Dirichlet character \(\chi_{2312}(61,\cdot)\)

• Label: 2312.61
• Modulus: $2312$
• Conductor: $2312$
• Order: $272$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(2312\)
Conductor:	\(2312\)
Order:	\(272\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 2312.bn

\(\chi_{2312}(5,\cdot)\) \(\chi_{2312}(29,\cdot)\) \(\chi_{2312}(37,\cdot)\) \(\chi_{2312}(45,\cdot)\) \(\chi_{2312}(61,\cdot)\) \(\chi_{2312}(109,\cdot)\) \(\chi_{2312}(125,\cdot)\) \(\chi_{2312}(133,\cdot)\) \(\chi_{2312}(141,\cdot)\) \(\chi_{2312}(165,\cdot)\) \(\chi_{2312}(173,\cdot)\) \(\chi_{2312}(181,\cdot)\) \(\chi_{2312}(197,\cdot)\) \(\chi_{2312}(245,\cdot)\) \(\chi_{2312}(261,\cdot)\) \(\chi_{2312}(269,\cdot)\) \(\chi_{2312}(277,\cdot)\) \(\chi_{2312}(301,\cdot)\) \(\chi_{2312}(309,\cdot)\) \(\chi_{2312}(317,\cdot)\) \(\chi_{2312}(333,\cdot)\) \(\chi_{2312}(381,\cdot)\) \(\chi_{2312}(397,\cdot)\) \(\chi_{2312}(405,\cdot)\) \(\chi_{2312}(413,\cdot)\) \(\chi_{2312}(437,\cdot)\) \(\chi_{2312}(445,\cdot)\) \(\chi_{2312}(453,\cdot)\) \(\chi_{2312}(469,\cdot)\) \(\chi_{2312}(517,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{272})$
Fixed field:	Number field defined by a degree 272 polynomial (not computed)

Values on generators

\((1735,1157,1737)\) → \((1,-1,e\left(\frac{259}{272}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(21\)	\(23\)
\( \chi_{ 2312 }(61, a) \)	\(-1\)	\(1\)	\(e\left(\frac{123}{272}\right)\)	\(e\left(\frac{151}{272}\right)\)	\(e\left(\frac{161}{272}\right)\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{109}{272}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{1}{136}\right)\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{93}{272}\right)\)