Basic properties
Modulus: | \(6040\) | |
Conductor: | \(755\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(150\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{755}(569,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6040.et
\(\chi_{6040}(49,\cdot)\) \(\chi_{6040}(169,\cdot)\) \(\chi_{6040}(209,\cdot)\) \(\chi_{6040}(289,\cdot)\) \(\chi_{6040}(489,\cdot)\) \(\chi_{6040}(569,\cdot)\) \(\chi_{6040}(609,\cdot)\) \(\chi_{6040}(649,\cdot)\) \(\chi_{6040}(1009,\cdot)\) \(\chi_{6040}(1329,\cdot)\) \(\chi_{6040}(1369,\cdot)\) \(\chi_{6040}(1449,\cdot)\) \(\chi_{6040}(1609,\cdot)\) \(\chi_{6040}(1649,\cdot)\) \(\chi_{6040}(1849,\cdot)\) \(\chi_{6040}(2169,\cdot)\) \(\chi_{6040}(2209,\cdot)\) \(\chi_{6040}(2409,\cdot)\) \(\chi_{6040}(2609,\cdot)\) \(\chi_{6040}(2729,\cdot)\) \(\chi_{6040}(2969,\cdot)\) \(\chi_{6040}(3089,\cdot)\) \(\chi_{6040}(3369,\cdot)\) \(\chi_{6040}(3609,\cdot)\) \(\chi_{6040}(3649,\cdot)\) \(\chi_{6040}(3769,\cdot)\) \(\chi_{6040}(3809,\cdot)\) \(\chi_{6040}(3849,\cdot)\) \(\chi_{6040}(3969,\cdot)\) \(\chi_{6040}(4249,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{75})$ |
Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\((1511,3021,2417,761)\) → \((1,1,-1,e\left(\frac{52}{75}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 6040 }(569, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{50}\right)\) | \(e\left(\frac{143}{150}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{13}{75}\right)\) | \(e\left(\frac{139}{150}\right)\) | \(e\left(\frac{107}{150}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{46}{75}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{49}{50}\right)\) |