Basic properties
Modulus: | \(4000\) | |
Conductor: | \(2000\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2000}(1379,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4000.cx
\(\chi_{4000}(39,\cdot)\) \(\chi_{4000}(119,\cdot)\) \(\chi_{4000}(279,\cdot)\) \(\chi_{4000}(359,\cdot)\) \(\chi_{4000}(439,\cdot)\) \(\chi_{4000}(519,\cdot)\) \(\chi_{4000}(679,\cdot)\) \(\chi_{4000}(759,\cdot)\) \(\chi_{4000}(839,\cdot)\) \(\chi_{4000}(919,\cdot)\) \(\chi_{4000}(1079,\cdot)\) \(\chi_{4000}(1159,\cdot)\) \(\chi_{4000}(1239,\cdot)\) \(\chi_{4000}(1319,\cdot)\) \(\chi_{4000}(1479,\cdot)\) \(\chi_{4000}(1559,\cdot)\) \(\chi_{4000}(1639,\cdot)\) \(\chi_{4000}(1719,\cdot)\) \(\chi_{4000}(1879,\cdot)\) \(\chi_{4000}(1959,\cdot)\) \(\chi_{4000}(2039,\cdot)\) \(\chi_{4000}(2119,\cdot)\) \(\chi_{4000}(2279,\cdot)\) \(\chi_{4000}(2359,\cdot)\) \(\chi_{4000}(2439,\cdot)\) \(\chi_{4000}(2519,\cdot)\) \(\chi_{4000}(2679,\cdot)\) \(\chi_{4000}(2759,\cdot)\) \(\chi_{4000}(2839,\cdot)\) \(\chi_{4000}(2919,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((2751,2501,1377)\) → \((-1,-i,e\left(\frac{1}{50}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 4000 }(1879, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{100}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{77}{100}\right)\) | \(e\left(\frac{3}{100}\right)\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{11}{100}\right)\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{67}{100}\right)\) |