Basic properties
| Modulus: | \(1339\) | |
| Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | 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.bt
\(\chi_{1339}(23,\cdot)\) \(\chi_{1339}(30,\cdot)\) \(\chi_{1339}(179,\cdot)\) \(\chi_{1339}(270,\cdot)\) \(\chi_{1339}(322,\cdot)\) \(\chi_{1339}(381,\cdot)\) \(\chi_{1339}(420,\cdot)\) \(\chi_{1339}(426,\cdot)\) \(\chi_{1339}(446,\cdot)\) \(\chi_{1339}(478,\cdot)\) \(\chi_{1339}(491,\cdot)\) \(\chi_{1339}(524,\cdot)\) \(\chi_{1339}(576,\cdot)\) \(\chi_{1339}(608,\cdot)\) \(\chi_{1339}(615,\cdot)\) \(\chi_{1339}(641,\cdot)\) \(\chi_{1339}(699,\cdot)\) \(\chi_{1339}(751,\cdot)\) \(\chi_{1339}(797,\cdot)\) \(\chi_{1339}(888,\cdot)\) \(\chi_{1339}(940,\cdot)\) \(\chi_{1339}(1044,\cdot)\) \(\chi_{1339}(1096,\cdot)\) \(\chi_{1339}(1102,\cdot)\) \(\chi_{1339}(1109,\cdot)\) \(\chi_{1339}(1141,\cdot)\) \(\chi_{1339}(1167,\cdot)\) \(\chi_{1339}(1226,\cdot)\) \(\chi_{1339}(1245,\cdot)\) \(\chi_{1339}(1297,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((1237,417)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{4}{17}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1339 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{102}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{71}{102}\right)\) | \(e\left(\frac{11}{102}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{47}{51}\right)\) | \(e\left(\frac{19}{102}\right)\) |