Basic properties
| Modulus: | \(8619\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(87,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8619.cu
\(\chi_{8619}(256,\cdot)\) \(\chi_{8619}(562,\cdot)\) \(\chi_{8619}(919,\cdot)\) \(\chi_{8619}(1225,\cdot)\) \(\chi_{8619}(1582,\cdot)\) \(\chi_{8619}(1888,\cdot)\) \(\chi_{8619}(2245,\cdot)\) \(\chi_{8619}(2551,\cdot)\) \(\chi_{8619}(2908,\cdot)\) \(\chi_{8619}(3214,\cdot)\) \(\chi_{8619}(3877,\cdot)\) \(\chi_{8619}(4234,\cdot)\) \(\chi_{8619}(4897,\cdot)\) \(\chi_{8619}(5203,\cdot)\) \(\chi_{8619}(5560,\cdot)\) \(\chi_{8619}(5866,\cdot)\) \(\chi_{8619}(6223,\cdot)\) \(\chi_{8619}(6529,\cdot)\) \(\chi_{8619}(6886,\cdot)\) \(\chi_{8619}(7192,\cdot)\) \(\chi_{8619}(7549,\cdot)\) \(\chi_{8619}(7855,\cdot)\) \(\chi_{8619}(8212,\cdot)\) \(\chi_{8619}(8518,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((5747,5917,2536)\) → \((1,e\left(\frac{2}{39}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(256, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) |