Basic properties
| Modulus: | \(6040\) | |
| Conductor: | \(755\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(300\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{755}(233,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6040.fl
\(\chi_{6040}(233,\cdot)\) \(\chi_{6040}(257,\cdot)\) \(\chi_{6040}(297,\cdot)\) \(\chi_{6040}(337,\cdot)\) \(\chi_{6040}(353,\cdot)\) \(\chi_{6040}(417,\cdot)\) \(\chi_{6040}(593,\cdot)\) \(\chi_{6040}(617,\cdot)\) \(\chi_{6040}(697,\cdot)\) \(\chi_{6040}(713,\cdot)\) \(\chi_{6040}(737,\cdot)\) \(\chi_{6040}(857,\cdot)\) \(\chi_{6040}(913,\cdot)\) \(\chi_{6040}(977,\cdot)\) \(\chi_{6040}(1017,\cdot)\) \(\chi_{6040}(1113,\cdot)\) \(\chi_{6040}(1153,\cdot)\) \(\chi_{6040}(1177,\cdot)\) \(\chi_{6040}(1297,\cdot)\) \(\chi_{6040}(1337,\cdot)\) \(\chi_{6040}(1473,\cdot)\) \(\chi_{6040}(1673,\cdot)\) \(\chi_{6040}(1713,\cdot)\) \(\chi_{6040}(1873,\cdot)\) \(\chi_{6040}(1953,\cdot)\) \(\chi_{6040}(1977,\cdot)\) \(\chi_{6040}(1993,\cdot)\) \(\chi_{6040}(2017,\cdot)\) \(\chi_{6040}(2097,\cdot)\) \(\chi_{6040}(2177,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{300})$ |
| Fixed field: | Number field defined by a degree 300 polynomial (not computed) |
Values on generators
\((1511,3021,2417,761)\) → \((1,1,-i,e\left(\frac{121}{150}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6040 }(233, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{239}{300}\right)\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{62}{75}\right)\) | \(e\left(\frac{97}{300}\right)\) | \(e\left(\frac{161}{300}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{29}{75}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{77}{100}\right)\) |