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.dw
\(\chi_{8619}(161,\cdot)\) \(\chi_{8619}(359,\cdot)\) \(\chi_{8619}(434,\cdot)\) \(\chi_{8619}(593,\cdot)\) \(\chi_{8619}(824,\cdot)\) \(\chi_{8619}(1022,\cdot)\) \(\chi_{8619}(1097,\cdot)\) \(\chi_{8619}(1256,\cdot)\) \(\chi_{8619}(1487,\cdot)\) \(\chi_{8619}(1685,\cdot)\) \(\chi_{8619}(1919,\cdot)\) \(\chi_{8619}(2150,\cdot)\) \(\chi_{8619}(2348,\cdot)\) \(\chi_{8619}(2423,\cdot)\) \(\chi_{8619}(2582,\cdot)\) \(\chi_{8619}(2813,\cdot)\) \(\chi_{8619}(3011,\cdot)\) \(\chi_{8619}(3086,\cdot)\) \(\chi_{8619}(3245,\cdot)\) \(\chi_{8619}(3476,\cdot)\) \(\chi_{8619}(3674,\cdot)\) \(\chi_{8619}(3749,\cdot)\) \(\chi_{8619}(3908,\cdot)\) \(\chi_{8619}(4139,\cdot)\) \(\chi_{8619}(4337,\cdot)\) \(\chi_{8619}(4412,\cdot)\) \(\chi_{8619}(4571,\cdot)\) \(\chi_{8619}(5075,\cdot)\) \(\chi_{8619}(5234,\cdot)\) \(\chi_{8619}(5465,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{104})$ |
| Fixed field: | Number field defined by a degree 104 polynomial (not computed) |
Values on generators
\((5747,5917,2536)\) → \((-1,e\left(\frac{27}{52}\right),e\left(\frac{5}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(161, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{31}{104}\right)\) | \(e\left(\frac{45}{104}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{7}{104}\right)\) | \(e\left(\frac{37}{104}\right)\) | \(e\left(\frac{21}{104}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(-1\) |