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 \(\chi_{287}(30,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2009.by
\(\chi_{2009}(30,\cdot)\) \(\chi_{2009}(67,\cdot)\) \(\chi_{2009}(116,\cdot)\) \(\chi_{2009}(177,\cdot)\) \(\chi_{2009}(263,\cdot)\) \(\chi_{2009}(275,\cdot)\) \(\chi_{2009}(422,\cdot)\) \(\chi_{2009}(520,\cdot)\) \(\chi_{2009}(557,\cdot)\) \(\chi_{2009}(667,\cdot)\) \(\chi_{2009}(704,\cdot)\) \(\chi_{2009}(716,\cdot)\) \(\chi_{2009}(753,\cdot)\) \(\chi_{2009}(814,\cdot)\) \(\chi_{2009}(949,\cdot)\) \(\chi_{2009}(1010,\cdot)\) \(\chi_{2009}(1047,\cdot)\) \(\chi_{2009}(1059,\cdot)\) \(\chi_{2009}(1096,\cdot)\) \(\chi_{2009}(1206,\cdot)\) \(\chi_{2009}(1243,\cdot)\) \(\chi_{2009}(1341,\cdot)\) \(\chi_{2009}(1488,\cdot)\) \(\chi_{2009}(1500,\cdot)\) \(\chi_{2009}(1586,\cdot)\) \(\chi_{2009}(1647,\cdot)\) \(\chi_{2009}(1696,\cdot)\) \(\chi_{2009}(1733,\cdot)\) \(\chi_{2009}(1782,\cdot)\) \(\chi_{2009}(1880,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{23}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2009 }(30, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{23}{120}\right)\) |