LMFDB - Embedded newform 755.1.c.d.754.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [755,1,Mod(754,755)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(755, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 1, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("755.754"); S:= CuspForms(chi, 1); N := Newforms(S);

Level:	$ N $	$=$	$ 755 = 5 \cdot 151 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	755.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$0.376794084538$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{6}$
Projective field:	Galois closure of 6.2.2850125.1

Embedding invariants

Embedding label			754.2
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	755.754

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+1.73205 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.00000 q^{9} -1.00000 q^{11} +1.73205 q^{12} -1.73205 q^{13} -1.73205 q^{15} +1.00000 q^{16} -1.00000 q^{19} -1.00000 q^{20} -1.73205 q^{23} +1.00000 q^{25} +1.73205 q^{27} +1.00000 q^{29} +1.00000 q^{31} -1.73205 q^{33} +2.00000 q^{36} -3.00000 q^{39} -1.00000 q^{44} -2.00000 q^{45} +1.73205 q^{48} -1.00000 q^{49} -1.73205 q^{52} +1.00000 q^{55} -1.73205 q^{57} +1.00000 q^{59} -1.73205 q^{60} +1.00000 q^{64} +1.73205 q^{65} +1.73205 q^{67} -3.00000 q^{69} +1.73205 q^{73} +1.73205 q^{75} -1.00000 q^{76} -1.00000 q^{80} +1.00000 q^{81} -1.73205 q^{83} +1.73205 q^{87} -1.73205 q^{92} +1.73205 q^{93} +1.00000 q^{95} -2.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{4} - 2 q^{5} + 4 q^{9} - 2 q^{11} + 2 q^{16} - 2 q^{19} - 2 q^{20} + 2 q^{25} + 2 q^{29} + 2 q^{31} + 4 q^{36} - 6 q^{39} - 2 q^{44} - 4 q^{45} - 2 q^{49} + 2 q^{55} + 2 q^{59} + 2 q^{64} - 6 q^{69}+ \cdots - 4 q^{99}+O(q^{100}) $ 2 * q + 2 * q^4 - 2 * q^5 + 4 * q^9 - 2 * q^11 + 2 * q^16 - 2 * q^19 - 2 * q^20 + 2 * q^25 + 2 * q^29 + 2 * q^31 + 4 * q^36 - 6 * q^39 - 2 * q^44 - 4 * q^45 - 2 * q^49 + 2 * q^55 + 2 * q^59 + 2 * q^64 - 6 * q^69 - 2 * q^76 - 2 * q^80 + 2 * q^81 + 2 * q^95 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/755\mathbb{Z}\right)^\times$.

$n$	$6$	$152$
$\chi(n)$	$-1$	$-1$

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	1.00000			$0$
$2$	0	0	−1.00000			$\pi$
$3$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$3$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$4$	1.00000	1.00000
$5$	−1.00000	−1.00000
$5$	−1.00000	−1.00000
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	0	0
$9$	2.00000	2.00000
$10$	0	0
$11$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$11$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$12$	1.73205	1.73205
$13$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$13$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$14$	0	0
$15$	−1.73205	−1.73205
$16$	1.00000	1.00000
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$19$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$20$	−1.00000	−1.00000
$21$	0	0
$22$	0	0
$23$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$23$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$24$	0	0
$25$	1.00000	1.00000
$26$	0	0
$27$	1.73205	1.73205
$28$	0	0
$29$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$29$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$30$	0	0
$31$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$31$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$32$	0	0
$33$	−1.73205	−1.73205
$34$	0	0
$35$	0	0
$36$	2.00000	2.00000
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	−3.00000	−3.00000
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	−1.00000	−1.00000
$45$	−2.00000	−2.00000
$46$	0	0
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	1.73205	1.73205
$49$	−1.00000	−1.00000
$50$	0	0
$51$	0	0
$52$	−1.73205	−1.73205
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	1.00000	1.00000
$56$	0	0
$57$	−1.73205	−1.73205
$58$	0	0
$59$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$59$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$60$	−1.73205	−1.73205
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	0	0
$64$	1.00000	1.00000
$65$	1.73205	1.73205
$66$	0	0
$67$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$67$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$68$	0	0
$69$	−3.00000	−3.00000
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	0	0
$73$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$73$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$74$	0	0
$75$	1.73205	1.73205
$76$	−1.00000	−1.00000
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	−1.00000	−1.00000
$81$	1.00000	1.00000
$82$	0	0
$83$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$83$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	1.73205	1.73205
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	0	0
$92$	−1.73205	−1.73205
$93$	1.73205	1.73205
$94$	0	0
$95$	1.00000	1.00000
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	−2.00000	−2.00000
$100$	1.00000	1.00000
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$107$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$108$	1.73205	1.73205
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	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
$115$	1.73205	1.73205
$116$	1.00000	1.00000
$117$	−3.46410	−3.46410
$118$	0	0
$119$	0	0
$120$	0	0
$121$	0	0
$122$	0	0
$123$	0	0
$124$	1.00000	1.00000
$125$	−1.00000	−1.00000
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	−1.73205	−1.73205
$133$	0	0
$134$	0	0
$135$	−1.73205	−1.73205
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	−2.00000	−2.00000	−1.00000			$\pi$
$139$	−2.00000	−2.00000	−1.00000			$\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	1.73205	1.73205
$144$	2.00000	2.00000
$145$	−1.00000	−1.00000
$146$	0	0
$147$	−1.73205	−1.73205
$148$	0	0
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	−1.00000	−1.00000
$151$	−1.00000	−1.00000
$152$	0	0
$153$	0	0
$154$	0	0
$155$	−1.00000	−1.00000
$156$	−3.00000	−3.00000
$157$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$157$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$163$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$164$	0	0
$165$	1.73205	1.73205
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	2.00000	2.00000
$170$	0	0
$171$	−2.00000	−2.00000
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−1.00000
$177$	1.73205	1.73205
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	−2.00000	−2.00000
$181$	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
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	2.00000	2.00000	1.00000			$0$
$191$	2.00000	2.00000	1.00000			$0$
$192$	1.73205	1.73205
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	3.00000	3.00000
$196$	−1.00000	−1.00000
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	0	0
$201$	3.00000	3.00000
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−3.46410	−3.46410
$208$	−1.73205	−1.73205
$209$	1.00000	1.00000
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	3.00000	3.00000
$220$	1.00000	1.00000
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	0	0
$225$	2.00000	2.00000
$226$	0	0
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	−1.73205	−1.73205
$229$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$229$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$233$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$234$	0	0
$235$	0	0
$236$	1.00000	1.00000
$237$	0	0
$238$	0	0
$239$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$239$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$240$	−1.73205	−1.73205
$241$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$241$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	1.00000	1.00000
$246$	0	0
$247$	1.73205	1.73205
$248$	0	0
$249$	−3.00000	−3.00000
$250$	0	0
$251$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$251$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$252$	0	0
$253$	1.73205	1.73205
$254$	0	0
$255$	0	0
$256$	1.00000	1.00000
$257$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$257$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$258$	0	0
$259$	0	0
$260$	1.73205	1.73205
$261$	2.00000	2.00000
$262$	0	0
$263$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$263$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	1.73205	1.73205
$269$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$269$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−1.00000	−1.00000
$276$	−3.00000	−3.00000
$277$	0	0		−	1.00000i	$-0.5\pi$
$277$	0	0			1.00000i	$0.5\pi$
$278$	0	0
$279$	2.00000	2.00000
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	0	0
$283$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$283$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$284$	0	0
$285$	1.73205	1.73205
$286$	0	0
$287$	0	0
$288$	0	0
$289$	1.00000	1.00000
$290$	0	0
$291$	0	0
$292$	1.73205	1.73205
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	0	0
$295$	−1.00000	−1.00000
$296$	0	0
$297$	−1.73205	−1.73205
$298$	0	0
$299$	3.00000	3.00000
$300$	1.73205	1.73205
$301$	0	0
$302$	0	0
$303$	0	0
$304$	−1.00000	−1.00000
$305$	0	0
$306$	0	0
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$311$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$317$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$318$	0	0
$319$	−1.00000	−1.00000
$320$	−1.00000	−1.00000
$321$	3.00000	3.00000
$322$	0	0
$323$	0	0
$324$	1.00000	1.00000
$325$	−1.73205	−1.73205
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−2.00000	−2.00000	−1.00000			$\pi$
$331$	−2.00000	−2.00000	−1.00000			$\pi$
$332$	−1.73205	−1.73205
$333$	0	0
$334$	0	0
$335$	−1.73205	−1.73205
$336$	0	0
$337$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$337$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	−1.00000	−1.00000
$342$	0	0
$343$	0	0
$344$	0	0
$345$	3.00000	3.00000
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	1.73205	1.73205
$349$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$349$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$350$	0	0
$351$	−3.00000	−3.00000
$352$	0	0
$353$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$353$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	0	0
$361$	0	0
$362$	0	0
$363$	0	0
$364$	0	0
$365$	−1.73205	−1.73205
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	−1.73205	−1.73205
$369$	0	0
$370$	0	0
$371$	0	0
$372$	1.73205	1.73205
$373$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$373$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$374$	0	0
$375$	−1.73205	−1.73205
$376$	0	0
$377$	−1.73205	−1.73205
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	1.00000	1.00000
$381$	0	0
$382$	0	0
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	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
$396$	−2.00000	−2.00000
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	1.00000	1.00000
$401$	−2.00000	−2.00000	−1.00000			$\pi$
$401$	−2.00000	−2.00000	−1.00000			$\pi$
$402$	0	0
$403$	−1.73205	−1.73205
$404$	0	0
$405$	−1.00000	−1.00000
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	1.73205	1.73205
$416$	0	0
$417$	−3.46410	−3.46410
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	1.73205	1.73205
$429$	3.00000	3.00000
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	1.73205	1.73205
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	−1.73205	−1.73205
$436$	0	0
$437$	1.73205	1.73205
$438$	0	0
$439$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$439$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$440$	0	0
$441$	−2.00000	−2.00000
$442$	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	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	−1.73205	−1.73205
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	0	0
$460$	1.73205	1.73205
$461$	2.00000	2.00000	1.00000			$0$
$461$	2.00000	2.00000	1.00000			$0$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	1.00000	1.00000
$465$	−1.73205	−1.73205
$466$	0	0
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	−3.46410	−3.46410
$469$	0	0
$470$	0	0
$471$	−3.00000	−3.00000
$472$	0	0
$473$	0	0
$474$	0	0
$475$	−1.00000	−1.00000
$476$	0	0
$477$	0	0
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	−3.00000	−3.00000
$490$	0	0
$491$	−2.00000	−2.00000	−1.00000			$\pi$
$491$	−2.00000	−2.00000	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	2.00000	2.00000
$496$	1.00000	1.00000
$497$	0	0
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	−1.00000	−1.00000
$501$	0	0
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	3.46410	3.46410
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−1.73205	−1.73205
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$521$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$522$	0	0
$523$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$523$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	−1.73205	−1.73205
$529$	2.00000	2.00000
$530$	0	0
$531$	2.00000	2.00000
$532$	0	0
$533$	0	0
$534$	0	0
$535$	−1.73205	−1.73205
$536$	0	0
$537$	0	0
$538$	0	0
$539$	1.00000	1.00000
$540$	−1.73205	−1.73205
$541$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$541$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	−1.00000	−1.00000
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	−2.00000	−2.00000
$557$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$557$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	2.00000	2.00000	1.00000			$0$
$569$	2.00000	2.00000	1.00000			$0$
$570$	0	0
$571$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$571$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$572$	1.73205	1.73205
$573$	3.46410	3.46410
$574$	0	0
$575$	−1.73205	−1.73205
$576$	2.00000	2.00000
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	0	0
$580$	−1.00000	−1.00000
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	3.46410	3.46410
$586$	0	0
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	−1.73205	−1.73205
$589$	−1.00000	−1.00000
$590$	0	0
$591$	0	0
$592$	0	0
$593$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$593$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	0	0
$601$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$601$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$602$	0	0
$603$	3.46410	3.46410
$604$	−1.00000	−1.00000
$605$	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
$617$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$617$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	−1.00000	−1.00000
$621$	−3.00000	−3.00000
$622$	0	0
$623$	0	0
$624$	−3.00000	−3.00000
$625$	1.00000	1.00000
$626$	0	0
$627$	1.73205	1.73205
$628$	−1.73205	−1.73205
$629$	0	0
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	1.73205	1.73205
$638$	0	0
$639$	0	0
$640$	0	0
$641$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$641$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	0	0
$649$	−1.00000	−1.00000
$650$	0	0
$651$	0	0
$652$	−1.73205	−1.73205
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	3.46410	3.46410
$658$	0	0
$659$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$659$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$660$	1.73205	1.73205
$661$	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
$667$	−1.73205	−1.73205
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	1.73205	1.73205
$676$	2.00000	2.00000
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$683$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$684$	−2.00000	−2.00000
$685$	0	0
$686$	0	0
$687$	−1.73205	−1.73205
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	2.00000	2.00000
$696$	0	0
$697$	0	0
$698$	0	0
$699$	−3.00000	−3.00000
$700$	0	0
$701$	−2.00000	−2.00000	−1.00000			$\pi$
$701$	−2.00000	−2.00000	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	−1.00000	−1.00000
$705$	0	0
$706$	0	0
$707$	0	0
$708$	1.73205	1.73205
$709$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$709$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	−1.73205	−1.73205
$714$	0	0
$715$	−1.73205	−1.73205
$716$	0	0
$717$	−1.73205	−1.73205
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	−2.00000	−2.00000
$721$	0	0
$722$	0	0
$723$	1.73205	1.73205
$724$	0	0
$725$	1.00000	1.00000
$726$	0	0
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	−1.00000	−1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$733$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$734$	0	0
$735$	1.73205	1.73205
$736$	0	0
$737$	−1.73205	−1.73205
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	3.00000	3.00000
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−3.46410	−3.46410
$748$	0	0
$749$	0	0
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	0	0
$753$	1.73205	1.73205
$754$	0	0
$755$	1.00000	1.00000
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	3.00000	3.00000
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	0	0
$764$	2.00000	2.00000
$765$	0	0
$766$	0	0
$767$	−1.73205	−1.73205
$768$	1.73205	1.73205
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	3.00000	3.00000
$772$	0	0
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	1.00000	1.00000
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	3.00000	3.00000
$781$	0	0
$782$	0	0
$783$	1.73205	1.73205
$784$	−1.00000	−1.00000
$785$	1.73205	1.73205
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	0	0
$789$	3.00000	3.00000
$790$	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
$803$	−1.73205	−1.73205
$804$	3.00000	3.00000
$805$	0	0
$806$	0	0
$807$	−1.73205	−1.73205
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	1.73205	1.73205
$816$	0	0
$817$	0	0
$818$	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	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	−1.73205	−1.73205
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	−3.46410	−3.46410
$829$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$829$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$830$	0	0
$831$	0	0
$832$	−1.73205	−1.73205
$833$	0	0
$834$	0	0
$835$	0	0
$836$	1.00000	1.00000
$837$	1.73205	1.73205
$838$	0	0
$839$	2.00000	2.00000	1.00000			$0$
$839$	2.00000	2.00000	1.00000			$0$
$840$	0	0
$841$	0	0
$842$	0	0
$843$	0	0
$844$	0	0
$845$	−2.00000	−2.00000
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−3.00000	−3.00000
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	2.00000	2.00000
$856$	0	0
$857$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$857$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	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
$867$	1.73205	1.73205
$868$	0	0
$869$	0	0
$870$	0	0
$871$	−3.00000	−3.00000
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	3.00000	3.00000
$877$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$877$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$878$	0	0
$879$	0	0
$880$	1.00000	1.00000
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	−1.73205	−1.73205
$886$	0	0
$887$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$887$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−1.00000	−1.00000
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	5.19615	5.19615
$898$	0	0
$899$	1.00000	1.00000
$900$	2.00000	2.00000
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$911$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$912$	−1.73205	−1.73205
$913$	1.73205	1.73205
$914$	0	0
$915$	0	0
$916$	−1.00000	−1.00000
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	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
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	1.00000	1.00000
$932$	−1.73205	−1.73205
$933$	−1.73205	−1.73205
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	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
$944$	1.00000	1.00000
$945$	0	0
$946$	0	0
$947$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$947$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$948$	0	0
$949$	−3.00000	−3.00000
$950$	0	0
$951$	3.00000	3.00000
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	−2.00000	−2.00000
$956$	−1.00000	−1.00000
$957$	−1.73205	−1.73205
$958$	0	0
$959$	0	0
$960$	−1.73205	−1.73205
$961$	0	0
$962$	0	0
$963$	3.46410	3.46410
$964$	1.00000	1.00000
$965$	0	0
$966$	0	0
$967$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$967$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	−3.00000	−3.00000
$976$	0	0
$977$	0	0		−	1.00000i	$-0.5\pi$
$977$	0	0			1.00000i	$0.5\pi$
$978$	0	0
$979$	0	0
$980$	1.00000	1.00000
$981$	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
$988$	1.73205	1.73205
$989$	0	0
$990$	0	0
$991$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$991$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$992$	0	0
$993$	−3.46410	−3.46410
$994$	0	0
$995$	0	0
$996$	−3.00000	−3.00000
$997$	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	755.1.c.d.754.2	yes	2
5.2	odd	4		3775.1.d.b.301.1		2
5.3	odd	4		3775.1.d.b.301.2		2
5.4	even	2	inner	755.1.c.d.754.1	✓	2
151.150	odd	2	inner	755.1.c.d.754.1	✓	2
755.452	even	4		3775.1.d.b.301.2		2
755.603	even	4		3775.1.d.b.301.1		2
755.754	odd	2	CM	755.1.c.d.754.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
755.1.c.d.754.1	✓	2	5.4	even	2	inner
755.1.c.d.754.1	✓	2	151.150	odd	2	inner
755.1.c.d.754.2	yes	2	1.1	even	1	trivial
755.1.c.d.754.2	yes	2	755.754	odd	2	CM
3775.1.d.b.301.1		2	5.2	odd	4
3775.1.d.b.301.1		2	755.603	even	4
3775.1.d.b.301.2		2	5.3	odd	4
3775.1.d.b.301.2		2	755.452	even	4

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:	\( N \)	\(=\)	\( 755 = 5 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	755.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.73205 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.00000 q^{9} -1.00000 q^{11} +1.73205 q^{12} -1.73205 q^{13} -1.73205 q^{15} +1.00000 q^{16} -1.00000 q^{19} -1.00000 q^{20} -1.73205 q^{23} +1.00000 q^{25} +1.73205 q^{27} +1.00000 q^{29} +1.00000 q^{31} -1.73205 q^{33} +2.00000 q^{36} -3.00000 q^{39} -1.00000 q^{44} -2.00000 q^{45} +1.73205 q^{48} -1.00000 q^{49} -1.73205 q^{52} +1.00000 q^{55} -1.73205 q^{57} +1.00000 q^{59} -1.73205 q^{60} +1.00000 q^{64} +1.73205 q^{65} +1.73205 q^{67} -3.00000 q^{69} +1.73205 q^{73} +1.73205 q^{75} -1.00000 q^{76} -1.00000 q^{80} +1.00000 q^{81} -1.73205 q^{83} +1.73205 q^{87} -1.73205 q^{92} +1.73205 q^{93} +1.00000 q^{95} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{4} - 2 q^{5} + 4 q^{9} - 2 q^{11} + 2 q^{16} - 2 q^{19} - 2 q^{20} + 2 q^{25} + 2 q^{29} + 2 q^{31} + 4 q^{36} - 6 q^{39} - 2 q^{44} - 4 q^{45} - 2 q^{49} + 2 q^{55} + 2 q^{59} + 2 q^{64} - 6 q^{69}+ \cdots - 4 q^{99}+O(q^{100}) \) 2 * q + 2 * q^4 - 2 * q^5 + 4 * q^9 - 2 * q^11 + 2 * q^16 - 2 * q^19 - 2 * q^20 + 2 * q^25 + 2 * q^29 + 2 * q^31 + 4 * q^36 - 6 * q^39 - 2 * q^44 - 4 * q^45 - 2 * q^49 + 2 * q^55 + 2 * q^59 + 2 * q^64 - 6 * q^69 - 2 * q^76 - 2 * q^80 + 2 * q^81 + 2 * q^95 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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