Dirichlet character \(\chi_{3503}(604,\cdot)\)

• Label: 3503.604
• Modulus: $3503$
• Conductor: $3503$
• Order: $560$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(3503\)
Conductor:	\(3503\)
Order:	\(560\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3503.cx

\(\chi_{3503}(23,\cdot)\) \(\chi_{3503}(27,\cdot)\) \(\chi_{3503}(29,\cdot)\) \(\chi_{3503}(46,\cdot)\) \(\chi_{3503}(54,\cdot)\) \(\chi_{3503}(58,\cdot)\) \(\chi_{3503}(89,\cdot)\) \(\chi_{3503}(108,\cdot)\) \(\chi_{3503}(116,\cdot)\) \(\chi_{3503}(147,\cdot)\) \(\chi_{3503}(151,\cdot)\) \(\chi_{3503}(209,\cdot)\) \(\chi_{3503}(232,\cdot)\) \(\chi_{3503}(246,\cdot)\) \(\chi_{3503}(263,\cdot)\) \(\chi_{3503}(271,\cdot)\) \(\chi_{3503}(294,\cdot)\) \(\chi_{3503}(302,\cdot)\) \(\chi_{3503}(306,\cdot)\) \(\chi_{3503}(333,\cdot)\) \(\chi_{3503}(356,\cdot)\) \(\chi_{3503}(368,\cdot)\) \(\chi_{3503}(418,\cdot)\) \(\chi_{3503}(432,\cdot)\) \(\chi_{3503}(449,\cdot)\) \(\chi_{3503}(457,\cdot)\) \(\chi_{3503}(511,\cdot)\) \(\chi_{3503}(519,\cdot)\) \(\chi_{3503}(542,\cdot)\) \(\chi_{3503}(585,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{560})$
Fixed field:	Number field defined by a degree 560 polynomial (not computed)

Values on generators

\((3165,342)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{23}{112}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 3503 }(604, a) \)	\(1\)	\(1\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{507}{560}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{227}{280}\right)\)	\(e\left(\frac{173}{560}\right)\)	\(e\left(\frac{83}{280}\right)\)