Basic properties
| Modulus: | \(1187\) | |
| Conductor: | \(1187\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1186\) | 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 1187.d
\(\chi_{1187}(2,\cdot)\) \(\chi_{1187}(5,\cdot)\) \(\chi_{1187}(6,\cdot)\) \(\chi_{1187}(7,\cdot)\) \(\chi_{1187}(8,\cdot)\) \(\chi_{1187}(15,\cdot)\) \(\chi_{1187}(17,\cdot)\) \(\chi_{1187}(18,\cdot)\) \(\chi_{1187}(19,\cdot)\) \(\chi_{1187}(20,\cdot)\) \(\chi_{1187}(21,\cdot)\) \(\chi_{1187}(22,\cdot)\) \(\chi_{1187}(24,\cdot)\) \(\chi_{1187}(26,\cdot)\) \(\chi_{1187}(28,\cdot)\) \(\chi_{1187}(29,\cdot)\) \(\chi_{1187}(31,\cdot)\) \(\chi_{1187}(32,\cdot)\) \(\chi_{1187}(45,\cdot)\) \(\chi_{1187}(46,\cdot)\) \(\chi_{1187}(47,\cdot)\) \(\chi_{1187}(50,\cdot)\) \(\chi_{1187}(51,\cdot)\) \(\chi_{1187}(53,\cdot)\) \(\chi_{1187}(54,\cdot)\) \(\chi_{1187}(55,\cdot)\) \(\chi_{1187}(57,\cdot)\) \(\chi_{1187}(59,\cdot)\) \(\chi_{1187}(60,\cdot)\) \(\chi_{1187}(61,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{593})$ |
| Fixed field: | Number field defined by a degree 1186 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{53}{1186}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1187 }(1184, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{1186}\right)\) | \(e\left(\frac{515}{593}\right)\) | \(e\left(\frac{53}{593}\right)\) | \(e\left(\frac{769}{1186}\right)\) | \(e\left(\frac{1083}{1186}\right)\) | \(e\left(\frac{1069}{1186}\right)\) | \(e\left(\frac{159}{1186}\right)\) | \(e\left(\frac{437}{593}\right)\) | \(e\left(\frac{411}{593}\right)\) | \(e\left(\frac{181}{593}\right)\) |