Basic properties
Modulus: | \(5776\) | |
Conductor: | \(2888\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2888}(1565,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5776.bx
\(\chi_{5776}(121,\cdot)\) \(\chi_{5776}(201,\cdot)\) \(\chi_{5776}(425,\cdot)\) \(\chi_{5776}(505,\cdot)\) \(\chi_{5776}(729,\cdot)\) \(\chi_{5776}(809,\cdot)\) \(\chi_{5776}(1033,\cdot)\) \(\chi_{5776}(1113,\cdot)\) \(\chi_{5776}(1337,\cdot)\) \(\chi_{5776}(1417,\cdot)\) \(\chi_{5776}(1641,\cdot)\) \(\chi_{5776}(1721,\cdot)\) \(\chi_{5776}(1945,\cdot)\) \(\chi_{5776}(2025,\cdot)\) \(\chi_{5776}(2249,\cdot)\) \(\chi_{5776}(2329,\cdot)\) \(\chi_{5776}(2553,\cdot)\) \(\chi_{5776}(2633,\cdot)\) \(\chi_{5776}(2857,\cdot)\) \(\chi_{5776}(2937,\cdot)\) \(\chi_{5776}(3161,\cdot)\) \(\chi_{5776}(3241,\cdot)\) \(\chi_{5776}(3465,\cdot)\) \(\chi_{5776}(3545,\cdot)\) \(\chi_{5776}(3769,\cdot)\) \(\chi_{5776}(3849,\cdot)\) \(\chi_{5776}(4073,\cdot)\) \(\chi_{5776}(4153,\cdot)\) \(\chi_{5776}(4377,\cdot)\) \(\chi_{5776}(4457,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((5055,1445,2529)\) → \((1,-1,e\left(\frac{34}{57}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 5776 }(121, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{114}\right)\) | \(e\left(\frac{101}{114}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{101}{114}\right)\) | \(e\left(\frac{5}{57}\right)\) |