Dirichlet character \(\chi_{1576}(35,\cdot)\)

• Label: 1576.35
• Modulus: $1576$
• Conductor: $1576$
• Order: $196$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

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

Galois orbit 1576.bi

\(\chi_{1576}(3,\cdot)\) \(\chi_{1576}(11,\cdot)\) \(\chi_{1576}(27,\cdot)\) \(\chi_{1576}(35,\cdot)\) \(\chi_{1576}(67,\cdot)\) \(\chi_{1576}(75,\cdot)\) \(\chi_{1576}(91,\cdot)\) \(\chi_{1576}(99,\cdot)\) \(\chi_{1576}(115,\cdot)\) \(\chi_{1576}(123,\cdot)\) \(\chi_{1576}(131,\cdot)\) \(\chi_{1576}(139,\cdot)\) \(\chi_{1576}(147,\cdot)\) \(\chi_{1576}(179,\cdot)\) \(\chi_{1576}(195,\cdot)\) \(\chi_{1576}(227,\cdot)\) \(\chi_{1576}(235,\cdot)\) \(\chi_{1576}(243,\cdot)\) \(\chi_{1576}(275,\cdot)\) \(\chi_{1576}(283,\cdot)\) \(\chi_{1576}(291,\cdot)\) \(\chi_{1576}(299,\cdot)\) \(\chi_{1576}(315,\cdot)\) \(\chi_{1576}(323,\cdot)\) \(\chi_{1576}(363,\cdot)\) \(\chi_{1576}(411,\cdot)\) \(\chi_{1576}(451,\cdot)\) \(\chi_{1576}(467,\cdot)\) \(\chi_{1576}(483,\cdot)\) \(\chi_{1576}(539,\cdot)\) ...

Related number fields

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

Values on generators

\((1183,789,593)\) → \((-1,-1,e\left(\frac{39}{196}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 1576 }(35, a) \)	\(1\)	\(1\)	\(e\left(\frac{3}{196}\right)\)	\(e\left(\frac{41}{196}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{151}{196}\right)\)	\(e\left(\frac{93}{196}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{125}{196}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{111}{196}\right)\)