Dirichlet character \(\chi_{71}(58,\cdot)\)

• Label: 71.58
• Modulus: $71$
• Conductor: $71$
• Order: $35$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(71\)
Conductor:	\(71\)
Order:	\(35\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 71.g

\(\chi_{71}(2,\cdot)\) \(\chi_{71}(3,\cdot)\) \(\chi_{71}(4,\cdot)\) \(\chi_{71}(6,\cdot)\) \(\chi_{71}(8,\cdot)\) \(\chi_{71}(9,\cdot)\) \(\chi_{71}(10,\cdot)\) \(\chi_{71}(12,\cdot)\) \(\chi_{71}(15,\cdot)\) \(\chi_{71}(16,\cdot)\) \(\chi_{71}(18,\cdot)\) \(\chi_{71}(19,\cdot)\) \(\chi_{71}(24,\cdot)\) \(\chi_{71}(27,\cdot)\) \(\chi_{71}(29,\cdot)\) \(\chi_{71}(36,\cdot)\) \(\chi_{71}(38,\cdot)\) \(\chi_{71}(40,\cdot)\) \(\chi_{71}(43,\cdot)\) \(\chi_{71}(49,\cdot)\) \(\chi_{71}(50,\cdot)\) \(\chi_{71}(58,\cdot)\) \(\chi_{71}(60,\cdot)\) \(\chi_{71}(64,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{35})$
Fixed field:	Number field defined by a degree 35 polynomial

Values on generators

\(7\) → \(e\left(\frac{2}{35}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 71 }(58, a) \)	\(1\)	\(1\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum