Dirichlet character \(\chi_{97020}(56407,\cdot)\)

• Label: 97020.56407
• Modulus: $97020$
• Conductor: $97020$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(97020\)
Conductor:	\(97020\)
Order:	\(84\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 97020.bas

\(\chi_{97020}(43,\cdot)\) \(\chi_{97020}(967,\cdot)\) \(\chi_{97020}(9283,\cdot)\) \(\chi_{97020}(13903,\cdot)\) \(\chi_{97020}(14827,\cdot)\) \(\chi_{97020}(19447,\cdot)\) \(\chi_{97020}(23143,\cdot)\) \(\chi_{97020}(27763,\cdot)\) \(\chi_{97020}(28687,\cdot)\) \(\chi_{97020}(33307,\cdot)\) \(\chi_{97020}(37003,\cdot)\) \(\chi_{97020}(41623,\cdot)\) \(\chi_{97020}(42547,\cdot)\) \(\chi_{97020}(47167,\cdot)\) \(\chi_{97020}(55483,\cdot)\) \(\chi_{97020}(56407,\cdot)\) \(\chi_{97020}(61027,\cdot)\) \(\chi_{97020}(64723,\cdot)\) \(\chi_{97020}(69343,\cdot)\) \(\chi_{97020}(74887,\cdot)\) \(\chi_{97020}(78583,\cdot)\) \(\chi_{97020}(84127,\cdot)\) \(\chi_{97020}(88747,\cdot)\) \(\chi_{97020}(92443,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Values on generators

\((48511,43121,77617,9901,44101)\) → \((-1,e\left(\frac{1}{3}\right),i,e\left(\frac{6}{7}\right),-1)\)

First values

\(a\)	\(-1\)	\(1\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\( \chi_{ 97020 }(56407, a) \)	\(-1\)	\(1\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(-1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)