LMFDB - Embedded newform 1859.1.i.a.1330.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,1,Mod(868,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("1859.868");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1859.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.927761858485$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
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:	$C_3\times D_{10}$
Artin field:	Galois closure of $\mathbb{Q}[x]/(x^{30} - \cdots)$

Embedding invariants

Embedding label			1330.1
Root			$-0.309017 - 0.535233i$ of defining polynomial
Character	$\chi$	$=$	1859.1330
Dual form			1859.1.i.a.868.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 1.40126i) q^{2} +(0.809017 - 1.40126i) q^{3} +(-0.809017 - 1.40126i) q^{4} +(1.30902 + 2.26728i) q^{6} +(0.309017 + 0.535233i) q^{7} +1.00000 q^{8} +(-0.809017 - 1.40126i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 1.40126i) q^{2} +(0.809017 - 1.40126i) q^{3} +(-0.809017 - 1.40126i) q^{4} +(1.30902 + 2.26728i) q^{6} +(0.309017 + 0.535233i) q^{7} +1.00000 q^{8} +(-0.809017 - 1.40126i) q^{9} +(0.500000 - 0.866025i) q^{11} -2.61803 q^{12} -1.00000 q^{14} +2.61803 q^{18} +(-0.809017 - 1.40126i) q^{19} +1.00000 q^{21} +(0.809017 + 1.40126i) q^{22} +(-0.309017 + 0.535233i) q^{23} +(0.809017 - 1.40126i) q^{24} +1.00000 q^{25} -1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(0.500000 + 0.866025i) q^{32} +(-0.809017 - 1.40126i) q^{33} +(-1.30902 + 2.26728i) q^{36} +2.61803 q^{38} +(0.309017 - 0.535233i) q^{41} +(-0.809017 + 1.40126i) q^{42} -1.61803 q^{44} +(-0.500000 - 0.866025i) q^{46} +(0.309017 - 0.535233i) q^{49} +(-0.809017 + 1.40126i) q^{50} -1.61803 q^{53} +(0.809017 - 1.40126i) q^{54} +(0.309017 + 0.535233i) q^{56} -2.61803 q^{57} +(0.500000 - 0.866025i) q^{63} -1.61803 q^{64} +2.61803 q^{66} +(0.500000 + 0.866025i) q^{69} +(-0.809017 - 1.40126i) q^{72} +1.61803 q^{73} +(0.809017 - 1.40126i) q^{75} +(-1.30902 + 2.26728i) q^{76} +0.618034 q^{77} +(0.500000 + 0.866025i) q^{82} -0.618034 q^{83} +(-0.809017 - 1.40126i) q^{84} +(0.500000 - 0.866025i) q^{88} +1.00000 q^{92} +1.61803 q^{96} +(0.500000 + 0.866025i) q^{98} -1.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} - q^{4} + 3 q^{6} - q^{7} + 4 q^{8} - q^{9}+O(q^{10}) $ 4 * q - q^2 + q^3 - q^4 + 3 * q^6 - q^7 + 4 * q^8 - q^9	$ 4 q - q^{2} + q^{3} - q^{4} + 3 q^{6} - q^{7} + 4 q^{8} - q^{9} + 2 q^{11} - 6 q^{12} - 4 q^{14} + 6 q^{18} - q^{19} + 4 q^{21} + q^{22} + q^{23} + q^{24} + 4 q^{25} - 4 q^{27} + 2 q^{28} + 2 q^{32} - q^{33} - 3 q^{36} + 6 q^{38} - q^{41} - q^{42} - 2 q^{44} - 2 q^{46} - q^{49} - q^{50} - 2 q^{53} + q^{54} - q^{56} - 6 q^{57} + 2 q^{63} - 2 q^{64} + 6 q^{66} + 2 q^{69} - q^{72} + 2 q^{73} + q^{75} - 3 q^{76} - 2 q^{77} + 2 q^{82} + 2 q^{83} - q^{84} + 2 q^{88} + 4 q^{92} + 2 q^{96} + 2 q^{98} - 2 q^{99}+O(q^{100}) $ 4 * q - q^2 + q^3 - q^4 + 3 * q^6 - q^7 + 4 * q^8 - q^9 + 2 * q^11 - 6 * q^12 - 4 * q^14 + 6 * q^18 - q^19 + 4 * q^21 + q^22 + q^23 + q^24 + 4 * q^25 - 4 * q^27 + 2 * q^28 + 2 * q^32 - q^33 - 3 * q^36 + 6 * q^38 - q^41 - q^42 - 2 * q^44 - 2 * q^46 - q^49 - q^50 - 2 * q^53 + q^54 - q^56 - 6 * q^57 + 2 * q^63 - 2 * q^64 + 6 * q^66 + 2 * q^69 - q^72 + 2 * q^73 + q^75 - 3 * q^76 - 2 * q^77 + 2 * q^82 + 2 * q^83 - q^84 + 2 * q^88 + 4 * q^92 + 2 * q^96 + 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$508$	$1354$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	0.104528	+	0.994522i	$0.466667\pi$
$2$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	−0.913545	+	0.406737i	$0.866667\pi$
$3$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$3$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$4$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$5$		0			0		1.00000			$0$
$5$		0			0		−1.00000			$\pi$
$6$	1.30902	+	2.26728i	1.30902	+	2.26728i
$7$	0.309017	+	0.535233i	0.309017	+	0.535233i	0.978148	−	0.207912i	$-0.0666667\pi$
$7$	0.309017	+	0.535233i	0.309017	+	0.535233i	−0.669131	+	0.743145i	$0.733333\pi$
$8$	1.00000			1.00000
$9$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$10$		0			0
$11$	0.500000	−	0.866025i	0.500000	−	0.866025i
$11$	0.500000	−	0.866025i	0.500000	−	0.866025i
$12$	−2.61803			−2.61803
$13$		0			0
$13$		0			0
$14$	−1.00000			−1.00000
$15$		0			0
$16$		0			0
$17$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$17$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$18$	2.61803			2.61803
$19$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	−0.913545	−	0.406737i	$-0.866667\pi$
$19$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	0.104528	−	0.994522i	$-0.466667\pi$
$20$		0			0
$21$	1.00000			1.00000
$22$	0.809017	+	1.40126i	0.809017	+	1.40126i
$23$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$23$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$24$	0.809017	−	1.40126i	0.809017	−	1.40126i
$25$	1.00000			1.00000
$26$		0			0
$27$	−1.00000			−1.00000
$28$	0.500000	−	0.866025i	0.500000	−	0.866025i
$29$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$29$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	0.500000	+	0.866025i	0.500000	+	0.866025i
$33$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$34$		0			0
$35$		0			0
$36$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$	2.61803			2.61803
$39$		0			0
$40$		0			0
$41$	0.309017	−	0.535233i	0.309017	−	0.535233i	−0.669131	−	0.743145i	$-0.733333\pi$
$41$	0.309017	−	0.535233i	0.309017	−	0.535233i	0.978148	+	0.207912i	$0.0666667\pi$
$42$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$43$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$43$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$44$	−1.61803			−1.61803
$45$		0			0
$46$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$		0			0
$49$	0.309017	−	0.535233i	0.309017	−	0.535233i
$50$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$51$		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	$0.800000\pi$
$54$	0.809017	−	1.40126i	0.809017	−	1.40126i
$55$		0			0
$56$	0.309017	+	0.535233i	0.309017	+	0.535233i
$57$	−2.61803			−2.61803
$58$		0			0
$59$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$59$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$60$		0			0
$61$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$61$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$62$		0			0
$63$	0.500000	−	0.866025i	0.500000	−	0.866025i
$64$	−1.61803			−1.61803
$65$		0			0
$66$	2.61803			2.61803
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$		0			0
$69$	0.500000	+	0.866025i	0.500000	+	0.866025i
$70$		0			0
$71$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$71$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$72$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$73$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$73$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$74$		0			0
$75$	0.809017	−	1.40126i	0.809017	−	1.40126i
$76$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$77$	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
$82$	0.500000	+	0.866025i	0.500000	+	0.866025i
$83$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$83$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$84$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	0.500000	−	0.866025i	0.500000	−	0.866025i
$89$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$89$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$90$		0			0
$91$		0			0
$92$	1.00000			1.00000
$93$		0			0
$94$		0			0
$95$		0			0
$96$	1.61803			1.61803
$97$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$97$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$98$	0.500000	+	0.866025i	0.500000	+	0.866025i
$99$	−1.61803			−1.61803
$100$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$101$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$101$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$102$		0			0
$103$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$103$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$104$		0			0
$105$		0			0
$106$	1.30902	−	2.26728i	1.30902	−	2.26728i
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	0.809017	+	1.40126i	0.809017	+	1.40126i
$109$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$109$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$113$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$114$	2.11803	−	3.66854i	2.11803	−	3.66854i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$		0			0
$123$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$124$		0			0
$125$		0			0
$126$	0.809017	+	1.40126i	0.809017	+	1.40126i
$127$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$127$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$128$	0.809017	−	1.40126i	0.809017	−	1.40126i
$129$		0			0
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$133$	0.500000	−	0.866025i	0.500000	−	0.866025i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$137$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$138$	−1.61803			−1.61803
$139$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$139$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$147$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$148$		0			0
$149$	0.309017	+	0.535233i	0.309017	+	0.535233i	0.978148	−	0.207912i	$-0.0666667\pi$
$149$	0.309017	+	0.535233i	0.309017	+	0.535233i	−0.669131	+	0.743145i	$0.733333\pi$
$150$	1.30902	+	2.26728i	1.30902	+	2.26728i
$151$	−2.00000			−2.00000			−1.00000			$\pi$
$151$	−2.00000			−2.00000			−1.00000			$\pi$
$152$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$153$		0			0
$154$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$155$		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
$159$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$160$		0			0
$161$	−0.381966			−0.381966
$162$		0			0
$163$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$163$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$164$	−1.00000			−1.00000
$165$		0			0
$166$	0.500000	−	0.866025i	0.500000	−	0.866025i
$167$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	0.104528	+	0.994522i	$0.466667\pi$
$167$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	−0.913545	+	0.406737i	$0.866667\pi$
$168$	1.00000			1.00000
$169$		0			0
$170$		0			0
$171$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$172$		0			0
$173$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$173$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$174$		0			0
$175$	0.309017	+	0.535233i	0.309017	+	0.535233i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$179$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$180$		0			0
$181$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$181$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$182$		0			0
$183$		0			0
$184$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$190$		0			0
$191$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$191$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$192$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$193$	0.309017	−	0.535233i	0.309017	−	0.535233i	−0.669131	−	0.743145i	$-0.733333\pi$
$193$	0.309017	−	0.535233i	0.309017	−	0.535233i	0.978148	+	0.207912i	$0.0666667\pi$
$194$		0			0
$195$		0			0
$196$	−1.00000			−1.00000
$197$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	0.104528	+	0.994522i	$0.466667\pi$
$197$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	−0.913545	+	0.406737i	$0.866667\pi$
$198$	1.30902	−	2.26728i	1.30902	−	2.26728i
$199$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$199$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$200$	1.00000			1.00000
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$207$	1.00000			1.00000
$208$		0			0
$209$	−1.61803			−1.61803
$210$		0			0
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$	1.30902	+	2.26728i	1.30902	+	2.26728i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	−1.00000			−1.00000
$217$		0			0
$218$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$219$	1.30902	−	2.26728i	1.30902	−	2.26728i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$223$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$224$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$225$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$226$	−2.61803			−2.61803
$227$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	−0.913545	−	0.406737i	$-0.866667\pi$
$227$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	0.104528	−	0.994522i	$-0.466667\pi$
$228$	2.11803	+	3.66854i	2.11803	+	3.66854i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$	0.500000	−	0.866025i	0.500000	−	0.866025i
$232$		0			0
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$239$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$240$		0			0
$241$	0.309017	+	0.535233i	0.309017	+	0.535233i	0.978148	−	0.207912i	$-0.0666667\pi$
$241$	0.309017	+	0.535233i	0.309017	+	0.535233i	−0.669131	+	0.743145i	$0.733333\pi$
$242$	1.61803			1.61803
$243$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$244$		0			0
$245$		0			0
$246$	1.61803			1.61803
$247$		0			0
$248$		0			0
$249$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$250$		0			0
$251$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$251$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$252$	−1.61803			−1.61803
$253$	0.309017	+	0.535233i	0.309017	+	0.535233i
$254$		0			0
$255$		0			0
$256$	0.500000	+	0.866025i	0.500000	+	0.866025i
$257$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$257$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$265$		0			0
$266$	0.809017	+	1.40126i	0.809017	+	1.40126i
$267$		0			0
$268$		0			0
$269$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$269$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$270$		0			0
$271$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	0.104528	+	0.994522i	$0.466667\pi$
$271$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	−0.913545	+	0.406737i	$0.866667\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.500000	−	0.866025i	0.500000	−	0.866025i
$276$	0.809017	−	1.40126i	0.809017	−	1.40126i
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$281$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$282$		0			0
$283$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$283$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.381966			0.381966
$288$	0.809017	−	1.40126i	0.809017	−	1.40126i
$289$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$290$		0			0
$291$		0			0
$292$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$293$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$293$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$294$	1.61803			1.61803
$295$		0			0
$296$		0			0
$297$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$298$	−1.00000			−1.00000
$299$		0			0
$300$	−2.61803			−2.61803
$301$		0			0
$302$	1.61803	−	2.80252i	1.61803	−	2.80252i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−2.00000			−2.00000			−1.00000			$\pi$
$307$	−2.00000			−2.00000			−1.00000			$\pi$
$308$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$309$	0.500000	−	0.866025i	0.500000	−	0.866025i
$310$		0			0
$311$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$311$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$312$		0			0
$313$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$313$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$314$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$315$		0			0
$316$		0			0
$317$		0			0		1.00000			$0$
$317$		0			0		−1.00000			$\pi$
$318$	−2.11803	−	3.66854i	−2.11803	−	3.66854i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	0.309017	−	0.535233i	0.309017	−	0.535233i
$323$		0			0
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.30902	−	2.26728i	1.30902	−	2.26728i
$328$	0.309017	−	0.535233i	0.309017	−	0.535233i
$329$		0			0
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$	0.500000	+	0.866025i	0.500000	+	0.866025i
$333$		0			0
$334$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$335$		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
$342$	−2.11803	−	3.66854i	−2.11803	−	3.66854i
$343$	1.00000			1.00000
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$		0			0
$349$	0.309017	−	0.535233i	0.309017	−	0.535233i	−0.669131	−	0.743145i	$-0.733333\pi$
$349$	0.309017	−	0.535233i	0.309017	−	0.535233i	0.978148	+	0.207912i	$0.0666667\pi$
$350$	−1.00000			−1.00000
$351$		0			0
$352$	1.00000			1.00000
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.61803	−	2.80252i	−1.61803	−	2.80252i
$359$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$359$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$360$		0			0
$361$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$362$	1.30902	−	2.26728i	1.30902	−	2.26728i
$363$	−1.61803			−1.61803
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$367$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$368$		0			0
$369$	−1.00000			−1.00000
$370$		0			0
$371$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$	1.00000			1.00000
$379$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$379$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$380$		0			0
$381$		0			0
$382$	−2.61803			−2.61803
$383$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$385$		0			0
$386$	0.500000	+	0.866025i	0.500000	+	0.866025i
$387$		0			0
$388$		0			0
$389$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$389$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$390$		0			0
$391$		0			0
$392$	0.309017	−	0.535233i	0.309017	−	0.535233i
$393$		0			0
$394$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$395$		0			0
$396$	1.30902	+	2.26728i	1.30902	+	2.26728i
$397$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$397$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$398$	−2.61803			−2.61803
$399$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$400$		0			0
$401$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$401$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$409$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$410$		0			0
$411$		0			0
$412$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$413$		0			0
$414$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$415$		0			0
$416$		0			0
$417$		0			0
$418$	1.30902	−	2.26728i	1.30902	−	2.26728i
$419$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$419$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$420$		0			0
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$		0			0
$423$		0			0
$424$	−1.61803			−1.61803
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.309017	−	0.535233i	0.309017	−	0.535233i	−0.669131	−	0.743145i	$-0.733333\pi$
$431$	0.309017	−	0.535233i	0.309017	−	0.535233i	0.978148	+	0.207912i	$0.0666667\pi$
$432$		0			0
$433$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$433$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$434$		0			0
$435$		0			0
$436$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$437$	1.00000			1.00000
$438$	2.11803	+	3.66854i	2.11803	+	3.66854i
$439$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$439$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$440$		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
$447$	1.00000			1.00000
$448$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$449$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$449$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$450$	2.61803			2.61803
$451$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$452$	1.30902	−	2.26728i	1.30902	−	2.26728i
$453$	−1.61803	+	2.80252i	−1.61803	+	2.80252i
$454$	2.61803			2.61803
$455$		0			0
$456$	−2.61803			−2.61803
$457$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	0.104528	+	0.994522i	$0.466667\pi$
$457$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	−0.913545	+	0.406737i	$0.866667\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	−0.913545	−	0.406737i	$-0.866667\pi$
$461$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	0.104528	−	0.994522i	$-0.466667\pi$
$462$	0.809017	+	1.40126i	0.809017	+	1.40126i
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.00000			2.00000			1.00000			$0$
$467$	2.00000			2.00000			1.00000			$0$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.500000	−	0.866025i	0.500000	−	0.866025i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$476$		0			0
$477$	1.30902	+	2.26728i	1.30902	+	2.26728i
$478$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$479$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$479$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$480$		0			0
$481$		0			0
$482$	−1.00000			−1.00000
$483$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$484$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$485$		0			0
$486$	1.61803			1.61803
$487$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$487$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$491$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$492$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$		0			0
$501$	1.30902	+	2.26728i	1.30902	+	2.26728i
$502$	1.00000			1.00000
$503$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$503$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$504$	0.500000	−	0.866025i	0.500000	−	0.866025i
$505$		0			0
$506$	−1.00000			−1.00000
$507$		0			0
$508$		0			0
$509$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$509$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$510$		0			0
$511$	0.500000	+	0.866025i	0.500000	+	0.866025i
$512$		0			0
$513$	0.809017	+	1.40126i	0.809017	+	1.40126i
$514$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$515$		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		0.500000	−	0.866025i	$-0.333333\pi$
$523$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$524$		0			0
$525$	1.00000			1.00000
$526$		0			0
$527$		0			0
$528$		0			0
$529$	0.309017	+	0.535233i	0.309017	+	0.535233i
$530$		0			0
$531$		0			0
$532$	−1.61803			−1.61803
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	1.61803	+	2.80252i	1.61803	+	2.80252i
$538$	1.00000			1.00000
$539$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$540$		0			0
$541$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$541$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$542$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$543$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$		0			0
$549$		0			0
$550$	0.809017	+	1.40126i	0.809017	+	1.40126i
$551$		0			0
$552$	0.500000	+	0.866025i	0.500000	+	0.866025i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.309017	−	0.535233i	0.309017	−	0.535233i	−0.669131	−	0.743145i	$-0.733333\pi$
$557$	0.309017	−	0.535233i	0.309017	−	0.535233i	0.978148	+	0.207912i	$0.0666667\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$563$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$563$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$569$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$	2.61803			2.61803
$574$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$575$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$576$	1.30902	+	2.26728i	1.30902	+	2.26728i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$579$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$580$		0			0
$581$	−0.190983	−	0.330792i	−0.190983	−	0.330792i
$582$		0			0
$583$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$584$	1.61803			1.61803
$585$		0			0
$586$	−3.23607			−3.23607
$587$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$587$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$588$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$589$		0			0
$590$		0			0
$591$	1.30902	+	2.26728i	1.30902	+	2.26728i
$592$		0			0
$593$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$593$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$594$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$595$		0			0
$596$	0.500000	−	0.866025i	0.500000	−	0.866025i
$597$	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	$0.800000\pi$
$600$	0.809017	−	1.40126i	0.809017	−	1.40126i
$601$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$601$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$		0			0
$604$	1.61803	+	2.80252i	1.61803	+	2.80252i
$605$		0			0
$606$		0			0
$607$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$607$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$608$	0.809017	−	1.40126i	0.809017	−	1.40126i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	0.104528	+	0.994522i	$0.466667\pi$
$613$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	−0.913545	+	0.406737i	$0.866667\pi$
$614$	1.61803	−	2.80252i	1.61803	−	2.80252i
$615$		0			0
$616$	0.618034			0.618034
$617$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$617$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$618$	0.809017	+	1.40126i	0.809017	+	1.40126i
$619$		0			0		1.00000			$0$
$619$		0			0		−1.00000			$\pi$
$620$		0			0
$621$	0.309017	−	0.535233i	0.309017	−	0.535233i
$622$	1.30902	−	2.26728i	1.30902	−	2.26728i
$623$		0			0
$624$		0			0
$625$	1.00000			1.00000
$626$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$627$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$628$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$629$		0			0
$630$		0			0
$631$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$631$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$632$		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
$641$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$641$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$642$		0			0
$643$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$643$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$644$	0.309017	+	0.535233i	0.309017	+	0.535233i
$645$		0			0
$646$		0			0
$647$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$647$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$653$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$654$	2.11803	+	3.66854i	2.11803	+	3.66854i
$655$		0			0
$656$		0			0
$657$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$658$		0			0
$659$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$659$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$660$		0			0
$661$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$661$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$662$		0			0
$663$		0			0
$664$	−0.618034			−0.618034
$665$		0			0
$666$		0			0
$667$		0			0
$668$	2.61803			2.61803
$669$		0			0
$670$		0			0
$671$		0			0
$672$	0.500000	+	0.866025i	0.500000	+	0.866025i
$673$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$673$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$674$		0			0
$675$	−1.00000			−1.00000
$676$		0			0
$677$		0			0		1.00000			$0$
$677$		0			0		−1.00000			$\pi$
$678$	−2.11803	+	3.66854i	−2.11803	+	3.66854i
$679$		0			0
$680$		0			0
$681$	−2.61803			−2.61803
$682$		0			0
$683$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$683$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$684$	4.23607			4.23607
$685$		0			0
$686$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$		0			0
$693$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.500000	+	0.866025i	0.500000	+	0.866025i
$699$		0			0
$700$	0.500000	−	0.866025i	0.500000	−	0.866025i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$		0			0
$704$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$709$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	3.23607			3.23607
$717$	1.30902	−	2.26728i	1.30902	−	2.26728i
$718$	0.500000	−	0.866025i	0.500000	−	0.866025i
$719$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$719$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$720$		0			0
$721$	0.190983	+	0.330792i	0.190983	+	0.330792i
$722$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$723$	1.00000			1.00000
$724$	1.30902	+	2.26728i	1.30902	+	2.26728i
$725$		0			0
$726$	1.30902	−	2.26728i	1.30902	−	2.26728i
$727$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$727$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$728$		0			0
$729$	−1.61803			−1.61803
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$733$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$734$	1.30902	+	2.26728i	1.30902	+	2.26728i
$735$		0			0
$736$	−0.618034			−0.618034
$737$		0			0
$738$	0.809017	−	1.40126i	0.809017	−	1.40126i
$739$	0.309017	−	0.535233i	0.309017	−	0.535233i	−0.669131	−	0.743145i	$-0.733333\pi$
$739$	0.309017	−	0.535233i	0.309017	−	0.535233i	0.978148	+	0.207912i	$0.0666667\pi$
$740$		0			0
$741$		0			0
$742$	1.61803			1.61803
$743$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$743$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.500000	+	0.866025i	0.500000	+	0.866025i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$751$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$752$		0			0
$753$	−1.00000			−1.00000
$754$		0			0
$755$		0			0
$756$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$757$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$757$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$758$		0			0
$759$	1.00000			1.00000
$760$		0			0
$761$	0.309017	+	0.535233i	0.309017	+	0.535233i	0.978148	−	0.207912i	$-0.0666667\pi$
$761$	0.309017	+	0.535233i	0.309017	+	0.535233i	−0.669131	+	0.743145i	$0.733333\pi$
$762$		0			0
$763$	0.500000	+	0.866025i	0.500000	+	0.866025i
$764$	1.30902	−	2.26728i	1.30902	−	2.26728i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.61803			1.61803
$769$	0.309017	−	0.535233i	0.309017	−	0.535233i	−0.669131	−	0.743145i	$-0.733333\pi$
$769$	0.309017	−	0.535233i	0.309017	−	0.535233i	0.978148	+	0.207912i	$0.0666667\pi$
$770$		0			0
$771$	0.500000	+	0.866025i	0.500000	+	0.866025i
$772$	−1.00000			−1.00000
$773$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$773$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	1.30902	−	2.26728i	1.30902	−	2.26728i
$779$	−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
$787$	0.309017	+	0.535233i	0.309017	+	0.535233i	0.978148	−	0.207912i	$-0.0666667\pi$
$787$	0.309017	+	0.535233i	0.309017	+	0.535233i	−0.669131	+	0.743145i	$0.733333\pi$
$788$	2.61803			2.61803
$789$		0			0
$790$		0			0
$791$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$792$	−1.61803			−1.61803
$793$		0			0
$794$		0			0
$795$		0			0
$796$	1.30902	−	2.26728i	1.30902	−	2.26728i
$797$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$797$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$798$	2.61803			2.61803
$799$		0			0
$800$	0.500000	+	0.866025i	0.500000	+	0.866025i
$801$		0			0
$802$		0			0
$803$	0.809017	−	1.40126i	0.809017	−	1.40126i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.00000			−1.00000
$808$		0			0
$809$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$809$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$810$		0			0
$811$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$811$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$812$		0			0
$813$	1.30902	+	2.26728i	1.30902	+	2.26728i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−3.23607			−3.23607
$819$		0			0
$820$		0			0
$821$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$821$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$822$		0			0
$823$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$823$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$824$	0.618034			0.618034
$825$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$826$		0			0
$827$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$827$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$828$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$829$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$829$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$	1.30902	+	2.26728i	1.30902	+	2.26728i
$837$		0			0
$838$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$839$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$839$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$840$		0			0
$841$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$842$		0			0
$843$	1.30902	−	2.26728i	1.30902	−	2.26728i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.309017	−	0.535233i	0.309017	−	0.535233i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$853$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$854$		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
$861$	0.309017	−	0.535233i	0.309017	−	0.535233i
$862$	0.500000	+	0.866025i	0.500000	+	0.866025i
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$865$		0			0
$866$	−2.61803			−2.61803
$867$	0.809017	+	1.40126i	0.809017	+	1.40126i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	1.61803			1.61803
$873$		0			0
$874$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$875$		0			0
$876$	−4.23607			−4.23607
$877$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	−0.913545	−	0.406737i	$-0.866667\pi$
$877$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	0.104528	−	0.994522i	$-0.466667\pi$
$878$		0			0
$879$	3.23607			3.23607
$880$		0			0
$881$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$881$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$882$	0.809017	−	1.40126i	0.809017	−	1.40126i
$883$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$883$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$884$		0			0
$885$		0			0
$886$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$887$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$887$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$895$		0			0
$896$	1.00000			1.00000
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$901$		0			0
$902$	1.00000			1.00000
$903$		0			0
$904$	0.809017	+	1.40126i	0.809017	+	1.40126i
$905$		0			0
$906$	−2.61803	−	4.53457i	−2.61803	−	4.53457i
$907$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$907$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$908$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$909$		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
$913$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$914$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$919$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$920$		0			0
$921$	−1.61803	+	2.80252i	−1.61803	+	2.80252i
$922$	2.61803			2.61803
$923$		0			0
$924$	−1.61803			−1.61803
$925$		0			0
$926$		0			0
$927$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$928$		0			0
$929$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$929$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$930$		0			0
$931$	−1.00000			−1.00000
$932$		0			0
$933$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$934$	−1.61803	+	2.80252i	−1.61803	+	2.80252i
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$	0.500000	−	0.866025i	0.500000	−	0.866025i
$940$		0			0
$941$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$941$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$942$	0.809017	+	1.40126i	0.809017	+	1.40126i
$943$	0.190983	+	0.330792i	0.190983	+	0.330792i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$947$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$948$		0			0
$949$		0			0
$950$	2.61803			2.61803
$951$		0			0
$952$		0			0
$953$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$953$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$954$	−4.23607			−4.23607
$955$		0			0
$956$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$957$		0			0
$958$	1.61803	+	2.80252i	1.61803	+	2.80252i
$959$		0			0
$960$		0			0
$961$	1.00000			1.00000
$962$		0			0
$963$		0			0
$964$	0.500000	−	0.866025i	0.500000	−	0.866025i
$965$		0			0
$966$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$967$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$967$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$968$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$969$		0			0
$970$		0			0
$971$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$971$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$972$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$977$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$982$		0			0
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$991$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	1.61803			1.61803
$997$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$997$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.1.i.a.1330.1		4
11.10	odd	2		1859.1.i.b.1330.2		4
13.2	odd	12		1859.1.k.c.1836.1		8
13.3	even	3	inner	1859.1.i.a.868.1		4
13.4	even	6		143.1.d.a.142.1	✓	2
13.5	odd	4		1859.1.k.c.1374.4		8
13.6	odd	12		1859.1.c.c.846.1		4
13.7	odd	12		1859.1.c.c.846.4		4
13.8	odd	4		1859.1.k.c.1374.1		8
13.9	even	3		143.1.d.b.142.2	yes	2
13.10	even	6		1859.1.i.b.868.2		4
13.11	odd	12		1859.1.k.c.1836.4		8
13.12	even	2		1859.1.i.b.1330.2		4
39.17	odd	6		1287.1.g.b.1000.2		2
39.35	odd	6		1287.1.g.a.1000.1		2
52.35	odd	6		2288.1.m.a.2001.2		2
52.43	odd	6		2288.1.m.b.2001.2		2
65.4	even	6		3575.1.h.f.2001.2		2
65.9	even	6		3575.1.h.e.2001.1		2
65.17	odd	12		3575.1.c.d.3574.1		4
65.22	odd	12		3575.1.c.c.3574.4		4
65.43	odd	12		3575.1.c.d.3574.4		4
65.48	odd	12		3575.1.c.c.3574.1		4
143.4	even	30		1573.1.l.b.1546.1		4
143.9	even	15		1573.1.l.a.766.1		4
143.10	odd	6	inner	1859.1.i.a.868.1		4
143.17	odd	30		1573.1.l.a.844.1		4
143.21	even	4		1859.1.k.c.1374.4		8
143.30	odd	30		1573.1.l.c.233.1		4
143.32	even	12		1859.1.c.c.846.4		4
143.35	odd	30		1573.1.l.d.766.1		4
143.43	odd	6		143.1.d.b.142.2	yes	2
143.48	even	15		1573.1.l.c.1546.1		4
143.54	even	12		1859.1.k.c.1836.4		8
143.61	odd	30		1573.1.l.d.844.1		4
143.69	even	30		1573.1.l.b.233.1		4
143.74	odd	30		1573.1.l.b.233.1		4
143.76	even	12		1859.1.k.c.1836.1		8
143.82	even	30		1573.1.l.d.844.1		4
143.87	odd	6		143.1.d.a.142.1	✓	2
143.95	odd	30		1573.1.l.c.1546.1		4
143.98	even	12		1859.1.c.c.846.1		4
143.108	even	30		1573.1.l.d.766.1		4
143.109	even	4		1859.1.k.c.1374.1		8
143.113	even	15		1573.1.l.c.233.1		4
143.120	odd	6		1859.1.i.b.868.2		4
143.126	even	15		1573.1.l.a.844.1		4
143.134	odd	30		1573.1.l.a.766.1		4
143.139	odd	30		1573.1.l.b.1546.1		4
143.142	odd	2	CM	1859.1.i.a.1330.1		4
429.230	even	6		1287.1.g.b.1000.2		2
429.329	even	6		1287.1.g.a.1000.1		2
572.43	even	6		2288.1.m.a.2001.2		2
572.87	even	6		2288.1.m.b.2001.2		2
715.43	even	12		3575.1.c.c.3574.1		4
715.87	even	12		3575.1.c.d.3574.1		4
715.329	odd	6		3575.1.h.e.2001.1		2
715.373	even	12		3575.1.c.d.3574.4		4
715.472	even	12		3575.1.c.c.3574.4		4
715.659	odd	6		3575.1.h.f.2001.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.1.d.a.142.1	✓	2	13.4	even	6
143.1.d.a.142.1	✓	2	143.87	odd	6
143.1.d.b.142.2	yes	2	13.9	even	3
143.1.d.b.142.2	yes	2	143.43	odd	6
1287.1.g.a.1000.1		2	39.35	odd	6
1287.1.g.a.1000.1		2	429.329	even	6
1287.1.g.b.1000.2		2	39.17	odd	6
1287.1.g.b.1000.2		2	429.230	even	6
1573.1.l.a.766.1		4	143.9	even	15
1573.1.l.a.766.1		4	143.134	odd	30
1573.1.l.a.844.1		4	143.17	odd	30
1573.1.l.a.844.1		4	143.126	even	15
1573.1.l.b.233.1		4	143.69	even	30
1573.1.l.b.233.1		4	143.74	odd	30
1573.1.l.b.1546.1		4	143.4	even	30
1573.1.l.b.1546.1		4	143.139	odd	30
1573.1.l.c.233.1		4	143.30	odd	30
1573.1.l.c.233.1		4	143.113	even	15
1573.1.l.c.1546.1		4	143.48	even	15
1573.1.l.c.1546.1		4	143.95	odd	30
1573.1.l.d.766.1		4	143.35	odd	30
1573.1.l.d.766.1		4	143.108	even	30
1573.1.l.d.844.1		4	143.61	odd	30
1573.1.l.d.844.1		4	143.82	even	30
1859.1.c.c.846.1		4	13.6	odd	12
1859.1.c.c.846.1		4	143.98	even	12
1859.1.c.c.846.4		4	13.7	odd	12
1859.1.c.c.846.4		4	143.32	even	12
1859.1.i.a.868.1		4	13.3	even	3	inner
1859.1.i.a.868.1		4	143.10	odd	6	inner
1859.1.i.a.1330.1		4	1.1	even	1	trivial
1859.1.i.a.1330.1		4	143.142	odd	2	CM
1859.1.i.b.868.2		4	13.10	even	6
1859.1.i.b.868.2		4	143.120	odd	6
1859.1.i.b.1330.2		4	11.10	odd	2
1859.1.i.b.1330.2		4	13.12	even	2
1859.1.k.c.1374.1		8	13.8	odd	4
1859.1.k.c.1374.1		8	143.109	even	4
1859.1.k.c.1374.4		8	13.5	odd	4
1859.1.k.c.1374.4		8	143.21	even	4
1859.1.k.c.1836.1		8	13.2	odd	12
1859.1.k.c.1836.1		8	143.76	even	12
1859.1.k.c.1836.4		8	13.11	odd	12
1859.1.k.c.1836.4		8	143.54	even	12
2288.1.m.a.2001.2		2	52.35	odd	6
2288.1.m.a.2001.2		2	572.43	even	6
2288.1.m.b.2001.2		2	52.43	odd	6
2288.1.m.b.2001.2		2	572.87	even	6
3575.1.c.c.3574.1		4	65.48	odd	12
3575.1.c.c.3574.1		4	715.43	even	12
3575.1.c.c.3574.4		4	65.22	odd	12
3575.1.c.c.3574.4		4	715.472	even	12
3575.1.c.d.3574.1		4	65.17	odd	12
3575.1.c.d.3574.1		4	715.87	even	12
3575.1.c.d.3574.4		4	65.43	odd	12
3575.1.c.d.3574.4		4	715.373	even	12
3575.1.h.e.2001.1		2	65.9	even	6
3575.1.h.e.2001.1		2	715.329	odd	6
3575.1.h.f.2001.2		2	65.4	even	6
3575.1.h.f.2001.2		2	715.659	odd	6

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.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 1.40126i) q^{2} +(0.809017 - 1.40126i) q^{3} +(-0.809017 - 1.40126i) q^{4} +(1.30902 + 2.26728i) q^{6} +(0.309017 + 0.535233i) q^{7} +1.00000 q^{8} +(-0.809017 - 1.40126i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 1.40126i) q^{2} +(0.809017 - 1.40126i) q^{3} +(-0.809017 - 1.40126i) q^{4} +(1.30902 + 2.26728i) q^{6} +(0.309017 + 0.535233i) q^{7} +1.00000 q^{8} +(-0.809017 - 1.40126i) q^{9} +(0.500000 - 0.866025i) q^{11} -2.61803 q^{12} -1.00000 q^{14} +2.61803 q^{18} +(-0.809017 - 1.40126i) q^{19} +1.00000 q^{21} +(0.809017 + 1.40126i) q^{22} +(-0.309017 + 0.535233i) q^{23} +(0.809017 - 1.40126i) q^{24} +1.00000 q^{25} -1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(0.500000 + 0.866025i) q^{32} +(-0.809017 - 1.40126i) q^{33} +(-1.30902 + 2.26728i) q^{36} +2.61803 q^{38} +(0.309017 - 0.535233i) q^{41} +(-0.809017 + 1.40126i) q^{42} -1.61803 q^{44} +(-0.500000 - 0.866025i) q^{46} +(0.309017 - 0.535233i) q^{49} +(-0.809017 + 1.40126i) q^{50} -1.61803 q^{53} +(0.809017 - 1.40126i) q^{54} +(0.309017 + 0.535233i) q^{56} -2.61803 q^{57} +(0.500000 - 0.866025i) q^{63} -1.61803 q^{64} +2.61803 q^{66} +(0.500000 + 0.866025i) q^{69} +(-0.809017 - 1.40126i) q^{72} +1.61803 q^{73} +(0.809017 - 1.40126i) q^{75} +(-1.30902 + 2.26728i) q^{76} +0.618034 q^{77} +(0.500000 + 0.866025i) q^{82} -0.618034 q^{83} +(-0.809017 - 1.40126i) q^{84} +(0.500000 - 0.866025i) q^{88} +1.00000 q^{92} +1.61803 q^{96} +(0.500000 + 0.866025i) q^{98} -1.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} - q^{4} + 3 q^{6} - q^{7} + 4 q^{8} - q^{9}+O(q^{10}) \) 4 * q - q^2 + q^3 - q^4 + 3 * q^6 - q^7 + 4 * q^8 - q^9	\( 4 q - q^{2} + q^{3} - q^{4} + 3 q^{6} - q^{7} + 4 q^{8} - q^{9} + 2 q^{11} - 6 q^{12} - 4 q^{14} + 6 q^{18} - q^{19} + 4 q^{21} + q^{22} + q^{23} + q^{24} + 4 q^{25} - 4 q^{27} + 2 q^{28} + 2 q^{32} - q^{33} - 3 q^{36} + 6 q^{38} - q^{41} - q^{42} - 2 q^{44} - 2 q^{46} - q^{49} - q^{50} - 2 q^{53} + q^{54} - q^{56} - 6 q^{57} + 2 q^{63} - 2 q^{64} + 6 q^{66} + 2 q^{69} - q^{72} + 2 q^{73} + q^{75} - 3 q^{76} - 2 q^{77} + 2 q^{82} + 2 q^{83} - q^{84} + 2 q^{88} + 4 q^{92} + 2 q^{96} + 2 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 + 3 * q^6 - q^7 + 4 * q^8 - q^9 + 2 * q^11 - 6 * q^12 - 4 * q^14 + 6 * q^18 - q^19 + 4 * q^21 + q^22 + q^23 + q^24 + 4 * q^25 - 4 * q^27 + 2 * q^28 + 2 * q^32 - q^33 - 3 * q^36 + 6 * q^38 - q^41 - q^42 - 2 * q^44 - 2 * q^46 - q^49 - q^50 - 2 * q^53 + q^54 - q^56 - 6 * q^57 + 2 * q^63 - 2 * q^64 + 6 * q^66 + 2 * q^69 - q^72 + 2 * q^73 + q^75 - 3 * q^76 - 2 * q^77 + 2 * q^82 + 2 * q^83 - q^84 + 2 * q^88 + 4 * q^92 + 2 * q^96 + 2 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more