Basic properties
| Modulus: | \(725\) | |
| Conductor: | \(725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | 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.bh
\(\chi_{725}(4,\cdot)\) \(\chi_{725}(9,\cdot)\) \(\chi_{725}(34,\cdot)\) \(\chi_{725}(64,\cdot)\) \(\chi_{725}(109,\cdot)\) \(\chi_{725}(129,\cdot)\) \(\chi_{725}(154,\cdot)\) \(\chi_{725}(179,\cdot)\) \(\chi_{725}(209,\cdot)\) \(\chi_{725}(254,\cdot)\) \(\chi_{725}(294,\cdot)\) \(\chi_{725}(354,\cdot)\) \(\chi_{725}(419,\cdot)\) \(\chi_{725}(439,\cdot)\) \(\chi_{725}(444,\cdot)\) \(\chi_{725}(469,\cdot)\) \(\chi_{725}(544,\cdot)\) \(\chi_{725}(564,\cdot)\) \(\chi_{725}(584,\cdot)\) \(\chi_{725}(589,\cdot)\) \(\chi_{725}(614,\cdot)\) \(\chi_{725}(644,\cdot)\) \(\chi_{725}(689,\cdot)\) \(\chi_{725}(709,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((552,176)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{9}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 725 }(709, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{61}{70}\right)\) |