Basic properties
Modulus: | \(2009\) | |
Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(105\) | 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.bw
\(\chi_{2009}(16,\cdot)\) \(\chi_{2009}(37,\cdot)\) \(\chi_{2009}(51,\cdot)\) \(\chi_{2009}(100,\cdot)\) \(\chi_{2009}(221,\cdot)\) \(\chi_{2009}(242,\cdot)\) \(\chi_{2009}(256,\cdot)\) \(\chi_{2009}(303,\cdot)\) \(\chi_{2009}(305,\cdot)\) \(\chi_{2009}(338,\cdot)\) \(\chi_{2009}(387,\cdot)\) \(\chi_{2009}(529,\cdot)\) \(\chi_{2009}(543,\cdot)\) \(\chi_{2009}(590,\cdot)\) \(\chi_{2009}(592,\cdot)\) \(\chi_{2009}(611,\cdot)\) \(\chi_{2009}(625,\cdot)\) \(\chi_{2009}(674,\cdot)\) \(\chi_{2009}(795,\cdot)\) \(\chi_{2009}(816,\cdot)\) \(\chi_{2009}(830,\cdot)\) \(\chi_{2009}(877,\cdot)\) \(\chi_{2009}(879,\cdot)\) \(\chi_{2009}(898,\cdot)\) \(\chi_{2009}(1082,\cdot)\) \(\chi_{2009}(1103,\cdot)\) \(\chi_{2009}(1117,\cdot)\) \(\chi_{2009}(1164,\cdot)\) \(\chi_{2009}(1166,\cdot)\) \(\chi_{2009}(1185,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{20}{21}\right),e\left(\frac{2}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 2009 }(305, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{29}{105}\right)\) |