Dirichlet character χ153(145,⋅)\chi_{153}(145,\cdot)

• Label: 153.145
• Modulus: $153$
• Conductor: $17$
• Order: $8$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$153$
Conductor:	$17$
Order:	$8$
Real:	no
Primitive:	no, induced from $\chi_{17}(9,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 153.l

$\chi_{153}(19,\cdot)$ $\chi_{153}(100,\cdot)$ $\chi_{153}(127,\cdot)$ $\chi_{153}(145,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{8})$
Fixed field:	$\Q(\zeta_{17})^+$

Values on generators

$(137,37)$ → $(1,e\left(\frac{1}{8}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{ 153 }(145, a)$	$1$	$1$	$-i$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$1$

Gauss sum

Jacobi sum

Kloosterman sum