Basic properties
| Modulus: | \(4001\) | |
| Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(160\) | 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 4001.p
\(\chi_{4001}(11,\cdot)\) \(\chi_{4001}(57,\cdot)\) \(\chi_{4001}(82,\cdot)\) \(\chi_{4001}(163,\cdot)\) \(\chi_{4001}(233,\cdot)\) \(\chi_{4001}(262,\cdot)\) \(\chi_{4001}(265,\cdot)\) \(\chi_{4001}(270,\cdot)\) \(\chi_{4001}(282,\cdot)\) \(\chi_{4001}(306,\cdot)\) \(\chi_{4001}(461,\cdot)\) \(\chi_{4001}(521,\cdot)\) \(\chi_{4001}(593,\cdot)\) \(\chi_{4001}(599,\cdot)\) \(\chi_{4001}(770,\cdot)\) \(\chi_{4001}(974,\cdot)\) \(\chi_{4001}(975,\cdot)\) \(\chi_{4001}(1030,\cdot)\) \(\chi_{4001}(1105,\cdot)\) \(\chi_{4001}(1147,\cdot)\) \(\chi_{4001}(1331,\cdot)\) \(\chi_{4001}(1415,\cdot)\) \(\chi_{4001}(1455,\cdot)\) \(\chi_{4001}(1500,\cdot)\) \(\chi_{4001}(1634,\cdot)\) \(\chi_{4001}(1649,\cdot)\) \(\chi_{4001}(1665,\cdot)\) \(\chi_{4001}(1700,\cdot)\) \(\chi_{4001}(1739,\cdot)\) \(\chi_{4001}(1825,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{160})$ |
| Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{57}{160}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4001 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{57}{160}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{101}{160}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{21}{32}\right)\) |