Basic properties
Modulus: | \(1849\) | |
Conductor: | \(1849\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(129\) | 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.k
\(\chi_{1849}(6,\cdot)\) \(\chi_{1849}(36,\cdot)\) \(\chi_{1849}(49,\cdot)\) \(\chi_{1849}(79,\cdot)\) \(\chi_{1849}(92,\cdot)\) \(\chi_{1849}(122,\cdot)\) \(\chi_{1849}(135,\cdot)\) \(\chi_{1849}(165,\cdot)\) \(\chi_{1849}(178,\cdot)\) \(\chi_{1849}(208,\cdot)\) \(\chi_{1849}(221,\cdot)\) \(\chi_{1849}(251,\cdot)\) \(\chi_{1849}(264,\cdot)\) \(\chi_{1849}(294,\cdot)\) \(\chi_{1849}(307,\cdot)\) \(\chi_{1849}(337,\cdot)\) \(\chi_{1849}(350,\cdot)\) \(\chi_{1849}(380,\cdot)\) \(\chi_{1849}(393,\cdot)\) \(\chi_{1849}(436,\cdot)\) \(\chi_{1849}(466,\cdot)\) \(\chi_{1849}(479,\cdot)\) \(\chi_{1849}(509,\cdot)\) \(\chi_{1849}(522,\cdot)\) \(\chi_{1849}(552,\cdot)\) \(\chi_{1849}(565,\cdot)\) \(\chi_{1849}(595,\cdot)\) \(\chi_{1849}(608,\cdot)\) \(\chi_{1849}(638,\cdot)\) \(\chi_{1849}(651,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{129})$ |
Fixed field: | Number field defined by a degree 129 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{68}{129}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1849 }(178, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{43}\right)\) | \(e\left(\frac{68}{129}\right)\) | \(e\left(\frac{22}{43}\right)\) | \(e\left(\frac{95}{129}\right)\) | \(e\left(\frac{101}{129}\right)\) | \(e\left(\frac{19}{129}\right)\) | \(e\left(\frac{33}{43}\right)\) | \(e\left(\frac{7}{129}\right)\) | \(e\left(\frac{128}{129}\right)\) | \(e\left(\frac{24}{43}\right)\) |