Basic properties
| Modulus: | \(6008\) | |
| Conductor: | \(6008\) | 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 6008.br
\(\chi_{6008}(61,\cdot)\) \(\chi_{6008}(197,\cdot)\) \(\chi_{6008}(229,\cdot)\) \(\chi_{6008}(405,\cdot)\) \(\chi_{6008}(637,\cdot)\) \(\chi_{6008}(717,\cdot)\) \(\chi_{6008}(837,\cdot)\) \(\chi_{6008}(941,\cdot)\) \(\chi_{6008}(1125,\cdot)\) \(\chi_{6008}(1373,\cdot)\) \(\chi_{6008}(1621,\cdot)\) \(\chi_{6008}(1901,\cdot)\) \(\chi_{6008}(1973,\cdot)\) \(\chi_{6008}(2133,\cdot)\) \(\chi_{6008}(2141,\cdot)\) \(\chi_{6008}(2285,\cdot)\) \(\chi_{6008}(2437,\cdot)\) \(\chi_{6008}(2453,\cdot)\) \(\chi_{6008}(2549,\cdot)\) \(\chi_{6008}(2781,\cdot)\) \(\chi_{6008}(3125,\cdot)\) \(\chi_{6008}(3277,\cdot)\) \(\chi_{6008}(3885,\cdot)\) \(\chi_{6008}(3949,\cdot)\) \(\chi_{6008}(4133,\cdot)\) \(\chi_{6008}(4613,\cdot)\) \(\chi_{6008}(4637,\cdot)\) \(\chi_{6008}(4669,\cdot)\) \(\chi_{6008}(4805,\cdot)\) \(\chi_{6008}(4813,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\((1503,3005,1505)\) → \((1,-1,e\left(\frac{58}{75}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6008 }(2285, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{150}\right)\) | \(e\left(\frac{101}{150}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{41}{75}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{53}{150}\right)\) | \(e\left(\frac{71}{75}\right)\) | \(e\left(\frac{32}{75}\right)\) | \(e\left(\frac{113}{150}\right)\) | \(e\left(\frac{107}{150}\right)\) |