LMFDB - Embedded newform 5184.2.d.e.2593.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5184,2,Mod(2593,5184)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5184, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5184.2593");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5184 = 2^{6} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5184.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$41.3944484078$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 576)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			2593.4
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	5184.2593
Dual form			5184.2.d.e.2593.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+O(q^{10})$	$q+5.44949i q^{11} +1.89898 q^{17} +8.34847i q^{19} +5.00000 q^{25} -12.7980 q^{41} -2.34847i q^{43} -7.00000 q^{49} -9.24745i q^{59} -14.3485i q^{67} +13.6969 q^{73} +18.0000i q^{83} -18.0000 q^{89} -19.6969 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q+O(q^{10}) $ 4 * q	$ 4 q - 12 q^{17} + 20 q^{25} - 12 q^{41} - 28 q^{49} - 4 q^{73} - 72 q^{89} - 20 q^{97}+O(q^{100}) $ 4 * q - 12 * q^17 + 20 * q^25 - 12 * q^41 - 28 * q^49 - 4 * q^73 - 72 * q^89 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5184\mathbb{Z}\right)^\times$.

$n$	$325$	$1217$	$2431$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	0	0
$2$	0	0
$3$	0	0
$3$	0	0
$4$	0	0
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	5.44949i	1.64308i	0.570149	+	0.821541i	$0.306886\pi$
$11$	5.44949i	1.64308i	−0.570149	+	0.821541i	$0.693114\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	1.89898	0.460570	0.230285	−	0.973123i	$-0.426034\pi$
$17$	1.89898	0.460570	0.230285	+	0.973123i	$0.426034\pi$
$18$	0	0
$19$	8.34847i	1.91527i	0.287984	+	0.957635i	$0.407015\pi$
$19$	8.34847i	1.91527i	−0.287984	+	0.957635i	$0.592985\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	5.00000	1.00000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−12.7980	−1.99871	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$	−12.7980	−1.99871	−0.999353	+	0.0359748i	$0.988546\pi$
$42$	0	0
$43$	− 2.34847i	− 0.358138i	−0.983836	−	0.179069i	$-0.942691\pi$
$43$	− 2.34847i	− 0.358138i	0.983836	−	0.179069i	$-0.0573086\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	− 9.24745i	− 1.20392i	−0.798528	−	0.601958i	$-0.794388\pi$
$59$	− 9.24745i	− 1.20392i	0.798528	−	0.601958i	$-0.205612\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	− 14.3485i	− 1.75294i	−0.481452	−	0.876472i	$-0.659891\pi$
$67$	− 14.3485i	− 1.75294i	0.481452	−	0.876472i	$-0.340109\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	13.6969	1.60311	0.801553	−	0.597924i	$-0.204008\pi$
$73$	13.6969	1.60311	0.801553	+	0.597924i	$0.204008\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	18.0000i	1.97576i	0.155230	+	0.987878i	$0.450388\pi$
$83$	18.0000i	1.97576i	−0.155230	+	0.987878i	$0.549612\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	−18.0000	−1.90800	−0.953998	−	0.299813i	$-0.903076\pi$
$89$	−18.0000	−1.90800	−0.953998	+	0.299813i	$0.903076\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−19.6969	−1.99992	−0.999961	−	0.00888289i	$-0.997172\pi$
$97$	−19.6969	−1.99992	−0.999961	+	0.00888289i	$0.997172\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	20.1464i	1.94763i	0.227345	+	0.973814i	$0.426996\pi$
$107$	20.1464i	1.94763i	−0.227345	+	0.973814i	$0.573004\pi$
$108$	0	0
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−18.0000	−1.69330	−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000	−1.69330	−0.846649	+	0.532152i	$0.821383\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−18.6969	−1.69972
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	18.0000i	1.57267i	0.617802	+	0.786334i	$0.288023\pi$
$131$	18.0000i	1.57267i	−0.617802	+	0.786334i	$0.711977\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	16.5959	1.41788	0.708942	−	0.705266i	$-0.249173\pi$
$137$	16.5959	1.41788	0.708942	+	0.705266i	$0.249173\pi$
$138$	0	0
$139$	− 3.65153i	− 0.309719i	−0.987937	−	0.154859i	$-0.950508\pi$
$139$	− 3.65153i	− 0.309719i	0.987937	−	0.154859i	$-0.0494925\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	− 2.00000i	− 0.156652i	−0.996928	−	0.0783260i	$-0.975042\pi$
$163$	− 2.00000i	− 0.156652i	0.996928	−	0.0783260i	$-0.0249575\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	13.0000	1.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	0	0
$179$	18.0000i	1.34538i	0.739923	+	0.672692i	$0.234862\pi$
$179$	18.0000i	1.34538i	−0.739923	+	0.672692i	$0.765138\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	10.3485i	0.756755i
$188$	0	0
$189$	0	0
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	25.6969	1.84971	0.924853	−	0.380325i	$-0.124188\pi$
$193$	25.6969	1.84971	0.924853	+	0.380325i	$0.124188\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	−45.4949	−3.14695
$210$	0	0
$211$	14.0000i	0.963800i	0.876226	+	0.481900i	$0.160053\pi$
$211$	14.0000i	0.963800i	−0.876226	+	0.481900i	$0.839947\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	12.5505i	0.833007i	0.909134	+	0.416503i	$0.136745\pi$
$227$	12.5505i	0.833007i	−0.909134	+	0.416503i	$0.863255\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−19.8990	−1.30363	−0.651813	−	0.758380i	$-0.725991\pi$
$233$	−19.8990	−1.30363	−0.651813	+	0.758380i	$0.725991\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	1.69694	0.109309	0.0546547	−	0.998505i	$-0.482594\pi$
$241$	1.69694	0.109309	0.0546547	+	0.998505i	$0.482594\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	− 23.9444i	− 1.51136i	−0.654943	−	0.755678i	$-0.727307\pi$
$251$	− 23.9444i	− 1.51136i	0.654943	−	0.755678i	$-0.272693\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−5.20204	−0.324494	−0.162247	−	0.986750i	$-0.551874\pi$
$257$	−5.20204	−0.324494	−0.162247	+	0.986750i	$0.551874\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	27.2474i	1.64308i
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	0	0
$283$	22.0000i	1.30776i	0.756596	+	0.653882i	$0.226861\pi$
$283$	22.0000i	1.30776i	−0.756596	+	0.653882i	$0.773139\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−13.3939	−0.787875
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	9.65153i	0.550842i	0.961324	+	0.275421i	$0.0888172\pi$
$307$	9.65153i	0.550842i	−0.961324	+	0.275421i	$0.911183\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	24.3939	1.37882	0.689412	−	0.724370i	$-0.257869\pi$
$313$	24.3939	1.37882	0.689412	+	0.724370i	$0.257869\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	15.8536i	0.882116i
$324$	0	0
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	− 26.0000i	− 1.42909i	−0.699590	−	0.714545i	$-0.746634\pi$
$331$	− 26.0000i	− 1.42909i	0.699590	−	0.714545i	$-0.253366\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	36.3939	1.98250	0.991250	−	0.131995i	$-0.0421382\pi$
$337$	36.3939	1.98250	0.991250	+	0.131995i	$0.0421382\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	34.8434i	1.87049i	0.354001	+	0.935245i	$0.384821\pi$
$347$	34.8434i	1.87049i	−0.354001	+	0.935245i	$0.615179\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	−34.5959	−1.84135	−0.920677	−	0.390324i	$-0.872363\pi$
$353$	−34.5959	−1.84135	−0.920677	+	0.390324i	$0.872363\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	−50.6969	−2.66826
$362$	0	0
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	− 26.3485i	− 1.35343i	−0.736245	−	0.676715i	$-0.763403\pi$
$379$	− 26.3485i	− 1.35343i	0.736245	−	0.676715i	$-0.236597\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	0	0
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	31.2929	1.56269	0.781345	−	0.624099i	$-0.214534\pi$
$401$	31.2929	1.56269	0.781345	+	0.624099i	$0.214534\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−18.3939	−0.909519	−0.454759	−	0.890614i	$-0.650275\pi$
$409$	−18.3939	−0.909519	−0.454759	+	0.890614i	$0.650275\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	18.0000i	0.879358i	0.898155	+	0.439679i	$0.144908\pi$
$419$	18.0000i	0.879358i	−0.898155	+	0.439679i	$0.855092\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	9.49490	0.460570
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	4.30306	0.206792	0.103396	−	0.994640i	$-0.467029\pi$
$433$	4.30306	0.206792	0.103396	+	0.994640i	$0.467029\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	− 23.4495i	− 1.11412i	−0.830473	−	0.557059i	$-0.811930\pi$
$443$	− 23.4495i	− 1.11412i	0.830473	−	0.557059i	$-0.188070\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	16.1010	0.759854	0.379927	−	0.925016i	$-0.375949\pi$
$449$	16.1010	0.759854	0.379927	+	0.925016i	$0.375949\pi$
$450$	0	0
$451$	− 69.7423i	− 3.28404i
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−42.3939	−1.98310	−0.991551	−	0.129718i	$-0.958593\pi$
$457$	−42.3939	−1.98310	−0.991551	+	0.129718i	$0.958593\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	0	0		−	1.00000i	$-0.5\pi$
$463$	0	0			1.00000i	$0.5\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	41.9444i	1.94095i	0.241192	+	0.970477i	$0.422462\pi$
$467$	41.9444i	1.94095i	−0.241192	+	0.970477i	$0.577538\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	12.7980	0.588451
$474$	0	0
$475$	41.7423i	1.91527i
$476$	0	0
$477$	0	0
$478$	0	0
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	0	0		−	1.00000i	$-0.5\pi$
$487$	0	0			1.00000i	$0.5\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	− 8.75255i	− 0.394997i	−0.980303	−	0.197499i	$-0.936718\pi$
$491$	− 8.75255i	− 0.394997i	0.980303	−	0.197499i	$-0.0632818\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	29.7423i	1.33145i	0.746197	+	0.665725i	$0.231878\pi$
$499$	29.7423i	1.33145i	−0.746197	+	0.665725i	$0.768122\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−42.1918	−1.84846	−0.924229	−	0.381839i	$-0.875291\pi$
$521$	−42.1918	−1.84846	−0.924229	+	0.381839i	$0.875291\pi$
$522$	0	0
$523$	38.0000i	1.66162i	0.556553	+	0.830812i	$0.312124\pi$
$523$	38.0000i	1.66162i	−0.556553	+	0.830812i	$0.687876\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−23.0000	−1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	− 38.1464i	− 1.64308i
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	− 15.6515i	− 0.669211i	−0.942358	−	0.334606i	$-0.891397\pi$
$547$	− 15.6515i	− 0.669211i	0.942358	−	0.334606i	$-0.108603\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	− 16.8434i	− 0.709863i	−0.934892	−	0.354932i	$-0.884504\pi$
$563$	− 16.8434i	− 0.709863i	0.934892	−	0.354932i	$-0.115496\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	1.40408	0.0588622	0.0294311	−	0.999567i	$-0.490630\pi$
$569$	1.40408	0.0588622	0.0294311	+	0.999567i	$0.490630\pi$
$570$	0	0
$571$	− 47.7423i	− 1.99796i	−0.0452101	−	0.998978i	$-0.514396\pi$
$571$	− 47.7423i	− 1.99796i	0.0452101	−	0.998978i	$-0.485604\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	12.3939	0.515964	0.257982	−	0.966150i	$-0.416942\pi$
$577$	12.3939	0.515964	0.257982	+	0.966150i	$0.416942\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	− 38.6413i	− 1.59490i	−0.603386	−	0.797449i	$-0.706182\pi$
$587$	− 38.6413i	− 1.59490i	0.603386	−	0.797449i	$-0.293818\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	−18.0000	−0.739171	−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000	−0.739171	−0.369586	+	0.929197i	$0.620500\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	37.6969	1.53769	0.768845	−	0.639435i	$-0.220832\pi$
$601$	37.6969	1.53769	0.768845	+	0.639435i	$0.220832\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	0	0
$606$	0	0
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−49.2929	−1.98446	−0.992228	−	0.124434i	$-0.960288\pi$
$617$	−49.2929	−1.98446	−0.992228	+	0.124434i	$0.960288\pi$
$618$	0	0
$619$	− 23.7423i	− 0.954285i	−0.878826	−	0.477143i	$-0.841672\pi$
$619$	− 23.7423i	− 0.954285i	0.878826	−	0.477143i	$-0.158328\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	25.0000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	45.4949	1.79694	0.898470	−	0.439034i	$-0.144679\pi$
$641$	45.4949	1.79694	0.898470	+	0.439034i	$0.144679\pi$
$642$	0	0
$643$	32.3485i	1.27570i	0.770161	+	0.637850i	$0.220176\pi$
$643$	32.3485i	1.27570i	−0.770161	+	0.637850i	$0.779824\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	0	0
$649$	50.3939	1.97813
$650$	0	0
$651$	0	0
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	18.0000i	0.701180i	0.936529	+	0.350590i	$0.114019\pi$
$659$	18.0000i	0.701180i	−0.936529	+	0.350590i	$0.885981\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	10.0000	0.385472	0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000	0.385472	0.192736	+	0.981251i	$0.438264\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	5.94439i	0.227456i	0.993512	+	0.113728i	$0.0362792\pi$
$683$	5.94439i	0.227456i	−0.993512	+	0.113728i	$0.963721\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	46.0000i	1.74992i	0.484193	+	0.874961i	$0.339113\pi$
$691$	46.0000i	1.74992i	−0.484193	+	0.874961i	$0.660887\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−24.3031	−0.920544
$698$	0	0
$699$	0	0
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	− 4.45969i	− 0.164948i
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	78.1918	2.88023
$738$	0	0
$739$	53.7423i	1.97694i	0.151403	+	0.988472i	$0.451621\pi$
$739$	53.7423i	1.97694i	−0.151403	+	0.988472i	$0.548379\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	54.0000	1.95750	0.978749	−	0.205061i	$-0.0657392\pi$
$761$	54.0000	1.95750	0.978749	+	0.205061i	$0.0657392\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−22.0000	−0.793340	−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000	−0.793340	−0.396670	+	0.917961i	$0.629834\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	− 106.843i	− 3.82806i
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	− 50.0000i	− 1.78231i	−0.453701	−	0.891154i	$-0.649897\pi$
$787$	− 50.0000i	− 1.78231i	0.453701	−	0.891154i	$-0.350103\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	0	0
$803$	74.6413i	2.63404i
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	45.9898	1.61692	0.808458	−	0.588555i	$-0.200303\pi$
$809$	45.9898	1.61692	0.808458	+	0.588555i	$0.200303\pi$
$810$	0	0
$811$	17.7423i	0.623018i	0.950243	+	0.311509i	$0.100834\pi$
$811$	17.7423i	0.623018i	−0.950243	+	0.311509i	$0.899166\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	19.6061	0.685931
$818$	0	0
$819$	0	0
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	0	0		−	1.00000i	$-0.5\pi$
$823$	0	0			1.00000i	$0.5\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	− 54.0000i	− 1.87776i	−0.344239	−	0.938882i	$-0.611863\pi$
$827$	− 54.0000i	− 1.87776i	0.344239	−	0.938882i	$-0.388137\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	−13.2929	−0.460570
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	29.0000	1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	54.0000	1.84460	0.922302	−	0.386469i	$-0.126305\pi$
$857$	54.0000	1.84460	0.922302	+	0.386469i	$0.126305\pi$
$858$	0	0
$859$	21.6515i	0.738741i	0.929282	+	0.369370i	$0.120427\pi$
$859$	21.6515i	0.738741i	−0.929282	+	0.369370i	$0.879573\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	0	0
$883$	52.4393i	1.76472i	0.470573	+	0.882361i	$0.344047\pi$
$883$	52.4393i	1.76472i	−0.470573	+	0.882361i	$0.655953\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	− 46.4393i	− 1.54199i	−0.636841	−	0.770996i	$-0.719759\pi$
$907$	− 46.4393i	− 1.54199i	0.636841	−	0.770996i	$-0.280241\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	−98.0908	−3.24633
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	54.0000	1.77168	0.885841	−	0.463988i	$-0.153582\pi$
$929$	54.0000	1.77168	0.885841	+	0.463988i	$0.153582\pi$
$930$	0	0
$931$	− 58.4393i	− 1.91527i
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	34.0000	1.11073	0.555366	−	0.831606i	$-0.312578\pi$
$937$	34.0000	1.11073	0.555366	+	0.831606i	$0.312578\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	− 31.5403i	− 1.02492i	−0.858710	−	0.512461i	$-0.828734\pi$
$947$	− 31.5403i	− 1.02492i	0.858710	−	0.512461i	$-0.171266\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	60.1918	1.94980	0.974902	−	0.222633i	$-0.0714650\pi$
$953$	60.1918	1.94980	0.974902	+	0.222633i	$0.0714650\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0	0		−	1.00000i	$-0.5\pi$
$967$	0	0			1.00000i	$0.5\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	− 54.0000i	− 1.73294i	−0.499227	−	0.866471i	$-0.666383\pi$
$971$	− 54.0000i	− 1.73294i	0.499227	−	0.866471i	$-0.333617\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−56.8888	−1.82003	−0.910017	−	0.414572i	$-0.863931\pi$
$977$	−56.8888	−1.82003	−0.910017	+	0.414572i	$0.863931\pi$
$978$	0	0
$979$	− 98.0908i	− 3.13500i
$980$	0	0
$981$	0	0
$982$	0	0
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5184.2.d.e.2593.4		4
3.2	odd	2		5184.2.d.l.2593.1		4
4.3	odd	2	inner	5184.2.d.e.2593.1		4
8.3	odd	2	CM	5184.2.d.e.2593.4		4
8.5	even	2	inner	5184.2.d.e.2593.1		4
9.2	odd	6		576.2.r.c.481.2	yes	8
9.4	even	3		1728.2.r.c.289.1		8
9.5	odd	6		576.2.r.c.97.3	yes	8
9.7	even	3		1728.2.r.c.1441.4		8
12.11	even	2		5184.2.d.l.2593.4		4
24.5	odd	2		5184.2.d.l.2593.4		4
24.11	even	2		5184.2.d.l.2593.1		4
36.7	odd	6		1728.2.r.c.1441.1		8
36.11	even	6		576.2.r.c.481.3	yes	8
36.23	even	6		576.2.r.c.97.2	✓	8
36.31	odd	6		1728.2.r.c.289.4		8
72.5	odd	6		576.2.r.c.97.2	✓	8
72.11	even	6		576.2.r.c.481.2	yes	8
72.13	even	6		1728.2.r.c.289.4		8
72.29	odd	6		576.2.r.c.481.3	yes	8
72.43	odd	6		1728.2.r.c.1441.4		8
72.59	even	6		576.2.r.c.97.3	yes	8
72.61	even	6		1728.2.r.c.1441.1		8
72.67	odd	6		1728.2.r.c.289.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.2.r.c.97.2	✓	8	36.23	even	6
576.2.r.c.97.2	✓	8	72.5	odd	6
576.2.r.c.97.3	yes	8	9.5	odd	6
576.2.r.c.97.3	yes	8	72.59	even	6
576.2.r.c.481.2	yes	8	9.2	odd	6
576.2.r.c.481.2	yes	8	72.11	even	6
576.2.r.c.481.3	yes	8	36.11	even	6
576.2.r.c.481.3	yes	8	72.29	odd	6
1728.2.r.c.289.1		8	9.4	even	3
1728.2.r.c.289.1		8	72.67	odd	6
1728.2.r.c.289.4		8	36.31	odd	6
1728.2.r.c.289.4		8	72.13	even	6
1728.2.r.c.1441.1		8	36.7	odd	6
1728.2.r.c.1441.1		8	72.61	even	6
1728.2.r.c.1441.4		8	9.7	even	3
1728.2.r.c.1441.4		8	72.43	odd	6
5184.2.d.e.2593.1		4	4.3	odd	2	inner
5184.2.d.e.2593.1		4	8.5	even	2	inner
5184.2.d.e.2593.4		4	1.1	even	1	trivial
5184.2.d.e.2593.4		4	8.3	odd	2	CM
5184.2.d.l.2593.1		4	3.2	odd	2
5184.2.d.l.2593.1		4	24.11	even	2
5184.2.d.l.2593.4		4	12.11	even	2
5184.2.d.l.2593.4		4	24.5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 5184 = 2^{6} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5184.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+O(q^{10})\)	\(q+5.44949i q^{11} +1.89898 q^{17} +8.34847i q^{19} +5.00000 q^{25} -12.7980 q^{41} -2.34847i q^{43} -7.00000 q^{49} -9.24745i q^{59} -14.3485i q^{67} +13.6969 q^{73} +18.0000i q^{83} -18.0000 q^{89} -19.6969 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q+O(q^{10}) \) 4 * q	\( 4 q - 12 q^{17} + 20 q^{25} - 12 q^{41} - 28 q^{49} - 4 q^{73} - 72 q^{89} - 20 q^{97}+O(q^{100}) \) 4 * q - 12 * q^17 + 20 * q^25 - 12 * q^41 - 28 * q^49 - 4 * q^73 - 72 * q^89 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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