Basic properties
| Modulus: | \(8030\) | |
| Conductor: | \(803\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{803}(71,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8030.fh
\(\chi_{8030}(71,\cdot)\) \(\chi_{8030}(91,\cdot)\) \(\chi_{8030}(361,\cdot)\) \(\chi_{8030}(401,\cdot)\) \(\chi_{8030}(641,\cdot)\) \(\chi_{8030}(801,\cdot)\) \(\chi_{8030}(1131,\cdot)\) \(\chi_{8030}(1501,\cdot)\) \(\chi_{8030}(2231,\cdot)\) \(\chi_{8030}(2281,\cdot)\) \(\chi_{8030}(2831,\cdot)\) \(\chi_{8030}(3281,\cdot)\) \(\chi_{8030}(3721,\cdot)\) \(\chi_{8030}(4051,\cdot)\) \(\chi_{8030}(4471,\cdot)\) \(\chi_{8030}(5021,\cdot)\) \(\chi_{8030}(5151,\cdot)\) \(\chi_{8030}(5201,\cdot)\) \(\chi_{8030}(5471,\cdot)\) \(\chi_{8030}(5751,\cdot)\) \(\chi_{8030}(5911,\cdot)\) \(\chi_{8030}(6241,\cdot)\) \(\chi_{8030}(7341,\cdot)\) \(\chi_{8030}(7661,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1607,2191,881)\) → \((1,e\left(\frac{2}{5}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 8030 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{17}{90}\right)\) |