Basic properties
| Modulus: | \(5290\) | |
| Conductor: | \(2645\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1012\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2645}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5290.w
\(\chi_{5290}(7,\cdot)\) \(\chi_{5290}(17,\cdot)\) \(\chi_{5290}(33,\cdot)\) \(\chi_{5290}(37,\cdot)\) \(\chi_{5290}(43,\cdot)\) \(\chi_{5290}(53,\cdot)\) \(\chi_{5290}(57,\cdot)\) \(\chi_{5290}(67,\cdot)\) \(\chi_{5290}(83,\cdot)\) \(\chi_{5290}(97,\cdot)\) \(\chi_{5290}(103,\cdot)\) \(\chi_{5290}(107,\cdot)\) \(\chi_{5290}(113,\cdot)\) \(\chi_{5290}(143,\cdot)\) \(\chi_{5290}(153,\cdot)\) \(\chi_{5290}(157,\cdot)\) \(\chi_{5290}(203,\cdot)\) \(\chi_{5290}(217,\cdot)\) \(\chi_{5290}(227,\cdot)\) \(\chi_{5290}(237,\cdot)\) \(\chi_{5290}(247,\cdot)\) \(\chi_{5290}(267,\cdot)\) \(\chi_{5290}(273,\cdot)\) \(\chi_{5290}(283,\cdot)\) \(\chi_{5290}(287,\cdot)\) \(\chi_{5290}(293,\cdot)\) \(\chi_{5290}(297,\cdot)\) \(\chi_{5290}(313,\cdot)\) \(\chi_{5290}(327,\cdot)\) \(\chi_{5290}(333,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1012})$ |
| Fixed field: | Number field defined by a degree 1012 polynomial (not computed) |
Values on generators
\((2117,2121)\) → \((i,e\left(\frac{129}{506}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 5290 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{839}{1012}\right)\) | \(e\left(\frac{139}{1012}\right)\) | \(e\left(\frac{333}{506}\right)\) | \(e\left(\frac{237}{506}\right)\) | \(e\left(\frac{191}{1012}\right)\) | \(e\left(\frac{651}{1012}\right)\) | \(e\left(\frac{181}{253}\right)\) | \(e\left(\frac{489}{506}\right)\) | \(e\left(\frac{493}{1012}\right)\) | \(e\left(\frac{375}{506}\right)\) |