Dirichlet character \(\chi_{1521}(185,\cdot)\)

• Label: 1521.185
• 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.bp

\(\chi_{1521}(68,\cdot)\) \(\chi_{1521}(74,\cdot)\) \(\chi_{1521}(185,\cdot)\) \(\chi_{1521}(302,\cdot)\) \(\chi_{1521}(308,\cdot)\) \(\chi_{1521}(419,\cdot)\) \(\chi_{1521}(425,\cdot)\) \(\chi_{1521}(536,\cdot)\) \(\chi_{1521}(542,\cdot)\) \(\chi_{1521}(659,\cdot)\) \(\chi_{1521}(770,\cdot)\) \(\chi_{1521}(776,\cdot)\) \(\chi_{1521}(887,\cdot)\) \(\chi_{1521}(893,\cdot)\) \(\chi_{1521}(1004,\cdot)\) \(\chi_{1521}(1010,\cdot)\) \(\chi_{1521}(1121,\cdot)\) \(\chi_{1521}(1127,\cdot)\) \(\chi_{1521}(1238,\cdot)\) \(\chi_{1521}(1244,\cdot)\) \(\chi_{1521}(1355,\cdot)\) \(\chi_{1521}(1361,\cdot)\) \(\chi_{1521}(1472,\cdot)\) \(\chi_{1521}(1478,\cdot)\)

Related number fields

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

Values on generators

\((677,847)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{1}{39}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 1521 }(185, a) \)	\(-1\)	\(1\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{19}{78}\right)\)