Basic properties
| Modulus: | \(6040\) | |
| Conductor: | \(6040\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(150\) | 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.fa
\(\chi_{6040}(69,\cdot)\) \(\chi_{6040}(349,\cdot)\) \(\chi_{6040}(589,\cdot)\) \(\chi_{6040}(629,\cdot)\) \(\chi_{6040}(749,\cdot)\) \(\chi_{6040}(789,\cdot)\) \(\chi_{6040}(829,\cdot)\) \(\chi_{6040}(949,\cdot)\) \(\chi_{6040}(1229,\cdot)\) \(\chi_{6040}(1549,\cdot)\) \(\chi_{6040}(1749,\cdot)\) \(\chi_{6040}(1829,\cdot)\) \(\chi_{6040}(1909,\cdot)\) \(\chi_{6040}(1949,\cdot)\) \(\chi_{6040}(2589,\cdot)\) \(\chi_{6040}(2629,\cdot)\) \(\chi_{6040}(2749,\cdot)\) \(\chi_{6040}(2909,\cdot)\) \(\chi_{6040}(2949,\cdot)\) \(\chi_{6040}(3069,\cdot)\) \(\chi_{6040}(3189,\cdot)\) \(\chi_{6040}(3229,\cdot)\) \(\chi_{6040}(3309,\cdot)\) \(\chi_{6040}(3509,\cdot)\) \(\chi_{6040}(3589,\cdot)\) \(\chi_{6040}(3629,\cdot)\) \(\chi_{6040}(3669,\cdot)\) \(\chi_{6040}(4029,\cdot)\) \(\chi_{6040}(4349,\cdot)\) \(\chi_{6040}(4389,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\((1511,3021,2417,761)\) → \((1,-1,-1,e\left(\frac{23}{75}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6040 }(69, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{7}{150}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{49}{150}\right)\) | \(e\left(\frac{43}{75}\right)\) | \(e\left(\frac{43}{150}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{133}{150}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{13}{25}\right)\) |