Dirichlet character \(\chi_{1576}(53,\cdot)\)

• Label: 1576.53
• Modulus: $1576$
• Conductor: $1576$
• Order: $98$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1576\)
Conductor:	\(1576\)
Order:	\(98\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1576.bf

\(\chi_{1576}(29,\cdot)\) \(\chi_{1576}(37,\cdot)\) \(\chi_{1576}(53,\cdot)\) \(\chi_{1576}(61,\cdot)\) \(\chi_{1576}(85,\cdot)\) \(\chi_{1576}(101,\cdot)\) \(\chi_{1576}(133,\cdot)\) \(\chi_{1576}(213,\cdot)\) \(\chi_{1576}(221,\cdot)\) \(\chi_{1576}(237,\cdot)\) \(\chi_{1576}(285,\cdot)\) \(\chi_{1576}(445,\cdot)\) \(\chi_{1576}(453,\cdot)\) \(\chi_{1576}(565,\cdot)\) \(\chi_{1576}(581,\cdot)\) \(\chi_{1576}(645,\cdot)\) \(\chi_{1576}(661,\cdot)\) \(\chi_{1576}(733,\cdot)\) \(\chi_{1576}(741,\cdot)\) \(\chi_{1576}(749,\cdot)\) \(\chi_{1576}(773,\cdot)\) \(\chi_{1576}(781,\cdot)\) \(\chi_{1576}(837,\cdot)\) \(\chi_{1576}(869,\cdot)\) \(\chi_{1576}(893,\cdot)\) \(\chi_{1576}(981,\cdot)\) \(\chi_{1576}(1013,\cdot)\) \(\chi_{1576}(1045,\cdot)\) \(\chi_{1576}(1061,\cdot)\) \(\chi_{1576}(1085,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{49})$
Fixed field:	Number field defined by a degree 98 polynomial

Values on generators

\((1183,789,593)\) → \((1,-1,e\left(\frac{18}{49}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 1576 }(53, a) \)	\(1\)	\(1\)	\(e\left(\frac{97}{98}\right)\)	\(e\left(\frac{19}{98}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{15}{98}\right)\)	\(e\left(\frac{67}{98}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{61}{98}\right)\)