Basic properties
| Modulus: | \(916\) | |
| Conductor: | \(916\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | 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 916.t
\(\chi_{916}(3,\cdot)\) \(\chi_{916}(19,\cdot)\) \(\chi_{916}(51,\cdot)\) \(\chi_{916}(55,\cdot)\) \(\chi_{916}(75,\cdot)\) \(\chi_{916}(83,\cdot)\) \(\chi_{916}(91,\cdot)\) \(\chi_{916}(111,\cdot)\) \(\chi_{916}(151,\cdot)\) \(\chi_{916}(159,\cdot)\) \(\chi_{916}(167,\cdot)\) \(\chi_{916}(171,\cdot)\) \(\chi_{916}(183,\cdot)\) \(\chi_{916}(243,\cdot)\) \(\chi_{916}(311,\cdot)\) \(\chi_{916}(355,\cdot)\) \(\chi_{916}(359,\cdot)\) \(\chi_{916}(387,\cdot)\) \(\chi_{916}(467,\cdot)\) \(\chi_{916}(483,\cdot)\) \(\chi_{916}(495,\cdot)\) \(\chi_{916}(539,\cdot)\) \(\chi_{916}(587,\cdot)\) \(\chi_{916}(607,\cdot)\) \(\chi_{916}(611,\cdot)\) \(\chi_{916}(631,\cdot)\) \(\chi_{916}(651,\cdot)\) \(\chi_{916}(675,\cdot)\) \(\chi_{916}(707,\cdot)\) \(\chi_{916}(735,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((459,693)\) → \((-1,e\left(\frac{8}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 916 }(55, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{114}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{59}{114}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{47}{114}\right)\) | \(e\left(\frac{4}{19}\right)\) |