Basic properties
Modulus: | \(529\) | |
Conductor: | \(529\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(506\) | 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 529.h
\(\chi_{529}(5,\cdot)\) \(\chi_{529}(7,\cdot)\) \(\chi_{529}(10,\cdot)\) \(\chi_{529}(11,\cdot)\) \(\chi_{529}(14,\cdot)\) \(\chi_{529}(15,\cdot)\) \(\chi_{529}(17,\cdot)\) \(\chi_{529}(19,\cdot)\) \(\chi_{529}(20,\cdot)\) \(\chi_{529}(21,\cdot)\) \(\chi_{529}(30,\cdot)\) \(\chi_{529}(33,\cdot)\) \(\chi_{529}(34,\cdot)\) \(\chi_{529}(37,\cdot)\) \(\chi_{529}(38,\cdot)\) \(\chi_{529}(40,\cdot)\) \(\chi_{529}(43,\cdot)\) \(\chi_{529}(44,\cdot)\) \(\chi_{529}(51,\cdot)\) \(\chi_{529}(53,\cdot)\) \(\chi_{529}(56,\cdot)\) \(\chi_{529}(57,\cdot)\) \(\chi_{529}(60,\cdot)\) \(\chi_{529}(61,\cdot)\) \(\chi_{529}(65,\cdot)\) \(\chi_{529}(66,\cdot)\) \(\chi_{529}(67,\cdot)\) \(\chi_{529}(74,\cdot)\) \(\chi_{529}(76,\cdot)\) \(\chi_{529}(79,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{253})$ |
Fixed field: | Number field defined by a degree 506 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{129}{506}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 529 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{250}{253}\right)\) | \(e\left(\frac{20}{253}\right)\) | \(e\left(\frac{247}{253}\right)\) | \(e\left(\frac{129}{506}\right)\) | \(e\left(\frac{17}{253}\right)\) | \(e\left(\frac{449}{506}\right)\) | \(e\left(\frac{244}{253}\right)\) | \(e\left(\frac{40}{253}\right)\) | \(e\left(\frac{123}{506}\right)\) | \(e\left(\frac{237}{506}\right)\) |