Basic properties
| Modulus: | \(6046\) | |
| Conductor: | \(3023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1511\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3023}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6046.c
\(\chi_{6046}(3,\cdot)\) \(\chi_{6046}(7,\cdot)\) \(\chi_{6046}(9,\cdot)\) \(\chi_{6046}(19,\cdot)\) \(\chi_{6046}(21,\cdot)\) \(\chi_{6046}(23,\cdot)\) \(\chi_{6046}(25,\cdot)\) \(\chi_{6046}(27,\cdot)\) \(\chi_{6046}(29,\cdot)\) \(\chi_{6046}(37,\cdot)\) \(\chi_{6046}(47,\cdot)\) \(\chi_{6046}(49,\cdot)\) \(\chi_{6046}(55,\cdot)\) \(\chi_{6046}(57,\cdot)\) \(\chi_{6046}(59,\cdot)\) \(\chi_{6046}(61,\cdot)\) \(\chi_{6046}(63,\cdot)\) \(\chi_{6046}(65,\cdot)\) \(\chi_{6046}(67,\cdot)\) \(\chi_{6046}(69,\cdot)\) \(\chi_{6046}(71,\cdot)\) \(\chi_{6046}(75,\cdot)\) \(\chi_{6046}(81,\cdot)\) \(\chi_{6046}(83,\cdot)\) \(\chi_{6046}(85,\cdot)\) \(\chi_{6046}(87,\cdot)\) \(\chi_{6046}(97,\cdot)\) \(\chi_{6046}(109,\cdot)\) \(\chi_{6046}(111,\cdot)\) \(\chi_{6046}(113,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1511})$ |
| Fixed field: | Number field defined by a degree 1511 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{506}{1511}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6046 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{1354}{1511}\right)\) | \(e\left(\frac{506}{1511}\right)\) | \(e\left(\frac{1402}{1511}\right)\) | \(e\left(\frac{1197}{1511}\right)\) | \(e\left(\frac{322}{1511}\right)\) | \(e\left(\frac{740}{1511}\right)\) | \(e\left(\frac{349}{1511}\right)\) | \(e\left(\frac{1031}{1511}\right)\) | \(e\left(\frac{1311}{1511}\right)\) | \(e\left(\frac{1245}{1511}\right)\) |