Dirichlet character \(\chi_{4563}(1537,\cdot)\)

• Label: 4563.1537
• Modulus: $4563$
• Conductor: $4563$
• Order: $117$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(4563\)
Conductor:	\(4563\)
Order:	\(117\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4563.ct

\(\chi_{4563}(16,\cdot)\) \(\chi_{4563}(133,\cdot)\) \(\chi_{4563}(139,\cdot)\) \(\chi_{4563}(250,\cdot)\) \(\chi_{4563}(256,\cdot)\) \(\chi_{4563}(367,\cdot)\) \(\chi_{4563}(373,\cdot)\) \(\chi_{4563}(490,\cdot)\) \(\chi_{4563}(601,\cdot)\) \(\chi_{4563}(607,\cdot)\) \(\chi_{4563}(718,\cdot)\) \(\chi_{4563}(724,\cdot)\) \(\chi_{4563}(835,\cdot)\) \(\chi_{4563}(841,\cdot)\) \(\chi_{4563}(952,\cdot)\) \(\chi_{4563}(958,\cdot)\) \(\chi_{4563}(1069,\cdot)\) \(\chi_{4563}(1075,\cdot)\) \(\chi_{4563}(1186,\cdot)\) \(\chi_{4563}(1192,\cdot)\) \(\chi_{4563}(1303,\cdot)\) \(\chi_{4563}(1309,\cdot)\) \(\chi_{4563}(1420,\cdot)\) \(\chi_{4563}(1426,\cdot)\) \(\chi_{4563}(1537,\cdot)\) \(\chi_{4563}(1654,\cdot)\) \(\chi_{4563}(1660,\cdot)\) \(\chi_{4563}(1771,\cdot)\) \(\chi_{4563}(1777,\cdot)\) \(\chi_{4563}(1888,\cdot)\) ...

Related number fields

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

Values on generators

\((677,3889)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{1}{39}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 4563 }(1537, a) \)	\(1\)	\(1\)	\(e\left(\frac{68}{117}\right)\)	\(e\left(\frac{19}{117}\right)\)	\(e\left(\frac{1}{117}\right)\)	\(e\left(\frac{74}{117}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{101}{117}\right)\)	\(e\left(\frac{25}{117}\right)\)	\(e\left(\frac{38}{117}\right)\)	\(e\left(\frac{1}{13}\right)\)