Basic properties
| Modulus: | \(1181\) | |
| Conductor: | \(1181\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1180\) | 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 1181.l
\(\chi_{1181}(7,\cdot)\) \(\chi_{1181}(10,\cdot)\) \(\chi_{1181}(12,\cdot)\) \(\chi_{1181}(13,\cdot)\) \(\chi_{1181}(15,\cdot)\) \(\chi_{1181}(18,\cdot)\) \(\chi_{1181}(28,\cdot)\) \(\chi_{1181}(29,\cdot)\) \(\chi_{1181}(31,\cdot)\) \(\chi_{1181}(33,\cdot)\) \(\chi_{1181}(34,\cdot)\) \(\chi_{1181}(40,\cdot)\) \(\chi_{1181}(42,\cdot)\) \(\chi_{1181}(43,\cdot)\) \(\chi_{1181}(46,\cdot)\) \(\chi_{1181}(48,\cdot)\) \(\chi_{1181}(50,\cdot)\) \(\chi_{1181}(51,\cdot)\) \(\chi_{1181}(52,\cdot)\) \(\chi_{1181}(60,\cdot)\) \(\chi_{1181}(65,\cdot)\) \(\chi_{1181}(67,\cdot)\) \(\chi_{1181}(69,\cdot)\) \(\chi_{1181}(72,\cdot)\) \(\chi_{1181}(73,\cdot)\) \(\chi_{1181}(74,\cdot)\) \(\chi_{1181}(77,\cdot)\) \(\chi_{1181}(78,\cdot)\) \(\chi_{1181}(79,\cdot)\) \(\chi_{1181}(82,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1180})$ |
| Fixed field: | Number field defined by a degree 1180 polynomial (not computed) |
Values on generators
\(7\) → \(e\left(\frac{667}{1180}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1181 }(12, a) \) | \(-1\) | \(1\) | \(e\left(\frac{233}{236}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{115}{118}\right)\) | \(e\left(\frac{379}{590}\right)\) | \(e\left(\frac{11}{295}\right)\) | \(e\left(\frac{667}{1180}\right)\) | \(e\left(\frac{227}{236}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{743}{1180}\right)\) | \(e\left(\frac{26}{59}\right)\) |