Basic properties
Modulus: | \(2888\) | |
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: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2888.bg
\(\chi_{2888}(49,\cdot)\) \(\chi_{2888}(121,\cdot)\) \(\chi_{2888}(201,\cdot)\) \(\chi_{2888}(273,\cdot)\) \(\chi_{2888}(353,\cdot)\) \(\chi_{2888}(425,\cdot)\) \(\chi_{2888}(505,\cdot)\) \(\chi_{2888}(577,\cdot)\) \(\chi_{2888}(657,\cdot)\) \(\chi_{2888}(729,\cdot)\) \(\chi_{2888}(809,\cdot)\) \(\chi_{2888}(881,\cdot)\) \(\chi_{2888}(961,\cdot)\) \(\chi_{2888}(1033,\cdot)\) \(\chi_{2888}(1113,\cdot)\) \(\chi_{2888}(1185,\cdot)\) \(\chi_{2888}(1265,\cdot)\) \(\chi_{2888}(1337,\cdot)\) \(\chi_{2888}(1417,\cdot)\) \(\chi_{2888}(1489,\cdot)\) \(\chi_{2888}(1569,\cdot)\) \(\chi_{2888}(1641,\cdot)\) \(\chi_{2888}(1721,\cdot)\) \(\chi_{2888}(1793,\cdot)\) \(\chi_{2888}(1945,\cdot)\) \(\chi_{2888}(2025,\cdot)\) \(\chi_{2888}(2177,\cdot)\) \(\chi_{2888}(2249,\cdot)\) \(\chi_{2888}(2329,\cdot)\) \(\chi_{2888}(2401,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((2167,1445,2529)\) → \((1,1,e\left(\frac{50}{57}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 2888 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{4}{57}\right)\) |