Basic properties
| Modulus: | \(1620\) | |
| Conductor: | \(1620\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1620.bv
\(\chi_{1620}(7,\cdot)\) \(\chi_{1620}(43,\cdot)\) \(\chi_{1620}(67,\cdot)\) \(\chi_{1620}(103,\cdot)\) \(\chi_{1620}(187,\cdot)\) \(\chi_{1620}(223,\cdot)\) \(\chi_{1620}(247,\cdot)\) \(\chi_{1620}(283,\cdot)\) \(\chi_{1620}(367,\cdot)\) \(\chi_{1620}(403,\cdot)\) \(\chi_{1620}(427,\cdot)\) \(\chi_{1620}(463,\cdot)\) \(\chi_{1620}(547,\cdot)\) \(\chi_{1620}(583,\cdot)\) \(\chi_{1620}(607,\cdot)\) \(\chi_{1620}(643,\cdot)\) \(\chi_{1620}(727,\cdot)\) \(\chi_{1620}(763,\cdot)\) \(\chi_{1620}(787,\cdot)\) \(\chi_{1620}(823,\cdot)\) \(\chi_{1620}(907,\cdot)\) \(\chi_{1620}(943,\cdot)\) \(\chi_{1620}(967,\cdot)\) \(\chi_{1620}(1003,\cdot)\) \(\chi_{1620}(1087,\cdot)\) \(\chi_{1620}(1123,\cdot)\) \(\chi_{1620}(1147,\cdot)\) \(\chi_{1620}(1183,\cdot)\) \(\chi_{1620}(1267,\cdot)\) \(\chi_{1620}(1303,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((811,1541,1297)\) → \((-1,e\left(\frac{2}{27}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 1620 }(907, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{108}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{37}{108}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{7}{108}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{25}{27}\right)\) |