Basic properties
Modulus: | \(6013\) | |
Conductor: | \(6013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | 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 6013.ca
\(\chi_{6013}(629,\cdot)\) \(\chi_{6013}(1042,\cdot)\) \(\chi_{6013}(1189,\cdot)\) \(\chi_{6013}(1217,\cdot)\) \(\chi_{6013}(1406,\cdot)\) \(\chi_{6013}(1441,\cdot)\) \(\chi_{6013}(1574,\cdot)\) \(\chi_{6013}(1854,\cdot)\) \(\chi_{6013}(2120,\cdot)\) \(\chi_{6013}(2365,\cdot)\) \(\chi_{6013}(2589,\cdot)\) \(\chi_{6013}(2603,\cdot)\) \(\chi_{6013}(2918,\cdot)\) \(\chi_{6013}(3324,\cdot)\) \(\chi_{6013}(3639,\cdot)\) \(\chi_{6013}(4017,\cdot)\) \(\chi_{6013}(4122,\cdot)\) \(\chi_{6013}(4262,\cdot)\) \(\chi_{6013}(4318,\cdot)\) \(\chi_{6013}(4570,\cdot)\) \(\chi_{6013}(4878,\cdot)\) \(\chi_{6013}(5347,\cdot)\) \(\chi_{6013}(5697,\cdot)\) \(\chi_{6013}(5893,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((5155,3438)\) → \((-1,e\left(\frac{53}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 6013 }(629, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{28}{39}\right)\) |