Basic properties
| Modulus: | \(6040\) | |
| Conductor: | \(604\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(150\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{604}(71,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6040.fe
\(\chi_{6040}(71,\cdot)\) \(\chi_{6040}(111,\cdot)\) \(\chi_{6040}(271,\cdot)\) \(\chi_{6040}(391,\cdot)\) \(\chi_{6040}(431,\cdot)\) \(\chi_{6040}(1071,\cdot)\) \(\chi_{6040}(1111,\cdot)\) \(\chi_{6040}(1191,\cdot)\) \(\chi_{6040}(1271,\cdot)\) \(\chi_{6040}(1471,\cdot)\) \(\chi_{6040}(1791,\cdot)\) \(\chi_{6040}(2071,\cdot)\) \(\chi_{6040}(2191,\cdot)\) \(\chi_{6040}(2231,\cdot)\) \(\chi_{6040}(2271,\cdot)\) \(\chi_{6040}(2391,\cdot)\) \(\chi_{6040}(2431,\cdot)\) \(\chi_{6040}(2671,\cdot)\) \(\chi_{6040}(2951,\cdot)\) \(\chi_{6040}(3071,\cdot)\) \(\chi_{6040}(3311,\cdot)\) \(\chi_{6040}(3431,\cdot)\) \(\chi_{6040}(3631,\cdot)\) \(\chi_{6040}(3831,\cdot)\) \(\chi_{6040}(3871,\cdot)\) \(\chi_{6040}(4191,\cdot)\) \(\chi_{6040}(4391,\cdot)\) \(\chi_{6040}(4431,\cdot)\) \(\chi_{6040}(4591,\cdot)\) \(\chi_{6040}(4671,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\((1511,3021,2417,761)\) → \((-1,1,1,e\left(\frac{17}{150}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6040 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{7}{75}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{23}{150}\right)\) | \(e\left(\frac{97}{150}\right)\) | \(e\left(\frac{43}{75}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{58}{75}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{25}\right)\) |