LMFDB - Embedded newform 1652.1.g.b.1651.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1652,1,Mod(1651,1652)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1652, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("1652.1651");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1652 = 2^{2} \cdot 7 \cdot 59 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1652.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:	$0.824455400870$
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 5.1.2729104.1

Embedding invariants

Embedding label			1651.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	1652.1651

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.61803 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.61803 q^{9} +1.61803 q^{11} +1.61803 q^{12} +0.618034 q^{13} +1.00000 q^{14} +1.00000 q^{16} -1.61803 q^{18} -0.618034 q^{19} -1.61803 q^{21} -1.61803 q^{22} -0.618034 q^{23} -1.61803 q^{24} +1.00000 q^{25} -0.618034 q^{26} +1.00000 q^{27} -1.00000 q^{28} -1.61803 q^{29} -1.00000 q^{32} +2.61803 q^{33} +1.61803 q^{36} +0.618034 q^{38} +1.00000 q^{39} +1.61803 q^{42} -0.618034 q^{43} +1.61803 q^{44} +0.618034 q^{46} +1.61803 q^{48} +1.00000 q^{49} -1.00000 q^{50} +0.618034 q^{52} +0.618034 q^{53} -1.00000 q^{54} +1.00000 q^{56} -1.00000 q^{57} +1.61803 q^{58} -1.00000 q^{59} +2.00000 q^{61} -1.61803 q^{63} +1.00000 q^{64} -2.61803 q^{66} +1.61803 q^{67} -1.00000 q^{69} -1.61803 q^{72} -1.61803 q^{73} +1.61803 q^{75} -0.618034 q^{76} -1.61803 q^{77} -1.00000 q^{78} -1.61803 q^{84} +0.618034 q^{86} -2.61803 q^{87} -1.61803 q^{88} -1.61803 q^{89} -0.618034 q^{91} -0.618034 q^{92} -1.61803 q^{96} -1.61803 q^{97} -1.00000 q^{98} +2.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{6} - 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^6 - 2 * q^7 - 2 * q^8 + q^9	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{6} - 2 q^{7} - 2 q^{8} + q^{9} + q^{11} + q^{12} - q^{13} + 2 q^{14} + 2 q^{16} - q^{18} + q^{19} - q^{21} - q^{22} + q^{23} - q^{24} + 2 q^{25} + q^{26} + 2 q^{27} - 2 q^{28} - q^{29} - 2 q^{32} + 3 q^{33} + q^{36} - q^{38} + 2 q^{39} + q^{42} + q^{43} + q^{44} - q^{46} + q^{48} + 2 q^{49} - 2 q^{50} - q^{52} - q^{53} - 2 q^{54} + 2 q^{56} - 2 q^{57} + q^{58} - 2 q^{59} + 4 q^{61} - q^{63} + 2 q^{64} - 3 q^{66} + q^{67} - 2 q^{69} - q^{72} - q^{73} + q^{75} + q^{76} - q^{77} - 2 q^{78} - q^{84} - q^{86} - 3 q^{87} - q^{88} - q^{89} + q^{91} + q^{92} - q^{96} - q^{97} - 2 q^{98} + 3 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^6 - 2 * q^7 - 2 * q^8 + q^9 + q^11 + q^12 - q^13 + 2 * q^14 + 2 * q^16 - q^18 + q^19 - q^21 - q^22 + q^23 - q^24 + 2 * q^25 + q^26 + 2 * q^27 - 2 * q^28 - q^29 - 2 * q^32 + 3 * q^33 + q^36 - q^38 + 2 * q^39 + q^42 + q^43 + q^44 - q^46 + q^48 + 2 * q^49 - 2 * q^50 - q^52 - q^53 - 2 * q^54 + 2 * q^56 - 2 * q^57 + q^58 - 2 * q^59 + 4 * q^61 - q^63 + 2 * q^64 - 3 * q^66 + q^67 - 2 * q^69 - q^72 - q^73 + q^75 + q^76 - q^77 - 2 * q^78 - q^84 - q^86 - 3 * q^87 - q^88 - q^89 + q^91 + q^92 - q^96 - q^97 - 2 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1652\mathbb{Z}\right)^\times$.

$n$	$533$	$827$	$1417$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.00000	−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
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	−1.61803	−1.61803
$7$	−1.00000	−1.00000
$7$	−1.00000	−1.00000
$8$	−1.00000	−1.00000
$9$	1.61803	1.61803
$10$	0	0
$11$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$11$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$12$	1.61803	1.61803
$13$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$13$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$14$	1.00000	1.00000
$15$	0	0
$16$	1.00000	1.00000
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	−1.61803	−1.61803
$19$	−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
$21$	−1.61803	−1.61803
$22$	−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	$0.600000\pi$
$24$	−1.61803	−1.61803
$25$	1.00000	1.00000
$26$	−0.618034	−0.618034
$27$	1.00000	1.00000
$28$	−1.00000	−1.00000
$29$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$29$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	−1.00000	−1.00000
$33$	2.61803	2.61803
$34$	0	0
$35$	0	0
$36$	1.61803	1.61803
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0.618034	0.618034
$39$	1.00000	1.00000
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	1.61803	1.61803
$43$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$43$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$44$	1.61803	1.61803
$45$	0	0
$46$	0.618034	0.618034
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	1.61803	1.61803
$49$	1.00000	1.00000
$50$	−1.00000	−1.00000
$51$	0	0
$52$	0.618034	0.618034
$53$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$53$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$54$	−1.00000	−1.00000
$55$	0	0
$56$	1.00000	1.00000
$57$	−1.00000	−1.00000
$58$	1.61803	1.61803
$59$	−1.00000	−1.00000
$59$	−1.00000	−1.00000
$60$	0	0
$61$	2.00000	2.00000	1.00000			$0$
$61$	2.00000	2.00000	1.00000			$0$
$62$	0	0
$63$	−1.61803	−1.61803
$64$	1.00000	1.00000
$65$	0	0
$66$	−2.61803	−2.61803
$67$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$67$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$68$	0	0
$69$	−1.00000	−1.00000
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	−1.61803	−1.61803
$73$	−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
$75$	1.61803	1.61803
$76$	−0.618034	−0.618034
$77$	−1.61803	−1.61803
$78$	−1.00000	−1.00000
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	−1.61803	−1.61803
$85$	0	0
$86$	0.618034	0.618034
$87$	−2.61803	−2.61803
$88$	−1.61803	−1.61803
$89$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$89$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$90$	0	0
$91$	−0.618034	−0.618034
$92$	−0.618034	−0.618034
$93$	0	0
$94$	0	0
$95$	0	0
$96$	−1.61803	−1.61803
$97$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$97$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$98$	−1.00000	−1.00000
$99$	2.61803	2.61803
$100$	1.00000	1.00000
$101$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$101$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$102$	0	0
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	−0.618034	−0.618034
$105$	0	0
$106$	−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
$112$	−1.00000	−1.00000
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	1.00000	1.00000
$115$	0	0
$116$	−1.61803	−1.61803
$117$	1.00000	1.00000
$118$	1.00000	1.00000
$119$	0	0
$120$	0	0
$121$	1.61803	1.61803
$122$	−2.00000	−2.00000
$123$	0	0
$124$	0	0
$125$	0	0
$126$	1.61803	1.61803
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	−1.00000	−1.00000
$129$	−1.00000	−1.00000
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	2.61803	2.61803
$133$	0.618034	0.618034
$134$	−1.61803	−1.61803
$135$	0	0
$136$	0	0
$137$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$137$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$138$	1.00000	1.00000
$139$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$139$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	1.00000	1.00000
$144$	1.61803	1.61803
$145$	0	0
$146$	1.61803	1.61803
$147$	1.61803	1.61803
$148$	0	0
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	−1.61803	−1.61803
$151$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$151$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$152$	0.618034	0.618034
$153$	0	0
$154$	1.61803	1.61803
$155$	0	0
$156$	1.00000	1.00000
$157$	−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
$159$	1.00000	1.00000
$160$	0	0
$161$	0.618034	0.618034
$162$	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	$0.600000\pi$
$168$	1.61803	1.61803
$169$	−0.618034	−0.618034
$170$	0	0
$171$	−1.00000	−1.00000
$172$	−0.618034	−0.618034
$173$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$173$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$174$	2.61803	2.61803
$175$	−1.00000	−1.00000
$176$	1.61803	1.61803
$177$	−1.61803	−1.61803
$178$	1.61803	1.61803
$179$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$179$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0.618034	0.618034
$183$	3.23607	3.23607
$184$	0.618034	0.618034
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	−1.00000	−1.00000
$190$	0	0
$191$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$191$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$192$	1.61803	1.61803
$193$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$193$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$194$	1.61803	1.61803
$195$	0	0
$196$	1.00000	1.00000
$197$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$197$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$198$	−2.61803	−2.61803
$199$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$199$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$200$	−1.00000	−1.00000
$201$	2.61803	2.61803
$202$	−0.618034	−0.618034
$203$	1.61803	1.61803
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−1.00000	−1.00000
$208$	0.618034	0.618034
$209$	−1.00000	−1.00000
$210$	0	0
$211$	−2.00000	−2.00000	−1.00000			$\pi$
$211$	−2.00000	−2.00000	−1.00000			$\pi$
$212$	0.618034	0.618034
$213$	0	0
$214$	0	0
$215$	0	0
$216$	−1.00000	−1.00000
$217$	0	0
$218$	0	0
$219$	−2.61803	−2.61803
$220$	0	0
$221$	0	0
$222$	0	0
$223$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$223$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$224$	1.00000	1.00000
$225$	1.61803	1.61803
$226$	0	0
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	−1.00000	−1.00000
$229$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$229$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$230$	0	0
$231$	−2.61803	−2.61803
$232$	1.61803	1.61803
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	−1.00000	−1.00000
$235$	0	0
$236$	−1.00000	−1.00000
$237$	0	0
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	−1.61803	−1.61803
$243$	−1.00000	−1.00000
$244$	2.00000	2.00000
$245$	0	0
$246$	0	0
$247$	−0.381966	−0.381966
$248$	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	$0.600000\pi$
$252$	−1.61803	−1.61803
$253$	−1.00000	−1.00000
$254$	0	0
$255$	0	0
$256$	1.00000	1.00000
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	1.00000	1.00000
$259$	0	0
$260$	0	0
$261$	−2.61803	−2.61803
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	−2.61803	−2.61803
$265$	0	0
$266$	−0.618034	−0.618034
$267$	−2.61803	−2.61803
$268$	1.61803	1.61803
$269$	2.00000	2.00000	1.00000			$0$
$269$	2.00000	2.00000	1.00000			$0$
$270$	0	0
$271$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$271$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$272$	0	0
$273$	−1.00000	−1.00000
$274$	1.61803	1.61803
$275$	1.61803	1.61803
$276$	−1.00000	−1.00000
$277$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$277$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$278$	−1.61803	−1.61803
$279$	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
$286$	−1.00000	−1.00000
$287$	0	0
$288$	−1.61803	−1.61803
$289$	1.00000	1.00000
$290$	0	0
$291$	−2.61803	−2.61803
$292$	−1.61803	−1.61803
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	−1.61803	−1.61803
$295$	0	0
$296$	0	0
$297$	1.61803	1.61803
$298$	0	0
$299$	−0.381966	−0.381966
$300$	1.61803	1.61803
$301$	0.618034	0.618034
$302$	−1.61803	−1.61803
$303$	1.00000	1.00000
$304$	−0.618034	−0.618034
$305$	0	0
$306$	0	0
$307$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$307$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$308$	−1.61803	−1.61803
$309$	0	0
$310$	0	0
$311$	−2.00000	−2.00000	−1.00000			$\pi$
$311$	−2.00000	−2.00000	−1.00000			$\pi$
$312$	−1.00000	−1.00000
$313$	2.00000	2.00000	1.00000			$0$
$313$	2.00000	2.00000	1.00000			$0$
$314$	1.61803	1.61803
$315$	0	0
$316$	0	0
$317$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$317$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$318$	−1.00000	−1.00000
$319$	−2.61803	−2.61803
$320$	0	0
$321$	0	0
$322$	−0.618034	−0.618034
$323$	0	0
$324$	0	0
$325$	0.618034	0.618034
$326$	0	0
$327$	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
$336$	−1.61803	−1.61803
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0.618034	0.618034
$339$	0	0
$340$	0	0
$341$	0	0
$342$	1.00000	1.00000
$343$	−1.00000	−1.00000
$344$	0.618034	0.618034
$345$	0	0
$346$	1.61803	1.61803
$347$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$347$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$348$	−2.61803	−2.61803
$349$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$349$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$350$	1.00000	1.00000
$351$	0.618034	0.618034
$352$	−1.61803	−1.61803
$353$	2.00000	2.00000	1.00000			$0$
$353$	2.00000	2.00000	1.00000			$0$
$354$	1.61803	1.61803
$355$	0	0
$356$	−1.61803	−1.61803
$357$	0	0
$358$	0.618034	0.618034
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	0	0
$361$	−0.618034	−0.618034
$362$	0	0
$363$	2.61803	2.61803
$364$	−0.618034	−0.618034
$365$	0	0
$366$	−3.23607	−3.23607
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	−0.618034	−0.618034
$369$	0	0
$370$	0	0
$371$	−0.618034	−0.618034
$372$	0	0
$373$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$373$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−1.00000	−1.00000
$378$	1.00000	1.00000
$379$	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
$389$	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
$392$	−1.00000	−1.00000
$393$	0	0
$394$	−0.618034	−0.618034
$395$	0	0
$396$	2.61803	2.61803
$397$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$397$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$398$	0.618034	0.618034
$399$	1.00000	1.00000
$400$	1.00000	1.00000
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	−2.61803	−2.61803
$403$	0	0
$404$	0.618034	0.618034
$405$	0	0
$406$	−1.61803	−1.61803
$407$	0	0
$408$	0	0
$409$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$409$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$410$	0	0
$411$	−2.61803	−2.61803
$412$	0	0
$413$	1.00000	1.00000
$414$	1.00000	1.00000
$415$	0	0
$416$	−0.618034	−0.618034
$417$	2.61803	2.61803
$418$	1.00000	1.00000
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	2.00000	2.00000
$423$	0	0
$424$	−0.618034	−0.618034
$425$	0	0
$426$	0	0
$427$	−2.00000	−2.00000
$428$	0	0
$429$	1.61803	1.61803
$430$	0	0
$431$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$431$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$432$	1.00000	1.00000
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0.381966	0.381966
$438$	2.61803	2.61803
$439$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$439$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$440$	0	0
$441$	1.61803	1.61803
$442$	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
$446$	−1.61803	−1.61803
$447$	0	0
$448$	−1.00000	−1.00000
$449$	2.00000	2.00000	1.00000			$0$
$449$	2.00000	2.00000	1.00000			$0$
$450$	−1.61803	−1.61803
$451$	0	0
$452$	0	0
$453$	2.61803	2.61803
$454$	0	0
$455$	0	0
$456$	1.00000	1.00000
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	1.61803	1.61803
$459$	0	0
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	2.61803	2.61803
$463$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$463$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$464$	−1.61803	−1.61803
$465$	0	0
$466$	0	0
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	1.00000	1.00000
$469$	−1.61803	−1.61803
$470$	0	0
$471$	−2.61803	−2.61803
$472$	1.00000	1.00000
$473$	−1.00000	−1.00000
$474$	0	0
$475$	−0.618034	−0.618034
$476$	0	0
$477$	1.00000	1.00000
$478$	0	0
$479$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$479$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	1.00000	1.00000
$484$	1.61803	1.61803
$485$	0	0
$486$	1.00000	1.00000
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	−2.00000	−2.00000
$489$	0	0
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0.381966	0.381966
$495$	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
$501$	−1.00000	−1.00000
$502$	0.618034	0.618034
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	1.61803	1.61803
$505$	0	0
$506$	1.00000	1.00000
$507$	−1.00000	−1.00000
$508$	0	0
$509$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$509$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$510$	0	0
$511$	1.61803	1.61803
$512$	−1.00000	−1.00000
$513$	−0.618034	−0.618034
$514$	0	0
$515$	0	0
$516$	−1.00000	−1.00000
$517$	0	0
$518$	0	0
$519$	−2.61803	−2.61803
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	2.61803	2.61803
$523$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$523$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$524$	0	0
$525$	−1.61803	−1.61803
$526$	0	0
$527$	0	0
$528$	2.61803	2.61803
$529$	−0.618034	−0.618034
$530$	0	0
$531$	−1.61803	−1.61803
$532$	0.618034	0.618034
$533$	0	0
$534$	2.61803	2.61803
$535$	0	0
$536$	−1.61803	−1.61803
$537$	−1.00000	−1.00000
$538$	−2.00000	−2.00000
$539$	1.61803	1.61803
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	−1.61803	−1.61803
$543$	0	0
$544$	0	0
$545$	0	0
$546$	1.00000	1.00000
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	−1.61803	−1.61803
$549$	3.23607	3.23607
$550$	−1.61803	−1.61803
$551$	1.00000	1.00000
$552$	1.00000	1.00000
$553$	0	0
$554$	−0.618034	−0.618034
$555$	0	0
$556$	1.61803	1.61803
$557$	2.00000	2.00000	1.00000			$0$
$557$	2.00000	2.00000	1.00000			$0$
$558$	0	0
$559$	−0.381966	−0.381966
$560$	0	0
$561$	0	0
$562$	−0.618034	−0.618034
$563$	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
$571$	−2.00000	−2.00000	−1.00000			$\pi$
$571$	−2.00000	−2.00000	−1.00000			$\pi$
$572$	1.00000	1.00000
$573$	−1.00000	−1.00000
$574$	0	0
$575$	−0.618034	−0.618034
$576$	1.61803	1.61803
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	−1.00000	−1.00000
$579$	−2.61803	−2.61803
$580$	0	0
$581$	0	0
$582$	2.61803	2.61803
$583$	1.00000	1.00000
$584$	1.61803	1.61803
$585$	0	0
$586$	0	0
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	1.61803	1.61803
$589$	0	0
$590$	0	0
$591$	1.00000	1.00000
$592$	0	0
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	−1.61803	−1.61803
$595$	0	0
$596$	0	0
$597$	−1.00000	−1.00000
$598$	0.381966	0.381966
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	−1.61803	−1.61803
$601$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$601$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$602$	−0.618034	−0.618034
$603$	2.61803	2.61803
$604$	1.61803	1.61803
$605$	0	0
$606$	−1.00000	−1.00000
$607$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$607$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$608$	0.618034	0.618034
$609$	2.61803	2.61803
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0.618034	0.618034
$615$	0	0
$616$	1.61803	1.61803
$617$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$617$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$618$	0	0
$619$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$619$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$620$	0	0
$621$	−0.618034	−0.618034
$622$	2.00000	2.00000
$623$	1.61803	1.61803
$624$	1.00000	1.00000
$625$	1.00000	1.00000
$626$	−2.00000	−2.00000
$627$	−1.61803	−1.61803
$628$	−1.61803	−1.61803
$629$	0	0
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	−3.23607	−3.23607
$634$	1.61803	1.61803
$635$	0	0
$636$	1.00000	1.00000
$637$	0.618034	0.618034
$638$	2.61803	2.61803
$639$	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
$643$	−2.00000	−2.00000	−1.00000			$\pi$
$643$	−2.00000	−2.00000	−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
$649$	−1.61803	−1.61803
$650$	−0.618034	−0.618034
$651$	0	0
$652$	0	0
$653$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$653$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−2.61803	−2.61803
$658$	0	0
$659$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$659$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$660$	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
$667$	1.00000	1.00000
$668$	−0.618034	−0.618034
$669$	2.61803	2.61803
$670$	0	0
$671$	3.23607	3.23607
$672$	1.61803	1.61803
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	1.00000	1.00000
$676$	−0.618034	−0.618034
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	1.61803	1.61803
$680$	0	0
$681$	0	0
$682$	0	0
$683$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$683$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$684$	−1.00000	−1.00000
$685$	0	0
$686$	1.00000	1.00000
$687$	−2.61803	−2.61803
$688$	−0.618034	−0.618034
$689$	0.381966	0.381966
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	−1.61803	−1.61803
$693$	−2.61803	−2.61803
$694$	−1.61803	−1.61803
$695$	0	0
$696$	2.61803	2.61803
$697$	0	0
$698$	1.61803	1.61803
$699$	0	0
$700$	−1.00000	−1.00000
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	−0.618034	−0.618034
$703$	0	0
$704$	1.61803	1.61803
$705$	0	0
$706$	−2.00000	−2.00000
$707$	−0.618034	−0.618034
$708$	−1.61803	−1.61803
$709$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$709$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$710$	0	0
$711$	0	0
$712$	1.61803	1.61803
$713$	0	0
$714$	0	0
$715$	0	0
$716$	−0.618034	−0.618034
$717$	0	0
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0	0
$721$	0	0
$722$	0.618034	0.618034
$723$	0	0
$724$	0	0
$725$	−1.61803	−1.61803
$726$	−2.61803	−2.61803
$727$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$727$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$728$	0.618034	0.618034
$729$	−1.61803	−1.61803
$730$	0	0
$731$	0	0
$732$	3.23607	3.23607
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	0	0
$736$	0.618034	0.618034
$737$	2.61803	2.61803
$738$	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
$741$	−0.618034	−0.618034
$742$	0.618034	0.618034
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	0	0
$746$	1.61803	1.61803
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−2.00000	−2.00000	−1.00000			$\pi$
$751$	−2.00000	−2.00000	−1.00000			$\pi$
$752$	0	0
$753$	−1.00000	−1.00000
$754$	1.00000	1.00000
$755$	0	0
$756$	−1.00000	−1.00000
$757$	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
$759$	−1.61803	−1.61803
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	0	0
$764$	−0.618034	−0.618034
$765$	0	0
$766$	0.618034	0.618034
$767$	−0.618034	−0.618034
$768$	1.61803	1.61803
$769$	2.00000	2.00000	1.00000			$0$
$769$	2.00000	2.00000	1.00000			$0$
$770$	0	0
$771$	0	0
$772$	−1.61803	−1.61803
$773$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$773$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$774$	1.00000	1.00000
$775$	0	0
$776$	1.61803	1.61803
$777$	0	0
$778$	−0.618034	−0.618034
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	−1.61803	−1.61803
$784$	1.00000	1.00000
$785$	0	0
$786$	0	0
$787$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$787$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$788$	0.618034	0.618034
$789$	0	0
$790$	0	0
$791$	0	0
$792$	−2.61803	−2.61803
$793$	1.23607	1.23607
$794$	−0.618034	−0.618034
$795$	0	0
$796$	−0.618034	−0.618034
$797$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$797$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$798$	−1.00000	−1.00000
$799$	0	0
$800$	−1.00000	−1.00000
$801$	−2.61803	−2.61803
$802$	0	0
$803$	−2.61803	−2.61803
$804$	2.61803	2.61803
$805$	0	0
$806$	0	0
$807$	3.23607	3.23607
$808$	−0.618034	−0.618034
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	1.61803	1.61803
$813$	2.61803	2.61803
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0.381966	0.381966
$818$	−0.618034	−0.618034
$819$	−1.00000	−1.00000
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	2.61803	2.61803
$823$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$823$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$824$	0	0
$825$	2.61803	2.61803
$826$	−1.00000	−1.00000
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	−1.00000	−1.00000
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	1.00000	1.00000
$832$	0.618034	0.618034
$833$	0	0
$834$	−2.61803	−2.61803
$835$	0	0
$836$	−1.00000	−1.00000
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	1.61803	1.61803
$842$	0	0
$843$	1.00000	1.00000
$844$	−2.00000	−2.00000
$845$	0	0
$846$	0	0
$847$	−1.61803	−1.61803
$848$	0.618034	0.618034
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	2.00000	2.00000
$855$	0	0
$856$	0	0
$857$	2.00000	2.00000	1.00000			$0$
$857$	2.00000	2.00000	1.00000			$0$
$858$	−1.61803	−1.61803
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	−1.61803	−1.61803
$863$	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
$865$	0	0
$866$	0	0
$867$	1.61803	1.61803
$868$	0	0
$869$	0	0
$870$	0	0
$871$	1.00000	1.00000
$872$	0	0
$873$	−2.61803	−2.61803
$874$	−0.381966	−0.381966
$875$	0	0
$876$	−2.61803	−2.61803
$877$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$877$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$878$	0.618034	0.618034
$879$	0	0
$880$	0	0
$881$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$881$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$882$	−1.61803	−1.61803
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	−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
$895$	0	0
$896$	1.00000	1.00000
$897$	−0.618034	−0.618034
$898$	−2.00000	−2.00000
$899$	0	0
$900$	1.61803	1.61803
$901$	0	0
$902$	0	0
$903$	1.00000	1.00000
$904$	0	0
$905$	0	0
$906$	−2.61803	−2.61803
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	1.00000	1.00000
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	−1.00000	−1.00000
$913$	0	0
$914$	0	0
$915$	0	0
$916$	−1.61803	−1.61803
$917$	0	0
$918$	0	0
$919$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$919$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$920$	0	0
$921$	−1.00000	−1.00000
$922$	0	0
$923$	0	0
$924$	−2.61803	−2.61803
$925$	0	0
$926$	0.618034	0.618034
$927$	0	0
$928$	1.61803	1.61803
$929$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$929$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$930$	0	0
$931$	−0.618034	−0.618034
$932$	0	0
$933$	−3.23607	−3.23607
$934$	0	0
$935$	0	0
$936$	−1.00000	−1.00000
$937$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$937$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$938$	1.61803	1.61803
$939$	3.23607	3.23607
$940$	0	0
$941$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$941$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$942$	2.61803	2.61803
$943$	0	0
$944$	−1.00000	−1.00000
$945$	0	0
$946$	1.00000	1.00000
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	−1.00000	−1.00000
$950$	0.618034	0.618034
$951$	−2.61803	−2.61803
$952$	0	0
$953$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$953$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$954$	−1.00000	−1.00000
$955$	0	0
$956$	0	0
$957$	−4.23607	−4.23607
$958$	−1.61803	−1.61803
$959$	1.61803	1.61803
$960$	0	0
$961$	1.00000	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	−1.00000	−1.00000
$967$	−2.00000	−2.00000	−1.00000			$\pi$
$967$	−2.00000	−2.00000	−1.00000			$\pi$
$968$	−1.61803	−1.61803
$969$	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	$0.200000\pi$
$972$	−1.00000	−1.00000
$973$	−1.61803	−1.61803
$974$	0	0
$975$	1.00000	1.00000
$976$	2.00000	2.00000
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	−2.61803	−2.61803
$980$	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
$988$	−0.381966	−0.381966
$989$	0.381966	0.381966
$990$	0	0
$991$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$991$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$992$	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	1652.1.g.b.1651.2	yes	2
4.3	odd	2		1652.1.g.c.1651.1	yes	2
7.6	odd	2		1652.1.g.a.1651.1	✓	2
28.27	even	2		1652.1.g.d.1651.2	yes	2
59.58	odd	2		1652.1.g.d.1651.2	yes	2
236.235	even	2		1652.1.g.a.1651.1	✓	2
413.412	even	2		1652.1.g.c.1651.1	yes	2
1652.1651	odd	2	CM	1652.1.g.b.1651.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1652.1.g.a.1651.1	✓	2	7.6	odd	2
1652.1.g.a.1651.1	✓	2	236.235	even	2
1652.1.g.b.1651.2	yes	2	1.1	even	1	trivial
1652.1.g.b.1651.2	yes	2	1652.1651	odd	2	CM
1652.1.g.c.1651.1	yes	2	4.3	odd	2
1652.1.g.c.1651.1	yes	2	413.412	even	2
1652.1.g.d.1651.2	yes	2	28.27	even	2
1652.1.g.d.1651.2	yes	2	59.58	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1652 = 2^{2} \cdot 7 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1652.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.61803 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.61803 q^{9} +1.61803 q^{11} +1.61803 q^{12} +0.618034 q^{13} +1.00000 q^{14} +1.00000 q^{16} -1.61803 q^{18} -0.618034 q^{19} -1.61803 q^{21} -1.61803 q^{22} -0.618034 q^{23} -1.61803 q^{24} +1.00000 q^{25} -0.618034 q^{26} +1.00000 q^{27} -1.00000 q^{28} -1.61803 q^{29} -1.00000 q^{32} +2.61803 q^{33} +1.61803 q^{36} +0.618034 q^{38} +1.00000 q^{39} +1.61803 q^{42} -0.618034 q^{43} +1.61803 q^{44} +0.618034 q^{46} +1.61803 q^{48} +1.00000 q^{49} -1.00000 q^{50} +0.618034 q^{52} +0.618034 q^{53} -1.00000 q^{54} +1.00000 q^{56} -1.00000 q^{57} +1.61803 q^{58} -1.00000 q^{59} +2.00000 q^{61} -1.61803 q^{63} +1.00000 q^{64} -2.61803 q^{66} +1.61803 q^{67} -1.00000 q^{69} -1.61803 q^{72} -1.61803 q^{73} +1.61803 q^{75} -0.618034 q^{76} -1.61803 q^{77} -1.00000 q^{78} -1.61803 q^{84} +0.618034 q^{86} -2.61803 q^{87} -1.61803 q^{88} -1.61803 q^{89} -0.618034 q^{91} -0.618034 q^{92} -1.61803 q^{96} -1.61803 q^{97} -1.00000 q^{98} +2.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{6} - 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^6 - 2 * q^7 - 2 * q^8 + q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{6} - 2 q^{7} - 2 q^{8} + q^{9} + q^{11} + q^{12} - q^{13} + 2 q^{14} + 2 q^{16} - q^{18} + q^{19} - q^{21} - q^{22} + q^{23} - q^{24} + 2 q^{25} + q^{26} + 2 q^{27} - 2 q^{28} - q^{29} - 2 q^{32} + 3 q^{33} + q^{36} - q^{38} + 2 q^{39} + q^{42} + q^{43} + q^{44} - q^{46} + q^{48} + 2 q^{49} - 2 q^{50} - q^{52} - q^{53} - 2 q^{54} + 2 q^{56} - 2 q^{57} + q^{58} - 2 q^{59} + 4 q^{61} - q^{63} + 2 q^{64} - 3 q^{66} + q^{67} - 2 q^{69} - q^{72} - q^{73} + q^{75} + q^{76} - q^{77} - 2 q^{78} - q^{84} - q^{86} - 3 q^{87} - q^{88} - q^{89} + q^{91} + q^{92} - q^{96} - q^{97} - 2 q^{98} + 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^6 - 2 * q^7 - 2 * q^8 + q^9 + q^11 + q^12 - q^13 + 2 * q^14 + 2 * q^16 - q^18 + q^19 - q^21 - q^22 + q^23 - q^24 + 2 * q^25 + q^26 + 2 * q^27 - 2 * q^28 - q^29 - 2 * q^32 + 3 * q^33 + q^36 - q^38 + 2 * q^39 + q^42 + q^43 + q^44 - q^46 + q^48 + 2 * q^49 - 2 * q^50 - q^52 - q^53 - 2 * q^54 + 2 * q^56 - 2 * q^57 + q^58 - 2 * q^59 + 4 * q^61 - q^63 + 2 * q^64 - 3 * q^66 + q^67 - 2 * q^69 - q^72 - q^73 + q^75 + q^76 - q^77 - 2 * q^78 - q^84 - q^86 - 3 * q^87 - q^88 - q^89 + q^91 + q^92 - q^96 - q^97 - 2 * q^98 + 3 * q^99

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