Basic properties
| Modulus: | \(2005\) | |
| Conductor: | \(401\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{401}(81,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2005.bo
\(\chi_{2005}(81,\cdot)\) \(\chi_{2005}(116,\cdot)\) \(\chi_{2005}(121,\cdot)\) \(\chi_{2005}(156,\cdot)\) \(\chi_{2005}(291,\cdot)\) \(\chi_{2005}(301,\cdot)\) \(\chi_{2005}(311,\cdot)\) \(\chi_{2005}(491,\cdot)\) \(\chi_{2005}(501,\cdot)\) \(\chi_{2005}(511,\cdot)\) \(\chi_{2005}(646,\cdot)\) \(\chi_{2005}(681,\cdot)\) \(\chi_{2005}(686,\cdot)\) \(\chi_{2005}(721,\cdot)\) \(\chi_{2005}(806,\cdot)\) \(\chi_{2005}(851,\cdot)\) \(\chi_{2005}(866,\cdot)\) \(\chi_{2005}(871,\cdot)\) \(\chi_{2005}(896,\cdot)\) \(\chi_{2005}(901,\cdot)\) \(\chi_{2005}(951,\cdot)\) \(\chi_{2005}(1006,\cdot)\) \(\chi_{2005}(1146,\cdot)\) \(\chi_{2005}(1221,\cdot)\) \(\chi_{2005}(1296,\cdot)\) \(\chi_{2005}(1316,\cdot)\) \(\chi_{2005}(1386,\cdot)\) \(\chi_{2005}(1421,\cdot)\) \(\chi_{2005}(1491,\cdot)\) \(\chi_{2005}(1511,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((402,1206)\) → \((1,e\left(\frac{1}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 2005 }(81, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{27}{100}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{19}{100}\right)\) |