Basic properties
Modulus: | \(2527\) | |
Conductor: | \(2527\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2527.bz
\(\chi_{2527}(12,\cdot)\) \(\chi_{2527}(122,\cdot)\) \(\chi_{2527}(145,\cdot)\) \(\chi_{2527}(255,\cdot)\) \(\chi_{2527}(278,\cdot)\) \(\chi_{2527}(388,\cdot)\) \(\chi_{2527}(411,\cdot)\) \(\chi_{2527}(521,\cdot)\) \(\chi_{2527}(544,\cdot)\) \(\chi_{2527}(677,\cdot)\) \(\chi_{2527}(787,\cdot)\) \(\chi_{2527}(810,\cdot)\) \(\chi_{2527}(920,\cdot)\) \(\chi_{2527}(943,\cdot)\) \(\chi_{2527}(1053,\cdot)\) \(\chi_{2527}(1076,\cdot)\) \(\chi_{2527}(1186,\cdot)\) \(\chi_{2527}(1209,\cdot)\) \(\chi_{2527}(1319,\cdot)\) \(\chi_{2527}(1342,\cdot)\) \(\chi_{2527}(1452,\cdot)\) \(\chi_{2527}(1475,\cdot)\) \(\chi_{2527}(1585,\cdot)\) \(\chi_{2527}(1608,\cdot)\) \(\chi_{2527}(1718,\cdot)\) \(\chi_{2527}(1741,\cdot)\) \(\chi_{2527}(1851,\cdot)\) \(\chi_{2527}(1984,\cdot)\) \(\chi_{2527}(2007,\cdot)\) \(\chi_{2527}(2117,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((1445,1807)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{77}{114}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 2527 }(544, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{7}{114}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{23}{57}\right)\) |