Dirichlet character \(\chi_{2312}(53,\cdot)\)

• Label: 2312.53
• Modulus: $2312$
• Conductor: $2312$
• Order: $136$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2312\)
Conductor:	\(2312\)
Order:	\(136\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2312.bh

\(\chi_{2312}(53,\cdot)\) \(\chi_{2312}(77,\cdot)\) \(\chi_{2312}(93,\cdot)\) \(\chi_{2312}(117,\cdot)\) \(\chi_{2312}(189,\cdot)\) \(\chi_{2312}(213,\cdot)\) \(\chi_{2312}(229,\cdot)\) \(\chi_{2312}(253,\cdot)\) \(\chi_{2312}(325,\cdot)\) \(\chi_{2312}(349,\cdot)\) \(\chi_{2312}(365,\cdot)\) \(\chi_{2312}(389,\cdot)\) \(\chi_{2312}(461,\cdot)\) \(\chi_{2312}(485,\cdot)\) \(\chi_{2312}(501,\cdot)\) \(\chi_{2312}(525,\cdot)\) \(\chi_{2312}(597,\cdot)\) \(\chi_{2312}(621,\cdot)\) \(\chi_{2312}(637,\cdot)\) \(\chi_{2312}(661,\cdot)\) \(\chi_{2312}(773,\cdot)\) \(\chi_{2312}(797,\cdot)\) \(\chi_{2312}(869,\cdot)\) \(\chi_{2312}(893,\cdot)\) \(\chi_{2312}(909,\cdot)\) \(\chi_{2312}(933,\cdot)\) \(\chi_{2312}(1005,\cdot)\) \(\chi_{2312}(1029,\cdot)\) \(\chi_{2312}(1045,\cdot)\) \(\chi_{2312}(1069,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{136})$
Fixed field:	Number field defined by a degree 136 polynomial (not computed)

Values on generators

\((1735,1157,1737)\) → \((1,-1,e\left(\frac{103}{136}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(21\)	\(23\)
\( \chi_{ 2312 }(53, a) \)	\(1\)	\(1\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{125}{136}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{121}{136}\right)\)