Basic properties
Modulus: | \(5445\) | |
Conductor: | \(5445\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5445.dn
\(\chi_{5445}(4,\cdot)\) \(\chi_{5445}(49,\cdot)\) \(\chi_{5445}(169,\cdot)\) \(\chi_{5445}(214,\cdot)\) \(\chi_{5445}(229,\cdot)\) \(\chi_{5445}(394,\cdot)\) \(\chi_{5445}(454,\cdot)\) \(\chi_{5445}(499,\cdot)\) \(\chi_{5445}(544,\cdot)\) \(\chi_{5445}(619,\cdot)\) \(\chi_{5445}(664,\cdot)\) \(\chi_{5445}(709,\cdot)\) \(\chi_{5445}(724,\cdot)\) \(\chi_{5445}(889,\cdot)\) \(\chi_{5445}(949,\cdot)\) \(\chi_{5445}(994,\cdot)\) \(\chi_{5445}(1039,\cdot)\) \(\chi_{5445}(1114,\cdot)\) \(\chi_{5445}(1159,\cdot)\) \(\chi_{5445}(1204,\cdot)\) \(\chi_{5445}(1384,\cdot)\) \(\chi_{5445}(1444,\cdot)\) \(\chi_{5445}(1489,\cdot)\) \(\chi_{5445}(1534,\cdot)\) \(\chi_{5445}(1609,\cdot)\) \(\chi_{5445}(1699,\cdot)\) \(\chi_{5445}(1714,\cdot)\) \(\chi_{5445}(1879,\cdot)\) \(\chi_{5445}(1984,\cdot)\) \(\chi_{5445}(2029,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((3026,4357,3511)\) → \((e\left(\frac{1}{3}\right),-1,e\left(\frac{1}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
\( \chi_{ 5445 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{281}{330}\right)\) | \(e\left(\frac{116}{165}\right)\) | \(e\left(\frac{317}{330}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{1}{330}\right)\) | \(e\left(\frac{134}{165}\right)\) | \(e\left(\frac{67}{165}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{29}{66}\right)\) |