Basic properties
| Modulus: | \(8038\) | |
| Conductor: | \(4019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(49\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4019}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8038.f
\(\chi_{8038}(3,\cdot)\) \(\chi_{8038}(9,\cdot)\) \(\chi_{8038}(27,\cdot)\) \(\chi_{8038}(81,\cdot)\) \(\chi_{8038}(91,\cdot)\) \(\chi_{8038}(243,\cdot)\) \(\chi_{8038}(265,\cdot)\) \(\chi_{8038}(311,\cdot)\) \(\chi_{8038}(517,\cdot)\) \(\chi_{8038}(729,\cdot)\) \(\chi_{8038}(795,\cdot)\) \(\chi_{8038}(819,\cdot)\) \(\chi_{8038}(933,\cdot)\) \(\chi_{8038}(1077,\cdot)\) \(\chi_{8038}(1655,\cdot)\) \(\chi_{8038}(1687,\cdot)\) \(\chi_{8038}(2035,\cdot)\) \(\chi_{8038}(2385,\cdot)\) \(\chi_{8038}(2457,\cdot)\) \(\chi_{8038}(2783,\cdot)\) \(\chi_{8038}(2799,\cdot)\) \(\chi_{8038}(3231,\cdot)\) \(\chi_{8038}(3607,\cdot)\) \(\chi_{8038}(4075,\cdot)\) \(\chi_{8038}(4187,\cdot)\) \(\chi_{8038}(4495,\cdot)\) \(\chi_{8038}(4523,\cdot)\) \(\chi_{8038}(4653,\cdot)\) \(\chi_{8038}(4965,\cdot)\) \(\chi_{8038}(5061,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{49})$ |
| Fixed field: | Number field defined by a degree 49 polynomial |
Values on generators
\(4021\) → \(e\left(\frac{25}{49}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8038 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{49}\right)\) | \(e\left(\frac{6}{49}\right)\) | \(e\left(\frac{47}{49}\right)\) | \(e\left(\frac{45}{49}\right)\) | \(e\left(\frac{8}{49}\right)\) | \(e\left(\frac{46}{49}\right)\) | \(e\left(\frac{4}{49}\right)\) | \(e\left(\frac{10}{49}\right)\) | \(e\left(\frac{45}{49}\right)\) | \(e\left(\frac{45}{49}\right)\) |