Dirichlet character \(\chi_{1521}(745,\cdot)\)

• Label: 1521.745
• Modulus: $1521$
• Conductor: $1521$
• Order: $78$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

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

Galois orbit 1521.bs

\(\chi_{1521}(43,\cdot)\) \(\chi_{1521}(49,\cdot)\) \(\chi_{1521}(160,\cdot)\) \(\chi_{1521}(166,\cdot)\) \(\chi_{1521}(277,\cdot)\) \(\chi_{1521}(283,\cdot)\) \(\chi_{1521}(394,\cdot)\) \(\chi_{1521}(400,\cdot)\) \(\chi_{1521}(511,\cdot)\) \(\chi_{1521}(517,\cdot)\) \(\chi_{1521}(628,\cdot)\) \(\chi_{1521}(634,\cdot)\) \(\chi_{1521}(745,\cdot)\) \(\chi_{1521}(751,\cdot)\) \(\chi_{1521}(862,\cdot)\) \(\chi_{1521}(979,\cdot)\) \(\chi_{1521}(985,\cdot)\) \(\chi_{1521}(1096,\cdot)\) \(\chi_{1521}(1102,\cdot)\) \(\chi_{1521}(1213,\cdot)\) \(\chi_{1521}(1219,\cdot)\) \(\chi_{1521}(1336,\cdot)\) \(\chi_{1521}(1447,\cdot)\) \(\chi_{1521}(1453,\cdot)\)

Related number fields

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

Values on generators

\((677,847)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{49}{78}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 1521 }(745, a) \)	\(1\)	\(1\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)