Basic properties
Modulus: | \(6008\) | |
Conductor: | \(3004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(150\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{3004}(2775,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6008.bv
\(\chi_{6008}(223,\cdot)\) \(\chi_{6008}(455,\cdot)\) \(\chi_{6008}(551,\cdot)\) \(\chi_{6008}(567,\cdot)\) \(\chi_{6008}(719,\cdot)\) \(\chi_{6008}(863,\cdot)\) \(\chi_{6008}(871,\cdot)\) \(\chi_{6008}(1031,\cdot)\) \(\chi_{6008}(1103,\cdot)\) \(\chi_{6008}(1383,\cdot)\) \(\chi_{6008}(1631,\cdot)\) \(\chi_{6008}(1879,\cdot)\) \(\chi_{6008}(2063,\cdot)\) \(\chi_{6008}(2167,\cdot)\) \(\chi_{6008}(2287,\cdot)\) \(\chi_{6008}(2367,\cdot)\) \(\chi_{6008}(2599,\cdot)\) \(\chi_{6008}(2775,\cdot)\) \(\chi_{6008}(2807,\cdot)\) \(\chi_{6008}(2943,\cdot)\) \(\chi_{6008}(3015,\cdot)\) \(\chi_{6008}(3087,\cdot)\) \(\chi_{6008}(3247,\cdot)\) \(\chi_{6008}(3255,\cdot)\) \(\chi_{6008}(3383,\cdot)\) \(\chi_{6008}(3471,\cdot)\) \(\chi_{6008}(3575,\cdot)\) \(\chi_{6008}(3703,\cdot)\) \(\chi_{6008}(3863,\cdot)\) \(\chi_{6008}(4055,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{75})$ |
Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\((1503,3005,1505)\) → \((-1,1,e\left(\frac{49}{150}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 6008 }(2775, a) \) | \(1\) | \(1\) | \(e\left(\frac{62}{75}\right)\) | \(e\left(\frac{32}{75}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{49}{75}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{71}{75}\right)\) | \(e\left(\frac{19}{75}\right)\) | \(e\left(\frac{71}{150}\right)\) | \(e\left(\frac{7}{150}\right)\) | \(e\left(\frac{74}{75}\right)\) |