LMFDB - Embedded newform 2304.2.a.w.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2304,2,Mod(1,2304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2304, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2304.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2304 = 2^{8} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2304.a (trivial)

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:	yes
Analytic conductor:	$18.3975326257$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 576)
Fricke sign:	$-1$
Sato-Tate group:	$N(\mathrm{U}(1))$

Embedding invariants

Embedding label			1.2
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	2304.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.46410 q^{7} +O(q^{10})$	$q+3.46410 q^{7} +6.92820 q^{13} +8.00000 q^{19} -5.00000 q^{25} -10.3923 q^{31} -6.92820 q^{37} +8.00000 q^{43} +5.00000 q^{49} -6.92820 q^{61} +16.0000 q^{67} +10.0000 q^{73} +17.3205 q^{79} +24.0000 q^{91} -14.0000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q+O(q^{10}) $ 2 * q	$ 2 q + 16 q^{19} - 10 q^{25} + 16 q^{43} + 10 q^{49} + 32 q^{67} + 20 q^{73} + 48 q^{91} - 28 q^{97}+O(q^{100}) $ 2 * q + 16 * q^19 - 10 * q^25 + 16 * q^43 + 10 * q^49 + 32 * q^67 + 20 * q^73 + 48 * q^91 - 28 * q^97

Display 100 coefficients 10 coefficients

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		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	3.46410	1.30931	0.654654	−	0.755929i	$-0.272814\pi$
$7$	3.46410	1.30931	0.654654	+	0.755929i	$0.272814\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	6.92820	1.92154	0.960769	−	0.277350i	$-0.0894562\pi$
$13$	6.92820	1.92154	0.960769	+	0.277350i	$0.0894562\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	8.00000	1.83533	0.917663	−	0.397360i	$-0.130073\pi$
$19$	8.00000	1.83533	0.917663	+	0.397360i	$0.130073\pi$
$20$	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		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	−10.3923	−1.86651	−0.933257	−	0.359211i	$-0.883046\pi$
$31$	−10.3923	−1.86651	−0.933257	+	0.359211i	$0.883046\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−6.92820	−1.13899	−0.569495	−	0.821995i	$-0.692861\pi$
$37$	−6.92820	−1.13899	−0.569495	+	0.821995i	$0.692861\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	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
$49$	5.00000	0.714286
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	−6.92820	−0.887066	−0.443533	−	0.896258i	$-0.646275\pi$
$61$	−6.92820	−0.887066	−0.443533	+	0.896258i	$0.646275\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	16.0000	1.95471	0.977356	−	0.211604i	$-0.0678686\pi$
$67$	16.0000	1.95471	0.977356	+	0.211604i	$0.0678686\pi$
$68$	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
$73$	10.0000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	17.3205	1.94871	0.974355	−	0.225018i	$-0.0722440\pi$
$79$	17.3205	1.94871	0.974355	+	0.225018i	$0.0722440\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	24.0000	2.51588
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−14.0000	−1.42148	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000	−1.42148	−0.710742	+	0.703452i	$0.751641\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	−3.46410	−0.341328	−0.170664	−	0.985329i	$-0.554591\pi$
$103$	−3.46410	−0.341328	−0.170664	+	0.985329i	$0.554591\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	−20.7846	−1.99080	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$	−20.7846	−1.99080	−0.995402	+	0.0957826i	$0.969465\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−11.0000	−1.00000
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	10.3923	0.922168	0.461084	−	0.887357i	$-0.347461\pi$
$127$	10.3923	0.922168	0.461084	+	0.887357i	$0.347461\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	27.7128	2.40301
$134$	0	0
$135$	0	0
$136$	0	0
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	0	0
$139$	16.0000	1.35710	0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000	1.35710	0.678551	+	0.734553i	$0.262608\pi$
$140$	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		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	−24.2487	−1.97333	−0.986666	−	0.162758i	$-0.947961\pi$
$151$	−24.2487	−1.97333	−0.986666	+	0.162758i	$0.947961\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	20.7846	1.65879	0.829396	−	0.558661i	$-0.188685\pi$
$157$	20.7846	1.65879	0.829396	+	0.558661i	$0.188685\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	8.00000	0.626608	0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000	0.626608	0.313304	+	0.949653i	$0.398564\pi$
$164$	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
$169$	35.0000	2.69231
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	−17.3205	−1.30931
$176$	0	0
$177$	0	0
$178$	0	0
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	6.92820	0.514969	0.257485	−	0.966282i	$-0.417106\pi$
$181$	6.92820	0.514969	0.257485	+	0.966282i	$0.417106\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	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
$193$	2.00000	0.143963	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000	0.143963	0.0719816	+	0.997406i	$0.477068\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	−3.46410	−0.245564	−0.122782	−	0.992434i	$-0.539182\pi$
$199$	−3.46410	−0.245564	−0.122782	+	0.992434i	$0.539182\pi$
$200$	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
$209$	0	0
$210$	0	0
$211$	16.0000	1.10149	0.550743	−	0.834675i	$-0.314345\pi$
$211$	16.0000	1.10149	0.550743	+	0.834675i	$0.314345\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−36.0000	−2.44384
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	10.3923	0.695920	0.347960	−	0.937509i	$-0.386874\pi$
$223$	10.3923	0.695920	0.347960	+	0.937509i	$0.386874\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	−20.7846	−1.37349	−0.686743	−	0.726900i	$-0.740960\pi$
$229$	−20.7846	−1.37349	−0.686743	+	0.726900i	$0.740960\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	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
$241$	14.0000	0.901819	0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000	0.901819	0.450910	+	0.892570i	$0.351100\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	55.4256	3.52665
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	0	0
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	−24.0000	−1.49129
$260$	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		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	−17.3205	−1.05215	−0.526073	−	0.850439i	$-0.676336\pi$
$271$	−17.3205	−1.05215	−0.526073	+	0.850439i	$0.676336\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−20.7846	−1.24883	−0.624413	−	0.781094i	$-0.714662\pi$
$277$	−20.7846	−1.24883	−0.624413	+	0.781094i	$0.714662\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	0	0
$283$	−32.0000	−1.90220	−0.951101	−	0.308879i	$-0.900046\pi$
$283$	−32.0000	−1.90220	−0.951101	+	0.308879i	$0.900046\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−17.0000	−1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	27.7128	1.59734
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	16.0000	0.913168	0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000	0.913168	0.456584	+	0.889680i	$0.349073\pi$
$308$	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
$313$	−22.0000	−1.24351	−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000	−1.24351	−0.621757	+	0.783210i	$0.713581\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	−34.6410	−1.92154
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−32.0000	−1.75888	−0.879440	−	0.476011i	$-0.842082\pi$
$331$	−32.0000	−1.75888	−0.879440	+	0.476011i	$0.842082\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	34.0000	1.85210	0.926049	−	0.377403i	$-0.123183\pi$
$337$	34.0000	1.85210	0.926049	+	0.377403i	$0.123183\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−6.92820	−0.374088
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	0	0
$349$	−34.6410	−1.85429	−0.927146	−	0.374701i	$-0.877745\pi$
$349$	−34.6410	−1.85429	−0.927146	+	0.374701i	$0.877745\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	0	0		−	1.00000i	$-0.5\pi$
$353$	0	0			1.00000i	$0.5\pi$
$354$	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
$361$	45.0000	2.36842
$362$	0	0
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−38.1051	−1.98907	−0.994535	−	0.104399i	$-0.966708\pi$
$367$	−38.1051	−1.98907	−0.994535	+	0.104399i	$0.966708\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−6.92820	−0.358729	−0.179364	−	0.983783i	$-0.557404\pi$
$373$	−6.92820	−0.358729	−0.179364	+	0.983783i	$0.557404\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	8.00000	0.410932	0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000	0.410932	0.205466	+	0.978664i	$0.434129\pi$
$380$	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		−	1.00000i	$-0.5\pi$
$389$	0	0			1.00000i	$0.5\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	20.7846	1.04315	0.521575	−	0.853206i	$-0.325345\pi$
$397$	20.7846	1.04315	0.521575	+	0.853206i	$0.325345\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	0	0
$403$	−72.0000	−3.58658
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−38.0000	−1.87898	−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−38.0000	−1.87898	−0.939490	+	0.342578i	$0.888700\pi$
$410$	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
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	34.6410	1.68830	0.844150	−	0.536107i	$-0.180106\pi$
$421$	34.6410	1.68830	0.844150	+	0.536107i	$0.180106\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−24.0000	−1.16144
$428$	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
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	−31.1769	−1.48799	−0.743996	−	0.668184i	$-0.767072\pi$
$439$	−31.1769	−1.48799	−0.743996	+	0.668184i	$0.767072\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	0	0		−	1.00000i	$-0.5\pi$
$449$	0	0			1.00000i	$0.5\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	0	0
$463$	38.1051	1.77090	0.885448	−	0.464739i	$-0.153852\pi$
$463$	38.1051	1.77090	0.885448	+	0.464739i	$0.153852\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	0	0
$469$	55.4256	2.55932
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	−40.0000	−1.83533
$476$	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
$481$	−48.0000	−2.18861
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	3.46410	0.156973	0.0784867	−	0.996915i	$-0.474991\pi$
$487$	3.46410	0.156973	0.0784867	+	0.996915i	$0.474991\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−32.0000	−1.43252	−0.716258	−	0.697835i	$-0.754147\pi$
$499$	−32.0000	−1.43252	−0.716258	+	0.697835i	$0.754147\pi$
$500$	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		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	34.6410	1.53243
$512$	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
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	0	0
$523$	8.00000	0.349816	0.174908	−	0.984585i	$-0.444037\pi$
$523$	8.00000	0.349816	0.174908	+	0.984585i	$0.444037\pi$
$524$	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
$539$	0	0
$540$	0	0
$541$	6.92820	0.297867	0.148933	−	0.988847i	$-0.452416\pi$
$541$	6.92820	0.297867	0.148933	+	0.988847i	$0.452416\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−40.0000	−1.71028	−0.855138	−	0.518400i	$-0.826528\pi$
$547$	−40.0000	−1.71028	−0.855138	+	0.518400i	$0.826528\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	60.0000	2.55146
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	55.4256	2.34425
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	0	0
$571$	16.0000	0.669579	0.334790	−	0.942293i	$-0.391335\pi$
$571$	16.0000	0.669579	0.334790	+	0.942293i	$0.391335\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	46.0000	1.91501	0.957503	−	0.288425i	$-0.0931316\pi$
$577$	46.0000	1.91501	0.957503	+	0.288425i	$0.0931316\pi$
$578$	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
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	−83.1384	−3.42566
$590$	0	0
$591$	0	0
$592$	0	0
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	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
$601$	−26.0000	−1.06056	−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000	−1.06056	−0.530281	+	0.847822i	$0.677914\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−45.0333	−1.82785	−0.913923	−	0.405887i	$-0.866962\pi$
$607$	−45.0333	−1.82785	−0.913923	+	0.405887i	$0.866962\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	48.4974	1.95879	0.979396	−	0.201948i	$-0.0647272\pi$
$613$	48.4974	1.95879	0.979396	+	0.201948i	$0.0647272\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0		−	1.00000i	$-0.5\pi$
$617$	0	0			1.00000i	$0.5\pi$
$618$	0	0
$619$	−32.0000	−1.28619	−0.643094	−	0.765787i	$-0.722350\pi$
$619$	−32.0000	−1.28619	−0.643094	+	0.765787i	$0.722350\pi$
$620$	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
$631$	−24.2487	−0.965326	−0.482663	−	0.875806i	$-0.660330\pi$
$631$	−24.2487	−0.965326	−0.482663	+	0.875806i	$0.660330\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	34.6410	1.37253
$638$	0	0
$639$	0	0
$640$	0	0
$641$	0	0		−	1.00000i	$-0.5\pi$
$641$	0	0			1.00000i	$0.5\pi$
$642$	0	0
$643$	−40.0000	−1.57745	−0.788723	−	0.614749i	$-0.789257\pi$
$643$	−40.0000	−1.57745	−0.788723	+	0.614749i	$0.789257\pi$
$644$	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
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	0	0		−	1.00000i	$-0.5\pi$
$653$	0	0			1.00000i	$0.5\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	−34.6410	−1.34738	−0.673690	−	0.739014i	$-0.735292\pi$
$661$	−34.6410	−1.34738	−0.673690	+	0.739014i	$0.735292\pi$
$662$	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
$673$	−50.0000	−1.92736	−0.963679	−	0.267063i	$-0.913947\pi$
$673$	−50.0000	−1.92736	−0.963679	+	0.267063i	$0.913947\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	−48.4974	−1.86116
$680$	0	0
$681$	0	0
$682$	0	0
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	0	0
$703$	−55.4256	−2.09042
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−48.4974	−1.82136	−0.910679	−	0.413114i	$-0.864441\pi$
$709$	−48.4974	−1.82136	−0.910679	+	0.413114i	$0.864441\pi$
$710$	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
$721$	−12.0000	−0.446903
$722$	0	0
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	31.1769	1.15629	0.578144	−	0.815935i	$-0.303777\pi$
$727$	31.1769	1.15629	0.578144	+	0.815935i	$0.303777\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−20.7846	−0.767697	−0.383849	−	0.923396i	$-0.625402\pi$
$733$	−20.7846	−0.767697	−0.383849	+	0.923396i	$0.625402\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	16.0000	0.588570	0.294285	−	0.955718i	$-0.404919\pi$
$739$	16.0000	0.588570	0.294285	+	0.955718i	$0.404919\pi$
$740$	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
$751$	17.3205	0.632034	0.316017	−	0.948753i	$-0.397654\pi$
$751$	17.3205	0.632034	0.316017	+	0.948753i	$0.397654\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−48.4974	−1.76267	−0.881334	−	0.472493i	$-0.843354\pi$
$757$	−48.4974	−1.76267	−0.881334	+	0.472493i	$0.843354\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0	0		−	1.00000i	$-0.5\pi$
$761$	0	0			1.00000i	$0.5\pi$
$762$	0	0
$763$	−72.0000	−2.60658
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	2.00000	0.0721218	0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000	0.0721218	0.0360609	+	0.999350i	$0.488519\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	0	0
$775$	51.9615	1.86651
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	56.0000	1.99618	0.998092	−	0.0617409i	$-0.0196653\pi$
$787$	56.0000	1.99618	0.998092	+	0.0617409i	$0.0196653\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−48.0000	−1.70453
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	0	0		−	1.00000i	$-0.5\pi$
$809$	0	0			1.00000i	$0.5\pi$
$810$	0	0
$811$	56.0000	1.96643	0.983213	−	0.182462i	$-0.0584065\pi$
$811$	56.0000	1.96643	0.983213	+	0.182462i	$0.0584065\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	64.0000	2.23908
$818$	0	0
$819$	0	0
$820$	0	0
$821$	0	0		−	1.00000i	$-0.5\pi$
$821$	0	0			1.00000i	$0.5\pi$
$822$	0	0
$823$	−24.2487	−0.845257	−0.422628	−	0.906303i	$-0.638892\pi$
$823$	−24.2487	−0.845257	−0.422628	+	0.906303i	$0.638892\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0		−	1.00000i	$-0.5\pi$
$827$	0	0			1.00000i	$0.5\pi$
$828$	0	0
$829$	34.6410	1.20313	0.601566	−	0.798823i	$-0.294544\pi$
$829$	34.6410	1.20313	0.601566	+	0.798823i	$0.294544\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	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
$847$	−38.1051	−1.30931
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	−6.92820	−0.237217	−0.118609	−	0.992941i	$-0.537843\pi$
$853$	−6.92820	−0.237217	−0.118609	+	0.992941i	$0.537843\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	0	0
$859$	56.0000	1.91070	0.955348	−	0.295484i	$-0.0954809\pi$
$859$	56.0000	1.91070	0.955348	+	0.295484i	$0.0954809\pi$
$860$	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
$871$	110.851	3.75605
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	48.4974	1.63764	0.818821	−	0.574049i	$-0.194628\pi$
$877$	48.4974	1.63764	0.818821	+	0.574049i	$0.194628\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	0	0		−	1.00000i	$-0.5\pi$
$881$	0	0			1.00000i	$0.5\pi$
$882$	0	0
$883$	8.00000	0.269221	0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000	0.269221	0.134611	+	0.990899i	$0.457022\pi$
$884$	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
$889$	36.0000	1.20740
$890$	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
$907$	−40.0000	−1.32818	−0.664089	−	0.747653i	$-0.731180\pi$
$907$	−40.0000	−1.32818	−0.664089	+	0.747653i	$0.731180\pi$
$908$	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
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	31.1769	1.02843	0.514216	−	0.857661i	$-0.328083\pi$
$919$	31.1769	1.02843	0.514216	+	0.857661i	$0.328083\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	34.6410	1.13899
$926$	0	0
$927$	0	0
$928$	0	0
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	40.0000	1.31095
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	26.0000	0.849383	0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000	0.849383	0.424691	+	0.905338i	$0.360383\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	0	0
$949$	69.2820	2.24899
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0		−	1.00000i	$-0.5\pi$
$953$	0	0			1.00000i	$0.5\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	77.0000	2.48387
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−58.8897	−1.89377	−0.946883	−	0.321578i	$-0.895787\pi$
$967$	−58.8897	−1.89377	−0.946883	+	0.321578i	$0.895787\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	55.4256	1.77686
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0		−	1.00000i	$-0.5\pi$
$977$	0	0			1.00000i	$0.5\pi$
$978$	0	0
$979$	0	0
$980$	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
$991$	45.0333	1.43053	0.715265	−	0.698853i	$-0.246306\pi$
$991$	45.0333	1.43053	0.715265	+	0.698853i	$0.246306\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−62.3538	−1.97477	−0.987383	−	0.158352i	$-0.949382\pi$
$997$	−62.3538	−1.97477	−0.987383	+	0.158352i	$0.949382\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2304.2.a.w.1.2		2
3.2	odd	2	CM	2304.2.a.w.1.2		2
4.3	odd	2		2304.2.a.v.1.1		2
8.3	odd	2	inner	2304.2.a.w.1.1		2
8.5	even	2		2304.2.a.v.1.2		2
12.11	even	2		2304.2.a.v.1.1		2
16.3	odd	4		576.2.d.c.289.4	yes	4
16.5	even	4		576.2.d.c.289.1	✓	4
16.11	odd	4		576.2.d.c.289.3	yes	4
16.13	even	4		576.2.d.c.289.2	yes	4
24.5	odd	2		2304.2.a.v.1.2		2
24.11	even	2	inner	2304.2.a.w.1.1		2
48.5	odd	4		576.2.d.c.289.1	✓	4
48.11	even	4		576.2.d.c.289.3	yes	4
48.29	odd	4		576.2.d.c.289.2	yes	4
48.35	even	4		576.2.d.c.289.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.2.d.c.289.1	✓	4	16.5	even	4
576.2.d.c.289.1	✓	4	48.5	odd	4
576.2.d.c.289.2	yes	4	16.13	even	4
576.2.d.c.289.2	yes	4	48.29	odd	4
576.2.d.c.289.3	yes	4	16.11	odd	4
576.2.d.c.289.3	yes	4	48.11	even	4
576.2.d.c.289.4	yes	4	16.3	odd	4
576.2.d.c.289.4	yes	4	48.35	even	4
2304.2.a.v.1.1		2	4.3	odd	2
2304.2.a.v.1.1		2	12.11	even	2
2304.2.a.v.1.2		2	8.5	even	2
2304.2.a.v.1.2		2	24.5	odd	2
2304.2.a.w.1.1		2	8.3	odd	2	inner
2304.2.a.w.1.1		2	24.11	even	2	inner
2304.2.a.w.1.2		2	1.1	even	1	trivial
2304.2.a.w.1.2		2	3.2	odd	2	CM

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:	\( N \)	\(=\)	\( 2304 = 2^{8} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2304.a (trivial)

\(f(q)\)	\(=\)	\(q+3.46410 q^{7} +O(q^{10})\)	\(q+3.46410 q^{7} +6.92820 q^{13} +8.00000 q^{19} -5.00000 q^{25} -10.3923 q^{31} -6.92820 q^{37} +8.00000 q^{43} +5.00000 q^{49} -6.92820 q^{61} +16.0000 q^{67} +10.0000 q^{73} +17.3205 q^{79} +24.0000 q^{91} -14.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q+O(q^{10}) \) 2 * q	\( 2 q + 16 q^{19} - 10 q^{25} + 16 q^{43} + 10 q^{49} + 32 q^{67} + 20 q^{73} + 48 q^{91} - 28 q^{97}+O(q^{100}) \) 2 * q + 16 * q^19 - 10 * q^25 + 16 * q^43 + 10 * q^49 + 32 * q^67 + 20 * q^73 + 48 * q^91 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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