Basic properties
Modulus: | \(193\) | |
Conductor: | \(193\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(64\) | 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.l
\(\chi_{193}(11,\cdot)\) \(\chi_{193}(13,\cdot)\) \(\chi_{193}(20,\cdot)\) \(\chi_{193}(29,\cdot)\) \(\chi_{193}(33,\cdot)\) \(\chi_{193}(35,\cdot)\) \(\chi_{193}(39,\cdot)\) \(\chi_{193}(60,\cdot)\) \(\chi_{193}(68,\cdot)\) \(\chi_{193}(71,\cdot)\) \(\chi_{193}(74,\cdot)\) \(\chi_{193}(76,\cdot)\) \(\chi_{193}(87,\cdot)\) \(\chi_{193}(88,\cdot)\) \(\chi_{193}(89,\cdot)\) \(\chi_{193}(94,\cdot)\) \(\chi_{193}(99,\cdot)\) \(\chi_{193}(104,\cdot)\) \(\chi_{193}(105,\cdot)\) \(\chi_{193}(106,\cdot)\) \(\chi_{193}(117,\cdot)\) \(\chi_{193}(119,\cdot)\) \(\chi_{193}(122,\cdot)\) \(\chi_{193}(125,\cdot)\) \(\chi_{193}(133,\cdot)\) \(\chi_{193}(154,\cdot)\) \(\chi_{193}(158,\cdot)\) \(\chi_{193}(160,\cdot)\) \(\chi_{193}(164,\cdot)\) \(\chi_{193}(173,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\(5\) → \(e\left(\frac{1}{64}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 193 }(125, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{1}{64}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{35}{64}\right)\) | \(e\left(\frac{55}{64}\right)\) |