Basic properties
Modulus: | \(735\) | |
Conductor: | \(245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{245}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 735.bv
\(\chi_{735}(37,\cdot)\) \(\chi_{735}(58,\cdot)\) \(\chi_{735}(88,\cdot)\) \(\chi_{735}(142,\cdot)\) \(\chi_{735}(163,\cdot)\) \(\chi_{735}(172,\cdot)\) \(\chi_{735}(193,\cdot)\) \(\chi_{735}(247,\cdot)\) \(\chi_{735}(268,\cdot)\) \(\chi_{735}(277,\cdot)\) \(\chi_{735}(298,\cdot)\) \(\chi_{735}(352,\cdot)\) \(\chi_{735}(382,\cdot)\) \(\chi_{735}(403,\cdot)\) \(\chi_{735}(457,\cdot)\) \(\chi_{735}(478,\cdot)\) \(\chi_{735}(487,\cdot)\) \(\chi_{735}(562,\cdot)\) \(\chi_{735}(583,\cdot)\) \(\chi_{735}(592,\cdot)\) \(\chi_{735}(613,\cdot)\) \(\chi_{735}(688,\cdot)\) \(\chi_{735}(697,\cdot)\) \(\chi_{735}(718,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((491,442,346)\) → \((1,i,e\left(\frac{16}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 735 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{59}{84}\right)\) |