Basic properties
| Modulus: | \(4034\) | |
| Conductor: | \(2017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2017}(93,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4034.z
\(\chi_{4034}(93,\cdot)\) \(\chi_{4034}(121,\cdot)\) \(\chi_{4034}(215,\cdot)\) \(\chi_{4034}(545,\cdot)\) \(\chi_{4034}(585,\cdot)\) \(\chi_{4034}(611,\cdot)\) \(\chi_{4034}(631,\cdot)\) \(\chi_{4034}(665,\cdot)\) \(\chi_{4034}(683,\cdot)\) \(\chi_{4034}(803,\cdot)\) \(\chi_{4034}(825,\cdot)\) \(\chi_{4034}(849,\cdot)\) \(\chi_{4034}(887,\cdot)\) \(\chi_{4034}(1119,\cdot)\) \(\chi_{4034}(1121,\cdot)\) \(\chi_{4034}(1205,\cdot)\) \(\chi_{4034}(1285,\cdot)\) \(\chi_{4034}(1295,\cdot)\) \(\chi_{4034}(1455,\cdot)\) \(\chi_{4034}(1491,\cdot)\) \(\chi_{4034}(1495,\cdot)\) \(\chi_{4034}(1515,\cdot)\) \(\chi_{4034}(1841,\cdot)\) \(\chi_{4034}(1967,\cdot)\) \(\chi_{4034}(2183,\cdot)\) \(\chi_{4034}(2413,\cdot)\) \(\chi_{4034}(2527,\cdot)\) \(\chi_{4034}(2699,\cdot)\) \(\chi_{4034}(2715,\cdot)\) \(\chi_{4034}(2927,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{85}{126}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4034 }(93, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{65}{126}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{101}{126}\right)\) | \(e\left(\frac{61}{63}\right)\) |