Basic properties
Modulus: | \(2009\) | |
Conductor: | \(287\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{287}(145,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2009.bx
\(\chi_{2009}(19,\cdot)\) \(\chi_{2009}(117,\cdot)\) \(\chi_{2009}(129,\cdot)\) \(\chi_{2009}(227,\cdot)\) \(\chi_{2009}(276,\cdot)\) \(\chi_{2009}(313,\cdot)\) \(\chi_{2009}(362,\cdot)\) \(\chi_{2009}(423,\cdot)\) \(\chi_{2009}(509,\cdot)\) \(\chi_{2009}(521,\cdot)\) \(\chi_{2009}(668,\cdot)\) \(\chi_{2009}(766,\cdot)\) \(\chi_{2009}(803,\cdot)\) \(\chi_{2009}(913,\cdot)\) \(\chi_{2009}(950,\cdot)\) \(\chi_{2009}(962,\cdot)\) \(\chi_{2009}(999,\cdot)\) \(\chi_{2009}(1060,\cdot)\) \(\chi_{2009}(1195,\cdot)\) \(\chi_{2009}(1256,\cdot)\) \(\chi_{2009}(1293,\cdot)\) \(\chi_{2009}(1305,\cdot)\) \(\chi_{2009}(1342,\cdot)\) \(\chi_{2009}(1452,\cdot)\) \(\chi_{2009}(1489,\cdot)\) \(\chi_{2009}(1587,\cdot)\) \(\chi_{2009}(1734,\cdot)\) \(\chi_{2009}(1746,\cdot)\) \(\chi_{2009}(1832,\cdot)\) \(\chi_{2009}(1893,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{29}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 2009 }(1293, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{89}{120}\right)\) |