Basic properties
| Modulus: | \(6004\) | |
| Conductor: | \(316\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{316}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.dt
\(\chi_{6004}(39,\cdot)\) \(\chi_{6004}(267,\cdot)\) \(\chi_{6004}(875,\cdot)\) \(\chi_{6004}(951,\cdot)\) \(\chi_{6004}(1255,\cdot)\) \(\chi_{6004}(1939,\cdot)\) \(\chi_{6004}(2091,\cdot)\) \(\chi_{6004}(2167,\cdot)\) \(\chi_{6004}(2319,\cdot)\) \(\chi_{6004}(2851,\cdot)\) \(\chi_{6004}(3079,\cdot)\) \(\chi_{6004}(3155,\cdot)\) \(\chi_{6004}(3307,\cdot)\) \(\chi_{6004}(3535,\cdot)\) \(\chi_{6004}(3687,\cdot)\) \(\chi_{6004}(3839,\cdot)\) \(\chi_{6004}(4143,\cdot)\) \(\chi_{6004}(4295,\cdot)\) \(\chi_{6004}(5131,\cdot)\) \(\chi_{6004}(5359,\cdot)\) \(\chi_{6004}(5435,\cdot)\) \(\chi_{6004}(5511,\cdot)\) \(\chi_{6004}(5663,\cdot)\) \(\chi_{6004}(5815,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((3003,2529,3953)\) → \((-1,1,e\left(\frac{53}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 6004 }(2851, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{1}{6}\right)\) |