Dirichlet character \(\chi_{401}(71,\cdot)\)

• Label: 401.71
• Modulus: $401$
• Conductor: $401$
• Order: $400$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(401\)
Conductor:	\(401\)
Order:	\(400\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 401.o

\(\chi_{401}(3,\cdot)\) \(\chi_{401}(6,\cdot)\) \(\chi_{401}(12,\cdot)\) \(\chi_{401}(13,\cdot)\) \(\chi_{401}(15,\cdot)\) \(\chi_{401}(17,\cdot)\) \(\chi_{401}(19,\cdot)\) \(\chi_{401}(21,\cdot)\) \(\chi_{401}(23,\cdot)\) \(\chi_{401}(24,\cdot)\) \(\chi_{401}(27,\cdot)\) \(\chi_{401}(31,\cdot)\) \(\chi_{401}(34,\cdot)\) \(\chi_{401}(37,\cdot)\) \(\chi_{401}(38,\cdot)\) \(\chi_{401}(42,\cdot)\) \(\chi_{401}(46,\cdot)\) \(\chi_{401}(52,\cdot)\) \(\chi_{401}(53,\cdot)\) \(\chi_{401}(54,\cdot)\) \(\chi_{401}(59,\cdot)\) \(\chi_{401}(60,\cdot)\) \(\chi_{401}(61,\cdot)\) \(\chi_{401}(62,\cdot)\) \(\chi_{401}(65,\cdot)\) \(\chi_{401}(66,\cdot)\) \(\chi_{401}(67,\cdot)\) \(\chi_{401}(71,\cdot)\) \(\chi_{401}(74,\cdot)\) \(\chi_{401}(75,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{400})$
Fixed field:	Number field defined by a degree 400 polynomial (not computed)

Values on generators

\(3\) → \(e\left(\frac{69}{400}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 401 }(71, a) \)	\(-1\)	\(1\)	\(e\left(\frac{97}{200}\right)\)	\(e\left(\frac{69}{400}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{263}{400}\right)\)	\(e\left(\frac{139}{200}\right)\)	\(e\left(\frac{91}{200}\right)\)	\(e\left(\frac{69}{200}\right)\)	\(e\left(\frac{153}{200}\right)\)	\(e\left(\frac{93}{200}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum