Dirichlet character \(\chi_{61152}(8747,\cdot)\)

• Label: 61152.8747
• Modulus: $61152$
• Conductor: $61152$
• Order: $168$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(61152\)
Conductor:	\(61152\)
Order:	\(168\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 61152.bnl

\(\chi_{61152}(11,\cdot)\) \(\chi_{61152}(1523,\cdot)\) \(\chi_{61152}(3971,\cdot)\) \(\chi_{61152}(5891,\cdot)\) \(\chi_{61152}(8171,\cdot)\) \(\chi_{61152}(8339,\cdot)\) \(\chi_{61152}(8747,\cdot)\) \(\chi_{61152}(12539,\cdot)\) \(\chi_{61152}(12707,\cdot)\) \(\chi_{61152}(13115,\cdot)\) \(\chi_{61152}(14627,\cdot)\) \(\chi_{61152}(16907,\cdot)\) \(\chi_{61152}(17075,\cdot)\) \(\chi_{61152}(17483,\cdot)\) \(\chi_{61152}(18995,\cdot)\) \(\chi_{61152}(21275,\cdot)\) \(\chi_{61152}(21851,\cdot)\) \(\chi_{61152}(23363,\cdot)\) \(\chi_{61152}(25643,\cdot)\) \(\chi_{61152}(25811,\cdot)\) \(\chi_{61152}(26219,\cdot)\) \(\chi_{61152}(27731,\cdot)\) \(\chi_{61152}(30011,\cdot)\) \(\chi_{61152}(30179,\cdot)\) \(\chi_{61152}(30587,\cdot)\) \(\chi_{61152}(32099,\cdot)\) \(\chi_{61152}(34547,\cdot)\) \(\chi_{61152}(36467,\cdot)\) \(\chi_{61152}(38747,\cdot)\) \(\chi_{61152}(38915,\cdot)\) ...

Related number fields

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

Values on generators

\((34399,53509,40769,18721,28225)\) → \((-1,e\left(\frac{5}{8}\right),-1,e\left(\frac{8}{21}\right),e\left(\frac{7}{12}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\( \chi_{ 61152 }(8747, a) \)	\(-1\)	\(1\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{23}{42}\right)\)