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
\((1237,417)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{2}{17}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1339 }(446, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{102}\right)\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{61}{102}\right)\) | \(e\left(\frac{31}{102}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{35}{102}\right)\) |