Dirichlet character \(\chi_{4563}(40,\cdot)\)

• Label: 4563.40
• 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.cu

\(\chi_{4563}(40,\cdot)\) \(\chi_{4563}(79,\cdot)\) \(\chi_{4563}(157,\cdot)\) \(\chi_{4563}(196,\cdot)\) \(\chi_{4563}(274,\cdot)\) \(\chi_{4563}(313,\cdot)\) \(\chi_{4563}(391,\cdot)\) \(\chi_{4563}(430,\cdot)\) \(\chi_{4563}(547,\cdot)\) \(\chi_{4563}(625,\cdot)\) \(\chi_{4563}(664,\cdot)\) \(\chi_{4563}(742,\cdot)\) \(\chi_{4563}(781,\cdot)\) \(\chi_{4563}(859,\cdot)\) \(\chi_{4563}(898,\cdot)\) \(\chi_{4563}(976,\cdot)\) \(\chi_{4563}(1093,\cdot)\) \(\chi_{4563}(1132,\cdot)\) \(\chi_{4563}(1210,\cdot)\) \(\chi_{4563}(1249,\cdot)\) \(\chi_{4563}(1327,\cdot)\) \(\chi_{4563}(1366,\cdot)\) \(\chi_{4563}(1444,\cdot)\) \(\chi_{4563}(1483,\cdot)\) \(\chi_{4563}(1561,\cdot)\) \(\chi_{4563}(1600,\cdot)\) \(\chi_{4563}(1678,\cdot)\) \(\chi_{4563}(1717,\cdot)\) \(\chi_{4563}(1795,\cdot)\) \(\chi_{4563}(1834,\cdot)\) ...

Related number fields

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

Values on generators

\((677,3889)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{1}{13}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 4563 }(40, a) \)	\(1\)	\(1\)	\(e\left(\frac{61}{117}\right)\)	\(e\left(\frac{5}{117}\right)\)	\(e\left(\frac{107}{117}\right)\)	\(e\left(\frac{40}{117}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{82}{117}\right)\)	\(e\left(\frac{101}{117}\right)\)	\(e\left(\frac{10}{117}\right)\)	\(e\left(\frac{35}{39}\right)\)