Basic properties
Modulus: | \(8470\) | |
Conductor: | \(847\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(165\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{847}(520,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.dc
\(\chi_{8470}(191,\cdot)\) \(\chi_{8470}(291,\cdot)\) \(\chi_{8470}(361,\cdot)\) \(\chi_{8470}(401,\cdot)\) \(\chi_{8470}(471,\cdot)\) \(\chi_{8470}(641,\cdot)\) \(\chi_{8470}(751,\cdot)\) \(\chi_{8470}(851,\cdot)\) \(\chi_{8470}(961,\cdot)\) \(\chi_{8470}(1061,\cdot)\) \(\chi_{8470}(1131,\cdot)\) \(\chi_{8470}(1171,\cdot)\) \(\chi_{8470}(1241,\cdot)\) \(\chi_{8470}(1411,\cdot)\) \(\chi_{8470}(1521,\cdot)\) \(\chi_{8470}(1621,\cdot)\) \(\chi_{8470}(1731,\cdot)\) \(\chi_{8470}(1831,\cdot)\) \(\chi_{8470}(1901,\cdot)\) \(\chi_{8470}(1941,\cdot)\) \(\chi_{8470}(2011,\cdot)\) \(\chi_{8470}(2291,\cdot)\) \(\chi_{8470}(2391,\cdot)\) \(\chi_{8470}(2601,\cdot)\) \(\chi_{8470}(2711,\cdot)\) \(\chi_{8470}(2781,\cdot)\) \(\chi_{8470}(2951,\cdot)\) \(\chi_{8470}(3061,\cdot)\) \(\chi_{8470}(3161,\cdot)\) \(\chi_{8470}(3271,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 165 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{34}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(3061, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{103}{165}\right)\) | \(e\left(\frac{161}{165}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{82}{165}\right)\) | \(e\left(\frac{104}{165}\right)\) |