Basic properties
| Modulus: | \(5776\) | |
| Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(57\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{361}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5776.bs
\(\chi_{5776}(49,\cdot)\) \(\chi_{5776}(273,\cdot)\) \(\chi_{5776}(353,\cdot)\) \(\chi_{5776}(577,\cdot)\) \(\chi_{5776}(657,\cdot)\) \(\chi_{5776}(881,\cdot)\) \(\chi_{5776}(961,\cdot)\) \(\chi_{5776}(1185,\cdot)\) \(\chi_{5776}(1265,\cdot)\) \(\chi_{5776}(1489,\cdot)\) \(\chi_{5776}(1569,\cdot)\) \(\chi_{5776}(1793,\cdot)\) \(\chi_{5776}(2177,\cdot)\) \(\chi_{5776}(2401,\cdot)\) \(\chi_{5776}(2481,\cdot)\) \(\chi_{5776}(2705,\cdot)\) \(\chi_{5776}(2785,\cdot)\) \(\chi_{5776}(3009,\cdot)\) \(\chi_{5776}(3089,\cdot)\) \(\chi_{5776}(3313,\cdot)\) \(\chi_{5776}(3393,\cdot)\) \(\chi_{5776}(3617,\cdot)\) \(\chi_{5776}(3697,\cdot)\) \(\chi_{5776}(3921,\cdot)\) \(\chi_{5776}(4001,\cdot)\) \(\chi_{5776}(4225,\cdot)\) \(\chi_{5776}(4305,\cdot)\) \(\chi_{5776}(4529,\cdot)\) \(\chi_{5776}(4609,\cdot)\) \(\chi_{5776}(4833,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((5055,1445,2529)\) → \((1,1,e\left(\frac{50}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 5776 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{4}{57}\right)\) |