Basic properties
| Modulus: | \(4019\) | |
| Conductor: | \(4019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(49\) | 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 4019.f
\(\chi_{4019}(3,\cdot)\) \(\chi_{4019}(9,\cdot)\) \(\chi_{4019}(27,\cdot)\) \(\chi_{4019}(56,\cdot)\) \(\chi_{4019}(81,\cdot)\) \(\chi_{4019}(91,\cdot)\) \(\chi_{4019}(168,\cdot)\) \(\chi_{4019}(243,\cdot)\) \(\chi_{4019}(265,\cdot)\) \(\chi_{4019}(311,\cdot)\) \(\chi_{4019}(476,\cdot)\) \(\chi_{4019}(504,\cdot)\) \(\chi_{4019}(517,\cdot)\) \(\chi_{4019}(634,\cdot)\) \(\chi_{4019}(729,\cdot)\) \(\chi_{4019}(795,\cdot)\) \(\chi_{4019}(819,\cdot)\) \(\chi_{4019}(933,\cdot)\) \(\chi_{4019}(946,\cdot)\) \(\chi_{4019}(1042,\cdot)\) \(\chi_{4019}(1077,\cdot)\) \(\chi_{4019}(1340,\cdot)\) \(\chi_{4019}(1370,\cdot)\) \(\chi_{4019}(1512,\cdot)\) \(\chi_{4019}(1655,\cdot)\) \(\chi_{4019}(1687,\cdot)\) \(\chi_{4019}(1902,\cdot)\) \(\chi_{4019}(2018,\cdot)\) \(\chi_{4019}(2035,\cdot)\) \(\chi_{4019}(2086,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{49})$ |
| Fixed field: | Number field defined by a degree 49 polynomial |
Values on generators
\(2\) → \(e\left(\frac{37}{49}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4019 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{49}\right)\) | \(e\left(\frac{48}{49}\right)\) | \(e\left(\frac{25}{49}\right)\) | \(e\left(\frac{3}{49}\right)\) | \(e\left(\frac{36}{49}\right)\) | \(e\left(\frac{48}{49}\right)\) | \(e\left(\frac{13}{49}\right)\) | \(e\left(\frac{47}{49}\right)\) | \(e\left(\frac{40}{49}\right)\) | \(e\left(\frac{4}{49}\right)\) |