Dirichlet character \(\chi_{475}(54,\cdot)\)

• Label: 475.54
• Modulus: $475$
• Conductor: $475$
• Order: $90$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(475\)
Conductor:	\(475\)
Order:	\(90\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 475.bg

\(\chi_{475}(4,\cdot)\) \(\chi_{475}(9,\cdot)\) \(\chi_{475}(44,\cdot)\) \(\chi_{475}(54,\cdot)\) \(\chi_{475}(104,\cdot)\) \(\chi_{475}(119,\cdot)\) \(\chi_{475}(139,\cdot)\) \(\chi_{475}(169,\cdot)\) \(\chi_{475}(194,\cdot)\) \(\chi_{475}(214,\cdot)\) \(\chi_{475}(234,\cdot)\) \(\chi_{475}(244,\cdot)\) \(\chi_{475}(264,\cdot)\) \(\chi_{475}(289,\cdot)\) \(\chi_{475}(294,\cdot)\) \(\chi_{475}(309,\cdot)\) \(\chi_{475}(329,\cdot)\) \(\chi_{475}(339,\cdot)\) \(\chi_{475}(359,\cdot)\) \(\chi_{475}(384,\cdot)\) \(\chi_{475}(389,\cdot)\) \(\chi_{475}(404,\cdot)\) \(\chi_{475}(434,\cdot)\) \(\chi_{475}(454,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{45})$
Fixed field:	Number field defined by a degree 90 polynomial

Values on generators

\((77,401)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{2}{9}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\( \chi_{ 475 }(54, a) \)	\(1\)	\(1\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{90}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum