LMFDB - Embedded newform 1512.2.cx.a.89.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1512,2,Mod(17,1512)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1512, 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("1512.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.cx (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$12.0733807856$
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			89.13
Character	$\chi$	$=$	1512.89
Dual form			1512.2.cx.a.17.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+0.542075 q^{5} +(-2.62378 - 0.340238i) q^{7} +0.769377i q^{11} +(2.96386 - 1.71119i) q^{13} +(-3.23477 - 5.60278i) q^{17} +(5.60413 + 3.23554i) q^{19} +0.115878i q^{23} -4.70615 q^{25} +(-4.40174 - 2.54135i) q^{29} +(4.01429 + 2.31765i) q^{31} +(-1.42229 - 0.184434i) q^{35} +(5.47518 - 9.48329i) q^{37} +(-4.04575 - 7.00745i) q^{41} +(3.32569 - 5.76026i) q^{43} +(-0.773085 - 1.33902i) q^{47} +(6.76848 + 1.78542i) q^{49} +(-0.221011 + 0.127601i) q^{53} +0.417060i q^{55} +(5.12056 - 8.86906i) q^{59} +(4.83167 - 2.78957i) q^{61} +(1.60664 - 0.927591i) q^{65} +(1.64175 - 2.84359i) q^{67} -5.67917i q^{71} +(-5.35354 + 3.09087i) q^{73} +(0.261771 - 2.01868i) q^{77} +(-2.01229 - 3.48540i) q^{79} +(-5.80057 + 10.0469i) q^{83} +(-1.75349 - 3.03713i) q^{85} +(-2.00832 + 3.47851i) q^{89} +(-8.35874 + 3.48136i) q^{91} +(3.03786 + 1.75391i) q^{95} +(-15.0653 - 8.69795i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$5$	0.542075			0.242423			0.121212	−	0.992627i	$-0.461322\pi$
$5$	0.542075			0.242423			0.121212	+	0.992627i	$0.461322\pi$
$6$		0			0
$7$	−2.62378	−	0.340238i	−0.991697	−	0.128598i
$7$	−2.62378	−	0.340238i	−0.991697	−	0.128598i
$8$		0			0
$9$		0			0
$10$		0			0
$11$			0.769377i			0.231976i	0.993251	+	0.115988i	$0.0370034\pi$
$11$			0.769377i			0.231976i	−0.993251	+	0.115988i	$0.962997\pi$
$12$		0			0
$13$	2.96386	−	1.71119i	0.822027	−	0.474598i	−0.0290877	−	0.999577i	$-0.509260\pi$
$13$	2.96386	−	1.71119i	0.822027	−	0.474598i	0.851115	+	0.524979i	$0.175927\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.23477	−	5.60278i	−0.784547	−	1.35887i	−0.929269	−	0.369403i	$-0.879562\pi$
$17$	−3.23477	−	5.60278i	−0.784547	−	1.35887i	0.144723	−	0.989472i	$-0.453771\pi$
$18$		0			0
$19$	5.60413	+	3.23554i	1.28567	+	0.742285i	0.977880	−	0.209168i	$-0.0670756\pi$
$19$	5.60413	+	3.23554i	1.28567	+	0.742285i	0.307795	+	0.951453i	$0.400409\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			0.115878i			0.0241621i	0.999927	+	0.0120811i	$0.00384562\pi$
$23$			0.115878i			0.0241621i	−0.999927	+	0.0120811i	$0.996154\pi$
$24$		0			0
$25$	−4.70615			−0.941231
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.40174	−	2.54135i	−0.817383	−	0.471916i	0.0321304	−	0.999484i	$-0.489771\pi$
$29$	−4.40174	−	2.54135i	−0.817383	−	0.471916i	−0.849513	+	0.527568i	$0.823104\pi$
$30$		0			0
$31$	4.01429	+	2.31765i	0.720987	+	0.416262i	0.815116	−	0.579298i	$-0.196673\pi$
$31$	4.01429	+	2.31765i	0.720987	+	0.416262i	−0.0941289	+	0.995560i	$0.530007\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.42229	−	0.184434i	−0.240410	−	0.0311751i
$36$		0			0
$37$	5.47518	−	9.48329i	0.900114	−	1.55904i	0.0727692	−	0.997349i	$-0.476816\pi$
$37$	5.47518	−	9.48329i	0.900114	−	1.55904i	0.827345	−	0.561694i	$-0.189850\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.04575	−	7.00745i	−0.631841	−	1.09438i	−0.987175	−	0.159641i	$-0.948966\pi$
$41$	−4.04575	−	7.00745i	−0.631841	−	1.09438i	0.355334	−	0.934739i	$-0.384367\pi$
$42$		0			0
$43$	3.32569	−	5.76026i	0.507162	−	0.878431i	−0.492803	−	0.870141i	$-0.664028\pi$
$43$	3.32569	−	5.76026i	0.507162	−	0.878431i	0.999966	−	0.00829006i	$-0.00263884\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.773085	−	1.33902i	−0.112766	−	0.195317i	0.804118	−	0.594469i	$-0.202638\pi$
$47$	−0.773085	−	1.33902i	−0.112766	−	0.195317i	−0.916885	+	0.399152i	$0.869304\pi$
$48$		0			0
$49$	6.76848	+	1.78542i	0.966925	+	0.255060i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.221011	+	0.127601i	−0.0303582	+	0.0175273i	−0.515102	−	0.857129i	$-0.672246\pi$
$53$	−0.221011	+	0.127601i	−0.0303582	+	0.0175273i	0.484744	+	0.874656i	$0.338913\pi$
$54$		0			0
$55$			0.417060i			0.0562364i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.12056	−	8.86906i	0.666640	−	1.15465i	−0.312198	−	0.950017i	$-0.601065\pi$
$59$	5.12056	−	8.86906i	0.666640	−	1.15465i	0.978838	−	0.204637i	$-0.0656013\pi$
$60$		0			0
$61$	4.83167	−	2.78957i	0.618632	−	0.357167i	−0.157704	−	0.987486i	$-0.550409\pi$
$61$	4.83167	−	2.78957i	0.618632	−	0.357167i	0.776336	+	0.630319i	$0.217076\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.60664	−	0.927591i	0.199279	−	0.115054i
$66$		0			0
$67$	1.64175	−	2.84359i	0.200571	−	0.347400i	−0.748141	−	0.663539i	$-0.769053\pi$
$67$	1.64175	−	2.84359i	0.200571	−	0.347400i	0.948713	+	0.316140i	$0.102387\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	5.67917i		−	0.673994i	−0.941506	−	0.336997i	$-0.890589\pi$
$71$		−	5.67917i		−	0.673994i	0.941506	−	0.336997i	$-0.109411\pi$
$72$		0			0
$73$	−5.35354	+	3.09087i	−0.626585	+	0.361759i	−0.779428	−	0.626492i	$-0.784490\pi$
$73$	−5.35354	+	3.09087i	−0.626585	+	0.361759i	0.152844	+	0.988250i	$0.451157\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.261771	−	2.01868i	0.0298316	−	0.230050i
$78$		0			0
$79$	−2.01229	−	3.48540i	−0.226401	−	0.392138i	0.730338	−	0.683086i	$-0.239363\pi$
$79$	−2.01229	−	3.48540i	−0.226401	−	0.392138i	−0.956739	+	0.290948i	$0.906029\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−5.80057	+	10.0469i	−0.636695	+	1.10279i	0.349458	+	0.936952i	$0.386366\pi$
$83$	−5.80057	+	10.0469i	−0.636695	+	1.10279i	−0.986153	+	0.165836i	$0.946968\pi$
$84$		0			0
$85$	−1.75349	−	3.03713i	−0.190192	−	0.329423i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.00832	+	3.47851i	−0.212881	+	0.368721i	−0.952615	−	0.304178i	$-0.901618\pi$
$89$	−2.00832	+	3.47851i	−0.212881	+	0.368721i	0.739734	+	0.672900i	$0.234951\pi$
$90$		0			0
$91$	−8.35874	+	3.48136i	−0.876234	+	0.364946i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.03786	+	1.75391i	0.311677	+	0.179947i
$96$		0			0
$97$	−15.0653	−	8.69795i	−1.52965	−	0.883143i	−0.999376	−	0.0353150i	$-0.988757\pi$
$97$	−15.0653	−	8.69795i	−1.52965	−	0.883143i	−0.530272	−	0.847828i	$-0.677910\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	16.5023			1.64204			0.821019	−	0.570902i	$-0.193406\pi$
$101$	16.5023			1.64204			0.821019	+	0.570902i	$0.193406\pi$
$102$		0			0
$103$			0.293992i			0.0289678i	0.999895	+	0.0144839i	$0.00461054\pi$
$103$			0.293992i			0.0289678i	−0.999895	+	0.0144839i	$0.995389\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.17327	−	1.83209i	−0.306772	−	0.177115i	0.338709	−	0.940891i	$-0.390010\pi$
$107$	−3.17327	−	1.83209i	−0.306772	−	0.177115i	−0.645481	+	0.763776i	$0.723343\pi$
$108$		0			0
$109$	1.26497	+	2.19099i	0.121162	+	0.209858i	0.920226	−	0.391387i	$-0.128005\pi$
$109$	1.26497	+	2.19099i	0.121162	+	0.209858i	−0.799064	+	0.601246i	$0.794671\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	11.9275	−	6.88637i	1.12205	−	0.647815i	0.180126	−	0.983644i	$-0.442350\pi$
$113$	11.9275	−	6.88637i	1.12205	−	0.647815i	0.941923	+	0.335828i	$0.109016\pi$
$114$		0			0
$115$			0.0628143i			0.00585746i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.58105	+	15.8011i	0.603284	+	1.44848i
$120$		0			0
$121$	10.4081			0.946187
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−5.26146			−0.470600
$126$		0			0
$127$	9.44974			0.838529			0.419265	−	0.907864i	$-0.362288\pi$
$127$	9.44974			0.838529			0.419265	+	0.907864i	$0.362288\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−12.5013			−1.09225			−0.546123	−	0.837705i	$-0.683897\pi$
$131$	−12.5013			−1.09225			−0.546123	+	0.837705i	$0.683897\pi$
$132$		0			0
$133$	−13.6032	−	10.3961i	−1.17954	−	0.901456i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	19.3033i		−	1.64919i	−0.565725	−	0.824594i	$-0.691404\pi$
$137$		−	19.3033i		−	1.64919i	0.565725	−	0.824594i	$-0.308596\pi$
$138$		0			0
$139$	0.863952	−	0.498803i	0.0732794	−	0.0423079i	−0.462913	−	0.886404i	$-0.653196\pi$
$139$	0.863952	−	0.498803i	0.0732794	−	0.0423079i	0.536192	+	0.844096i	$0.319862\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.31655	+	2.28033i	0.110095	+	0.190690i
$144$		0			0
$145$	−2.38607	−	1.37760i	−0.198153	−	0.114403i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			19.6506i			1.60984i	0.593383	+	0.804920i	$0.297792\pi$
$149$			19.6506i			1.60984i	−0.593383	+	0.804920i	$0.702208\pi$
$150$		0			0
$151$	17.0342			1.38622			0.693111	−	0.720831i	$-0.256240\pi$
$151$	17.0342			1.38622			0.693111	+	0.720831i	$0.256240\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.17604	+	1.25634i	0.174784	+	0.100912i
$156$		0			0
$157$	−0.977815	−	0.564542i	−0.0780381	−	0.0450553i	0.460473	−	0.887674i	$-0.347680\pi$
$157$	−0.977815	−	0.564542i	−0.0780381	−	0.0450553i	−0.538511	+	0.842618i	$0.681013\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.0394259	−	0.304037i	0.00310720	−	0.0239615i
$162$		0			0
$163$	−8.60142	+	14.8981i	−0.673715	+	1.16691i	0.303127	+	0.952950i	$0.401969\pi$
$163$	−8.60142	+	14.8981i	−0.673715	+	1.16691i	−0.976843	+	0.213959i	$0.931364\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.22256	−	3.84959i	−0.171987	−	0.297890i	0.767128	−	0.641495i	$-0.221685\pi$
$167$	−2.22256	−	3.84959i	−0.171987	−	0.297890i	−0.939114	+	0.343605i	$0.888352\pi$
$168$		0			0
$169$	−0.643682	+	1.11489i	−0.0495140	+	0.0857607i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.94291	−	17.2216i	−0.755946	−	1.30934i	−0.944903	−	0.327351i	$-0.893844\pi$
$173$	−9.94291	−	17.2216i	−0.755946	−	1.30934i	0.188957	−	0.981985i	$-0.439489\pi$
$174$		0			0
$175$	12.3479	+	1.60121i	0.933416	+	0.121040i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.71472	−	0.989994i	0.128164	−	0.0739956i	−0.434547	−	0.900649i	$-0.643092\pi$
$179$	1.71472	−	0.989994i	0.128164	−	0.0739956i	0.562711	+	0.826653i	$0.309758\pi$
$180$		0			0
$181$			5.68137i			0.422293i	0.977454	+	0.211146i	$0.0677197\pi$
$181$			5.68137i			0.422293i	−0.977454	+	0.211146i	$0.932280\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.96796	−	5.14065i	0.218209	−	0.377948i
$186$		0			0
$187$	4.31065	−	2.48876i	0.315226	−	0.181996i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.59419	−	2.07511i	0.260066	−	0.150149i	−0.364298	−	0.931282i	$-0.618691\pi$
$191$	3.59419	−	2.07511i	0.260066	−	0.150149i	0.624365	+	0.781133i	$0.285358\pi$
$192$		0			0
$193$	−2.93533	+	5.08413i	−0.211289	+	0.365964i	−0.952118	−	0.305730i	$-0.901100\pi$
$193$	−2.93533	+	5.08413i	−0.211289	+	0.365964i	0.740829	+	0.671694i	$0.234433\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	3.37912i		−	0.240753i	−0.992728	−	0.120376i	$-0.961590\pi$
$197$		−	3.37912i		−	0.240753i	0.992728	−	0.120376i	$-0.0384101\pi$
$198$		0			0
$199$	−4.03812	+	2.33141i	−0.286255	+	0.165269i	−0.636252	−	0.771482i	$-0.719516\pi$
$199$	−4.03812	+	2.33141i	−0.286255	+	0.165269i	0.349997	+	0.936751i	$0.386183\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	10.6846	+	8.16558i	0.749908	+	0.573111i
$204$		0			0
$205$	−2.19310	−	3.79856i	−0.153173	−	0.265303i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.48935	+	4.31168i	−0.172192	+	0.298245i
$210$		0			0
$211$	−3.09622	−	5.36281i	−0.213153	−	0.369191i	0.739547	−	0.673105i	$-0.235040\pi$
$211$	−3.09622	−	5.36281i	−0.213153	−	0.369191i	−0.952699	+	0.303914i	$0.901706\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.80277	−	3.12249i	0.122948	−	0.212952i
$216$		0			0
$217$	−9.74406	−	7.44682i	−0.661470	−	0.505523i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−19.1748	−	11.0706i	−1.28984	−	0.744688i
$222$		0			0
$223$	−8.84510	−	5.10672i	−0.592312	−	0.341971i	0.173699	−	0.984799i	$-0.444428\pi$
$223$	−8.84510	−	5.10672i	−0.592312	−	0.341971i	−0.766011	+	0.642827i	$0.777761\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−16.2479			−1.07841			−0.539205	−	0.842175i	$-0.681275\pi$
$227$	−16.2479			−1.07841			−0.539205	+	0.842175i	$0.681275\pi$
$228$		0			0
$229$		−	8.67789i		−	0.573451i	−0.958013	−	0.286726i	$-0.907433\pi$
$229$		−	8.67789i		−	0.573451i	0.958013	−	0.286726i	$-0.0925668\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	19.0308	+	10.9874i	1.24675	+	0.719811i	0.970460	−	0.241263i	$-0.0775617\pi$
$233$	19.0308	+	10.9874i	1.24675	+	0.719811i	0.276290	+	0.961074i	$0.410895\pi$
$234$		0			0
$235$	−0.419070	−	0.725851i	−0.0273371	−	0.0473493i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−14.3752	+	8.29955i	−0.929857	+	0.536853i	−0.886766	−	0.462218i	$-0.847054\pi$
$239$	−14.3752	+	8.29955i	−0.929857	+	0.536853i	−0.0430908	+	0.999071i	$0.513720\pi$
$240$		0			0
$241$			11.0022i			0.708716i	0.935110	+	0.354358i	$0.115301\pi$
$241$			11.0022i			0.708716i	−0.935110	+	0.354358i	$0.884699\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.66902	+	0.967831i	0.234405	+	0.0618325i
$246$		0			0
$247$	22.1465			1.40915
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−18.0406			−1.13871			−0.569356	−	0.822091i	$-0.692808\pi$
$251$	−18.0406			−1.13871			−0.569356	+	0.822091i	$0.692808\pi$
$252$		0			0
$253$	−0.0891535			−0.00560503
$254$		0			0
$255$		0			0
$256$		0			0
$257$	14.4064			0.898648			0.449324	−	0.893369i	$-0.351665\pi$
$257$	14.4064			0.898648			0.449324	+	0.893369i	$0.351665\pi$
$258$		0			0
$259$	−17.5923	+	23.0192i	−1.09313	+	1.43035i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			24.9490i			1.53842i	0.638997	+	0.769209i	$0.279350\pi$
$263$			24.9490i			1.53842i	−0.638997	+	0.769209i	$0.720650\pi$
$264$		0			0
$265$	−0.119805	+	0.0691692i	−0.00735954	+	0.00424903i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	11.0059	+	19.0627i	0.671040	+	1.16228i	0.977609	+	0.210428i	$0.0674856\pi$
$269$	11.0059	+	19.0627i	0.671040	+	1.16228i	−0.306569	+	0.951848i	$0.599181\pi$
$270$		0			0
$271$	22.7444	+	13.1315i	1.38162	+	0.797680i	0.992352	−	0.123443i	$-0.0393935\pi$
$271$	22.7444	+	13.1315i	1.38162	+	0.797680i	0.389271	+	0.921123i	$0.372727\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	3.62081i		−	0.218343i
$276$		0			0
$277$	4.76411			0.286248			0.143124	−	0.989705i	$-0.454285\pi$
$277$	4.76411			0.286248			0.143124	+	0.989705i	$0.454285\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−19.1963	−	11.0830i	−1.14515	−	0.661155i	−0.197452	−	0.980312i	$-0.563267\pi$
$281$	−19.1963	−	11.0830i	−1.14515	−	0.661155i	−0.947702	+	0.319158i	$0.896600\pi$
$282$		0			0
$283$	−2.51629	−	1.45278i	−0.149578	−	0.0863590i	0.423343	−	0.905970i	$-0.360857\pi$
$283$	−2.51629	−	1.45278i	−0.149578	−	0.0863590i	−0.572921	+	0.819611i	$0.694190\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.23098	+	19.7626i	0.485860	+	1.16655i
$288$		0			0
$289$	−12.4275	+	21.5250i	−0.731027	+	1.26618i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	13.9866	+	24.2255i	0.817104	+	1.41527i	0.907807	+	0.419388i	$0.137755\pi$
$293$	13.9866	+	24.2255i	0.817104	+	1.41527i	−0.0907025	+	0.995878i	$0.528911\pi$
$294$		0			0
$295$	2.77573	−	4.80770i	0.161609	−	0.279915i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.198288	+	0.343445i	0.0114673	+	0.0198619i
$300$		0			0
$301$	−10.6857	+	13.9821i	−0.615915	+	0.805917i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.61913	−	1.51215i	0.149971	−	0.0865857i
$306$		0			0
$307$			30.3968i			1.73484i	0.497579	+	0.867419i	$0.334223\pi$
$307$			30.3968i			1.73484i	−0.497579	+	0.867419i	$0.665777\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−13.9130	+	24.0980i	−0.788934	+	1.36647i	0.137686	+	0.990476i	$0.456034\pi$
$311$	−13.9130	+	24.0980i	−0.788934	+	1.36647i	−0.926620	+	0.375998i	$0.877300\pi$
$312$		0			0
$313$	0.0403324	−	0.0232859i	0.00227972	−	0.00131620i	−0.498860	−	0.866683i	$-0.666248\pi$
$313$	0.0403324	−	0.0232859i	0.00227972	−	0.00131620i	0.501139	+	0.865367i	$0.332914\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.35604	−	4.24701i	0.413156	−	0.238536i	−0.278989	−	0.960294i	$-0.589999\pi$
$317$	7.35604	−	4.24701i	0.413156	−	0.238536i	0.692145	+	0.721758i	$0.256666\pi$
$318$		0			0
$319$	1.95525	−	3.38660i	0.109473	−	0.189613i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	41.8649i		−	2.32943i
$324$		0			0
$325$	−13.9484	+	8.05311i	−0.773718	+	0.446706i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.57282	+	3.77634i	0.0867125	+	0.208196i
$330$		0			0
$331$	−3.62730	−	6.28268i	−0.199375	−	0.345327i	0.748951	−	0.662625i	$-0.230558\pi$
$331$	−3.62730	−	6.28268i	−0.199375	−	0.345327i	−0.948326	+	0.317298i	$0.897224\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.889950	−	1.54144i	0.0486232	−	0.0842178i
$336$		0			0
$337$	−4.82349	−	8.35454i	−0.262752	−	0.455101i	0.704220	−	0.709982i	$-0.251297\pi$
$337$	−4.82349	−	8.35454i	−0.262752	−	0.455101i	−0.966972	+	0.254881i	$0.917964\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.78315	+	3.08850i	−0.0965627	+	0.167252i
$342$		0			0
$343$	−17.1515	−	6.98745i	−0.926097	−	0.377287i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.3105	+	6.53014i	0.607182	+	0.350556i	0.771862	−	0.635791i	$-0.219326\pi$
$347$	11.3105	+	6.53014i	0.607182	+	0.350556i	−0.164680	+	0.986347i	$0.552659\pi$
$348$		0			0
$349$	−17.4929	−	10.0995i	−0.936372	−	0.540614i	−0.0475506	−	0.998869i	$-0.515142\pi$
$349$	−17.4929	−	10.0995i	−0.936372	−	0.540614i	−0.888821	+	0.458254i	$0.848475\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−4.10843			−0.218670			−0.109335	−	0.994005i	$-0.534872\pi$
$353$	−4.10843			−0.218670			−0.109335	+	0.994005i	$0.534872\pi$
$354$		0			0
$355$		−	3.07854i		−	0.163392i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	28.7322	+	16.5885i	1.51643	+	0.875510i	0.999814	+	0.0192910i	$0.00614090\pi$
$359$	28.7322	+	16.5885i	1.51643	+	0.875510i	0.516613	+	0.856219i	$0.327192\pi$
$360$		0			0
$361$	11.4375	+	19.8103i	0.601973	+	1.04265i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.90202	+	1.67548i	−0.151899	+	0.0876988i
$366$		0			0
$367$			3.17611i			0.165792i	0.996558	+	0.0828958i	$0.0264169\pi$
$367$			3.17611i			0.165792i	−0.996558	+	0.0828958i	$0.973583\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.623300	−	0.259601i	0.0323601	−	0.0134778i
$372$		0			0
$373$	20.9606			1.08530			0.542649	−	0.839960i	$-0.317422\pi$
$373$	20.9606			1.08530			0.542649	+	0.839960i	$0.317422\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−17.3949			−0.895881
$378$		0			0
$379$	−20.1198			−1.03348			−0.516742	−	0.856141i	$-0.672855\pi$
$379$	−20.1198			−1.03348			−0.516742	+	0.856141i	$0.672855\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−25.1676			−1.28601			−0.643003	−	0.765864i	$-0.722312\pi$
$383$	−25.1676			−1.28601			−0.643003	+	0.765864i	$0.722312\pi$
$384$		0			0
$385$	0.141900	−	1.09427i	0.00723187	−	0.0557694i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	20.0980i		−	1.01901i	−0.860468	−	0.509505i	$-0.829829\pi$
$389$		−	20.0980i		−	1.01901i	0.860468	−	0.509505i	$-0.170171\pi$
$390$		0			0
$391$	0.649237	−	0.374837i	0.0328333	−	0.0189563i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.09081	−	1.88935i	−0.0548848	−	0.0950633i
$396$		0			0
$397$	6.64273	+	3.83518i	0.333389	+	0.192482i	0.657345	−	0.753590i	$-0.271680\pi$
$397$	6.64273	+	3.83518i	0.333389	+	0.192482i	−0.323956	+	0.946072i	$0.605013\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			3.54909i			0.177233i	0.996066	+	0.0886165i	$0.0282446\pi$
$401$			3.54909i			0.177233i	−0.996066	+	0.0886165i	$0.971755\pi$
$402$		0			0
$403$	15.8637			0.790228
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.29622	+	4.21248i	0.361660	+	0.208805i
$408$		0			0
$409$	−2.98914	−	1.72578i	−0.147804	−	0.0853345i	0.424274	−	0.905534i	$-0.360529\pi$
$409$	−2.98914	−	1.72578i	−0.147804	−	0.0853345i	−0.572078	+	0.820199i	$0.693863\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−16.4528	+	21.5283i	−0.809590	+	1.05934i
$414$		0			0
$415$	−3.14434	+	5.44616i	−0.154350	+	0.267342i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−8.49112	−	14.7071i	−0.414818	−	0.718487i	0.580591	−	0.814195i	$-0.302822\pi$
$419$	−8.49112	−	14.7071i	−0.414818	−	0.718487i	−0.995409	+	0.0957088i	$0.969488\pi$
$420$		0			0
$421$	10.3437	−	17.9158i	0.504120	−	0.873162i	−0.495869	−	0.868398i	$-0.665150\pi$
$421$	10.3437	−	17.9158i	0.504120	−	0.873162i	0.999989	−	0.00476397i	$-0.00151642\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	15.2233	+	26.3676i	0.738440	+	1.27901i
$426$		0			0
$427$	−13.6264	+	5.67530i	−0.659426	+	0.274647i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	32.0588	−	18.5091i	1.54422	−	0.891554i	0.545651	−	0.838012i	$-0.316282\pi$
$431$	32.0588	−	18.5091i	1.54422	−	0.891554i	0.998566	−	0.0535418i	$-0.0170511\pi$
$432$		0			0
$433$		−	15.2206i		−	0.731453i	−0.930722	−	0.365727i	$-0.880821\pi$
$433$		−	15.2206i		−	0.731453i	0.930722	−	0.365727i	$-0.119179\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.374927	+	0.649392i	−0.0179352	+	0.0310646i
$438$		0			0
$439$	−28.4122	+	16.4038i	−1.35604	+	0.782909i	−0.989087	−	0.147331i	$-0.952932\pi$
$439$	−28.4122	+	16.4038i	−1.35604	+	0.782909i	−0.366951	+	0.930240i	$0.619598\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	20.5791	−	11.8813i	0.977740	−	0.564499i	0.0761532	−	0.997096i	$-0.475736\pi$
$443$	20.5791	−	11.8813i	0.977740	−	0.564499i	0.901587	+	0.432597i	$0.142403\pi$
$444$		0			0
$445$	−1.08866	+	1.88561i	−0.0516074	+	0.0893866i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			21.8105i			1.02930i	0.857400	+	0.514651i	$0.172079\pi$
$449$			21.8105i			1.02930i	−0.857400	+	0.514651i	$0.827921\pi$
$450$		0			0
$451$	5.39137	−	3.11271i	0.253870	−	0.146572i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−4.53106	+	1.88716i	−0.212420	+	0.0884715i
$456$		0			0
$457$	19.8532	+	34.3867i	0.928693	+	1.60854i	0.785511	+	0.618848i	$0.212400\pi$
$457$	19.8532	+	34.3867i	0.928693	+	1.60854i	0.143182	+	0.989696i	$0.454266\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.37073	+	12.7665i	−0.343289	+	0.594594i	−0.985041	−	0.172318i	$-0.944874\pi$
$461$	−7.37073	+	12.7665i	−0.343289	+	0.594594i	0.641752	+	0.766912i	$0.278208\pi$
$462$		0			0
$463$	−12.4381	−	21.5434i	−0.578046	−	1.00120i	−0.995703	−	0.0926000i	$-0.970482\pi$
$463$	−12.4381	−	21.5434i	−0.578046	−	1.00120i	0.417658	−	0.908604i	$-0.362851\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6.70092	+	11.6063i	−0.310081	+	0.537077i	−0.978380	−	0.206817i	$-0.933690\pi$
$467$	−6.70092	+	11.6063i	−0.310081	+	0.537077i	0.668298	+	0.743893i	$0.267023\pi$
$468$		0			0
$469$	−5.27509	+	6.90238i	−0.243581	+	0.318722i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.43181	+	2.55870i	0.203775	+	0.117649i
$474$		0			0
$475$	−26.3739	−	15.2270i	−1.21012	−	0.698661i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	41.1461			1.88001			0.940007	−	0.341154i	$-0.110818\pi$
$479$	41.1461			1.88001			0.940007	+	0.341154i	$0.110818\pi$
$480$		0			0
$481$		−	37.4762i		−	1.70877i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−8.16651	−	4.71494i	−0.370822	−	0.214094i
$486$		0			0
$487$	−14.7695	−	25.5814i	−0.669268	−	1.15921i	−0.978109	−	0.208092i	$-0.933275\pi$
$487$	−14.7695	−	25.5814i	−0.669268	−	1.15921i	0.308841	−	0.951114i	$-0.400059\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−8.53341	+	4.92676i	−0.385107	+	0.222342i	−0.680038	−	0.733177i	$-0.738037\pi$
$491$	−8.53341	+	4.92676i	−0.385107	+	0.222342i	0.294931	+	0.955519i	$0.404703\pi$
$492$		0			0
$493$			32.8827i			1.48096i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.93227	+	14.9009i	−0.0866741	+	0.668397i
$498$		0			0
$499$	−40.7751			−1.82534			−0.912671	−	0.408694i	$-0.865984\pi$
$499$	−40.7751			−1.82534			−0.912671	+	0.408694i	$0.865984\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	23.6750			1.05561			0.527807	−	0.849364i	$-0.323014\pi$
$503$	23.6750			1.05561			0.527807	+	0.849364i	$0.323014\pi$
$504$		0			0
$505$	8.94547			0.398068
$506$		0			0
$507$		0			0
$508$		0			0
$509$	28.7676			1.27510			0.637551	−	0.770408i	$-0.279948\pi$
$509$	28.7676			1.27510			0.637551	+	0.770408i	$0.279948\pi$
$510$		0			0
$511$	15.0982	−	6.28829i	0.667903	−	0.278178i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			0.159365i			0.00702248i
$516$		0			0
$517$	1.03021	−	0.594794i	0.0453087	−	0.0261590i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	3.64967	+	6.32142i	0.159895	+	0.276947i	0.934831	−	0.355094i	$-0.115551\pi$
$521$	3.64967	+	6.32142i	0.159895	+	0.276947i	−0.774936	+	0.632040i	$0.782218\pi$
$522$		0			0
$523$	−21.2167	−	12.2495i	−0.927742	−	0.535632i	−0.0416450	−	0.999132i	$-0.513260\pi$
$523$	−21.2167	−	12.2495i	−0.927742	−	0.535632i	−0.886097	+	0.463501i	$0.846593\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	29.9882i		−	1.30631i
$528$		0			0
$529$	22.9866			0.999416
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−23.9821	−	13.8461i	−1.03878	−	0.599740i
$534$		0			0
$535$	−1.72015	−	0.993131i	−0.0743687	−	0.0429368i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.37366	+	5.20751i	−0.0591678	+	0.224303i
$540$		0			0
$541$	−12.1854	+	21.1057i	−0.523891	+	0.907406i	0.475722	+	0.879596i	$0.342187\pi$
$541$	−12.1854	+	21.1057i	−0.523891	+	0.907406i	−0.999613	+	0.0278106i	$0.991146\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.685707	+	1.18768i	0.0293724	+	0.0508746i
$546$		0			0
$547$	19.3409	−	33.4994i	0.826957	−	1.43233i	−0.0734566	−	0.997298i	$-0.523403\pi$
$547$	19.3409	−	33.4994i	0.826957	−	1.43233i	0.900414	−	0.435034i	$-0.143264\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−16.4453	−	28.4840i	−0.700592	−	1.21346i
$552$		0			0
$553$	4.09396	+	9.82958i	0.174093	+	0.417996i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−5.55184	+	3.20536i	−0.235239	+	0.135815i	−0.612987	−	0.790093i	$-0.710032\pi$
$557$	−5.55184	+	3.20536i	−0.235239	+	0.135815i	0.377748	+	0.925909i	$0.376699\pi$
$558$		0			0
$559$		−	22.7635i		−	0.962792i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	8.47537	−	14.6798i	0.357194	−	0.618678i	−0.630297	−	0.776354i	$-0.717067\pi$
$563$	8.47537	−	14.6798i	0.357194	−	0.618678i	0.987491	+	0.157676i	$0.0504001\pi$
$564$		0			0
$565$	6.46562	−	3.73293i	0.272011	−	0.157046i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−10.8854	+	6.28471i	−0.456341	+	0.263469i	−0.710505	−	0.703693i	$-0.751533\pi$
$569$	−10.8854	+	6.28471i	−0.456341	+	0.263469i	0.254163	+	0.967161i	$0.418200\pi$
$570$		0			0
$571$	4.82080	−	8.34988i	0.201744	−	0.349431i	−0.747346	−	0.664435i	$-0.768672\pi$
$571$	4.82080	−	8.34988i	0.201744	−	0.349431i	0.949091	+	0.315003i	$0.102006\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	0.545337i		−	0.0227421i
$576$		0			0
$577$	20.9563	−	12.0991i	0.872421	−	0.503692i	0.00426870	−	0.999991i	$-0.498641\pi$
$577$	20.9563	−	12.0991i	0.872421	−	0.503692i	0.868152	+	0.496299i	$0.165308\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	18.6378	−	24.3873i	0.773225	−	1.01175i
$582$		0			0
$583$	−0.0981731	−	0.170041i	−0.00406592	−	0.00704237i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.5498	+	21.7368i	−0.517984	+	0.897175i	0.481798	+	0.876283i	$0.339984\pi$
$587$	−12.5498	+	21.7368i	−0.517984	+	0.897175i	−0.999782	+	0.0208923i	$0.993349\pi$
$588$		0			0
$589$	14.9977	+	25.9768i	0.617970	+	1.07035i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	19.1605	−	33.1869i	0.786826	−	1.36282i	−0.141076	−	0.989999i	$-0.545056\pi$
$593$	19.1605	−	33.1869i	0.786826	−	1.36282i	0.927902	−	0.372824i	$-0.121610\pi$
$594$		0			0
$595$	3.56743	+	8.56537i	0.146250	+	0.351146i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.10762	−	0.639484i	−0.0452561	−	0.0261286i	0.477201	−	0.878794i	$-0.341651\pi$
$599$	−1.10762	−	0.639484i	−0.0452561	−	0.0261286i	−0.522457	+	0.852665i	$0.674985\pi$
$600$		0			0
$601$	−31.2150	−	18.0220i	−1.27329	−	0.735133i	−0.297682	−	0.954665i	$-0.596214\pi$
$601$	−31.2150	−	18.0220i	−1.27329	−	0.735133i	−0.975605	+	0.219532i	$0.929547\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	5.64195			0.229378
$606$		0			0
$607$			45.1639i			1.83315i	0.399867	+	0.916573i	$0.369056\pi$
$607$			45.1639i			1.83315i	−0.399867	+	0.916573i	$0.630944\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.58264	−	2.64579i	−0.185394	−	0.107037i
$612$		0			0
$613$	−9.50638	−	16.4655i	−0.383959	−	0.665037i	0.607665	−	0.794193i	$-0.292106\pi$
$613$	−9.50638	−	16.4655i	−0.383959	−	0.665037i	−0.991624	+	0.129157i	$0.958773\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−17.2379	+	9.95232i	−0.693973	+	0.400665i	−0.805099	−	0.593141i	$-0.797888\pi$
$617$	−17.2379	+	9.95232i	−0.693973	+	0.400665i	0.111126	+	0.993806i	$0.464554\pi$
$618$		0			0
$619$			25.4529i			1.02304i	0.859272	+	0.511519i	$0.170917\pi$
$619$			25.4529i			1.02304i	−0.859272	+	0.511519i	$0.829083\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	6.45291	−	8.44355i	0.258530	−	0.338283i
$624$		0			0
$625$	20.6787			0.827147
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−70.8438			−2.82473
$630$		0			0
$631$	40.8171			1.62490			0.812452	−	0.583028i	$-0.198132\pi$
$631$	40.8171			1.62490			0.812452	+	0.583028i	$0.198132\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5.12247			0.203279
$636$		0			0
$637$	23.1160	−	6.29039i	0.915890	−	0.249234i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			9.98592i			0.394420i	0.980361	+	0.197210i	$0.0631881\pi$
$641$			9.98592i			0.394420i	−0.980361	+	0.197210i	$0.936812\pi$
$642$		0			0
$643$	−4.32793	+	2.49873i	−0.170677	+	0.0985403i	−0.582905	−	0.812540i	$-0.698084\pi$
$643$	−4.32793	+	2.49873i	−0.170677	+	0.0985403i	0.412228	+	0.911081i	$0.364751\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.04602	+	8.73996i	0.198379	+	0.343603i	0.948003	−	0.318261i	$-0.103099\pi$
$647$	5.04602	+	8.73996i	0.198379	+	0.343603i	−0.749624	+	0.661864i	$0.769766\pi$
$648$		0			0
$649$	6.82365	+	3.93964i	0.267852	+	0.154644i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			17.1169i			0.669835i	0.942247	+	0.334918i	$0.108708\pi$
$653$			17.1169i			0.669835i	−0.942247	+	0.334918i	$0.891292\pi$
$654$		0			0
$655$	−6.77666			−0.264786
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−12.7790	−	7.37798i	−0.497800	−	0.287405i	0.230004	−	0.973190i	$-0.426126\pi$
$659$	−12.7790	−	7.37798i	−0.497800	−	0.287405i	−0.727805	+	0.685784i	$0.759459\pi$
$660$		0			0
$661$	−26.0082	−	15.0158i	−1.01160	−	0.584048i	−0.0999403	−	0.994993i	$-0.531865\pi$
$661$	−26.0082	−	15.0158i	−1.01160	−	0.584048i	−0.911660	+	0.410946i	$0.865199\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−7.37393	−	5.63547i	−0.285949	−	0.218534i
$666$		0			0
$667$	0.294485	−	0.510063i	0.0114025	−	0.0197497i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.14623	+	3.71737i	0.0828542	+	0.143508i
$672$		0			0
$673$	18.1953	−	31.5152i	0.701378	−	1.21482i	−0.266605	−	0.963806i	$-0.585902\pi$
$673$	18.1953	−	31.5152i	0.701378	−	1.21482i	0.967983	−	0.251016i	$-0.0807648\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9.16096	+	15.8672i	0.352084	+	0.609828i	0.986614	−	0.163070i	$-0.0521398\pi$
$677$	9.16096	+	15.8672i	0.352084	+	0.609828i	−0.634530	+	0.772898i	$0.718806\pi$
$678$		0			0
$679$	36.5687	+	27.9473i	1.40338	+	1.07252i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	6.46067	−	3.73007i	0.247210	−	0.142727i	−0.371276	−	0.928523i	$-0.621080\pi$
$683$	6.46067	−	3.73007i	0.247210	−	0.142727i	0.618486	+	0.785796i	$0.287746\pi$
$684$		0			0
$685$		−	10.4638i		−	0.399802i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.436698	+	0.756383i	−0.0166369	+	0.0288159i
$690$		0			0
$691$	−15.1699	+	8.75833i	−0.577089	+	0.333182i	−0.759976	−	0.649952i	$-0.774789\pi$
$691$	−15.1699	+	8.75833i	−0.577089	+	0.333182i	0.182887	+	0.983134i	$0.441456\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.468327	−	0.270389i	0.0177646	−	0.0102564i
$696$		0			0
$697$	−26.1742	+	45.3350i	−0.991417	+	1.71718i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	37.8622i		−	1.43004i	−0.699106	−	0.715018i	$-0.746418\pi$
$701$		−	37.8622i		−	1.43004i	0.699106	−	0.715018i	$-0.253582\pi$
$702$		0			0
$703$	61.3672	−	35.4304i	2.31451	−	1.33628i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−43.2984	−	5.61469i	−1.62840	−	0.211162i
$708$		0			0
$709$	18.5507	+	32.1307i	0.696686	+	1.20670i	0.969609	+	0.244659i	$0.0786761\pi$
$709$	18.5507	+	32.1307i	0.696686	+	1.20670i	−0.272923	+	0.962036i	$0.587991\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.268563	+	0.465165i	−0.0100578	+	0.0174206i
$714$		0			0
$715$	0.713667	+	1.23611i	0.0266896	+	0.0462278i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	5.73941	−	9.94096i	0.214044	−	0.370735i	−0.738932	−	0.673780i	$-0.764670\pi$
$719$	5.73941	−	9.94096i	0.214044	−	0.370735i	0.952976	+	0.303044i	$0.0980031\pi$
$720$		0			0
$721$	0.100027	−	0.771370i	0.00372520	−	0.0287273i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	20.7153	+	11.9600i	0.769346	+	0.444182i
$726$		0			0
$727$	−13.1105	−	7.56936i	−0.486242	−	0.280732i	0.236772	−	0.971565i	$-0.423911\pi$
$727$	−13.1105	−	7.56936i	−0.486242	−	0.280732i	−0.723014	+	0.690833i	$0.757244\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−43.0313			−1.59157
$732$		0			0
$733$		−	9.20011i		−	0.339814i	−0.985460	−	0.169907i	$-0.945653\pi$
$733$		−	9.20011i		−	0.339814i	0.985460	−	0.169907i	$-0.0543467\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.18779	+	1.26312i	0.0805884	+	0.0465277i
$738$		0			0
$739$	−14.6669	−	25.4038i	−0.539529	−	0.934492i	−0.998929	−	0.0462628i	$-0.985269\pi$
$739$	−14.6669	−	25.4038i	−0.539529	−	0.934492i	0.459400	−	0.888230i	$-0.348065\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	33.9829	−	19.6200i	1.24671	−	0.719789i	0.276259	−	0.961083i	$-0.410905\pi$
$743$	33.9829	−	19.6200i	1.24671	−	0.719789i	0.970452	+	0.241294i	$0.0775719\pi$
$744$		0			0
$745$			10.6521i			0.390263i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	7.70264	+	5.88668i	0.281448	+	0.215094i
$750$		0			0
$751$	21.0068			0.766549			0.383274	−	0.923635i	$-0.374796\pi$
$751$	21.0068			0.766549			0.383274	+	0.923635i	$0.374796\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	9.23380			0.336052
$756$		0			0
$757$	12.1528			0.441703			0.220851	−	0.975307i	$-0.429116\pi$
$757$	12.1528			0.441703			0.220851	+	0.975307i	$0.429116\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−14.4805			−0.524919			−0.262459	−	0.964943i	$-0.584534\pi$
$761$	−14.4805			−0.524919			−0.262459	+	0.964943i	$0.584534\pi$
$762$		0			0
$763$	−2.57354	−	6.17906i	−0.0931684	−	0.223697i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	35.0489i		−	1.26554i
$768$		0			0
$769$	−6.13371	+	3.54130i	−0.221187	+	0.127702i	−0.606500	−	0.795084i	$-0.707427\pi$
$769$	−6.13371	+	3.54130i	−0.221187	+	0.127702i	0.385313	+	0.922786i	$0.374094\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−19.1640	−	33.1930i	−0.689280	−	1.19387i	−0.972071	−	0.234687i	$-0.924593\pi$
$773$	−19.1640	−	33.1930i	−0.689280	−	1.19387i	0.282791	−	0.959182i	$-0.408740\pi$
$774$		0			0
$775$	−18.8918	−	10.9072i	−0.678615	−	0.391799i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	52.3609i		−	1.87602i
$780$		0			0
$781$	4.36942			0.156350
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.530049	−	0.306024i	−0.0189183	−	0.0109225i
$786$		0			0
$787$	−13.5265	−	7.80954i	−0.482168	−	0.278380i	0.239151	−	0.970982i	$-0.423131\pi$
$787$	−13.5265	−	7.80954i	−0.482168	−	0.278380i	−0.721320	+	0.692602i	$0.756464\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−33.6383	+	14.0101i	−1.19604	+	0.498143i
$792$		0			0
$793$	9.54693	−	16.5358i	0.339022	−	0.587203i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	12.0230	+	20.8244i	0.425875	+	0.737637i	0.996502	−	0.0835726i	$-0.0266330\pi$
$797$	12.0230	+	20.8244i	0.425875	+	0.737637i	−0.570627	+	0.821210i	$0.693300\pi$
$798$		0			0
$799$	−5.00151	+	8.66286i	−0.176941	+	0.306470i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.37804	−	4.11889i	−0.0839193	−	0.145352i
$804$		0			0
$805$	0.0213718	−	0.164811i	0.000753257	−	0.00580883i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−25.2846	+	14.5980i	−0.888958	+	0.513240i	−0.873601	−	0.486642i	$-0.838222\pi$
$809$	−25.2846	+	14.5980i	−0.888958	+	0.513240i	−0.0153562	+	0.999882i	$0.504888\pi$
$810$		0			0
$811$		−	26.0991i		−	0.916464i	−0.888833	−	0.458232i	$-0.848483\pi$
$811$		−	26.0991i		−	0.916464i	0.888833	−	0.458232i	$-0.151517\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−4.66261	+	8.07589i	−0.163324	+	0.282886i
$816$		0			0
$817$	37.2751	−	21.5208i	1.30409	−	0.752917i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	47.6231	−	27.4952i	1.66206	−	0.959590i	0.690329	−	0.723496i	$-0.257466\pi$
$821$	47.6231	−	27.4952i	1.66206	−	0.959590i	0.971730	−	0.236094i	$-0.0758674\pi$
$822$		0			0
$823$	9.05785	−	15.6887i	0.315737	−	0.546872i	−0.663857	−	0.747860i	$-0.731082\pi$
$823$	9.05785	−	15.6887i	0.315737	−	0.546872i	0.979594	+	0.200987i	$0.0644150\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	38.1934i		−	1.32812i	−0.747681	−	0.664058i	$-0.768833\pi$
$827$		−	38.1934i		−	1.32812i	0.747681	−	0.664058i	$-0.231167\pi$
$828$		0			0
$829$	47.0722	−	27.1771i	1.63488	−	0.943901i	0.652327	−	0.757938i	$-0.273793\pi$
$829$	47.0722	−	27.1771i	1.63488	−	0.943901i	0.982557	−	0.185963i	$-0.0595404\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−11.8911	−	43.6977i	−0.412003	−	1.51404i
$834$		0			0
$835$	−1.20479	−	2.08677i	−0.0416936	−	0.0722155i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−13.3919	+	23.1955i	−0.462341	+	0.800798i	−0.999077	−	0.0429523i	$-0.986324\pi$
$839$	−13.3919	+	23.1955i	−0.462341	+	0.800798i	0.536736	+	0.843750i	$0.319657\pi$
$840$		0			0
$841$	−1.58312	−	2.74205i	−0.0545904	−	0.0945534i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.348924	+	0.604354i	−0.0120033	+	0.0207904i
$846$		0			0
$847$	−27.3085	−	3.54121i	−0.938331	−	0.121678i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.09890	+	0.634450i	0.0376698	+	0.0217487i
$852$		0			0
$853$	15.6735	+	9.04908i	0.536649	+	0.309835i	0.743720	−	0.668491i	$-0.233060\pi$
$853$	15.6735	+	9.04908i	0.536649	+	0.309835i	−0.207071	+	0.978326i	$0.566393\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−35.3122			−1.20624			−0.603120	−	0.797650i	$-0.706076\pi$
$857$	−35.3122			−1.20624			−0.603120	+	0.797650i	$0.706076\pi$
$858$		0			0
$859$		−	23.2786i		−	0.794254i	−0.917764	−	0.397127i	$-0.870007\pi$
$859$		−	23.2786i		−	0.794254i	0.917764	−	0.397127i	$-0.129993\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−28.3933	−	16.3929i	−0.966520	−	0.558020i	−0.0683462	−	0.997662i	$-0.521772\pi$
$863$	−28.3933	−	16.3929i	−0.966520	−	0.558020i	−0.898173	+	0.439641i	$0.855106\pi$
$864$		0			0
$865$	−5.38980	−	9.33541i	−0.183259	−	0.317414i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.68158	−	1.54821i	0.0909665	−	0.0525195i
$870$		0			0
$871$		−	11.2373i		−	0.380763i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	13.8049	+	1.79015i	0.466692	+	0.0605181i
$876$		0			0
$877$	21.5376			0.727273			0.363636	−	0.931541i	$-0.381535\pi$
$877$	21.5376			0.727273			0.363636	+	0.931541i	$0.381535\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	22.9322			0.772606			0.386303	−	0.922372i	$-0.373752\pi$
$881$	22.9322			0.772606			0.386303	+	0.922372i	$0.373752\pi$
$882$		0			0
$883$	31.8225			1.07091			0.535455	−	0.844564i	$-0.320140\pi$
$883$	31.8225			1.07091			0.535455	+	0.844564i	$0.320140\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	22.2271			0.746312			0.373156	−	0.927769i	$-0.378276\pi$
$887$	22.2271			0.746312			0.373156	+	0.927769i	$0.378276\pi$
$888$		0			0
$889$	−24.7941	−	3.21516i	−0.831567	−	0.107833i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	10.0054i		−	0.334818i
$894$		0			0
$895$	0.929507	−	0.536651i	0.0310700	−	0.0179383i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−11.7799	−	20.4034i	−0.392881	−	0.680491i
$900$		0			0
$901$	1.42984	+	0.825518i	0.0476349	+	0.0275020i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			3.07973i			0.102374i
$906$		0			0
$907$	39.8198			1.32219			0.661097	−	0.750301i	$-0.270091\pi$
$907$	39.8198			1.32219			0.661097	+	0.750301i	$0.270091\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5.87819	−	3.39378i	−0.194753	−	0.112441i	0.399453	−	0.916754i	$-0.369200\pi$
$911$	−5.87819	−	3.39378i	−0.194753	−	0.112441i	−0.594206	+	0.804313i	$0.702534\pi$
$912$		0			0
$913$	−7.72984	−	4.46282i	−0.255820	−	0.147698i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	32.8008	+	4.25342i	1.08318	+	0.140460i
$918$		0			0
$919$	14.0173	−	24.2787i	0.462389	−	0.800882i	−0.536690	−	0.843779i	$-0.680326\pi$
$919$	14.0173	−	24.2787i	0.462389	−	0.800882i	0.999079	+	0.0428977i	$0.0136590\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−9.71812	−	16.8323i	−0.319876	−	0.554041i
$924$		0			0
$925$	−25.7670	+	44.6298i	−0.847215	+	1.46742i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	8.87040	+	15.3640i	0.291028	+	0.504076i	0.974053	−	0.226319i	$-0.0726693\pi$
$929$	8.87040	+	15.3640i	0.291028	+	0.504076i	−0.683025	+	0.730395i	$0.739336\pi$
$930$		0			0
$931$	32.1546	+	31.9054i	1.05382	+	1.04566i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.33670	−	1.34909i	0.0764182	−	0.0441200i
$936$		0			0
$937$			10.2459i			0.334719i	0.985896	+	0.167360i	$0.0535241\pi$
$937$			10.2459i			0.334719i	−0.985896	+	0.167360i	$0.946476\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−4.99827	+	8.65726i	−0.162939	+	0.282219i	−0.935921	−	0.352209i	$-0.885431\pi$
$941$	−4.99827	+	8.65726i	−0.162939	+	0.282219i	0.772982	+	0.634427i	$0.218764\pi$
$942$		0			0
$943$	0.812006	−	0.468812i	0.0264426	−	0.0152666i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	41.7852	−	24.1247i	1.35784	−	0.783948i	0.368505	−	0.929626i	$-0.379870\pi$
$947$	41.7852	−	24.1247i	1.35784	−	0.783948i	0.989332	+	0.145678i	$0.0465363\pi$
$948$		0			0
$949$	−10.5781	+	18.3218i	−0.343380	+	0.594751i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			40.4708i			1.31098i	0.755205	+	0.655489i	$0.227537\pi$
$953$			40.4708i			1.31098i	−0.755205	+	0.655489i	$0.772463\pi$
$954$		0			0
$955$	1.94832	−	1.12486i	0.0630462	−	0.0363997i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−6.56769	+	50.6476i	−0.212082	+	1.63549i
$960$		0			0
$961$	−4.75701	−	8.23938i	−0.153452	−	0.265787i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.59117	+	2.75598i	−0.0512215	+	0.0887182i
$966$		0			0
$967$	−14.6566	−	25.3860i	−0.471325	−	0.816359i	0.528137	−	0.849159i	$-0.322891\pi$
$967$	−14.6566	−	25.3860i	−0.471325	−	0.816359i	−0.999462	+	0.0328000i	$0.989558\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−9.02830	+	15.6375i	−0.289732	+	0.501831i	−0.973746	−	0.227639i	$-0.926900\pi$
$971$	−9.02830	+	15.6375i	−0.289732	+	0.501831i	0.684014	+	0.729469i	$0.260233\pi$
$972$		0			0
$973$	−2.43653	+	1.01480i	−0.0781117	+	0.0325330i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−33.9886	−	19.6233i	−1.08739	−	0.627805i	−0.154510	−	0.987991i	$-0.549380\pi$
$977$	−33.9886	−	19.6233i	−1.08739	−	0.627805i	−0.932880	+	0.360186i	$0.882713\pi$
$978$		0			0
$979$	−2.67628	−	1.54515i	−0.0855344	−	0.0493833i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	26.4668			0.844159			0.422079	−	0.906559i	$-0.361300\pi$
$983$	26.4668			0.844159			0.422079	+	0.906559i	$0.361300\pi$
$984$		0			0
$985$		−	1.83174i		−	0.0583640i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.667484	+	0.385372i	0.0212248	+	0.0122541i
$990$		0			0
$991$	7.32864	+	12.6936i	0.232802	+	0.403225i	0.958632	−	0.284650i	$-0.0918773\pi$
$991$	7.32864	+	12.6936i	0.232802	+	0.403225i	−0.725830	+	0.687875i	$0.758544\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.18896	+	1.26380i	−0.0693948	+	0.0400651i
$996$		0			0
$997$		−	3.93872i		−	0.124741i	−0.998053	−	0.0623703i	$-0.980134\pi$
$997$		−	3.93872i		−	0.124741i	0.998053	−	0.0623703i	$-0.0198660\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.cx.a.89.13		48
3.2	odd	2		504.2.cx.a.425.1	yes	48
4.3	odd	2		3024.2.df.e.1601.13		48
7.3	odd	6		1512.2.bs.a.521.13		48
9.4	even	3		504.2.bs.a.257.8	✓	48
9.5	odd	6		1512.2.bs.a.1097.13		48
12.11	even	2		1008.2.df.e.929.24		48
21.17	even	6		504.2.bs.a.353.8	yes	48
28.3	even	6		3024.2.ca.e.2033.13		48
36.23	even	6		3024.2.ca.e.2609.13		48
36.31	odd	6		1008.2.ca.e.257.17		48
63.31	odd	6		504.2.cx.a.185.1	yes	48
63.59	even	6	inner	1512.2.cx.a.17.13		48
84.59	odd	6		1008.2.ca.e.353.17		48
252.31	even	6		1008.2.df.e.689.24		48
252.59	odd	6		3024.2.df.e.17.13		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.8	✓	48	9.4	even	3
504.2.bs.a.353.8	yes	48	21.17	even	6
504.2.cx.a.185.1	yes	48	63.31	odd	6
504.2.cx.a.425.1	yes	48	3.2	odd	2
1008.2.ca.e.257.17		48	36.31	odd	6
1008.2.ca.e.353.17		48	84.59	odd	6
1008.2.df.e.689.24		48	252.31	even	6
1008.2.df.e.929.24		48	12.11	even	2
1512.2.bs.a.521.13		48	7.3	odd	6
1512.2.bs.a.1097.13		48	9.5	odd	6
1512.2.cx.a.17.13		48	63.59	even	6	inner
1512.2.cx.a.89.13		48	1.1	even	1	trivial
3024.2.ca.e.2033.13		48	28.3	even	6
3024.2.ca.e.2609.13		48	36.23	even	6
3024.2.df.e.17.13		48	252.59	odd	6
3024.2.df.e.1601.13		48	4.3	odd	2

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.cx (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.542075 q^{5} +(-2.62378 - 0.340238i) q^{7} +0.769377i q^{11} +(2.96386 - 1.71119i) q^{13} +(-3.23477 - 5.60278i) q^{17} +(5.60413 + 3.23554i) q^{19} +0.115878i q^{23} -4.70615 q^{25} +(-4.40174 - 2.54135i) q^{29} +(4.01429 + 2.31765i) q^{31} +(-1.42229 - 0.184434i) q^{35} +(5.47518 - 9.48329i) q^{37} +(-4.04575 - 7.00745i) q^{41} +(3.32569 - 5.76026i) q^{43} +(-0.773085 - 1.33902i) q^{47} +(6.76848 + 1.78542i) q^{49} +(-0.221011 + 0.127601i) q^{53} +0.417060i q^{55} +(5.12056 - 8.86906i) q^{59} +(4.83167 - 2.78957i) q^{61} +(1.60664 - 0.927591i) q^{65} +(1.64175 - 2.84359i) q^{67} -5.67917i q^{71} +(-5.35354 + 3.09087i) q^{73} +(0.261771 - 2.01868i) q^{77} +(-2.01229 - 3.48540i) q^{79} +(-5.80057 + 10.0469i) q^{83} +(-1.75349 - 3.03713i) q^{85} +(-2.00832 + 3.47851i) q^{89} +(-8.35874 + 3.48136i) q^{91} +(3.03786 + 1.75391i) q^{95} +(-15.0653 - 8.69795i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{25} - 18 q^{29} + 18 q^{31} + 6 q^{41} - 6 q^{43} - 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} + 6 q^{79} + 18 q^{89} + 6 q^{91} + 54 q^{95}+O(q^{100}) \) 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