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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 735.bt
\(\chi_{735}(2,\cdot)\) \(\chi_{735}(23,\cdot)\) \(\chi_{735}(32,\cdot)\) \(\chi_{735}(53,\cdot)\) \(\chi_{735}(107,\cdot)\) \(\chi_{735}(137,\cdot)\) \(\chi_{735}(158,\cdot)\) \(\chi_{735}(212,\cdot)\) \(\chi_{735}(233,\cdot)\) \(\chi_{735}(242,\cdot)\) \(\chi_{735}(317,\cdot)\) \(\chi_{735}(338,\cdot)\) \(\chi_{735}(347,\cdot)\) \(\chi_{735}(368,\cdot)\) \(\chi_{735}(443,\cdot)\) \(\chi_{735}(452,\cdot)\) \(\chi_{735}(473,\cdot)\) \(\chi_{735}(527,\cdot)\) \(\chi_{735}(548,\cdot)\) \(\chi_{735}(578,\cdot)\) \(\chi_{735}(632,\cdot)\) \(\chi_{735}(653,\cdot)\) \(\chi_{735}(662,\cdot)\) \(\chi_{735}(683,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((491,442,346)\) → \((-1,-i,e\left(\frac{5}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 735 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{67}{84}\right)\) |