Dirichlet character \(\chi_{44100}(5303,\cdot)\)

• Label: 44100.5303
• Modulus: $44100$
• Conductor: $44100$
• Order: $420$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(44100\)
Conductor:	\(44100\)
Order:	\(420\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 44100.rr

\(\chi_{44100}(23,\cdot)\) \(\chi_{44100}(527,\cdot)\) \(\chi_{44100}(767,\cdot)\) \(\chi_{44100}(1283,\cdot)\) \(\chi_{44100}(1523,\cdot)\) \(\chi_{44100}(1787,\cdot)\) \(\chi_{44100}(2783,\cdot)\) \(\chi_{44100}(3047,\cdot)\) \(\chi_{44100}(3287,\cdot)\) \(\chi_{44100}(4547,\cdot)\) \(\chi_{44100}(5063,\cdot)\) \(\chi_{44100}(5303,\cdot)\) \(\chi_{44100}(6323,\cdot)\) \(\chi_{44100}(6563,\cdot)\) \(\chi_{44100}(6827,\cdot)\) \(\chi_{44100}(7067,\cdot)\) \(\chi_{44100}(7583,\cdot)\) \(\chi_{44100}(7823,\cdot)\) \(\chi_{44100}(8087,\cdot)\) \(\chi_{44100}(8327,\cdot)\) \(\chi_{44100}(9347,\cdot)\) \(\chi_{44100}(9587,\cdot)\) \(\chi_{44100}(10103,\cdot)\) \(\chi_{44100}(11363,\cdot)\) \(\chi_{44100}(11603,\cdot)\) \(\chi_{44100}(11867,\cdot)\) \(\chi_{44100}(12863,\cdot)\) \(\chi_{44100}(13127,\cdot)\) \(\chi_{44100}(13367,\cdot)\) \(\chi_{44100}(13883,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{420})$
Fixed field:	Number field defined by a degree 420 polynomial (not computed)

Values on generators

\((22051,34301,15877,9901)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{7}{20}\right),e\left(\frac{20}{21}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 44100 }(5303, a) \)	\(-1\)	\(1\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{361}{420}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{157}{420}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{263}{420}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{11}{84}\right)\)