Basic properties
| Modulus: | \(2005\) | |
| Conductor: | \(401\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(200\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{401}(261,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2005.bx
\(\chi_{2005}(11,\cdot)\) \(\chi_{2005}(36,\cdot)\) \(\chi_{2005}(111,\cdot)\) \(\chi_{2005}(166,\cdot)\) \(\chi_{2005}(176,\cdot)\) \(\chi_{2005}(181,\cdot)\) \(\chi_{2005}(186,\cdot)\) \(\chi_{2005}(201,\cdot)\) \(\chi_{2005}(221,\cdot)\) \(\chi_{2005}(226,\cdot)\) \(\chi_{2005}(241,\cdot)\) \(\chi_{2005}(261,\cdot)\) \(\chi_{2005}(346,\cdot)\) \(\chi_{2005}(351,\cdot)\) \(\chi_{2005}(361,\cdot)\) \(\chi_{2005}(391,\cdot)\) \(\chi_{2005}(411,\cdot)\) \(\chi_{2005}(441,\cdot)\) \(\chi_{2005}(451,\cdot)\) \(\chi_{2005}(456,\cdot)\) \(\chi_{2005}(541,\cdot)\) \(\chi_{2005}(561,\cdot)\) \(\chi_{2005}(576,\cdot)\) \(\chi_{2005}(581,\cdot)\) \(\chi_{2005}(601,\cdot)\) \(\chi_{2005}(616,\cdot)\) \(\chi_{2005}(621,\cdot)\) \(\chi_{2005}(626,\cdot)\) \(\chi_{2005}(636,\cdot)\) \(\chi_{2005}(691,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{200})$ |
| Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\((402,1206)\) → \((1,e\left(\frac{181}{200}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 2005 }(261, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{181}{200}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{87}{200}\right)\) | \(e\left(\frac{11}{100}\right)\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{57}{100}\right)\) | \(e\left(\frac{193}{200}\right)\) | \(e\left(\frac{139}{200}\right)\) |