Basic properties
Modulus: | \(735\) | |
Conductor: | \(735\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 735.bs
\(\chi_{735}(17,\cdot)\) \(\chi_{735}(38,\cdot)\) \(\chi_{735}(47,\cdot)\) \(\chi_{735}(122,\cdot)\) \(\chi_{735}(143,\cdot)\) \(\chi_{735}(152,\cdot)\) \(\chi_{735}(173,\cdot)\) \(\chi_{735}(248,\cdot)\) \(\chi_{735}(257,\cdot)\) \(\chi_{735}(278,\cdot)\) \(\chi_{735}(332,\cdot)\) \(\chi_{735}(353,\cdot)\) \(\chi_{735}(383,\cdot)\) \(\chi_{735}(437,\cdot)\) \(\chi_{735}(458,\cdot)\) \(\chi_{735}(467,\cdot)\) \(\chi_{735}(488,\cdot)\) \(\chi_{735}(542,\cdot)\) \(\chi_{735}(563,\cdot)\) \(\chi_{735}(572,\cdot)\) \(\chi_{735}(593,\cdot)\) \(\chi_{735}(647,\cdot)\) \(\chi_{735}(677,\cdot)\) \(\chi_{735}(698,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((491,442,346)\) → \((-1,i,e\left(\frac{31}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 735 }(437, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{25}{84}\right)\) |