Basic properties
| Modulus: | \(6040\) | |
| Conductor: | \(3020\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(150\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3020}(199,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6040.ey
\(\chi_{6040}(199,\cdot)\) \(\chi_{6040}(559,\cdot)\) \(\chi_{6040}(599,\cdot)\) \(\chi_{6040}(639,\cdot)\) \(\chi_{6040}(719,\cdot)\) \(\chi_{6040}(919,\cdot)\) \(\chi_{6040}(999,\cdot)\) \(\chi_{6040}(1039,\cdot)\) \(\chi_{6040}(1159,\cdot)\) \(\chi_{6040}(1279,\cdot)\) \(\chi_{6040}(1319,\cdot)\) \(\chi_{6040}(1479,\cdot)\) \(\chi_{6040}(1599,\cdot)\) \(\chi_{6040}(1639,\cdot)\) \(\chi_{6040}(2279,\cdot)\) \(\chi_{6040}(2319,\cdot)\) \(\chi_{6040}(2399,\cdot)\) \(\chi_{6040}(2479,\cdot)\) \(\chi_{6040}(2679,\cdot)\) \(\chi_{6040}(2999,\cdot)\) \(\chi_{6040}(3279,\cdot)\) \(\chi_{6040}(3399,\cdot)\) \(\chi_{6040}(3439,\cdot)\) \(\chi_{6040}(3479,\cdot)\) \(\chi_{6040}(3599,\cdot)\) \(\chi_{6040}(3639,\cdot)\) \(\chi_{6040}(3879,\cdot)\) \(\chi_{6040}(4159,\cdot)\) \(\chi_{6040}(4279,\cdot)\) \(\chi_{6040}(4519,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\((1511,3021,2417,761)\) → \((-1,1,-1,e\left(\frac{61}{150}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6040 }(199, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{37}{150}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{109}{150}\right)\) | \(e\left(\frac{13}{75}\right)\) | \(e\left(\frac{13}{150}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{14}{75}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{41}{50}\right)\) |