Basic properties
Modulus: | \(5054\) | |
Conductor: | \(2527\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2527}(444,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5054.by
\(\chi_{5054}(45,\cdot)\) \(\chi_{5054}(201,\cdot)\) \(\chi_{5054}(311,\cdot)\) \(\chi_{5054}(467,\cdot)\) \(\chi_{5054}(577,\cdot)\) \(\chi_{5054}(733,\cdot)\) \(\chi_{5054}(843,\cdot)\) \(\chi_{5054}(999,\cdot)\) \(\chi_{5054}(1109,\cdot)\) \(\chi_{5054}(1265,\cdot)\) \(\chi_{5054}(1531,\cdot)\) \(\chi_{5054}(1641,\cdot)\) \(\chi_{5054}(1797,\cdot)\) \(\chi_{5054}(1907,\cdot)\) \(\chi_{5054}(2063,\cdot)\) \(\chi_{5054}(2173,\cdot)\) \(\chi_{5054}(2329,\cdot)\) \(\chi_{5054}(2439,\cdot)\) \(\chi_{5054}(2705,\cdot)\) \(\chi_{5054}(2861,\cdot)\) \(\chi_{5054}(2971,\cdot)\) \(\chi_{5054}(3127,\cdot)\) \(\chi_{5054}(3237,\cdot)\) \(\chi_{5054}(3393,\cdot)\) \(\chi_{5054}(3503,\cdot)\) \(\chi_{5054}(3659,\cdot)\) \(\chi_{5054}(3769,\cdot)\) \(\chi_{5054}(3925,\cdot)\) \(\chi_{5054}(4035,\cdot)\) \(\chi_{5054}(4191,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((1445,1807)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{31}{57}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 5054 }(2971, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{1}{114}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{8}{57}\right)\) | \(e\left(\frac{49}{114}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{11}{38}\right)\) |