LMFDB - Embedded newform 3467.1.b.a.3466.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3467,1,Mod(3466,3467)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3467, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3467.3466");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3467 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3467.b (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:	$1.73025839880$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\Q(\zeta_{38})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 8x^{7} + 7x^{6} + 21x^{5} - 15x^{4} - 20x^{3} + 10x^{2} + 5x - 1 $ x^9 - x^8 - 8x^7 + 7x^6 + 21x^5 - 15x^4 - 20x^3 + 10x^2 + 5*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{19}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{19} - \cdots)$

Embedding invariants

Embedding label			3466.4
Root			$1.35456$ of defining polynomial
Character	$\chi$	$=$	3467.3466

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.803391 q^{3} +1.00000 q^{4} -0.354563 q^{9} -1.75895 q^{11} -0.803391 q^{12} +0.490971 q^{13} +1.00000 q^{16} +1.09390 q^{17} -1.97272 q^{23} +1.00000 q^{25} +1.08824 q^{27} -0.165159 q^{29} +1.57828 q^{31} +1.41312 q^{33} -0.354563 q^{36} +1.89163 q^{37} -0.394442 q^{39} +1.89163 q^{41} -0.165159 q^{43} -1.75895 q^{44} -0.803391 q^{48} +1.00000 q^{49} -0.878826 q^{51} +0.490971 q^{52} +1.00000 q^{64} +1.09390 q^{67} +1.09390 q^{68} +1.58487 q^{69} +0.490971 q^{71} -1.97272 q^{73} -0.803391 q^{75} -1.75895 q^{79} -0.519722 q^{81} +0.132687 q^{87} +1.57828 q^{89} -1.97272 q^{92} -1.26798 q^{93} -1.35456 q^{97} +0.623658 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - q^{3} + 9 q^{4} + 8 q^{9} - q^{11} - q^{12} - q^{13} + 9 q^{16} - q^{17} - q^{23} + 9 q^{25} - 2 q^{27} - q^{29} - q^{31} - 2 q^{33} + 8 q^{36} - q^{37} - 2 q^{39} - q^{41} - q^{43} - q^{44}+ \cdots - 3 q^{99}+O(q^{100}) $ 9 * q - q^3 + 9 * q^4 + 8 * q^9 - q^11 - q^12 - q^13 + 9 * q^16 - q^17 - q^23 + 9 * q^25 - 2 * q^27 - q^29 - q^31 - 2 * q^33 + 8 * q^36 - q^37 - 2 * q^39 - q^41 - q^43 - q^44 - q^48 + 9 * q^49 - 2 * q^51 - q^52 + 9 * q^64 - q^67 - q^68 - 2 * q^69 - q^71 - q^73 - q^75 - q^79 + 7 * q^81 - 2 * q^87 - q^89 - q^92 - 2 * q^93 - q^97 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3467\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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			$\pi$
$3$	−0.803391	−0.803391	−0.401695	−	0.915773i	$-0.631579\pi$
$3$	−0.803391	−0.803391	−0.401695	+	0.915773i	$0.631579\pi$
$4$	1.00000	1.00000
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	0	0
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	0	0
$9$	−0.354563	−0.354563
$10$	0	0
$11$	−1.75895	−1.75895	−0.879474	−	0.475947i	$-0.842105\pi$
$11$	−1.75895	−1.75895	−0.879474	+	0.475947i	$0.842105\pi$
$12$	−0.803391	−0.803391
$13$	0.490971	0.490971	0.245485	−	0.969400i	$-0.421053\pi$
$13$	0.490971	0.490971	0.245485	+	0.969400i	$0.421053\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	1.00000
$17$	1.09390	1.09390	0.546948	−	0.837166i	$-0.315789\pi$
$17$	1.09390	1.09390	0.546948	+	0.837166i	$0.315789\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−1.97272	−1.97272	−0.986361	−	0.164595i	$-0.947368\pi$
$23$	−1.97272	−1.97272	−0.986361	+	0.164595i	$0.947368\pi$
$24$	0	0
$25$	1.00000	1.00000
$26$	0	0
$27$	1.08824	1.08824
$28$	0	0
$29$	−0.165159	−0.165159	−0.0825793	−	0.996584i	$-0.526316\pi$
$29$	−0.165159	−0.165159	−0.0825793	+	0.996584i	$0.526316\pi$
$30$	0	0
$31$	1.57828	1.57828	0.789141	−	0.614213i	$-0.210526\pi$
$31$	1.57828	1.57828	0.789141	+	0.614213i	$0.210526\pi$
$32$	0	0
$33$	1.41312	1.41312
$34$	0	0
$35$	0	0
$36$	−0.354563	−0.354563
$37$	1.89163	1.89163	0.945817	−	0.324699i	$-0.105263\pi$
$37$	1.89163	1.89163	0.945817	+	0.324699i	$0.105263\pi$
$38$	0	0
$39$	−0.394442	−0.394442
$40$	0	0
$41$	1.89163	1.89163	0.945817	−	0.324699i	$-0.105263\pi$
$41$	1.89163	1.89163	0.945817	+	0.324699i	$0.105263\pi$
$42$	0	0
$43$	−0.165159	−0.165159	−0.0825793	−	0.996584i	$-0.526316\pi$
$43$	−0.165159	−0.165159	−0.0825793	+	0.996584i	$0.526316\pi$
$44$	−1.75895	−1.75895
$45$	0	0
$46$	0	0
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	−0.803391	−0.803391
$49$	1.00000	1.00000
$50$	0	0
$51$	−0.878826	−0.878826
$52$	0.490971	0.490971
$53$	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
$59$	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			$\pi$
$62$	0	0
$63$	0	0
$64$	1.00000	1.00000
$65$	0	0
$66$	0	0
$67$	1.09390	1.09390	0.546948	−	0.837166i	$-0.315789\pi$
$67$	1.09390	1.09390	0.546948	+	0.837166i	$0.315789\pi$
$68$	1.09390	1.09390
$69$	1.58487	1.58487
$70$	0	0
$71$	0.490971	0.490971	0.245485	−	0.969400i	$-0.421053\pi$
$71$	0.490971	0.490971	0.245485	+	0.969400i	$0.421053\pi$
$72$	0	0
$73$	−1.97272	−1.97272	−0.986361	−	0.164595i	$-0.947368\pi$
$73$	−1.97272	−1.97272	−0.986361	+	0.164595i	$0.947368\pi$
$74$	0	0
$75$	−0.803391	−0.803391
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−1.75895	−1.75895	−0.879474	−	0.475947i	$-0.842105\pi$
$79$	−1.75895	−1.75895	−0.879474	+	0.475947i	$0.842105\pi$
$80$	0	0
$81$	−0.519722	−0.519722
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0.132687	0.132687
$88$	0	0
$89$	1.57828	1.57828	0.789141	−	0.614213i	$-0.210526\pi$
$89$	1.57828	1.57828	0.789141	+	0.614213i	$0.210526\pi$
$90$	0	0
$91$	0	0
$92$	−1.97272	−1.97272
$93$	−1.26798	−1.26798
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−1.35456	−1.35456	−0.677282	−	0.735724i	$-0.736842\pi$
$97$	−1.35456	−1.35456	−0.677282	+	0.735724i	$0.736842\pi$
$98$	0	0
$99$	0.623658	0.623658
$100$	1.00000	1.00000
$101$	−1.35456	−1.35456	−0.677282	−	0.735724i	$-0.736842\pi$
$101$	−1.35456	−1.35456	−0.677282	+	0.735724i	$0.736842\pi$
$102$	0	0
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	1.57828	1.57828	0.789141	−	0.614213i	$-0.210526\pi$
$107$	1.57828	1.57828	0.789141	+	0.614213i	$0.210526\pi$
$108$	1.08824	1.08824
$109$	−1.97272	−1.97272	−0.986361	−	0.164595i	$-0.947368\pi$
$109$	−1.97272	−1.97272	−0.986361	+	0.164595i	$0.947368\pi$
$110$	0	0
$111$	−1.51972	−1.51972
$112$	0	0
$113$	1.57828	1.57828	0.789141	−	0.614213i	$-0.210526\pi$
$113$	1.57828	1.57828	0.789141	+	0.614213i	$0.210526\pi$
$114$	0	0
$115$	0	0
$116$	−0.165159	−0.165159
$117$	−0.174080	−0.174080
$118$	0	0
$119$	0	0
$120$	0	0
$121$	2.09390	2.09390
$122$	0	0
$123$	−1.51972	−1.51972
$124$	1.57828	1.57828
$125$	0	0
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	0	0
$129$	0.132687	0.132687
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	1.41312	1.41312
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	−0.863592	−0.863592
$144$	−0.354563	−0.354563
$145$	0	0
$146$	0	0
$147$	−0.803391	−0.803391
$148$	1.89163	1.89163
$149$	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			$\pi$
$152$	0	0
$153$	−0.387855	−0.387855
$154$	0	0
$155$	0	0
$156$	−0.394442	−0.394442
$157$	−1.97272	−1.97272	−0.986361	−	0.164595i	$-0.947368\pi$
$157$	−1.97272	−1.97272	−0.986361	+	0.164595i	$0.947368\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−1.35456	−1.35456	−0.677282	−	0.735724i	$-0.736842\pi$
$163$	−1.35456	−1.35456	−0.677282	+	0.735724i	$0.736842\pi$
$164$	1.89163	1.89163
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	−0.758948	−0.758948
$170$	0	0
$171$	0	0
$172$	−0.165159	−0.165159
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0	0
$176$	−1.75895	−1.75895
$177$	0	0
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	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
$187$	−1.92411	−1.92411
$188$	0	0
$189$	0	0
$190$	0	0
$191$	1.89163	1.89163	0.945817	−	0.324699i	$-0.105263\pi$
$191$	1.89163	1.89163	0.945817	+	0.324699i	$0.105263\pi$
$192$	−0.803391	−0.803391
$193$	−1.35456	−1.35456	−0.677282	−	0.735724i	$-0.736842\pi$
$193$	−1.35456	−1.35456	−0.677282	+	0.735724i	$0.736842\pi$
$194$	0	0
$195$	0	0
$196$	1.00000	1.00000
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	−0.165159	−0.165159	−0.0825793	−	0.996584i	$-0.526316\pi$
$199$	−0.165159	−0.165159	−0.0825793	+	0.996584i	$0.526316\pi$
$200$	0	0
$201$	−0.878826	−0.878826
$202$	0	0
$203$	0	0
$204$	−0.878826	−0.878826
$205$	0	0
$206$	0	0
$207$	0.699455	0.699455
$208$	0.490971	0.490971
$209$	0	0
$210$	0	0
$211$	1.89163	1.89163	0.945817	−	0.324699i	$-0.105263\pi$
$211$	1.89163	1.89163	0.945817	+	0.324699i	$0.105263\pi$
$212$	0	0
$213$	−0.394442	−0.394442
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	1.58487	1.58487
$220$	0	0
$221$	0.537071	0.537071
$222$	0	0
$223$	1.09390	1.09390	0.546948	−	0.837166i	$-0.315789\pi$
$223$	1.09390	1.09390	0.546948	+	0.837166i	$0.315789\pi$
$224$	0	0
$225$	−0.354563	−0.354563
$226$	0	0
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0.490971	0.490971	0.245485	−	0.969400i	$-0.421053\pi$
$233$	0.490971	0.490971	0.245485	+	0.969400i	$0.421053\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	1.41312	1.41312
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	−0.670704	−0.670704
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	0	0
$253$	3.46992	3.46992
$254$	0	0
$255$	0	0
$256$	1.00000	1.00000
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0.0585592	0.0585592
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−1.26798	−1.26798
$268$	1.09390	1.09390
$269$	−0.165159	−0.165159	−0.0825793	−	0.996584i	$-0.526316\pi$
$269$	−0.165159	−0.165159	−0.0825793	+	0.996584i	$0.526316\pi$
$270$	0	0
$271$	1.57828	1.57828	0.789141	−	0.614213i	$-0.210526\pi$
$271$	1.57828	1.57828	0.789141	+	0.614213i	$0.210526\pi$
$272$	1.09390	1.09390
$273$	0	0
$274$	0	0
$275$	−1.75895	−1.75895
$276$	1.58487	1.58487
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	−0.559600	−0.559600
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0.490971	0.490971
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	0.196609	0.196609
$290$	0	0
$291$	1.08824	1.08824
$292$	−1.97272	−1.97272
$293$	−0.803391	−0.803391	−0.401695	−	0.915773i	$-0.631579\pi$
$293$	−0.803391	−0.803391	−0.401695	+	0.915773i	$0.631579\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−1.91416	−1.91416
$298$	0	0
$299$	−0.968550	−0.968550
$300$	−0.803391	−0.803391
$301$	0	0
$302$	0	0
$303$	1.08824	1.08824
$304$	0	0
$305$	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
$311$	0.490971	0.490971	0.245485	−	0.969400i	$-0.421053\pi$
$311$	0.490971	0.490971	0.245485	+	0.969400i	$0.421053\pi$
$312$	0	0
$313$	−0.803391	−0.803391	−0.401695	−	0.915773i	$-0.631579\pi$
$313$	−0.803391	−0.803391	−0.401695	+	0.915773i	$0.631579\pi$
$314$	0	0
$315$	0	0
$316$	−1.75895	−1.75895
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0.290505	0.290505
$320$	0	0
$321$	−1.26798	−1.26798
$322$	0	0
$323$	0	0
$324$	−0.519722	−0.519722
$325$	0.490971	0.490971
$326$	0	0
$327$	1.58487	1.58487
$328$	0	0
$329$	0	0
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	−0.670704	−0.670704
$334$	0	0
$335$	0	0
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	−1.26798	−1.26798
$340$	0	0
$341$	−2.77611	−2.77611
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−1.35456	−1.35456	−0.677282	−	0.735724i	$-0.736842\pi$
$347$	−1.35456	−1.35456	−0.677282	+	0.735724i	$0.736842\pi$
$348$	0.132687	0.132687
$349$	1.89163	1.89163	0.945817	−	0.324699i	$-0.105263\pi$
$349$	1.89163	1.89163	0.945817	+	0.324699i	$0.105263\pi$
$350$	0	0
$351$	0.534296	0.534296
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	1.57828	1.57828
$357$	0	0
$358$	0	0
$359$	−0.803391	−0.803391	−0.401695	−	0.915773i	$-0.631579\pi$
$359$	−0.803391	−0.803391	−0.401695	+	0.915773i	$0.631579\pi$
$360$	0	0
$361$	1.00000	1.00000
$362$	0	0
$363$	−1.68222	−1.68222
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	−1.97272	−1.97272
$369$	−0.670704	−0.670704
$370$	0	0
$371$	0	0
$372$	−1.26798	−1.26798
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−0.0810881	−0.0810881
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	−0.165159	−0.165159	−0.0825793	−	0.996584i	$-0.526316\pi$
$383$	−0.165159	−0.165159	−0.0825793	+	0.996584i	$0.526316\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0.0585592	0.0585592
$388$	−1.35456	−1.35456
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	−2.15795	−2.15795
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0.623658	0.623658
$397$	−1.75895	−1.75895	−0.879474	−	0.475947i	$-0.842105\pi$
$397$	−1.75895	−1.75895	−0.879474	+	0.475947i	$0.842105\pi$
$398$	0	0
$399$	0	0
$400$	1.00000	1.00000
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	0.774890	0.774890
$404$	−1.35456	−1.35456
$405$	0	0
$406$	0	0
$407$	−3.32729	−3.32729
$408$	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	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	−0.165159	−0.165159	−0.0825793	−	0.996584i	$-0.526316\pi$
$421$	−0.165159	−0.165159	−0.0825793	+	0.996584i	$0.526316\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	1.09390	1.09390
$426$	0	0
$427$	0	0
$428$	1.57828	1.57828
$429$	0.693802	0.693802
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	1.08824	1.08824
$433$	−1.75895	−1.75895	−0.879474	−	0.475947i	$-0.842105\pi$
$433$	−1.75895	−1.75895	−0.879474	+	0.475947i	$0.842105\pi$
$434$	0	0
$435$	0	0
$436$	−1.97272	−1.97272
$437$	0	0
$438$	0	0
$439$	−1.35456	−1.35456	−0.677282	−	0.735724i	$-0.736842\pi$
$439$	−1.35456	−1.35456	−0.677282	+	0.735724i	$0.736842\pi$
$440$	0	0
$441$	−0.354563	−0.354563
$442$	0	0
$443$	−0.803391	−0.803391	−0.401695	−	0.915773i	$-0.631579\pi$
$443$	−0.803391	−0.803391	−0.401695	+	0.915773i	$0.631579\pi$
$444$	−1.51972	−1.51972
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	0.490971	0.490971	0.245485	−	0.969400i	$-0.421053\pi$
$449$	0.490971	0.490971	0.245485	+	0.969400i	$0.421053\pi$
$450$	0	0
$451$	−3.32729	−3.32729
$452$	1.57828	1.57828
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−1.75895	−1.75895	−0.879474	−	0.475947i	$-0.842105\pi$
$457$	−1.75895	−1.75895	−0.879474	+	0.475947i	$0.842105\pi$
$458$	0	0
$459$	1.19043	1.19043
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	−0.165159	−0.165159
$465$	0	0
$466$	0	0
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	−0.174080	−0.174080
$469$	0	0
$470$	0	0
$471$	1.58487	1.58487
$472$	0	0
$473$	0.290505	0.290505
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	0	0
$479$	1.09390	1.09390	0.546948	−	0.837166i	$-0.315789\pi$
$479$	1.09390	1.09390	0.546948	+	0.837166i	$0.315789\pi$
$480$	0	0
$481$	0.928738	0.928738
$482$	0	0
$483$	0	0
$484$	2.09390	2.09390
$485$	0	0
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	1.08824	1.08824
$490$	0	0
$491$	0.490971	0.490971	0.245485	−	0.969400i	$-0.421053\pi$
$491$	0.490971	0.490971	0.245485	+	0.969400i	$0.421053\pi$
$492$	−1.51972	−1.51972
$493$	−0.180666	−0.180666
$494$	0	0
$495$	0	0
$496$	1.57828	1.57828
$497$	0	0
$498$	0	0
$499$	−1.35456	−1.35456	−0.677282	−	0.735724i	$-0.736842\pi$
$499$	−1.35456	−1.35456	−0.677282	+	0.735724i	$0.736842\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	−1.35456	−1.35456	−0.677282	−	0.735724i	$-0.736842\pi$
$503$	−1.35456	−1.35456	−0.677282	+	0.735724i	$0.736842\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0.609731	0.609731
$508$	0	0
$509$	−1.97272	−1.97272	−0.986361	−	0.164595i	$-0.947368\pi$
$509$	−1.97272	−1.97272	−0.986361	+	0.164595i	$0.947368\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0.132687	0.132687
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	1.09390	1.09390	0.546948	−	0.837166i	$-0.315789\pi$
$521$	1.09390	1.09390	0.546948	+	0.837166i	$0.315789\pi$
$522$	0	0
$523$	−0.803391	−0.803391	−0.401695	−	0.915773i	$-0.631579\pi$
$523$	−0.803391	−0.803391	−0.401695	+	0.915773i	$0.631579\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	1.72648	1.72648
$528$	1.41312	1.41312
$529$	2.89163	2.89163
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0.928738	0.928738
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	−1.75895	−1.75895
$540$	0	0
$541$	−0.803391	−0.803391	−0.401695	−	0.915773i	$-0.631579\pi$
$541$	−0.803391	−0.803391	−0.401695	+	0.915773i	$0.631579\pi$
$542$	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
$551$	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
$559$	−0.0810881	−0.0810881
$560$	0	0
$561$	1.54581	1.54581
$562$	0	0
$563$	−1.35456	−1.35456	−0.677282	−	0.735724i	$-0.736842\pi$
$563$	−1.35456	−1.35456	−0.677282	+	0.735724i	$0.736842\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	1.57828	1.57828	0.789141	−	0.614213i	$-0.210526\pi$
$571$	1.57828	1.57828	0.789141	+	0.614213i	$0.210526\pi$
$572$	−0.863592	−0.863592
$573$	−1.51972	−1.51972
$574$	0	0
$575$	−1.97272	−1.97272
$576$	−0.354563	−0.354563
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	1.08824	1.08824
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−1.97272	−1.97272	−0.986361	−	0.164595i	$-0.947368\pi$
$587$	−1.97272	−1.97272	−0.986361	+	0.164595i	$0.947368\pi$
$588$	−0.803391	−0.803391
$589$	0	0
$590$	0	0
$591$	0	0
$592$	1.89163	1.89163
$593$	1.89163	1.89163	0.945817	−	0.324699i	$-0.105263\pi$
$593$	1.89163	1.89163	0.945817	+	0.324699i	$0.105263\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0.132687	0.132687
$598$	0	0
$599$	−0.803391	−0.803391	−0.401695	−	0.915773i	$-0.631579\pi$
$599$	−0.803391	−0.803391	−0.401695	+	0.915773i	$0.631579\pi$
$600$	0	0
$601$	0.490971	0.490971	0.245485	−	0.969400i	$-0.421053\pi$
$601$	0.490971	0.490971	0.245485	+	0.969400i	$0.421053\pi$
$602$	0	0
$603$	−0.387855	−0.387855
$604$	0	0
$605$	0	0
$606$	0	0
$607$	0.490971	0.490971	0.245485	−	0.969400i	$-0.421053\pi$
$607$	0.490971	0.490971	0.245485	+	0.969400i	$0.421053\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	−0.387855	−0.387855
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	1.09390	1.09390	0.546948	−	0.837166i	$-0.315789\pi$
$619$	1.09390	1.09390	0.546948	+	0.837166i	$0.315789\pi$
$620$	0	0
$621$	−2.14680	−2.14680
$622$	0	0
$623$	0	0
$624$	−0.394442	−0.394442
$625$	1.00000	1.00000
$626$	0	0
$627$	0	0
$628$	−1.97272	−1.97272
$629$	2.06925	2.06925
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	−1.51972	−1.51972
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0.490971	0.490971
$638$	0	0
$639$	−0.174080	−0.174080
$640$	0	0
$641$	−0.803391	−0.803391	−0.401695	−	0.915773i	$-0.631579\pi$
$641$	−0.803391	−0.803391	−0.401695	+	0.915773i	$0.631579\pi$
$642$	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
$649$	0	0
$650$	0	0
$651$	0	0
$652$	−1.35456	−1.35456
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	1.89163	1.89163
$657$	0.699455	0.699455
$658$	0	0
$659$	1.57828	1.57828	0.789141	−	0.614213i	$-0.210526\pi$
$659$	1.57828	1.57828	0.789141	+	0.614213i	$0.210526\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	−0.431478	−0.431478
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0.325812	0.325812
$668$	0	0
$669$	−0.878826	−0.878826
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	1.08824	1.08824
$676$	−0.758948	−0.758948
$677$	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
$683$	1.57828	1.57828	0.789141	−	0.614213i	$-0.210526\pi$
$683$	1.57828	1.57828	0.789141	+	0.614213i	$0.210526\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	−0.165159	−0.165159
$689$	0	0
$690$	0	0
$691$	−1.97272	−1.97272	−0.986361	−	0.164595i	$-0.947368\pi$
$691$	−1.97272	−1.97272	−0.986361	+	0.164595i	$0.947368\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	2.06925	2.06925
$698$	0	0
$699$	−0.394442	−0.394442
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	−1.75895	−1.75895
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−0.803391	−0.803391	−0.401695	−	0.915773i	$-0.631579\pi$
$709$	−0.803391	−0.803391	−0.401695	+	0.915773i	$0.631579\pi$
$710$	0	0
$711$	0.623658	0.623658
$712$	0	0
$713$	−3.11351	−3.11351
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	1.09390	1.09390	0.546948	−	0.837166i	$-0.315789\pi$
$719$	1.09390	1.09390	0.546948	+	0.837166i	$0.315789\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	−0.165159	−0.165159
$726$	0	0
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	1.05856	1.05856
$730$	0	0
$731$	−0.180666	−0.180666
$732$	0	0
$733$	−0.803391	−0.803391	−0.401695	−	0.915773i	$-0.631579\pi$
$733$	−0.803391	−0.803391	−0.401695	+	0.915773i	$0.631579\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−1.92411	−1.92411
$738$	0	0
$739$	0.490971	0.490971	0.245485	−	0.969400i	$-0.421053\pi$
$739$	0.490971	0.490971	0.245485	+	0.969400i	$0.421053\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	1.09390	1.09390	0.546948	−	0.837166i	$-0.315789\pi$
$743$	1.09390	1.09390	0.546948	+	0.837166i	$0.315789\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	−1.92411	−1.92411
$749$	0	0
$750$	0	0
$751$	−0.165159	−0.165159	−0.0825793	−	0.996584i	$-0.526316\pi$
$751$	−0.165159	−0.165159	−0.0825793	+	0.996584i	$0.526316\pi$
$752$	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
$759$	−2.78770	−2.78770
$760$	0	0
$761$	−1.97272	−1.97272	−0.986361	−	0.164595i	$-0.947368\pi$
$761$	−1.97272	−1.97272	−0.986361	+	0.164595i	$0.947368\pi$
$762$	0	0
$763$	0	0
$764$	1.89163	1.89163
$765$	0	0
$766$	0	0
$767$	0	0
$768$	−0.803391	−0.803391
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0	0
$772$	−1.35456	−1.35456
$773$	−1.75895	−1.75895	−0.879474	−	0.475947i	$-0.842105\pi$
$773$	−1.75895	−1.75895	−0.879474	+	0.475947i	$0.842105\pi$
$774$	0	0
$775$	1.57828	1.57828
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	−0.863592	−0.863592
$782$	0	0
$783$	−0.179733	−0.179733
$784$	1.00000	1.00000
$785$	0	0
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	−0.165159	−0.165159
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	−0.559600	−0.559600
$802$	0	0
$803$	3.46992	3.46992
$804$	−0.878826	−0.878826
$805$	0	0
$806$	0	0
$807$	0.132687	0.132687
$808$	0	0
$809$	−0.803391	−0.803391	−0.401695	−	0.915773i	$-0.631579\pi$
$809$	−0.803391	−0.803391	−0.401695	+	0.915773i	$0.631579\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	−1.26798	−1.26798
$814$	0	0
$815$	0	0
$816$	−0.878826	−0.878826
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	1.57828	1.57828	0.789141	−	0.614213i	$-0.210526\pi$
$821$	1.57828	1.57828	0.789141	+	0.614213i	$0.210526\pi$
$822$	0	0
$823$	1.89163	1.89163	0.945817	−	0.324699i	$-0.105263\pi$
$823$	1.89163	1.89163	0.945817	+	0.324699i	$0.105263\pi$
$824$	0	0
$825$	1.41312	1.41312
$826$	0	0
$827$	1.89163	1.89163	0.945817	−	0.324699i	$-0.105263\pi$
$827$	1.89163	1.89163	0.945817	+	0.324699i	$0.105263\pi$
$828$	0.699455	0.699455
$829$	1.09390	1.09390	0.546948	−	0.837166i	$-0.315789\pi$
$829$	1.09390	1.09390	0.546948	+	0.837166i	$0.315789\pi$
$830$	0	0
$831$	0	0
$832$	0.490971	0.490971
$833$	1.09390	1.09390
$834$	0	0
$835$	0	0
$836$	0	0
$837$	1.71755	1.71755
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	−0.972723	−0.972723
$842$	0	0
$843$	0	0
$844$	1.89163	1.89163
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	0	0
$850$	0	0
$851$	−3.73167	−3.73167
$852$	−0.394442	−0.394442
$853$	−0.165159	−0.165159	−0.0825793	−	0.996584i	$-0.526316\pi$
$853$	−0.165159	−0.165159	−0.0825793	+	0.996584i	$0.526316\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−0.803391	−0.803391	−0.401695	−	0.915773i	$-0.631579\pi$
$863$	−0.803391	−0.803391	−0.401695	+	0.915773i	$0.631579\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−0.157954	−0.157954
$868$	0	0
$869$	3.09390	3.09390
$870$	0	0
$871$	0.537071	0.537071
$872$	0	0
$873$	0.480278	0.480278
$874$	0	0
$875$	0	0
$876$	1.58487	1.58487
$877$	1.09390	1.09390	0.546948	−	0.837166i	$-0.315789\pi$
$877$	1.09390	1.09390	0.546948	+	0.837166i	$0.315789\pi$
$878$	0	0
$879$	0.645437	0.645437
$880$	0	0
$881$	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			$\pi$
$884$	0.537071	0.537071
$885$	0	0
$886$	0	0
$887$	2.00000	2.00000	1.00000			$0$
$887$	2.00000	2.00000	1.00000			$0$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0.914163	0.914163
$892$	1.09390	1.09390
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0.778124	0.778124
$898$	0	0
$899$	−0.260667	−0.260667
$900$	−0.354563	−0.354563
$901$	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
$909$	0.480278	0.480278
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	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
$923$	0.241052	0.241052
$924$	0	0
$925$	1.89163	1.89163
$926$	0	0
$927$	0	0
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	0.490971	0.490971
$933$	−0.394442	−0.394442
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	0.645437	0.645437
$940$	0	0
$941$	−1.75895	−1.75895	−0.879474	−	0.475947i	$-0.842105\pi$
$941$	−1.75895	−1.75895	−0.879474	+	0.475947i	$0.842105\pi$
$942$	0	0
$943$	−3.73167	−3.73167
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−1.35456	−1.35456	−0.677282	−	0.735724i	$-0.736842\pi$
$947$	−1.35456	−1.35456	−0.677282	+	0.735724i	$0.736842\pi$
$948$	1.41312	1.41312
$949$	−0.968550	−0.968550
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−0.233389	−0.233389
$958$	0	0
$959$	0	0
$960$	0	0
$961$	1.49097	1.49097
$962$	0	0
$963$	−0.559600	−0.559600
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	−0.670704	−0.670704
$973$	0	0
$974$	0	0
$975$	−0.394442	−0.394442
$976$	0	0
$977$	2.00000	2.00000	1.00000			$0$
$977$	2.00000	2.00000	1.00000			$0$
$978$	0	0
$979$	−2.77611	−2.77611
$980$	0	0
$981$	0.699455	0.699455
$982$	0	0
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0.325812	0.325812
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−1.75895	−1.75895	−0.879474	−	0.475947i	$-0.842105\pi$
$997$	−1.75895	−1.75895	−0.879474	+	0.475947i	$0.842105\pi$
$998$	0	0
$999$	2.05856	2.05856

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3467.1.b.a.3466.4	✓	9
3467.3466	odd	2	CM	3467.1.b.a.3466.4	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3467.1.b.a.3466.4	✓	9	1.1	even	1	trivial
3467.1.b.a.3466.4	✓	9	3467.3466	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:	\( N \)	\(=\)	\( 3467 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3467.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.803391 q^{3} +1.00000 q^{4} -0.354563 q^{9} -1.75895 q^{11} -0.803391 q^{12} +0.490971 q^{13} +1.00000 q^{16} +1.09390 q^{17} -1.97272 q^{23} +1.00000 q^{25} +1.08824 q^{27} -0.165159 q^{29} +1.57828 q^{31} +1.41312 q^{33} -0.354563 q^{36} +1.89163 q^{37} -0.394442 q^{39} +1.89163 q^{41} -0.165159 q^{43} -1.75895 q^{44} -0.803391 q^{48} +1.00000 q^{49} -0.878826 q^{51} +0.490971 q^{52} +1.00000 q^{64} +1.09390 q^{67} +1.09390 q^{68} +1.58487 q^{69} +0.490971 q^{71} -1.97272 q^{73} -0.803391 q^{75} -1.75895 q^{79} -0.519722 q^{81} +0.132687 q^{87} +1.57828 q^{89} -1.97272 q^{92} -1.26798 q^{93} -1.35456 q^{97} +0.623658 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - q^{3} + 9 q^{4} + 8 q^{9} - q^{11} - q^{12} - q^{13} + 9 q^{16} - q^{17} - q^{23} + 9 q^{25} - 2 q^{27} - q^{29} - q^{31} - 2 q^{33} + 8 q^{36} - q^{37} - 2 q^{39} - q^{41} - q^{43} - q^{44}+ \cdots - 3 q^{99}+O(q^{100}) \) 9 * q - q^3 + 9 * q^4 + 8 * q^9 - q^11 - q^12 - q^13 + 9 * q^16 - q^17 - q^23 + 9 * q^25 - 2 * q^27 - q^29 - q^31 - 2 * q^33 + 8 * q^36 - q^37 - 2 * q^39 - q^41 - q^43 - q^44 - q^48 + 9 * q^49 - 2 * q^51 - q^52 + 9 * q^64 - q^67 - q^68 - 2 * q^69 - q^71 - q^73 - q^75 - q^79 + 7 * q^81 - 2 * q^87 - q^89 - q^92 - 2 * q^93 - q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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