Basic properties
| Modulus: | \(6004\) | |
| Conductor: | \(79\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{79}(50,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.cx
\(\chi_{6004}(761,\cdot)\) \(\chi_{6004}(913,\cdot)\) \(\chi_{6004}(1217,\cdot)\) \(\chi_{6004}(1369,\cdot)\) \(\chi_{6004}(1521,\cdot)\) \(\chi_{6004}(1749,\cdot)\) \(\chi_{6004}(1901,\cdot)\) \(\chi_{6004}(1977,\cdot)\) \(\chi_{6004}(2205,\cdot)\) \(\chi_{6004}(2737,\cdot)\) \(\chi_{6004}(2889,\cdot)\) \(\chi_{6004}(2965,\cdot)\) \(\chi_{6004}(3117,\cdot)\) \(\chi_{6004}(3801,\cdot)\) \(\chi_{6004}(4105,\cdot)\) \(\chi_{6004}(4181,\cdot)\) \(\chi_{6004}(4789,\cdot)\) \(\chi_{6004}(5017,\cdot)\) \(\chi_{6004}(5245,\cdot)\) \(\chi_{6004}(5397,\cdot)\) \(\chi_{6004}(5549,\cdot)\) \(\chi_{6004}(5625,\cdot)\) \(\chi_{6004}(5701,\cdot)\) \(\chi_{6004}(5929,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((3003,2529,3953)\) → \((1,1,e\left(\frac{25}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 6004 }(761, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{2}{3}\right)\) |