Basic properties
Modulus: | \(1089\) | |
Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{121}(30,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1089.ba
\(\chi_{1089}(19,\cdot)\) \(\chi_{1089}(28,\cdot)\) \(\chi_{1089}(46,\cdot)\) \(\chi_{1089}(73,\cdot)\) \(\chi_{1089}(127,\cdot)\) \(\chi_{1089}(145,\cdot)\) \(\chi_{1089}(172,\cdot)\) \(\chi_{1089}(217,\cdot)\) \(\chi_{1089}(226,\cdot)\) \(\chi_{1089}(244,\cdot)\) \(\chi_{1089}(271,\cdot)\) \(\chi_{1089}(316,\cdot)\) \(\chi_{1089}(325,\cdot)\) \(\chi_{1089}(343,\cdot)\) \(\chi_{1089}(370,\cdot)\) \(\chi_{1089}(415,\cdot)\) \(\chi_{1089}(424,\cdot)\) \(\chi_{1089}(442,\cdot)\) \(\chi_{1089}(469,\cdot)\) \(\chi_{1089}(514,\cdot)\) \(\chi_{1089}(523,\cdot)\) \(\chi_{1089}(541,\cdot)\) \(\chi_{1089}(568,\cdot)\) \(\chi_{1089}(613,\cdot)\) \(\chi_{1089}(622,\cdot)\) \(\chi_{1089}(640,\cdot)\) \(\chi_{1089}(667,\cdot)\) \(\chi_{1089}(712,\cdot)\) \(\chi_{1089}(721,\cdot)\) \(\chi_{1089}(739,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((848,244)\) → \((1,e\left(\frac{53}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 1089 }(514, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{67}{110}\right)\) |