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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4000.db
\(\chi_{4000}(11,\cdot)\) \(\chi_{4000}(91,\cdot)\) \(\chi_{4000}(131,\cdot)\) \(\chi_{4000}(171,\cdot)\) \(\chi_{4000}(211,\cdot)\) \(\chi_{4000}(291,\cdot)\) \(\chi_{4000}(331,\cdot)\) \(\chi_{4000}(371,\cdot)\) \(\chi_{4000}(411,\cdot)\) \(\chi_{4000}(491,\cdot)\) \(\chi_{4000}(531,\cdot)\) \(\chi_{4000}(571,\cdot)\) \(\chi_{4000}(611,\cdot)\) \(\chi_{4000}(691,\cdot)\) \(\chi_{4000}(731,\cdot)\) \(\chi_{4000}(771,\cdot)\) \(\chi_{4000}(811,\cdot)\) \(\chi_{4000}(891,\cdot)\) \(\chi_{4000}(931,\cdot)\) \(\chi_{4000}(971,\cdot)\) \(\chi_{4000}(1011,\cdot)\) \(\chi_{4000}(1091,\cdot)\) \(\chi_{4000}(1131,\cdot)\) \(\chi_{4000}(1171,\cdot)\) \(\chi_{4000}(1211,\cdot)\) \(\chi_{4000}(1291,\cdot)\) \(\chi_{4000}(1331,\cdot)\) \(\chi_{4000}(1371,\cdot)\) \(\chi_{4000}(1411,\cdot)\) \(\chi_{4000}(1491,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{200})$ |
Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\((2751,2501,1377)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{16}{25}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 4000 }(491, a) \) | \(-1\) | \(1\) | \(e\left(\frac{171}{200}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{71}{100}\right)\) | \(e\left(\frac{53}{200}\right)\) | \(e\left(\frac{67}{200}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{79}{200}\right)\) | \(e\left(\frac{1}{200}\right)\) | \(e\left(\frac{9}{100}\right)\) | \(e\left(\frac{113}{200}\right)\) |