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 \(\chi_{4015}(59,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8030.gg
\(\chi_{8030}(59,\cdot)\) \(\chi_{8030}(159,\cdot)\) \(\chi_{8030}(179,\cdot)\) \(\chi_{8030}(279,\cdot)\) \(\chi_{8030}(339,\cdot)\) \(\chi_{8030}(379,\cdot)\) \(\chi_{8030}(399,\cdot)\) \(\chi_{8030}(449,\cdot)\) \(\chi_{8030}(599,\cdot)\) \(\chi_{8030}(719,\cdot)\) \(\chi_{8030}(829,\cdot)\) \(\chi_{8030}(889,\cdot)\) \(\chi_{8030}(929,\cdot)\) \(\chi_{8030}(1109,\cdot)\) \(\chi_{8030}(1269,\cdot)\) \(\chi_{8030}(1329,\cdot)\) \(\chi_{8030}(1489,\cdot)\) \(\chi_{8030}(1499,\cdot)\) \(\chi_{8030}(1659,\cdot)\) \(\chi_{8030}(1699,\cdot)\) \(\chi_{8030}(1719,\cdot)\) \(\chi_{8030}(1929,\cdot)\) \(\chi_{8030}(2029,\cdot)\) \(\chi_{8030}(2039,\cdot)\) \(\chi_{8030}(2049,\cdot)\) \(\chi_{8030}(2159,\cdot)\) \(\chi_{8030}(2249,\cdot)\) \(\chi_{8030}(2369,\cdot)\) \(\chi_{8030}(2429,\cdot)\) \(\chi_{8030}(2469,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{360})$ |
| Fixed field: | Number field defined by a degree 360 polynomial (not computed) |
Values on generators
\((1607,2191,881)\) → \((-1,e\left(\frac{1}{5}\right),e\left(\frac{5}{72}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 8030 }(59, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{287}{360}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{163}{180}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{299}{360}\right)\) |