Basic properties
| Modulus: | \(4003\) | |
| Conductor: | \(4003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1334\) | 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.n
\(\chi_{4003}(8,\cdot)\) \(\chi_{4003}(20,\cdot)\) \(\chi_{4003}(21,\cdot)\) \(\chi_{4003}(27,\cdot)\) \(\chi_{4003}(41,\cdot)\) \(\chi_{4003}(48,\cdot)\) \(\chi_{4003}(50,\cdot)\) \(\chi_{4003}(57,\cdot)\) \(\chi_{4003}(58,\cdot)\) \(\chi_{4003}(74,\cdot)\) \(\chi_{4003}(88,\cdot)\) \(\chi_{4003}(92,\cdot)\) \(\chi_{4003}(98,\cdot)\) \(\chi_{4003}(104,\cdot)\) \(\chi_{4003}(106,\cdot)\) \(\chi_{4003}(107,\cdot)\) \(\chi_{4003}(118,\cdot)\) \(\chi_{4003}(120,\cdot)\) \(\chi_{4003}(124,\cdot)\) \(\chi_{4003}(125,\cdot)\) \(\chi_{4003}(145,\cdot)\) \(\chi_{4003}(158,\cdot)\) \(\chi_{4003}(162,\cdot)\) \(\chi_{4003}(178,\cdot)\) \(\chi_{4003}(179,\cdot)\) \(\chi_{4003}(185,\cdot)\) \(\chi_{4003}(201,\cdot)\) \(\chi_{4003}(220,\cdot)\) \(\chi_{4003}(230,\cdot)\) \(\chi_{4003}(231,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{667})$ |
| Fixed field: | Number field defined by a degree 1334 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{183}{1334}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4003 }(21, a) \) | \(-1\) | \(1\) | \(e\left(\frac{183}{1334}\right)\) | \(e\left(\frac{757}{1334}\right)\) | \(e\left(\frac{183}{667}\right)\) | \(e\left(\frac{1059}{1334}\right)\) | \(e\left(\frac{470}{667}\right)\) | \(e\left(\frac{497}{667}\right)\) | \(e\left(\frac{549}{1334}\right)\) | \(e\left(\frac{90}{667}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{192}{667}\right)\) |