Basic properties
Modulus: | \(163\) | |
Conductor: | \(163\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(81\) | 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 163.i
\(\chi_{163}(4,\cdot)\) \(\chi_{163}(9,\cdot)\) \(\chi_{163}(10,\cdot)\) \(\chi_{163}(14,\cdot)\) \(\chi_{163}(15,\cdot)\) \(\chi_{163}(16,\cdot)\) \(\chi_{163}(24,\cdot)\) \(\chi_{163}(26,\cdot)\) \(\chi_{163}(33,\cdot)\) \(\chi_{163}(34,\cdot)\) \(\chi_{163}(35,\cdot)\) \(\chi_{163}(39,\cdot)\) \(\chi_{163}(41,\cdot)\) \(\chi_{163}(43,\cdot)\) \(\chi_{163}(46,\cdot)\) \(\chi_{163}(47,\cdot)\) \(\chi_{163}(49,\cdot)\) \(\chi_{163}(51,\cdot)\) \(\chi_{163}(54,\cdot)\) \(\chi_{163}(55,\cdot)\) \(\chi_{163}(56,\cdot)\) \(\chi_{163}(57,\cdot)\) \(\chi_{163}(60,\cdot)\) \(\chi_{163}(62,\cdot)\) \(\chi_{163}(69,\cdot)\) \(\chi_{163}(71,\cdot)\) \(\chi_{163}(74,\cdot)\) \(\chi_{163}(81,\cdot)\) \(\chi_{163}(83,\cdot)\) \(\chi_{163}(84,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{81})$ |
Fixed field: | Number field defined by a degree 81 polynomial |
Values on generators
\(2\) → \(e\left(\frac{14}{81}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 163 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{81}\right)\) | \(e\left(\frac{37}{81}\right)\) | \(e\left(\frac{28}{81}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{50}{81}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{74}{81}\right)\) | \(e\left(\frac{62}{81}\right)\) | \(e\left(\frac{10}{81}\right)\) |