Basic properties
| Modulus: | \(6040\) | |
| Conductor: | \(3020\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(300\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3020}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6040.fg
\(\chi_{6040}(47,\cdot)\) \(\chi_{6040}(103,\cdot)\) \(\chi_{6040}(287,\cdot)\) \(\chi_{6040}(327,\cdot)\) \(\chi_{6040}(423,\cdot)\) \(\chi_{6040}(447,\cdot)\) \(\chi_{6040}(463,\cdot)\) \(\chi_{6040}(487,\cdot)\) \(\chi_{6040}(527,\cdot)\) \(\chi_{6040}(543,\cdot)\) \(\chi_{6040}(647,\cdot)\) \(\chi_{6040}(703,\cdot)\) \(\chi_{6040}(743,\cdot)\) \(\chi_{6040}(927,\cdot)\) \(\chi_{6040}(943,\cdot)\) \(\chi_{6040}(1247,\cdot)\) \(\chi_{6040}(1263,\cdot)\) \(\chi_{6040}(1303,\cdot)\) \(\chi_{6040}(1447,\cdot)\) \(\chi_{6040}(1503,\cdot)\) \(\chi_{6040}(1527,\cdot)\) \(\chi_{6040}(1607,\cdot)\) \(\chi_{6040}(1647,\cdot)\) \(\chi_{6040}(1703,\cdot)\) \(\chi_{6040}(1823,\cdot)\) \(\chi_{6040}(2063,\cdot)\) \(\chi_{6040}(2183,\cdot)\) \(\chi_{6040}(2287,\cdot)\) \(\chi_{6040}(2327,\cdot)\) \(\chi_{6040}(2447,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{300})$ |
| Fixed field: | Number field defined by a degree 300 polynomial (not computed) |
Values on generators
\((1511,3021,2417,761)\) → \((-1,1,i,e\left(\frac{13}{75}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6040 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{109}{300}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{119}{150}\right)\) | \(e\left(\frac{257}{300}\right)\) | \(e\left(\frac{91}{300}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{49}{75}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{87}{100}\right)\) |