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.u
\(\chi_{319}(7,\cdot)\) \(\chi_{319}(24,\cdot)\) \(\chi_{319}(52,\cdot)\) \(\chi_{319}(74,\cdot)\) \(\chi_{319}(83,\cdot)\) \(\chi_{319}(94,\cdot)\) \(\chi_{319}(107,\cdot)\) \(\chi_{319}(112,\cdot)\) \(\chi_{319}(123,\cdot)\) \(\chi_{319}(139,\cdot)\) \(\chi_{319}(140,\cdot)\) \(\chi_{319}(161,\cdot)\) \(\chi_{319}(194,\cdot)\) \(\chi_{319}(226,\cdot)\) \(\chi_{319}(227,\cdot)\) \(\chi_{319}(228,\cdot)\) \(\chi_{319}(239,\cdot)\) \(\chi_{319}(248,\cdot)\) \(\chi_{319}(255,\cdot)\) \(\chi_{319}(277,\cdot)\) \(\chi_{319}(281,\cdot)\) \(\chi_{319}(310,\cdot)\) \(\chi_{319}(314,\cdot)\) \(\chi_{319}(315,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((233,89)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{4}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 319 }(228, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(1\) |