Dirichlet character \(\chi_{1576}(1541,\cdot)\)

• Label: 1576.1541
• Modulus: $1576$
• Conductor: $1576$
• Order: $196$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1576\)
Conductor:	\(1576\)
Order:	\(196\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1576.bg

\(\chi_{1576}(5,\cdot)\) \(\chi_{1576}(13,\cdot)\) \(\chi_{1576}(21,\cdot)\) \(\chi_{1576}(45,\cdot)\) \(\chi_{1576}(117,\cdot)\) \(\chi_{1576}(125,\cdot)\) \(\chi_{1576}(141,\cdot)\) \(\chi_{1576}(149,\cdot)\) \(\chi_{1576}(165,\cdot)\) \(\chi_{1576}(189,\cdot)\) \(\chi_{1576}(205,\cdot)\) \(\chi_{1576}(229,\cdot)\) \(\chi_{1576}(245,\cdot)\) \(\chi_{1576}(253,\cdot)\) \(\chi_{1576}(269,\cdot)\) \(\chi_{1576}(277,\cdot)\) \(\chi_{1576}(349,\cdot)\) \(\chi_{1576}(373,\cdot)\) \(\chi_{1576}(381,\cdot)\) \(\chi_{1576}(389,\cdot)\) \(\chi_{1576}(397,\cdot)\) \(\chi_{1576}(405,\cdot)\) \(\chi_{1576}(421,\cdot)\) \(\chi_{1576}(429,\cdot)\) \(\chi_{1576}(461,\cdot)\) \(\chi_{1576}(469,\cdot)\) \(\chi_{1576}(485,\cdot)\) \(\chi_{1576}(493,\cdot)\) \(\chi_{1576}(509,\cdot)\) \(\chi_{1576}(517,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{196})$
Fixed field:	Number field defined by a degree 196 polynomial (not computed)

Values on generators

\((1183,789,593)\) → \((1,-1,e\left(\frac{137}{196}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 1576 }(1541, a) \)	\(-1\)	\(1\)	\(e\left(\frac{3}{196}\right)\)	\(e\left(\frac{139}{196}\right)\)	\(e\left(\frac{5}{98}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{151}{196}\right)\)	\(e\left(\frac{191}{196}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{27}{196}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{196}\right)\)