LMFDB - Embedded newform 2288.1.m.b.2001.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2288,1,Mod(2001,2288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2288, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2288.2001");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2288 = 2^{4} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2288.m (of order $2$, degree $1$, not 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:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Projective image:	$D_{5}$
Projective field:	Galois closure of 5.1.20449.1
Artin image:	$D_{10}$
Artin field:	Galois closure of 10.0.428197479424.4

Embedding invariants

Embedding label			2001.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	2288.2001

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.618034 q^{3} +1.61803 q^{7} -0.618034 q^{9} +O(q^{10})$	$q-0.618034 q^{3} +1.61803 q^{7} -0.618034 q^{9} -1.00000 q^{11} +1.00000 q^{13} -0.618034 q^{19} -1.00000 q^{21} +1.61803 q^{23} +1.00000 q^{25} +1.00000 q^{27} +0.618034 q^{33} -0.618034 q^{39} -1.61803 q^{41} +1.61803 q^{49} +0.618034 q^{53} +0.381966 q^{57} -1.00000 q^{63} -1.00000 q^{69} +0.618034 q^{73} -0.618034 q^{75} -1.61803 q^{77} +1.61803 q^{83} +1.61803 q^{91} +0.618034 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} + q^{7} + q^{9}+O(q^{10}) $ 2 * q + q^3 + q^7 + q^9	$ 2 q + q^{3} + q^{7} + q^{9} - 2 q^{11} + 2 q^{13} + q^{19} - 2 q^{21} + q^{23} + 2 q^{25} + 2 q^{27} - q^{33} + q^{39} - q^{41} + q^{49} - q^{53} + 3 q^{57} - 2 q^{63} - 2 q^{69} - q^{73} + q^{75} - q^{77} + q^{83} + q^{91} - q^{99}+O(q^{100}) $ 2 * q + q^3 + q^7 + q^9 - 2 * q^11 + 2 * q^13 + q^19 - 2 * q^21 + q^23 + 2 * q^25 + 2 * q^27 - q^33 + q^39 - q^41 + q^49 - q^53 + 3 * q^57 - 2 * q^63 - 2 * q^69 - q^73 + q^75 - q^77 + q^83 + q^91 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2288\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$1717$	$2081$
$\chi(n)$	$1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	0	0
$2$	0	0
$3$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$3$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$4$	0	0
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	0	0
$7$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$7$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$8$	0	0
$9$	−0.618034	−0.618034
$10$	0	0
$11$	−1.00000	−1.00000
$11$	−1.00000	−1.00000
$12$	0	0
$13$	1.00000	1.00000
$13$	1.00000	1.00000
$14$	0	0
$15$	0	0
$16$	0	0
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$19$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$20$	0	0
$21$	−1.00000	−1.00000
$22$	0	0
$23$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$23$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$24$	0	0
$25$	1.00000	1.00000
$26$	0	0
$27$	1.00000	1.00000
$28$	0	0
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0	0
$33$	0.618034	0.618034
$34$	0	0
$35$	0	0
$36$	0	0
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	−0.618034	−0.618034
$40$	0	0
$41$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$41$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	0	0
$49$	1.61803	1.61803
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$53$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0.381966	0.381966
$58$	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
$63$	−1.00000	−1.00000
$64$	0	0
$65$	0	0
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0	0
$69$	−1.00000	−1.00000
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	0	0
$73$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$73$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$74$	0	0
$75$	−0.618034	−0.618034
$76$	0	0
$77$	−1.61803	−1.61803
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$83$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	1.61803	1.61803
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	0.618034	0.618034
$100$	0	0
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$103$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0	0
$109$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$109$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$113$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−0.618034	−0.618034
$118$	0	0
$119$	0	0
$120$	0	0
$121$	1.00000	1.00000
$122$	0	0
$123$	1.00000	1.00000
$124$	0	0
$125$	0	0
$126$	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			$\pi$
$132$	0	0
$133$	−1.00000	−1.00000
$134$	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
$143$	−1.00000	−1.00000
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−1.00000	−1.00000
$148$	0	0
$149$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$149$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$150$	0	0
$151$	−2.00000	−2.00000	−1.00000			$\pi$
$151$	−2.00000	−2.00000	−1.00000			$\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$157$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$158$	0	0
$159$	−0.381966	−0.381966
$160$	0	0
$161$	2.61803	2.61803
$162$	0	0
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$167$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$168$	0	0
$169$	1.00000	1.00000
$170$	0	0
$171$	0.381966	0.381966
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	1.61803	1.61803
$176$	0	0
$177$	0	0
$178$	0	0
$179$	−2.00000	−2.00000	−1.00000			$\pi$
$179$	−2.00000	−2.00000	−1.00000			$\pi$
$180$	0	0
$181$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$181$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	1.61803	1.61803
$190$	0	0
$191$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$191$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$192$	0	0
$193$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$193$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$197$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$198$	0	0
$199$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$199$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−1.00000	−1.00000
$208$	0	0
$209$	0.618034	0.618034
$210$	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
$219$	−0.381966	−0.381966
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	0	0
$225$	−0.618034	−0.618034
$226$	0	0
$227$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$227$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	1.00000	1.00000
$232$	0	0
$233$	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	0
$239$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$239$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$240$	0	0
$241$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$241$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$242$	0	0
$243$	−1.00000	−1.00000
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−0.618034	−0.618034
$248$	0	0
$249$	−1.00000	−1.00000
$250$	0	0
$251$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$251$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$252$	0	0
$253$	−1.61803	−1.61803
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$257$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$269$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$270$	0	0
$271$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$271$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$272$	0	0
$273$	−1.00000	−1.00000
$274$	0	0
$275$	−1.00000	−1.00000
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$281$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−2.61803	−2.61803
$288$	0	0
$289$	1.00000	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	2.00000	2.00000	1.00000			$0$
$293$	2.00000	2.00000	1.00000			$0$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−1.00000	−1.00000
$298$	0	0
$299$	1.61803	1.61803
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−2.00000	−2.00000	−1.00000			$\pi$
$307$	−2.00000	−2.00000	−1.00000			$\pi$
$308$	0	0
$309$	−1.00000	−1.00000
$310$	0	0
$311$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$311$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$312$	0	0
$313$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$313$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	1.00000	1.00000
$326$	0	0
$327$	−0.381966	−0.381966
$328$	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	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	−0.381966	−0.381966
$340$	0	0
$341$	0	0
$342$	0	0
$343$	1.00000	1.00000
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$349$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$350$	0	0
$351$	1.00000	1.00000
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$359$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$360$	0	0
$361$	−0.618034	−0.618034
$362$	0	0
$363$	−0.618034	−0.618034
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$367$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$368$	0	0
$369$	1.00000	1.00000
$370$	0	0
$371$	1.00000	1.00000
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	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
$389$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$389$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0.618034	0.618034
$400$	0	0
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	2.00000	2.00000	1.00000			$0$
$409$	2.00000	2.00000	1.00000			$0$
$410$	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
$419$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$419$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$420$	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
$428$	0	0
$429$	0.618034	0.618034
$430$	0	0
$431$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$431$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$432$	0	0
$433$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$433$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−1.00000	−1.00000
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	−1.00000	−1.00000
$442$	0	0
$443$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$443$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	1.00000	1.00000
$448$	0	0
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	0	0
$451$	1.61803	1.61803
$452$	0	0
$453$	1.23607	1.23607
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$457$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$461$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−2.00000	−2.00000	−1.00000			$\pi$
$467$	−2.00000	−2.00000	−1.00000			$\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	1.00000	1.00000
$472$	0	0
$473$	0	0
$474$	0	0
$475$	−0.618034	−0.618034
$476$	0	0
$477$	−0.381966	−0.381966
$478$	0	0
$479$	−2.00000	−2.00000	−1.00000			$\pi$
$479$	−2.00000	−2.00000	−1.00000			$\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	−1.61803	−1.61803
$484$	0	0
$485$	0	0
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	0	0
$501$	0.381966	0.381966
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−0.618034	−0.618034
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	1.00000	1.00000
$512$	0	0
$513$	−0.618034	−0.618034
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$521$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	−1.00000	−1.00000
$526$	0	0
$527$	0	0
$528$	0	0
$529$	1.61803	1.61803
$530$	0	0
$531$	0	0
$532$	0	0
$533$	−1.61803	−1.61803
$534$	0	0
$535$	0	0
$536$	0	0
$537$	1.23607	1.23607
$538$	0	0
$539$	−1.61803	−1.61803
$540$	0	0
$541$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$541$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$542$	0	0
$543$	−0.381966	−0.381966
$544$	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
$557$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$557$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$558$	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
$569$	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
$573$	0.381966	0.381966
$574$	0	0
$575$	1.61803	1.61803
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	1.00000	1.00000
$580$	0	0
$581$	2.61803	2.61803
$582$	0	0
$583$	−0.618034	−0.618034
$584$	0	0
$585$	0	0
$586$	0	0
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	−0.381966	−0.381966
$592$	0	0
$593$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$593$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0.381966	0.381966
$598$	0	0
$599$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$599$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	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	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$613$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	1.61803	1.61803
$622$	0	0
$623$	0	0
$624$	0	0
$625$	1.00000	1.00000
$626$	0	0
$627$	−0.381966	−0.381966
$628$	0	0
$629$	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
$637$	1.61803	1.61803
$638$	0	0
$639$	0	0
$640$	0	0
$641$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$641$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$647$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	2.00000	2.00000	1.00000			$0$
$653$	2.00000	2.00000	1.00000			$0$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−0.381966	−0.381966
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	1.00000	1.00000
$676$	0	0
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0.381966	0.381966
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0.618034	0.618034
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	1.00000	1.00000
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0.381966	0.381966
$718$	0	0
$719$	−2.00000	−2.00000	−1.00000			$\pi$
$719$	−2.00000	−2.00000	−1.00000			$\pi$
$720$	0	0
$721$	2.61803	2.61803
$722$	0	0
$723$	1.00000	1.00000
$724$	0	0
$725$	0	0
$726$	0	0
$727$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$727$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$728$	0	0
$729$	0.618034	0.618034
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$733$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$739$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$740$	0	0
$741$	0.381966	0.381966
$742$	0	0
$743$	−2.00000	−2.00000	−1.00000			$\pi$
$743$	−2.00000	−2.00000	−1.00000			$\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−1.00000	−1.00000
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$751$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$752$	0	0
$753$	−1.00000	−1.00000
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$757$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$758$	0	0
$759$	1.00000	1.00000
$760$	0	0
$761$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$761$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$762$	0	0
$763$	1.00000	1.00000
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$769$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$770$	0	0
$771$	1.00000	1.00000
$772$	0	0
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	1.00000	1.00000
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$787$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	1.00000	1.00000
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	2.00000	2.00000	1.00000			$0$
$797$	2.00000	2.00000	1.00000			$0$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	0	0
$803$	−0.618034	−0.618034
$804$	0	0
$805$	0	0
$806$	0	0
$807$	1.00000	1.00000
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$811$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$812$	0	0
$813$	0.381966	0.381966
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	−1.00000	−1.00000
$820$	0	0
$821$	2.00000	2.00000	1.00000			$0$
$821$	2.00000	2.00000	1.00000			$0$
$822$	0	0
$823$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$823$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$824$	0	0
$825$	0.618034	0.618034
$826$	0	0
$827$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$827$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$828$	0	0
$829$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$829$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$830$	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	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	1.00000	1.00000
$842$	0	0
$843$	−0.381966	−0.381966
$844$	0	0
$845$	0	0
$846$	0	0
$847$	1.61803	1.61803
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$853$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$859$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$860$	0	0
$861$	1.61803	1.61803
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−0.618034	−0.618034
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$877$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$878$	0	0
$879$	−1.23607	−1.23607
$880$	0	0
$881$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$881$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$882$	0	0
$883$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$883$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−1.00000	−1.00000
$898$	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
$907$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$907$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$911$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$912$	0	0
$913$	−1.61803	−1.61803
$914$	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
$921$	1.23607	1.23607
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−1.00000	−1.00000
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	−1.00000	−1.00000
$932$	0	0
$933$	0.381966	0.381966
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	1.00000	1.00000
$940$	0	0
$941$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$941$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$942$	0	0
$943$	−2.61803	−2.61803
$944$	0	0
$945$	0	0
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	0.618034	0.618034
$950$	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	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	1.00000	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$967$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$971$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	−0.618034	−0.618034
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−0.381966	−0.381966
$982$	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	0
$990$	0	0
$991$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$991$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2288.1.m.b.2001.1		2
4.3	odd	2		143.1.d.a.142.2	✓	2
11.10	odd	2		2288.1.m.a.2001.1		2
12.11	even	2		1287.1.g.b.1000.1		2
13.12	even	2		2288.1.m.a.2001.1		2
20.3	even	4		3575.1.c.d.3574.2		4
20.7	even	4		3575.1.c.d.3574.3		4
20.19	odd	2		3575.1.h.f.2001.1		2
44.3	odd	10		1573.1.l.d.233.1		4
44.7	even	10		1573.1.l.a.1546.1		4
44.15	odd	10		1573.1.l.d.1546.1		4
44.19	even	10		1573.1.l.a.233.1		4
44.27	odd	10		1573.1.l.b.844.1		4
44.31	odd	10		1573.1.l.b.766.1		4
44.35	even	10		1573.1.l.c.766.1		4
44.39	even	10		1573.1.l.c.844.1		4
44.43	even	2		143.1.d.b.142.1	yes	2
52.3	odd	6		1859.1.i.b.1330.1		4
52.7	even	12		1859.1.k.c.1836.3		8
52.11	even	12		1859.1.k.c.1374.2		8
52.15	even	12		1859.1.k.c.1374.3		8
52.19	even	12		1859.1.k.c.1836.2		8
52.23	odd	6		1859.1.i.a.1330.2		4
52.31	even	4		1859.1.c.c.846.2		4
52.35	odd	6		1859.1.i.b.868.1		4
52.43	odd	6		1859.1.i.a.868.2		4
52.47	even	4		1859.1.c.c.846.3		4
52.51	odd	2		143.1.d.b.142.1	yes	2
132.131	odd	2		1287.1.g.a.1000.2		2
143.142	odd	2	CM	2288.1.m.b.2001.1		2
156.155	even	2		1287.1.g.a.1000.2		2
220.43	odd	4		3575.1.c.c.3574.3		4
220.87	odd	4		3575.1.c.c.3574.2		4
220.219	even	2		3575.1.h.e.2001.2		2
260.103	even	4		3575.1.c.c.3574.3		4
260.207	even	4		3575.1.c.c.3574.2		4
260.259	odd	2		3575.1.h.e.2001.2		2
572.43	even	6		1859.1.i.b.868.1		4
572.51	even	10		1573.1.l.d.1546.1		4
572.87	even	6		1859.1.i.a.868.2		4
572.103	odd	10		1573.1.l.a.1546.1		4
572.175	odd	12		1859.1.k.c.1836.3		8
572.207	odd	10		1573.1.l.c.766.1		4
572.219	odd	12		1859.1.k.c.1374.3		8
572.259	even	10		1573.1.l.b.844.1		4
572.263	even	6		1859.1.i.a.1330.2		4
572.307	odd	4		1859.1.c.c.846.2		4
572.311	odd	10		1573.1.l.a.233.1		4
572.395	odd	4		1859.1.c.c.846.3		4
572.415	even	10		1573.1.l.d.233.1		4
572.439	even	6		1859.1.i.b.1330.1		4
572.467	odd	10		1573.1.l.c.844.1		4
572.483	odd	12		1859.1.k.c.1374.2		8
572.519	even	10		1573.1.l.b.766.1		4
572.527	odd	12		1859.1.k.c.1836.2		8
572.571	even	2		143.1.d.a.142.2	✓	2
1716.1715	odd	2		1287.1.g.b.1000.1		2
2860.1143	odd	4		3575.1.c.d.3574.2		4
2860.2287	odd	4		3575.1.c.d.3574.3		4
2860.2859	even	2		3575.1.h.f.2001.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.1.d.a.142.2	✓	2	4.3	odd	2
143.1.d.a.142.2	✓	2	572.571	even	2
143.1.d.b.142.1	yes	2	44.43	even	2
143.1.d.b.142.1	yes	2	52.51	odd	2
1287.1.g.a.1000.2		2	132.131	odd	2
1287.1.g.a.1000.2		2	156.155	even	2
1287.1.g.b.1000.1		2	12.11	even	2
1287.1.g.b.1000.1		2	1716.1715	odd	2
1573.1.l.a.233.1		4	44.19	even	10
1573.1.l.a.233.1		4	572.311	odd	10
1573.1.l.a.1546.1		4	44.7	even	10
1573.1.l.a.1546.1		4	572.103	odd	10
1573.1.l.b.766.1		4	44.31	odd	10
1573.1.l.b.766.1		4	572.519	even	10
1573.1.l.b.844.1		4	44.27	odd	10
1573.1.l.b.844.1		4	572.259	even	10
1573.1.l.c.766.1		4	44.35	even	10
1573.1.l.c.766.1		4	572.207	odd	10
1573.1.l.c.844.1		4	44.39	even	10
1573.1.l.c.844.1		4	572.467	odd	10
1573.1.l.d.233.1		4	44.3	odd	10
1573.1.l.d.233.1		4	572.415	even	10
1573.1.l.d.1546.1		4	44.15	odd	10
1573.1.l.d.1546.1		4	572.51	even	10
1859.1.c.c.846.2		4	52.31	even	4
1859.1.c.c.846.2		4	572.307	odd	4
1859.1.c.c.846.3		4	52.47	even	4
1859.1.c.c.846.3		4	572.395	odd	4
1859.1.i.a.868.2		4	52.43	odd	6
1859.1.i.a.868.2		4	572.87	even	6
1859.1.i.a.1330.2		4	52.23	odd	6
1859.1.i.a.1330.2		4	572.263	even	6
1859.1.i.b.868.1		4	52.35	odd	6
1859.1.i.b.868.1		4	572.43	even	6
1859.1.i.b.1330.1		4	52.3	odd	6
1859.1.i.b.1330.1		4	572.439	even	6
1859.1.k.c.1374.2		8	52.11	even	12
1859.1.k.c.1374.2		8	572.483	odd	12
1859.1.k.c.1374.3		8	52.15	even	12
1859.1.k.c.1374.3		8	572.219	odd	12
1859.1.k.c.1836.2		8	52.19	even	12
1859.1.k.c.1836.2		8	572.527	odd	12
1859.1.k.c.1836.3		8	52.7	even	12
1859.1.k.c.1836.3		8	572.175	odd	12
2288.1.m.a.2001.1		2	11.10	odd	2
2288.1.m.a.2001.1		2	13.12	even	2
2288.1.m.b.2001.1		2	1.1	even	1	trivial
2288.1.m.b.2001.1		2	143.142	odd	2	CM
3575.1.c.c.3574.2		4	220.87	odd	4
3575.1.c.c.3574.2		4	260.207	even	4
3575.1.c.c.3574.3		4	220.43	odd	4
3575.1.c.c.3574.3		4	260.103	even	4
3575.1.c.d.3574.2		4	20.3	even	4
3575.1.c.d.3574.2		4	2860.1143	odd	4
3575.1.c.d.3574.3		4	20.7	even	4
3575.1.c.d.3574.3		4	2860.2287	odd	4
3575.1.h.e.2001.2		2	220.219	even	2
3575.1.h.e.2001.2		2	260.259	odd	2
3575.1.h.f.2001.1		2	20.19	odd	2
3575.1.h.f.2001.1		2	2860.2859	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2288 = 2^{4} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2288.m (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.618034 q^{3} +1.61803 q^{7} -0.618034 q^{9} +O(q^{10})\)	\(q-0.618034 q^{3} +1.61803 q^{7} -0.618034 q^{9} -1.00000 q^{11} +1.00000 q^{13} -0.618034 q^{19} -1.00000 q^{21} +1.61803 q^{23} +1.00000 q^{25} +1.00000 q^{27} +0.618034 q^{33} -0.618034 q^{39} -1.61803 q^{41} +1.61803 q^{49} +0.618034 q^{53} +0.381966 q^{57} -1.00000 q^{63} -1.00000 q^{69} +0.618034 q^{73} -0.618034 q^{75} -1.61803 q^{77} +1.61803 q^{83} +1.61803 q^{91} +0.618034 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} + q^{7} + q^{9}+O(q^{10}) \) 2 * q + q^3 + q^7 + q^9	\( 2 q + q^{3} + q^{7} + q^{9} - 2 q^{11} + 2 q^{13} + q^{19} - 2 q^{21} + q^{23} + 2 q^{25} + 2 q^{27} - q^{33} + q^{39} - q^{41} + q^{49} - q^{53} + 3 q^{57} - 2 q^{63} - 2 q^{69} - q^{73} + q^{75} - q^{77} + q^{83} + q^{91} - q^{99}+O(q^{100}) \) 2 * q + q^3 + q^7 + q^9 - 2 * q^11 + 2 * q^13 + q^19 - 2 * q^21 + q^23 + 2 * q^25 + 2 * q^27 - q^33 + q^39 - q^41 + q^49 - q^53 + 3 * q^57 - 2 * q^63 - 2 * q^69 - q^73 + q^75 - q^77 + q^83 + q^91 - q^99

Introduction

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