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.cc
\(\chi_{6013}(402,\cdot)\) \(\chi_{6013}(647,\cdot)\) \(\chi_{6013}(747,\cdot)\) \(\chi_{6013}(871,\cdot)\) \(\chi_{6013}(885,\cdot)\) \(\chi_{6013}(1062,\cdot)\) \(\chi_{6013}(1200,\cdot)\) \(\chi_{6013}(1440,\cdot)\) \(\chi_{6013}(1685,\cdot)\) \(\chi_{6013}(2301,\cdot)\) \(\chi_{6013}(2404,\cdot)\) \(\chi_{6013}(2600,\cdot)\) \(\chi_{6013}(2852,\cdot)\) \(\chi_{6013}(3120,\cdot)\) \(\chi_{6013}(3629,\cdot)\) \(\chi_{6013}(4175,\cdot)\) \(\chi_{6013}(4478,\cdot)\) \(\chi_{6013}(4625,\cdot)\) \(\chi_{6013}(4653,\cdot)\) \(\chi_{6013}(4842,\cdot)\) \(\chi_{6013}(4924,\cdot)\) \(\chi_{6013}(5010,\cdot)\) \(\chi_{6013}(5290,\cdot)\) \(\chi_{6013}(5736,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((5155,3438)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{29}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 6013 }(402, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{32}{39}\right)\) |