Basic properties
Modulus: | \(8470\) | |
Conductor: | \(847\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{847}(740,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.di
\(\chi_{8470}(31,\cdot)\) \(\chi_{8470}(201,\cdot)\) \(\chi_{8470}(311,\cdot)\) \(\chi_{8470}(411,\cdot)\) \(\chi_{8470}(521,\cdot)\) \(\chi_{8470}(621,\cdot)\) \(\chi_{8470}(691,\cdot)\) \(\chi_{8470}(731,\cdot)\) \(\chi_{8470}(801,\cdot)\) \(\chi_{8470}(1081,\cdot)\) \(\chi_{8470}(1181,\cdot)\) \(\chi_{8470}(1391,\cdot)\) \(\chi_{8470}(1501,\cdot)\) \(\chi_{8470}(1571,\cdot)\) \(\chi_{8470}(1741,\cdot)\) \(\chi_{8470}(1851,\cdot)\) \(\chi_{8470}(1951,\cdot)\) \(\chi_{8470}(2061,\cdot)\) \(\chi_{8470}(2161,\cdot)\) \(\chi_{8470}(2231,\cdot)\) \(\chi_{8470}(2271,\cdot)\) \(\chi_{8470}(2341,\cdot)\) \(\chi_{8470}(2511,\cdot)\) \(\chi_{8470}(2621,\cdot)\) \(\chi_{8470}(2721,\cdot)\) \(\chi_{8470}(2831,\cdot)\) \(\chi_{8470}(3001,\cdot)\) \(\chi_{8470}(3041,\cdot)\) \(\chi_{8470}(3111,\cdot)\) \(\chi_{8470}(3281,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{4}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(3281, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{131}{330}\right)\) | \(e\left(\frac{67}{330}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{29}{330}\right)\) | \(e\left(\frac{119}{165}\right)\) |