Basic properties
Modulus: | \(2009\) | |
Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(56\) | 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.bo
\(\chi_{2009}(27,\cdot)\) \(\chi_{2009}(55,\cdot)\) \(\chi_{2009}(167,\cdot)\) \(\chi_{2009}(202,\cdot)\) \(\chi_{2009}(314,\cdot)\) \(\chi_{2009}(454,\cdot)\) \(\chi_{2009}(601,\cdot)\) \(\chi_{2009}(629,\cdot)\) \(\chi_{2009}(741,\cdot)\) \(\chi_{2009}(776,\cdot)\) \(\chi_{2009}(888,\cdot)\) \(\chi_{2009}(916,\cdot)\) \(\chi_{2009}(1063,\cdot)\) \(\chi_{2009}(1203,\cdot)\) \(\chi_{2009}(1315,\cdot)\) \(\chi_{2009}(1350,\cdot)\) \(\chi_{2009}(1462,\cdot)\) \(\chi_{2009}(1490,\cdot)\) \(\chi_{2009}(1602,\cdot)\) \(\chi_{2009}(1637,\cdot)\) \(\chi_{2009}(1749,\cdot)\) \(\chi_{2009}(1777,\cdot)\) \(\chi_{2009}(1889,\cdot)\) \(\chi_{2009}(1924,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{56})$ |
Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((493,785)\) → \((e\left(\frac{1}{14}\right),e\left(\frac{1}{8}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 2009 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{9}{56}\right)\) |