Basic properties
Modulus: | \(10009\) | |
Conductor: | \(10009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(556\) | 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 10009.p
\(\chi_{10009}(8,\cdot)\) \(\chi_{10009}(49,\cdot)\) \(\chi_{10009}(60,\cdot)\) \(\chi_{10009}(108,\cdot)\) \(\chi_{10009}(208,\cdot)\) \(\chi_{10009}(250,\cdot)\) \(\chi_{10009}(254,\cdot)\) \(\chi_{10009}(290,\cdot)\) \(\chi_{10009}(335,\cdot)\) \(\chi_{10009}(408,\cdot)\) \(\chi_{10009}(450,\cdot)\) \(\chi_{10009}(454,\cdot)\) \(\chi_{10009}(482,\cdot)\) \(\chi_{10009}(512,\cdot)\) \(\chi_{10009}(515,\cdot)\) \(\chi_{10009}(522,\cdot)\) \(\chi_{10009}(524,\cdot)\) \(\chi_{10009}(552,\cdot)\) \(\chi_{10009}(599,\cdot)\) \(\chi_{10009}(603,\cdot)\) \(\chi_{10009}(656,\cdot)\) \(\chi_{10009}(695,\cdot)\) \(\chi_{10009}(726,\cdot)\) \(\chi_{10009}(742,\cdot)\) \(\chi_{10009}(790,\cdot)\) \(\chi_{10009}(810,\cdot)\) \(\chi_{10009}(821,\cdot)\) \(\chi_{10009}(826,\cdot)\) \(\chi_{10009}(926,\cdot)\) \(\chi_{10009}(927,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{556})$ |
Fixed field: | Number field defined by a degree 556 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{167}{556}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 10009 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{267}{278}\right)\) | \(e\left(\frac{79}{278}\right)\) | \(e\left(\frac{128}{139}\right)\) | \(e\left(\frac{60}{139}\right)\) | \(e\left(\frac{34}{139}\right)\) | \(e\left(\frac{229}{556}\right)\) | \(e\left(\frac{245}{278}\right)\) | \(e\left(\frac{79}{139}\right)\) | \(e\left(\frac{109}{278}\right)\) | \(e\left(\frac{167}{556}\right)\) |