Basic properties
| Modulus: | \(8619\) | |
| Conductor: | \(2873\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2873}(4,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8619.eo
\(\chi_{8619}(4,\cdot)\) \(\chi_{8619}(166,\cdot)\) \(\chi_{8619}(472,\cdot)\) \(\chi_{8619}(667,\cdot)\) \(\chi_{8619}(829,\cdot)\) \(\chi_{8619}(1024,\cdot)\) \(\chi_{8619}(1135,\cdot)\) \(\chi_{8619}(1492,\cdot)\) \(\chi_{8619}(1687,\cdot)\) \(\chi_{8619}(1798,\cdot)\) \(\chi_{8619}(1993,\cdot)\) \(\chi_{8619}(2155,\cdot)\) \(\chi_{8619}(2350,\cdot)\) \(\chi_{8619}(2461,\cdot)\) \(\chi_{8619}(2656,\cdot)\) \(\chi_{8619}(2818,\cdot)\) \(\chi_{8619}(3013,\cdot)\) \(\chi_{8619}(3124,\cdot)\) \(\chi_{8619}(3319,\cdot)\) \(\chi_{8619}(3481,\cdot)\) \(\chi_{8619}(3676,\cdot)\) \(\chi_{8619}(3787,\cdot)\) \(\chi_{8619}(3982,\cdot)\) \(\chi_{8619}(4144,\cdot)\) \(\chi_{8619}(4339,\cdot)\) \(\chi_{8619}(4450,\cdot)\) \(\chi_{8619}(4645,\cdot)\) \(\chi_{8619}(4807,\cdot)\) \(\chi_{8619}(5002,\cdot)\) \(\chi_{8619}(5113,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((5747,5917,2536)\) → \((1,e\left(\frac{1}{78}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) |