Dirichlet character \(\chi_{475}(61,\cdot)\)

• Label: 475.61
• Modulus: $475$
• Conductor: $475$
• Order: $45$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(475\)
Conductor:	\(475\)
Order:	\(45\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 475.bc

\(\chi_{475}(6,\cdot)\) \(\chi_{475}(16,\cdot)\) \(\chi_{475}(36,\cdot)\) \(\chi_{475}(61,\cdot)\) \(\chi_{475}(66,\cdot)\) \(\chi_{475}(81,\cdot)\) \(\chi_{475}(111,\cdot)\) \(\chi_{475}(131,\cdot)\) \(\chi_{475}(156,\cdot)\) \(\chi_{475}(161,\cdot)\) \(\chi_{475}(196,\cdot)\) \(\chi_{475}(206,\cdot)\) \(\chi_{475}(256,\cdot)\) \(\chi_{475}(271,\cdot)\) \(\chi_{475}(291,\cdot)\) \(\chi_{475}(321,\cdot)\) \(\chi_{475}(346,\cdot)\) \(\chi_{475}(366,\cdot)\) \(\chi_{475}(386,\cdot)\) \(\chi_{475}(396,\cdot)\) \(\chi_{475}(416,\cdot)\) \(\chi_{475}(441,\cdot)\) \(\chi_{475}(446,\cdot)\) \(\chi_{475}(461,\cdot)\)

Related number fields

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

Values on generators

\((77,401)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{1}{9}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\( \chi_{ 475 }(61, a) \)	\(1\)	\(1\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{34}{45}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum