Basic properties
| Modulus: | \(2005\) | |
| Conductor: | \(2005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | 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.bk
\(\chi_{2005}(48,\cdot)\) \(\chi_{2005}(142,\cdot)\) \(\chi_{2005}(148,\cdot)\) \(\chi_{2005}(153,\cdot)\) \(\chi_{2005}(157,\cdot)\) \(\chi_{2005}(158,\cdot)\) \(\chi_{2005}(243,\cdot)\) \(\chi_{2005}(248,\cdot)\) \(\chi_{2005}(253,\cdot)\) \(\chi_{2005}(317,\cdot)\) \(\chi_{2005}(353,\cdot)\) \(\chi_{2005}(477,\cdot)\) \(\chi_{2005}(613,\cdot)\) \(\chi_{2005}(647,\cdot)\) \(\chi_{2005}(683,\cdot)\) \(\chi_{2005}(828,\cdot)\) \(\chi_{2005}(957,\cdot)\) \(\chi_{2005}(973,\cdot)\) \(\chi_{2005}(1127,\cdot)\) \(\chi_{2005}(1287,\cdot)\) \(\chi_{2005}(1433,\cdot)\) \(\chi_{2005}(1447,\cdot)\) \(\chi_{2005}(1462,\cdot)\) \(\chi_{2005}(1578,\cdot)\) \(\chi_{2005}(1637,\cdot)\) \(\chi_{2005}(1672,\cdot)\) \(\chi_{2005}(1712,\cdot)\) \(\chi_{2005}(1723,\cdot)\) \(\chi_{2005}(1793,\cdot)\) \(\chi_{2005}(1897,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((402,1206)\) → \((-i,e\left(\frac{21}{80}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 2005 }(48, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{79}{80}\right)\) |