Basic properties
Modulus: | \(2005\) | |
Conductor: | \(2005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(200\) | 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 2005.bu
\(\chi_{2005}(9,\cdot)\) \(\chi_{2005}(44,\cdot)\) \(\chi_{2005}(89,\cdot)\) \(\chi_{2005}(109,\cdot)\) \(\chi_{2005}(144,\cdot)\) \(\chi_{2005}(154,\cdot)\) \(\chi_{2005}(159,\cdot)\) \(\chi_{2005}(169,\cdot)\) \(\chi_{2005}(229,\cdot)\) \(\chi_{2005}(289,\cdot)\) \(\chi_{2005}(319,\cdot)\) \(\chi_{2005}(354,\cdot)\) \(\chi_{2005}(394,\cdot)\) \(\chi_{2005}(399,\cdot)\) \(\chi_{2005}(409,\cdot)\) \(\chi_{2005}(429,\cdot)\) \(\chi_{2005}(444,\cdot)\) \(\chi_{2005}(459,\cdot)\) \(\chi_{2005}(474,\cdot)\) \(\chi_{2005}(479,\cdot)\) \(\chi_{2005}(504,\cdot)\) \(\chi_{2005}(529,\cdot)\) \(\chi_{2005}(539,\cdot)\) \(\chi_{2005}(599,\cdot)\) \(\chi_{2005}(604,\cdot)\) \(\chi_{2005}(664,\cdot)\) \(\chi_{2005}(674,\cdot)\) \(\chi_{2005}(699,\cdot)\) \(\chi_{2005}(724,\cdot)\) \(\chi_{2005}(729,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{200})$ |
Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\((402,1206)\) → \((-1,e\left(\frac{107}{200}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 2005 }(159, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{100}\right)\) | \(e\left(\frac{7}{200}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{89}{200}\right)\) | \(e\left(\frac{67}{100}\right)\) | \(e\left(\frac{23}{100}\right)\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{79}{100}\right)\) | \(e\left(\frac{171}{200}\right)\) | \(e\left(\frac{33}{200}\right)\) |