Dirichlet character \(\chi_{3503}(9,\cdot)\)

• Label: 3503.9
• Modulus: $3503$
• Conductor: $3503$
• Order: $840$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(3503\)
Conductor:	\(3503\)
Order:	\(840\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3503.cz

\(\chi_{3503}(9,\cdot)\) \(\chi_{3503}(41,\cdot)\) \(\chi_{3503}(50,\cdot)\) \(\chi_{3503}(51,\cdot)\) \(\chi_{3503}(72,\cdot)\) \(\chi_{3503}(82,\cdot)\) \(\chi_{3503}(100,\cdot)\) \(\chi_{3503}(102,\cdot)\) \(\chi_{3503}(138,\cdot)\) \(\chi_{3503}(144,\cdot)\) \(\chi_{3503}(164,\cdot)\) \(\chi_{3503}(165,\cdot)\) \(\chi_{3503}(174,\cdot)\) \(\chi_{3503}(175,\cdot)\) \(\chi_{3503}(195,\cdot)\) \(\chi_{3503}(200,\cdot)\) \(\chi_{3503}(204,\cdot)\) \(\chi_{3503}(235,\cdot)\) \(\chi_{3503}(237,\cdot)\) \(\chi_{3503}(257,\cdot)\) \(\chi_{3503}(262,\cdot)\) \(\chi_{3503}(267,\cdot)\) \(\chi_{3503}(276,\cdot)\) \(\chi_{3503}(288,\cdot)\) \(\chi_{3503}(289,\cdot)\) \(\chi_{3503}(298,\cdot)\) \(\chi_{3503}(317,\cdot)\) \(\chi_{3503}(328,\cdot)\) \(\chi_{3503}(330,\cdot)\) \(\chi_{3503}(348,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{840})$
Fixed field:	Number field defined by a degree 840 polynomial (not computed)

Values on generators

\((3165,342)\) → \((e\left(\frac{1}{15}\right),e\left(\frac{1}{56}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 3503 }(9, a) \)	\(1\)	\(1\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{71}{840}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{137}{168}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{71}{420}\right)\)	\(e\left(\frac{529}{840}\right)\)	\(e\left(\frac{359}{420}\right)\)