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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 319.w
\(\chi_{319}(3,\cdot)\) \(\chi_{319}(14,\cdot)\) \(\chi_{319}(15,\cdot)\) \(\chi_{319}(26,\cdot)\) \(\chi_{319}(27,\cdot)\) \(\chi_{319}(31,\cdot)\) \(\chi_{319}(37,\cdot)\) \(\chi_{319}(47,\cdot)\) \(\chi_{319}(48,\cdot)\) \(\chi_{319}(60,\cdot)\) \(\chi_{319}(69,\cdot)\) \(\chi_{319}(97,\cdot)\) \(\chi_{319}(102,\cdot)\) \(\chi_{319}(108,\cdot)\) \(\chi_{319}(113,\cdot)\) \(\chi_{319}(114,\cdot)\) \(\chi_{319}(119,\cdot)\) \(\chi_{319}(124,\cdot)\) \(\chi_{319}(126,\cdot)\) \(\chi_{319}(130,\cdot)\) \(\chi_{319}(135,\cdot)\) \(\chi_{319}(137,\cdot)\) \(\chi_{319}(147,\cdot)\) \(\chi_{319}(148,\cdot)\) \(\chi_{319}(159,\cdot)\) \(\chi_{319}(163,\cdot)\) \(\chi_{319}(185,\cdot)\) \(\chi_{319}(192,\cdot)\) \(\chi_{319}(201,\cdot)\) \(\chi_{319}(213,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((233,89)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{19}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 319 }(113, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{140}\right)\) | \(e\left(\frac{111}{140}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{61}{140}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(-i\) |