Basic properties
Modulus: | \(1849\) | |
Conductor: | \(1849\) | 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 1849.i
\(\chi_{1849}(44,\cdot)\) \(\chi_{1849}(87,\cdot)\) \(\chi_{1849}(130,\cdot)\) \(\chi_{1849}(173,\cdot)\) \(\chi_{1849}(216,\cdot)\) \(\chi_{1849}(259,\cdot)\) \(\chi_{1849}(302,\cdot)\) \(\chi_{1849}(345,\cdot)\) \(\chi_{1849}(388,\cdot)\) \(\chi_{1849}(431,\cdot)\) \(\chi_{1849}(474,\cdot)\) \(\chi_{1849}(517,\cdot)\) \(\chi_{1849}(560,\cdot)\) \(\chi_{1849}(603,\cdot)\) \(\chi_{1849}(646,\cdot)\) \(\chi_{1849}(689,\cdot)\) \(\chi_{1849}(732,\cdot)\) \(\chi_{1849}(775,\cdot)\) \(\chi_{1849}(818,\cdot)\) \(\chi_{1849}(861,\cdot)\) \(\chi_{1849}(904,\cdot)\) \(\chi_{1849}(947,\cdot)\) \(\chi_{1849}(990,\cdot)\) \(\chi_{1849}(1033,\cdot)\) \(\chi_{1849}(1076,\cdot)\) \(\chi_{1849}(1119,\cdot)\) \(\chi_{1849}(1162,\cdot)\) \(\chi_{1849}(1205,\cdot)\) \(\chi_{1849}(1248,\cdot)\) \(\chi_{1849}(1291,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{43})$ |
Fixed field: | 43.43.162686032778208990102858628859785420567496242104134005559503199497609643882923419981647276367075859293620549051195773051892887390454194801.1 |
Values on generators
\(3\) → \(e\left(\frac{13}{43}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1849 }(1119, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{43}\right)\) | \(e\left(\frac{13}{43}\right)\) | \(e\left(\frac{24}{43}\right)\) | \(e\left(\frac{15}{43}\right)\) | \(e\left(\frac{25}{43}\right)\) | \(e\left(\frac{3}{43}\right)\) | \(e\left(\frac{36}{43}\right)\) | \(e\left(\frac{26}{43}\right)\) | \(e\left(\frac{27}{43}\right)\) | \(e\left(\frac{34}{43}\right)\) |