LMFDB - Embedded newform 833.1.h.b.815.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,1,Mod(509,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("833.509");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	833.h (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:	$0.415721155523$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 119)
Projective image:	$D_{5}$
Projective field:	Galois closure of 5.1.14161.1
Artin image:	$C_3\times D_5$
Artin field:	Galois closure of 15.3.334095024862954369.1

Embedding invariants

Embedding label			815.2
Root			$-0.309017 + 0.535233i$ of defining polynomial
Character	$\chi$	$=$	833.815
Dual form			833.1.h.b.509.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 1.40126i) q^{2} +(0.809017 - 1.40126i) q^{3} +(-0.809017 + 1.40126i) q^{4} +(-0.309017 - 0.535233i) q^{5} +2.61803 q^{6} -1.00000 q^{8} +(-0.809017 - 1.40126i) q^{9} +O(q^{10})$	\(q+(0.809017 + 1.40126i) q^{2} +(0.809017 - 1.40126i) q^{3} +(-0.809017 + 1.40126i) q^{4} +(-0.309017 - 0.535233i) q^{5} +2.61803 q^{6} -1.00000 q^{8} +(-0.809017 - 1.40126i) q^{9} +(0.500000 - 0.866025i) q^{10} +(1.30902 + 2.26728i) q^{12} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{17} +(1.30902 - 2.26728i) q^{18} +1.00000 q^{20} +(-0.809017 + 1.40126i) q^{24} +(0.309017 - 0.535233i) q^{25} -1.00000 q^{27} +(-0.809017 - 1.40126i) q^{30} +(-0.309017 + 0.535233i) q^{31} +(-0.500000 + 0.866025i) q^{32} -1.61803 q^{34} +2.61803 q^{36} +(0.309017 + 0.535233i) q^{40} -1.61803 q^{41} -1.61803 q^{43} +(-0.500000 + 0.866025i) q^{45} +1.00000 q^{50} +(0.809017 + 1.40126i) q^{51} +(-0.309017 + 0.535233i) q^{53} +(-0.809017 - 1.40126i) q^{54} +(0.809017 - 1.40126i) q^{60} +(0.809017 + 1.40126i) q^{61} -1.00000 q^{62} -1.61803 q^{64} +(-0.309017 + 0.535233i) q^{67} +(-0.809017 - 1.40126i) q^{68} +(0.809017 + 1.40126i) q^{72} +(0.809017 - 1.40126i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(-1.30902 - 2.26728i) q^{82} +0.618034 q^{85} +(-1.30902 - 2.26728i) q^{86} -1.61803 q^{90} +(0.500000 + 0.866025i) q^{93} +(0.809017 + 1.40126i) q^{96} +0.618034 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} - 4 q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 + q^3 - q^4 + q^5 + 6 * q^6 - 4 * q^8 - q^9	$ 4 q + q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} - 4 q^{8} - q^{9} + 2 q^{10} + 3 q^{12} - 4 q^{15} - 2 q^{17} + 3 q^{18} + 4 q^{20} - q^{24} - q^{25} - 4 q^{27} - q^{30} + q^{31} - 2 q^{32} - 2 q^{34} + 6 q^{36} - q^{40} - 2 q^{41} - 2 q^{43} - 2 q^{45} + 4 q^{50} + q^{51} + q^{53} - q^{54} + q^{60} + q^{61} - 4 q^{62} - 2 q^{64} + q^{67} - q^{68} + q^{72} + q^{73} - 2 q^{75} - 3 q^{82} - 2 q^{85} - 3 q^{86} - 2 q^{90} + 2 q^{93} + q^{96} - 2 q^{97}+O(q^{100}) $ 4 * q + q^2 + q^3 - q^4 + q^5 + 6 * q^6 - 4 * q^8 - q^9 + 2 * q^10 + 3 * q^12 - 4 * q^15 - 2 * q^17 + 3 * q^18 + 4 * q^20 - q^24 - q^25 - 4 * q^27 - q^30 + q^31 - 2 * q^32 - 2 * q^34 + 6 * q^36 - q^40 - 2 * q^41 - 2 * q^43 - 2 * q^45 + 4 * q^50 + q^51 + q^53 - q^54 + q^60 + q^61 - 4 * q^62 - 2 * q^64 + q^67 - q^68 + q^72 + q^73 - 2 * q^75 - 3 * q^82 - 2 * q^85 - 3 * q^86 - 2 * q^90 + 2 * q^93 + q^96 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$2$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$3$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	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
$5$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$5$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$6$	2.61803			2.61803
$7$		0			0
$7$		0			0
$8$	−1.00000			−1.00000
$9$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$10$	0.500000	−	0.866025i	0.500000	−	0.866025i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	1.30902	+	2.26728i	1.30902	+	2.26728i
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$		0			0
$15$	−1.00000			−1.00000
$16$		0			0
$17$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$17$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$18$	1.30902	−	2.26728i	1.30902	−	2.26728i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	1.00000			1.00000
$21$		0			0
$22$		0			0
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$25$	0.309017	−	0.535233i	0.309017	−	0.535233i
$26$		0			0
$27$	−1.00000			−1.00000
$28$		0			0
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$31$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$31$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$32$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$33$		0			0
$34$	−1.61803			−1.61803
$35$		0			0
$36$	2.61803			2.61803
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$		0			0
$39$		0			0
$40$	0.309017	+	0.535233i	0.309017	+	0.535233i
$41$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$41$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$42$		0			0
$43$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$43$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$44$		0			0
$45$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$46$		0			0
$47$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$47$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$48$		0			0
$49$		0			0
$50$	1.00000			1.00000
$51$	0.809017	+	1.40126i	0.809017	+	1.40126i
$52$		0			0
$53$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$53$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$54$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$59$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$60$	0.809017	−	1.40126i	0.809017	−	1.40126i
$61$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$61$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$62$	−1.00000			−1.00000
$63$		0			0
$64$	−1.61803			−1.61803
$65$		0			0
$66$		0			0
$67$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$67$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$68$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$69$		0			0
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	0.809017	+	1.40126i	0.809017	+	1.40126i
$73$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$73$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$74$		0			0
$75$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$79$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$80$		0			0
$81$		0			0
$82$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$	0.618034			0.618034
$86$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$87$		0			0
$88$		0			0
$89$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$89$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$90$	−1.61803			−1.61803
$91$		0			0
$92$		0			0
$93$	0.500000	+	0.866025i	0.500000	+	0.866025i
$94$		0			0
$95$		0			0
$96$	0.809017	+	1.40126i	0.809017	+	1.40126i
$97$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$97$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$98$		0			0
$99$		0			0
$100$	0.500000	+	0.866025i	0.500000	+	0.866025i
$101$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$101$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$102$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$		0			0
$105$		0			0
$106$	−1.00000			−1.00000
$107$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$107$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$108$	0.809017	−	1.40126i	0.809017	−	1.40126i
$109$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$109$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$	1.00000			1.00000
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$123$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$124$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$125$	−1.00000			−1.00000
$126$		0			0
$127$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$127$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$128$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$129$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$130$		0			0
$131$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$131$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$132$		0			0
$133$		0			0
$134$	−1.00000			−1.00000
$135$	0.309017	+	0.535233i	0.309017	+	0.535233i
$136$	0.500000	−	0.866025i	0.500000	−	0.866025i
$137$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$137$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$138$		0			0
$139$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$139$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$	2.61803			2.61803
$147$		0			0
$148$		0			0
$149$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$149$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$150$	0.809017	−	1.40126i	0.809017	−	1.40126i
$151$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$151$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$152$		0			0
$153$	1.61803			1.61803
$154$		0			0
$155$	0.381966			0.381966
$156$		0			0
$157$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$157$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$158$		0			0
$159$	0.500000	+	0.866025i	0.500000	+	0.866025i
$160$	0.618034			0.618034
$161$		0			0
$162$		0			0
$163$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$163$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$164$	1.30902	−	2.26728i	1.30902	−	2.26728i
$165$		0			0
$166$		0			0
$167$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$167$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$168$		0			0
$169$	1.00000			1.00000
$170$	0.500000	+	0.866025i	0.500000	+	0.866025i
$171$		0			0
$172$	1.30902	−	2.26728i	1.30902	−	2.26728i
$173$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$173$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$179$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$180$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$181$	2.00000			2.00000			1.00000			$0$
$181$	2.00000			2.00000			1.00000			$0$
$182$		0			0
$183$	2.61803			2.61803
$184$		0			0
$185$		0			0
$186$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$191$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$192$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$193$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$193$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$194$	0.500000	+	0.866025i	0.500000	+	0.866025i
$195$		0			0
$196$		0			0
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$199$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$200$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$201$	0.500000	+	0.866025i	0.500000	+	0.866025i
$202$		0			0
$203$		0			0
$204$	−2.61803			−2.61803
$205$	0.500000	+	0.866025i	0.500000	+	0.866025i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		1.00000			$0$
$211$		0			0		−1.00000			$\pi$
$212$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$213$		0			0
$214$		0			0
$215$	0.500000	+	0.866025i	0.500000	+	0.866025i
$216$	1.00000			1.00000
$217$		0			0
$218$		0			0
$219$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$		0			0
$225$	−1.00000			−1.00000
$226$		0			0
$227$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$227$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$228$		0			0
$229$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$229$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$233$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$239$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$240$		0			0
$241$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$241$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$242$	0.809017	−	1.40126i	0.809017	−	1.40126i
$243$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$244$	−2.61803			−2.61803
$245$		0			0
$246$	−4.23607			−4.23607
$247$		0			0
$248$	0.309017	−	0.535233i	0.309017	−	0.535233i
$249$		0			0
$250$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$		0			0
$253$		0			0
$254$	0.500000	+	0.866025i	0.500000	+	0.866025i
$255$	0.500000	−	0.866025i	0.500000	−	0.866025i
$256$	0.500000	−	0.866025i	0.500000	−	0.866025i
$257$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$257$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$258$	−4.23607			−4.23607
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.61803	−	2.80252i	1.61803	−	2.80252i
$263$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$263$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$	0.381966			0.381966
$266$		0			0
$267$		0			0
$268$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$269$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$269$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$270$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$271$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$271$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$272$		0			0
$273$		0			0
$274$	2.61803			2.61803
$275$		0			0
$276$		0			0
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$	0.500000	+	0.866025i	0.500000	+	0.866025i
$279$	1.00000			1.00000
$280$		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
$283$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$283$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	1.61803			1.61803
$289$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$290$		0			0
$291$	0.500000	−	0.866025i	0.500000	−	0.866025i
$292$	1.30902	+	2.26728i	1.30902	+	2.26728i
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$299$		0			0
$300$	1.61803			1.61803
$301$		0			0
$302$	2.61803			2.61803
$303$		0			0
$304$		0			0
$305$	0.500000	−	0.866025i	0.500000	−	0.866025i
$306$	1.30902	+	2.26728i	1.30902	+	2.26728i
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$	0.309017	+	0.535233i	0.309017	+	0.535233i
$311$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$311$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$312$		0			0
$313$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$313$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$317$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$318$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$319$		0			0
$320$	0.500000	+	0.866025i	0.500000	+	0.866025i
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$		0			0
$326$		0			0
$327$		0			0
$328$	1.61803			1.61803
$329$		0			0
$330$		0			0
$331$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$331$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$332$		0			0
$333$		0			0
$334$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$335$	0.381966			0.381966
$336$		0			0
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$	0.809017	+	1.40126i	0.809017	+	1.40126i
$339$		0			0
$340$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$341$		0			0
$342$		0			0
$343$		0			0
$344$	1.61803			1.61803
$345$		0			0
$346$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$347$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$347$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$348$		0			0
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		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
$358$	2.61803			2.61803
$359$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$359$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$360$	0.500000	−	0.866025i	0.500000	−	0.866025i
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$	1.61803	+	2.80252i	1.61803	+	2.80252i
$363$	−1.61803			−1.61803
$364$		0			0
$365$	−1.00000			−1.00000
$366$	2.11803	+	3.66854i	2.11803	+	3.66854i
$367$	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
$369$	1.30902	+	2.26728i	1.30902	+	2.26728i
$370$		0			0
$371$		0			0
$372$	−1.61803			−1.61803
$373$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$373$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$374$		0			0
$375$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	0.500000	−	0.866025i	0.500000	−	0.866025i
$382$	0.500000	−	0.866025i	0.500000	−	0.866025i
$383$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$	−2.61803			−2.61803
$385$		0			0
$386$		0			0
$387$	1.30902	+	2.26728i	1.30902	+	2.26728i
$388$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$389$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$389$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−3.23607			−3.23607
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$397$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$398$	2.61803			2.61803
$399$		0			0
$400$		0			0
$401$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$401$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$402$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$409$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$409$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$410$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$411$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.500000	−	0.866025i	0.500000	−	0.866025i
$418$		0			0
$419$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$419$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$420$		0			0
$421$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$421$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$422$		0			0
$423$		0			0
$424$	0.309017	−	0.535233i	0.309017	−	0.535233i
$425$	0.309017	+	0.535233i	0.309017	+	0.535233i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$		0			0
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	2.11803	−	3.66854i	2.11803	−	3.66854i
$439$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$439$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$443$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	2.61803			2.61803
$448$		0			0
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$451$		0			0
$452$		0			0
$453$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$454$	−1.00000			−1.00000
$455$		0			0
$456$		0			0
$457$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$457$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$458$		0			0
$459$	0.500000	−	0.866025i	0.500000	−	0.866025i
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$463$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$464$		0			0
$465$	0.309017	−	0.535233i	0.309017	−	0.535233i
$466$		0			0
$467$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$467$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.00000			1.00000
$478$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$479$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$479$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$480$	0.500000	−	0.866025i	0.500000	−	0.866025i
$481$		0			0
$482$	−1.00000			−1.00000
$483$		0			0
$484$	1.61803			1.61803
$485$	−0.190983	−	0.330792i	−0.190983	−	0.330792i
$486$	0.809017	−	1.40126i	0.809017	−	1.40126i
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$489$		0			0
$490$		0			0
$491$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$491$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$492$	−2.11803	−	3.66854i	−2.11803	−	3.66854i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$	0.809017	−	1.40126i	0.809017	−	1.40126i
$501$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$502$		0			0
$503$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$503$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.809017	−	1.40126i	0.809017	−	1.40126i
$508$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$509$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$509$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$510$	1.61803			1.61803
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$		0			0
$516$	−2.11803	−	3.66854i	−2.11803	−	3.66854i
$517$		0			0
$518$		0			0
$519$	2.61803			2.61803
$520$		0			0
$521$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$521$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$522$		0			0
$523$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$523$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$524$	3.23607			3.23607
$525$		0			0
$526$	−3.23607			−3.23607
$527$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$528$		0			0
$529$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$530$	0.309017	+	0.535233i	0.309017	+	0.535233i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.309017	−	0.535233i	0.309017	−	0.535233i
$537$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$538$	−3.23607			−3.23607
$539$		0			0
$540$	−1.00000			−1.00000
$541$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$541$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$542$		0			0
$543$	1.61803	−	2.80252i	1.61803	−	2.80252i
$544$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$545$		0			0
$546$		0			0
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$	1.30902	+	2.26728i	1.30902	+	2.26728i
$549$	1.30902	−	2.26728i	1.30902	−	2.26728i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$557$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$557$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$558$	0.809017	+	1.40126i	0.809017	+	1.40126i
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.500000	+	0.866025i	0.500000	+	0.866025i
$563$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$563$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$564$		0			0
$565$		0			0
$566$	−1.00000			−1.00000
$567$		0			0
$568$		0			0
$569$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$569$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$570$		0			0
$571$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$571$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$	−1.00000			−1.00000
$574$		0			0
$575$		0			0
$576$	1.30902	+	2.26728i	1.30902	+	2.26728i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	0.809017	−	1.40126i	0.809017	−	1.40126i
$579$		0			0
$580$		0			0
$581$		0			0
$582$	1.61803			1.61803
$583$		0			0
$584$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$585$		0			0
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$593$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$594$		0			0
$595$		0			0
$596$	−2.61803			−2.61803
$597$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$598$		0			0
$599$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$599$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$600$	0.500000	+	0.866025i	0.500000	+	0.866025i
$601$	2.00000			2.00000			1.00000			$0$
$601$	2.00000			2.00000			1.00000			$0$
$602$		0			0
$603$	1.00000			1.00000
$604$	1.30902	+	2.26728i	1.30902	+	2.26728i
$605$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$606$		0			0
$607$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$607$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$608$		0			0
$609$		0			0
$610$	1.61803			1.61803
$611$		0			0
$612$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$613$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$613$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$614$		0			0
$615$	1.61803			1.61803
$616$		0			0
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$		0			0
$619$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$619$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$620$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$621$		0			0
$622$	−1.00000			−1.00000
$623$		0			0
$624$		0			0
$625$		0			0
$626$	0.500000	−	0.866025i	0.500000	−	0.866025i
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$631$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.190983	−	0.330792i	−0.190983	−	0.330792i
$636$	−1.61803			−1.61803
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$641$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$641$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$642$		0			0
$643$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$643$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$644$		0			0
$645$	1.61803			1.61803
$646$		0			0
$647$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$647$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$		0			0
$655$	−0.618034	+	1.07047i	−0.618034	+	1.07047i
$656$		0			0
$657$	−2.61803			−2.61803
$658$		0			0
$659$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$659$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$660$		0			0
$661$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$661$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$662$	0.500000	−	0.866025i	0.500000	−	0.866025i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	1.30902	−	2.26728i	1.30902	−	2.26728i
$669$		0			0
$670$	0.309017	+	0.535233i	0.309017	+	0.535233i
$671$		0			0
$672$		0			0
$673$		0			0		1.00000			$0$
$673$		0			0		−1.00000			$\pi$
$674$		0			0
$675$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$676$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$677$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$677$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$678$		0			0
$679$		0			0
$680$	−0.618034			−0.618034
$681$	0.500000	+	0.866025i	0.500000	+	0.866025i
$682$		0			0
$683$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$683$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$684$		0			0
$685$	−1.00000			−1.00000
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$691$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$692$	−2.61803			−2.61803
$693$		0			0
$694$		0			0
$695$	−0.190983	−	0.330792i	−0.190983	−	0.330792i
$696$		0			0
$697$	0.809017	−	1.40126i	0.809017	−	1.40126i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	2.00000			2.00000			1.00000			$0$
$701$	2.00000			2.00000			1.00000			$0$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		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
$716$	1.30902	+	2.26728i	1.30902	+	2.26728i
$717$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$718$	0.500000	−	0.866025i	0.500000	−	0.866025i
$719$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$719$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$720$		0			0
$721$		0			0
$722$	−1.61803			−1.61803
$723$	0.500000	+	0.866025i	0.500000	+	0.866025i
$724$	−1.61803	+	2.80252i	−1.61803	+	2.80252i
$725$		0			0
$726$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	−1.61803			−1.61803
$730$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$731$	0.809017	−	1.40126i	0.809017	−	1.40126i
$732$	−2.11803	+	3.66854i	−2.11803	+	3.66854i
$733$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$733$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$734$	2.61803			2.61803
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−2.11803	+	3.66854i	−2.11803	+	3.66854i
$739$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$739$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		1.00000			$0$
$743$		0			0		−1.00000			$\pi$
$744$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$745$	0.500000	−	0.866025i	0.500000	−	0.866025i
$746$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	−2.61803			−2.61803
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−1.00000			−1.00000
$756$		0			0
$757$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$757$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$761$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$762$	1.61803			1.61803
$763$		0			0
$764$	1.00000			1.00000
$765$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$766$		0			0
$767$		0			0
$768$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$773$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$774$	−2.11803	+	3.66854i	−2.11803	+	3.66854i
$775$	0.190983	+	0.330792i	0.190983	+	0.330792i
$776$	−0.618034			−0.618034
$777$		0			0
$778$	−1.00000			−1.00000
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$	−2.61803	−	4.53457i	−2.61803	−	4.53457i
$787$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$787$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$788$		0			0
$789$	1.61803	+	2.80252i	1.61803	+	2.80252i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	0.500000	−	0.866025i	0.500000	−	0.866025i
$795$	0.309017	−	0.535233i	0.309017	−	0.535233i
$796$	1.30902	+	2.26728i	1.30902	+	2.26728i
$797$		0			0		1.00000			$0$
$797$		0			0		−1.00000			$\pi$
$798$		0			0
$799$		0			0
$800$	0.309017	+	0.535233i	0.309017	+	0.535233i
$801$		0			0
$802$		0			0
$803$		0			0
$804$	−1.61803			−1.61803
$805$		0			0
$806$		0			0
$807$	1.61803	+	2.80252i	1.61803	+	2.80252i
$808$		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
$811$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$811$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	−1.61803			−1.61803
$821$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$821$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$822$	2.11803	−	3.66854i	2.11803	−	3.66854i
$823$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$823$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$		0			0
$829$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$829$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$	1.61803			1.61803
$835$	0.500000	+	0.866025i	0.500000	+	0.866025i
$836$		0			0
$837$	0.309017	−	0.535233i	0.309017	−	0.535233i
$838$	0.500000	+	0.866025i	0.500000	+	0.866025i
$839$	2.00000			2.00000			1.00000			$0$
$839$	2.00000			2.00000			1.00000			$0$
$840$		0			0
$841$	1.00000			1.00000
$842$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$843$	0.500000	−	0.866025i	0.500000	−	0.866025i
$844$		0			0
$845$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.500000	+	0.866025i	0.500000	+	0.866025i
$850$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$851$		0			0
$852$		0			0
$853$	2.00000			2.00000			1.00000			$0$
$853$	2.00000			2.00000			1.00000			$0$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$857$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$858$		0			0
$859$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$859$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$860$	−1.61803			−1.61803
$861$		0			0
$862$		0			0
$863$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$863$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$864$	0.500000	−	0.866025i	0.500000	−	0.866025i
$865$	0.500000	−	0.866025i	0.500000	−	0.866025i
$866$		0			0
$867$	−1.61803			−1.61803
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$874$		0			0
$875$		0			0
$876$	4.23607			4.23607
$877$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$877$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$878$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$879$		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	$0.400000\pi$
$882$		0			0
$883$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$883$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$884$		0			0
$885$		0			0
$886$	1.61803	−	2.80252i	1.61803	−	2.80252i
$887$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$887$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$	2.11803	+	3.66854i	2.11803	+	3.66854i
$895$	−1.00000			−1.00000
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.809017	−	1.40126i	0.809017	−	1.40126i
$901$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.618034	−	1.07047i	−0.618034	−	1.07047i
$906$	2.11803	−	3.66854i	2.11803	−	3.66854i
$907$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$907$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$908$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$909$		0			0
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$	0.500000	−	0.866025i	0.500000	−	0.866025i
$915$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$916$		0			0
$917$		0			0
$918$	1.61803			1.61803
$919$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$919$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$927$		0			0
$928$		0			0
$929$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$929$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$930$	1.00000			1.00000
$931$		0			0
$932$		0			0
$933$	0.500000	+	0.866025i	0.500000	+	0.866025i
$934$		0			0
$935$		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
$941$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$941$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$947$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$953$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$954$	0.809017	+	1.40126i	0.809017	+	1.40126i
$955$	−0.190983	+	0.330792i	−0.190983	+	0.330792i
$956$	1.30902	−	2.26728i	1.30902	−	2.26728i
$957$		0			0
$958$	2.61803			2.61803
$959$		0			0
$960$	1.61803			1.61803
$961$	0.309017	+	0.535233i	0.309017	+	0.535233i
$962$		0			0
$963$		0			0
$964$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$965$		0			0
$966$		0			0
$967$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$967$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$968$	0.500000	+	0.866025i	0.500000	+	0.866025i
$969$		0			0
$970$	0.309017	−	0.535233i	0.309017	−	0.535233i
$971$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$971$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$972$	1.61803			1.61803
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$977$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	0.500000	+	0.866025i	0.500000	+	0.866025i
$983$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$983$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$984$	1.30902	−	2.26728i	1.30902	−	2.26728i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$991$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$992$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$993$	−1.00000			−1.00000
$994$		0			0
$995$	−1.00000			−1.00000
$996$		0			0
$997$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$997$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.1.h.b.815.2		4
7.2	even	3	inner	833.1.h.b.509.2		4
7.3	odd	6		119.1.d.b.118.1	yes	2
7.4	even	3		119.1.d.a.118.1	✓	2
7.5	odd	6		833.1.h.a.509.2		4
7.6	odd	2		833.1.h.a.815.2		4
17.16	even	2		833.1.h.a.815.2		4
21.11	odd	6		1071.1.h.b.118.2		2
21.17	even	6		1071.1.h.a.118.2		2
28.3	even	6		1904.1.n.a.1665.1		2
28.11	odd	6		1904.1.n.b.1665.2		2
35.3	even	12		2975.1.b.a.2974.4		4
35.4	even	6		2975.1.h.d.951.2		2
35.17	even	12		2975.1.b.a.2974.1		4
35.18	odd	12		2975.1.b.b.2974.4		4
35.24	odd	6		2975.1.h.c.951.2		2
35.32	odd	12		2975.1.b.b.2974.1		4
119.3	even	48		2023.1.l.b.1266.2		16
119.4	even	12		2023.1.c.e.1735.4		4
119.10	even	48		2023.1.l.b.1889.4		16
119.11	odd	48		2023.1.l.b.1868.2		16
119.16	even	6		833.1.h.a.509.2		4
119.24	even	48		2023.1.l.b.1889.3		16
119.25	even	24		2023.1.f.b.1483.4		8
119.31	even	48		2023.1.l.b.1266.1		16
119.32	even	24		2023.1.f.b.251.2		8
119.33	odd	6	inner	833.1.h.b.509.2		4
119.38	odd	12		2023.1.c.e.1735.3		4
119.39	odd	48		2023.1.l.b.468.4		16
119.45	even	48		2023.1.l.b.1868.1		16
119.46	odd	48		2023.1.l.b.468.3		16
119.53	even	24		2023.1.f.b.251.1		8
119.59	odd	24		2023.1.f.b.1483.3		8
119.60	even	24		2023.1.f.b.1483.3		8
119.66	odd	24		2023.1.f.b.251.1		8
119.67	even	6		119.1.d.b.118.1	yes	2
119.73	even	48		2023.1.l.b.468.3		16
119.74	odd	48		2023.1.l.b.1868.1		16
119.80	even	48		2023.1.l.b.468.4		16
119.81	even	12		2023.1.c.e.1735.3		4
119.87	odd	24		2023.1.f.b.251.2		8
119.88	odd	48		2023.1.l.b.1266.1		16
119.94	odd	24		2023.1.f.b.1483.4		8
119.95	odd	48		2023.1.l.b.1889.3		16
119.101	odd	6		119.1.d.a.118.1	✓	2
119.108	even	48		2023.1.l.b.1868.2		16
119.109	odd	48		2023.1.l.b.1889.4		16
119.115	odd	12		2023.1.c.e.1735.4		4
119.116	odd	48		2023.1.l.b.1266.2		16
119.118	odd	2	CM	833.1.h.b.815.2		4
357.101	even	6		1071.1.h.b.118.2		2
357.305	odd	6		1071.1.h.a.118.2		2
476.67	odd	6		1904.1.n.a.1665.1		2
476.339	even	6		1904.1.n.b.1665.2		2
595.67	odd	12		2975.1.b.a.2974.1		4
595.339	odd	6		2975.1.h.d.951.2		2
595.424	even	6		2975.1.h.c.951.2		2
595.458	even	12		2975.1.b.b.2974.4		4
595.543	odd	12		2975.1.b.a.2974.4		4
595.577	even	12		2975.1.b.b.2974.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.1.d.a.118.1	✓	2	7.4	even	3
119.1.d.a.118.1	✓	2	119.101	odd	6
119.1.d.b.118.1	yes	2	7.3	odd	6
119.1.d.b.118.1	yes	2	119.67	even	6
833.1.h.a.509.2		4	7.5	odd	6
833.1.h.a.509.2		4	119.16	even	6
833.1.h.a.815.2		4	7.6	odd	2
833.1.h.a.815.2		4	17.16	even	2
833.1.h.b.509.2		4	7.2	even	3	inner
833.1.h.b.509.2		4	119.33	odd	6	inner
833.1.h.b.815.2		4	1.1	even	1	trivial
833.1.h.b.815.2		4	119.118	odd	2	CM
1071.1.h.a.118.2		2	21.17	even	6
1071.1.h.a.118.2		2	357.305	odd	6
1071.1.h.b.118.2		2	21.11	odd	6
1071.1.h.b.118.2		2	357.101	even	6
1904.1.n.a.1665.1		2	28.3	even	6
1904.1.n.a.1665.1		2	476.67	odd	6
1904.1.n.b.1665.2		2	28.11	odd	6
1904.1.n.b.1665.2		2	476.339	even	6
2023.1.c.e.1735.3		4	119.38	odd	12
2023.1.c.e.1735.3		4	119.81	even	12
2023.1.c.e.1735.4		4	119.4	even	12
2023.1.c.e.1735.4		4	119.115	odd	12
2023.1.f.b.251.1		8	119.53	even	24
2023.1.f.b.251.1		8	119.66	odd	24
2023.1.f.b.251.2		8	119.32	even	24
2023.1.f.b.251.2		8	119.87	odd	24
2023.1.f.b.1483.3		8	119.59	odd	24
2023.1.f.b.1483.3		8	119.60	even	24
2023.1.f.b.1483.4		8	119.25	even	24
2023.1.f.b.1483.4		8	119.94	odd	24
2023.1.l.b.468.3		16	119.46	odd	48
2023.1.l.b.468.3		16	119.73	even	48
2023.1.l.b.468.4		16	119.39	odd	48
2023.1.l.b.468.4		16	119.80	even	48
2023.1.l.b.1266.1		16	119.31	even	48
2023.1.l.b.1266.1		16	119.88	odd	48
2023.1.l.b.1266.2		16	119.3	even	48
2023.1.l.b.1266.2		16	119.116	odd	48
2023.1.l.b.1868.1		16	119.45	even	48
2023.1.l.b.1868.1		16	119.74	odd	48
2023.1.l.b.1868.2		16	119.11	odd	48
2023.1.l.b.1868.2		16	119.108	even	48
2023.1.l.b.1889.3		16	119.24	even	48
2023.1.l.b.1889.3		16	119.95	odd	48
2023.1.l.b.1889.4		16	119.10	even	48
2023.1.l.b.1889.4		16	119.109	odd	48
2975.1.b.a.2974.1		4	35.17	even	12
2975.1.b.a.2974.1		4	595.67	odd	12
2975.1.b.a.2974.4		4	35.3	even	12
2975.1.b.a.2974.4		4	595.543	odd	12
2975.1.b.b.2974.1		4	35.32	odd	12
2975.1.b.b.2974.1		4	595.577	even	12
2975.1.b.b.2974.4		4	35.18	odd	12
2975.1.b.b.2974.4		4	595.458	even	12
2975.1.h.c.951.2		2	35.24	odd	6
2975.1.h.c.951.2		2	595.424	even	6
2975.1.h.d.951.2		2	35.4	even	6
2975.1.h.d.951.2		2	595.339	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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	833.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 1.40126i) q^{2} +(0.809017 - 1.40126i) q^{3} +(-0.809017 + 1.40126i) q^{4} +(-0.309017 - 0.535233i) q^{5} +2.61803 q^{6} -1.00000 q^{8} +(-0.809017 - 1.40126i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 1.40126i) q^{2} +(0.809017 - 1.40126i) q^{3} +(-0.809017 + 1.40126i) q^{4} +(-0.309017 - 0.535233i) q^{5} +2.61803 q^{6} -1.00000 q^{8} +(-0.809017 - 1.40126i) q^{9} +(0.500000 - 0.866025i) q^{10} +(1.30902 + 2.26728i) q^{12} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{17} +(1.30902 - 2.26728i) q^{18} +1.00000 q^{20} +(-0.809017 + 1.40126i) q^{24} +(0.309017 - 0.535233i) q^{25} -1.00000 q^{27} +(-0.809017 - 1.40126i) q^{30} +(-0.309017 + 0.535233i) q^{31} +(-0.500000 + 0.866025i) q^{32} -1.61803 q^{34} +2.61803 q^{36} +(0.309017 + 0.535233i) q^{40} -1.61803 q^{41} -1.61803 q^{43} +(-0.500000 + 0.866025i) q^{45} +1.00000 q^{50} +(0.809017 + 1.40126i) q^{51} +(-0.309017 + 0.535233i) q^{53} +(-0.809017 - 1.40126i) q^{54} +(0.809017 - 1.40126i) q^{60} +(0.809017 + 1.40126i) q^{61} -1.00000 q^{62} -1.61803 q^{64} +(-0.309017 + 0.535233i) q^{67} +(-0.809017 - 1.40126i) q^{68} +(0.809017 + 1.40126i) q^{72} +(0.809017 - 1.40126i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(-1.30902 - 2.26728i) q^{82} +0.618034 q^{85} +(-1.30902 - 2.26728i) q^{86} -1.61803 q^{90} +(0.500000 + 0.866025i) q^{93} +(0.809017 + 1.40126i) q^{96} +0.618034 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} - 4 q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 + q^3 - q^4 + q^5 + 6 * q^6 - 4 * q^8 - q^9	\( 4 q + q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} - 4 q^{8} - q^{9} + 2 q^{10} + 3 q^{12} - 4 q^{15} - 2 q^{17} + 3 q^{18} + 4 q^{20} - q^{24} - q^{25} - 4 q^{27} - q^{30} + q^{31} - 2 q^{32} - 2 q^{34} + 6 q^{36} - q^{40} - 2 q^{41} - 2 q^{43} - 2 q^{45} + 4 q^{50} + q^{51} + q^{53} - q^{54} + q^{60} + q^{61} - 4 q^{62} - 2 q^{64} + q^{67} - q^{68} + q^{72} + q^{73} - 2 q^{75} - 3 q^{82} - 2 q^{85} - 3 q^{86} - 2 q^{90} + 2 q^{93} + q^{96} - 2 q^{97}+O(q^{100}) \) 4 * q + q^2 + q^3 - q^4 + q^5 + 6 * q^6 - 4 * q^8 - q^9 + 2 * q^10 + 3 * q^12 - 4 * q^15 - 2 * q^17 + 3 * q^18 + 4 * q^20 - q^24 - q^25 - 4 * q^27 - q^30 + q^31 - 2 * q^32 - 2 * q^34 + 6 * q^36 - q^40 - 2 * q^41 - 2 * q^43 - 2 * q^45 + 4 * q^50 + q^51 + q^53 - q^54 + q^60 + q^61 - 4 * q^62 - 2 * q^64 + q^67 - q^68 + q^72 + q^73 - 2 * q^75 - 3 * q^82 - 2 * q^85 - 3 * q^86 - 2 * q^90 + 2 * q^93 + q^96 - 2 * q^97

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