Basic properties
| Modulus: | \(1169\) | |
| Conductor: | \(1169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(498\) | 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 1169.p
\(\chi_{1169}(23,\cdot)\) \(\chi_{1169}(30,\cdot)\) \(\chi_{1169}(37,\cdot)\) \(\chi_{1169}(39,\cdot)\) \(\chi_{1169}(46,\cdot)\) \(\chi_{1169}(51,\cdot)\) \(\chi_{1169}(53,\cdot)\) \(\chi_{1169}(60,\cdot)\) \(\chi_{1169}(67,\cdot)\) \(\chi_{1169}(74,\cdot)\) \(\chi_{1169}(79,\cdot)\) \(\chi_{1169}(86,\cdot)\) \(\chi_{1169}(95,\cdot)\) \(\chi_{1169}(102,\cdot)\) \(\chi_{1169}(109,\cdot)\) \(\chi_{1169}(123,\cdot)\) \(\chi_{1169}(135,\cdot)\) \(\chi_{1169}(142,\cdot)\) \(\chi_{1169}(149,\cdot)\) \(\chi_{1169}(151,\cdot)\) \(\chi_{1169}(156,\cdot)\) \(\chi_{1169}(158,\cdot)\) \(\chi_{1169}(163,\cdot)\) \(\chi_{1169}(165,\cdot)\) \(\chi_{1169}(172,\cdot)\) \(\chi_{1169}(177,\cdot)\) \(\chi_{1169}(184,\cdot)\) \(\chi_{1169}(193,\cdot)\) \(\chi_{1169}(207,\cdot)\) \(\chi_{1169}(212,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{249})$ |
| Fixed field: | Number field defined by a degree 498 polynomial (not computed) |
Values on generators
\((836,673)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{99}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1169 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{130}{249}\right)\) | \(e\left(\frac{98}{249}\right)\) | \(e\left(\frac{11}{249}\right)\) | \(e\left(\frac{131}{498}\right)\) | \(e\left(\frac{76}{83}\right)\) | \(e\left(\frac{47}{83}\right)\) | \(e\left(\frac{196}{249}\right)\) | \(e\left(\frac{391}{498}\right)\) | \(e\left(\frac{8}{249}\right)\) | \(e\left(\frac{109}{249}\right)\) |