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.bt
\(\chi_{6008}(11,\cdot)\) \(\chi_{6008}(83,\cdot)\) \(\chi_{6008}(243,\cdot)\) \(\chi_{6008}(251,\cdot)\) \(\chi_{6008}(379,\cdot)\) \(\chi_{6008}(467,\cdot)\) \(\chi_{6008}(571,\cdot)\) \(\chi_{6008}(699,\cdot)\) \(\chi_{6008}(859,\cdot)\) \(\chi_{6008}(1051,\cdot)\) \(\chi_{6008}(1195,\cdot)\) \(\chi_{6008}(1203,\cdot)\) \(\chi_{6008}(1339,\cdot)\) \(\chi_{6008}(1371,\cdot)\) \(\chi_{6008}(1395,\cdot)\) \(\chi_{6008}(1875,\cdot)\) \(\chi_{6008}(2059,\cdot)\) \(\chi_{6008}(2123,\cdot)\) \(\chi_{6008}(2731,\cdot)\) \(\chi_{6008}(2883,\cdot)\) \(\chi_{6008}(3227,\cdot)\) \(\chi_{6008}(3459,\cdot)\) \(\chi_{6008}(3555,\cdot)\) \(\chi_{6008}(3571,\cdot)\) \(\chi_{6008}(3723,\cdot)\) \(\chi_{6008}(3867,\cdot)\) \(\chi_{6008}(3875,\cdot)\) \(\chi_{6008}(4035,\cdot)\) \(\chi_{6008}(4107,\cdot)\) \(\chi_{6008}(4387,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{75})$ |
Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\((1503,3005,1505)\) → \((-1,-1,e\left(\frac{133}{150}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 6008 }(1203, a) \) | \(1\) | \(1\) | \(e\left(\frac{133}{150}\right)\) | \(e\left(\frac{13}{150}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{58}{75}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{139}{150}\right)\) | \(e\left(\frac{73}{75}\right)\) | \(e\left(\frac{107}{150}\right)\) | \(e\left(\frac{47}{75}\right)\) | \(e\left(\frac{91}{150}\right)\) |