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 \(\chi_{2527}(866,\cdot)\) | 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
\((1445,1807)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{47}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 5054 }(3393, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{53}{114}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{89}{114}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{13}{38}\right)\) |