Basic properties
| Modulus: | \(319\) | |
| Conductor: | \(319\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(35\) | 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.s
\(\chi_{319}(16,\cdot)\) \(\chi_{319}(20,\cdot)\) \(\chi_{319}(25,\cdot)\) \(\chi_{319}(36,\cdot)\) \(\chi_{319}(49,\cdot)\) \(\chi_{319}(53,\cdot)\) \(\chi_{319}(81,\cdot)\) \(\chi_{319}(82,\cdot)\) \(\chi_{319}(103,\cdot)\) \(\chi_{319}(136,\cdot)\) \(\chi_{319}(141,\cdot)\) \(\chi_{319}(152,\cdot)\) \(\chi_{319}(168,\cdot)\) \(\chi_{319}(169,\cdot)\) \(\chi_{319}(170,\cdot)\) \(\chi_{319}(181,\cdot)\) \(\chi_{319}(190,\cdot)\) \(\chi_{319}(223,\cdot)\) \(\chi_{319}(256,\cdot)\) \(\chi_{319}(257,\cdot)\) \(\chi_{319}(268,\cdot)\) \(\chi_{319}(284,\cdot)\) \(\chi_{319}(306,\cdot)\) \(\chi_{319}(313,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((233,89)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{6}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 319 }(20, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(1\) |