Basic properties
| Modulus: | \(4003\) | |
| Conductor: | \(4003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(4002\) | 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 4003.p
\(\chi_{4003}(2,\cdot)\) \(\chi_{4003}(3,\cdot)\) \(\chi_{4003}(5,\cdot)\) \(\chi_{4003}(12,\cdot)\) \(\chi_{4003}(14,\cdot)\) \(\chi_{4003}(18,\cdot)\) \(\chi_{4003}(22,\cdot)\) \(\chi_{4003}(23,\cdot)\) \(\chi_{4003}(26,\cdot)\) \(\chi_{4003}(30,\cdot)\) \(\chi_{4003}(31,\cdot)\) \(\chi_{4003}(32,\cdot)\) \(\chi_{4003}(33,\cdot)\) \(\chi_{4003}(34,\cdot)\) \(\chi_{4003}(35,\cdot)\) \(\chi_{4003}(39,\cdot)\) \(\chi_{4003}(43,\cdot)\) \(\chi_{4003}(45,\cdot)\) \(\chi_{4003}(47,\cdot)\) \(\chi_{4003}(51,\cdot)\) \(\chi_{4003}(55,\cdot)\) \(\chi_{4003}(56,\cdot)\) \(\chi_{4003}(61,\cdot)\) \(\chi_{4003}(65,\cdot)\) \(\chi_{4003}(71,\cdot)\) \(\chi_{4003}(72,\cdot)\) \(\chi_{4003}(80,\cdot)\) \(\chi_{4003}(85,\cdot)\) \(\chi_{4003}(87,\cdot)\) \(\chi_{4003}(95,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{2001})$ |
| Fixed field: | Number field defined by a degree 4002 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{2135}{4002}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4003 }(14, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2135}{4002}\right)\) | \(e\left(\frac{1717}{4002}\right)\) | \(e\left(\frac{134}{2001}\right)\) | \(e\left(\frac{3017}{4002}\right)\) | \(e\left(\frac{642}{667}\right)\) | \(e\left(\frac{907}{2001}\right)\) | \(e\left(\frac{801}{1334}\right)\) | \(e\left(\frac{1717}{2001}\right)\) | \(e\left(\frac{25}{87}\right)\) | \(e\left(\frac{302}{667}\right)\) |