Dirichlet character χ637(543,⋅)\chi_{637}(543,\cdot)

• Label: 637.543
• Modulus: $637$
• Conductor: $637$
• Order: $42$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$637$
Conductor:	$637$
Order:	$42$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 637.bp

$\chi_{637}(88,\cdot)$ $\chi_{637}(121,\cdot)$ $\chi_{637}(179,\cdot)$ $\chi_{637}(212,\cdot)$ $\chi_{637}(270,\cdot)$ $\chi_{637}(303,\cdot)$ $\chi_{637}(394,\cdot)$ $\chi_{637}(452,\cdot)$ $\chi_{637}(485,\cdot)$ $\chi_{637}(543,\cdot)$ $\chi_{637}(576,\cdot)$ $\chi_{637}(634,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{21})$
Fixed field:	42.42.16423600478713504434070778628293678810006717122913176085381268066336462525553883868883157384200587461557.2

Values on generators

$(248,197)$ → $(e\left(\frac{5}{21}\right),e\left(\frac{5}{6}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{ 637 }(543, a)$	$1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{21}\right)$

Gauss sum

Jacobi sum

Kloosterman sum