Basic properties
Modulus: | \(293\) | |
Conductor: | \(293\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(292\) | 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 293.f
\(\chi_{293}(2,\cdot)\) \(\chi_{293}(3,\cdot)\) \(\chi_{293}(5,\cdot)\) \(\chi_{293}(7,\cdot)\) \(\chi_{293}(8,\cdot)\) \(\chi_{293}(11,\cdot)\) \(\chi_{293}(12,\cdot)\) \(\chi_{293}(13,\cdot)\) \(\chi_{293}(18,\cdot)\) \(\chi_{293}(19,\cdot)\) \(\chi_{293}(20,\cdot)\) \(\chi_{293}(23,\cdot)\) \(\chi_{293}(27,\cdot)\) \(\chi_{293}(28,\cdot)\) \(\chi_{293}(29,\cdot)\) \(\chi_{293}(30,\cdot)\) \(\chi_{293}(32,\cdot)\) \(\chi_{293}(34,\cdot)\) \(\chi_{293}(41,\cdot)\) \(\chi_{293}(42,\cdot)\) \(\chi_{293}(44,\cdot)\) \(\chi_{293}(45,\cdot)\) \(\chi_{293}(47,\cdot)\) \(\chi_{293}(48,\cdot)\) \(\chi_{293}(50,\cdot)\) \(\chi_{293}(51,\cdot)\) \(\chi_{293}(52,\cdot)\) \(\chi_{293}(62,\cdot)\) \(\chi_{293}(63,\cdot)\) \(\chi_{293}(66,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{292})$ |
Fixed field: | Number field defined by a degree 292 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{5}{292}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 293 }(32, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{292}\right)\) | \(e\left(\frac{201}{292}\right)\) | \(e\left(\frac{5}{146}\right)\) | \(e\left(\frac{281}{292}\right)\) | \(e\left(\frac{103}{146}\right)\) | \(e\left(\frac{189}{292}\right)\) | \(e\left(\frac{15}{292}\right)\) | \(e\left(\frac{55}{146}\right)\) | \(e\left(\frac{143}{146}\right)\) | \(e\left(\frac{283}{292}\right)\) |