$
$797$	−8.71139	−	15.0886i	−0.308573	−	0.534465i	−0.978050	+	0.208368i	$0.933185\pi$
$798$		0			0
$799$	2.54815	−	4.41352i	0.0901469	−	0.156139i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.88398	−	3.26315i	−0.0664842	−	0.115154i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	3.04097	+	5.26712i	0.106915	+	0.185182i	0.914519	−	0.404543i	$-0.132569\pi$
$809$	3.04097	+	5.26712i	0.106915	+	0.185182i	−0.807604	+	0.589725i	$0.799236\pi$
$810$		0			0
$811$	−14.6219			−0.513443			−0.256722	−	0.966485i	$-0.582642\pi$
$811$	−14.6219			−0.513443			−0.256722	+	0.966485i	$0.582642\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−3.13236	+	5.42540i	−0.109722	+	0.190044i
$816$		0			0
$817$	1.43443	+	2.48450i	0.0501842	+	0.0869216i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.87162	−	8.43789i	−0.170021	−	0.294484i	0.768406	−	0.639962i	$-0.221050\pi$
$821$	−4.87162	−	8.43789i	−0.170021	−	0.294484i	−0.938427	+	0.345478i	$0.887717\pi$
$822$		0			0
$823$	−5.38983	+	9.33546i	−0.187878	+	0.325414i	−0.944542	−	0.328389i	$-0.893494\pi$
$823$	−5.38983	+	9.33546i	−0.187878	+	0.325414i	0.756665	+	0.653803i	$0.226827\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−13.0521			−0.453867			−0.226933	−	0.973910i	$-0.572870\pi$
$827$	−13.0521			−0.453867			−0.226933	+	0.973910i	$0.572870\pi$
$828$		0			0
$829$	−24.5548	−	42.5301i	−0.852822	−	1.47713i	−0.878651	−	0.477465i	$-0.841556\pi$
$829$	−24.5548	−	42.5301i	−0.852822	−	1.47713i	0.0258286	−	0.999666i	$-0.491778\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−12.6154	−	21.8506i	−0.436575	−	0.756170i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−12.0830	+	20.9284i	−0.417151	+	0.722527i	−0.995652	−	0.0931549i	$-0.970305\pi$
$839$	−12.0830	+	20.9284i	−0.417151	+	0.722527i	0.578500	+	0.815682i	$0.303638\pi$
$840$		0			0
$841$	−35.4341	−	61.3737i	−1.22187	−	2.11633i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.104456	−	0.180923i	0.00359339	−	0.00622393i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	27.0243	−	46.8075i	0.926382	−	1.60454i
$852$		0			0
$853$	−2.72681	+	4.72297i	−0.0933641	+	0.161711i	−0.908925	−	0.416960i	$-0.863095\pi$
$853$	−2.72681	+	4.72297i	−0.0933641	+	0.161711i	0.815561	+	0.578672i	$0.196429\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	32.8388			1.12175			0.560876	−	0.827900i	$-0.310464\pi$
$857$	32.8388			1.12175			0.560876	+	0.827900i	$0.310464\pi$
$858$		0			0
$859$	−52.6598			−1.79673			−0.898365	−	0.439249i	$-0.855245\pi$
$859$	−52.6598			−1.79673			−0.898365	+	0.439249i	$0.855245\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−24.4095	+	42.2784i	−0.830908	+	1.43917i	0.0664116	+	0.997792i	$0.478845\pi$
$863$	−24.4095	+	42.2784i	−0.830908	+	1.43917i	−0.897319	+	0.441382i	$0.854488\pi$
$864$		0			0
$865$	−9.80445	−	16.9818i	−0.333361	−	0.577398i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	6.57746	+	11.3925i	0.223125	+	0.386464i
$870$		0			0
$871$	−8.13080			−0.275502
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−25.0745			−0.846706			−0.423353	−	0.905965i	$-0.639147\pi$
$877$	−25.0745			−0.846706			−0.423353	+	0.905965i	$0.639147\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−16.2437			−0.547263			−0.273632	−	0.961835i	$-0.588225\pi$
$881$	−16.2437			−0.547263			−0.273632	+	0.961835i	$0.588225\pi$
$882$		0			0
$883$	29.7137			0.999945			0.499973	−	0.866041i	$-0.333343\pi$
$883$	29.7137			0.999945			0.499973	+	0.866041i	$0.333343\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−15.7471			−0.528734			−0.264367	−	0.964422i	$-0.585163\pi$
$887$	−15.7471			−0.528734			−0.264367	+	0.964422i	$0.585163\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	14.3361			0.479738
$894$		0			0
$895$	−18.1616	−	31.4568i	−0.607076	−	1.05149i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−16.5312	−	28.6328i	−0.551345	−	0.954957i
$900$		0			0
$901$	−2.40614	+	4.16756i	−0.0801602	+	0.138842i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−24.5078			−0.814666
$906$		0			0
$907$	−2.58003			−0.0856684			−0.0428342	−	0.999082i	$-0.513639\pi$
$907$	−2.58003			−0.0856684			−0.0428342	+	0.999082i	$0.513639\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−23.2170	+	40.2130i	−0.769214	+	1.33232i	0.168776	+	0.985654i	$0.446019\pi$
$911$	−23.2170	+	40.2130i	−0.769214	+	1.33232i	−0.937990	+	0.346663i	$0.887315\pi$
$912$		0			0
$913$	2.64236	−	4.57671i	0.0874495	−	0.151467i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−2.84387	+	4.92572i	−0.0938106	+	0.162485i	−0.909112	−	0.416553i	$-0.863238\pi$
$919$	−2.84387	+	4.92572i	−0.0938106	+	0.162485i	0.815301	+	0.579037i	$0.196571\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−17.0191	−	29.4780i	−0.560191	−	0.970279i
$924$		0			0
$925$	−11.7040	+	20.2718i	−0.384824	+	0.666534i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−23.9803	−	41.5350i	−0.786767	−	1.36272i	−0.927938	−	0.372734i	$-0.878420\pi$
$929$	−23.9803	−	41.5350i	−0.786767	−	1.36272i	0.141172	−	0.989985i	$-0.454913\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.384758	+	0.666421i	0.0125829	+	0.0217943i
$936$		0			0
$937$	25.3542			0.828285			0.414142	−	0.910212i	$-0.364082\pi$
$937$	25.3542			0.828285			0.414142	+	0.910212i	$0.364082\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.25651	+	2.17634i	−0.0409611	+	0.0709468i	−0.885779	−	0.464107i	$-0.846375\pi$
$941$	−1.25651	+	2.17634i	−0.0409611	+	0.0709468i	0.844818	+	0.535054i	$0.179709\pi$
$942$		0			0
$943$	21.6097	+	37.4292i	0.703710	+	1.21886i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.26537	+	12.5840i	0.236093	+	0.408925i	0.959590	−	0.281403i	$-0.0907997\pi$
$947$	7.26537	+	12.5840i	0.236093	+	0.408925i	−0.723497	+	0.690328i	$0.757466\pi$
$948$		0			0
$949$	8.17147	−	14.1534i	0.265257	−	0.459439i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	36.5564			1.18418			0.592089	−	0.805873i	$-0.298303\pi$
$953$	36.5564			1.18418			0.592089	+	0.805873i	$0.298303\pi$
$954$		0			0
$955$	8.26605	+	14.3172i	0.267483	+	0.463294i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	10.0272	+	17.3676i	0.323458	+	0.560246i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.573726	−	0.993722i	0.0184689	−	0.0319890i
$966$		0			0
$967$	8.06111	+	13.9623i	0.259228	+	0.448996i	0.966035	−	0.258410i	$-0.0831986\pi$
$967$	8.06111	+	13.9623i	0.259228	+	0.448996i	−0.706807	+	0.707406i	$0.749865\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	8.60100	−	14.8974i	0.276019	−	0.478079i	−0.694373	−	0.719616i	$-0.744318\pi$
$971$	8.60100	−	14.8974i	0.276019	−	0.478079i	0.970392	+	0.241537i	$0.0776514\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	20.1225	−	34.8532i	0.643776	−	1.11505i	−0.340806	−	0.940133i	$-0.610700\pi$
$977$	20.1225	−	34.8532i	0.643776	−	1.11505i	0.984583	−	0.174920i	$-0.0559666\pi$
$978$		0			0
$979$	0.443873	−	0.768810i	0.0141862	−	0.0245713i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	20.5520			0.655506			0.327753	−	0.944763i	$-0.393709\pi$
$983$	20.5520			0.655506			0.327753	+	0.944763i	$0.393709\pi$
$984$		0			0
$985$	15.7813			0.502834
$986$		0			0
$987$		0			0
$988$		0			0
$989$	5.20330	−	9.01237i	0.165455	−	0.286577i
$990$		0			0
$991$	−14.9872	−	25.9586i	−0.476083	−	0.824601i	0.523541	−	0.852000i	$-0.324611\pi$
$991$	−14.9872	−	25.9586i	−0.476083	−	0.824601i	−0.999625	+	0.0273998i	$0.991277\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−4.36537	−	7.56105i	−0.138392	−	0.239701i
$996$		0			0
$997$	12.0389			0.381275			0.190638	−	0.981660i	$-0.438944\pi$
$997$	12.0389			0.381275			0.190638	+	0.981660i	$0.438944\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.l.i.3313.3		14
3.2	odd	2		1764.2.l.i.961.3		14
7.2	even	3		5292.2.j.g.3529.5		14
7.3	odd	6		756.2.i.b.613.3		14
7.4	even	3		5292.2.i.i.2125.5		14
7.5	odd	6		5292.2.j.h.3529.3		14
7.6	odd	2		756.2.l.b.289.5		14
9.4	even	3		5292.2.i.i.1549.5		14
9.5	odd	6		1764.2.i.i.373.4		14
21.2	odd	6		1764.2.j.h.1177.7		14
21.5	even	6		1764.2.j.g.1177.1		14
21.11	odd	6		1764.2.i.i.1537.4		14
21.17	even	6		252.2.i.b.25.4	✓	14
21.20	even	2		252.2.l.b.205.5	yes	14
28.3	even	6		3024.2.q.j.2881.3		14
28.27	even	2		3024.2.t.j.289.5		14
63.4	even	3	inner	5292.2.l.i.361.3		14
63.5	even	6		1764.2.j.g.589.1		14
63.13	odd	6		756.2.i.b.37.3		14
63.20	even	6		2268.2.k.e.1297.5		14
63.23	odd	6		1764.2.j.h.589.7		14
63.31	odd	6		756.2.l.b.361.5		14
63.32	odd	6		1764.2.l.i.949.3		14
63.34	odd	6		2268.2.k.f.1297.3		14
63.38	even	6		2268.2.k.e.1621.5		14
63.40	odd	6		5292.2.j.h.1765.3		14
63.41	even	6		252.2.i.b.121.4	yes	14
63.52	odd	6		2268.2.k.f.1621.3		14
63.58	even	3		5292.2.j.g.1765.5		14
63.59	even	6		252.2.l.b.193.5	yes	14
84.59	odd	6		1008.2.q.j.529.4		14
84.83	odd	2		1008.2.t.j.961.3		14
252.31	even	6		3024.2.t.j.1873.5		14
252.59	odd	6		1008.2.t.j.193.3		14
252.139	even	6		3024.2.q.j.2305.3		14
252.167	odd	6		1008.2.q.j.625.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.4	✓	14	21.17	even	6
252.2.i.b.121.4	yes	14	63.41	even	6
252.2.l.b.193.5	yes	14	63.59	even	6
252.2.l.b.205.5	yes	14	21.20	even	2
756.2.i.b.37.3		14	63.13	odd	6
756.2.i.b.613.3		14	7.3	odd	6
756.2.l.b.289.5		14	7.6	odd	2
756.2.l.b.361.5		14	63.31	odd	6
1008.2.q.j.529.4		14	84.59	odd	6
1008.2.q.j.625.4		14	252.167	odd	6
1008.2.t.j.193.3		14	252.59	odd	6
1008.2.t.j.961.3		14	84.83	odd	2
1764.2.i.i.373.4		14	9.5	odd	6
1764.2.i.i.1537.4		14	21.11	odd	6
1764.2.j.g.589.1		14	63.5	even	6
1764.2.j.g.1177.1		14	21.5	even	6
1764.2.j.h.589.7		14	63.23	odd	6
1764.2.j.h.1177.7		14	21.2	odd	6
1764.2.l.i.949.3		14	63.32	odd	6
1764.2.l.i.961.3		14	3.2	odd	2
2268.2.k.e.1297.5		14	63.20	even	6
2268.2.k.e.1621.5		14	63.38	even	6
2268.2.k.f.1297.3		14	63.34	odd	6
2268.2.k.f.1621.3		14	63.52	odd	6
3024.2.q.j.2305.3		14	252.139	even	6
3024.2.q.j.2881.3		14	28.3	even	6
3024.2.t.j.289.5		14	28.27	even	2
3024.2.t.j.1873.5		14	252.31	even	6
5292.2.i.i.1549.5		14	9.4	even	3
5292.2.i.i.2125.5		14	7.4	even	3
5292.2.j.g.1765.5		14	63.58	even	3
5292.2.j.g.3529.5		14	7.2	even	3
5292.2.j.h.1765.3		14	63.40	odd	6
5292.2.j.h.3529.3		14	7.5	odd	6
5292.2.l.i.361.3		14	63.4	even	3	inner
5292.2.l.i.3313.3		14	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.52940 q^{5} -0.835636 q^{11} +(-1.81222 - 3.13886i) q^{13} +(0.301057 + 0.521446i) q^{17} +(-0.846884 + 1.46685i) q^{19} +6.14405 q^{23} -2.66092 q^{25} +(-4.99671 + 8.65455i) q^{29} +(-1.65421 + 2.86517i) q^{31} +(4.39846 - 7.61835i) q^{37} +(3.51718 + 6.09194i) q^{41} +(0.846884 - 1.46685i) q^{43} +(-4.23200 - 7.33004i) q^{47} +(3.99616 + 6.92155i) q^{53} +1.27803 q^{55} +(-0.0652138 + 0.112954i) q^{59} +(-2.38343 - 4.12822i) q^{61} +(2.77162 + 4.80059i) q^{65} +(1.12166 - 1.94278i) q^{67} +9.39130 q^{71} +(2.25454 + 3.90498i) q^{73} +(-7.87120 - 13.6333i) q^{79} +(-3.16210 + 5.47692i) q^{83} +(-0.460438 - 0.797501i) q^{85} +(-0.531180 + 0.920030i) q^{89} +(1.29523 - 2.24340i) q^{95} +(7.76364 - 13.4470i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 4 q^{5} + 4 q^{11} - 2 q^{13} + 2 q^{17} - 7 q^{19} + 22 q^{23} + 18 q^{25} - q^{29} + q^{31} + 10 q^{37} - 33 q^{41} + 7 q^{43} - 3 q^{47} + 15 q^{53} + 28 q^{55} - 14 q^{59} + 10 q^{61} - 15 q^{65}+ \cdots + 18 q^{97}+O(q^{100}) \) 14 * q + 4 * q^5 + 4 * q^11 - 2 * q^13 + 2 * q^17 - 7 * q^19 + 22 * q^23 + 18 * q^25 - q^29 + q^31 + 10 * q^37 - 33 * q^41 + 7 * q^43 - 3 * q^47 + 15 * q^53 + 28 * q^55 - 14 * q^59 + 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 - 21 * q^73 - 10 * q^79 - 25 * q^83 + 8 * q^85 - 6 * q^89 + 28 * q^95 + 18 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more