Dirichlet character χ4160(1309,⋅)\chi_{4160}(1309,\cdot)

• Label: 4160.1309
• Modulus: $4160$
• Conductor: $4160$
• Order: $48$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4160$
Conductor:	$4160$
Order:	$48$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4160.jp

$\chi_{4160}(29,\cdot)$ $\chi_{4160}(269,\cdot)$ $\chi_{4160}(549,\cdot)$ $\chi_{4160}(789,\cdot)$ $\chi_{4160}(1069,\cdot)$ $\chi_{4160}(1309,\cdot)$ $\chi_{4160}(1589,\cdot)$ $\chi_{4160}(1829,\cdot)$ $\chi_{4160}(2109,\cdot)$ $\chi_{4160}(2349,\cdot)$ $\chi_{4160}(2629,\cdot)$ $\chi_{4160}(2869,\cdot)$ $\chi_{4160}(3149,\cdot)$ $\chi_{4160}(3389,\cdot)$ $\chi_{4160}(3669,\cdot)$ $\chi_{4160}(3909,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{48})$
Fixed field:	Number field defined by a degree 48 polynomial

Values on generators

$(4031,261,2497,1601)$ → $(1,e\left(\frac{11}{16}\right),-1,e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 4160 }(1309, a)$	$1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{48}\right)$