Dirichlet character \(\chi_{1521}(1166,\cdot)\)

• Label: 1521.1166
• 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.bz

\(\chi_{1521}(29,\cdot)\) \(\chi_{1521}(113,\cdot)\) \(\chi_{1521}(230,\cdot)\) \(\chi_{1521}(263,\cdot)\) \(\chi_{1521}(347,\cdot)\) \(\chi_{1521}(380,\cdot)\) \(\chi_{1521}(464,\cdot)\) \(\chi_{1521}(497,\cdot)\) \(\chi_{1521}(581,\cdot)\) \(\chi_{1521}(614,\cdot)\) \(\chi_{1521}(731,\cdot)\) \(\chi_{1521}(815,\cdot)\) \(\chi_{1521}(848,\cdot)\) \(\chi_{1521}(932,\cdot)\) \(\chi_{1521}(965,\cdot)\) \(\chi_{1521}(1049,\cdot)\) \(\chi_{1521}(1082,\cdot)\) \(\chi_{1521}(1166,\cdot)\) \(\chi_{1521}(1199,\cdot)\) \(\chi_{1521}(1283,\cdot)\) \(\chi_{1521}(1316,\cdot)\) \(\chi_{1521}(1400,\cdot)\) \(\chi_{1521}(1433,\cdot)\) \(\chi_{1521}(1517,\cdot)\)

Related number fields

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

Values on generators

\((677,847)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{17}{39}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 1521 }(1166, a) \)	\(-1\)	\(1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{11}{78}\right)\)