Basic properties
| Modulus: | \(4235\) | |
| 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 \(\chi_{847}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4235.dc
\(\chi_{4235}(16,\cdot)\) \(\chi_{4235}(86,\cdot)\) \(\chi_{4235}(191,\cdot)\) \(\chi_{4235}(256,\cdot)\) \(\chi_{4235}(291,\cdot)\) \(\chi_{4235}(361,\cdot)\) \(\chi_{4235}(401,\cdot)\) \(\chi_{4235}(466,\cdot)\) \(\chi_{4235}(471,\cdot)\) \(\chi_{4235}(576,\cdot)\) \(\chi_{4235}(641,\cdot)\) \(\chi_{4235}(676,\cdot)\) \(\chi_{4235}(746,\cdot)\) \(\chi_{4235}(751,\cdot)\) \(\chi_{4235}(786,\cdot)\) \(\chi_{4235}(851,\cdot)\) \(\chi_{4235}(961,\cdot)\) \(\chi_{4235}(1026,\cdot)\) \(\chi_{4235}(1061,\cdot)\) \(\chi_{4235}(1131,\cdot)\) \(\chi_{4235}(1136,\cdot)\) \(\chi_{4235}(1171,\cdot)\) \(\chi_{4235}(1236,\cdot)\) \(\chi_{4235}(1241,\cdot)\) \(\chi_{4235}(1346,\cdot)\) \(\chi_{4235}(1411,\cdot)\) \(\chi_{4235}(1446,\cdot)\) \(\chi_{4235}(1516,\cdot)\) \(\chi_{4235}(1521,\cdot)\) \(\chi_{4235}(1556,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 165 polynomial (not computed) |
Values on generators
\((2542,1816,2906)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{2}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 4235 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{116}{165}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{67}{165}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{134}{165}\right)\) | \(e\left(\frac{19}{165}\right)\) |