Basic properties
| Modulus: | \(8030\) | |
| Conductor: | \(803\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(360\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{803}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8030.gi
\(\chi_{8030}(31,\cdot)\) \(\chi_{8030}(141,\cdot)\) \(\chi_{8030}(191,\cdot)\) \(\chi_{8030}(471,\cdot)\) \(\chi_{8030}(531,\cdot)\) \(\chi_{8030}(631,\cdot)\) \(\chi_{8030}(691,\cdot)\) \(\chi_{8030}(741,\cdot)\) \(\chi_{8030}(861,\cdot)\) \(\chi_{8030}(1061,\cdot)\) \(\chi_{8030}(1081,\cdot)\) \(\chi_{8030}(1181,\cdot)\) \(\chi_{8030}(1281,\cdot)\) \(\chi_{8030}(1301,\cdot)\) \(\chi_{8030}(1401,\cdot)\) \(\chi_{8030}(1611,\cdot)\) \(\chi_{8030}(1621,\cdot)\) \(\chi_{8030}(1721,\cdot)\) \(\chi_{8030}(1741,\cdot)\) \(\chi_{8030}(1791,\cdot)\) \(\chi_{8030}(1851,\cdot)\) \(\chi_{8030}(1951,\cdot)\) \(\chi_{8030}(2011,\cdot)\) \(\chi_{8030}(2161,\cdot)\) \(\chi_{8030}(2291,\cdot)\) \(\chi_{8030}(2341,\cdot)\) \(\chi_{8030}(2381,\cdot)\) \(\chi_{8030}(2451,\cdot)\) \(\chi_{8030}(2511,\cdot)\) \(\chi_{8030}(2721,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{360})$ |
| Fixed field: | Number field defined by a degree 360 polynomial (not computed) |
Values on generators
\((1607,2191,881)\) → \((1,e\left(\frac{3}{5}\right),e\left(\frac{11}{72}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 8030 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{221}{360}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{49}{180}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{197}{360}\right)\) |