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 \(\chi_{2527}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5054.bt
\(\chi_{5054}(37,\cdot)\) \(\chi_{5054}(151,\cdot)\) \(\chi_{5054}(303,\cdot)\) \(\chi_{5054}(417,\cdot)\) \(\chi_{5054}(569,\cdot)\) \(\chi_{5054}(683,\cdot)\) \(\chi_{5054}(835,\cdot)\) \(\chi_{5054}(949,\cdot)\) \(\chi_{5054}(1101,\cdot)\) \(\chi_{5054}(1215,\cdot)\) \(\chi_{5054}(1367,\cdot)\) \(\chi_{5054}(1481,\cdot)\) \(\chi_{5054}(1633,\cdot)\) \(\chi_{5054}(1747,\cdot)\) \(\chi_{5054}(1899,\cdot)\) \(\chi_{5054}(2013,\cdot)\) \(\chi_{5054}(2279,\cdot)\) \(\chi_{5054}(2431,\cdot)\) \(\chi_{5054}(2545,\cdot)\) \(\chi_{5054}(2697,\cdot)\) \(\chi_{5054}(2811,\cdot)\) \(\chi_{5054}(2963,\cdot)\) \(\chi_{5054}(3077,\cdot)\) \(\chi_{5054}(3229,\cdot)\) \(\chi_{5054}(3343,\cdot)\) \(\chi_{5054}(3495,\cdot)\) \(\chi_{5054}(3761,\cdot)\) \(\chi_{5054}(3875,\cdot)\) \(\chi_{5054}(4027,\cdot)\) \(\chi_{5054}(4141,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((1445,1807)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{5}{38}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 5054 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{114}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{33}{38}\right)\) |