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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1620.bt
\(\chi_{1620}(23,\cdot)\) \(\chi_{1620}(47,\cdot)\) \(\chi_{1620}(83,\cdot)\) \(\chi_{1620}(167,\cdot)\) \(\chi_{1620}(203,\cdot)\) \(\chi_{1620}(227,\cdot)\) \(\chi_{1620}(263,\cdot)\) \(\chi_{1620}(347,\cdot)\) \(\chi_{1620}(383,\cdot)\) \(\chi_{1620}(407,\cdot)\) \(\chi_{1620}(443,\cdot)\) \(\chi_{1620}(527,\cdot)\) \(\chi_{1620}(563,\cdot)\) \(\chi_{1620}(587,\cdot)\) \(\chi_{1620}(623,\cdot)\) \(\chi_{1620}(707,\cdot)\) \(\chi_{1620}(743,\cdot)\) \(\chi_{1620}(767,\cdot)\) \(\chi_{1620}(803,\cdot)\) \(\chi_{1620}(887,\cdot)\) \(\chi_{1620}(923,\cdot)\) \(\chi_{1620}(947,\cdot)\) \(\chi_{1620}(983,\cdot)\) \(\chi_{1620}(1067,\cdot)\) \(\chi_{1620}(1103,\cdot)\) \(\chi_{1620}(1127,\cdot)\) \(\chi_{1620}(1163,\cdot)\) \(\chi_{1620}(1247,\cdot)\) \(\chi_{1620}(1283,\cdot)\) \(\chi_{1620}(1307,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((811,1541,1297)\) → \((-1,e\left(\frac{1}{54}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 1620 }(83, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{108}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{43}{108}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{103}{108}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{53}{54}\right)\) |