Basic properties
Modulus: | \(5445\) | |
Conductor: | \(1089\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(165\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1089}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5445.dc
\(\chi_{5445}(16,\cdot)\) \(\chi_{5445}(31,\cdot)\) \(\chi_{5445}(196,\cdot)\) \(\chi_{5445}(256,\cdot)\) \(\chi_{5445}(301,\cdot)\) \(\chi_{5445}(346,\cdot)\) \(\chi_{5445}(421,\cdot)\) \(\chi_{5445}(466,\cdot)\) \(\chi_{5445}(526,\cdot)\) \(\chi_{5445}(691,\cdot)\) \(\chi_{5445}(751,\cdot)\) \(\chi_{5445}(796,\cdot)\) \(\chi_{5445}(841,\cdot)\) \(\chi_{5445}(916,\cdot)\) \(\chi_{5445}(961,\cdot)\) \(\chi_{5445}(1006,\cdot)\) \(\chi_{5445}(1021,\cdot)\) \(\chi_{5445}(1186,\cdot)\) \(\chi_{5445}(1246,\cdot)\) \(\chi_{5445}(1336,\cdot)\) \(\chi_{5445}(1411,\cdot)\) \(\chi_{5445}(1456,\cdot)\) \(\chi_{5445}(1501,\cdot)\) \(\chi_{5445}(1516,\cdot)\) \(\chi_{5445}(1681,\cdot)\) \(\chi_{5445}(1741,\cdot)\) \(\chi_{5445}(1786,\cdot)\) \(\chi_{5445}(1831,\cdot)\) \(\chi_{5445}(1906,\cdot)\) \(\chi_{5445}(1951,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 165 polynomial (not computed) |
Values on generators
\((3026,4357,3511)\) → \((e\left(\frac{1}{3}\right),1,e\left(\frac{43}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
\( \chi_{ 5445 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{38}{165}\right)\) | \(e\left(\frac{133}{165}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{104}{165}\right)\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{76}{165}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{13}{33}\right)\) |