Dirichlet character χ760(507,⋅)\chi_{760}(507,\cdot)

• Label: 760.507
• Modulus: $760$
• Conductor: $760$
• Order: $36$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$760$
Conductor:	$760$
Order:	$36$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 760.cn

$\chi_{760}(3,\cdot)$ $\chi_{760}(67,\cdot)$ $\chi_{760}(147,\cdot)$ $\chi_{760}(203,\cdot)$ $\chi_{760}(243,\cdot)$ $\chi_{760}(307,\cdot)$ $\chi_{760}(363,\cdot)$ $\chi_{760}(507,\cdot)$ $\chi_{760}(523,\cdot)$ $\chi_{760}(547,\cdot)$ $\chi_{760}(603,\cdot)$ $\chi_{760}(667,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{36})$
Fixed field:	36.0.4031181156993454136731178943694064571490658196389888000000000000000000000000000.1

Values on generators

$(191,381,457,401)$ → $(-1,-1,i,e\left(\frac{5}{18}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 760 }(507, a)$	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{18}\right)$

Gauss sum

Jacobi sum

Kloosterman sum