LMFDB - Embedded newform 2007.1.d.c.1783.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2007,1,Mod(1783,2007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2007, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("2007.1783");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2007 = 3^{2} \cdot 223 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2007.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:	yes
Analytic conductor:	$1.00162348035$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{28})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 7x^{4} + 14x^{2} - 7 $ x^6 - 7x^4 + 14x^2 - 7
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{14}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{14} - \cdots)$

Embedding invariants

Embedding label			1783.3
Root			$0.867767$ of defining polynomial
Character	$\chi$	$=$	2007.1783

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.867767 q^{2} -0.246980 q^{4} +0.445042 q^{7} +1.08209 q^{8} +O(q^{10})$	$q-0.867767 q^{2} -0.246980 q^{4} +0.445042 q^{7} +1.08209 q^{8} -0.386193 q^{14} -0.692021 q^{16} -1.56366 q^{17} +1.24698 q^{19} +1.00000 q^{25} -0.109916 q^{28} +0.867767 q^{29} +1.80194 q^{31} -0.481575 q^{32} +1.35690 q^{34} -0.445042 q^{37} -1.08209 q^{38} -1.94986 q^{41} -1.80194 q^{43} +1.56366 q^{47} -0.801938 q^{49} -0.867767 q^{50} +1.56366 q^{53} +0.481575 q^{56} -0.753020 q^{58} -1.56366 q^{62} +1.10992 q^{64} +0.386193 q^{68} +1.80194 q^{73} +0.386193 q^{74} -0.307979 q^{76} +1.69202 q^{82} +0.867767 q^{83} +1.56366 q^{86} +1.94986 q^{89} -1.35690 q^{94} +0.695895 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 8 q^{4} + 2 q^{7}+O(q^{10}) $ 6 * q + 8 * q^4 + 2 * q^7	$ 6 q + 8 q^{4} + 2 q^{7} + 6 q^{16} - 2 q^{19} + 6 q^{25} - 2 q^{28} + 2 q^{31} - 2 q^{37} - 2 q^{43} + 4 q^{49} - 14 q^{58} + 8 q^{64} + 2 q^{73} - 12 q^{76}+O(q^{100}) $ 6 * q + 8 * q^4 + 2 * q^7 + 6 * q^16 - 2 * q^19 + 6 * q^25 - 2 * q^28 + 2 * q^31 - 2 * q^37 - 2 * q^43 + 4 * q^49 - 14 * q^58 + 8 * q^64 + 2 * q^73 - 12 * q^76

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2007\mathbb{Z}\right)^\times$.

$n$	$226$	$893$
$\chi(n)$	$-1$	$1$

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 $

$2$	−0.867767	−0.867767	−0.433884	−	0.900969i	$-0.642857\pi$
$2$	−0.867767	−0.867767	−0.433884	+	0.900969i	$0.642857\pi$
$3$	0	0
$3$	0	0
$4$	−0.246980	−0.246980
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	0	0
$7$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$7$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$8$	1.08209	1.08209
$9$	0	0
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	−0.386193	−0.386193
$15$	0	0
$16$	−0.692021	−0.692021
$17$	−1.56366	−1.56366	−0.781831	−	0.623490i	$-0.785714\pi$
$17$	−1.56366	−1.56366	−0.781831	+	0.623490i	$0.785714\pi$
$18$	0	0
$19$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$19$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	0	0
$25$	1.00000	1.00000
$26$	0	0
$27$	0	0
$28$	−0.109916	−0.109916
$29$	0.867767	0.867767	0.433884	−	0.900969i	$-0.357143\pi$
$29$	0.867767	0.867767	0.433884	+	0.900969i	$0.357143\pi$
$30$	0	0
$31$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$31$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$32$	−0.481575	−0.481575
$33$	0	0
$34$	1.35690	1.35690
$35$	0	0
$36$	0	0
$37$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$37$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$38$	−1.08209	−1.08209
$39$	0	0
$40$	0	0
$41$	−1.94986	−1.94986	−0.974928	−	0.222521i	$-0.928571\pi$
$41$	−1.94986	−1.94986	−0.974928	+	0.222521i	$0.928571\pi$
$42$	0	0
$43$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$43$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	1.56366	1.56366	0.781831	−	0.623490i	$-0.214286\pi$
$47$	1.56366	1.56366	0.781831	+	0.623490i	$0.214286\pi$
$48$	0	0
$49$	−0.801938	−0.801938
$50$	−0.867767	−0.867767
$51$	0	0
$52$	0	0
$53$	1.56366	1.56366	0.781831	−	0.623490i	$-0.214286\pi$
$53$	1.56366	1.56366	0.781831	+	0.623490i	$0.214286\pi$
$54$	0	0
$55$	0	0
$56$	0.481575	0.481575
$57$	0	0
$58$	−0.753020	−0.753020
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	−1.56366	−1.56366
$63$	0	0
$64$	1.10992	1.10992
$65$	0	0
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0.386193	0.386193
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	0	0
$73$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$73$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$74$	0.386193	0.386193
$75$	0	0
$76$	−0.307979	−0.307979
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	0	0
$82$	1.69202	1.69202
$83$	0.867767	0.867767	0.433884	−	0.900969i	$-0.357143\pi$
$83$	0.867767	0.867767	0.433884	+	0.900969i	$0.357143\pi$
$84$	0	0
$85$	0	0
$86$	1.56366	1.56366
$87$	0	0
$88$	0	0
$89$	1.94986	1.94986	0.974928	−	0.222521i	$-0.0714286\pi$
$89$	1.94986	1.94986	0.974928	+	0.222521i	$0.0714286\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	−1.35690	−1.35690
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0.695895	0.695895
$99$	0	0
$100$	−0.246980	−0.246980
$101$	1.94986	1.94986	0.974928	−	0.222521i	$-0.0714286\pi$
$101$	1.94986	1.94986	0.974928	+	0.222521i	$0.0714286\pi$
$102$	0	0
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	0	0
$106$	−1.35690	−1.35690
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0	0
$109$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$109$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$110$	0	0
$111$	0	0
$112$	−0.307979	−0.307979
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	0	0
$116$	−0.214321	−0.214321
$117$	0	0
$118$	0	0
$119$	−0.695895	−0.695895
$120$	0	0
$121$	1.00000	1.00000
$122$	0	0
$123$	0	0
$124$	−0.445042	−0.445042
$125$	0	0
$126$	0	0
$127$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$127$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$128$	−0.481575	−0.481575
$129$	0	0
$130$	0	0
$131$	−1.94986	−1.94986	−0.974928	−	0.222521i	$-0.928571\pi$
$131$	−1.94986	−1.94986	−0.974928	+	0.222521i	$0.928571\pi$
$132$	0	0
$133$	0.554958	0.554958
$134$	0	0
$135$	0	0
$136$	−1.69202	−1.69202
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$139$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	−1.56366	−1.56366
$147$	0	0
$148$	0.109916	0.109916
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	1.34934	1.34934
$153$	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
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0.481575	0.481575
$165$	0	0
$166$	−0.753020	−0.753020
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	1.00000	1.00000
$170$	0	0
$171$	0	0
$172$	0.445042	0.445042
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0.445042	0.445042
$176$	0	0
$177$	0	0
$178$	−1.69202	−1.69202
$179$	1.94986	1.94986	0.974928	−	0.222521i	$-0.0714286\pi$
$179$	1.94986	1.94986	0.974928	+	0.222521i	$0.0714286\pi$
$180$	0	0
$181$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$181$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	−0.386193	−0.386193
$189$	0	0
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	0	0
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	0.198062	0.198062
$197$	−1.94986	−1.94986	−0.974928	−	0.222521i	$-0.928571\pi$
$197$	−1.94986	−1.94986	−0.974928	+	0.222521i	$0.928571\pi$
$198$	0	0
$199$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$199$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$200$	1.08209	1.08209
$201$	0	0
$202$	−1.69202	−1.69202
$203$	0.386193	0.386193
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$211$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$212$	−0.386193	−0.386193
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0.801938	0.801938
$218$	−1.08209	−1.08209
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	−1.00000	−1.00000
$223$	−1.00000	−1.00000
$224$	−0.214321	−0.214321
$225$	0	0
$226$	0	0
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	0.939001	0.939001
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0.603875	0.603875
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$241$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$242$	−0.867767	−0.867767
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	1.94986	1.94986
$249$	0	0
$250$	0	0
$251$	−0.867767	−0.867767	−0.433884	−	0.900969i	$-0.642857\pi$
$251$	−0.867767	−0.867767	−0.433884	+	0.900969i	$0.642857\pi$
$252$	0	0
$253$	0	0
$254$	1.08209	1.08209
$255$	0	0
$256$	−0.692021	−0.692021
$257$	−0.867767	−0.867767	−0.433884	−	0.900969i	$-0.642857\pi$
$257$	−0.867767	−0.867767	−0.433884	+	0.900969i	$0.642857\pi$
$258$	0	0
$259$	−0.198062	−0.198062
$260$	0	0
$261$	0	0
$262$	1.69202	1.69202
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	0	0
$266$	−0.481575	−0.481575
$267$	0	0
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	1.08209	1.08209
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0.386193	0.386193
$279$	0	0
$280$	0	0
$281$	0.867767	0.867767	0.433884	−	0.900969i	$-0.357143\pi$
$281$	0.867767	0.867767	0.433884	+	0.900969i	$0.357143\pi$
$282$	0	0
$283$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$283$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−0.867767	−0.867767
$288$	0	0
$289$	1.44504	1.44504
$290$	0	0
$291$	0	0
$292$	−0.445042	−0.445042
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	0	0
$296$	−0.481575	−0.481575
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	−0.801938	−0.801938
$302$	0	0
$303$	0	0
$304$	−0.862937	−0.862937
$305$	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
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−0.867767	−0.867767	−0.433884	−	0.900969i	$-0.642857\pi$
$317$	−0.867767	−0.867767	−0.433884	+	0.900969i	$0.642857\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	−1.94986	−1.94986
$324$	0	0
$325$	0	0
$326$	0	0
$327$	0	0
$328$	−2.10992	−2.10992
$329$	0.695895	0.695895
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	−0.214321	−0.214321
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	−0.867767	−0.867767
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−0.801938	−0.801938
$344$	−1.94986	−1.94986
$345$	0	0
$346$	0	0
$347$	1.56366	1.56366	0.781831	−	0.623490i	$-0.214286\pi$
$347$	1.56366	1.56366	0.781831	+	0.623490i	$0.214286\pi$
$348$	0	0
$349$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$349$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$350$	−0.386193	−0.386193
$351$	0	0
$352$	0	0
$353$	0.867767	0.867767	0.433884	−	0.900969i	$-0.357143\pi$
$353$	0.867767	0.867767	0.433884	+	0.900969i	$0.357143\pi$
$354$	0	0
$355$	0	0
$356$	−0.481575	−0.481575
$357$	0	0
$358$	−1.69202	−1.69202
$359$	−1.56366	−1.56366	−0.781831	−	0.623490i	$-0.785714\pi$
$359$	−1.56366	−1.56366	−0.781831	+	0.623490i	$0.785714\pi$
$360$	0	0
$361$	0.554958	0.554958
$362$	1.56366	1.56366
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−2.00000	−2.00000	−1.00000			$\pi$
$367$	−2.00000	−2.00000	−1.00000			$\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0.695895	0.695895
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	0	0
$376$	1.69202	1.69202
$377$	0	0
$378$	0	0
$379$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$379$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$380$	0	0
$381$	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
$389$	−1.94986	−1.94986	−0.974928	−	0.222521i	$-0.928571\pi$
$389$	−1.94986	−1.94986	−0.974928	+	0.222521i	$0.928571\pi$
$390$	0	0
$391$	0	0
$392$	−0.867767	−0.867767
$393$	0	0
$394$	1.69202	1.69202
$395$	0	0
$396$	0	0
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	1.56366	1.56366
$399$	0	0
$400$	−0.692021	−0.692021
$401$	1.56366	1.56366	0.781831	−	0.623490i	$-0.214286\pi$
$401$	1.56366	1.56366	0.781831	+	0.623490i	$0.214286\pi$
$402$	0	0
$403$	0	0
$404$	−0.481575	−0.481575
$405$	0	0
$406$	−0.335126	−0.335126
$407$	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
$415$	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
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	1.08209	1.08209
$423$	0	0
$424$	1.69202	1.69202
$425$	−1.56366	−1.56366
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	0	0
$433$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$433$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$434$	−0.695895	−0.695895
$435$	0	0
$436$	−0.307979	−0.307979
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−1.94986	−1.94986	−0.974928	−	0.222521i	$-0.928571\pi$
$443$	−1.94986	−1.94986	−0.974928	+	0.222521i	$0.928571\pi$
$444$	0	0
$445$	0	0
$446$	0.867767	0.867767
$447$	0	0
$448$	0.493959	0.493959
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	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
$460$	0	0
$461$	−0.867767	−0.867767	−0.433884	−	0.900969i	$-0.642857\pi$
$461$	−0.867767	−0.867767	−0.433884	+	0.900969i	$0.642857\pi$
$462$	0	0
$463$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$463$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$464$	−0.600514	−0.600514
$465$	0	0
$466$	0	0
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	1.24698	1.24698
$476$	0.171872	0.171872
$477$	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
$482$	1.08209	1.08209
$483$	0	0
$484$	−0.246980	−0.246980
$485$	0	0
$486$	0	0
$487$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$487$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	−1.35690	−1.35690
$494$	0	0
$495$	0	0
$496$	−1.24698	−1.24698
$497$	0	0
$498$	0	0
$499$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$499$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$500$	0	0
$501$	0	0
$502$	0.753020	0.753020
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	0.307979	0.307979
$509$	−1.56366	−1.56366	−0.781831	−	0.623490i	$-0.785714\pi$
$509$	−1.56366	−1.56366	−0.781831	+	0.623490i	$0.785714\pi$
$510$	0	0
$511$	0.801938	0.801938
$512$	1.08209	1.08209
$513$	0	0
$514$	0.753020	0.753020
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0.171872	0.171872
$519$	0	0
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0.481575	0.481575
$525$	0	0
$526$	0	0
$527$	−2.81762	−2.81762
$528$	0	0
$529$	1.00000	1.00000
$530$	0	0
$531$	0	0
$532$	−0.137063	−0.137063
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	0	0
$544$	0.753020	0.753020
$545$	0	0
$546$	0	0
$547$	−2.00000	−2.00000	−1.00000			$\pi$
$547$	−2.00000	−2.00000	−1.00000			$\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	1.08209	1.08209
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0.109916	0.109916
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	−0.753020	−0.753020
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	0	0
$566$	0.386193	0.386193
$567$	0	0
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	0.753020	0.753020
$575$	0	0
$576$	0	0
$577$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$577$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$578$	−1.25396	−1.25396
$579$	0	0
$580$	0	0
$581$	0.386193	0.386193
$582$	0	0
$583$	0	0
$584$	1.94986	1.94986
$585$	0	0
$586$	0	0
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	0	0
$589$	2.24698	2.24698
$590$	0	0
$591$	0	0
$592$	0.307979	0.307979
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	1.94986	1.94986	0.974928	−	0.222521i	$-0.0714286\pi$
$599$	1.94986	1.94986	0.974928	+	0.222521i	$0.0714286\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0.695895	0.695895
$603$	0	0
$604$	0	0
$605$	0	0
$606$	0	0
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	−0.600514	−0.600514
$609$	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
$617$	1.94986	1.94986	0.974928	−	0.222521i	$-0.0714286\pi$
$617$	1.94986	1.94986	0.974928	+	0.222521i	$0.0714286\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0.867767	0.867767
$624$	0	0
$625$	1.00000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0.695895	0.695895
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	0	0
$634$	0.753020	0.753020
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	0	0
$643$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$643$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$644$	0	0
$645$	0	0
$646$	1.69202	1.69202
$647$	−1.94986	−1.94986	−0.974928	−	0.222521i	$-0.928571\pi$
$647$	−1.94986	−1.94986	−0.974928	+	0.222521i	$0.928571\pi$
$648$	0	0
$649$	0	0
$650$	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
$656$	1.34934	1.34934
$657$	0	0
$658$	−0.603875	−0.603875
$659$	1.94986	1.94986	0.974928	−	0.222521i	$-0.0714286\pi$
$659$	1.94986	1.94986	0.974928	+	0.222521i	$0.0714286\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	0	0
$664$	0.939001	0.939001
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$673$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$674$	0	0
$675$	0	0
$676$	−0.246980	−0.246980
$677$	−1.56366	−1.56366	−0.781831	−	0.623490i	$-0.785714\pi$
$677$	−1.56366	−1.56366	−0.781831	+	0.623490i	$0.785714\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	−1.56366	−1.56366	−0.781831	−	0.623490i	$-0.785714\pi$
$683$	−1.56366	−1.56366	−0.781831	+	0.623490i	$0.785714\pi$
$684$	0	0
$685$	0	0
$686$	0.695895	0.695895
$687$	0	0
$688$	1.24698	1.24698
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	0	0
$694$	−1.35690	−1.35690
$695$	0	0
$696$	0	0
$697$	3.04892	3.04892
$698$	−1.08209	−1.08209
$699$	0	0
$700$	−0.109916	−0.109916
$701$	1.56366	1.56366	0.781831	−	0.623490i	$-0.214286\pi$
$701$	1.56366	1.56366	0.781831	+	0.623490i	$0.214286\pi$
$702$	0	0
$703$	−0.554958	−0.554958
$704$	0	0
$705$	0	0
$706$	−0.753020	−0.753020
$707$	0.867767	0.867767
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	2.10992	2.10992
$713$	0	0
$714$	0	0
$715$	0	0
$716$	−0.481575	−0.481575
$717$	0	0
$718$	1.35690	1.35690
$719$	1.56366	1.56366	0.781831	−	0.623490i	$-0.214286\pi$
$719$	1.56366	1.56366	0.781831	+	0.623490i	$0.214286\pi$
$720$	0	0
$721$	0	0
$722$	−0.481575	−0.481575
$723$	0	0
$724$	0.445042	0.445042
$725$	0.867767	0.867767
$726$	0	0
$727$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$727$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	2.81762	2.81762
$732$	0	0
$733$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$733$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$734$	1.73553	1.73553
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	0	0
$742$	−0.603875	−0.603875
$743$	1.56366	1.56366	0.781831	−	0.623490i	$-0.214286\pi$
$743$	1.56366	1.56366	0.781831	+	0.623490i	$0.214286\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$751$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$752$	−1.08209	−1.08209
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	−1.56366	−1.56366
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	0.554958	0.554958
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$769$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	1.80194	1.80194
$776$	0	0
$777$	0	0
$778$	1.69202	1.69202
$779$	−2.43143	−2.43143
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0.554958	0.554958
$785$	0	0
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	0.481575	0.481575
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0.445042	0.445042
$797$	−1.94986	−1.94986	−0.974928	−	0.222521i	$-0.928571\pi$
$797$	−1.94986	−1.94986	−0.974928	+	0.222521i	$0.928571\pi$
$798$	0	0
$799$	−2.44504	−2.44504
$800$	−0.481575	−0.481575
$801$	0	0
$802$	−1.35690	−1.35690
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	2.10992	2.10992
$809$	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			$\pi$
$812$	−0.0953818	−0.0953818
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−2.24698	−2.24698
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−1.56366	−1.56366	−0.781831	−	0.623490i	$-0.785714\pi$
$821$	−1.56366	−1.56366	−0.781831	+	0.623490i	$0.785714\pi$
$822$	0	0
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	1.25396	1.25396
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	−0.246980	−0.246980
$842$	0	0
$843$	0	0
$844$	0.307979	0.307979
$845$	0	0
$846$	0	0
$847$	0.445042	0.445042
$848$	−1.08209	−1.08209
$849$	0	0
$850$	1.35690	1.35690
$851$	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
$857$	−1.94986	−1.94986	−0.974928	−	0.222521i	$-0.928571\pi$
$857$	−1.94986	−1.94986	−0.974928	+	0.222521i	$0.928571\pi$
$858$	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	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	0	0
$866$	−0.386193	−0.386193
$867$	0	0
$868$	−0.198062	−0.198062
$869$	0	0
$870$	0	0
$871$	0	0
$872$	1.34934	1.34934
$873$	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
$881$	−0.867767	−0.867767	−0.433884	−	0.900969i	$-0.642857\pi$
$881$	−0.867767	−0.867767	−0.433884	+	0.900969i	$0.642857\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	1.69202	1.69202
$887$	0.867767	0.867767	0.433884	−	0.900969i	$-0.357143\pi$
$887$	0.867767	0.867767	0.433884	+	0.900969i	$0.357143\pi$
$888$	0	0
$889$	−0.554958	−0.554958
$890$	0	0
$891$	0	0
$892$	0.246980	0.246980
$893$	1.94986	1.94986
$894$	0	0
$895$	0	0
$896$	−0.214321	−0.214321
$897$	0	0
$898$	0	0
$899$	1.56366	1.56366
$900$	0	0
$901$	−2.44504	−2.44504
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$907$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	−1.94986	−1.94986	−0.974928	−	0.222521i	$-0.928571\pi$
$911$	−1.94986	−1.94986	−0.974928	+	0.222521i	$0.928571\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−0.867767	−0.867767
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	0.753020	0.753020
$923$	0	0
$924$	0	0
$925$	−0.445042	−0.445042
$926$	1.56366	1.56366
$927$	0	0
$928$	−0.417895	−0.417895
$929$	1.56366	1.56366	0.781831	−	0.623490i	$-0.214286\pi$
$929$	1.56366	1.56366	0.781831	+	0.623490i	$0.214286\pi$
$930$	0	0
$931$	−1.00000	−1.00000
$932$	0	0
$933$	0	0
$934$	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		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	1.56366	1.56366	0.781831	−	0.623490i	$-0.214286\pi$
$947$	1.56366	1.56366	0.781831	+	0.623490i	$0.214286\pi$
$948$	0	0
$949$	0	0
$950$	−1.08209	−1.08209
$951$	0	0
$952$	−0.753020	−0.753020
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	2.24698	2.24698
$962$	0	0
$963$	0	0
$964$	0.307979	0.307979
$965$	0	0
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	1.08209	1.08209
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	0	0
$973$	−0.198062	−0.198062
$974$	−1.08209	−1.08209
$975$	0	0
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	0	0
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	0	0
$985$	0	0
$986$	1.17747	1.17747
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	−0.867767	−0.867767
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$997$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$998$	0.386193	0.386193
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2007.1.d.c.1783.3	✓	6
3.2	odd	2	inner	2007.1.d.c.1783.4	yes	6
223.222	odd	2	CM	2007.1.d.c.1783.3	✓	6
669.668	even	2	inner	2007.1.d.c.1783.4	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2007.1.d.c.1783.3	✓	6	1.1	even	1	trivial
2007.1.d.c.1783.3	✓	6	223.222	odd	2	CM
2007.1.d.c.1783.4	yes	6	3.2	odd	2	inner
2007.1.d.c.1783.4	yes	6	669.668	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2007 = 3^{2} \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2007.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.867767 q^{2} -0.246980 q^{4} +0.445042 q^{7} +1.08209 q^{8} +O(q^{10})\)	\(q-0.867767 q^{2} -0.246980 q^{4} +0.445042 q^{7} +1.08209 q^{8} -0.386193 q^{14} -0.692021 q^{16} -1.56366 q^{17} +1.24698 q^{19} +1.00000 q^{25} -0.109916 q^{28} +0.867767 q^{29} +1.80194 q^{31} -0.481575 q^{32} +1.35690 q^{34} -0.445042 q^{37} -1.08209 q^{38} -1.94986 q^{41} -1.80194 q^{43} +1.56366 q^{47} -0.801938 q^{49} -0.867767 q^{50} +1.56366 q^{53} +0.481575 q^{56} -0.753020 q^{58} -1.56366 q^{62} +1.10992 q^{64} +0.386193 q^{68} +1.80194 q^{73} +0.386193 q^{74} -0.307979 q^{76} +1.69202 q^{82} +0.867767 q^{83} +1.56366 q^{86} +1.94986 q^{89} -1.35690 q^{94} +0.695895 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 8 q^{4} + 2 q^{7}+O(q^{10}) \) 6 * q + 8 * q^4 + 2 * q^7	\( 6 q + 8 q^{4} + 2 q^{7} + 6 q^{16} - 2 q^{19} + 6 q^{25} - 2 q^{28} + 2 q^{31} - 2 q^{37} - 2 q^{43} + 4 q^{49} - 14 q^{58} + 8 q^{64} + 2 q^{73} - 12 q^{76}+O(q^{100}) \) 6 * q + 8 * q^4 + 2 * q^7 + 6 * q^16 - 2 * q^19 + 6 * q^25 - 2 * q^28 + 2 * q^31 - 2 * q^37 - 2 * q^43 + 4 * q^49 - 14 * q^58 + 8 * q^64 + 2 * q^73 - 12 * q^76

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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