Basic properties
Modulus: | \(293\) | |
Conductor: | \(293\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(146\) | 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 293.e
\(\chi_{293}(4,\cdot)\) \(\chi_{293}(6,\cdot)\) \(\chi_{293}(9,\cdot)\) \(\chi_{293}(10,\cdot)\) \(\chi_{293}(14,\cdot)\) \(\chi_{293}(15,\cdot)\) \(\chi_{293}(21,\cdot)\) \(\chi_{293}(25,\cdot)\) \(\chi_{293}(31,\cdot)\) \(\chi_{293}(35,\cdot)\) \(\chi_{293}(37,\cdot)\) \(\chi_{293}(43,\cdot)\) \(\chi_{293}(49,\cdot)\) \(\chi_{293}(58,\cdot)\) \(\chi_{293}(61,\cdot)\) \(\chi_{293}(64,\cdot)\) \(\chi_{293}(67,\cdot)\) \(\chi_{293}(68,\cdot)\) \(\chi_{293}(71,\cdot)\) \(\chi_{293}(83,\cdot)\) \(\chi_{293}(87,\cdot)\) \(\chi_{293}(88,\cdot)\) \(\chi_{293}(96,\cdot)\) \(\chi_{293}(97,\cdot)\) \(\chi_{293}(102,\cdot)\) \(\chi_{293}(104,\cdot)\) \(\chi_{293}(107,\cdot)\) \(\chi_{293}(121,\cdot)\) \(\chi_{293}(132,\cdot)\) \(\chi_{293}(143,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{73})$ |
Fixed field: | Number field defined by a degree 146 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{79}{146}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 293 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{146}\right)\) | \(e\left(\frac{139}{146}\right)\) | \(e\left(\frac{6}{73}\right)\) | \(e\left(\frac{89}{146}\right)\) | \(e\left(\frac{36}{73}\right)\) | \(e\left(\frac{37}{146}\right)\) | \(e\left(\frac{91}{146}\right)\) | \(e\left(\frac{66}{73}\right)\) | \(e\left(\frac{11}{73}\right)\) | \(e\left(\frac{33}{146}\right)\) |