Basic properties
Modulus: | \(173\) | |
Conductor: | \(173\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(172\) | 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 173.f
\(\chi_{173}(2,\cdot)\) \(\chi_{173}(3,\cdot)\) \(\chi_{173}(5,\cdot)\) \(\chi_{173}(7,\cdot)\) \(\chi_{173}(8,\cdot)\) \(\chi_{173}(11,\cdot)\) \(\chi_{173}(12,\cdot)\) \(\chi_{173}(17,\cdot)\) \(\chi_{173}(18,\cdot)\) \(\chi_{173}(19,\cdot)\) \(\chi_{173}(20,\cdot)\) \(\chi_{173}(26,\cdot)\) \(\chi_{173}(27,\cdot)\) \(\chi_{173}(28,\cdot)\) \(\chi_{173}(30,\cdot)\) \(\chi_{173}(32,\cdot)\) \(\chi_{173}(39,\cdot)\) \(\chi_{173}(42,\cdot)\) \(\chi_{173}(44,\cdot)\) \(\chi_{173}(45,\cdot)\) \(\chi_{173}(46,\cdot)\) \(\chi_{173}(48,\cdot)\) \(\chi_{173}(50,\cdot)\) \(\chi_{173}(53,\cdot)\) \(\chi_{173}(58,\cdot)\) \(\chi_{173}(59,\cdot)\) \(\chi_{173}(61,\cdot)\) \(\chi_{173}(62,\cdot)\) \(\chi_{173}(63,\cdot)\) \(\chi_{173}(65,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{172})$ |
Fixed field: | Number field defined by a degree 172 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{67}{172}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 173 }(30, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{172}\right)\) | \(e\left(\frac{89}{172}\right)\) | \(e\left(\frac{67}{86}\right)\) | \(e\left(\frac{33}{172}\right)\) | \(e\left(\frac{39}{43}\right)\) | \(e\left(\frac{1}{172}\right)\) | \(e\left(\frac{29}{172}\right)\) | \(e\left(\frac{3}{86}\right)\) | \(e\left(\frac{25}{43}\right)\) | \(e\left(\frac{165}{172}\right)\) |