Basic properties
| Modulus: | \(8009\) | |
| Conductor: | \(8009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2002\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8009.bd
\(\chi_{8009}(4,\cdot)\) \(\chi_{8009}(10,\cdot)\) \(\chi_{8009}(22,\cdot)\) \(\chi_{8009}(28,\cdot)\) \(\chi_{8009}(55,\cdot)\) \(\chi_{8009}(64,\cdot)\) \(\chi_{8009}(72,\cdot)\) \(\chi_{8009}(81,\cdot)\) \(\chi_{8009}(83,\cdot)\) \(\chi_{8009}(91,\cdot)\) \(\chi_{8009}(93,\cdot)\) \(\chi_{8009}(106,\cdot)\) \(\chi_{8009}(121,\cdot)\) \(\chi_{8009}(127,\cdot)\) \(\chi_{8009}(138,\cdot)\) \(\chi_{8009}(142,\cdot)\) \(\chi_{8009}(154,\cdot)\) \(\chi_{8009}(160,\cdot)\) \(\chi_{8009}(175,\cdot)\) \(\chi_{8009}(180,\cdot)\) \(\chi_{8009}(193,\cdot)\) \(\chi_{8009}(196,\cdot)\) \(\chi_{8009}(208,\cdot)\) \(\chi_{8009}(221,\cdot)\) \(\chi_{8009}(234,\cdot)\) \(\chi_{8009}(265,\cdot)\) \(\chi_{8009}(291,\cdot)\) \(\chi_{8009}(298,\cdot)\) \(\chi_{8009}(311,\cdot)\) \(\chi_{8009}(321,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1001})$ |
| Fixed field: | Number field defined by a degree 2002 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1315}{2002}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8009 }(28, a) \) | \(1\) | \(1\) | \(e\left(\frac{412}{1001}\right)\) | \(e\left(\frac{1315}{2002}\right)\) | \(e\left(\frac{824}{1001}\right)\) | \(e\left(\frac{73}{77}\right)\) | \(e\left(\frac{137}{2002}\right)\) | \(e\left(\frac{172}{1001}\right)\) | \(e\left(\frac{235}{1001}\right)\) | \(e\left(\frac{314}{1001}\right)\) | \(e\left(\frac{360}{1001}\right)\) | \(e\left(\frac{419}{1001}\right)\) |