Dirichlet character \(\chi_{2312}(11,\cdot)\)

• Label: 2312.11
• Modulus: $2312$
• Conductor: $2312$
• Order: $272$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

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

Galois orbit 2312.bl

\(\chi_{2312}(3,\cdot)\) \(\chi_{2312}(11,\cdot)\) \(\chi_{2312}(27,\cdot)\) \(\chi_{2312}(91,\cdot)\) \(\chi_{2312}(99,\cdot)\) \(\chi_{2312}(107,\cdot)\) \(\chi_{2312}(139,\cdot)\) \(\chi_{2312}(147,\cdot)\) \(\chi_{2312}(163,\cdot)\) \(\chi_{2312}(211,\cdot)\) \(\chi_{2312}(227,\cdot)\) \(\chi_{2312}(235,\cdot)\) \(\chi_{2312}(243,\cdot)\) \(\chi_{2312}(267,\cdot)\) \(\chi_{2312}(275,\cdot)\) \(\chi_{2312}(283,\cdot)\) \(\chi_{2312}(299,\cdot)\) \(\chi_{2312}(347,\cdot)\) \(\chi_{2312}(363,\cdot)\) \(\chi_{2312}(371,\cdot)\) \(\chi_{2312}(379,\cdot)\) \(\chi_{2312}(403,\cdot)\) \(\chi_{2312}(411,\cdot)\) \(\chi_{2312}(419,\cdot)\) \(\chi_{2312}(435,\cdot)\) \(\chi_{2312}(483,\cdot)\) \(\chi_{2312}(499,\cdot)\) \(\chi_{2312}(507,\cdot)\) \(\chi_{2312}(515,\cdot)\) \(\chi_{2312}(539,\cdot)\) ...

Related number fields

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

Values on generators

\((1735,1157,1737)\) → \((-1,-1,e\left(\frac{23}{272}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(21\)	\(23\)
\( \chi_{ 2312 }(11, a) \)	\(1\)	\(1\)	\(e\left(\frac{23}{272}\right)\)	\(e\left(\frac{235}{272}\right)\)	\(e\left(\frac{165}{272}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{257}{272}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{97}{272}\right)\)