Basic properties
Modulus: | \(4000\) | |
Conductor: | \(4000\) | 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 4000.da
\(\chi_{4000}(29,\cdot)\) \(\chi_{4000}(69,\cdot)\) \(\chi_{4000}(109,\cdot)\) \(\chi_{4000}(189,\cdot)\) \(\chi_{4000}(229,\cdot)\) \(\chi_{4000}(269,\cdot)\) \(\chi_{4000}(309,\cdot)\) \(\chi_{4000}(389,\cdot)\) \(\chi_{4000}(429,\cdot)\) \(\chi_{4000}(469,\cdot)\) \(\chi_{4000}(509,\cdot)\) \(\chi_{4000}(589,\cdot)\) \(\chi_{4000}(629,\cdot)\) \(\chi_{4000}(669,\cdot)\) \(\chi_{4000}(709,\cdot)\) \(\chi_{4000}(789,\cdot)\) \(\chi_{4000}(829,\cdot)\) \(\chi_{4000}(869,\cdot)\) \(\chi_{4000}(909,\cdot)\) \(\chi_{4000}(989,\cdot)\) \(\chi_{4000}(1029,\cdot)\) \(\chi_{4000}(1069,\cdot)\) \(\chi_{4000}(1109,\cdot)\) \(\chi_{4000}(1189,\cdot)\) \(\chi_{4000}(1229,\cdot)\) \(\chi_{4000}(1269,\cdot)\) \(\chi_{4000}(1309,\cdot)\) \(\chi_{4000}(1389,\cdot)\) \(\chi_{4000}(1429,\cdot)\) \(\chi_{4000}(1469,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{200})$ |
Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\((2751,2501,1377)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{21}{50}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 4000 }(1229, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{200}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{13}{100}\right)\) | \(e\left(\frac{59}{200}\right)\) | \(e\left(\frac{101}{200}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{137}{200}\right)\) | \(e\left(\frac{3}{200}\right)\) | \(e\left(\frac{27}{100}\right)\) | \(e\left(\frac{139}{200}\right)\) |