Dirichlet character \(\chi_{4563}(1147,\cdot)\)

• Label: 4563.1147
• 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.cs

\(\chi_{4563}(61,\cdot)\) \(\chi_{4563}(94,\cdot)\) \(\chi_{4563}(178,\cdot)\) \(\chi_{4563}(211,\cdot)\) \(\chi_{4563}(295,\cdot)\) \(\chi_{4563}(328,\cdot)\) \(\chi_{4563}(412,\cdot)\) \(\chi_{4563}(445,\cdot)\) \(\chi_{4563}(562,\cdot)\) \(\chi_{4563}(646,\cdot)\) \(\chi_{4563}(679,\cdot)\) \(\chi_{4563}(763,\cdot)\) \(\chi_{4563}(796,\cdot)\) \(\chi_{4563}(880,\cdot)\) \(\chi_{4563}(913,\cdot)\) \(\chi_{4563}(997,\cdot)\) \(\chi_{4563}(1030,\cdot)\) \(\chi_{4563}(1114,\cdot)\) \(\chi_{4563}(1147,\cdot)\) \(\chi_{4563}(1231,\cdot)\) \(\chi_{4563}(1264,\cdot)\) \(\chi_{4563}(1348,\cdot)\) \(\chi_{4563}(1381,\cdot)\) \(\chi_{4563}(1465,\cdot)\) \(\chi_{4563}(1582,\cdot)\) \(\chi_{4563}(1615,\cdot)\) \(\chi_{4563}(1699,\cdot)\) \(\chi_{4563}(1732,\cdot)\) \(\chi_{4563}(1816,\cdot)\) \(\chi_{4563}(1849,\cdot)\) ...

Related number fields

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

Values on generators

\((677,3889)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{4}{39}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 4563 }(1147, a) \)	\(1\)	\(1\)	\(e\left(\frac{64}{117}\right)\)	\(e\left(\frac{11}{117}\right)\)	\(e\left(\frac{17}{117}\right)\)	\(e\left(\frac{10}{117}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{40}{117}\right)\)	\(e\left(\frac{74}{117}\right)\)	\(e\left(\frac{22}{117}\right)\)	\(e\left(\frac{25}{39}\right)\)