Basic properties
| Modulus: | \(6009\) | |
| 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 \(\chi_{2003}(40,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6009.bc
\(\chi_{6009}(10,\cdot)\) \(\chi_{6009}(13,\cdot)\) \(\chi_{6009}(19,\cdot)\) \(\chi_{6009}(25,\cdot)\) \(\chi_{6009}(40,\cdot)\) \(\chi_{6009}(49,\cdot)\) \(\chi_{6009}(52,\cdot)\) \(\chi_{6009}(55,\cdot)\) \(\chi_{6009}(58,\cdot)\) \(\chi_{6009}(73,\cdot)\) \(\chi_{6009}(82,\cdot)\) \(\chi_{6009}(85,\cdot)\) \(\chi_{6009}(100,\cdot)\) \(\chi_{6009}(115,\cdot)\) \(\chi_{6009}(130,\cdot)\) \(\chi_{6009}(136,\cdot)\) \(\chi_{6009}(145,\cdot)\) \(\chi_{6009}(160,\cdot)\) \(\chi_{6009}(166,\cdot)\) \(\chi_{6009}(169,\cdot)\) \(\chi_{6009}(181,\cdot)\) \(\chi_{6009}(187,\cdot)\) \(\chi_{6009}(196,\cdot)\) \(\chi_{6009}(205,\cdot)\) \(\chi_{6009}(211,\cdot)\) \(\chi_{6009}(217,\cdot)\) \(\chi_{6009}(220,\cdot)\) \(\chi_{6009}(223,\cdot)\) \(\chi_{6009}(229,\cdot)\) \(\chi_{6009}(247,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1001})$ |
| Fixed field: | Number field defined by a degree 1001 polynomial (not computed) |
Values on generators
\((4007,2008)\) → \((1,e\left(\frac{4}{1001}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 6009 }(40, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{143}\right)\) | \(e\left(\frac{98}{143}\right)\) | \(e\left(\frac{4}{1001}\right)\) | \(e\left(\frac{492}{1001}\right)\) | \(e\left(\frac{4}{143}\right)\) | \(e\left(\frac{347}{1001}\right)\) | \(e\left(\frac{28}{143}\right)\) | \(e\left(\frac{971}{1001}\right)\) | \(e\left(\frac{835}{1001}\right)\) | \(e\left(\frac{53}{143}\right)\) |