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
\(2\) → \(e\left(\frac{127}{162}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 163 }(76, a) \) | \(-1\) | \(1\) | \(e\left(\frac{127}{162}\right)\) | \(e\left(\frac{29}{162}\right)\) | \(e\left(\frac{46}{81}\right)\) | \(e\left(\frac{41}{54}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{37}{162}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{29}{81}\right)\) | \(e\left(\frac{44}{81}\right)\) | \(e\left(\frac{137}{162}\right)\) |