Basic properties
Modulus: | \(193\) | |
Conductor: | \(193\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(192\) | 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 193.n
\(\chi_{193}(5,\cdot)\) \(\chi_{193}(10,\cdot)\) \(\chi_{193}(15,\cdot)\) \(\chi_{193}(17,\cdot)\) \(\chi_{193}(19,\cdot)\) \(\chi_{193}(22,\cdot)\) \(\chi_{193}(26,\cdot)\) \(\chi_{193}(30,\cdot)\) \(\chi_{193}(34,\cdot)\) \(\chi_{193}(37,\cdot)\) \(\chi_{193}(38,\cdot)\) \(\chi_{193}(40,\cdot)\) \(\chi_{193}(41,\cdot)\) \(\chi_{193}(44,\cdot)\) \(\chi_{193}(45,\cdot)\) \(\chi_{193}(47,\cdot)\) \(\chi_{193}(51,\cdot)\) \(\chi_{193}(52,\cdot)\) \(\chi_{193}(53,\cdot)\) \(\chi_{193}(57,\cdot)\) \(\chi_{193}(58,\cdot)\) \(\chi_{193}(61,\cdot)\) \(\chi_{193}(66,\cdot)\) \(\chi_{193}(70,\cdot)\) \(\chi_{193}(73,\cdot)\) \(\chi_{193}(77,\cdot)\) \(\chi_{193}(78,\cdot)\) \(\chi_{193}(79,\cdot)\) \(\chi_{193}(80,\cdot)\) \(\chi_{193}(82,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{192})$ |
Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{85}{192}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 193 }(15, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{96}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{85}{192}\right)\) | \(e\left(\frac{23}{96}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{95}{192}\right)\) | \(e\left(\frac{1}{64}\right)\) |