Basic properties
Modulus: | \(725\) | |
Conductor: | \(725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(35\) | 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 725.be
\(\chi_{725}(16,\cdot)\) \(\chi_{725}(36,\cdot)\) \(\chi_{725}(81,\cdot)\) \(\chi_{725}(111,\cdot)\) \(\chi_{725}(136,\cdot)\) \(\chi_{725}(141,\cdot)\) \(\chi_{725}(161,\cdot)\) \(\chi_{725}(181,\cdot)\) \(\chi_{725}(256,\cdot)\) \(\chi_{725}(281,\cdot)\) \(\chi_{725}(286,\cdot)\) \(\chi_{725}(306,\cdot)\) \(\chi_{725}(371,\cdot)\) \(\chi_{725}(431,\cdot)\) \(\chi_{725}(471,\cdot)\) \(\chi_{725}(516,\cdot)\) \(\chi_{725}(546,\cdot)\) \(\chi_{725}(571,\cdot)\) \(\chi_{725}(596,\cdot)\) \(\chi_{725}(616,\cdot)\) \(\chi_{725}(661,\cdot)\) \(\chi_{725}(691,\cdot)\) \(\chi_{725}(716,\cdot)\) \(\chi_{725}(721,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((552,176)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{5}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 725 }(81, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{16}{35}\right)\) |