Basic properties
| Modulus: | \(8619\) | |
| Conductor: | \(2873\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2873}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8619.du
\(\chi_{8619}(16,\cdot)\) \(\chi_{8619}(373,\cdot)\) \(\chi_{8619}(679,\cdot)\) \(\chi_{8619}(1342,\cdot)\) \(\chi_{8619}(1699,\cdot)\) \(\chi_{8619}(2362,\cdot)\) \(\chi_{8619}(2668,\cdot)\) \(\chi_{8619}(3025,\cdot)\) \(\chi_{8619}(3331,\cdot)\) \(\chi_{8619}(3688,\cdot)\) \(\chi_{8619}(3994,\cdot)\) \(\chi_{8619}(4351,\cdot)\) \(\chi_{8619}(4657,\cdot)\) \(\chi_{8619}(5014,\cdot)\) \(\chi_{8619}(5320,\cdot)\) \(\chi_{8619}(5677,\cdot)\) \(\chi_{8619}(5983,\cdot)\) \(\chi_{8619}(6340,\cdot)\) \(\chi_{8619}(6646,\cdot)\) \(\chi_{8619}(7003,\cdot)\) \(\chi_{8619}(7309,\cdot)\) \(\chi_{8619}(7666,\cdot)\) \(\chi_{8619}(7972,\cdot)\) \(\chi_{8619}(8329,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((5747,5917,2536)\) → \((1,e\left(\frac{1}{39}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{2}{3}\right)\) |