LMFDB - Embedded newform 1287.1.g.b.1000.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1287,1,Mod(1000,1287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1287, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1287.1000");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1287 = 3^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1287.g (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:	$0.642296671259$
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:	$\Z[a_1, a_2]$
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 10.0.101613269043.1

Embedding invariants

Embedding label			1000.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	1287.1000

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.61803 q^{2} +1.61803 q^{4} +0.618034 q^{7} +1.00000 q^{8} +O(q^{10})$	$q+1.61803 q^{2} +1.61803 q^{4} +0.618034 q^{7} +1.00000 q^{8} -1.00000 q^{11} +1.00000 q^{13} +1.00000 q^{14} -1.61803 q^{19} -1.61803 q^{22} -0.618034 q^{23} +1.00000 q^{25} +1.61803 q^{26} +1.00000 q^{28} -1.00000 q^{32} -2.61803 q^{38} -0.618034 q^{41} -1.61803 q^{44} -1.00000 q^{46} -0.618034 q^{49} +1.61803 q^{50} +1.61803 q^{52} +1.61803 q^{53} +0.618034 q^{56} -1.61803 q^{64} -1.61803 q^{73} -2.61803 q^{76} -0.618034 q^{77} -1.00000 q^{82} -0.618034 q^{83} -1.00000 q^{88} +0.618034 q^{91} -1.00000 q^{92} -1.00000 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{4} - q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q + q^2 + q^4 - q^7 + 2 * q^8	$ 2 q + q^{2} + q^{4} - q^{7} + 2 q^{8} - 2 q^{11} + 2 q^{13} + 2 q^{14} - q^{19} - q^{22} + q^{23} + 2 q^{25} + q^{26} + 2 q^{28} - 2 q^{32} - 3 q^{38} + q^{41} - q^{44} - 2 q^{46} + q^{49} + q^{50} + q^{52} + q^{53} - q^{56} - q^{64} - q^{73} - 3 q^{76} + q^{77} - 2 q^{82} + q^{83} - 2 q^{88} - q^{91} - 2 q^{92} - 2 q^{98}+O(q^{100}) $ 2 * q + q^2 + q^4 - q^7 + 2 * q^8 - 2 * q^11 + 2 * q^13 + 2 * q^14 - q^19 - q^22 + q^23 + 2 * q^25 + q^26 + 2 * q^28 - 2 * q^32 - 3 * q^38 + q^41 - q^44 - 2 * q^46 + q^49 + q^50 + q^52 + q^53 - q^56 - q^64 - q^73 - 3 * q^76 + q^77 - 2 * q^82 + q^83 - 2 * q^88 - q^91 - 2 * q^92 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1287\mathbb{Z}\right)^\times$.

$n$	$496$	$937$	$1145$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$2$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$3$	0	0
$3$	0	0
$4$	1.61803	1.61803
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	0	0
$7$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$7$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$8$	1.00000	1.00000
$9$	0	0
$10$	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
$14$	1.00000	1.00000
$15$	0	0
$16$	0	0
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$19$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$20$	0	0
$21$	0	0
$22$	−1.61803	−1.61803
$23$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$23$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$24$	0	0
$25$	1.00000	1.00000
$26$	1.61803	1.61803
$27$	0	0
$28$	1.00000	1.00000
$29$	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			$\pi$
$32$	−1.00000	−1.00000
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	−2.61803	−2.61803
$39$	0	0
$40$	0	0
$41$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$41$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	−1.61803	−1.61803
$45$	0	0
$46$	−1.00000	−1.00000
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	0	0
$49$	−0.618034	−0.618034
$50$	1.61803	1.61803
$51$	0	0
$52$	1.61803	1.61803
$53$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$53$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$54$	0	0
$55$	0	0
$56$	0.618034	0.618034
$57$	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
$64$	−1.61803	−1.61803
$65$	0	0
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	0	0
$73$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$73$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$74$	0	0
$75$	0	0
$76$	−2.61803	−2.61803
$77$	−0.618034	−0.618034
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	0	0
$82$	−1.00000	−1.00000
$83$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$83$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	−1.00000	−1.00000
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	0.618034	0.618034
$92$	−1.00000	−1.00000
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	−1.00000	−1.00000
$99$	0	0
$100$	1.61803	1.61803
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$103$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$104$	1.00000	1.00000
$105$	0	0
$106$	2.61803	2.61803
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0	0
$109$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$109$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$113$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	1.00000	1.00000
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	−1.61803	−1.61803
$129$	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
$146$	−2.61803	−2.61803
$147$	0	0
$148$	0	0
$149$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$149$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$150$	0	0
$151$	2.00000	2.00000	1.00000			$0$
$151$	2.00000	2.00000	1.00000			$0$
$152$	−1.61803	−1.61803
$153$	0	0
$154$	−1.00000	−1.00000
$155$	0	0
$156$	0	0
$157$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$157$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−0.381966	−0.381966
$162$	0	0
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	−1.00000	−1.00000
$165$	0	0
$166$	−1.00000	−1.00000
$167$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$167$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$168$	0	0
$169$	1.00000	1.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0.618034	0.618034
$176$	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
$181$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$181$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$182$	1.00000	1.00000
$183$	0	0
$184$	−0.618034	−0.618034
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$191$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$192$	0	0
$193$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$193$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$194$	0	0
$195$	0	0
$196$	−1.00000	−1.00000
$197$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$197$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$198$	0	0
$199$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$199$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$200$	1.00000	1.00000
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	1.00000	1.00000
$207$	0	0
$208$	0	0
$209$	1.61803	1.61803
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	2.61803	2.61803
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	−2.61803	−2.61803
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	−0.618034	−0.618034
$225$	0	0
$226$	2.61803	2.61803
$227$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$227$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$228$	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	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
$239$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$239$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$240$	0	0
$241$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$241$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$242$	1.61803	1.61803
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−1.61803	−1.61803
$248$	0	0
$249$	0	0
$250$	0	0
$251$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$251$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$252$	0	0
$253$	0.618034	0.618034
$254$	0	0
$255$	0	0
$256$	−1.00000	−1.00000
$257$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$257$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$258$	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
$266$	−1.61803	−1.61803
$267$	0	0
$268$	0	0
$269$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$269$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$270$	0	0
$271$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$271$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$272$	0	0
$273$	0	0
$274$	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
$281$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$281$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	0	0
$286$	−1.61803	−1.61803
$287$	−0.381966	−0.381966
$288$	0	0
$289$	1.00000	1.00000
$290$	0	0
$291$	0	0
$292$	−2.61803	−2.61803
$293$	−2.00000	−2.00000	−1.00000			$\pi$
$293$	−2.00000	−2.00000	−1.00000			$\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	−1.00000	−1.00000
$299$	−0.618034	−0.618034
$300$	0	0
$301$	0	0
$302$	3.23607	3.23607
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	2.00000	2.00000	1.00000			$0$
$307$	2.00000	2.00000	1.00000			$0$
$308$	−1.00000	−1.00000
$309$	0	0
$310$	0	0
$311$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$311$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$312$	0	0
$313$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$313$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$314$	1.00000	1.00000
$315$	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
$322$	−0.618034	−0.618034
$323$	0	0
$324$	0	0
$325$	1.00000	1.00000
$326$	0	0
$327$	0	0
$328$	−0.618034	−0.618034
$329$	0	0
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	−1.00000	−1.00000
$333$	0	0
$334$	2.61803	2.61803
$335$	0	0
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	1.61803	1.61803
$339$	0	0
$340$	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
$349$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$349$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$350$	1.00000	1.00000
$351$	0	0
$352$	1.00000	1.00000
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	−3.23607	−3.23607
$359$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$359$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$360$	0	0
$361$	1.61803	1.61803
$362$	−2.61803	−2.61803
$363$	0	0
$364$	1.00000	1.00000
$365$	0	0
$366$	0	0
$367$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$367$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$368$	0	0
$369$	0	0
$370$	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
$382$	2.61803	2.61803
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0	0
$385$	0	0
$386$	1.00000	1.00000
$387$	0	0
$388$	0	0
$389$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$389$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$390$	0	0
$391$	0	0
$392$	−0.618034	−0.618034
$393$	0	0
$394$	2.61803	2.61803
$395$	0	0
$396$	0	0
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	−2.61803	−2.61803
$399$	0	0
$400$	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
$412$	1.00000	1.00000
$413$	0	0
$414$	0	0
$415$	0	0
$416$	−1.00000	−1.00000
$417$	0	0
$418$	2.61803	2.61803
$419$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$419$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	0	0
$424$	1.61803	1.61803
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$431$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$432$	0	0
$433$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$433$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$434$	0	0
$435$	0	0
$436$	−2.61803	−2.61803
$437$	1.00000	1.00000
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$443$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	−1.00000	−1.00000
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	0	0
$451$	0.618034	0.618034
$452$	2.61803	2.61803
$453$	0	0
$454$	2.61803	2.61803
$455$	0	0
$456$	0	0
$457$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$457$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$461$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$462$	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
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	−1.61803	−1.61803
$476$	0	0
$477$	0	0
$478$	2.61803	2.61803
$479$	−2.00000	−2.00000	−1.00000			$\pi$
$479$	−2.00000	−2.00000	−1.00000			$\pi$
$480$	0	0
$481$	0	0
$482$	1.00000	1.00000
$483$	0	0
$484$	1.61803	1.61803
$485$	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
$494$	−2.61803	−2.61803
$495$	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	0
$502$	−1.00000	−1.00000
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	0	0
$506$	1.00000	1.00000
$507$	0	0
$508$	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	0
$514$	−1.00000	−1.00000
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$521$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−0.618034	−0.618034
$530$	0	0
$531$	0	0
$532$	−1.61803	−1.61803
$533$	−0.618034	−0.618034
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	−1.00000	−1.00000
$539$	0.618034	0.618034
$540$	0	0
$541$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$541$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$542$	−2.61803	−2.61803
$543$	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
$550$	−1.61803	−1.61803
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$557$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	2.61803	2.61803
$563$	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			$\pi$
$572$	−1.61803	−1.61803
$573$	0	0
$574$	−0.618034	−0.618034
$575$	−0.618034	−0.618034
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	1.61803	1.61803
$579$	0	0
$580$	0	0
$581$	−0.381966	−0.381966
$582$	0	0
$583$	−1.61803	−1.61803
$584$	−1.61803	−1.61803
$585$	0	0
$586$	−3.23607	−3.23607
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$593$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$594$	0	0
$595$	0	0
$596$	−1.00000	−1.00000
$597$	0	0
$598$	−1.00000	−1.00000
$599$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$599$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	0	0
$604$	3.23607	3.23607
$605$	0	0
$606$	0	0
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	1.61803	1.61803
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$613$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$614$	3.23607	3.23607
$615$	0	0
$616$	−0.618034	−0.618034
$617$	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
$621$	0	0
$622$	2.61803	2.61803
$623$	0	0
$624$	0	0
$625$	1.00000	1.00000
$626$	1.00000	1.00000
$627$	0	0
$628$	1.00000	1.00000
$629$	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
$637$	−0.618034	−0.618034
$638$	0	0
$639$	0	0
$640$	0	0
$641$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$641$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	−0.618034	−0.618034
$645$	0	0
$646$	0	0
$647$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$647$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$648$	0	0
$649$	0	0
$650$	1.61803	1.61803
$651$	0	0
$652$	0	0
$653$	−2.00000	−2.00000	−1.00000			$\pi$
$653$	−2.00000	−2.00000	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	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
$664$	−0.618034	−0.618034
$665$	0	0
$666$	0	0
$667$	0	0
$668$	2.61803	2.61803
$669$	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
$675$	0	0
$676$	1.61803	1.61803
$677$	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
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	0	0
$686$	−1.61803	−1.61803
$687$	0	0
$688$	0	0
$689$	1.61803	1.61803
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	1.00000	1.00000
$699$	0	0
$700$	1.00000	1.00000
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	1.61803	1.61803
$705$	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
$716$	−3.23607	−3.23607
$717$	0	0
$718$	−1.00000	−1.00000
$719$	−2.00000	−2.00000	−1.00000			$\pi$
$719$	−2.00000	−2.00000	−1.00000			$\pi$
$720$	0	0
$721$	0.381966	0.381966
$722$	2.61803	2.61803
$723$	0	0
$724$	−2.61803	−2.61803
$725$	0	0
$726$	0	0
$727$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$727$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$728$	0.618034	0.618034
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$733$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$734$	−2.61803	−2.61803
$735$	0	0
$736$	0.618034	0.618034
$737$	0	0
$738$	0	0
$739$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$739$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$740$	0	0
$741$	0	0
$742$	1.61803	1.61803
$743$	−2.00000	−2.00000	−1.00000			$\pi$
$743$	−2.00000	−2.00000	−1.00000			$\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$751$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$757$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$761$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$762$	0	0
$763$	−1.00000	−1.00000
$764$	2.61803	2.61803
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$769$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$770$	0	0
$771$	0	0
$772$	1.00000	1.00000
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	2.61803	2.61803
$779$	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
$787$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$787$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$788$	2.61803	2.61803
$789$	0	0
$790$	0	0
$791$	1.00000	1.00000
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	−2.61803	−2.61803
$797$	−2.00000	−2.00000	−1.00000			$\pi$
$797$	−2.00000	−2.00000	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	−1.00000	−1.00000
$801$	0	0
$802$	0	0
$803$	1.61803	1.61803
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$811$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	3.23607	3.23607
$819$	0	0
$820$	0	0
$821$	−2.00000	−2.00000	−1.00000			$\pi$
$821$	−2.00000	−2.00000	−1.00000			$\pi$
$822$	0	0
$823$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$823$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$824$	0.618034	0.618034
$825$	0	0
$826$	0	0
$827$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$827$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$828$	0	0
$829$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$829$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$830$	0	0
$831$	0	0
$832$	−1.61803	−1.61803
$833$	0	0
$834$	0	0
$835$	0	0
$836$	2.61803	2.61803
$837$	0	0
$838$	−1.00000	−1.00000
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	1.00000	1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0.618034	0.618034
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$853$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$859$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$860$	0	0
$861$	0	0
$862$	−1.00000	−1.00000
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	0	0
$866$	−2.61803	−2.61803
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	−1.61803	−1.61803
$873$	0	0
$874$	1.61803	1.61803
$875$	0	0
$876$	0	0
$877$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$877$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$881$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$882$	0	0
$883$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$883$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$884$	0	0
$885$	0	0
$886$	−1.00000	−1.00000
$887$	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
$896$	−1.00000	−1.00000
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	0	0
$902$	1.00000	1.00000
$903$	0	0
$904$	1.61803	1.61803
$905$	0	0
$906$	0	0
$907$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$907$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$908$	2.61803	2.61803
$909$	0	0
$910$	0	0
$911$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$911$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$912$	0	0
$913$	0.618034	0.618034
$914$	−2.61803	−2.61803
$915$	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
$922$	2.61803	2.61803
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	1.00000	1.00000
$932$	0	0
$933$	0	0
$934$	−3.23607	−3.23607
$935$	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
$941$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$941$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$942$	0	0
$943$	0.381966	0.381966
$944$	0	0
$945$	0	0
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	−1.61803	−1.61803
$950$	−2.61803	−2.61803
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	0	0
$956$	2.61803	2.61803
$957$	0	0
$958$	−3.23607	−3.23607
$959$	0	0
$960$	0	0
$961$	1.00000	1.00000
$962$	0	0
$963$	0	0
$964$	1.00000	1.00000
$965$	0	0
$966$	0	0
$967$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$967$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$968$	1.00000	1.00000
$969$	0	0
$970$	0	0
$971$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$971$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	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
$986$	0	0
$987$	0	0
$988$	−2.61803	−2.61803
$989$	0	0
$990$	0	0
$991$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$991$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$992$	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	1287.1.g.b.1000.2		2
3.2	odd	2		143.1.d.a.142.1	✓	2
11.10	odd	2		1287.1.g.a.1000.1		2
12.11	even	2		2288.1.m.b.2001.2		2
13.12	even	2		1287.1.g.a.1000.1		2
15.2	even	4		3575.1.c.d.3574.1		4
15.8	even	4		3575.1.c.d.3574.4		4
15.14	odd	2		3575.1.h.f.2001.2		2
33.2	even	10		1573.1.l.a.766.1		4
33.5	odd	10		1573.1.l.d.844.1		4
33.8	even	10		1573.1.l.c.233.1		4
33.14	odd	10		1573.1.l.b.233.1		4
33.17	even	10		1573.1.l.a.844.1		4
33.20	odd	10		1573.1.l.d.766.1		4
33.26	odd	10		1573.1.l.b.1546.1		4
33.29	even	10		1573.1.l.c.1546.1		4
33.32	even	2		143.1.d.b.142.2	yes	2
39.2	even	12		1859.1.k.c.1374.1		8
39.5	even	4		1859.1.c.c.846.4		4
39.8	even	4		1859.1.c.c.846.1		4
39.11	even	12		1859.1.k.c.1374.4		8
39.17	odd	6		1859.1.i.a.868.1		4
39.20	even	12		1859.1.k.c.1836.1		8
39.23	odd	6		1859.1.i.a.1330.1		4
39.29	odd	6		1859.1.i.b.1330.2		4
39.32	even	12		1859.1.k.c.1836.4		8
39.35	odd	6		1859.1.i.b.868.2		4
39.38	odd	2		143.1.d.b.142.2	yes	2
132.131	odd	2		2288.1.m.a.2001.2		2
143.142	odd	2	CM	1287.1.g.b.1000.2		2
156.155	even	2		2288.1.m.a.2001.2		2
165.32	odd	4		3575.1.c.c.3574.4		4
165.98	odd	4		3575.1.c.c.3574.1		4
165.164	even	2		3575.1.h.e.2001.1		2
195.38	even	4		3575.1.c.c.3574.1		4
195.77	even	4		3575.1.c.c.3574.4		4
195.194	odd	2		3575.1.h.e.2001.1		2
429.32	odd	12		1859.1.k.c.1836.1		8
429.38	odd	10		1573.1.l.a.844.1		4
429.98	odd	12		1859.1.k.c.1836.4		8
429.116	even	10		1573.1.l.d.844.1		4
429.164	odd	4		1859.1.c.c.846.4		4
429.194	even	10		1573.1.l.b.1546.1		4
429.197	odd	12		1859.1.k.c.1374.4		8
429.230	even	6		1859.1.i.a.868.1		4
429.233	even	10		1573.1.l.d.766.1		4
429.263	even	6		1859.1.i.a.1330.1		4
429.272	even	10		1573.1.l.b.233.1		4
429.296	even	6		1859.1.i.b.1330.2		4
429.311	odd	10		1573.1.l.c.233.1		4
429.329	even	6		1859.1.i.b.868.2		4
429.350	odd	10		1573.1.l.a.766.1		4
429.362	odd	12		1859.1.k.c.1374.1		8
429.389	odd	10		1573.1.l.c.1546.1		4
429.395	odd	4		1859.1.c.c.846.1		4
429.428	even	2		143.1.d.a.142.1	✓	2
1716.1715	odd	2		2288.1.m.b.2001.2		2
2145.428	odd	4		3575.1.c.d.3574.4		4
2145.857	odd	4		3575.1.c.d.3574.1		4
2145.2144	even	2		3575.1.h.f.2001.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.1.d.a.142.1	✓	2	3.2	odd	2
143.1.d.a.142.1	✓	2	429.428	even	2
143.1.d.b.142.2	yes	2	33.32	even	2
143.1.d.b.142.2	yes	2	39.38	odd	2
1287.1.g.a.1000.1		2	11.10	odd	2
1287.1.g.a.1000.1		2	13.12	even	2
1287.1.g.b.1000.2		2	1.1	even	1	trivial
1287.1.g.b.1000.2		2	143.142	odd	2	CM
1573.1.l.a.766.1		4	33.2	even	10
1573.1.l.a.766.1		4	429.350	odd	10
1573.1.l.a.844.1		4	33.17	even	10
1573.1.l.a.844.1		4	429.38	odd	10
1573.1.l.b.233.1		4	33.14	odd	10
1573.1.l.b.233.1		4	429.272	even	10
1573.1.l.b.1546.1		4	33.26	odd	10
1573.1.l.b.1546.1		4	429.194	even	10
1573.1.l.c.233.1		4	33.8	even	10
1573.1.l.c.233.1		4	429.311	odd	10
1573.1.l.c.1546.1		4	33.29	even	10
1573.1.l.c.1546.1		4	429.389	odd	10
1573.1.l.d.766.1		4	33.20	odd	10
1573.1.l.d.766.1		4	429.233	even	10
1573.1.l.d.844.1		4	33.5	odd	10
1573.1.l.d.844.1		4	429.116	even	10
1859.1.c.c.846.1		4	39.8	even	4
1859.1.c.c.846.1		4	429.395	odd	4
1859.1.c.c.846.4		4	39.5	even	4
1859.1.c.c.846.4		4	429.164	odd	4
1859.1.i.a.868.1		4	39.17	odd	6
1859.1.i.a.868.1		4	429.230	even	6
1859.1.i.a.1330.1		4	39.23	odd	6
1859.1.i.a.1330.1		4	429.263	even	6
1859.1.i.b.868.2		4	39.35	odd	6
1859.1.i.b.868.2		4	429.329	even	6
1859.1.i.b.1330.2		4	39.29	odd	6
1859.1.i.b.1330.2		4	429.296	even	6
1859.1.k.c.1374.1		8	39.2	even	12
1859.1.k.c.1374.1		8	429.362	odd	12
1859.1.k.c.1374.4		8	39.11	even	12
1859.1.k.c.1374.4		8	429.197	odd	12
1859.1.k.c.1836.1		8	39.20	even	12
1859.1.k.c.1836.1		8	429.32	odd	12
1859.1.k.c.1836.4		8	39.32	even	12
1859.1.k.c.1836.4		8	429.98	odd	12
2288.1.m.a.2001.2		2	132.131	odd	2
2288.1.m.a.2001.2		2	156.155	even	2
2288.1.m.b.2001.2		2	12.11	even	2
2288.1.m.b.2001.2		2	1716.1715	odd	2
3575.1.c.c.3574.1		4	165.98	odd	4
3575.1.c.c.3574.1		4	195.38	even	4
3575.1.c.c.3574.4		4	165.32	odd	4
3575.1.c.c.3574.4		4	195.77	even	4
3575.1.c.d.3574.1		4	15.2	even	4
3575.1.c.d.3574.1		4	2145.857	odd	4
3575.1.c.d.3574.4		4	15.8	even	4
3575.1.c.d.3574.4		4	2145.428	odd	4
3575.1.h.e.2001.1		2	165.164	even	2
3575.1.h.e.2001.1		2	195.194	odd	2
3575.1.h.f.2001.2		2	15.14	odd	2
3575.1.h.f.2001.2		2	2145.2144	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:	\( N \)	\(=\)	\( 1287 = 3^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1287.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.61803 q^{2} +1.61803 q^{4} +0.618034 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.61803 q^{2} +1.61803 q^{4} +0.618034 q^{7} +1.00000 q^{8} -1.00000 q^{11} +1.00000 q^{13} +1.00000 q^{14} -1.61803 q^{19} -1.61803 q^{22} -0.618034 q^{23} +1.00000 q^{25} +1.61803 q^{26} +1.00000 q^{28} -1.00000 q^{32} -2.61803 q^{38} -0.618034 q^{41} -1.61803 q^{44} -1.00000 q^{46} -0.618034 q^{49} +1.61803 q^{50} +1.61803 q^{52} +1.61803 q^{53} +0.618034 q^{56} -1.61803 q^{64} -1.61803 q^{73} -2.61803 q^{76} -0.618034 q^{77} -1.00000 q^{82} -0.618034 q^{83} -1.00000 q^{88} +0.618034 q^{91} -1.00000 q^{92} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{4} - q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q + q^2 + q^4 - q^7 + 2 * q^8	\( 2 q + q^{2} + q^{4} - q^{7} + 2 q^{8} - 2 q^{11} + 2 q^{13} + 2 q^{14} - q^{19} - q^{22} + q^{23} + 2 q^{25} + q^{26} + 2 q^{28} - 2 q^{32} - 3 q^{38} + q^{41} - q^{44} - 2 q^{46} + q^{49} + q^{50} + q^{52} + q^{53} - q^{56} - q^{64} - q^{73} - 3 q^{76} + q^{77} - 2 q^{82} + q^{83} - 2 q^{88} - q^{91} - 2 q^{92} - 2 q^{98}+O(q^{100}) \) 2 * q + q^2 + q^4 - q^7 + 2 * q^8 - 2 * q^11 + 2 * q^13 + 2 * q^14 - q^19 - q^22 + q^23 + 2 * q^25 + q^26 + 2 * q^28 - 2 * q^32 - 3 * q^38 + q^41 - q^44 - 2 * q^46 + q^49 + q^50 + q^52 + q^53 - q^56 - q^64 - q^73 - 3 * q^76 + q^77 - 2 * q^82 + q^83 - 2 * q^88 - q^91 - 2 * q^92 - 2 * q^98

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