Dirichlet character χ4760(29,⋅)\chi_{4760}(29,\cdot)

• Label: 4760.29
• Modulus: $4760$
• Conductor: $680$
• Order: $16$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$4760$
Conductor:	$680$
Order:	$16$
Real:	no
Primitive:	no, induced from $\chi_{680}(29,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 4760.ia

$\chi_{4760}(29,\cdot)$ $\chi_{4760}(309,\cdot)$ $\chi_{4760}(589,\cdot)$ $\chi_{4760}(1149,\cdot)$ $\chi_{4760}(2829,\cdot)$ $\chi_{4760}(3389,\cdot)$ $\chi_{4760}(3669,\cdot)$ $\chi_{4760}(3949,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{16})$
Fixed field:	16.0.18759175710374728781004800000000.1

Values on generators

$(1191,2381,2857,1361,3641)$ → $(1,-1,-1,1,e\left(\frac{13}{16}\right))$

First values

$a$	$-1$	$1$	$3$	$9$	$11$	$13$	$19$	$23$	$27$	$29$	$31$	$33$
$\chi_{ 4760 }(29, a)$	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{16}\right)$	$1$