Dirichlet character \(\chi_{4563}(392,\cdot)\)

• Label: 4563.392
• Modulus: $4563$
• Conductor: $4563$
• Order: $468$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(4563\)
Conductor:	\(4563\)
Order:	\(468\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4563.dr

\(\chi_{4563}(20,\cdot)\) \(\chi_{4563}(41,\cdot)\) \(\chi_{4563}(50,\cdot)\) \(\chi_{4563}(110,\cdot)\) \(\chi_{4563}(137,\cdot)\) \(\chi_{4563}(158,\cdot)\) \(\chi_{4563}(167,\cdot)\) \(\chi_{4563}(227,\cdot)\) \(\chi_{4563}(254,\cdot)\) \(\chi_{4563}(275,\cdot)\) \(\chi_{4563}(284,\cdot)\) \(\chi_{4563}(344,\cdot)\) \(\chi_{4563}(371,\cdot)\) \(\chi_{4563}(392,\cdot)\) \(\chi_{4563}(401,\cdot)\) \(\chi_{4563}(461,\cdot)\) \(\chi_{4563}(509,\cdot)\) \(\chi_{4563}(518,\cdot)\) \(\chi_{4563}(578,\cdot)\) \(\chi_{4563}(605,\cdot)\) \(\chi_{4563}(626,\cdot)\) \(\chi_{4563}(635,\cdot)\) \(\chi_{4563}(722,\cdot)\) \(\chi_{4563}(743,\cdot)\) \(\chi_{4563}(752,\cdot)\) \(\chi_{4563}(812,\cdot)\) \(\chi_{4563}(839,\cdot)\) \(\chi_{4563}(860,\cdot)\) \(\chi_{4563}(869,\cdot)\) \(\chi_{4563}(929,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{468})$
Fixed field:	Number field defined by a degree 468 polynomial (not computed)

Values on generators

\((677,3889)\) → \((e\left(\frac{17}{18}\right),e\left(\frac{61}{156}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 4563 }(392, a) \)	\(1\)	\(1\)	\(e\left(\frac{157}{468}\right)\)	\(e\left(\frac{157}{234}\right)\)	\(e\left(\frac{113}{468}\right)\)	\(e\left(\frac{445}{468}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{259}{468}\right)\)	\(e\left(\frac{67}{234}\right)\)	\(e\left(\frac{40}{117}\right)\)	\(e\left(\frac{10}{39}\right)\)