Dirichlet character χ967(513,⋅)\chi_{967}(513,\cdot)

• Label: 967.513
• Modulus: $967$
• Conductor: $967$
• Order: $69$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$967$
Conductor:	$967$
Order:	$69$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 967.k

$\chi_{967}(15,\cdot)$ $\chi_{967}(39,\cdot)$ $\chi_{967}(53,\cdot)$ $\chi_{967}(61,\cdot)$ $\chi_{967}(68,\cdot)$ $\chi_{967}(73,\cdot)$ $\chi_{967}(113,\cdot)$ $\chi_{967}(124,\cdot)$ $\chi_{967}(128,\cdot)$ $\chi_{967}(129,\cdot)$ $\chi_{967}(145,\cdot)$ $\chi_{967}(190,\cdot)$ $\chi_{967}(198,\cdot)$ $\chi_{967}(202,\cdot)$ $\chi_{967}(225,\cdot)$ $\chi_{967}(241,\cdot)$ $\chi_{967}(280,\cdot)$ $\chi_{967}(321,\cdot)$ $\chi_{967}(335,\cdot)$ $\chi_{967}(341,\cdot)$ $\chi_{967}(352,\cdot)$ $\chi_{967}(377,\cdot)$ $\chi_{967}(400,\cdot)$ $\chi_{967}(421,\cdot)$ $\chi_{967}(445,\cdot)$ $\chi_{967}(494,\cdot)$ $\chi_{967}(513,\cdot)$ $\chi_{967}(524,\cdot)$ $\chi_{967}(539,\cdot)$ $\chi_{967}(554,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{69})$
Fixed field:	Number field defined by a degree 69 polynomial

Values on generators

$5$ → $e\left(\frac{25}{69}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 967 }(513, a)$	$1$	$1$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{17}{23}\right)$

Gauss sum

Jacobi sum

Kloosterman sum