Basic properties
| Modulus: | \(5445\) | |
| Conductor: | \(1089\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1089}(211,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5445.dm
\(\chi_{5445}(61,\cdot)\) \(\chi_{5445}(106,\cdot)\) \(\chi_{5445}(151,\cdot)\) \(\chi_{5445}(211,\cdot)\) \(\chi_{5445}(376,\cdot)\) \(\chi_{5445}(391,\cdot)\) \(\chi_{5445}(436,\cdot)\) \(\chi_{5445}(556,\cdot)\) \(\chi_{5445}(601,\cdot)\) \(\chi_{5445}(646,\cdot)\) \(\chi_{5445}(706,\cdot)\) \(\chi_{5445}(871,\cdot)\) \(\chi_{5445}(886,\cdot)\) \(\chi_{5445}(931,\cdot)\) \(\chi_{5445}(976,\cdot)\) \(\chi_{5445}(1051,\cdot)\) \(\chi_{5445}(1096,\cdot)\) \(\chi_{5445}(1141,\cdot)\) \(\chi_{5445}(1366,\cdot)\) \(\chi_{5445}(1381,\cdot)\) \(\chi_{5445}(1426,\cdot)\) \(\chi_{5445}(1471,\cdot)\) \(\chi_{5445}(1591,\cdot)\) \(\chi_{5445}(1636,\cdot)\) \(\chi_{5445}(1696,\cdot)\) \(\chi_{5445}(1861,\cdot)\) \(\chi_{5445}(1876,\cdot)\) \(\chi_{5445}(1921,\cdot)\) \(\chi_{5445}(1966,\cdot)\) \(\chi_{5445}(2041,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((3026,4357,3511)\) → \((e\left(\frac{1}{3}\right),1,e\left(\frac{31}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 5445 }(211, a) \) | \(-1\) | \(1\) | \(e\left(\frac{203}{330}\right)\) | \(e\left(\frac{38}{165}\right)\) | \(e\left(\frac{101}{330}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{43}{330}\right)\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{76}{165}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{13}{33}\right)\) |