Dirichlet character \(\chi_{1521}(524,\cdot)\)

• Label: 1521.524
• Modulus: $1521$
• Conductor: $1521$
• Order: $78$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1521\)
Conductor:	\(1521\)
Order:	\(78\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1521.bx

\(\chi_{1521}(56,\cdot)\) \(\chi_{1521}(140,\cdot)\) \(\chi_{1521}(173,\cdot)\) \(\chi_{1521}(257,\cdot)\) \(\chi_{1521}(290,\cdot)\) \(\chi_{1521}(374,\cdot)\) \(\chi_{1521}(407,\cdot)\) \(\chi_{1521}(491,\cdot)\) \(\chi_{1521}(524,\cdot)\) \(\chi_{1521}(608,\cdot)\) \(\chi_{1521}(641,\cdot)\) \(\chi_{1521}(725,\cdot)\) \(\chi_{1521}(758,\cdot)\) \(\chi_{1521}(842,\cdot)\) \(\chi_{1521}(875,\cdot)\) \(\chi_{1521}(959,\cdot)\) \(\chi_{1521}(1076,\cdot)\) \(\chi_{1521}(1109,\cdot)\) \(\chi_{1521}(1193,\cdot)\) \(\chi_{1521}(1226,\cdot)\) \(\chi_{1521}(1310,\cdot)\) \(\chi_{1521}(1343,\cdot)\) \(\chi_{1521}(1427,\cdot)\) \(\chi_{1521}(1460,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 78 polynomial

Values on generators

\((677,847)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{73}{78}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 1521 }(524, a) \)	\(-1\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)