Basic properties
| Modulus: | \(8005\) | |
| Conductor: | \(1601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(400\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1601}(21,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8005.cp
\(\chi_{8005}(21,\cdot)\) \(\chi_{8005}(51,\cdot)\) \(\chi_{8005}(81,\cdot)\) \(\chi_{8005}(91,\cdot)\) \(\chi_{8005}(106,\cdot)\) \(\chi_{8005}(151,\cdot)\) \(\chi_{8005}(221,\cdot)\) \(\chi_{8005}(326,\cdot)\) \(\chi_{8005}(336,\cdot)\) \(\chi_{8005}(351,\cdot)\) \(\chi_{8005}(381,\cdot)\) \(\chi_{8005}(506,\cdot)\) \(\chi_{8005}(541,\cdot)\) \(\chi_{8005}(651,\cdot)\) \(\chi_{8005}(691,\cdot)\) \(\chi_{8005}(761,\cdot)\) \(\chi_{8005}(766,\cdot)\) \(\chi_{8005}(786,\cdot)\) \(\chi_{8005}(801,\cdot)\) \(\chi_{8005}(816,\cdot)\) \(\chi_{8005}(831,\cdot)\) \(\chi_{8005}(981,\cdot)\) \(\chi_{8005}(1021,\cdot)\) \(\chi_{8005}(1076,\cdot)\) \(\chi_{8005}(1101,\cdot)\) \(\chi_{8005}(1206,\cdot)\) \(\chi_{8005}(1256,\cdot)\) \(\chi_{8005}(1281,\cdot)\) \(\chi_{8005}(1296,\cdot)\) \(\chi_{8005}(1391,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{400})$ |
| Fixed field: | Number field defined by a degree 400 polynomial (not computed) |
Values on generators
\((1602,4806)\) → \((1,e\left(\frac{147}{400}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 8005 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{100}\right)\) | \(e\left(\frac{147}{400}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{191}{400}\right)\) | \(e\left(\frac{289}{400}\right)\) | \(e\left(\frac{33}{100}\right)\) | \(e\left(\frac{147}{200}\right)\) | \(e\left(\frac{251}{400}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{11}{16}\right)\) |