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 \(\chi_{2873}(322,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8619.dq
\(\chi_{8619}(322,\cdot)\) \(\chi_{8619}(628,\cdot)\) \(\chi_{8619}(985,\cdot)\) \(\chi_{8619}(1291,\cdot)\) \(\chi_{8619}(1648,\cdot)\) \(\chi_{8619}(1954,\cdot)\) \(\chi_{8619}(2311,\cdot)\) \(\chi_{8619}(2617,\cdot)\) \(\chi_{8619}(2974,\cdot)\) \(\chi_{8619}(3280,\cdot)\) \(\chi_{8619}(3637,\cdot)\) \(\chi_{8619}(3943,\cdot)\) \(\chi_{8619}(4300,\cdot)\) \(\chi_{8619}(4606,\cdot)\) \(\chi_{8619}(4963,\cdot)\) \(\chi_{8619}(5269,\cdot)\) \(\chi_{8619}(5626,\cdot)\) \(\chi_{8619}(5932,\cdot)\) \(\chi_{8619}(6289,\cdot)\) \(\chi_{8619}(6595,\cdot)\) \(\chi_{8619}(7258,\cdot)\) \(\chi_{8619}(7615,\cdot)\) \(\chi_{8619}(8278,\cdot)\) \(\chi_{8619}(8584,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((5747,5917,2536)\) → \((1,e\left(\frac{41}{78}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(322, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{1}{6}\right)\) |