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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1169.o
\(\chi_{1169}(5,\cdot)\) \(\chi_{1169}(10,\cdot)\) \(\chi_{1169}(17,\cdot)\) \(\chi_{1169}(26,\cdot)\) \(\chi_{1169}(40,\cdot)\) \(\chi_{1169}(45,\cdot)\) \(\chi_{1169}(52,\cdot)\) \(\chi_{1169}(59,\cdot)\) \(\chi_{1169}(68,\cdot)\) \(\chi_{1169}(73,\cdot)\) \(\chi_{1169}(80,\cdot)\) \(\chi_{1169}(82,\cdot)\) \(\chi_{1169}(101,\cdot)\) \(\chi_{1169}(103,\cdot)\) \(\chi_{1169}(110,\cdot)\) \(\chi_{1169}(117,\cdot)\) \(\chi_{1169}(129,\cdot)\) \(\chi_{1169}(131,\cdot)\) \(\chi_{1169}(136,\cdot)\) \(\chi_{1169}(138,\cdot)\) \(\chi_{1169}(143,\cdot)\) \(\chi_{1169}(145,\cdot)\) \(\chi_{1169}(159,\cdot)\) \(\chi_{1169}(164,\cdot)\) \(\chi_{1169}(180,\cdot)\) \(\chi_{1169}(187,\cdot)\) \(\chi_{1169}(201,\cdot)\) \(\chi_{1169}(206,\cdot)\) \(\chi_{1169}(208,\cdot)\) \(\chi_{1169}(213,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{249})$ |
| Fixed field: | Number field defined by a degree 498 polynomial (not computed) |
Values on generators
\((836,673)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{53}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1169 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{249}\right)\) | \(e\left(\frac{89}{498}\right)\) | \(e\left(\frac{52}{249}\right)\) | \(e\left(\frac{38}{249}\right)\) | \(e\left(\frac{47}{166}\right)\) | \(e\left(\frac{26}{83}\right)\) | \(e\left(\frac{89}{249}\right)\) | \(e\left(\frac{64}{249}\right)\) | \(e\left(\frac{151}{249}\right)\) | \(e\left(\frac{193}{498}\right)\) |