LMFDB - Embedded newform 1859.1.c.c.846.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,1,Mod(846,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1859.846");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1859.c (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:	no
Analytic conductor:	$0.927761858485$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 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:	$C_4\times D_5$
Artin field:	Galois closure of $\mathbb{Q}[x]/(x^{20} - \cdots)$

Embedding invariants

Embedding label			846.4
Root			$-1.61803i$ of defining polynomial
Character	$\chi$	$=$	1859.846
Dual form			1859.1.c.c.846.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.61803i q^{2} -1.61803 q^{3} -1.61803 q^{4} -2.61803i q^{6} +0.618034i q^{7} -1.00000i q^{8} +1.61803 q^{9} +O(q^{10})$	$q+1.61803i q^{2} -1.61803 q^{3} -1.61803 q^{4} -2.61803i q^{6} +0.618034i q^{7} -1.00000i q^{8} +1.61803 q^{9} +1.00000i q^{11} +2.61803 q^{12} -1.00000 q^{14} +2.61803i q^{18} +1.61803i q^{19} -1.00000i q^{21} -1.61803 q^{22} -0.618034 q^{23} +1.61803i q^{24} -1.00000 q^{25} -1.00000 q^{27} -1.00000i q^{28} -1.00000i q^{32} -1.61803i q^{33} -2.61803 q^{36} -2.61803 q^{38} -0.618034i q^{41} +1.61803 q^{42} -1.61803i q^{44} -1.00000i q^{46} +0.618034 q^{49} -1.61803i q^{50} -1.61803 q^{53} -1.61803i q^{54} +0.618034 q^{56} -2.61803i q^{57} +1.00000i q^{63} +1.61803 q^{64} +2.61803 q^{66} +1.00000 q^{69} -1.61803i q^{72} -1.61803i q^{73} +1.61803 q^{75} -2.61803i q^{76} -0.618034 q^{77} +1.00000 q^{82} -0.618034i q^{83} +1.61803i q^{84} +1.00000 q^{88} +1.00000 q^{92} +1.61803i q^{96} +1.00000i q^{98} +1.61803i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^4 + 2 * q^9	$ 4 q - 2 q^{3} - 2 q^{4} + 2 q^{9} + 6 q^{12} - 4 q^{14} - 2 q^{22} + 2 q^{23} - 4 q^{25} - 4 q^{27} - 6 q^{36} - 6 q^{38} + 2 q^{42} - 2 q^{49} - 2 q^{53} - 2 q^{56} + 2 q^{64} + 6 q^{66} + 4 q^{69} + 2 q^{75} + 2 q^{77} + 4 q^{82} + 4 q^{88} + 4 q^{92}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^4 + 2 * q^9 + 6 * q^12 - 4 * q^14 - 2 * q^22 + 2 * q^23 - 4 * q^25 - 4 * q^27 - 6 * q^36 - 6 * q^38 + 2 * q^42 - 2 * q^49 - 2 * q^53 - 2 * q^56 + 2 * q^64 + 6 * q^66 + 4 * q^69 + 2 * q^75 + 2 * q^77 + 4 * q^82 + 4 * q^88 + 4 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1859\mathbb{Z}\right)^\times$.

$n$	$508$	$1354$
$\chi(n)$	$-1$	$1$

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 $

$2$	1.61803i	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$2$	1.61803i	1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$3$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$3$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$4$	−1.61803	−1.61803
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	− 2.61803i	− 2.61803i
$7$	0.618034i	0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$7$	0.618034i	0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$8$	− 1.00000i	− 1.00000i
$9$	1.61803	1.61803
$10$	0	0
$11$	1.00000i	1.00000i
$11$	1.00000i	1.00000i
$12$	2.61803	2.61803
$13$	0	0
$13$	0	0
$14$	−1.00000	−1.00000
$15$	0	0
$16$	0	0
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	2.61803i	2.61803i
$19$	1.61803i	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$19$	1.61803i	1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$20$	0	0
$21$	− 1.00000i	− 1.00000i
$22$	−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	$0.600000\pi$
$24$	1.61803i	1.61803i
$25$	−1.00000	−1.00000
$26$	0	0
$27$	−1.00000	−1.00000
$28$	− 1.00000i	− 1.00000i
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	− 1.00000i	− 1.00000i
$33$	− 1.61803i	− 1.61803i
$34$	0	0
$35$	0	0
$36$	−2.61803	−2.61803
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	−2.61803	−2.61803
$39$	0	0
$40$	0	0
$41$	− 0.618034i	− 0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$41$	− 0.618034i	− 0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$42$	1.61803	1.61803
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	− 1.61803i	− 1.61803i
$45$	0	0
$46$	− 1.00000i	− 1.00000i
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	0.618034	0.618034
$50$	− 1.61803i	− 1.61803i
$51$	0	0
$52$	0	0
$53$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$53$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$54$	− 1.61803i	− 1.61803i
$55$	0	0
$56$	0.618034	0.618034
$57$	− 2.61803i	− 2.61803i
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	1.00000i	1.00000i
$64$	1.61803	1.61803
$65$	0	0
$66$	2.61803	2.61803
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	0	0
$69$	1.00000	1.00000
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	− 1.61803i	− 1.61803i
$73$	− 1.61803i	− 1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$73$	− 1.61803i	− 1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$74$	0	0
$75$	1.61803	1.61803
$76$	− 2.61803i	− 2.61803i
$77$	−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
$83$	− 0.618034i	− 0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$83$	− 0.618034i	− 0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$84$	1.61803i	1.61803i
$85$	0	0
$86$	0	0
$87$	0	0
$88$	1.00000	1.00000
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	0	0
$92$	1.00000	1.00000
$93$	0	0
$94$	0	0
$95$	0	0
$96$	1.61803i	1.61803i
$97$	0	0		−	1.00000i	$-0.5\pi$
$97$	0	0			1.00000i	$0.5\pi$
$98$	1.00000i	1.00000i
$99$	1.61803i	1.61803i
$100$	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	$-0.600000\pi$
$103$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$104$	0	0
$105$	0	0
$106$	− 2.61803i	− 2.61803i
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	1.61803	1.61803
$109$	1.61803i	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$109$	1.61803i	1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$113$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$114$	4.23607	4.23607
$115$	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
$123$	1.00000i	1.00000i
$124$	0	0
$125$	0	0
$126$	−1.61803	−1.61803
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	1.61803i	1.61803i
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	2.61803i	2.61803i
$133$	−1.00000	−1.00000
$134$	0	0
$135$	0	0
$136$	0	0
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	1.61803i	1.61803i
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	2.61803	2.61803
$147$	−1.00000	−1.00000
$148$	0	0
$149$	− 0.618034i	− 0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$149$	− 0.618034i	− 0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$150$	2.61803i	2.61803i
$151$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$151$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$152$	1.61803	1.61803
$153$	0	0
$154$	− 1.00000i	− 1.00000i
$155$	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
$159$	2.61803	2.61803
$160$	0	0
$161$	− 0.381966i	− 0.381966i
$162$	0	0
$163$	0	0		−	1.00000i	$-0.5\pi$
$163$	0	0			1.00000i	$0.5\pi$
$164$	1.00000i	1.00000i
$165$	0	0
$166$	1.00000	1.00000
$167$	− 1.61803i	− 1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$167$	− 1.61803i	− 1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$168$	−1.00000	−1.00000
$169$	0	0
$170$	0	0
$171$	2.61803i	2.61803i
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	− 0.618034i	− 0.618034i
$176$	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	$-0.200000\pi$
$181$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$182$	0	0
$183$	0	0
$184$	0.618034i	0.618034i
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	− 0.618034i	− 0.618034i
$190$	0	0
$191$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$191$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$192$	−2.61803	−2.61803
$193$	0.618034i	0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$193$	0.618034i	0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$194$	0	0
$195$	0	0
$196$	−1.00000	−1.00000
$197$	1.61803i	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$197$	1.61803i	1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$198$	−2.61803	−2.61803
$199$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$199$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$200$	1.00000i	1.00000i
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	− 1.00000i	− 1.00000i
$207$	−1.00000	−1.00000
$208$	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
$216$	1.00000i	1.00000i
$217$	0	0
$218$	−2.61803	−2.61803
$219$	2.61803i	2.61803i
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0.618034	0.618034
$225$	−1.61803	−1.61803
$226$	− 2.61803i	− 2.61803i
$227$	1.61803i	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$227$	1.61803i	1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$228$	4.23607i	4.23607i
$229$	0	0		−	1.00000i	$-0.5\pi$
$229$	0	0			1.00000i	$0.5\pi$
$230$	0	0
$231$	1.00000	1.00000
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	1.61803i	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$239$	1.61803i	1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$240$	0	0
$241$	0.618034i	0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$241$	0.618034i	0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$242$	− 1.61803i	− 1.61803i
$243$	1.00000	1.00000
$244$	0	0
$245$	0	0
$246$	−1.61803	−1.61803
$247$	0	0
$248$	0	0
$249$	1.00000i	1.00000i
$250$	0	0
$251$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$251$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$252$	− 1.61803i	− 1.61803i
$253$	− 0.618034i	− 0.618034i
$254$	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			$\pi$
$264$	−1.61803	−1.61803
$265$	0	0
$266$	− 1.61803i	− 1.61803i
$267$	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	$0.400000\pi$
$270$	0	0
$271$	− 1.61803i	− 1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$271$	− 1.61803i	− 1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	− 1.00000i	− 1.00000i
$276$	−1.61803	−1.61803
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	− 1.61803i	− 1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$281$	− 1.61803i	− 1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0.381966	0.381966
$288$	− 1.61803i	− 1.61803i
$289$	1.00000	1.00000
$290$	0	0
$291$	0	0
$292$	2.61803i	2.61803i
$293$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$293$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$294$	− 1.61803i	− 1.61803i
$295$	0	0
$296$	0	0
$297$	− 1.00000i	− 1.00000i
$298$	1.00000	1.00000
$299$	0	0
$300$	−2.61803	−2.61803
$301$	0	0
$302$	−3.23607	−3.23607
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$307$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$308$	1.00000	1.00000
$309$	1.00000	1.00000
$310$	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	$0.400000\pi$
$314$	1.00000i	1.00000i
$315$	0	0
$316$	0	0
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	4.23607i	4.23607i
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0.618034	0.618034
$323$	0	0
$324$	0	0
$325$	0	0
$326$	0	0
$327$	− 2.61803i	− 2.61803i
$328$	−0.618034	−0.618034
$329$	0	0
$330$	0	0
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	1.00000i	1.00000i
$333$	0	0
$334$	2.61803	2.61803
$335$	0	0
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	2.61803	2.61803
$340$	0	0
$341$	0	0
$342$	−4.23607	−4.23607
$343$	1.00000i	1.00000i
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	0.618034i	0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$349$	0.618034i	0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$350$	1.00000	1.00000
$351$	0	0
$352$	1.00000	1.00000
$353$	0	0		−	1.00000i	$-0.5\pi$
$353$	0	0			1.00000i	$0.5\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	− 3.23607i	− 3.23607i
$359$	0.618034i	0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$359$	0.618034i	0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$360$	0	0
$361$	−1.61803	−1.61803
$362$	2.61803i	2.61803i
$363$	1.61803	1.61803
$364$	0	0
$365$	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
$369$	− 1.00000i	− 1.00000i
$370$	0	0
$371$	− 1.00000i	− 1.00000i
$372$	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
$378$	1.00000	1.00000
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	0	0
$381$	0	0
$382$	− 2.61803i	− 2.61803i
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	− 2.61803i	− 2.61803i
$385$	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
$392$	− 0.618034i	− 0.618034i
$393$	0	0
$394$	−2.61803	−2.61803
$395$	0	0
$396$	− 2.61803i	− 2.61803i
$397$	0	0		−	1.00000i	$-0.5\pi$
$397$	0	0			1.00000i	$0.5\pi$
$398$	2.61803i	2.61803i
$399$	1.61803	1.61803
$400$	0	0
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$409$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$410$	0	0
$411$	0	0
$412$	1.00000	1.00000
$413$	0	0
$414$	− 1.61803i	− 1.61803i
$415$	0	0
$416$	0	0
$417$	0	0
$418$	− 2.61803i	− 2.61803i
$419$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$419$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$420$	0	0
$421$	0	0		−	1.00000i	$-0.5\pi$
$421$	0	0			1.00000i	$0.5\pi$
$422$	0	0
$423$	0	0
$424$	1.61803i	1.61803i
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	− 0.618034i	− 0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$431$	− 0.618034i	− 0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$432$	0	0
$433$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$433$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$434$	0	0
$435$	0	0
$436$	− 2.61803i	− 2.61803i
$437$	− 1.00000i	− 1.00000i
$438$	−4.23607	−4.23607
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	1.00000	1.00000
$442$	0	0
$443$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$443$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	1.00000i	1.00000i
$448$	1.00000i	1.00000i
$449$	0	0		−	1.00000i	$-0.5\pi$
$449$	0	0			1.00000i	$0.5\pi$
$450$	− 2.61803i	− 2.61803i
$451$	0.618034	0.618034
$452$	2.61803	2.61803
$453$	− 3.23607i	− 3.23607i
$454$	−2.61803	−2.61803
$455$	0	0
$456$	−2.61803	−2.61803
$457$	1.61803i	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$457$	1.61803i	1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	1.61803i	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$461$	1.61803i	1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$462$	1.61803i	1.61803i
$463$	0	0		−	1.00000i	$-0.5\pi$
$463$	0	0			1.00000i	$0.5\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−2.00000	−2.00000	−1.00000			$\pi$
$467$	−2.00000	−2.00000	−1.00000			$\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−1.00000	−1.00000
$472$	0	0
$473$	0	0
$474$	0	0
$475$	− 1.61803i	− 1.61803i
$476$	0	0
$477$	−2.61803	−2.61803
$478$	−2.61803	−2.61803
$479$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$479$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$480$	0	0
$481$	0	0
$482$	−1.00000	−1.00000
$483$	0.618034i	0.618034i
$484$	1.61803	1.61803
$485$	0	0
$486$	1.61803i	1.61803i
$487$	0	0		−	1.00000i	$-0.5\pi$
$487$	0	0			1.00000i	$0.5\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	− 1.61803i	− 1.61803i
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	−1.61803	−1.61803
$499$	0	0		−	1.00000i	$-0.5\pi$
$499$	0	0			1.00000i	$0.5\pi$
$500$	0	0
$501$	2.61803i	2.61803i
$502$	− 1.00000i	− 1.00000i
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	1.00000	1.00000
$505$	0	0
$506$	1.00000	1.00000
$507$	0	0
$508$	0	0
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	1.00000	1.00000
$512$	0	0
$513$	− 1.61803i	− 1.61803i
$514$	− 1.00000i	− 1.00000i
$515$	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	$-0.400000\pi$
$521$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	1.00000i	1.00000i
$526$	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	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	3.23607	3.23607
$538$	1.00000i	1.00000i
$539$	0.618034i	0.618034i
$540$	0	0
$541$	0.618034i	0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$541$	0.618034i	0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$542$	2.61803	2.61803
$543$	−2.61803	−2.61803
$544$	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
$552$	− 1.00000i	− 1.00000i
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0.618034i	0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$557$	0.618034i	0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$558$	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			$\pi$
$572$	0	0
$573$	2.61803	2.61803
$574$	0.618034i	0.618034i
$575$	0.618034	0.618034
$576$	2.61803	2.61803
$577$	0	0		−	1.00000i	$-0.5\pi$
$577$	0	0			1.00000i	$0.5\pi$
$578$	1.61803i	1.61803i
$579$	− 1.00000i	− 1.00000i
$580$	0	0
$581$	0.381966	0.381966
$582$	0	0
$583$	− 1.61803i	− 1.61803i
$584$	−1.61803	−1.61803
$585$	0	0
$586$	−3.23607	−3.23607
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	1.61803	1.61803
$589$	0	0
$590$	0	0
$591$	− 2.61803i	− 2.61803i
$592$	0	0
$593$	0.618034i	0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$593$	0.618034i	0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$594$	1.61803	1.61803
$595$	0	0
$596$	1.00000i	1.00000i
$597$	−2.61803	−2.61803
$598$	0	0
$599$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$599$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$600$	− 1.61803i	− 1.61803i
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	0	0
$604$	− 3.23607i	− 3.23607i
$605$	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
$613$	1.61803i	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$613$	1.61803i	1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$614$	−3.23607	−3.23607
$615$	0	0
$616$	0.618034i	0.618034i
$617$	0	0		−	1.00000i	$-0.5\pi$
$617$	0	0			1.00000i	$0.5\pi$
$618$	1.61803i	1.61803i
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	0	0
$621$	0.618034	0.618034
$622$	2.61803i	2.61803i
$623$	0	0
$624$	0	0
$625$	1.00000	1.00000
$626$	1.00000i	1.00000i
$627$	2.61803	2.61803
$628$	−1.00000	−1.00000
$629$	0	0
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	−4.23607	−4.23607
$637$	0	0
$638$	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		−	1.00000i	$-0.5\pi$
$643$	0	0			1.00000i	$0.5\pi$
$644$	0.618034i	0.618034i
$645$	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
$650$	0	0
$651$	0	0
$652$	0	0
$653$	2.00000	2.00000	1.00000			$0$
$653$	2.00000	2.00000	1.00000			$0$
$654$	4.23607	4.23607
$655$	0	0
$656$	0	0
$657$	− 2.61803i	− 2.61803i
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	0	0		−	1.00000i	$-0.5\pi$
$661$	0	0			1.00000i	$0.5\pi$
$662$	0	0
$663$	0	0
$664$	−0.618034	−0.618034
$665$	0	0
$666$	0	0
$667$	0	0
$668$	2.61803i	2.61803i
$669$	0	0
$670$	0	0
$671$	0	0
$672$	−1.00000	−1.00000
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	1.00000	1.00000
$676$	0	0
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	4.23607i	4.23607i
$679$	0	0
$680$	0	0
$681$	− 2.61803i	− 2.61803i
$682$	0	0
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	− 4.23607i	− 4.23607i
$685$	0	0
$686$	−1.61803	−1.61803
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0	0		−	1.00000i	$-0.5\pi$
$691$	0	0			1.00000i	$0.5\pi$
$692$	0	0
$693$	−1.00000	−1.00000
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	−1.00000	−1.00000
$699$	0	0
$700$	1.00000i	1.00000i
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	1.61803i	1.61803i
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	0	0		−	1.00000i	$-0.5\pi$
$709$	0	0			1.00000i	$0.5\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	3.23607	3.23607
$717$	− 2.61803i	− 2.61803i
$718$	−1.00000	−1.00000
$719$	−2.00000	−2.00000	−1.00000			$\pi$
$719$	−2.00000	−2.00000	−1.00000			$\pi$
$720$	0	0
$721$	− 0.381966i	− 0.381966i
$722$	− 2.61803i	− 2.61803i
$723$	− 1.00000i	− 1.00000i
$724$	−2.61803	−2.61803
$725$	0	0
$726$	2.61803i	2.61803i
$727$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$727$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$728$	0	0
$729$	−1.61803	−1.61803
$730$	0	0
$731$	0	0
$732$	0	0
$733$	− 0.618034i	− 0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$733$	− 0.618034i	− 0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$734$	− 2.61803i	− 2.61803i
$735$	0	0
$736$	0.618034i	0.618034i
$737$	0	0
$738$	1.61803	1.61803
$739$	0.618034i	0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$739$	0.618034i	0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$740$	0	0
$741$	0	0
$742$	1.61803	1.61803
$743$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$743$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	− 1.00000i	− 1.00000i
$748$	0	0
$749$	0	0
$750$	0	0
$751$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$751$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$752$	0	0
$753$	1.00000	1.00000
$754$	0	0
$755$	0	0
$756$	1.00000i	1.00000i
$757$	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
$759$	1.00000i	1.00000i
$760$	0	0
$761$	0.618034i	0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$761$	0.618034i	0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$762$	0	0
$763$	−1.00000	−1.00000
$764$	2.61803	2.61803
$765$	0	0
$766$	0	0
$767$	0	0
$768$	1.61803	1.61803
$769$	− 0.618034i	− 0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$769$	− 0.618034i	− 0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$770$	0	0
$771$	1.00000	1.00000
$772$	− 1.00000i	− 1.00000i
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	2.61803i	2.61803i
$779$	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
$787$	0.618034i	0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$787$	0.618034i	0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$788$	− 2.61803i	− 2.61803i
$789$	0	0
$790$	0	0
$791$	− 1.00000i	− 1.00000i
$792$	1.61803	1.61803
$793$	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			$\pi$
$798$	2.61803i	2.61803i
$799$	0	0
$800$	1.00000i	1.00000i
$801$	0	0
$802$	0	0
$803$	1.61803	1.61803
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−1.00000	−1.00000
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	− 0.618034i	− 0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$811$	− 0.618034i	− 0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$812$	0	0
$813$	2.61803i	2.61803i
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	3.23607	3.23607
$819$	0	0
$820$	0	0
$821$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$821$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$822$	0	0
$823$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$823$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$824$	0.618034i	0.618034i
$825$	1.61803i	1.61803i
$826$	0	0
$827$	− 1.61803i	− 1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$827$	− 1.61803i	− 1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$828$	1.61803	1.61803
$829$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$829$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	2.61803	2.61803
$837$	0	0
$838$	1.00000i	1.00000i
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	1.00000	1.00000
$842$	0	0
$843$	2.61803i	2.61803i
$844$	0	0
$845$	0	0
$846$	0	0
$847$	− 0.618034i	− 0.618034i
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	− 1.61803i	− 1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$853$	− 1.61803i	− 1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$854$	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
$861$	−0.618034	−0.618034
$862$	1.00000	1.00000
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	1.00000i	1.00000i
$865$	0	0
$866$	2.61803i	2.61803i
$867$	−1.61803	−1.61803
$868$	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
$876$	− 4.23607i	− 4.23607i
$877$	1.61803i	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$877$	1.61803i	1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$878$	0	0
$879$	− 3.23607i	− 3.23607i
$880$	0	0
$881$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$881$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$882$	1.61803i	1.61803i
$883$	1.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$883$	1.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$884$	0	0
$885$	0	0
$886$	1.00000i	1.00000i
$887$	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
$894$	−1.61803	−1.61803
$895$	0	0
$896$	−1.00000	−1.00000
$897$	0	0
$898$	0	0
$899$	0	0
$900$	2.61803	2.61803
$901$	0	0
$902$	1.00000i	1.00000i
$903$	0	0
$904$	1.61803i	1.61803i
$905$	0	0
$906$	5.23607	5.23607
$907$	−0.618034	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$907$	−0.618034	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$908$	− 2.61803i	− 2.61803i
$909$	0	0
$910$	0	0
$911$	0.618034	0.618034	0.309017	−	0.951057i	$-0.400000\pi$
$911$	0.618034	0.618034	0.309017	+	0.951057i	$0.400000\pi$
$912$	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
$921$	− 3.23607i	− 3.23607i
$922$	−2.61803	−2.61803
$923$	0	0
$924$	−1.61803	−1.61803
$925$	0	0
$926$	0	0
$927$	−1.00000	−1.00000
$928$	0	0
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	1.00000i	1.00000i
$932$	0	0
$933$	−2.61803	−2.61803
$934$	− 3.23607i	− 3.23607i
$935$	0	0
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	−1.00000	−1.00000
$940$	0	0
$941$	1.61803i	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$941$	1.61803i	1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$942$	− 1.61803i	− 1.61803i
$943$	0.381966i	0.381966i
$944$	0	0
$945$	0	0
$946$	0	0
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	0	0
$949$	0	0
$950$	2.61803	2.61803
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	− 4.23607i	− 4.23607i
$955$	0	0
$956$	− 2.61803i	− 2.61803i
$957$	0	0
$958$	−3.23607	−3.23607
$959$	0	0
$960$	0	0
$961$	−1.00000	−1.00000
$962$	0	0
$963$	0	0
$964$	− 1.00000i	− 1.00000i
$965$	0	0
$966$	−1.00000	−1.00000
$967$	1.61803i	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$967$	1.61803i	1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$968$	1.00000i	1.00000i
$969$	0	0
$970$	0	0
$971$	−1.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$971$	−1.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$972$	−1.61803	−1.61803
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0		−	1.00000i	$-0.5\pi$
$977$	0	0			1.00000i	$0.5\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	2.61803i	2.61803i
$982$	0	0
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	1.00000	1.00000
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	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
$996$	− 1.61803i	− 1.61803i
$997$	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	1859.1.c.c.846.4		4
11.10	odd	2	inner	1859.1.c.c.846.1		4
13.2	odd	12		1859.1.i.a.1330.1		4
13.3	even	3		1859.1.k.c.1374.1		8
13.4	even	6		1859.1.k.c.1836.1		8
13.5	odd	4		143.1.d.b.142.2	yes	2
13.6	odd	12		1859.1.i.a.868.1		4
13.7	odd	12		1859.1.i.b.868.2		4
13.8	odd	4		143.1.d.a.142.1	✓	2
13.9	even	3		1859.1.k.c.1836.4		8
13.10	even	6		1859.1.k.c.1374.4		8
13.11	odd	12		1859.1.i.b.1330.2		4
13.12	even	2	inner	1859.1.c.c.846.1		4
39.5	even	4		1287.1.g.a.1000.1		2
39.8	even	4		1287.1.g.b.1000.2		2
52.31	even	4		2288.1.m.a.2001.2		2
52.47	even	4		2288.1.m.b.2001.2		2
65.8	even	4		3575.1.c.d.3574.4		4
65.18	even	4		3575.1.c.c.3574.1		4
65.34	odd	4		3575.1.h.f.2001.2		2
65.44	odd	4		3575.1.h.e.2001.1		2
65.47	even	4		3575.1.c.d.3574.1		4
65.57	even	4		3575.1.c.c.3574.4		4
143.5	odd	20		1573.1.l.a.844.1		4
143.8	even	20		1573.1.l.c.233.1		4
143.10	odd	6		1859.1.k.c.1374.1		8
143.18	even	20		1573.1.l.b.1546.1		4
143.21	even	4		143.1.d.b.142.2	yes	2
143.31	odd	20		1573.1.l.a.766.1		4
143.32	even	12		1859.1.i.b.868.2		4
143.43	odd	6		1859.1.k.c.1836.4		8
143.47	odd	20		1573.1.l.b.233.1		4
143.54	even	12		1859.1.i.b.1330.2		4
143.57	even	20		1573.1.l.d.766.1		4
143.60	odd	20		1573.1.l.d.844.1		4
143.70	odd	20		1573.1.l.c.1546.1		4
143.73	even	20		1573.1.l.c.1546.1		4
143.76	even	12		1859.1.i.a.1330.1		4
143.83	even	20		1573.1.l.d.844.1		4
143.86	odd	20		1573.1.l.d.766.1		4
143.87	odd	6		1859.1.k.c.1836.1		8
143.96	even	20		1573.1.l.b.233.1		4
143.98	even	12		1859.1.i.a.868.1		4
143.109	even	4		143.1.d.a.142.1	✓	2
143.112	even	20		1573.1.l.a.766.1		4
143.120	odd	6		1859.1.k.c.1374.4		8
143.125	odd	20		1573.1.l.b.1546.1		4
143.135	odd	20		1573.1.l.c.233.1		4
143.138	even	20		1573.1.l.a.844.1		4
143.142	odd	2	CM	1859.1.c.c.846.4		4
429.164	odd	4		1287.1.g.a.1000.1		2
429.395	odd	4		1287.1.g.b.1000.2		2
572.307	odd	4		2288.1.m.a.2001.2		2
572.395	odd	4		2288.1.m.b.2001.2		2
715.109	even	4		3575.1.h.f.2001.2		2
715.164	even	4		3575.1.h.e.2001.1		2
715.252	odd	4		3575.1.c.d.3574.1		4
715.307	odd	4		3575.1.c.c.3574.4		4
715.538	odd	4		3575.1.c.d.3574.4		4
715.593	odd	4		3575.1.c.c.3574.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.1.d.a.142.1	✓	2	13.8	odd	4
143.1.d.a.142.1	✓	2	143.109	even	4
143.1.d.b.142.2	yes	2	13.5	odd	4
143.1.d.b.142.2	yes	2	143.21	even	4
1287.1.g.a.1000.1		2	39.5	even	4
1287.1.g.a.1000.1		2	429.164	odd	4
1287.1.g.b.1000.2		2	39.8	even	4
1287.1.g.b.1000.2		2	429.395	odd	4
1573.1.l.a.766.1		4	143.31	odd	20
1573.1.l.a.766.1		4	143.112	even	20
1573.1.l.a.844.1		4	143.5	odd	20
1573.1.l.a.844.1		4	143.138	even	20
1573.1.l.b.233.1		4	143.47	odd	20
1573.1.l.b.233.1		4	143.96	even	20
1573.1.l.b.1546.1		4	143.18	even	20
1573.1.l.b.1546.1		4	143.125	odd	20
1573.1.l.c.233.1		4	143.8	even	20
1573.1.l.c.233.1		4	143.135	odd	20
1573.1.l.c.1546.1		4	143.70	odd	20
1573.1.l.c.1546.1		4	143.73	even	20
1573.1.l.d.766.1		4	143.57	even	20
1573.1.l.d.766.1		4	143.86	odd	20
1573.1.l.d.844.1		4	143.60	odd	20
1573.1.l.d.844.1		4	143.83	even	20
1859.1.c.c.846.1		4	11.10	odd	2	inner
1859.1.c.c.846.1		4	13.12	even	2	inner
1859.1.c.c.846.4		4	1.1	even	1	trivial
1859.1.c.c.846.4		4	143.142	odd	2	CM
1859.1.i.a.868.1		4	13.6	odd	12
1859.1.i.a.868.1		4	143.98	even	12
1859.1.i.a.1330.1		4	13.2	odd	12
1859.1.i.a.1330.1		4	143.76	even	12
1859.1.i.b.868.2		4	13.7	odd	12
1859.1.i.b.868.2		4	143.32	even	12
1859.1.i.b.1330.2		4	13.11	odd	12
1859.1.i.b.1330.2		4	143.54	even	12
1859.1.k.c.1374.1		8	13.3	even	3
1859.1.k.c.1374.1		8	143.10	odd	6
1859.1.k.c.1374.4		8	13.10	even	6
1859.1.k.c.1374.4		8	143.120	odd	6
1859.1.k.c.1836.1		8	13.4	even	6
1859.1.k.c.1836.1		8	143.87	odd	6
1859.1.k.c.1836.4		8	13.9	even	3
1859.1.k.c.1836.4		8	143.43	odd	6
2288.1.m.a.2001.2		2	52.31	even	4
2288.1.m.a.2001.2		2	572.307	odd	4
2288.1.m.b.2001.2		2	52.47	even	4
2288.1.m.b.2001.2		2	572.395	odd	4
3575.1.c.c.3574.1		4	65.18	even	4
3575.1.c.c.3574.1		4	715.593	odd	4
3575.1.c.c.3574.4		4	65.57	even	4
3575.1.c.c.3574.4		4	715.307	odd	4
3575.1.c.d.3574.1		4	65.47	even	4
3575.1.c.d.3574.1		4	715.252	odd	4
3575.1.c.d.3574.4		4	65.8	even	4
3575.1.c.d.3574.4		4	715.538	odd	4
3575.1.h.e.2001.1		2	65.44	odd	4
3575.1.h.e.2001.1		2	715.164	even	4
3575.1.h.f.2001.2		2	65.34	odd	4
3575.1.h.f.2001.2		2	715.109	even	4

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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1859.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.61803i q^{2} -1.61803 q^{3} -1.61803 q^{4} -2.61803i q^{6} +0.618034i q^{7} -1.00000i q^{8} +1.61803 q^{9} +O(q^{10})\)	\(q+1.61803i q^{2} -1.61803 q^{3} -1.61803 q^{4} -2.61803i q^{6} +0.618034i q^{7} -1.00000i q^{8} +1.61803 q^{9} +1.00000i q^{11} +2.61803 q^{12} -1.00000 q^{14} +2.61803i q^{18} +1.61803i q^{19} -1.00000i q^{21} -1.61803 q^{22} -0.618034 q^{23} +1.61803i q^{24} -1.00000 q^{25} -1.00000 q^{27} -1.00000i q^{28} -1.00000i q^{32} -1.61803i q^{33} -2.61803 q^{36} -2.61803 q^{38} -0.618034i q^{41} +1.61803 q^{42} -1.61803i q^{44} -1.00000i q^{46} +0.618034 q^{49} -1.61803i q^{50} -1.61803 q^{53} -1.61803i q^{54} +0.618034 q^{56} -2.61803i q^{57} +1.00000i q^{63} +1.61803 q^{64} +2.61803 q^{66} +1.00000 q^{69} -1.61803i q^{72} -1.61803i q^{73} +1.61803 q^{75} -2.61803i q^{76} -0.618034 q^{77} +1.00000 q^{82} -0.618034i q^{83} +1.61803i q^{84} +1.00000 q^{88} +1.00000 q^{92} +1.61803i q^{96} +1.00000i q^{98} +1.61803i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^4 + 2 * q^9	\( 4 q - 2 q^{3} - 2 q^{4} + 2 q^{9} + 6 q^{12} - 4 q^{14} - 2 q^{22} + 2 q^{23} - 4 q^{25} - 4 q^{27} - 6 q^{36} - 6 q^{38} + 2 q^{42} - 2 q^{49} - 2 q^{53} - 2 q^{56} + 2 q^{64} + 6 q^{66} + 4 q^{69} + 2 q^{75} + 2 q^{77} + 4 q^{82} + 4 q^{88} + 4 q^{92}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^4 + 2 * q^9 + 6 * q^12 - 4 * q^14 - 2 * q^22 + 2 * q^23 - 4 * q^25 - 4 * q^27 - 6 * q^36 - 6 * q^38 + 2 * q^42 - 2 * q^49 - 2 * q^53 - 2 * q^56 + 2 * q^64 + 6 * q^66 + 4 * q^69 + 2 * q^75 + 2 * q^77 + 4 * q^82 + 4 * q^88 + 4 * q^92

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