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.u
\(\chi_{916}(71,\cdot)\) \(\chi_{916}(99,\cdot)\) \(\chi_{916}(103,\cdot)\) \(\chi_{916}(147,\cdot)\) \(\chi_{916}(215,\cdot)\) \(\chi_{916}(275,\cdot)\) \(\chi_{916}(287,\cdot)\) \(\chi_{916}(291,\cdot)\) \(\chi_{916}(299,\cdot)\) \(\chi_{916}(307,\cdot)\) \(\chi_{916}(347,\cdot)\) \(\chi_{916}(367,\cdot)\) \(\chi_{916}(375,\cdot)\) \(\chi_{916}(383,\cdot)\) \(\chi_{916}(403,\cdot)\) \(\chi_{916}(407,\cdot)\) \(\chi_{916}(439,\cdot)\) \(\chi_{916}(455,\cdot)\) \(\chi_{916}(463,\cdot)\) \(\chi_{916}(491,\cdot)\) \(\chi_{916}(503,\cdot)\) \(\chi_{916}(507,\cdot)\) \(\chi_{916}(543,\cdot)\) \(\chi_{916}(555,\cdot)\) \(\chi_{916}(639,\cdot)\) \(\chi_{916}(667,\cdot)\) \(\chi_{916}(699,\cdot)\) \(\chi_{916}(723,\cdot)\) \(\chi_{916}(743,\cdot)\) \(\chi_{916}(763,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((459,693)\) → \((-1,e\left(\frac{23}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 916 }(375, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{114}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{7}{114}\right)\) | \(e\left(\frac{21}{38}\right)\) |