Dirichlet character \(\chi_{305760}(73691,\cdot)\)

• Label: 305760.73691
• Modulus: $305760$
• Conductor: $61152$
• Order: $168$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(305760\)
Conductor:	\(61152\)
Order:	\(168\)
Real:	no
Primitive:	no, induced from \(\chi_{61152}(12539,\cdot)\)
Minimal:	yes
Parity:	odd

Galois orbit 305760.fmx

\(\chi_{305760}(11,\cdot)\) \(\chi_{305760}(3971,\cdot)\) \(\chi_{305760}(5891,\cdot)\) \(\chi_{305760}(8171,\cdot)\) \(\chi_{305760}(21851,\cdot)\) \(\chi_{305760}(25811,\cdot)\) \(\chi_{305760}(27731,\cdot)\) \(\chi_{305760}(30011,\cdot)\) \(\chi_{305760}(43691,\cdot)\) \(\chi_{305760}(47651,\cdot)\) \(\chi_{305760}(49571,\cdot)\) \(\chi_{305760}(51851,\cdot)\) \(\chi_{305760}(69491,\cdot)\) \(\chi_{305760}(73691,\cdot)\) \(\chi_{305760}(87371,\cdot)\) \(\chi_{305760}(91331,\cdot)\) \(\chi_{305760}(93251,\cdot)\) \(\chi_{305760}(109211,\cdot)\) \(\chi_{305760}(115091,\cdot)\) \(\chi_{305760}(117371,\cdot)\) \(\chi_{305760}(131051,\cdot)\) \(\chi_{305760}(135011,\cdot)\) \(\chi_{305760}(136931,\cdot)\) \(\chi_{305760}(139211,\cdot)\) \(\chi_{305760}(152891,\cdot)\) \(\chi_{305760}(156851,\cdot)\) \(\chi_{305760}(158771,\cdot)\) \(\chi_{305760}(161051,\cdot)\) \(\chi_{305760}(174731,\cdot)\) \(\chi_{305760}(178691,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{168})$
Fixed field:	Number field defined by a degree 168 polynomial (not computed)

Values on generators

\((95551,114661,101921,183457,18721,211681)\) → \((-1,e\left(\frac{1}{8}\right),-1,1,e\left(\frac{4}{21}\right),e\left(\frac{11}{12}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\( \chi_{ 305760 }(73691, a) \)	\(-1\)	\(1\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{17}{84}\right)\)