Basic properties
| Modulus: | \(319\) | |
| Conductor: | \(319\) | 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 319.x
\(\chi_{319}(2,\cdot)\) \(\chi_{319}(8,\cdot)\) \(\chi_{319}(18,\cdot)\) \(\chi_{319}(19,\cdot)\) \(\chi_{319}(39,\cdot)\) \(\chi_{319}(40,\cdot)\) \(\chi_{319}(50,\cdot)\) \(\chi_{319}(61,\cdot)\) \(\chi_{319}(68,\cdot)\) \(\chi_{319}(72,\cdot)\) \(\chi_{319}(73,\cdot)\) \(\chi_{319}(79,\cdot)\) \(\chi_{319}(84,\cdot)\) \(\chi_{319}(85,\cdot)\) \(\chi_{319}(90,\cdot)\) \(\chi_{319}(95,\cdot)\) \(\chi_{319}(101,\cdot)\) \(\chi_{319}(105,\cdot)\) \(\chi_{319}(106,\cdot)\) \(\chi_{319}(118,\cdot)\) \(\chi_{319}(127,\cdot)\) \(\chi_{319}(134,\cdot)\) \(\chi_{319}(156,\cdot)\) \(\chi_{319}(160,\cdot)\) \(\chi_{319}(171,\cdot)\) \(\chi_{319}(172,\cdot)\) \(\chi_{319}(182,\cdot)\) \(\chi_{319}(184,\cdot)\) \(\chi_{319}(189,\cdot)\) \(\chi_{319}(193,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((233,89)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{15}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 319 }(172, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{140}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{99}{140}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(-i\) |