Basic properties
| Modulus: | \(4235\) | |
| Conductor: | \(4235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4235.dn
\(\chi_{4235}(59,\cdot)\) \(\chi_{4235}(159,\cdot)\) \(\chi_{4235}(229,\cdot)\) \(\chi_{4235}(234,\cdot)\) \(\chi_{4235}(334,\cdot)\) \(\chi_{4235}(339,\cdot)\) \(\chi_{4235}(509,\cdot)\) \(\chi_{4235}(544,\cdot)\) \(\chi_{4235}(619,\cdot)\) \(\chi_{4235}(654,\cdot)\) \(\chi_{4235}(719,\cdot)\) \(\chi_{4235}(724,\cdot)\) \(\chi_{4235}(829,\cdot)\) \(\chi_{4235}(894,\cdot)\) \(\chi_{4235}(929,\cdot)\) \(\chi_{4235}(999,\cdot)\) \(\chi_{4235}(1004,\cdot)\) \(\chi_{4235}(1039,\cdot)\) \(\chi_{4235}(1104,\cdot)\) \(\chi_{4235}(1109,\cdot)\) \(\chi_{4235}(1214,\cdot)\) \(\chi_{4235}(1279,\cdot)\) \(\chi_{4235}(1314,\cdot)\) \(\chi_{4235}(1384,\cdot)\) \(\chi_{4235}(1389,\cdot)\) \(\chi_{4235}(1424,\cdot)\) \(\chi_{4235}(1489,\cdot)\) \(\chi_{4235}(1494,\cdot)\) \(\chi_{4235}(1599,\cdot)\) \(\chi_{4235}(1664,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((2542,1816,2906)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{47}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 4235 }(1039, a) \) | \(-1\) | \(1\) | \(e\left(\frac{227}{330}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{62}{165}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{124}{165}\right)\) | \(e\left(\frac{89}{165}\right)\) |