Basic properties
| Modulus: | \(8619\) | |
| Conductor: | \(8619\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 8619.ek
\(\chi_{8619}(50,\cdot)\) \(\chi_{8619}(254,\cdot)\) \(\chi_{8619}(305,\cdot)\) \(\chi_{8619}(509,\cdot)\) \(\chi_{8619}(713,\cdot)\) \(\chi_{8619}(917,\cdot)\) \(\chi_{8619}(968,\cdot)\) \(\chi_{8619}(1172,\cdot)\) \(\chi_{8619}(1376,\cdot)\) \(\chi_{8619}(1580,\cdot)\) \(\chi_{8619}(1631,\cdot)\) \(\chi_{8619}(1835,\cdot)\) \(\chi_{8619}(2039,\cdot)\) \(\chi_{8619}(2243,\cdot)\) \(\chi_{8619}(2294,\cdot)\) \(\chi_{8619}(2498,\cdot)\) \(\chi_{8619}(2702,\cdot)\) \(\chi_{8619}(2906,\cdot)\) \(\chi_{8619}(2957,\cdot)\) \(\chi_{8619}(3161,\cdot)\) \(\chi_{8619}(3365,\cdot)\) \(\chi_{8619}(3569,\cdot)\) \(\chi_{8619}(3620,\cdot)\) \(\chi_{8619}(3824,\cdot)\) \(\chi_{8619}(4028,\cdot)\) \(\chi_{8619}(4232,\cdot)\) \(\chi_{8619}(4283,\cdot)\) \(\chi_{8619}(4487,\cdot)\) \(\chi_{8619}(4691,\cdot)\) \(\chi_{8619}(4895,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((5747,5917,2536)\) → \((-1,e\left(\frac{19}{156}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(50, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{85}{156}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) |