Basic properties
| Modulus: | \(1013\) | |
| Conductor: | \(1013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1012\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1013.l
\(\chi_{1013}(3,\cdot)\) \(\chi_{1013}(5,\cdot)\) \(\chi_{1013}(7,\cdot)\) \(\chi_{1013}(12,\cdot)\) \(\chi_{1013}(17,\cdot)\) \(\chi_{1013}(18,\cdot)\) \(\chi_{1013}(20,\cdot)\) \(\chi_{1013}(26,\cdot)\) \(\chi_{1013}(27,\cdot)\) \(\chi_{1013}(28,\cdot)\) \(\chi_{1013}(29,\cdot)\) \(\chi_{1013}(30,\cdot)\) \(\chi_{1013}(31,\cdot)\) \(\chi_{1013}(33,\cdot)\) \(\chi_{1013}(37,\cdot)\) \(\chi_{1013}(38,\cdot)\) \(\chi_{1013}(39,\cdot)\) \(\chi_{1013}(41,\cdot)\) \(\chi_{1013}(42,\cdot)\) \(\chi_{1013}(47,\cdot)\) \(\chi_{1013}(48,\cdot)\) \(\chi_{1013}(50,\cdot)\) \(\chi_{1013}(55,\cdot)\) \(\chi_{1013}(57,\cdot)\) \(\chi_{1013}(59,\cdot)\) \(\chi_{1013}(61,\cdot)\) \(\chi_{1013}(63,\cdot)\) \(\chi_{1013}(67,\cdot)\) \(\chi_{1013}(68,\cdot)\) \(\chi_{1013}(69,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1012})$ |
| Fixed field: | Number field defined by a degree 1012 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{181}{1012}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1013 }(26, a) \) | \(-1\) | \(1\) | \(e\left(\frac{85}{92}\right)\) | \(e\left(\frac{181}{1012}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{397}{1012}\right)\) | \(e\left(\frac{26}{253}\right)\) | \(e\left(\frac{849}{1012}\right)\) | \(e\left(\frac{71}{92}\right)\) | \(e\left(\frac{181}{506}\right)\) | \(e\left(\frac{80}{253}\right)\) | \(e\left(\frac{11}{46}\right)\) |