Basic properties
| Modulus: | \(5929\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(237,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5929.bi
\(\chi_{5929}(118,\cdot)\) \(\chi_{5929}(475,\cdot)\) \(\chi_{5929}(524,\cdot)\) \(\chi_{5929}(699,\cdot)\) \(\chi_{5929}(965,\cdot)\) \(\chi_{5929}(1546,\cdot)\) \(\chi_{5929}(2169,\cdot)\) \(\chi_{5929}(2218,\cdot)\) \(\chi_{5929}(2393,\cdot)\) \(\chi_{5929}(2659,\cdot)\) \(\chi_{5929}(3016,\cdot)\) \(\chi_{5929}(3065,\cdot)\) \(\chi_{5929}(3240,\cdot)\) \(\chi_{5929}(3506,\cdot)\) \(\chi_{5929}(3863,\cdot)\) \(\chi_{5929}(3912,\cdot)\) \(\chi_{5929}(4087,\cdot)\) \(\chi_{5929}(4353,\cdot)\) \(\chi_{5929}(4710,\cdot)\) \(\chi_{5929}(4759,\cdot)\) \(\chi_{5929}(4934,\cdot)\) \(\chi_{5929}(5200,\cdot)\) \(\chi_{5929}(5557,\cdot)\) \(\chi_{5929}(5606,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1816,2059)\) → \((e\left(\frac{5}{14}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 5929 }(2393, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{24}{35}\right)\) |