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.bz
\(\chi_{1339}(36,\cdot)\) \(\chi_{1339}(121,\cdot)\) \(\chi_{1339}(153,\cdot)\) \(\chi_{1339}(166,\cdot)\) \(\chi_{1339}(186,\cdot)\) \(\chi_{1339}(225,\cdot)\) \(\chi_{1339}(244,\cdot)\) \(\chi_{1339}(303,\cdot)\) \(\chi_{1339}(361,\cdot)\) \(\chi_{1339}(368,\cdot)\) \(\chi_{1339}(400,\cdot)\) \(\chi_{1339}(472,\cdot)\) \(\chi_{1339}(504,\cdot)\) \(\chi_{1339}(530,\cdot)\) \(\chi_{1339}(667,\cdot)\) \(\chi_{1339}(725,\cdot)\) \(\chi_{1339}(738,\cdot)\) \(\chi_{1339}(803,\cdot)\) \(\chi_{1339}(849,\cdot)\) \(\chi_{1339}(953,\cdot)\) \(\chi_{1339}(959,\cdot)\) \(\chi_{1339}(985,\cdot)\) \(\chi_{1339}(1037,\cdot)\) \(\chi_{1339}(1063,\cdot)\) \(\chi_{1339}(1128,\cdot)\) \(\chi_{1339}(1135,\cdot)\) \(\chi_{1339}(1161,\cdot)\) \(\chi_{1339}(1174,\cdot)\) \(\chi_{1339}(1252,\cdot)\) \(\chi_{1339}(1265,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((1237,417)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{32}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1339 }(36, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{13}{102}\right)\) | \(e\left(\frac{25}{102}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{29}{51}\right)\) | \(e\left(\frac{11}{102}\right)\) |