Basic properties
| Modulus: | \(8030\) | |
| Conductor: | \(4015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(360\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4015}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8030.gf
\(\chi_{8030}(13,\cdot)\) \(\chi_{8030}(107,\cdot)\) \(\chi_{8030}(193,\cdot)\) \(\chi_{8030}(303,\cdot)\) \(\chi_{8030}(337,\cdot)\) \(\chi_{8030}(453,\cdot)\) \(\chi_{8030}(497,\cdot)\) \(\chi_{8030}(613,\cdot)\) \(\chi_{8030}(677,\cdot)\) \(\chi_{8030}(743,\cdot)\) \(\chi_{8030}(1053,\cdot)\) \(\chi_{8030}(1183,\cdot)\) \(\chi_{8030}(1207,\cdot)\) \(\chi_{8030}(1227,\cdot)\) \(\chi_{8030}(1283,\cdot)\) \(\chi_{8030}(1427,\cdot)\) \(\chi_{8030}(1547,\cdot)\) \(\chi_{8030}(1707,\cdot)\) \(\chi_{8030}(1723,\cdot)\) \(\chi_{8030}(1757,\cdot)\) \(\chi_{8030}(1883,\cdot)\) \(\chi_{8030}(2097,\cdot)\) \(\chi_{8030}(2323,\cdot)\) \(\chi_{8030}(2383,\cdot)\) \(\chi_{8030}(2437,\cdot)\) \(\chi_{8030}(2477,\cdot)\) \(\chi_{8030}(2493,\cdot)\) \(\chi_{8030}(2527,\cdot)\) \(\chi_{8030}(2613,\cdot)\) \(\chi_{8030}(2763,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{360})$ |
| Fixed field: | Number field defined by a degree 360 polynomial (not computed) |
Values on generators
\((1607,2191,881)\) → \((-i,e\left(\frac{1}{10}\right),e\left(\frac{59}{72}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 8030 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{251}{360}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{109}{180}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{317}{360}\right)\) |