Basic properties
| Modulus: | \(1775\) | |
| Conductor: | \(1775\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1775.dd
\(\chi_{1775}(3,\cdot)\) \(\chi_{1775}(27,\cdot)\) \(\chi_{1775}(38,\cdot)\) \(\chi_{1775}(58,\cdot)\) \(\chi_{1775}(98,\cdot)\) \(\chi_{1775}(158,\cdot)\) \(\chi_{1775}(253,\cdot)\) \(\chi_{1775}(262,\cdot)\) \(\chi_{1775}(263,\cdot)\) \(\chi_{1775}(288,\cdot)\) \(\chi_{1775}(302,\cdot)\) \(\chi_{1775}(303,\cdot)\) \(\chi_{1775}(308,\cdot)\) \(\chi_{1775}(327,\cdot)\) \(\chi_{1775}(342,\cdot)\) \(\chi_{1775}(373,\cdot)\) \(\chi_{1775}(398,\cdot)\) \(\chi_{1775}(428,\cdot)\) \(\chi_{1775}(442,\cdot)\) \(\chi_{1775}(533,\cdot)\) \(\chi_{1775}(583,\cdot)\) \(\chi_{1775}(592,\cdot)\) \(\chi_{1775}(628,\cdot)\) \(\chi_{1775}(688,\cdot)\) \(\chi_{1775}(703,\cdot)\) \(\chi_{1775}(787,\cdot)\) \(\chi_{1775}(817,\cdot)\) \(\chi_{1775}(867,\cdot)\) \(\chi_{1775}(933,\cdot)\) \(\chi_{1775}(952,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((427,1001)\) → \((e\left(\frac{7}{20}\right),e\left(\frac{13}{35}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1775 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{81}{140}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{17}{140}\right)\) | \(e\left(\frac{103}{140}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{37}{140}\right)\) | \(e\left(\frac{19}{140}\right)\) |