Basic properties
| Modulus: | \(6023\) | |
| Conductor: | \(6023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(474\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6023.ba
\(\chi_{6023}(31,\cdot)\) \(\chi_{6023}(65,\cdot)\) \(\chi_{6023}(103,\cdot)\) \(\chi_{6023}(145,\cdot)\) \(\chi_{6023}(160,\cdot)\) \(\chi_{6023}(179,\cdot)\) \(\chi_{6023}(221,\cdot)\) \(\chi_{6023}(240,\cdot)\) \(\chi_{6023}(259,\cdot)\) \(\chi_{6023}(278,\cdot)\) \(\chi_{6023}(430,\cdot)\) \(\chi_{6023}(540,\cdot)\) \(\chi_{6023}(544,\cdot)\) \(\chi_{6023}(597,\cdot)\) \(\chi_{6023}(658,\cdot)\) \(\chi_{6023}(677,\cdot)\) \(\chi_{6023}(715,\cdot)\) \(\chi_{6023}(734,\cdot)\) \(\chi_{6023}(810,\cdot)\) \(\chi_{6023}(962,\cdot)\) \(\chi_{6023}(1000,\cdot)\) \(\chi_{6023}(1072,\cdot)\) \(\chi_{6023}(1133,\cdot)\) \(\chi_{6023}(1186,\cdot)\) \(\chi_{6023}(1224,\cdot)\) \(\chi_{6023}(1228,\cdot)\) \(\chi_{6023}(1243,\cdot)\) \(\chi_{6023}(1262,\cdot)\) \(\chi_{6023}(1304,\cdot)\) \(\chi_{6023}(1319,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{237})$ |
| Fixed field: | Number field defined by a degree 474 polynomial (not computed) |
Values on generators
\((952,5074)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{52}{79}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6023 }(6016, a) \) | \(-1\) | \(1\) | \(e\left(\frac{233}{474}\right)\) | \(e\left(\frac{347}{474}\right)\) | \(e\left(\frac{233}{237}\right)\) | \(e\left(\frac{67}{237}\right)\) | \(e\left(\frac{53}{237}\right)\) | \(e\left(\frac{72}{79}\right)\) | \(e\left(\frac{75}{158}\right)\) | \(e\left(\frac{110}{237}\right)\) | \(e\left(\frac{367}{474}\right)\) | \(e\left(\frac{45}{79}\right)\) |