Dirichlet character \(\chi_{3175}(447,\cdot)\)

• Label: 3175.447
• Modulus: $3175$
• Conductor: $3175$
• Order: $420$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(3175\)
Conductor:	\(3175\)
Order:	\(420\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3175.co

\(\chi_{3175}(27,\cdot)\) \(\chi_{3175}(33,\cdot)\) \(\chi_{3175}(77,\cdot)\) \(\chi_{3175}(102,\cdot)\) \(\chi_{3175}(137,\cdot)\) \(\chi_{3175}(167,\cdot)\) \(\chi_{3175}(178,\cdot)\) \(\chi_{3175}(287,\cdot)\) \(\chi_{3175}(308,\cdot)\) \(\chi_{3175}(408,\cdot)\) \(\chi_{3175}(447,\cdot)\) \(\chi_{3175}(458,\cdot)\) \(\chi_{3175}(483,\cdot)\) \(\chi_{3175}(513,\cdot)\) \(\chi_{3175}(548,\cdot)\) \(\chi_{3175}(562,\cdot)\) \(\chi_{3175}(588,\cdot)\) \(\chi_{3175}(597,\cdot)\) \(\chi_{3175}(662,\cdot)\) \(\chi_{3175}(712,\cdot)\) \(\chi_{3175}(737,\cdot)\) \(\chi_{3175}(767,\cdot)\) \(\chi_{3175}(772,\cdot)\) \(\chi_{3175}(802,\cdot)\) \(\chi_{3175}(813,\cdot)\) \(\chi_{3175}(828,\cdot)\) \(\chi_{3175}(842,\cdot)\) \(\chi_{3175}(922,\cdot)\) \(\chi_{3175}(978,\cdot)\) \(\chi_{3175}(1067,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{420})$
Fixed field:	Number field defined by a degree 420 polynomial (not computed)

Values on generators

\((1652,3051)\) → \((e\left(\frac{17}{20}\right),e\left(\frac{5}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\( \chi_{ 3175 }(447, a) \)	\(1\)	\(1\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{29}{420}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{29}{210}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{383}{420}\right)\)	\(e\left(\frac{143}{420}\right)\)