Basic properties
| Modulus: | \(1339\) | |
| Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(204\) | 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 1339.cc
\(\chi_{1339}(45,\cdot)\) \(\chi_{1339}(54,\cdot)\) \(\chi_{1339}(71,\cdot)\) \(\chi_{1339}(124,\cdot)\) \(\chi_{1339}(180,\cdot)\) \(\chi_{1339}(189,\cdot)\) \(\chi_{1339}(202,\cdot)\) \(\chi_{1339}(227,\cdot)\) \(\chi_{1339}(249,\cdot)\) \(\chi_{1339}(284,\cdot)\) \(\chi_{1339}(292,\cdot)\) \(\chi_{1339}(305,\cdot)\) \(\chi_{1339}(353,\cdot)\) \(\chi_{1339}(397,\cdot)\) \(\chi_{1339}(418,\cdot)\) \(\chi_{1339}(423,\cdot)\) \(\chi_{1339}(466,\cdot)\) \(\chi_{1339}(496,\cdot)\) \(\chi_{1339}(500,\cdot)\) \(\chi_{1339}(526,\cdot)\) \(\chi_{1339}(527,\cdot)\) \(\chi_{1339}(535,\cdot)\) \(\chi_{1339}(566,\cdot)\) \(\chi_{1339}(600,\cdot)\) \(\chi_{1339}(630,\cdot)\) \(\chi_{1339}(661,\cdot)\) \(\chi_{1339}(669,\cdot)\) \(\chi_{1339}(683,\cdot)\) \(\chi_{1339}(756,\cdot)\) \(\chi_{1339}(761,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1237,417)\) → \((e\left(\frac{5}{12}\right),e\left(\frac{79}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1339 }(45, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{204}\right)\) | \(e\left(\frac{89}{102}\right)\) | \(e\left(\frac{101}{102}\right)\) | \(e\left(\frac{107}{204}\right)\) | \(e\left(\frac{25}{68}\right)\) | \(e\left(\frac{139}{204}\right)\) | \(e\left(\frac{33}{68}\right)\) | \(e\left(\frac{38}{51}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{11}{68}\right)\) |