Basic properties
Modulus: | \(193\) | |
Conductor: | \(193\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(96\) | 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 193.m
\(\chi_{193}(2,\cdot)\) \(\chi_{193}(6,\cdot)\) \(\chi_{193}(18,\cdot)\) \(\chi_{193}(25,\cdot)\) \(\chi_{193}(31,\cdot)\) \(\chi_{193}(32,\cdot)\) \(\chi_{193}(54,\cdot)\) \(\chi_{193}(56,\cdot)\) \(\chi_{193}(65,\cdot)\) \(\chi_{193}(75,\cdot)\) \(\chi_{193}(83,\cdot)\) \(\chi_{193}(86,\cdot)\) \(\chi_{193}(92,\cdot)\) \(\chi_{193}(93,\cdot)\) \(\chi_{193}(95,\cdot)\) \(\chi_{193}(96,\cdot)\) \(\chi_{193}(97,\cdot)\) \(\chi_{193}(98,\cdot)\) \(\chi_{193}(100,\cdot)\) \(\chi_{193}(101,\cdot)\) \(\chi_{193}(107,\cdot)\) \(\chi_{193}(110,\cdot)\) \(\chi_{193}(118,\cdot)\) \(\chi_{193}(128,\cdot)\) \(\chi_{193}(137,\cdot)\) \(\chi_{193}(139,\cdot)\) \(\chi_{193}(161,\cdot)\) \(\chi_{193}(162,\cdot)\) \(\chi_{193}(168,\cdot)\) \(\chi_{193}(175,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\(5\) → \(e\left(\frac{5}{96}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 193 }(18, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{5}{96}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(-i\) | \(e\left(\frac{79}{96}\right)\) | \(e\left(\frac{17}{32}\right)\) |