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 \(\chi_{4015}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8030.gl
\(\chi_{8030}(47,\cdot)\) \(\chi_{8030}(53,\cdot)\) \(\chi_{8030}(93,\cdot)\) \(\chi_{8030}(113,\cdot)\) \(\chi_{8030}(157,\cdot)\) \(\chi_{8030}(427,\cdot)\) \(\chi_{8030}(433,\cdot)\) \(\chi_{8030}(443,\cdot)\) \(\chi_{8030}(467,\cdot)\) \(\chi_{8030}(537,\cdot)\) \(\chi_{8030}(597,\cdot)\) \(\chi_{8030}(643,\cdot)\) \(\chi_{8030}(763,\cdot)\) \(\chi_{8030}(823,\cdot)\) \(\chi_{8030}(907,\cdot)\) \(\chi_{8030}(983,\cdot)\) \(\chi_{8030}(1037,\cdot)\) \(\chi_{8030}(1137,\cdot)\) \(\chi_{8030}(1197,\cdot)\) \(\chi_{8030}(1213,\cdot)\) \(\chi_{8030}(1373,\cdot)\) \(\chi_{8030}(1577,\cdot)\) \(\chi_{8030}(1637,\cdot)\) \(\chi_{8030}(1853,\cdot)\) \(\chi_{8030}(2083,\cdot)\) \(\chi_{8030}(2237,\cdot)\) \(\chi_{8030}(2303,\cdot)\) \(\chi_{8030}(2347,\cdot)\) \(\chi_{8030}(2423,\cdot)\) \(\chi_{8030}(2467,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{360})$ |
| Fixed field: | Number field defined by a degree 360 polynomial (not computed) |
Values on generators
\((1607,2191,881)\) → \((-i,e\left(\frac{3}{5}\right),e\left(\frac{53}{72}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 8030 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{101}{360}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{169}{180}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{167}{360}\right)\) |