Basic properties
| Modulus: | \(4235\) | |
| 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 \(\chi_{847}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4235.dl
\(\chi_{4235}(61,\cdot)\) \(\chi_{4235}(96,\cdot)\) \(\chi_{4235}(101,\cdot)\) \(\chi_{4235}(171,\cdot)\) \(\chi_{4235}(206,\cdot)\) \(\chi_{4235}(271,\cdot)\) \(\chi_{4235}(376,\cdot)\) \(\chi_{4235}(381,\cdot)\) \(\chi_{4235}(446,\cdot)\) \(\chi_{4235}(486,\cdot)\) \(\chi_{4235}(556,\cdot)\) \(\chi_{4235}(591,\cdot)\) \(\chi_{4235}(656,\cdot)\) \(\chi_{4235}(761,\cdot)\) \(\chi_{4235}(831,\cdot)\) \(\chi_{4235}(866,\cdot)\) \(\chi_{4235}(871,\cdot)\) \(\chi_{4235}(976,\cdot)\) \(\chi_{4235}(1041,\cdot)\) \(\chi_{4235}(1146,\cdot)\) \(\chi_{4235}(1151,\cdot)\) \(\chi_{4235}(1216,\cdot)\) \(\chi_{4235}(1251,\cdot)\) \(\chi_{4235}(1256,\cdot)\) \(\chi_{4235}(1326,\cdot)\) \(\chi_{4235}(1361,\cdot)\) \(\chi_{4235}(1426,\cdot)\) \(\chi_{4235}(1531,\cdot)\) \(\chi_{4235}(1536,\cdot)\) \(\chi_{4235}(1601,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((2542,1816,2906)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{109}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 4235 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{217}{330}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{52}{165}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{104}{165}\right)\) | \(e\left(\frac{64}{165}\right)\) |