Basic properties
| Modulus: | \(4006\) | |
| Conductor: | \(2003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1001\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2003}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4006.o
\(\chi_{4006}(3,\cdot)\) \(\chi_{4006}(9,\cdot)\) \(\chi_{4006}(13,\cdot)\) \(\chi_{4006}(19,\cdot)\) \(\chi_{4006}(25,\cdot)\) \(\chi_{4006}(27,\cdot)\) \(\chi_{4006}(35,\cdot)\) \(\chi_{4006}(39,\cdot)\) \(\chi_{4006}(47,\cdot)\) \(\chi_{4006}(49,\cdot)\) \(\chi_{4006}(55,\cdot)\) \(\chi_{4006}(59,\cdot)\) \(\chi_{4006}(73,\cdot)\) \(\chi_{4006}(75,\cdot)\) \(\chi_{4006}(77,\cdot)\) \(\chi_{4006}(81,\cdot)\) \(\chi_{4006}(85,\cdot)\) \(\chi_{4006}(101,\cdot)\) \(\chi_{4006}(105,\cdot)\) \(\chi_{4006}(107,\cdot)\) \(\chi_{4006}(115,\cdot)\) \(\chi_{4006}(117,\cdot)\) \(\chi_{4006}(119,\cdot)\) \(\chi_{4006}(145,\cdot)\) \(\chi_{4006}(147,\cdot)\) \(\chi_{4006}(159,\cdot)\) \(\chi_{4006}(161,\cdot)\) \(\chi_{4006}(167,\cdot)\) \(\chi_{4006}(169,\cdot)\) \(\chi_{4006}(171,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1001})$ |
| Fixed field: | Number field defined by a degree 1001 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{123}{1001}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4006 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{516}{1001}\right)\) | \(e\left(\frac{123}{1001}\right)\) | \(e\left(\frac{114}{1001}\right)\) | \(e\left(\frac{31}{1001}\right)\) | \(e\left(\frac{3}{143}\right)\) | \(e\left(\frac{579}{1001}\right)\) | \(e\left(\frac{639}{1001}\right)\) | \(e\left(\frac{72}{91}\right)\) | \(e\left(\frac{108}{1001}\right)\) | \(e\left(\frac{90}{143}\right)\) |