Dirichlet character \(\chi_{1521}(635,\cdot)\)

• Label: 1521.635
• Modulus: $1521$
• Conductor: $1521$
• Order: $156$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1521\)
Conductor:	\(1521\)
Order:	\(156\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1521.cb

\(\chi_{1521}(20,\cdot)\) \(\chi_{1521}(41,\cdot)\) \(\chi_{1521}(50,\cdot)\) \(\chi_{1521}(110,\cdot)\) \(\chi_{1521}(137,\cdot)\) \(\chi_{1521}(158,\cdot)\) \(\chi_{1521}(167,\cdot)\) \(\chi_{1521}(227,\cdot)\) \(\chi_{1521}(254,\cdot)\) \(\chi_{1521}(275,\cdot)\) \(\chi_{1521}(284,\cdot)\) \(\chi_{1521}(344,\cdot)\) \(\chi_{1521}(371,\cdot)\) \(\chi_{1521}(392,\cdot)\) \(\chi_{1521}(401,\cdot)\) \(\chi_{1521}(461,\cdot)\) \(\chi_{1521}(509,\cdot)\) \(\chi_{1521}(518,\cdot)\) \(\chi_{1521}(578,\cdot)\) \(\chi_{1521}(605,\cdot)\) \(\chi_{1521}(626,\cdot)\) \(\chi_{1521}(635,\cdot)\) \(\chi_{1521}(722,\cdot)\) \(\chi_{1521}(743,\cdot)\) \(\chi_{1521}(752,\cdot)\) \(\chi_{1521}(812,\cdot)\) \(\chi_{1521}(839,\cdot)\) \(\chi_{1521}(860,\cdot)\) \(\chi_{1521}(869,\cdot)\) \(\chi_{1521}(929,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{156})$
Fixed field:	Number field defined by a degree 156 polynomial (not computed)

Values on generators

\((677,847)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{7}{156}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 1521 }(635, a) \)	\(1\)	\(1\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)