Dirichlet character χ931(37,⋅)\chi_{931}(37,\cdot)

• Label: 931.37
• Modulus: $931$
• Conductor: $931$
• Order: $42$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$931$
Conductor:	$931$
Order:	$42$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 931.bq

$\chi_{931}(37,\cdot)$ $\chi_{931}(151,\cdot)$ $\chi_{931}(170,\cdot)$ $\chi_{931}(284,\cdot)$ $\chi_{931}(303,\cdot)$ $\chi_{931}(417,\cdot)$ $\chi_{931}(436,\cdot)$ $\chi_{931}(550,\cdot)$ $\chi_{931}(683,\cdot)$ $\chi_{931}(702,\cdot)$ $\chi_{931}(816,\cdot)$ $\chi_{931}(835,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{21})$
Fixed field:	Number field defined by a degree 42 polynomial

Values on generators

$(248,344)$ → $(e\left(\frac{16}{21}\right),-1)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{ 931 }(37, a)$	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{37}{42}\right)$

Gauss sum

Jacobi sum

Kloosterman sum