Basic properties
Modulus: | \(293\) | |
Conductor: | \(293\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(73\) | 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.d
\(\chi_{293}(16,\cdot)\) \(\chi_{293}(17,\cdot)\) \(\chi_{293}(22,\cdot)\) \(\chi_{293}(24,\cdot)\) \(\chi_{293}(26,\cdot)\) \(\chi_{293}(33,\cdot)\) \(\chi_{293}(36,\cdot)\) \(\chi_{293}(38,\cdot)\) \(\chi_{293}(39,\cdot)\) \(\chi_{293}(40,\cdot)\) \(\chi_{293}(46,\cdot)\) \(\chi_{293}(53,\cdot)\) \(\chi_{293}(54,\cdot)\) \(\chi_{293}(55,\cdot)\) \(\chi_{293}(56,\cdot)\) \(\chi_{293}(57,\cdot)\) \(\chi_{293}(59,\cdot)\) \(\chi_{293}(60,\cdot)\) \(\chi_{293}(65,\cdot)\) \(\chi_{293}(69,\cdot)\) \(\chi_{293}(73,\cdot)\) \(\chi_{293}(77,\cdot)\) \(\chi_{293}(81,\cdot)\) \(\chi_{293}(82,\cdot)\) \(\chi_{293}(84,\cdot)\) \(\chi_{293}(90,\cdot)\) \(\chi_{293}(91,\cdot)\) \(\chi_{293}(94,\cdot)\) \(\chi_{293}(95,\cdot)\) \(\chi_{293}(100,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{73})$ |
Fixed field: | Number field defined by a degree 73 polynomial |
Values on generators
\(2\) → \(e\left(\frac{45}{73}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 293 }(54, a) \) | \(1\) | \(1\) | \(e\left(\frac{45}{73}\right)\) | \(e\left(\frac{57}{73}\right)\) | \(e\left(\frac{17}{73}\right)\) | \(e\left(\frac{47}{73}\right)\) | \(e\left(\frac{29}{73}\right)\) | \(e\left(\frac{22}{73}\right)\) | \(e\left(\frac{62}{73}\right)\) | \(e\left(\frac{41}{73}\right)\) | \(e\left(\frac{19}{73}\right)\) | \(e\left(\frac{65}{73}\right)\) |