Basic properties
| Modulus: | \(319\) | |
| Conductor: | \(319\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 319.v
\(\chi_{319}(6,\cdot)\) \(\chi_{319}(13,\cdot)\) \(\chi_{319}(35,\cdot)\) \(\chi_{319}(51,\cdot)\) \(\chi_{319}(62,\cdot)\) \(\chi_{319}(63,\cdot)\) \(\chi_{319}(96,\cdot)\) \(\chi_{319}(129,\cdot)\) \(\chi_{319}(138,\cdot)\) \(\chi_{319}(149,\cdot)\) \(\chi_{319}(150,\cdot)\) \(\chi_{319}(151,\cdot)\) \(\chi_{319}(167,\cdot)\) \(\chi_{319}(178,\cdot)\) \(\chi_{319}(183,\cdot)\) \(\chi_{319}(216,\cdot)\) \(\chi_{319}(237,\cdot)\) \(\chi_{319}(238,\cdot)\) \(\chi_{319}(266,\cdot)\) \(\chi_{319}(270,\cdot)\) \(\chi_{319}(283,\cdot)\) \(\chi_{319}(294,\cdot)\) \(\chi_{319}(299,\cdot)\) \(\chi_{319}(303,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((233,89)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{3}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 319 }(35, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(-1\) |