Dirichlet character \(\chi_{4693}(1085,\cdot)\)

• Label: 4693.1085
• Modulus: $4693$
• Conductor: $4693$
• Order: $684$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(4693\)
Conductor:	\(4693\)
Order:	\(684\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4693.dr

\(\chi_{4693}(15,\cdot)\) \(\chi_{4693}(33,\cdot)\) \(\chi_{4693}(59,\cdot)\) \(\chi_{4693}(67,\cdot)\) \(\chi_{4693}(71,\cdot)\) \(\chi_{4693}(89,\cdot)\) \(\chi_{4693}(97,\cdot)\) \(\chi_{4693}(98,\cdot)\) \(\chi_{4693}(136,\cdot)\) \(\chi_{4693}(167,\cdot)\) \(\chi_{4693}(184,\cdot)\) \(\chi_{4693}(219,\cdot)\) \(\chi_{4693}(280,\cdot)\) \(\chi_{4693}(306,\cdot)\) \(\chi_{4693}(314,\cdot)\) \(\chi_{4693}(318,\cdot)\) \(\chi_{4693}(336,\cdot)\) \(\chi_{4693}(344,\cdot)\) \(\chi_{4693}(345,\cdot)\) \(\chi_{4693}(383,\cdot)\) \(\chi_{4693}(414,\cdot)\) \(\chi_{4693}(431,\cdot)\) \(\chi_{4693}(466,\cdot)\) \(\chi_{4693}(509,\cdot)\) \(\chi_{4693}(527,\cdot)\) \(\chi_{4693}(553,\cdot)\) \(\chi_{4693}(561,\cdot)\) \(\chi_{4693}(565,\cdot)\) \(\chi_{4693}(583,\cdot)\) \(\chi_{4693}(591,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{684})$
Fixed field:	Number field defined by a degree 684 polynomial (not computed)

Values on generators

\((1445,3251)\) → \((e\left(\frac{5}{12}\right),e\left(\frac{1}{342}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 4693 }(1085, a) \)	\(1\)	\(1\)	\(e\left(\frac{287}{684}\right)\)	\(e\left(\frac{25}{342}\right)\)	\(e\left(\frac{287}{342}\right)\)	\(e\left(\frac{293}{684}\right)\)	\(e\left(\frac{337}{684}\right)\)	\(e\left(\frac{5}{228}\right)\)	\(e\left(\frac{59}{228}\right)\)	\(e\left(\frac{25}{171}\right)\)	\(e\left(\frac{145}{171}\right)\)	\(e\left(\frac{49}{228}\right)\)