Basic properties
| Modulus: | \(1171\) | |
| Conductor: | \(1171\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1170\) | 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 1171.x
\(\chi_{1171}(2,\cdot)\) \(\chi_{1171}(10,\cdot)\) \(\chi_{1171}(12,\cdot)\) \(\chi_{1171}(18,\cdot)\) \(\chi_{1171}(26,\cdot)\) \(\chi_{1171}(35,\cdot)\) \(\chi_{1171}(37,\cdot)\) \(\chi_{1171}(40,\cdot)\) \(\chi_{1171}(42,\cdot)\) \(\chi_{1171}(43,\cdot)\) \(\chi_{1171}(44,\cdot)\) \(\chi_{1171}(46,\cdot)\) \(\chi_{1171}(51,\cdot)\) \(\chi_{1171}(55,\cdot)\) \(\chi_{1171}(57,\cdot)\) \(\chi_{1171}(62,\cdot)\) \(\chi_{1171}(69,\cdot)\) \(\chi_{1171}(72,\cdot)\) \(\chi_{1171}(75,\cdot)\) \(\chi_{1171}(79,\cdot)\) \(\chi_{1171}(82,\cdot)\) \(\chi_{1171}(83,\cdot)\) \(\chi_{1171}(94,\cdot)\) \(\chi_{1171}(99,\cdot)\) \(\chi_{1171}(101,\cdot)\) \(\chi_{1171}(108,\cdot)\) \(\chi_{1171}(112,\cdot)\) \(\chi_{1171}(116,\cdot)\) \(\chi_{1171}(118,\cdot)\) \(\chi_{1171}(123,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{585})$ |
| Fixed field: | Number field defined by a degree 1170 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{349}{1170}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1171 }(46, a) \) | \(-1\) | \(1\) | \(e\left(\frac{349}{1170}\right)\) | \(e\left(\frac{55}{234}\right)\) | \(e\left(\frac{349}{585}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{29}{234}\right)\) | \(e\left(\frac{349}{390}\right)\) | \(e\left(\frac{55}{117}\right)\) | \(e\left(\frac{791}{1170}\right)\) | \(e\left(\frac{373}{390}\right)\) |