Dirichlet character \(\chi_{3871}(457,\cdot)\)

• Label: 3871.457
• Modulus: $3871$
• Conductor: $3871$
• Order: $273$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(3871\)
Conductor:	\(3871\)
Order:	\(273\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3871.cn

\(\chi_{3871}(46,\cdot)\) \(\chi_{3871}(65,\cdot)\) \(\chi_{3871}(100,\cdot)\) \(\chi_{3871}(144,\cdot)\) \(\chi_{3871}(179,\cdot)\) \(\chi_{3871}(247,\cdot)\) \(\chi_{3871}(289,\cdot)\) \(\chi_{3871}(326,\cdot)\) \(\chi_{3871}(338,\cdot)\) \(\chi_{3871}(354,\cdot)\) \(\chi_{3871}(368,\cdot)\) \(\chi_{3871}(380,\cdot)\) \(\chi_{3871}(403,\cdot)\) \(\chi_{3871}(417,\cdot)\) \(\chi_{3871}(457,\cdot)\) \(\chi_{3871}(492,\cdot)\) \(\chi_{3871}(536,\cdot)\) \(\chi_{3871}(541,\cdot)\) \(\chi_{3871}(571,\cdot)\) \(\chi_{3871}(599,\cdot)\) \(\chi_{3871}(620,\cdot)\) \(\chi_{3871}(653,\cdot)\) \(\chi_{3871}(697,\cdot)\) \(\chi_{3871}(732,\cdot)\) \(\chi_{3871}(800,\cdot)\) \(\chi_{3871}(828,\cdot)\) \(\chi_{3871}(842,\cdot)\) \(\chi_{3871}(877,\cdot)\) \(\chi_{3871}(879,\cdot)\) \(\chi_{3871}(891,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{273})$
Fixed field:	Number field defined by a degree 273 polynomial (not computed)

Values on generators

\((2845,1030)\) → \((e\left(\frac{10}{21}\right),e\left(\frac{10}{13}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 3871 }(457, a) \)	\(1\)	\(1\)	\(e\left(\frac{125}{273}\right)\)	\(e\left(\frac{67}{273}\right)\)	\(e\left(\frac{250}{273}\right)\)	\(e\left(\frac{137}{273}\right)\)	\(e\left(\frac{64}{91}\right)\)	\(e\left(\frac{34}{91}\right)\)	\(e\left(\frac{134}{273}\right)\)	\(e\left(\frac{262}{273}\right)\)	\(e\left(\frac{97}{273}\right)\)	\(e\left(\frac{44}{273}\right)\)