LMFDB - Embedded newform 3024.2.df.e.17.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(17,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.11
Character	$\chi$	$=$	3024.17
Dual form			3024.2.df.e.1601.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+0.203178 q^{5} +(1.27132 + 2.32029i) q^{7} +4.46863i q^{11} +(1.25586 + 0.725070i) q^{13} +(1.60586 - 2.78143i) q^{17} +(6.20156 - 3.58047i) q^{19} -1.26655i q^{23} -4.95872 q^{25} +(0.944433 - 0.545269i) q^{29} +(5.60021 - 3.23328i) q^{31} +(0.258305 + 0.471432i) q^{35} +(3.02855 + 5.24561i) q^{37} +(0.370687 - 0.642048i) q^{41} +(4.69802 + 8.13721i) q^{43} +(-0.0465845 + 0.0806866i) q^{47} +(-3.76748 + 5.89967i) q^{49} +(-9.35260 - 5.39973i) q^{53} +0.907929i q^{55} +(5.16447 + 8.94512i) q^{59} +(-7.34727 - 4.24195i) q^{61} +(0.255163 + 0.147318i) q^{65} +(-4.02663 - 6.97432i) q^{67} +15.6777i q^{71} +(0.984428 + 0.568360i) q^{73} +(-10.3685 + 5.68108i) q^{77} +(-5.86893 + 10.1653i) q^{79} +(-2.29931 - 3.98252i) q^{83} +(0.326276 - 0.565127i) q^{85} +(3.52692 + 6.10881i) q^{89} +(-0.0857700 + 3.83575i) q^{91} +(1.26002 - 0.727474i) q^{95} +(-3.17914 + 1.83548i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{25} - 18 q^{29} - 18 q^{31} + 6 q^{41} + 6 q^{43} + 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} - 6 q^{79} + 18 q^{89} - 6 q^{91} - 54 q^{95}+O(q^{100}) $ 48 * q + 48 * q^25 - 18 * q^29 - 18 * q^31 + 6 * q^41 + 6 * q^43 + 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 - 6 * q^79 + 18 * q^89 - 6 * q^91 - 54 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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
$5$	0.203178			0.0908641			0.0454320	−	0.998967i	$-0.485534\pi$
$5$	0.203178			0.0908641			0.0454320	+	0.998967i	$0.485534\pi$
$6$		0			0
$7$	1.27132	+	2.32029i	0.480515	+	0.876987i
$7$	1.27132	+	2.32029i	0.480515	+	0.876987i
$8$		0			0
$9$		0			0
$10$		0			0
$11$			4.46863i			1.34734i	0.739031	+	0.673672i	$0.235284\pi$
$11$			4.46863i			1.34734i	−0.739031	+	0.673672i	$0.764716\pi$
$12$		0			0
$13$	1.25586	+	0.725070i	0.348312	+	0.201098i	0.663942	−	0.747784i	$-0.268882\pi$
$13$	1.25586	+	0.725070i	0.348312	+	0.201098i	−0.315629	+	0.948883i	$0.602216\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.60586	−	2.78143i	0.389478	−	0.674596i	−0.602901	−	0.797816i	$-0.705989\pi$
$17$	1.60586	−	2.78143i	0.389478	−	0.674596i	0.992379	+	0.123220i	$0.0393220\pi$
$18$		0			0
$19$	6.20156	−	3.58047i	1.42274	−	0.821417i	0.426203	−	0.904627i	$-0.359851\pi$
$19$	6.20156	−	3.58047i	1.42274	−	0.821417i	0.996532	+	0.0832106i	$0.0265174\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	1.26655i		−	0.264095i	−0.991243	−	0.132047i	$-0.957845\pi$
$23$		−	1.26655i		−	0.264095i	0.991243	−	0.132047i	$-0.0421551\pi$
$24$		0			0
$25$	−4.95872			−0.991744
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.944433	−	0.545269i	0.175377	−	0.101254i	−0.409742	−	0.912202i	$-0.634381\pi$
$29$	0.944433	−	0.545269i	0.175377	−	0.101254i	0.585119	+	0.810948i	$0.301048\pi$
$30$		0			0
$31$	5.60021	−	3.23328i	1.00583	−	0.580715i	0.0958603	−	0.995395i	$-0.469440\pi$
$31$	5.60021	−	3.23328i	1.00583	−	0.580715i	0.909967	+	0.414680i	$0.136106\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.258305	+	0.471432i	0.0436616	+	0.0796866i
$36$		0			0
$37$	3.02855	+	5.24561i	0.497891	+	0.862373i	0.999997	−	0.00243316i	$-0.000774500\pi$
$37$	3.02855	+	5.24561i	0.497891	+	0.862373i	−0.502106	+	0.864806i	$0.667441\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.370687	−	0.642048i	0.0578915	−	0.100271i	−0.835627	−	0.549297i	$-0.814896\pi$
$41$	0.370687	−	0.642048i	0.0578915	−	0.100271i	0.893519	+	0.449026i	$0.148229\pi$
$42$		0			0
$43$	4.69802	+	8.13721i	0.716442	+	1.24091i	0.962401	+	0.271633i	$0.0875638\pi$
$43$	4.69802	+	8.13721i	0.716442	+	1.24091i	−0.245959	+	0.969280i	$0.579103\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.0465845	+	0.0806866i	−0.00679504	+	0.0117694i	−0.869403	−	0.494104i	$-0.835496\pi$
$47$	−0.0465845	+	0.0806866i	−0.00679504	+	0.0117694i	0.862608	+	0.505873i	$0.168830\pi$
$48$		0			0
$49$	−3.76748	+	5.89967i	−0.538211	+	0.842810i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−9.35260	−	5.39973i	−1.28468	−	0.741710i	−0.306979	−	0.951716i	$-0.599318\pi$
$53$	−9.35260	−	5.39973i	−1.28468	−	0.741710i	−0.977700	+	0.210007i	$0.932651\pi$
$54$		0			0
$55$			0.907929i			0.122425i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.16447	+	8.94512i	0.672356	+	1.16456i	0.977234	+	0.212164i	$0.0680511\pi$
$59$	5.16447	+	8.94512i	0.672356	+	1.16456i	−0.304878	+	0.952392i	$0.598616\pi$
$60$		0			0
$61$	−7.34727	−	4.24195i	−0.940722	−	0.543126i	−0.0505352	−	0.998722i	$-0.516093\pi$
$61$	−7.34727	−	4.24195i	−0.940722	−	0.543126i	−0.890186	+	0.455596i	$0.849426\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.255163	+	0.147318i	0.0316491	+	0.0182726i
$66$		0			0
$67$	−4.02663	−	6.97432i	−0.491931	−	0.852049i	0.508026	−	0.861342i	$-0.330375\pi$
$67$	−4.02663	−	6.97432i	−0.491931	−	0.852049i	−0.999957	+	0.00929244i	$0.997042\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			15.6777i			1.86060i	0.366802	+	0.930299i	$0.380453\pi$
$71$			15.6777i			1.86060i	−0.366802	+	0.930299i	$0.619547\pi$
$72$		0			0
$73$	0.984428	+	0.568360i	0.115219	+	0.0665215i	0.556502	−	0.830846i	$-0.312143\pi$
$73$	0.984428	+	0.568360i	0.115219	+	0.0665215i	−0.441283	+	0.897368i	$0.645477\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−10.3685	+	5.68108i	−1.18160	+	0.647419i
$78$		0			0
$79$	−5.86893	+	10.1653i	−0.660306	+	1.14368i	0.320229	+	0.947340i	$0.396240\pi$
$79$	−5.86893	+	10.1653i	−0.660306	+	1.14368i	−0.980535	+	0.196344i	$0.937093\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.29931	−	3.98252i	−0.252382	−	0.437139i	0.711799	−	0.702383i	$-0.247881\pi$
$83$	−2.29931	−	3.98252i	−0.252382	−	0.437139i	−0.964181	+	0.265245i	$0.914547\pi$
$84$		0			0
$85$	0.326276	−	0.565127i	0.0353896	−	0.0612966i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.52692	+	6.10881i	0.373853	+	0.647532i	0.990155	−	0.139978i	$-0.0447032\pi$
$89$	3.52692	+	6.10881i	0.373853	+	0.647532i	−0.616302	+	0.787510i	$0.711370\pi$
$90$		0			0
$91$	−0.0857700	+	3.83575i	−0.00899114	+	0.402096i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.26002	−	0.727474i	0.129276	−	0.0746373i
$96$		0			0
$97$	−3.17914	+	1.83548i	−0.322793	+	0.186365i	−0.652637	−	0.757671i	$-0.726337\pi$
$97$	−3.17914	+	1.83548i	−0.322793	+	0.186365i	0.329844	+	0.944036i	$0.393004\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	13.1682			1.31029			0.655143	−	0.755505i	$-0.272609\pi$
$101$	13.1682			1.31029			0.655143	+	0.755505i	$0.272609\pi$
$102$		0			0
$103$			13.5351i			1.33365i	0.745214	+	0.666826i	$0.232347\pi$
$103$			13.5351i			1.33365i	−0.745214	+	0.666826i	$0.767653\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	13.0095	−	7.51105i	1.25768	−	0.726121i	0.285056	−	0.958511i	$-0.407988\pi$
$107$	13.0095	−	7.51105i	1.25768	−	0.726121i	0.972623	+	0.232390i	$0.0746545\pi$
$108$		0			0
$109$	2.72560	−	4.72088i	0.261065	−	0.452178i	−0.705460	−	0.708750i	$-0.749260\pi$
$109$	2.72560	−	4.72088i	0.261065	−	0.452178i	0.966525	+	0.256571i	$0.0825928\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.03027	+	3.48158i	0.567280	+	0.327519i	0.756062	−	0.654500i	$-0.227121\pi$
$113$	6.03027	+	3.48158i	0.567280	+	0.327519i	−0.188782	+	0.982019i	$0.560454\pi$
$114$		0			0
$115$		−	0.257336i		−	0.0239967i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	8.49529	+	0.189961i	0.778762	+	0.0174137i
$120$		0			0
$121$	−8.96868			−0.815335
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−2.02340			−0.180978
$126$		0			0
$127$	−2.68718			−0.238448			−0.119224	−	0.992867i	$-0.538041\pi$
$127$	−2.68718			−0.238448			−0.119224	+	0.992867i	$0.538041\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.13987			0.536443			0.268222	−	0.963357i	$-0.413564\pi$
$131$	6.13987			0.536443			0.268222	+	0.963357i	$0.413564\pi$
$132$		0			0
$133$	16.1919	+	9.83747i	1.40402	+	0.853017i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			4.28221i			0.365854i	0.983127	+	0.182927i	$0.0585571\pi$
$137$			4.28221i			0.365854i	−0.983127	+	0.182927i	$0.941443\pi$
$138$		0			0
$139$	−3.43981	−	1.98597i	−0.291761	−	0.168448i	0.346975	−	0.937874i	$-0.387209\pi$
$139$	−3.43981	−	1.98597i	−0.291761	−	0.168448i	−0.638736	+	0.769426i	$0.720542\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.24007	+	5.61197i	−0.270948	+	0.469296i
$144$		0			0
$145$	0.191888	−	0.110787i	0.0159355	−	0.00920034i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	4.63300i		−	0.379550i	−0.981828	−	0.189775i	$-0.939224\pi$
$149$		−	4.63300i		−	0.379550i	0.981828	−	0.189775i	$-0.0607759\pi$
$150$		0			0
$151$	15.6948			1.27722			0.638612	−	0.769529i	$-0.279509\pi$
$151$	15.6948			1.27722			0.638612	+	0.769529i	$0.279509\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.13784	−	0.656933i	0.0913936	−	0.0527661i
$156$		0			0
$157$	−6.55598	+	3.78510i	−0.523224	+	0.302084i	−0.738253	−	0.674524i	$-0.764349\pi$
$157$	−6.55598	+	3.78510i	−0.523224	+	0.302084i	0.215029	+	0.976608i	$0.431016\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.93877	−	1.61020i	0.231607	−	0.126901i
$162$		0			0
$163$	3.97454	+	6.88410i	0.311310	+	0.539204i	0.978646	−	0.205552i	$-0.0658990\pi$
$163$	3.97454	+	6.88410i	0.311310	+	0.539204i	−0.667337	+	0.744756i	$0.732566\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.72342	−	2.98506i	0.133363	−	0.230991i	−0.791608	−	0.611029i	$-0.790756\pi$
$167$	1.72342	−	2.98506i	0.133363	−	0.230991i	0.924971	+	0.380038i	$0.124089\pi$
$168$		0			0
$169$	−5.44855	−	9.43716i	−0.419119	−	0.725936i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.21800	−	12.5019i	0.548775	−	0.950505i	−0.449584	−	0.893238i	$-0.648428\pi$
$173$	7.21800	−	12.5019i	0.548775	−	0.950505i	0.998359	−	0.0572675i	$-0.0182388\pi$
$174$		0			0
$175$	−6.30413	−	11.5057i	−0.476548	−	0.869746i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−19.7102	−	11.3797i	−1.47321	−	0.850558i	−0.473665	−	0.880705i	$-0.657069\pi$
$179$	−19.7102	−	11.3797i	−1.47321	−	0.850558i	−0.999545	+	0.0301471i	$0.990402\pi$
$180$		0			0
$181$			8.95105i			0.665326i	0.943046	+	0.332663i	$0.107947\pi$
$181$			8.95105i			0.665326i	−0.943046	+	0.332663i	$0.892053\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.615337	+	1.06579i	0.0452404	+	0.0783587i
$186$		0			0
$187$	12.4292	+	7.17600i	0.908913	+	0.524761i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	21.2572	+	12.2729i	1.53812	+	0.888033i	0.998949	+	0.0458359i	$0.0145951\pi$
$191$	21.2572	+	12.2729i	1.53812	+	0.888033i	0.539170	+	0.842197i	$0.318738\pi$
$192$		0			0
$193$	−2.28259	−	3.95356i	−0.164305	−	0.284584i	0.772104	−	0.635497i	$-0.219205\pi$
$193$	−2.28259	−	3.95356i	−0.164305	−	0.284584i	−0.936408	+	0.350913i	$0.885871\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	12.1315i		−	0.864333i	−0.901794	−	0.432166i	$-0.857749\pi$
$197$		−	12.1315i		−	0.864333i	0.901794	−	0.432166i	$-0.142251\pi$
$198$		0			0
$199$	−12.8273	−	7.40587i	−0.909306	−	0.524988i	−0.0290981	−	0.999577i	$-0.509264\pi$
$199$	−12.8273	−	7.40587i	−0.909306	−	0.524988i	−0.880208	+	0.474589i	$0.842597\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.46586	+	1.49814i	0.173070	+	0.105149i
$204$		0			0
$205$	0.0753154	−	0.130450i	0.00526026	−	0.00911104i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	15.9998	+	27.7125i	1.10673	+	1.91691i
$210$		0			0
$211$	3.77116	−	6.53184i	0.259617	−	0.449670i	−0.706522	−	0.707691i	$-0.749737\pi$
$211$	3.77116	−	6.53184i	0.259617	−	0.449670i	0.966139	+	0.258021i	$0.0830703\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.954536	+	1.65331i	0.0650988	+	0.112754i
$216$		0			0
$217$	14.6218	+	8.88356i	0.992594	+	0.603055i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	4.03346	−	2.32872i	0.271320	−	0.156647i
$222$		0			0
$223$	−25.2846	+	14.5980i	−1.69318	+	0.977557i	−0.741255	+	0.671224i	$0.765769\pi$
$223$	−25.2846	+	14.5980i	−1.69318	+	0.977557i	−0.951924	+	0.306334i	$0.900898\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	29.1575			1.93525			0.967625	−	0.252391i	$-0.0812169\pi$
$227$	29.1575			1.93525			0.967625	+	0.252391i	$0.0812169\pi$
$228$		0			0
$229$			17.4121i			1.15062i	0.817934	+	0.575312i	$0.195119\pi$
$229$			17.4121i			1.15062i	−0.817934	+	0.575312i	$0.804881\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−14.3517	+	8.28596i	−0.940212	+	0.542831i	−0.890027	−	0.455908i	$-0.849314\pi$
$233$	−14.3517	+	8.28596i	−0.940212	+	0.542831i	−0.0501850	+	0.998740i	$0.515981\pi$
$234$		0			0
$235$	−0.00946495	+	0.0163938i	−0.000617425	+	0.00106941i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−8.45527	−	4.88165i	−0.546926	−	0.315768i	0.200955	−	0.979600i	$-0.435595\pi$
$239$	−8.45527	−	4.88165i	−0.546926	−	0.315768i	−0.747881	+	0.663833i	$0.768929\pi$
$240$		0			0
$241$			10.8582i			0.699437i	0.936855	+	0.349719i	$0.113723\pi$
$241$			10.8582i			0.699437i	−0.936855	+	0.349719i	$0.886277\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.765469	+	1.19869i	−0.0489040	+	0.0765812i
$246$		0			0
$247$	10.3844			0.660741
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−27.4155			−1.73045			−0.865224	−	0.501385i	$-0.832824\pi$
$251$	−27.4155			−1.73045			−0.865224	+	0.501385i	$0.832824\pi$
$252$		0			0
$253$	5.65976			0.355826
$254$		0			0
$255$		0			0
$256$		0			0
$257$	27.3169			1.70398			0.851989	−	0.523559i	$-0.175396\pi$
$257$	27.3169			1.70398			0.851989	+	0.523559i	$0.175396\pi$
$258$		0			0
$259$	−8.32106	+	13.6960i	−0.517045	+	0.851027i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			13.8160i			0.851928i	0.904740	+	0.425964i	$0.140065\pi$
$263$			13.8160i			0.851928i	−0.904740	+	0.425964i	$0.859935\pi$
$264$		0			0
$265$	−1.90025	−	1.09711i	−0.116731	−	0.0673948i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.7471	+	18.6145i	−0.655260	+	1.13494i	0.326568	+	0.945174i	$0.394108\pi$
$269$	−10.7471	+	18.6145i	−0.655260	+	1.13494i	−0.981828	+	0.189770i	$0.939226\pi$
$270$		0			0
$271$	−27.2614	+	15.7394i	−1.65601	+	0.956101i	−0.681488	+	0.731829i	$0.738667\pi$
$271$	−27.2614	+	15.7394i	−1.65601	+	0.956101i	−0.974527	+	0.224271i	$0.928000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	22.1587i		−	1.33622i
$276$		0			0
$277$	−11.8408			−0.711445			−0.355722	−	0.934592i	$-0.615765\pi$
$277$	−11.8408			−0.711445			−0.355722	+	0.934592i	$0.615765\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	19.4588	−	11.2346i	1.16082	−	0.670198i	0.209317	−	0.977848i	$-0.432876\pi$
$281$	19.4588	−	11.2346i	1.16082	−	0.670198i	0.951500	+	0.307650i	$0.0995425\pi$
$282$		0			0
$283$	1.17672	−	0.679378i	0.0699486	−	0.0403848i	−0.464618	−	0.885511i	$-0.653808\pi$
$283$	1.17672	−	0.679378i	0.0699486	−	0.0403848i	0.534566	+	0.845126i	$0.320475\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.96100	+	0.0438493i	0.115754	+	0.00258834i
$288$		0			0
$289$	3.34242	+	5.78925i	0.196613	+	0.340544i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8.10060	−	14.0307i	0.473242	−	0.819680i	−0.526289	−	0.850306i	$-0.676417\pi$
$293$	8.10060	−	14.0307i	0.473242	−	0.819680i	0.999531	+	0.0306263i	$0.00975018\pi$
$294$		0			0
$295$	1.04931	+	1.81745i	0.0610931	+	0.105816i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.918339	−	1.59061i	0.0531089	−	0.0919873i
$300$		0			0
$301$	−12.9080	+	21.2458i	−0.744003	+	1.22459i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.49281	−	0.861872i	−0.0854778	−	0.0493506i
$306$		0			0
$307$		−	9.22930i		−	0.526744i	−0.964694	−	0.263372i	$-0.915165\pi$
$307$		−	9.22930i		−	0.526744i	0.964694	−	0.263372i	$-0.0848346\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.313334	−	0.542711i	−0.0177676	−	0.0307743i	0.857005	−	0.515308i	$-0.172323\pi$
$311$	−0.313334	−	0.542711i	−0.0177676	−	0.0307743i	−0.874772	+	0.484534i	$0.838989\pi$
$312$		0			0
$313$	−4.43528	−	2.56071i	−0.250697	−	0.144740i	0.369387	−	0.929276i	$-0.379568\pi$
$313$	−4.43528	−	2.56071i	−0.250697	−	0.144740i	−0.620083	+	0.784536i	$0.712901\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.62803	+	2.09464i	0.203770	+	0.117647i	0.598413	−	0.801188i	$-0.295798\pi$
$317$	3.62803	+	2.09464i	0.203770	+	0.117647i	−0.394643	+	0.918835i	$0.629132\pi$
$318$		0			0
$319$	2.43661	+	4.22033i	0.136424	+	0.236293i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	22.9990i		−	1.27970i
$324$		0			0
$325$	−6.22744	−	3.59542i	−0.345436	−	0.199438i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.246440	−	0.00551057i	−0.0135867	−	0.000303808i
$330$		0			0
$331$	12.9710	−	22.4664i	0.712949	−	1.23486i	−0.250797	−	0.968040i	$-0.580693\pi$
$331$	12.9710	−	22.4664i	0.712949	−	1.23486i	0.963745	−	0.266824i	$-0.0859741\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.818123	−	1.41703i	−0.0446989	−	0.0774207i
$336$		0			0
$337$	8.40130	−	14.5515i	0.457648	−	0.792669i	−0.541188	−	0.840901i	$-0.682025\pi$
$337$	8.40130	−	14.5515i	0.457648	−	0.792669i	0.998836	+	0.0482321i	$0.0153587\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	14.4484	+	25.0253i	0.782423	+	1.35520i
$342$		0			0
$343$	−18.4786	−	1.24124i	−0.997752	−	0.0670206i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−25.0574	+	14.4669i	−1.34515	+	0.776624i	−0.987558	−	0.157253i	$-0.949736\pi$
$347$	−25.0574	+	14.4669i	−1.34515	+	0.776624i	−0.357594	+	0.933877i	$0.616403\pi$
$348$		0			0
$349$	20.7481	−	11.9789i	1.11062	−	0.641217i	0.171630	−	0.985161i	$-0.445097\pi$
$349$	20.7481	−	11.9789i	1.11062	−	0.641217i	0.938990	+	0.343944i	$0.111763\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−15.5894			−0.829743			−0.414871	−	0.909880i	$-0.636173\pi$
$353$	−15.5894			−0.829743			−0.414871	+	0.909880i	$0.636173\pi$
$354$		0			0
$355$			3.18536i			0.169062i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−11.7053	+	6.75809i	−0.617785	+	0.356678i	−0.776006	−	0.630726i	$-0.782757\pi$
$359$	−11.7053	+	6.75809i	−0.617785	+	0.356678i	0.158221	+	0.987404i	$0.449424\pi$
$360$		0			0
$361$	16.1396	−	27.9545i	0.849451	−	1.47129i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.200014	+	0.115478i	0.0104692	+	0.00604442i
$366$		0			0
$367$		−	19.1785i		−	1.00111i	−0.865705	−	0.500554i	$-0.833130\pi$
$367$		−	19.1785i		−	1.00111i	0.865705	−	0.500554i	$-0.166870\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.638745	−	28.5655i	0.0331620	−	1.48305i
$372$		0			0
$373$	2.53539			0.131278			0.0656388	−	0.997843i	$-0.479091\pi$
$373$	2.53539			0.131278			0.0656388	+	0.997843i	$0.479091\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.58143			0.0814479
$378$		0			0
$379$	−6.11511			−0.314112			−0.157056	−	0.987590i	$-0.550200\pi$
$379$	−6.11511			−0.314112			−0.157056	+	0.987590i	$0.550200\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	5.67449			0.289953			0.144976	−	0.989435i	$-0.453689\pi$
$383$	5.67449			0.289953			0.144976	+	0.989435i	$0.453689\pi$
$384$		0			0
$385$	−2.10666	+	1.15427i	−0.107365	+	0.0588271i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			7.88653i			0.399863i	0.979810	+	0.199932i	$0.0640720\pi$
$389$			7.88653i			0.399863i	−0.979810	+	0.199932i	$0.935928\pi$
$390$		0			0
$391$	−3.52283	−	2.03391i	−0.178157	−	0.102859i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.19244	+	2.06536i	−0.0599981	+	0.103920i
$396$		0			0
$397$	10.2548	−	5.92061i	0.514674	−	0.297147i	−0.220079	−	0.975482i	$-0.570632\pi$
$397$	10.2548	−	5.92061i	0.514674	−	0.297147i	0.734753	+	0.678335i	$0.237298\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	38.1732i		−	1.90628i	−0.302534	−	0.953139i	$-0.597832\pi$
$401$		−	38.1732i		−	1.90628i	0.302534	−	0.953139i	$-0.402168\pi$
$402$		0			0
$403$	9.37742			0.467123
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−23.4407	+	13.5335i	−1.16191	+	0.670831i
$408$		0			0
$409$	11.2828	−	6.51411i	0.557897	−	0.322102i	−0.194404	−	0.980922i	$-0.562277\pi$
$409$	11.2828	−	6.51411i	0.557897	−	0.322102i	0.752301	+	0.658820i	$0.228944\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−14.1896	+	23.3552i	−0.698222	+	1.14923i
$414$		0			0
$415$	−0.467170	−	0.809162i	−0.0229325	−	0.0397202i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	15.1454	−	26.2325i	0.739899	−	1.28154i	−0.212641	−	0.977130i	$-0.568207\pi$
$419$	15.1454	−	26.2325i	0.739899	−	1.28154i	0.952540	−	0.304412i	$-0.0984601\pi$
$420$		0			0
$421$	−3.20295	−	5.54767i	−0.156102	−	0.270377i	0.777358	−	0.629059i	$-0.216560\pi$
$421$	−3.20295	−	5.54767i	−0.156102	−	0.270377i	−0.933460	+	0.358682i	$0.883226\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−7.96301	+	13.7923i	−0.386263	+	0.669027i
$426$		0			0
$427$	0.501789	−	22.4407i	0.0242833	−	1.08598i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	10.0071	+	5.77758i	0.482023	+	0.278296i	0.721259	−	0.692665i	$-0.243564\pi$
$431$	10.0071	+	5.77758i	0.482023	+	0.278296i	−0.239236	+	0.970961i	$0.576897\pi$
$432$		0			0
$433$			0.696999i			0.0334956i	0.999860	+	0.0167478i	$0.00533125\pi$
$433$			0.696999i			0.0334956i	−0.999860	+	0.0167478i	$0.994669\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.53486	−	7.85460i	−0.216932	−	0.375737i
$438$		0			0
$439$	−20.4771	−	11.8224i	−0.977316	−	0.564254i	−0.0758575	−	0.997119i	$-0.524169\pi$
$439$	−20.4771	−	11.8224i	−0.977316	−	0.564254i	−0.901459	+	0.432865i	$0.857503\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	11.3308	+	6.54184i	0.538343	+	0.310812i	0.744407	−	0.667726i	$-0.232732\pi$
$443$	11.3308	+	6.54184i	0.538343	+	0.310812i	−0.206064	+	0.978538i	$0.566066\pi$
$444$		0			0
$445$	0.716594	+	1.24118i	0.0339698	+	0.0588374i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	11.5463i		−	0.544906i	−0.962169	−	0.272453i	$-0.912165\pi$
$449$		−	11.5463i		−	0.544906i	0.962169	−	0.272453i	$-0.0878348\pi$
$450$		0			0
$451$	2.86908	+	1.65646i	0.135100	+	0.0779998i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.0174266	+	0.779341i	−0.000816971	+	0.0365361i
$456$		0			0
$457$	5.51833	−	9.55803i	0.258137	−	0.447106i	−0.707606	−	0.706607i	$-0.750225\pi$
$457$	5.51833	−	9.55803i	0.258137	−	0.447106i	0.965743	+	0.259501i	$0.0835582\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6.69369	+	11.5938i	0.311756	+	0.539978i	0.978743	−	0.205092i	$-0.0657494\pi$
$461$	6.69369	+	11.5938i	0.311756	+	0.539978i	−0.666986	+	0.745070i	$0.732416\pi$
$462$		0			0
$463$	−10.6622	+	18.4675i	−0.495515	+	0.858258i	−0.999987	−	0.00517079i	$-0.998354\pi$
$463$	−10.6622	+	18.4675i	−0.495515	+	0.858258i	0.504471	+	0.863428i	$0.331687\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	7.97308	+	13.8098i	0.368950	+	0.639041i	0.989402	−	0.145204i	$-0.0463839\pi$
$467$	7.97308	+	13.8098i	0.368950	+	0.639041i	−0.620451	+	0.784245i	$0.713051\pi$
$468$		0			0
$469$	11.0633	−	18.2096i	0.510856	−	0.840839i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−36.3622	+	20.9937i	−1.67194	+	0.965293i
$474$		0			0
$475$	−30.7518	+	17.7546i	−1.41099	+	0.814635i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−30.7187			−1.40357			−0.701787	−	0.712387i	$-0.747614\pi$
$479$	−30.7187			−1.40357			−0.701787	+	0.712387i	$0.747614\pi$
$480$		0			0
$481$			8.78365i			0.400500i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.645933	+	0.372930i	−0.0293303	+	0.0169339i
$486$		0			0
$487$	−0.423250	+	0.733091i	−0.0191793	+	0.0332195i	−0.875456	−	0.483298i	$-0.839439\pi$
$487$	−0.423250	+	0.733091i	−0.0191793	+	0.0332195i	0.856276	+	0.516518i	$0.172772\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.78204	+	1.02886i	0.0804225	+	0.0464319i	0.539672	−	0.841875i	$-0.318548\pi$
$491$	1.78204	+	1.02886i	0.0804225	+	0.0464319i	−0.459249	+	0.888307i	$0.651882\pi$
$492$		0			0
$493$		−	3.50250i		−	0.157745i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−36.3767	+	19.9314i	−1.63172	+	0.894045i
$498$		0			0
$499$	41.1863			1.84375			0.921877	−	0.387483i	$-0.126655\pi$
$499$	41.1863			1.84375			0.921877	+	0.387483i	$0.126655\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.48781			0.0663383			0.0331692	−	0.999450i	$-0.489440\pi$
$503$	1.48781			0.0663383			0.0331692	+	0.999450i	$0.489440\pi$
$504$		0			0
$505$	2.67549			0.119058
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.7882			−0.744123			−0.372062	−	0.928208i	$-0.621349\pi$
$509$	−16.7882			−0.744123			−0.372062	+	0.928208i	$0.621349\pi$
$510$		0			0
$511$	−0.0672325	+	3.00673i	−0.00297419	+	0.133010i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			2.75004i			0.121181i
$516$		0			0
$517$	−0.360559	−	0.208169i	−0.0158574	−	0.00915526i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.00777	+	1.74551i	−0.0441512	+	0.0764722i	−0.887257	−	0.461276i	$-0.847392\pi$
$521$	−1.00777	+	1.74551i	−0.0441512	+	0.0764722i	0.843105	+	0.537749i	$0.180725\pi$
$522$		0			0
$523$	37.4865	−	21.6429i	1.63917	−	0.946376i	0.658052	−	0.752973i	$-0.271381\pi$
$523$	37.4865	−	21.6429i	1.63917	−	0.946376i	0.981119	−	0.193403i	$-0.0619526\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	20.7688i		−	0.904704i
$528$		0			0
$529$	21.3958			0.930254
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.931059	−	0.537547i	0.0403286	−	0.0232837i
$534$		0			0
$535$	2.64325	−	1.52608i	0.114278	−	0.0659783i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−26.3635	−	16.8355i	−1.13556	−	0.725155i
$540$		0			0
$541$	12.3502	+	21.3912i	0.530977	+	0.919679i	0.999347	+	0.0361463i	$0.0115082\pi$
$541$	12.3502	+	21.3912i	0.530977	+	0.919679i	−0.468370	+	0.883533i	$0.655158\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.553783	−	0.959181i	0.0237215	−	0.0410868i
$546$		0			0
$547$	5.52320	+	9.56646i	0.236155	+	0.409032i	0.959608	−	0.281342i	$-0.0907794\pi$
$547$	5.52320	+	9.56646i	0.236155	+	0.409032i	−0.723453	+	0.690374i	$0.757446\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.90464	−	6.76304i	0.166343	−	0.288115i
$552$		0			0
$553$	−31.0477	−	0.694248i	−1.32028	−	0.0295224i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−22.3351	−	12.8952i	−0.946369	−	0.546386i	−0.0544176	−	0.998518i	$-0.517330\pi$
$557$	−22.3351	−	12.8952i	−0.946369	−	0.546386i	−0.891951	+	0.452132i	$0.850664\pi$
$558$		0			0
$559$			13.6256i			0.576300i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−18.9859	−	32.8846i	−0.800161	−	1.38592i	−0.919510	−	0.393067i	$-0.871414\pi$
$563$	−18.9859	−	32.8846i	−0.800161	−	1.38592i	0.119349	−	0.992852i	$-0.461919\pi$
$564$		0			0
$565$	1.22522	+	0.707381i	0.0515454	+	0.0297597i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−19.8834	−	11.4797i	−0.833555	−	0.481253i	0.0215131	−	0.999769i	$-0.493152\pi$
$569$	−19.8834	−	11.4797i	−0.833555	−	0.481253i	−0.855068	+	0.518515i	$0.826485\pi$
$570$		0			0
$571$	−5.91228	−	10.2404i	−0.247421	−	0.428546i	0.715388	−	0.698727i	$-0.246250\pi$
$571$	−5.91228	−	10.2404i	−0.247421	−	0.428546i	−0.962810	+	0.270181i	$0.912916\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			6.28048i			0.261914i
$576$		0			0
$577$	−22.4185	−	12.9433i	−0.933293	−	0.538837i	−0.0454415	−	0.998967i	$-0.514469\pi$
$577$	−22.4185	−	12.9433i	−0.933293	−	0.538837i	−0.887852	+	0.460130i	$0.847803\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	6.31743	−	10.3981i	0.262091	−	0.431387i
$582$		0			0
$583$	24.1294	−	41.7933i	0.999338	−	1.73090i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.28769	−	2.23034i	−0.0531487	−	0.0920562i	0.838227	−	0.545321i	$-0.183592\pi$
$587$	−1.28769	−	2.23034i	−0.0531487	−	0.0920562i	−0.891376	+	0.453265i	$0.850259\pi$
$588$		0			0
$589$	23.1534	−	40.1028i	0.954018	−	1.65241i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−11.0904	−	19.2092i	−0.455430	−	0.788828i	0.543283	−	0.839550i	$-0.317181\pi$
$593$	−11.0904	−	19.2092i	−0.455430	−	0.788828i	−0.998713	+	0.0507220i	$0.983848\pi$
$594$		0			0
$595$	1.72606	+	0.0385959i	0.0707615	+	0.00158228i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−22.0096	+	12.7072i	−0.899287	+	0.519204i	−0.876969	−	0.480547i	$-0.840438\pi$
$599$	−22.0096	+	12.7072i	−0.899287	+	0.519204i	−0.0223184	+	0.999751i	$0.507105\pi$
$600$		0			0
$601$	−3.04486	+	1.75795i	−0.124203	+	0.0717084i	−0.560814	−	0.827942i	$-0.689512\pi$
$601$	−3.04486	+	1.75795i	−0.124203	+	0.0717084i	0.436612	+	0.899650i	$0.356178\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.82224			−0.0740847
$606$		0			0
$607$			32.7626i			1.32979i	0.746936	+	0.664896i	$0.231524\pi$
$607$			32.7626i			1.32979i	−0.746936	+	0.664896i	$0.768476\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.117007	+	0.0675539i	−0.00473359	+	0.00273294i
$612$		0			0
$613$	−0.757167	+	1.31145i	−0.0305817	+	0.0529691i	−0.880911	−	0.473282i	$-0.843069\pi$
$613$	−0.757167	+	1.31145i	−0.0305817	+	0.0529691i	0.850329	+	0.526251i	$0.176403\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.52621	+	3.76791i	0.262735	+	0.151690i	0.625582	−	0.780159i	$-0.284862\pi$
$617$	6.52621	+	3.76791i	0.262735	+	0.151690i	−0.362846	+	0.931849i	$0.618195\pi$
$618$		0			0
$619$		−	32.6456i		−	1.31214i	−0.754702	−	0.656068i	$-0.772218\pi$
$619$		−	32.6456i		−	1.31214i	0.754702	−	0.656068i	$-0.227782\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−9.69033	+	15.9497i	−0.388235	+	0.639013i
$624$		0			0
$625$	24.3825			0.975299
$626$		0			0
$627$		0			0
$628$		0			0
$629$	19.4537			0.775672
$630$		0			0
$631$	6.79887			0.270659			0.135329	−	0.990801i	$-0.456791\pi$
$631$	6.79887			0.270659			0.135329	+	0.990801i	$0.456791\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.545976			−0.0216664
$636$		0			0
$637$	−9.00908	+	4.67746i	−0.356953	+	0.185328i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	32.4927i		−	1.28338i	−0.766962	−	0.641692i	$-0.778233\pi$
$641$		−	32.4927i		−	1.28338i	0.766962	−	0.641692i	$-0.221767\pi$
$642$		0			0
$643$	−20.5970	−	11.8917i	−0.812267	−	0.468963i	0.0354756	−	0.999371i	$-0.488705\pi$
$643$	−20.5970	−	11.8917i	−0.812267	−	0.468963i	−0.847742	+	0.530408i	$0.822039\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−11.1964	+	19.3928i	−0.440177	+	0.762410i	−0.997702	−	0.0677505i	$-0.978418\pi$
$647$	−11.1964	+	19.3928i	−0.440177	+	0.762410i	0.557525	+	0.830160i	$0.311751\pi$
$648$		0			0
$649$	−39.9725	+	23.0781i	−1.56906	+	0.905895i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	40.7245i		−	1.59367i	−0.604196	−	0.796836i	$-0.706506\pi$
$653$		−	40.7245i		−	1.59367i	0.604196	−	0.796836i	$-0.293494\pi$
$654$		0			0
$655$	1.24749			0.0487434
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−24.8786	+	14.3637i	−0.969134	+	0.559530i	−0.898972	−	0.438006i	$-0.855685\pi$
$659$	−24.8786	+	14.3637i	−0.969134	+	0.559530i	−0.0701619	+	0.997536i	$0.522352\pi$
$660$		0			0
$661$	32.3398	−	18.6714i	1.25787	−	0.726234i	0.285213	−	0.958464i	$-0.407936\pi$
$661$	32.3398	−	18.6714i	1.25787	−	0.726234i	0.972661	+	0.232230i	$0.0746023\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	3.28985	+	1.99876i	0.127575	+	0.0775086i
$666$		0			0
$667$	−0.690612	−	1.19617i	−0.0267406	−	0.0463161i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	18.9557	−	32.8323i	0.731777	−	1.26748i
$672$		0			0
$673$	−16.5131	−	28.6015i	−0.636532	−	1.10251i	−0.986188	−	0.165628i	$-0.947035\pi$
$673$	−16.5131	−	28.6015i	−0.636532	−	1.10251i	0.349656	−	0.936878i	$-0.386298\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	10.4381	−	18.0793i	0.401169	−	0.694845i	−0.592698	−	0.805424i	$-0.701937\pi$
$677$	10.4381	−	18.0793i	0.401169	−	0.694845i	0.993867	+	0.110580i	$0.0352707\pi$
$678$		0			0
$679$	−8.30056	−	5.04304i	−0.318546	−	0.193534i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.17377	−	0.677674i	−0.0449129	−	0.0259305i	0.477375	−	0.878699i	$-0.341588\pi$
$683$	−1.17377	−	0.677674i	−0.0449129	−	0.0259305i	−0.522288	+	0.852769i	$0.674922\pi$
$684$		0			0
$685$			0.870051i			0.0332430i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−7.83036	−	13.5626i	−0.298313	−	0.516693i
$690$		0			0
$691$	9.62041	+	5.55435i	0.365978	+	0.211297i	0.671700	−	0.740823i	$-0.265564\pi$
$691$	9.62041	+	5.55435i	0.365978	+	0.211297i	−0.305722	+	0.952121i	$0.598898\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.698894	−	0.403507i	−0.0265106	−	0.0153059i
$696$		0			0
$697$	−1.19054	−	2.06208i	−0.0450950	−	0.0781068i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	0.375966i		−	0.0142000i	−0.999975	−	0.00710002i	$-0.997740\pi$
$701$		−	0.375966i		−	0.0142000i	0.999975	−	0.00710002i	$-0.00226003\pi$
$702$		0			0
$703$	37.5635	+	21.6873i	1.41674	+	0.817953i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	16.7410	+	30.5540i	0.629612	+	1.14910i
$708$		0			0
$709$	−1.94936	+	3.37639i	−0.0732098	+	0.126803i	−0.900306	−	0.435257i	$-0.856658\pi$
$709$	−1.94936	+	3.37639i	−0.0732098	+	0.126803i	0.827097	+	0.562060i	$0.189991\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−4.09512	−	7.09296i	−0.153364	−	0.265634i
$714$		0			0
$715$	−0.658312	+	1.14023i	−0.0246195	+	0.0426422i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	24.4338	+	42.3205i	0.911225	+	1.57829i	0.812336	+	0.583190i	$0.198196\pi$
$719$	24.4338	+	42.3205i	0.911225	+	1.57829i	0.0988894	+	0.995098i	$0.468471\pi$
$720$		0			0
$721$	−31.4053	+	17.2075i	−1.16959	+	0.640840i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4.68318	+	2.70384i	−0.173929	+	0.100418i
$726$		0			0
$727$	11.8420	−	6.83700i	0.439196	−	0.253570i	−0.264060	−	0.964506i	$-0.585062\pi$
$727$	11.8420	−	6.83700i	0.439196	−	0.253570i	0.703257	+	0.710936i	$0.251728\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	30.1775			1.11615
$732$		0			0
$733$		−	16.1607i		−	0.596910i	−0.954424	−	0.298455i	$-0.903529\pi$
$733$		−	16.1607i		−	0.596910i	0.954424	−	0.298455i	$-0.0964713\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	31.1657	−	17.9935i	1.14800	−	0.662800i
$738$		0			0
$739$	15.7914	−	27.3515i	0.580895	−	1.00614i	−0.414478	−	0.910059i	$-0.636036\pi$
$739$	15.7914	−	27.3515i	0.580895	−	1.00614i	0.995374	−	0.0960807i	$-0.0306307\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−8.63924	−	4.98787i	−0.316943	−	0.182987i	0.333086	−	0.942896i	$-0.391910\pi$
$743$	−8.63924	−	4.98787i	−0.316943	−	0.182987i	−0.650029	+	0.759909i	$0.725243\pi$
$744$		0			0
$745$		−	0.941325i		−	0.0344875i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	33.9671	+	20.6369i	1.24113	+	0.754055i
$750$		0			0
$751$	20.9066			0.762892			0.381446	−	0.924391i	$-0.375426\pi$
$751$	20.9066			0.762892			0.381446	+	0.924391i	$0.375426\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	3.18884			0.116054
$756$		0			0
$757$	−50.5460			−1.83713			−0.918563	−	0.395274i	$-0.870650\pi$
$757$	−50.5460			−1.83713			−0.918563	+	0.395274i	$0.870650\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	20.8424			0.755535			0.377768	−	0.925900i	$-0.376692\pi$
$761$	20.8424			0.755535			0.377768	+	0.925900i	$0.376692\pi$
$762$		0			0
$763$	14.4189	+	0.322417i	0.522000	+	0.0116723i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			14.9784i			0.540838i
$768$		0			0
$769$	25.3167	+	14.6166i	0.912944	+	0.527088i	0.881377	−	0.472413i	$-0.156617\pi$
$769$	25.3167	+	14.6166i	0.912944	+	0.527088i	0.0315668	+	0.999502i	$0.489950\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−10.9472	+	18.9612i	−0.393745	+	0.681986i	−0.992940	−	0.118617i	$-0.962154\pi$
$773$	−10.9472	+	18.9612i	−0.393745	+	0.681986i	0.599195	+	0.800603i	$0.295487\pi$
$774$		0			0
$775$	−27.7699	+	16.0329i	−0.997523	+	0.575920i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	5.30893i		−	0.190212i
$780$		0			0
$781$	−70.0578			−2.50686
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.33203	+	0.769050i	−0.0475423	+	0.0274486i
$786$		0			0
$787$	−7.08328	+	4.08953i	−0.252492	+	0.145776i	−0.620905	−	0.783886i	$-0.713235\pi$
$787$	−7.08328	+	4.08953i	−0.252492	+	0.145776i	0.368413	+	0.929662i	$0.379901\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−0.411843	+	18.4182i	−0.0146435	+	0.654875i
$792$		0			0
$793$	−6.15142	−	10.6546i	−0.218443	−	0.378355i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−4.86546	+	8.42722i	−0.172343	+	0.298508i	−0.939239	−	0.343265i	$-0.888467\pi$
$797$	−4.86546	+	8.42722i	−0.172343	+	0.298508i	0.766895	+	0.641772i	$0.221801\pi$
$798$		0			0
$799$	0.149616	+	0.259143i	0.00529304	+	0.00916782i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.53979	+	4.39905i	−0.0896273	+	0.155239i
$804$		0			0
$805$	0.597094	−	0.327157i	0.0210448	−	0.0115308i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−36.2263	−	20.9153i	−1.27365	−	0.735341i	−0.297976	−	0.954574i	$-0.596311\pi$
$809$	−36.2263	−	20.9153i	−1.27365	−	0.735341i	−0.975673	+	0.219232i	$0.929645\pi$
$810$		0			0
$811$		−	40.7323i		−	1.43031i	−0.698968	−	0.715153i	$-0.746357\pi$
$811$		−	40.7323i		−	1.43031i	0.698968	−	0.715153i	$-0.253643\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.807539	+	1.39870i	0.0282869	+	0.0489943i
$816$		0			0
$817$	58.2701	+	33.6423i	2.03861	+	1.17699i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−19.3422	−	11.1672i	−0.675049	−	0.389740i	0.122938	−	0.992414i	$-0.460768\pi$
$821$	−19.3422	−	11.1672i	−0.675049	−	0.389740i	−0.797987	+	0.602675i	$0.794102\pi$
$822$		0			0
$823$	−13.5308	−	23.4360i	−0.471654	−	0.816929i	0.527820	−	0.849356i	$-0.323009\pi$
$823$	−13.5308	−	23.4360i	−0.471654	−	0.816929i	−0.999474	+	0.0324276i	$0.989676\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	22.1709i		−	0.770957i	−0.922717	−	0.385479i	$-0.874036\pi$
$827$		−	22.1709i		−	0.770957i	0.922717	−	0.385479i	$-0.125964\pi$
$828$		0			0
$829$	−32.2166	−	18.6003i	−1.11893	−	0.646013i	−0.177801	−	0.984066i	$-0.556898\pi$
$829$	−32.2166	−	18.6003i	−1.11893	−	0.646013i	−0.941127	+	0.338053i	$0.890232\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	10.3595	+	19.9530i	0.358935	+	0.691331i
$834$		0			0
$835$	0.350162	−	0.606499i	0.0121179	−	0.0209888i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−7.96294	−	13.7922i	−0.274911	−	0.476160i	0.695202	−	0.718815i	$-0.255315\pi$
$839$	−7.96294	−	13.7922i	−0.274911	−	0.476160i	−0.970113	+	0.242655i	$0.921982\pi$
$840$		0			0
$841$	−13.9054	+	24.0848i	−0.479495	+	0.830510i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.10703	−	1.91743i	−0.0380829	−	0.0659615i
$846$		0			0
$847$	−11.4021	−	20.8099i	−0.391781	−	0.715038i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	6.64384	−	3.83582i	0.227748	−	0.131490i
$852$		0			0
$853$	40.4364	−	23.3459i	1.38451	−	0.799350i	0.391824	−	0.920040i	$-0.371844\pi$
$853$	40.4364	−	23.3459i	1.38451	−	0.799350i	0.992690	+	0.120690i	$0.0385107\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	5.33848			0.182359			0.0911795	−	0.995834i	$-0.470936\pi$
$857$	5.33848			0.182359			0.0911795	+	0.995834i	$0.470936\pi$
$858$		0			0
$859$		−	10.0559i		−	0.343102i	−0.985175	−	0.171551i	$-0.945122\pi$
$859$		−	10.0559i		−	0.343102i	0.985175	−	0.171551i	$-0.0548779\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	32.7144	−	18.8877i	1.11361	−	0.642943i	0.173849	−	0.984772i	$-0.444380\pi$
$863$	32.7144	−	18.8877i	1.11361	−	0.642943i	0.939762	+	0.341829i	$0.111046\pi$
$864$		0			0
$865$	1.46654	−	2.54012i	0.0498639	−	0.0863668i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−45.4249	−	26.2261i	−1.54094	−	0.889659i
$870$		0			0
$871$		−	11.6783i		−	0.395706i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.57239	−	4.69486i	−0.0869626	−	0.158715i
$876$		0			0
$877$	−46.5264			−1.57109			−0.785543	−	0.618807i	$-0.787616\pi$
$877$	−46.5264			−1.57109			−0.785543	+	0.618807i	$0.787616\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−31.9474			−1.07633			−0.538167	−	0.842838i	$-0.680883\pi$
$881$	−31.9474			−1.07633			−0.538167	+	0.842838i	$0.680883\pi$
$882$		0			0
$883$	38.2919			1.28862			0.644312	−	0.764763i	$-0.277144\pi$
$883$	38.2919			1.28862			0.644312	+	0.764763i	$0.277144\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	40.6168			1.36378			0.681889	−	0.731455i	$-0.261159\pi$
$887$	40.6168			1.36378			0.681889	+	0.731455i	$0.261159\pi$
$888$		0			0
$889$	−3.41627	−	6.23502i	−0.114578	−	0.209116i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			0.667177i			0.0223262i
$894$		0			0
$895$	−4.00469	−	2.31211i	−0.133862	−	0.0772852i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.52602	−	6.10724i	0.117599	−	0.203688i
$900$		0			0
$901$	−30.0379	+	17.3424i	−1.00071	+	0.577760i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			1.81866i			0.0604543i
$906$		0			0
$907$	29.9969			0.996030			0.498015	−	0.867168i	$-0.334062\pi$
$907$	29.9969			0.996030			0.498015	+	0.867168i	$0.334062\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−34.2362	+	19.7663i	−1.13430	+	0.654886i	−0.945012	−	0.327036i	$-0.893950\pi$
$911$	−34.2362	+	19.7663i	−1.13430	+	0.654886i	−0.189284	+	0.981922i	$0.560617\pi$
$912$		0			0
$913$	17.7964	−	10.2748i	0.588976	−	0.340045i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	7.80576	+	14.2463i	0.257769	+	0.470453i
$918$		0			0
$919$	−9.74272	−	16.8749i	−0.321383	−	0.556651i	0.659391	−	0.751800i	$-0.270814\pi$
$919$	−9.74272	−	16.8749i	−0.321383	−	0.556651i	−0.980774	+	0.195149i	$0.937481\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−11.3674	+	19.6889i	−0.374163	+	0.648069i
$924$		0			0
$925$	−15.0178	−	26.0115i	−0.493781	−	0.855253i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	6.93060	−	12.0041i	0.227386	−	0.393843i	−0.729647	−	0.683824i	$-0.760316\pi$
$929$	6.93060	−	12.0041i	0.227386	−	0.393843i	0.957032	+	0.289981i	$0.0936489\pi$
$930$		0			0
$931$	−2.24061	+	50.0765i	−0.0734330	+	1.64119i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.52534	+	1.45801i	0.0825876	+	0.0476819i
$936$		0			0
$937$			5.38328i			0.175864i	0.996126	+	0.0879320i	$0.0280258\pi$
$937$			5.38328i			0.175864i	−0.996126	+	0.0879320i	$0.971974\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3.28619	−	5.69185i	−0.107127	−	0.185549i	0.807478	−	0.589897i	$-0.200832\pi$
$941$	−3.28619	−	5.69185i	−0.107127	−	0.185549i	−0.914605	+	0.404348i	$0.867498\pi$
$942$		0			0
$943$	−0.813188	−	0.469494i	−0.0264810	−	0.0152888i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−27.7081	−	15.9973i	−0.900392	−	0.519841i	−0.0230644	−	0.999734i	$-0.507342\pi$
$947$	−27.7081	−	15.9973i	−0.900392	−	0.519841i	−0.877327	+	0.479893i	$0.840676\pi$
$948$		0			0
$949$	0.824201	+	1.42756i	0.0267547	+	0.0463405i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	51.5312i		−	1.66926i	−0.550812	−	0.834629i	$-0.685682\pi$
$953$		−	51.5312i		−	1.66926i	0.550812	−	0.834629i	$-0.314318\pi$
$954$		0			0
$955$	4.31901	+	2.49358i	0.139760	+	0.0806903i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−9.93595	+	5.44407i	−0.320849	+	0.175798i
$960$		0			0
$961$	5.40825	−	9.36736i	0.174460	−	0.302173i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.463773	−	0.803278i	−0.0149294	−	0.0258584i
$966$		0			0
$967$	−6.01867	+	10.4246i	−0.193547	+	0.335234i	−0.946423	−	0.322929i	$-0.895333\pi$
$967$	−6.01867	+	10.4246i	−0.193547	+	0.335234i	0.752876	+	0.658162i	$0.228666\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	23.4783	+	40.6656i	0.753454	+	1.30502i	0.946139	+	0.323761i	$0.104947\pi$
$971$	23.4783	+	40.6656i	0.753454	+	1.30502i	−0.192685	+	0.981261i	$0.561719\pi$
$972$		0			0
$973$	0.234925	−	10.5062i	0.00753135	−	0.336812i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	28.4083	−	16.4015i	0.908863	−	0.524732i	0.0287976	−	0.999585i	$-0.490832\pi$
$977$	28.4083	−	16.4015i	0.908863	−	0.524732i	0.880065	+	0.474853i	$0.157499\pi$
$978$		0			0
$979$	−27.2980	+	15.7605i	−0.872448	+	0.503708i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	30.0145			0.957314			0.478657	−	0.878002i	$-0.341124\pi$
$983$	30.0145			0.957314			0.478657	+	0.878002i	$0.341124\pi$
$984$		0			0
$985$		−	2.46485i		−	0.0785368i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	10.3062	−	5.95029i	0.327718	−	0.189208i
$990$		0			0
$991$	−24.9364	+	43.1911i	−0.792131	+	1.37201i	0.132514	+	0.991181i	$0.457695\pi$
$991$	−24.9364	+	43.1911i	−0.792131	+	1.37201i	−0.924645	+	0.380831i	$0.875638\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.60624	−	1.50471i	−0.0826232	−	0.0477026i
$996$		0			0
$997$			1.48520i			0.0470368i	0.999723	+	0.0235184i	$0.00748683\pi$
$997$			1.48520i			0.0470368i	−0.999723	+	0.0235184i	$0.992513\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.df.e.17.11		48
3.2	odd	2		1008.2.df.e.689.22		48
4.3	odd	2		1512.2.cx.a.17.11		48
7.5	odd	6		3024.2.ca.e.2609.11		48
9.2	odd	6		3024.2.ca.e.2033.11		48
9.7	even	3		1008.2.ca.e.353.15		48
12.11	even	2		504.2.cx.a.185.3	yes	48
21.5	even	6		1008.2.ca.e.257.15		48
28.19	even	6		1512.2.bs.a.1097.11		48
36.7	odd	6		504.2.bs.a.353.10	yes	48
36.11	even	6		1512.2.bs.a.521.11		48
63.47	even	6	inner	3024.2.df.e.1601.11		48
63.61	odd	6		1008.2.df.e.929.22		48
84.47	odd	6		504.2.bs.a.257.10	✓	48
252.47	odd	6		1512.2.cx.a.89.11		48
252.187	even	6		504.2.cx.a.425.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.10	✓	48	84.47	odd	6
504.2.bs.a.353.10	yes	48	36.7	odd	6
504.2.cx.a.185.3	yes	48	12.11	even	2
504.2.cx.a.425.3	yes	48	252.187	even	6
1008.2.ca.e.257.15		48	21.5	even	6
1008.2.ca.e.353.15		48	9.7	even	3
1008.2.df.e.689.22		48	3.2	odd	2
1008.2.df.e.929.22		48	63.61	odd	6
1512.2.bs.a.521.11		48	36.11	even	6
1512.2.bs.a.1097.11		48	28.19	even	6
1512.2.cx.a.17.11		48	4.3	odd	2
1512.2.cx.a.89.11		48	252.47	odd	6
3024.2.ca.e.2033.11		48	9.2	odd	6
3024.2.ca.e.2609.11		48	7.5	odd	6
3024.2.df.e.17.11		48	1.1	even	1	trivial
3024.2.df.e.1601.11		48	63.47	even	6	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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.203178 q^{5} +(1.27132 + 2.32029i) q^{7} +4.46863i q^{11} +(1.25586 + 0.725070i) q^{13} +(1.60586 - 2.78143i) q^{17} +(6.20156 - 3.58047i) q^{19} -1.26655i q^{23} -4.95872 q^{25} +(0.944433 - 0.545269i) q^{29} +(5.60021 - 3.23328i) q^{31} +(0.258305 + 0.471432i) q^{35} +(3.02855 + 5.24561i) q^{37} +(0.370687 - 0.642048i) q^{41} +(4.69802 + 8.13721i) q^{43} +(-0.0465845 + 0.0806866i) q^{47} +(-3.76748 + 5.89967i) q^{49} +(-9.35260 - 5.39973i) q^{53} +0.907929i q^{55} +(5.16447 + 8.94512i) q^{59} +(-7.34727 - 4.24195i) q^{61} +(0.255163 + 0.147318i) q^{65} +(-4.02663 - 6.97432i) q^{67} +15.6777i q^{71} +(0.984428 + 0.568360i) q^{73} +(-10.3685 + 5.68108i) q^{77} +(-5.86893 + 10.1653i) q^{79} +(-2.29931 - 3.98252i) q^{83} +(0.326276 - 0.565127i) q^{85} +(3.52692 + 6.10881i) q^{89} +(-0.0857700 + 3.83575i) q^{91} +(1.26002 - 0.727474i) q^{95} +(-3.17914 + 1.83548i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{25} - 18 q^{29} - 18 q^{31} + 6 q^{41} + 6 q^{43} + 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} - 6 q^{79} + 18 q^{89} - 6 q^{91} - 54 q^{95}+O(q^{100}) \) 48 * q + 48 * q^25 - 18 * q^29 - 18 * q^31 + 6 * q^41 + 6 * q^43 + 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 - 6 * q^79 + 18 * q^89 - 6 * q^91 - 54 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more