Basic properties
Modulus: | \(2527\) | |
Conductor: | \(2527\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(57\) | 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.bm
\(\chi_{2527}(39,\cdot)\) \(\chi_{2527}(58,\cdot)\) \(\chi_{2527}(172,\cdot)\) \(\chi_{2527}(191,\cdot)\) \(\chi_{2527}(305,\cdot)\) \(\chi_{2527}(324,\cdot)\) \(\chi_{2527}(438,\cdot)\) \(\chi_{2527}(457,\cdot)\) \(\chi_{2527}(571,\cdot)\) \(\chi_{2527}(590,\cdot)\) \(\chi_{2527}(704,\cdot)\) \(\chi_{2527}(837,\cdot)\) \(\chi_{2527}(856,\cdot)\) \(\chi_{2527}(970,\cdot)\) \(\chi_{2527}(989,\cdot)\) \(\chi_{2527}(1103,\cdot)\) \(\chi_{2527}(1122,\cdot)\) \(\chi_{2527}(1236,\cdot)\) \(\chi_{2527}(1255,\cdot)\) \(\chi_{2527}(1369,\cdot)\) \(\chi_{2527}(1388,\cdot)\) \(\chi_{2527}(1502,\cdot)\) \(\chi_{2527}(1521,\cdot)\) \(\chi_{2527}(1635,\cdot)\) \(\chi_{2527}(1654,\cdot)\) \(\chi_{2527}(1768,\cdot)\) \(\chi_{2527}(1787,\cdot)\) \(\chi_{2527}(1901,\cdot)\) \(\chi_{2527}(1920,\cdot)\) \(\chi_{2527}(2034,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((1445,1807)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{10}{19}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 2527 }(571, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{31}{57}\right)\) |