Dirichlet character χ121(2,⋅)\chi_{121}(2,\cdot)

• Label: 121.2
• Modulus: $121$
• Conductor: $121$
• Order: $110$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$121$
Conductor:	$121$
Order:	$110$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 121.h

$\chi_{121}(2,\cdot)$ $\chi_{121}(6,\cdot)$ $\chi_{121}(7,\cdot)$ $\chi_{121}(8,\cdot)$ $\chi_{121}(13,\cdot)$ $\chi_{121}(17,\cdot)$ $\chi_{121}(18,\cdot)$ $\chi_{121}(19,\cdot)$ $\chi_{121}(24,\cdot)$ $\chi_{121}(28,\cdot)$ $\chi_{121}(29,\cdot)$ $\chi_{121}(30,\cdot)$ $\chi_{121}(35,\cdot)$ $\chi_{121}(39,\cdot)$ $\chi_{121}(41,\cdot)$ $\chi_{121}(46,\cdot)$ $\chi_{121}(50,\cdot)$ $\chi_{121}(51,\cdot)$ $\chi_{121}(52,\cdot)$ $\chi_{121}(57,\cdot)$ $\chi_{121}(61,\cdot)$ $\chi_{121}(62,\cdot)$ $\chi_{121}(63,\cdot)$ $\chi_{121}(68,\cdot)$ $\chi_{121}(72,\cdot)$ $\chi_{121}(73,\cdot)$ $\chi_{121}(74,\cdot)$ $\chi_{121}(79,\cdot)$ $\chi_{121}(83,\cdot)$ $\chi_{121}(84,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{55})$
Fixed field:	Number field defined by a degree 110 polynomial (not computed)

Values on generators

$2$ → $e\left(\frac{1}{110}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{ 121 }(2, a)$	$-1$	$1$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$

Gauss sum

Jacobi sum

Kloosterman sum