Dirichlet character χ637(418,⋅)\chi_{637}(418,\cdot)

• Label: 637.418
• Modulus: $637$
• Conductor: $637$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$637$
Conductor:	$637$
Order:	$84$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 637.cd

$\chi_{637}(45,\cdot)$ $\chi_{637}(54,\cdot)$ $\chi_{637}(59,\cdot)$ $\chi_{637}(89,\cdot)$ $\chi_{637}(136,\cdot)$ $\chi_{637}(145,\cdot)$ $\chi_{637}(150,\cdot)$ $\chi_{637}(180,\cdot)$ $\chi_{637}(236,\cdot)$ $\chi_{637}(241,\cdot)$ $\chi_{637}(271,\cdot)$ $\chi_{637}(318,\cdot)$ $\chi_{637}(327,\cdot)$ $\chi_{637}(332,\cdot)$ $\chi_{637}(409,\cdot)$ $\chi_{637}(418,\cdot)$ $\chi_{637}(453,\cdot)$ $\chi_{637}(500,\cdot)$ $\chi_{637}(514,\cdot)$ $\chi_{637}(544,\cdot)$ $\chi_{637}(591,\cdot)$ $\chi_{637}(600,\cdot)$ $\chi_{637}(605,\cdot)$ $\chi_{637}(635,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Values on generators

$(248,197)$ → $(e\left(\frac{17}{42}\right),e\left(\frac{1}{12}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{ 637 }(418, a)$	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{20}{21}\right)$

Gauss sum

Jacobi sum

Kloosterman sum