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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2527.bx
\(\chi_{2527}(45,\cdot)\) \(\chi_{2527}(178,\cdot)\) \(\chi_{2527}(201,\cdot)\) \(\chi_{2527}(311,\cdot)\) \(\chi_{2527}(334,\cdot)\) \(\chi_{2527}(444,\cdot)\) \(\chi_{2527}(467,\cdot)\) \(\chi_{2527}(577,\cdot)\) \(\chi_{2527}(600,\cdot)\) \(\chi_{2527}(710,\cdot)\) \(\chi_{2527}(733,\cdot)\) \(\chi_{2527}(843,\cdot)\) \(\chi_{2527}(866,\cdot)\) \(\chi_{2527}(976,\cdot)\) \(\chi_{2527}(999,\cdot)\) \(\chi_{2527}(1109,\cdot)\) \(\chi_{2527}(1132,\cdot)\) \(\chi_{2527}(1242,\cdot)\) \(\chi_{2527}(1265,\cdot)\) \(\chi_{2527}(1398,\cdot)\) \(\chi_{2527}(1508,\cdot)\) \(\chi_{2527}(1531,\cdot)\) \(\chi_{2527}(1641,\cdot)\) \(\chi_{2527}(1664,\cdot)\) \(\chi_{2527}(1774,\cdot)\) \(\chi_{2527}(1797,\cdot)\) \(\chi_{2527}(1907,\cdot)\) \(\chi_{2527}(1930,\cdot)\) \(\chi_{2527}(2040,\cdot)\) \(\chi_{2527}(2063,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((1445,1807)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{14}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2527 }(467, a) \) | \(-1\) | \(1\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{17}{114}\right)\) | \(e\left(\frac{101}{114}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{7}{114}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{91}{114}\right)\) |