Basic properties
| Modulus: | \(6040\) | |
| Conductor: | \(6040\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(300\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6040.fk
\(\chi_{6040}(43,\cdot)\) \(\chi_{6040}(187,\cdot)\) \(\chi_{6040}(267,\cdot)\) \(\chi_{6040}(307,\cdot)\) \(\chi_{6040}(323,\cdot)\) \(\chi_{6040}(347,\cdot)\) \(\chi_{6040}(643,\cdot)\) \(\chi_{6040}(707,\cdot)\) \(\chi_{6040}(843,\cdot)\) \(\chi_{6040}(923,\cdot)\) \(\chi_{6040}(1003,\cdot)\) \(\chi_{6040}(1027,\cdot)\) \(\chi_{6040}(1043,\cdot)\) \(\chi_{6040}(1067,\cdot)\) \(\chi_{6040}(1147,\cdot)\) \(\chi_{6040}(1307,\cdot)\) \(\chi_{6040}(1347,\cdot)\) \(\chi_{6040}(1547,\cdot)\) \(\chi_{6040}(1683,\cdot)\) \(\chi_{6040}(1723,\cdot)\) \(\chi_{6040}(1843,\cdot)\) \(\chi_{6040}(1867,\cdot)\) \(\chi_{6040}(1907,\cdot)\) \(\chi_{6040}(2003,\cdot)\) \(\chi_{6040}(2043,\cdot)\) \(\chi_{6040}(2107,\cdot)\) \(\chi_{6040}(2163,\cdot)\) \(\chi_{6040}(2283,\cdot)\) \(\chi_{6040}(2307,\cdot)\) \(\chi_{6040}(2323,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{300})$ |
| Fixed field: | Number field defined by a degree 300 polynomial (not computed) |
Values on generators
\((1511,3021,2417,761)\) → \((-1,-1,-i,e\left(\frac{4}{75}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6040 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{100}\right)\) | \(e\left(\frac{247}{300}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{1}{75}\right)\) | \(e\left(\frac{281}{300}\right)\) | \(e\left(\frac{253}{300}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{59}{150}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{71}{100}\right)\) |