Basic properties
| Modulus: | \(725\) | |
| Conductor: | \(725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(140\) | 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.bn
\(\chi_{725}(2,\cdot)\) \(\chi_{725}(8,\cdot)\) \(\chi_{725}(72,\cdot)\) \(\chi_{725}(73,\cdot)\) \(\chi_{725}(77,\cdot)\) \(\chi_{725}(113,\cdot)\) \(\chi_{725}(127,\cdot)\) \(\chi_{725}(137,\cdot)\) \(\chi_{725}(147,\cdot)\) \(\chi_{725}(153,\cdot)\) \(\chi_{725}(163,\cdot)\) \(\chi_{725}(177,\cdot)\) \(\chi_{725}(213,\cdot)\) \(\chi_{725}(217,\cdot)\) \(\chi_{725}(222,\cdot)\) \(\chi_{725}(258,\cdot)\) \(\chi_{725}(272,\cdot)\) \(\chi_{725}(288,\cdot)\) \(\chi_{725}(292,\cdot)\) \(\chi_{725}(298,\cdot)\) \(\chi_{725}(308,\cdot)\) \(\chi_{725}(322,\cdot)\) \(\chi_{725}(358,\cdot)\) \(\chi_{725}(362,\cdot)\) \(\chi_{725}(363,\cdot)\) \(\chi_{725}(367,\cdot)\) \(\chi_{725}(403,\cdot)\) \(\chi_{725}(417,\cdot)\) \(\chi_{725}(427,\cdot)\) \(\chi_{725}(433,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((552,176)\) → \((e\left(\frac{17}{20}\right),e\left(\frac{25}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 725 }(272, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{129}{140}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{31}{140}\right)\) |