LMFDB - Embedded newform 1160.1.o.a.579.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1160,1,Mod(579,1160)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1160.579"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1160, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 1])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 1160 = 2^{3} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1160.o (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2,1,2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$0.578915414654$
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:	yes
Projective image:	$D_{5}$
Projective field:	Galois closure of 5.1.1345600.2

Embedding invariants

Embedding label			579.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	1160.579

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.61803 q^{6} -0.618034 q^{7} -1.00000 q^{8} +1.61803 q^{9} +1.00000 q^{10} +1.61803 q^{12} +1.61803 q^{13} +0.618034 q^{14} -1.61803 q^{15} +1.00000 q^{16} -0.618034 q^{17} -1.61803 q^{18} -1.00000 q^{20} -1.00000 q^{21} +1.61803 q^{23} -1.61803 q^{24} +1.00000 q^{25} -1.61803 q^{26} +1.00000 q^{27} -0.618034 q^{28} +1.00000 q^{29} +1.61803 q^{30} +0.618034 q^{31} -1.00000 q^{32} +0.618034 q^{34} +0.618034 q^{35} +1.61803 q^{36} +2.61803 q^{39} +1.00000 q^{40} +1.00000 q^{42} -0.618034 q^{43} -1.61803 q^{45} -1.61803 q^{46} +1.61803 q^{48} -0.618034 q^{49} -1.00000 q^{50} -1.00000 q^{51} +1.61803 q^{52} -0.618034 q^{53} -1.00000 q^{54} +0.618034 q^{56} -1.00000 q^{58} -1.61803 q^{59} -1.61803 q^{60} -1.61803 q^{61} -0.618034 q^{62} -1.00000 q^{63} +1.00000 q^{64} -1.61803 q^{65} -0.618034 q^{68} +2.61803 q^{69} -0.618034 q^{70} -1.61803 q^{72} -0.618034 q^{73} +1.61803 q^{75} -2.61803 q^{78} -1.61803 q^{79} -1.00000 q^{80} -1.00000 q^{84} +0.618034 q^{85} +0.618034 q^{86} +1.61803 q^{87} +1.61803 q^{90} -1.00000 q^{91} +1.61803 q^{92} +1.00000 q^{93} -1.61803 q^{96} +1.61803 q^{97} +0.618034 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} - q^{6} + q^{7} - 2 q^{8} + q^{9} + 2 q^{10} + q^{12} + q^{13} - q^{14} - q^{15} + 2 q^{16} + q^{17} - q^{18} - 2 q^{20} - 2 q^{21} + q^{23} - q^{24}+ \cdots - q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 - q^6 + q^7 - 2 * q^8 + q^9 + 2 * q^10 + q^12 + q^13 - q^14 - q^15 + 2 * q^16 + q^17 - q^18 - 2 * q^20 - 2 * q^21 + q^23 - q^24 + 2 * q^25 - q^26 + 2 * q^27 + q^28 + 2 * q^29 + q^30 - q^31 - 2 * q^32 - q^34 - q^35 + q^36 + 3 * q^39 + 2 * q^40 + 2 * q^42 + q^43 - q^45 - q^46 + q^48 + q^49 - 2 * q^50 - 2 * q^51 + q^52 + q^53 - 2 * q^54 - q^56 - 2 * q^58 - q^59 - q^60 - q^61 + q^62 - 2 * q^63 + 2 * q^64 - q^65 + q^68 + 3 * q^69 + q^70 - q^72 + q^73 + q^75 - 3 * q^78 - q^79 - 2 * q^80 - 2 * q^84 - q^85 - q^86 + q^87 + q^90 - 2 * q^91 + q^92 + 2 * q^93 - q^96 + q^97 - q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1160\mathbb{Z}\right)^\times$.

$n$	$321$	$581$	$697$	$871$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−1.00000	−1.00000
$2$	−1.00000	−1.00000
$3$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$3$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$4$	1.00000	1.00000
$5$	−1.00000	−1.00000
$5$	−1.00000	−1.00000
$6$	−1.61803	−1.61803
$7$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$7$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$8$	−1.00000	−1.00000
$9$	1.61803	1.61803
$10$	1.00000	1.00000
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	1.61803	1.61803
$13$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$13$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$14$	0.618034	0.618034
$15$	−1.61803	−1.61803
$16$	1.00000	1.00000
$17$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$17$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$18$	−1.61803	−1.61803
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	−1.00000	−1.00000
$21$	−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	$0.200000\pi$
$24$	−1.61803	−1.61803
$25$	1.00000	1.00000
$26$	−1.61803	−1.61803
$27$	1.00000	1.00000
$28$	−0.618034	−0.618034
$29$	1.00000	1.00000
$29$	1.00000	1.00000
$30$	1.61803	1.61803
$31$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$31$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$32$	−1.00000	−1.00000
$33$	0	0
$34$	0.618034	0.618034
$35$	0.618034	0.618034
$36$	1.61803	1.61803
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	2.61803	2.61803
$40$	1.00000	1.00000
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	1.00000	1.00000
$43$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$43$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$44$	0	0
$45$	−1.61803	−1.61803
$46$	−1.61803	−1.61803
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	1.61803	1.61803
$49$	−0.618034	−0.618034
$50$	−1.00000	−1.00000
$51$	−1.00000	−1.00000
$52$	1.61803	1.61803
$53$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$53$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$54$	−1.00000	−1.00000
$55$	0	0
$56$	0.618034	0.618034
$57$	0	0
$58$	−1.00000	−1.00000
$59$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$59$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$60$	−1.61803	−1.61803
$61$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$61$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$62$	−0.618034	−0.618034
$63$	−1.00000	−1.00000
$64$	1.00000	1.00000
$65$	−1.61803	−1.61803
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	−0.618034	−0.618034
$69$	2.61803	2.61803
$70$	−0.618034	−0.618034
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	−1.61803	−1.61803
$73$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$73$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$74$	0	0
$75$	1.61803	1.61803
$76$	0	0
$77$	0	0
$78$	−2.61803	−2.61803
$79$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$79$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$80$	−1.00000	−1.00000
$81$	0	0
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	−1.00000	−1.00000
$85$	0.618034	0.618034
$86$	0.618034	0.618034
$87$	1.61803	1.61803
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	1.61803	1.61803
$91$	−1.00000	−1.00000
$92$	1.61803	1.61803
$93$	1.00000	1.00000
$94$	0	0
$95$	0	0
$96$	−1.61803	−1.61803
$97$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$97$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$98$	0.618034	0.618034
$99$	0	0
$100$	1.00000	1.00000
$101$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$101$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$102$	1.00000	1.00000
$103$	−2.00000	−2.00000	−1.00000			$\pi$
$103$	−2.00000	−2.00000	−1.00000			$\pi$
$104$	−1.61803	−1.61803
$105$	1.00000	1.00000
$106$	0.618034	0.618034
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	1.00000	1.00000
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0	0
$112$	−0.618034	−0.618034
$113$	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
$115$	−1.61803	−1.61803
$116$	1.00000	1.00000
$117$	2.61803	2.61803
$118$	1.61803	1.61803
$119$	0.381966	0.381966
$120$	1.61803	1.61803
$121$	1.00000	1.00000
$122$	1.61803	1.61803
$123$	0	0
$124$	0.618034	0.618034
$125$	−1.00000	−1.00000
$126$	1.00000	1.00000
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	−1.00000	−1.00000
$129$	−1.00000	−1.00000
$130$	1.61803	1.61803
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	−1.00000	−1.00000
$136$	0.618034	0.618034
$137$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$137$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$138$	−2.61803	−2.61803
$139$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$139$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$140$	0.618034	0.618034
$141$	0	0
$142$	0	0
$143$	0	0
$144$	1.61803	1.61803
$145$	−1.00000	−1.00000
$146$	0.618034	0.618034
$147$	−1.00000	−1.00000
$148$	0	0
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	−1.61803	−1.61803
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	−1.00000	−1.00000
$154$	0	0
$155$	−0.618034	−0.618034
$156$	2.61803	2.61803
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	1.61803	1.61803
$159$	−1.00000	−1.00000
$160$	1.00000	1.00000
$161$	−1.00000	−1.00000
$162$	0	0
$163$	−2.00000	−2.00000	−1.00000			$\pi$
$163$	−2.00000	−2.00000	−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	$0.600000\pi$
$168$	1.00000	1.00000
$169$	1.61803	1.61803
$170$	−0.618034	−0.618034
$171$	0	0
$172$	−0.618034	−0.618034
$173$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$173$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$174$	−1.61803	−1.61803
$175$	−0.618034	−0.618034
$176$	0	0
$177$	−2.61803	−2.61803
$178$	0	0
$179$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$179$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$180$	−1.61803	−1.61803
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	1.00000	1.00000
$183$	−2.61803	−2.61803
$184$	−1.61803	−1.61803
$185$	0	0
$186$	−1.00000	−1.00000
$187$	0	0
$188$	0	0
$189$	−0.618034	−0.618034
$190$	0	0
$191$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$191$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$192$	1.61803	1.61803
$193$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$193$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$194$	−1.61803	−1.61803
$195$	−2.61803	−2.61803
$196$	−0.618034	−0.618034
$197$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$197$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	−1.00000	−1.00000
$201$	0	0
$202$	1.61803	1.61803
$203$	−0.618034	−0.618034
$204$	−1.00000	−1.00000
$205$	0	0
$206$	2.00000	2.00000
$207$	2.61803	2.61803
$208$	1.61803	1.61803
$209$	0	0
$210$	−1.00000	−1.00000
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	−0.618034	−0.618034
$213$	0	0
$214$	0	0
$215$	0.618034	0.618034
$216$	−1.00000	−1.00000
$217$	−0.381966	−0.381966
$218$	0	0
$219$	−1.00000	−1.00000
$220$	0	0
$221$	−1.00000	−1.00000
$222$	0	0
$223$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$223$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$224$	0.618034	0.618034
$225$	1.61803	1.61803
$226$	−1.61803	−1.61803
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$229$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$230$	1.61803	1.61803
$231$	0	0
$232$	−1.00000	−1.00000
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	−2.61803	−2.61803
$235$	0	0
$236$	−1.61803	−1.61803
$237$	−2.61803	−2.61803
$238$	−0.381966	−0.381966
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	−1.61803	−1.61803
$241$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$241$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$242$	−1.00000	−1.00000
$243$	−1.00000	−1.00000
$244$	−1.61803	−1.61803
$245$	0.618034	0.618034
$246$	0	0
$247$	0	0
$248$	−0.618034	−0.618034
$249$	0	0
$250$	1.00000	1.00000
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	−1.00000	−1.00000
$253$	0	0
$254$	0	0
$255$	1.00000	1.00000
$256$	1.00000	1.00000
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	1.00000	1.00000
$259$	0	0
$260$	−1.61803	−1.61803
$261$	1.61803	1.61803
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	0.618034	0.618034
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$269$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$270$	1.00000	1.00000
$271$	2.00000	2.00000	1.00000			$0$
$271$	2.00000	2.00000	1.00000			$0$
$272$	−0.618034	−0.618034
$273$	−1.61803	−1.61803
$274$	−1.61803	−1.61803
$275$	0	0
$276$	2.61803	2.61803
$277$	−2.00000	−2.00000	−1.00000			$\pi$
$277$	−2.00000	−2.00000	−1.00000			$\pi$
$278$	−0.618034	−0.618034
$279$	1.00000	1.00000
$280$	−0.618034	−0.618034
$281$	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
$287$	0	0
$288$	−1.61803	−1.61803
$289$	−0.618034	−0.618034
$290$	1.00000	1.00000
$291$	2.61803	2.61803
$292$	−0.618034	−0.618034
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	1.00000	1.00000
$295$	1.61803	1.61803
$296$	0	0
$297$	0	0
$298$	0	0
$299$	2.61803	2.61803
$300$	1.61803	1.61803
$301$	0.381966	0.381966
$302$	0	0
$303$	−2.61803	−2.61803
$304$	0	0
$305$	1.61803	1.61803
$306$	1.00000	1.00000
$307$	−2.00000	−2.00000	−1.00000			$\pi$
$307$	−2.00000	−2.00000	−1.00000			$\pi$
$308$	0	0
$309$	−3.23607	−3.23607
$310$	0.618034	0.618034
$311$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$311$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$312$	−2.61803	−2.61803
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	1.00000	1.00000
$316$	−1.61803	−1.61803
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	1.00000	1.00000
$319$	0	0
$320$	−1.00000	−1.00000
$321$	0	0
$322$	1.00000	1.00000
$323$	0	0
$324$	0	0
$325$	1.61803	1.61803
$326$	2.00000	2.00000
$327$	0	0
$328$	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
$334$	0.618034	0.618034
$335$	0	0
$336$	−1.00000	−1.00000
$337$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$337$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$338$	−1.61803	−1.61803
$339$	2.61803	2.61803
$340$	0.618034	0.618034
$341$	0	0
$342$	0	0
$343$	1.00000	1.00000
$344$	0.618034	0.618034
$345$	−2.61803	−2.61803
$346$	−1.61803	−1.61803
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	1.61803	1.61803
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0.618034	0.618034
$351$	1.61803	1.61803
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	2.61803	2.61803
$355$	0	0
$356$	0	0
$357$	0.618034	0.618034
$358$	1.61803	1.61803
$359$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$359$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$360$	1.61803	1.61803
$361$	1.00000	1.00000
$362$	0	0
$363$	1.61803	1.61803
$364$	−1.00000	−1.00000
$365$	0.618034	0.618034
$366$	2.61803	2.61803
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	1.61803	1.61803
$369$	0	0
$370$	0	0
$371$	0.381966	0.381966
$372$	1.00000	1.00000
$373$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$373$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$374$	0	0
$375$	−1.61803	−1.61803
$376$	0	0
$377$	1.61803	1.61803
$378$	0.618034	0.618034
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	0	0
$381$	0	0
$382$	−0.618034	−0.618034
$383$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$383$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$384$	−1.61803	−1.61803
$385$	0	0
$386$	−1.61803	−1.61803
$387$	−1.00000	−1.00000
$388$	1.61803	1.61803
$389$	2.00000	2.00000	1.00000			$0$
$389$	2.00000	2.00000	1.00000			$0$
$390$	2.61803	2.61803
$391$	−1.00000	−1.00000
$392$	0.618034	0.618034
$393$	0	0
$394$	0.618034	0.618034
$395$	1.61803	1.61803
$396$	0	0
$397$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$397$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$398$	0	0
$399$	0	0
$400$	1.00000	1.00000
$401$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$401$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$402$	0	0
$403$	1.00000	1.00000
$404$	−1.61803	−1.61803
$405$	0	0
$406$	0.618034	0.618034
$407$	0	0
$408$	1.00000	1.00000
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	2.61803	2.61803
$412$	−2.00000	−2.00000
$413$	1.00000	1.00000
$414$	−2.61803	−2.61803
$415$	0	0
$416$	−1.61803	−1.61803
$417$	1.00000	1.00000
$418$	0	0
$419$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$419$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$420$	1.00000	1.00000
$421$	2.00000	2.00000	1.00000			$0$
$421$	2.00000	2.00000	1.00000			$0$
$422$	0	0
$423$	0	0
$424$	0.618034	0.618034
$425$	−0.618034	−0.618034
$426$	0	0
$427$	1.00000	1.00000
$428$	0	0
$429$	0	0
$430$	−0.618034	−0.618034
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	1.00000	1.00000
$433$	−2.00000	−2.00000	−1.00000			$\pi$
$433$	−2.00000	−2.00000	−1.00000			$\pi$
$434$	0.381966	0.381966
$435$	−1.61803	−1.61803
$436$	0	0
$437$	0	0
$438$	1.00000	1.00000
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	−1.00000	−1.00000
$442$	1.00000	1.00000
$443$	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
$446$	−1.61803	−1.61803
$447$	0	0
$448$	−0.618034	−0.618034
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	−1.61803	−1.61803
$451$	0	0
$452$	1.61803	1.61803
$453$	0	0
$454$	0	0
$455$	1.00000	1.00000
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	−0.618034	−0.618034
$459$	−0.618034	−0.618034
$460$	−1.61803	−1.61803
$461$	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
$463$	−2.00000	−2.00000	−1.00000			$\pi$
$463$	−2.00000	−2.00000	−1.00000			$\pi$
$464$	1.00000	1.00000
$465$	−1.00000	−1.00000
$466$	0	0
$467$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$467$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$468$	2.61803	2.61803
$469$	0	0
$470$	0	0
$471$	0	0
$472$	1.61803	1.61803
$473$	0	0
$474$	2.61803	2.61803
$475$	0	0
$476$	0.381966	0.381966
$477$	−1.00000	−1.00000
$478$	0	0
$479$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$479$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$480$	1.61803	1.61803
$481$	0	0
$482$	1.61803	1.61803
$483$	−1.61803	−1.61803
$484$	1.00000	1.00000
$485$	−1.61803	−1.61803
$486$	1.00000	1.00000
$487$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$487$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$488$	1.61803	1.61803
$489$	−3.23607	−3.23607
$490$	−0.618034	−0.618034
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	−0.618034	−0.618034
$494$	0	0
$495$	0	0
$496$	0.618034	0.618034
$497$	0	0
$498$	0	0
$499$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$499$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$500$	−1.00000	−1.00000
$501$	−1.00000	−1.00000
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	1.00000	1.00000
$505$	1.61803	1.61803
$506$	0	0
$507$	2.61803	2.61803
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	−1.00000	−1.00000
$511$	0.381966	0.381966
$512$	−1.00000	−1.00000
$513$	0	0
$514$	0	0
$515$	2.00000	2.00000
$516$	−1.00000	−1.00000
$517$	0	0
$518$	0	0
$519$	2.61803	2.61803
$520$	1.61803	1.61803
$521$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$521$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$522$	−1.61803	−1.61803
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	−1.00000	−1.00000
$526$	0	0
$527$	−0.381966	−0.381966
$528$	0	0
$529$	1.61803	1.61803
$530$	−0.618034	−0.618034
$531$	−2.61803	−2.61803
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−2.61803	−2.61803
$538$	−0.618034	−0.618034
$539$	0	0
$540$	−1.00000	−1.00000
$541$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$541$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$542$	−2.00000	−2.00000
$543$	0	0
$544$	0.618034	0.618034
$545$	0	0
$546$	1.61803	1.61803
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	1.61803	1.61803
$549$	−2.61803	−2.61803
$550$	0	0
$551$	0	0
$552$	−2.61803	−2.61803
$553$	1.00000	1.00000
$554$	2.00000	2.00000
$555$	0	0
$556$	0.618034	0.618034
$557$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$557$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$558$	−1.00000	−1.00000
$559$	−1.00000	−1.00000
$560$	0.618034	0.618034
$561$	0	0
$562$	−0.618034	−0.618034
$563$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$563$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$564$	0	0
$565$	−1.61803	−1.61803
$566$	0	0
$567$	0	0
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$571$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$572$	0	0
$573$	1.00000	1.00000
$574$	0	0
$575$	1.61803	1.61803
$576$	1.61803	1.61803
$577$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$577$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$578$	0.618034	0.618034
$579$	2.61803	2.61803
$580$	−1.00000	−1.00000
$581$	0	0
$582$	−2.61803	−2.61803
$583$	0	0
$584$	0.618034	0.618034
$585$	−2.61803	−2.61803
$586$	0	0
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	−1.00000	−1.00000
$589$	0	0
$590$	−1.61803	−1.61803
$591$	−1.00000	−1.00000
$592$	0	0
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	−0.381966	−0.381966
$596$	0	0
$597$	0	0
$598$	−2.61803	−2.61803
$599$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$599$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$600$	−1.61803	−1.61803
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	−0.381966	−0.381966
$603$	0	0
$604$	0	0
$605$	−1.00000	−1.00000
$606$	2.61803	2.61803
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	0	0
$609$	−1.00000	−1.00000
$610$	−1.61803	−1.61803
$611$	0	0
$612$	−1.00000	−1.00000
$613$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$613$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$614$	2.00000	2.00000
$615$	0	0
$616$	0	0
$617$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$617$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$618$	3.23607	3.23607
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	−0.618034	−0.618034
$621$	1.61803	1.61803
$622$	1.61803	1.61803
$623$	0	0
$624$	2.61803	2.61803
$625$	1.00000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	−1.00000	−1.00000
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	1.61803	1.61803
$633$	0	0
$634$	0	0
$635$	0	0
$636$	−1.00000	−1.00000
$637$	−1.00000	−1.00000
$638$	0	0
$639$	0	0
$640$	1.00000	1.00000
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	−1.00000	−1.00000
$645$	1.00000	1.00000
$646$	0	0
$647$	−2.00000	−2.00000	−1.00000			$\pi$
$647$	−2.00000	−2.00000	−1.00000			$\pi$
$648$	0	0
$649$	0	0
$650$	−1.61803	−1.61803
$651$	−0.618034	−0.618034
$652$	−2.00000	−2.00000
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−1.00000	−1.00000
$658$	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
$663$	−1.61803	−1.61803
$664$	0	0
$665$	0	0
$666$	0	0
$667$	1.61803	1.61803
$668$	−0.618034	−0.618034
$669$	2.61803	2.61803
$670$	0	0
$671$	0	0
$672$	1.00000	1.00000
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0.618034	0.618034
$675$	1.00000	1.00000
$676$	1.61803	1.61803
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	−2.61803	−2.61803
$679$	−1.00000	−1.00000
$680$	−0.618034	−0.618034
$681$	0	0
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	−1.61803	−1.61803
$686$	−1.00000	−1.00000
$687$	1.00000	1.00000
$688$	−0.618034	−0.618034
$689$	−1.00000	−1.00000
$690$	2.61803	2.61803
$691$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$691$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$692$	1.61803	1.61803
$693$	0	0
$694$	0	0
$695$	−0.618034	−0.618034
$696$	−1.61803	−1.61803
$697$	0	0
$698$	0	0
$699$	0	0
$700$	−0.618034	−0.618034
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	−1.61803	−1.61803
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	1.00000	1.00000
$708$	−2.61803	−2.61803
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	−2.61803	−2.61803
$712$	0	0
$713$	1.00000	1.00000
$714$	−0.618034	−0.618034
$715$	0	0
$716$	−1.61803	−1.61803
$717$	0	0
$718$	1.61803	1.61803
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	−1.61803	−1.61803
$721$	1.23607	1.23607
$722$	−1.00000	−1.00000
$723$	−2.61803	−2.61803
$724$	0	0
$725$	1.00000	1.00000
$726$	−1.61803	−1.61803
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	1.00000	1.00000
$729$	−1.61803	−1.61803
$730$	−0.618034	−0.618034
$731$	0.381966	0.381966
$732$	−2.61803	−2.61803
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	1.00000	1.00000
$736$	−1.61803	−1.61803
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	0	0
$742$	−0.381966	−0.381966
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	−1.00000	−1.00000
$745$	0	0
$746$	0.618034	0.618034
$747$	0	0
$748$	0	0
$749$	0	0
$750$	1.61803	1.61803
$751$	2.00000	2.00000	1.00000			$0$
$751$	2.00000	2.00000	1.00000			$0$
$752$	0	0
$753$	0	0
$754$	−1.61803	−1.61803
$755$	0	0
$756$	−0.618034	−0.618034
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$761$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$762$	0	0
$763$	0	0
$764$	0.618034	0.618034
$765$	1.00000	1.00000
$766$	0.618034	0.618034
$767$	−2.61803	−2.61803
$768$	1.61803	1.61803
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0	0
$772$	1.61803	1.61803
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	1.00000	1.00000
$775$	0.618034	0.618034
$776$	−1.61803	−1.61803
$777$	0	0
$778$	−2.00000	−2.00000
$779$	0	0
$780$	−2.61803	−2.61803
$781$	0	0
$782$	1.00000	1.00000
$783$	1.00000	1.00000
$784$	−0.618034	−0.618034
$785$	0	0
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	−0.618034	−0.618034
$789$	0	0
$790$	−1.61803	−1.61803
$791$	−1.00000	−1.00000
$792$	0	0
$793$	−2.61803	−2.61803
$794$	0.618034	0.618034
$795$	1.00000	1.00000
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	−1.00000	−1.00000
$801$	0	0
$802$	1.61803	1.61803
$803$	0	0
$804$	0	0
$805$	1.00000	1.00000
$806$	−1.00000	−1.00000
$807$	1.00000	1.00000
$808$	1.61803	1.61803
$809$	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	$0.400000\pi$
$812$	−0.618034	−0.618034
$813$	3.23607	3.23607
$814$	0	0
$815$	2.00000	2.00000
$816$	−1.00000	−1.00000
$817$	0	0
$818$	0	0
$819$	−1.61803	−1.61803
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	−2.61803	−2.61803
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	2.00000	2.00000
$825$	0	0
$826$	−1.00000	−1.00000
$827$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$827$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$828$	2.61803	2.61803
$829$	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
$831$	−3.23607	−3.23607
$832$	1.61803	1.61803
$833$	0.381966	0.381966
$834$	−1.00000	−1.00000
$835$	0.618034	0.618034
$836$	0	0
$837$	0.618034	0.618034
$838$	−0.618034	−0.618034
$839$	2.00000	2.00000	1.00000			$0$
$839$	2.00000	2.00000	1.00000			$0$
$840$	−1.00000	−1.00000
$841$	1.00000	1.00000
$842$	−2.00000	−2.00000
$843$	1.00000	1.00000
$844$	0	0
$845$	−1.61803	−1.61803
$846$	0	0
$847$	−0.618034	−0.618034
$848$	−0.618034	−0.618034
$849$	0	0
$850$	0.618034	0.618034
$851$	0	0
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	−1.00000	−1.00000
$855$	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			$\pi$
$860$	0.618034	0.618034
$861$	0	0
$862$	0	0
$863$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$863$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$864$	−1.00000	−1.00000
$865$	−1.61803	−1.61803
$866$	2.00000	2.00000
$867$	−1.00000	−1.00000
$868$	−0.381966	−0.381966
$869$	0	0
$870$	1.61803	1.61803
$871$	0	0
$872$	0	0
$873$	2.61803	2.61803
$874$	0	0
$875$	0.618034	0.618034
$876$	−1.00000	−1.00000
$877$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$877$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	1.00000	1.00000
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	−1.00000	−1.00000
$885$	2.61803	2.61803
$886$	−1.61803	−1.61803
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	1.61803	1.61803
$893$	0	0
$894$	0	0
$895$	1.61803	1.61803
$896$	0.618034	0.618034
$897$	4.23607	4.23607
$898$	0	0
$899$	0.618034	0.618034
$900$	1.61803	1.61803
$901$	0.381966	0.381966
$902$	0	0
$903$	0.618034	0.618034
$904$	−1.61803	−1.61803
$905$	0	0
$906$	0	0
$907$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$907$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$908$	0	0
$909$	−2.61803	−2.61803
$910$	−1.00000	−1.00000
$911$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$911$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	2.61803	2.61803
$916$	0.618034	0.618034
$917$	0	0
$918$	0.618034	0.618034
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	1.61803	1.61803
$921$	−3.23607	−3.23607
$922$	−0.618034	−0.618034
$923$	0	0
$924$	0	0
$925$	0	0
$926$	2.00000	2.00000
$927$	−3.23607	−3.23607
$928$	−1.00000	−1.00000
$929$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$929$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$930$	1.00000	1.00000
$931$	0	0
$932$	0	0
$933$	−2.61803	−2.61803
$934$	0.618034	0.618034
$935$	0	0
$936$	−2.61803	−2.61803
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	−1.61803	−1.61803
$945$	0.618034	0.618034
$946$	0	0
$947$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$947$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$948$	−2.61803	−2.61803
$949$	−1.00000	−1.00000
$950$	0	0
$951$	0	0
$952$	−0.381966	−0.381966
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	1.00000	1.00000
$955$	−0.618034	−0.618034
$956$	0	0
$957$	0	0
$958$	−0.618034	−0.618034
$959$	−1.00000	−1.00000
$960$	−1.61803	−1.61803
$961$	−0.618034	−0.618034
$962$	0	0
$963$	0	0
$964$	−1.61803	−1.61803
$965$	−1.61803	−1.61803
$966$	1.61803	1.61803
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	−1.00000	−1.00000
$969$	0	0
$970$	1.61803	1.61803
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	−1.00000	−1.00000
$973$	−0.381966	−0.381966
$974$	−1.61803	−1.61803
$975$	2.61803	2.61803
$976$	−1.61803	−1.61803
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	3.23607	3.23607
$979$	0	0
$980$	0.618034	0.618034
$981$	0	0
$982$	0	0
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	0	0
$985$	0.618034	0.618034
$986$	0.618034	0.618034
$987$	0	0
$988$	0	0
$989$	−1.00000	−1.00000
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	−0.618034	−0.618034
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	1.61803	1.61803
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1160.1.o.a.579.2	✓	2
5.4	even	2		1160.1.o.d.579.1	yes	2
8.3	odd	2		1160.1.o.b.579.2	yes	2
29.28	even	2		1160.1.o.c.579.1	yes	2
40.19	odd	2		1160.1.o.c.579.1	yes	2
145.144	even	2		1160.1.o.b.579.2	yes	2
232.115	odd	2		1160.1.o.d.579.1	yes	2
1160.579	odd	2	CM	1160.1.o.a.579.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1160.1.o.a.579.2	✓	2	1.1	even	1	trivial
1160.1.o.a.579.2	✓	2	1160.579	odd	2	CM
1160.1.o.b.579.2	yes	2	8.3	odd	2
1160.1.o.b.579.2	yes	2	145.144	even	2
1160.1.o.c.579.1	yes	2	29.28	even	2
1160.1.o.c.579.1	yes	2	40.19	odd	2
1160.1.o.d.579.1	yes	2	5.4	even	2
1160.1.o.d.579.1	yes	2	232.115	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1160 = 2^{3} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1160.o (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.61803 q^{6} -0.618034 q^{7} -1.00000 q^{8} +1.61803 q^{9} +1.00000 q^{10} +1.61803 q^{12} +1.61803 q^{13} +0.618034 q^{14} -1.61803 q^{15} +1.00000 q^{16} -0.618034 q^{17} -1.61803 q^{18} -1.00000 q^{20} -1.00000 q^{21} +1.61803 q^{23} -1.61803 q^{24} +1.00000 q^{25} -1.61803 q^{26} +1.00000 q^{27} -0.618034 q^{28} +1.00000 q^{29} +1.61803 q^{30} +0.618034 q^{31} -1.00000 q^{32} +0.618034 q^{34} +0.618034 q^{35} +1.61803 q^{36} +2.61803 q^{39} +1.00000 q^{40} +1.00000 q^{42} -0.618034 q^{43} -1.61803 q^{45} -1.61803 q^{46} +1.61803 q^{48} -0.618034 q^{49} -1.00000 q^{50} -1.00000 q^{51} +1.61803 q^{52} -0.618034 q^{53} -1.00000 q^{54} +0.618034 q^{56} -1.00000 q^{58} -1.61803 q^{59} -1.61803 q^{60} -1.61803 q^{61} -0.618034 q^{62} -1.00000 q^{63} +1.00000 q^{64} -1.61803 q^{65} -0.618034 q^{68} +2.61803 q^{69} -0.618034 q^{70} -1.61803 q^{72} -0.618034 q^{73} +1.61803 q^{75} -2.61803 q^{78} -1.61803 q^{79} -1.00000 q^{80} -1.00000 q^{84} +0.618034 q^{85} +0.618034 q^{86} +1.61803 q^{87} +1.61803 q^{90} -1.00000 q^{91} +1.61803 q^{92} +1.00000 q^{93} -1.61803 q^{96} +1.61803 q^{97} +0.618034 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} - q^{6} + q^{7} - 2 q^{8} + q^{9} + 2 q^{10} + q^{12} + q^{13} - q^{14} - q^{15} + 2 q^{16} + q^{17} - q^{18} - 2 q^{20} - 2 q^{21} + q^{23} - q^{24}+ \cdots - q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 - q^6 + q^7 - 2 * q^8 + q^9 + 2 * q^10 + q^12 + q^13 - q^14 - q^15 + 2 * q^16 + q^17 - q^18 - 2 * q^20 - 2 * q^21 + q^23 - q^24 + 2 * q^25 - q^26 + 2 * q^27 + q^28 + 2 * q^29 + q^30 - q^31 - 2 * q^32 - q^34 - q^35 + q^36 + 3 * q^39 + 2 * q^40 + 2 * q^42 + q^43 - q^45 - q^46 + q^48 + q^49 - 2 * q^50 - 2 * q^51 + q^52 + q^53 - 2 * q^54 - q^56 - 2 * q^58 - q^59 - q^60 - q^61 + q^62 - 2 * q^63 + 2 * q^64 - q^65 + q^68 + 3 * q^69 + q^70 - q^72 + q^73 + q^75 - 3 * q^78 - q^79 - 2 * q^80 - 2 * q^84 - q^85 - q^86 + q^87 + q^90 - 2 * q^91 + q^92 + 2 * q^93 - q^96 + q^97 - q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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