Basic properties
Modulus: | \(8026\) | |
Conductor: | \(4013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(59\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{4013}(263,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8026.f
\(\chi_{8026}(263,\cdot)\) \(\chi_{8026}(279,\cdot)\) \(\chi_{8026}(301,\cdot)\) \(\chi_{8026}(425,\cdot)\) \(\chi_{8026}(607,\cdot)\) \(\chi_{8026}(655,\cdot)\) \(\chi_{8026}(807,\cdot)\) \(\chi_{8026}(885,\cdot)\) \(\chi_{8026}(957,\cdot)\) \(\chi_{8026}(1143,\cdot)\) \(\chi_{8026}(1527,\cdot)\) \(\chi_{8026}(1577,\cdot)\) \(\chi_{8026}(1803,\cdot)\) \(\chi_{8026}(2127,\cdot)\) \(\chi_{8026}(2145,\cdot)\) \(\chi_{8026}(2163,\cdot)\) \(\chi_{8026}(2247,\cdot)\) \(\chi_{8026}(2315,\cdot)\) \(\chi_{8026}(2885,\cdot)\) \(\chi_{8026}(3027,\cdot)\) \(\chi_{8026}(3565,\cdot)\) \(\chi_{8026}(3647,\cdot)\) \(\chi_{8026}(3719,\cdot)\) \(\chi_{8026}(3805,\cdot)\) \(\chi_{8026}(3899,\cdot)\) \(\chi_{8026}(4053,\cdot)\) \(\chi_{8026}(4067,\cdot)\) \(\chi_{8026}(4189,\cdot)\) \(\chi_{8026}(4215,\cdot)\) \(\chi_{8026}(4311,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{59})$ |
Fixed field: | Number field defined by a degree 59 polynomial |
Values on generators
\(4015\) → \(e\left(\frac{10}{59}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8026 }(263, a) \) | \(1\) | \(1\) | \(e\left(\frac{45}{59}\right)\) | \(e\left(\frac{49}{59}\right)\) | \(e\left(\frac{42}{59}\right)\) | \(e\left(\frac{31}{59}\right)\) | \(e\left(\frac{8}{59}\right)\) | \(e\left(\frac{20}{59}\right)\) | \(e\left(\frac{35}{59}\right)\) | \(e\left(\frac{30}{59}\right)\) | \(e\left(\frac{15}{59}\right)\) | \(e\left(\frac{28}{59}\right)\) |