Dirichlet character χ107(3,⋅)\chi_{107}(3,\cdot)

• Label: 107.3
• Modulus: $107$
• Conductor: $107$
• Order: $53$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$107$
Conductor:	$107$
Order:	$53$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 107.c

$\chi_{107}(3,\cdot)$ $\chi_{107}(4,\cdot)$ $\chi_{107}(9,\cdot)$ $\chi_{107}(10,\cdot)$ $\chi_{107}(11,\cdot)$ $\chi_{107}(12,\cdot)$ $\chi_{107}(13,\cdot)$ $\chi_{107}(14,\cdot)$ $\chi_{107}(16,\cdot)$ $\chi_{107}(19,\cdot)$ $\chi_{107}(23,\cdot)$ $\chi_{107}(25,\cdot)$ $\chi_{107}(27,\cdot)$ $\chi_{107}(29,\cdot)$ $\chi_{107}(30,\cdot)$ $\chi_{107}(33,\cdot)$ $\chi_{107}(34,\cdot)$ $\chi_{107}(35,\cdot)$ $\chi_{107}(36,\cdot)$ $\chi_{107}(37,\cdot)$ $\chi_{107}(39,\cdot)$ $\chi_{107}(40,\cdot)$ $\chi_{107}(41,\cdot)$ $\chi_{107}(42,\cdot)$ $\chi_{107}(44,\cdot)$ $\chi_{107}(47,\cdot)$ $\chi_{107}(48,\cdot)$ $\chi_{107}(49,\cdot)$ $\chi_{107}(52,\cdot)$ $\chi_{107}(53,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{53})$
Fixed field:	Number field defined by a degree 53 polynomial

Values on generators

$2$ → $e\left(\frac{35}{53}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 107 }(3, a)$	$1$	$1$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{28}{53}\right)$

Gauss sum

Jacobi sum

Kloosterman sum