Basic properties
| Modulus: | \(538\) | |
| Conductor: | \(269\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(67\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{269}(21,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 538.d
\(\chi_{538}(5,\cdot)\) \(\chi_{538}(21,\cdot)\) \(\chi_{538}(23,\cdot)\) \(\chi_{538}(25,\cdot)\) \(\chi_{538}(37,\cdot)\) \(\chi_{538}(41,\cdot)\) \(\chi_{538}(47,\cdot)\) \(\chi_{538}(53,\cdot)\) \(\chi_{538}(57,\cdot)\) \(\chi_{538}(61,\cdot)\) \(\chi_{538}(67,\cdot)\) \(\chi_{538}(81,\cdot)\) \(\chi_{538}(87,\cdot)\) \(\chi_{538}(93,\cdot)\) \(\chi_{538}(99,\cdot)\) \(\chi_{538}(105,\cdot)\) \(\chi_{538}(115,\cdot)\) \(\chi_{538}(117,\cdot)\) \(\chi_{538}(119,\cdot)\) \(\chi_{538}(121,\cdot)\) \(\chi_{538}(125,\cdot)\) \(\chi_{538}(131,\cdot)\) \(\chi_{538}(143,\cdot)\) \(\chi_{538}(169,\cdot)\) \(\chi_{538}(173,\cdot)\) \(\chi_{538}(177,\cdot)\) \(\chi_{538}(185,\cdot)\) \(\chi_{538}(205,\cdot)\) \(\chi_{538}(213,\cdot)\) \(\chi_{538}(235,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{67})$ |
| Fixed field: | Number field defined by a degree 67 polynomial |
Values on generators
\(271\) → \(e\left(\frac{32}{67}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 538 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{67}\right)\) | \(e\left(\frac{23}{67}\right)\) | \(e\left(\frac{5}{67}\right)\) | \(e\left(\frac{8}{67}\right)\) | \(e\left(\frac{57}{67}\right)\) | \(e\left(\frac{55}{67}\right)\) | \(e\left(\frac{27}{67}\right)\) | \(e\left(\frac{10}{67}\right)\) | \(e\left(\frac{34}{67}\right)\) | \(e\left(\frac{9}{67}\right)\) |