Basic properties
| Modulus: | \(361\) | |
| Conductor: | \(361\) | 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 361.j
\(\chi_{361}(8,\cdot)\) \(\chi_{361}(12,\cdot)\) \(\chi_{361}(27,\cdot)\) \(\chi_{361}(31,\cdot)\) \(\chi_{361}(46,\cdot)\) \(\chi_{361}(50,\cdot)\) \(\chi_{361}(65,\cdot)\) \(\chi_{361}(84,\cdot)\) \(\chi_{361}(88,\cdot)\) \(\chi_{361}(103,\cdot)\) \(\chi_{361}(107,\cdot)\) \(\chi_{361}(122,\cdot)\) \(\chi_{361}(126,\cdot)\) \(\chi_{361}(141,\cdot)\) \(\chi_{361}(145,\cdot)\) \(\chi_{361}(160,\cdot)\) \(\chi_{361}(164,\cdot)\) \(\chi_{361}(179,\cdot)\) \(\chi_{361}(183,\cdot)\) \(\chi_{361}(198,\cdot)\) \(\chi_{361}(202,\cdot)\) \(\chi_{361}(217,\cdot)\) \(\chi_{361}(221,\cdot)\) \(\chi_{361}(236,\cdot)\) \(\chi_{361}(240,\cdot)\) \(\chi_{361}(255,\cdot)\) \(\chi_{361}(259,\cdot)\) \(\chi_{361}(274,\cdot)\) \(\chi_{361}(278,\cdot)\) \(\chi_{361}(297,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{31}{114}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 361 }(122, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{114}\right)\) | \(e\left(\frac{91}{114}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{41}{114}\right)\) | \(e\left(\frac{14}{19}\right)\) |