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 \(\chi_{316}(39,\cdot)\) | 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
\((3003,2529,3953)\) → \((-1,1,e\left(\frac{35}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 6004 }(39, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{1}{6}\right)\) |