Basic properties
| Modulus: | \(173\) | |
| Conductor: | \(173\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(43\) | 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 173.d
\(\chi_{173}(6,\cdot)\) \(\chi_{173}(10,\cdot)\) \(\chi_{173}(14,\cdot)\) \(\chi_{173}(16,\cdot)\) \(\chi_{173}(22,\cdot)\) \(\chi_{173}(23,\cdot)\) \(\chi_{173}(29,\cdot)\) \(\chi_{173}(36,\cdot)\) \(\chi_{173}(43,\cdot)\) \(\chi_{173}(47,\cdot)\) \(\chi_{173}(51,\cdot)\) \(\chi_{173}(52,\cdot)\) \(\chi_{173}(57,\cdot)\) \(\chi_{173}(60,\cdot)\) \(\chi_{173}(81,\cdot)\) \(\chi_{173}(83,\cdot)\) \(\chi_{173}(84,\cdot)\) \(\chi_{173}(85,\cdot)\) \(\chi_{173}(95,\cdot)\) \(\chi_{173}(96,\cdot)\) \(\chi_{173}(100,\cdot)\) \(\chi_{173}(106,\cdot)\) \(\chi_{173}(109,\cdot)\) \(\chi_{173}(117,\cdot)\) \(\chi_{173}(118,\cdot)\) \(\chi_{173}(119,\cdot)\) \(\chi_{173}(124,\cdot)\) \(\chi_{173}(132,\cdot)\) \(\chi_{173}(133,\cdot)\) \(\chi_{173}(135,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{43})$ |
| Fixed field: | Number field defined by a degree 43 polynomial |
Values on generators
\(2\) → \(e\left(\frac{18}{43}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 173 }(95, a) \) | \(1\) | \(1\) | \(e\left(\frac{18}{43}\right)\) | \(e\left(\frac{13}{43}\right)\) | \(e\left(\frac{36}{43}\right)\) | \(e\left(\frac{14}{43}\right)\) | \(e\left(\frac{31}{43}\right)\) | \(e\left(\frac{33}{43}\right)\) | \(e\left(\frac{11}{43}\right)\) | \(e\left(\frac{26}{43}\right)\) | \(e\left(\frac{32}{43}\right)\) | \(e\left(\frac{27}{43}\right)\) |