Basic properties
| Modulus: | \(1153\) | |
| Conductor: | \(1153\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1152\) | 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 1153.x
\(\chi_{1153}(5,\cdot)\) \(\chi_{1153}(10,\cdot)\) \(\chi_{1153}(14,\cdot)\) \(\chi_{1153}(15,\cdot)\) \(\chi_{1153}(17,\cdot)\) \(\chi_{1153}(19,\cdot)\) \(\chi_{1153}(21,\cdot)\) \(\chi_{1153}(28,\cdot)\) \(\chi_{1153}(31,\cdot)\) \(\chi_{1153}(34,\cdot)\) \(\chi_{1153}(40,\cdot)\) \(\chi_{1153}(42,\cdot)\) \(\chi_{1153}(51,\cdot)\) \(\chi_{1153}(60,\cdot)\) \(\chi_{1153}(63,\cdot)\) \(\chi_{1153}(65,\cdot)\) \(\chi_{1153}(73,\cdot)\) \(\chi_{1153}(74,\cdot)\) \(\chi_{1153}(76,\cdot)\) \(\chi_{1153}(77,\cdot)\) \(\chi_{1153}(80,\cdot)\) \(\chi_{1153}(83,\cdot)\) \(\chi_{1153}(90,\cdot)\) \(\chi_{1153}(103,\cdot)\) \(\chi_{1153}(110,\cdot)\) \(\chi_{1153}(111,\cdot)\) \(\chi_{1153}(112,\cdot)\) \(\chi_{1153}(113,\cdot)\) \(\chi_{1153}(114,\cdot)\) \(\chi_{1153}(115,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1152})$ |
| Fixed field: | Number field defined by a degree 1152 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{1}{1152}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1153 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{288}\right)\) | \(e\left(\frac{215}{576}\right)\) | \(e\left(\frac{31}{144}\right)\) | \(e\left(\frac{1}{1152}\right)\) | \(e\left(\frac{277}{576}\right)\) | \(e\left(\frac{13}{384}\right)\) | \(e\left(\frac{31}{96}\right)\) | \(e\left(\frac{215}{288}\right)\) | \(e\left(\frac{125}{1152}\right)\) | \(e\left(\frac{403}{576}\right)\) |