Basic properties
| Modulus: | \(6042\) | |
| Conductor: | \(3021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(468\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3021}(497,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.cs
\(\chi_{6042}(41,\cdot)\) \(\chi_{6042}(71,\cdot)\) \(\chi_{6042}(167,\cdot)\) \(\chi_{6042}(173,\cdot)\) \(\chi_{6042}(185,\cdot)\) \(\chi_{6042}(257,\cdot)\) \(\chi_{6042}(287,\cdot)\) \(\chi_{6042}(299,\cdot)\) \(\chi_{6042}(383,\cdot)\) \(\chi_{6042}(485,\cdot)\) \(\chi_{6042}(497,\cdot)\) \(\chi_{6042}(509,\cdot)\) \(\chi_{6042}(527,\cdot)\) \(\chi_{6042}(641,\cdot)\) \(\chi_{6042}(737,\cdot)\) \(\chi_{6042}(773,\cdot)\) \(\chi_{6042}(827,\cdot)\) \(\chi_{6042}(851,\cdot)\) \(\chi_{6042}(869,\cdot)\) \(\chi_{6042}(887,\cdot)\) \(\chi_{6042}(1055,\cdot)\) \(\chi_{6042}(1079,\cdot)\) \(\chi_{6042}(1115,\cdot)\) \(\chi_{6042}(1169,\cdot)\) \(\chi_{6042}(1193,\cdot)\) \(\chi_{6042}(1199,\cdot)\) \(\chi_{6042}(1211,\cdot)\) \(\chi_{6042}(1307,\cdot)\) \(\chi_{6042}(1313,\cdot)\) \(\chi_{6042}(1343,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{468})$ |
| Fixed field: | Number field defined by a degree 468 polynomial (not computed) |
Values on generators
\((2015,4771,2281)\) → \((-1,e\left(\frac{13}{18}\right),e\left(\frac{49}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6042 }(497, a) \) | \(-1\) | \(1\) | \(e\left(\frac{161}{468}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{53}{234}\right)\) | \(e\left(\frac{17}{117}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{161}{234}\right)\) | \(e\left(\frac{29}{234}\right)\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{407}{468}\right)\) |