Basic properties
| Modulus: | \(163\) | |
| Conductor: | \(163\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(162\) | 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 163.j
\(\chi_{163}(2,\cdot)\) \(\chi_{163}(3,\cdot)\) \(\chi_{163}(7,\cdot)\) \(\chi_{163}(11,\cdot)\) \(\chi_{163}(12,\cdot)\) \(\chi_{163}(18,\cdot)\) \(\chi_{163}(19,\cdot)\) \(\chi_{163}(20,\cdot)\) \(\chi_{163}(29,\cdot)\) \(\chi_{163}(32,\cdot)\) \(\chi_{163}(42,\cdot)\) \(\chi_{163}(44,\cdot)\) \(\chi_{163}(45,\cdot)\) \(\chi_{163}(50,\cdot)\) \(\chi_{163}(52,\cdot)\) \(\chi_{163}(63,\cdot)\) \(\chi_{163}(66,\cdot)\) \(\chi_{163}(67,\cdot)\) \(\chi_{163}(68,\cdot)\) \(\chi_{163}(70,\cdot)\) \(\chi_{163}(72,\cdot)\) \(\chi_{163}(73,\cdot)\) \(\chi_{163}(75,\cdot)\) \(\chi_{163}(76,\cdot)\) \(\chi_{163}(79,\cdot)\) \(\chi_{163}(80,\cdot)\) \(\chi_{163}(82,\cdot)\) \(\chi_{163}(89,\cdot)\) \(\chi_{163}(92,\cdot)\) \(\chi_{163}(94,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{81})$ |
| Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{101}{162}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 163 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{162}\right)\) | \(e\left(\frac{157}{162}\right)\) | \(e\left(\frac{20}{81}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{83}{162}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{76}{81}\right)\) | \(e\left(\frac{79}{81}\right)\) | \(e\left(\frac{49}{162}\right)\) |