Dirichlet character \(\chi_{4563}(1492,\cdot)\)

• Label: 4563.1492
• Modulus: $4563$
• Conductor: $4563$
• Order: $234$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(4563\)
Conductor:	\(4563\)
Order:	\(234\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4563.df

\(\chi_{4563}(4,\cdot)\) \(\chi_{4563}(88,\cdot)\) \(\chi_{4563}(121,\cdot)\) \(\chi_{4563}(205,\cdot)\) \(\chi_{4563}(238,\cdot)\) \(\chi_{4563}(322,\cdot)\) \(\chi_{4563}(355,\cdot)\) \(\chi_{4563}(439,\cdot)\) \(\chi_{4563}(472,\cdot)\) \(\chi_{4563}(556,\cdot)\) \(\chi_{4563}(589,\cdot)\) \(\chi_{4563}(673,\cdot)\) \(\chi_{4563}(706,\cdot)\) \(\chi_{4563}(790,\cdot)\) \(\chi_{4563}(907,\cdot)\) \(\chi_{4563}(940,\cdot)\) \(\chi_{4563}(1024,\cdot)\) \(\chi_{4563}(1057,\cdot)\) \(\chi_{4563}(1141,\cdot)\) \(\chi_{4563}(1174,\cdot)\) \(\chi_{4563}(1258,\cdot)\) \(\chi_{4563}(1291,\cdot)\) \(\chi_{4563}(1408,\cdot)\) \(\chi_{4563}(1492,\cdot)\) \(\chi_{4563}(1525,\cdot)\) \(\chi_{4563}(1609,\cdot)\) \(\chi_{4563}(1642,\cdot)\) \(\chi_{4563}(1726,\cdot)\) \(\chi_{4563}(1759,\cdot)\) \(\chi_{4563}(1843,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{117})$
Fixed field:	Number field defined by a degree 234 polynomial (not computed)

Values on generators

\((677,3889)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{59}{78}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 4563 }(1492, a) \)	\(1\)	\(1\)	\(e\left(\frac{151}{234}\right)\)	\(e\left(\frac{34}{117}\right)\)	\(e\left(\frac{59}{234}\right)\)	\(e\left(\frac{37}{234}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{109}{234}\right)\)	\(e\left(\frac{94}{117}\right)\)	\(e\left(\frac{68}{117}\right)\)	\(e\left(\frac{10}{13}\right)\)