Basic properties
Modulus: | \(2057\) | |
Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{121}(69,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2057.y
\(\chi_{2057}(69,\cdot)\) \(\chi_{2057}(86,\cdot)\) \(\chi_{2057}(103,\cdot)\) \(\chi_{2057}(137,\cdot)\) \(\chi_{2057}(256,\cdot)\) \(\chi_{2057}(273,\cdot)\) \(\chi_{2057}(290,\cdot)\) \(\chi_{2057}(324,\cdot)\) \(\chi_{2057}(443,\cdot)\) \(\chi_{2057}(460,\cdot)\) \(\chi_{2057}(477,\cdot)\) \(\chi_{2057}(630,\cdot)\) \(\chi_{2057}(647,\cdot)\) \(\chi_{2057}(664,\cdot)\) \(\chi_{2057}(698,\cdot)\) \(\chi_{2057}(817,\cdot)\) \(\chi_{2057}(834,\cdot)\) \(\chi_{2057}(851,\cdot)\) \(\chi_{2057}(885,\cdot)\) \(\chi_{2057}(1004,\cdot)\) \(\chi_{2057}(1021,\cdot)\) \(\chi_{2057}(1038,\cdot)\) \(\chi_{2057}(1072,\cdot)\) \(\chi_{2057}(1191,\cdot)\) \(\chi_{2057}(1208,\cdot)\) \(\chi_{2057}(1225,\cdot)\) \(\chi_{2057}(1259,\cdot)\) \(\chi_{2057}(1378,\cdot)\) \(\chi_{2057}(1395,\cdot)\) \(\chi_{2057}(1446,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((970,122)\) → \((e\left(\frac{24}{55}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 2057 }(69, a) \) | \(1\) | \(1\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) |