Basic properties
| Modulus: | \(8619\) | |
| Conductor: | \(8619\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(104\) | 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.ed
\(\chi_{8619}(8,\cdot)\) \(\chi_{8619}(83,\cdot)\) \(\chi_{8619}(281,\cdot)\) \(\chi_{8619}(512,\cdot)\) \(\chi_{8619}(671,\cdot)\) \(\chi_{8619}(1175,\cdot)\) \(\chi_{8619}(1334,\cdot)\) \(\chi_{8619}(1409,\cdot)\) \(\chi_{8619}(1607,\cdot)\) \(\chi_{8619}(1838,\cdot)\) \(\chi_{8619}(1997,\cdot)\) \(\chi_{8619}(2072,\cdot)\) \(\chi_{8619}(2270,\cdot)\) \(\chi_{8619}(2501,\cdot)\) \(\chi_{8619}(2660,\cdot)\) \(\chi_{8619}(2735,\cdot)\) \(\chi_{8619}(2933,\cdot)\) \(\chi_{8619}(3164,\cdot)\) \(\chi_{8619}(3323,\cdot)\) \(\chi_{8619}(3398,\cdot)\) \(\chi_{8619}(3596,\cdot)\) \(\chi_{8619}(3827,\cdot)\) \(\chi_{8619}(4061,\cdot)\) \(\chi_{8619}(4259,\cdot)\) \(\chi_{8619}(4490,\cdot)\) \(\chi_{8619}(4649,\cdot)\) \(\chi_{8619}(4724,\cdot)\) \(\chi_{8619}(4922,\cdot)\) \(\chi_{8619}(5153,\cdot)\) \(\chi_{8619}(5312,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{104})$ |
| Fixed field: | Number field defined by a degree 104 polynomial (not computed) |
Values on generators
\((5747,5917,2536)\) → \((-1,e\left(\frac{1}{52}\right),e\left(\frac{5}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{83}{104}\right)\) | \(e\left(\frac{97}{104}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{7}{104}\right)\) | \(e\left(\frac{89}{104}\right)\) | \(e\left(\frac{21}{104}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(1\) |