Basic properties
| Modulus: | \(5929\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(35\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(323,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5929.ba
\(\chi_{5929}(323,\cdot)\) \(\chi_{5929}(372,\cdot)\) \(\chi_{5929}(729,\cdot)\) \(\chi_{5929}(995,\cdot)\) \(\chi_{5929}(1170,\cdot)\) \(\chi_{5929}(1219,\cdot)\) \(\chi_{5929}(1576,\cdot)\) \(\chi_{5929}(1842,\cdot)\) \(\chi_{5929}(2017,\cdot)\) \(\chi_{5929}(2066,\cdot)\) \(\chi_{5929}(2423,\cdot)\) \(\chi_{5929}(2689,\cdot)\) \(\chi_{5929}(2864,\cdot)\) \(\chi_{5929}(2913,\cdot)\) \(\chi_{5929}(3270,\cdot)\) \(\chi_{5929}(3536,\cdot)\) \(\chi_{5929}(3711,\cdot)\) \(\chi_{5929}(3760,\cdot)\) \(\chi_{5929}(4383,\cdot)\) \(\chi_{5929}(4964,\cdot)\) \(\chi_{5929}(5230,\cdot)\) \(\chi_{5929}(5405,\cdot)\) \(\chi_{5929}(5454,\cdot)\) \(\chi_{5929}(5811,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((1816,2059)\) → \((e\left(\frac{3}{7}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 5929 }(323, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{12}{35}\right)\) |