Basic properties
| Modulus: | \(4001\) | |
| Conductor: | \(4001\) | 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 4001.q
\(\chi_{4001}(5,\cdot)\) \(\chi_{4001}(32,\cdot)\) \(\chi_{4001}(79,\cdot)\) \(\chi_{4001}(125,\cdot)\) \(\chi_{4001}(214,\cdot)\) \(\chi_{4001}(261,\cdot)\) \(\chi_{4001}(338,\cdot)\) \(\chi_{4001}(347,\cdot)\) \(\chi_{4001}(357,\cdot)\) \(\chi_{4001}(448,\cdot)\) \(\chi_{4001}(494,\cdot)\) \(\chi_{4001}(509,\cdot)\) \(\chi_{4001}(520,\cdot)\) \(\chi_{4001}(637,\cdot)\) \(\chi_{4001}(722,\cdot)\) \(\chi_{4001}(731,\cdot)\) \(\chi_{4001}(760,\cdot)\) \(\chi_{4001}(761,\cdot)\) \(\chi_{4001}(800,\cdot)\) \(\chi_{4001}(803,\cdot)\) \(\chi_{4001}(821,\cdot)\) \(\chi_{4001}(857,\cdot)\) \(\chi_{4001}(863,\cdot)\) \(\chi_{4001}(916,\cdot)\) \(\chi_{4001}(919,\cdot)\) \(\chi_{4001}(923,\cdot)\) \(\chi_{4001}(931,\cdot)\) \(\chi_{4001}(980,\cdot)\) \(\chi_{4001}(997,\cdot)\) \(\chi_{4001}(1005,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{200})$ |
| Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{149}{200}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4001 }(79, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{149}{200}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{57}{200}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{49}{100}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{5}{8}\right)\) |