Basic properties
| Modulus: | \(1169\) | |
| Conductor: | \(1169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(249\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1169.m
\(\chi_{1169}(2,\cdot)\) \(\chi_{1169}(4,\cdot)\) \(\chi_{1169}(9,\cdot)\) \(\chi_{1169}(11,\cdot)\) \(\chi_{1169}(16,\cdot)\) \(\chi_{1169}(18,\cdot)\) \(\chi_{1169}(25,\cdot)\) \(\chi_{1169}(32,\cdot)\) \(\chi_{1169}(44,\cdot)\) \(\chi_{1169}(58,\cdot)\) \(\chi_{1169}(65,\cdot)\) \(\chi_{1169}(72,\cdot)\) \(\chi_{1169}(81,\cdot)\) \(\chi_{1169}(88,\cdot)\) \(\chi_{1169}(93,\cdot)\) \(\chi_{1169}(100,\cdot)\) \(\chi_{1169}(107,\cdot)\) \(\chi_{1169}(114,\cdot)\) \(\chi_{1169}(116,\cdot)\) \(\chi_{1169}(121,\cdot)\) \(\chi_{1169}(128,\cdot)\) \(\chi_{1169}(130,\cdot)\) \(\chi_{1169}(137,\cdot)\) \(\chi_{1169}(144,\cdot)\) \(\chi_{1169}(170,\cdot)\) \(\chi_{1169}(179,\cdot)\) \(\chi_{1169}(186,\cdot)\) \(\chi_{1169}(191,\cdot)\) \(\chi_{1169}(198,\cdot)\) \(\chi_{1169}(200,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{249})$ |
| Fixed field: | Number field defined by a degree 249 polynomial (not computed) |
Values on generators
\((836,673)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{31}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1169 }(18, a) \) | \(1\) | \(1\) | \(e\left(\frac{68}{249}\right)\) | \(e\left(\frac{193}{249}\right)\) | \(e\left(\frac{136}{249}\right)\) | \(e\left(\frac{176}{249}\right)\) | \(e\left(\frac{4}{83}\right)\) | \(e\left(\frac{68}{83}\right)\) | \(e\left(\frac{137}{249}\right)\) | \(e\left(\frac{244}{249}\right)\) | \(e\left(\frac{31}{249}\right)\) | \(e\left(\frac{80}{249}\right)\) |