Basic properties
Modulus: | \(2009\) | |
Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | 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 2009.bu
\(\chi_{2009}(9,\cdot)\) \(\chi_{2009}(32,\cdot)\) \(\chi_{2009}(114,\cdot)\) \(\chi_{2009}(296,\cdot)\) \(\chi_{2009}(319,\cdot)\) \(\chi_{2009}(401,\cdot)\) \(\chi_{2009}(501,\cdot)\) \(\chi_{2009}(583,\cdot)\) \(\chi_{2009}(688,\cdot)\) \(\chi_{2009}(788,\cdot)\) \(\chi_{2009}(870,\cdot)\) \(\chi_{2009}(893,\cdot)\) \(\chi_{2009}(975,\cdot)\) \(\chi_{2009}(1075,\cdot)\) \(\chi_{2009}(1180,\cdot)\) \(\chi_{2009}(1262,\cdot)\) \(\chi_{2009}(1362,\cdot)\) \(\chi_{2009}(1444,\cdot)\) \(\chi_{2009}(1467,\cdot)\) \(\chi_{2009}(1649,\cdot)\) \(\chi_{2009}(1731,\cdot)\) \(\chi_{2009}(1754,\cdot)\) \(\chi_{2009}(1836,\cdot)\) \(\chi_{2009}(1936,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((493,785)\) → \((e\left(\frac{2}{21}\right),-i)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 2009 }(1649, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{25}{84}\right)\) |