Basic properties
Modulus: | \(1089\) | |
Conductor: | \(363\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{363}(266,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1089.bb
\(\chi_{1089}(8,\cdot)\) \(\chi_{1089}(17,\cdot)\) \(\chi_{1089}(35,\cdot)\) \(\chi_{1089}(62,\cdot)\) \(\chi_{1089}(107,\cdot)\) \(\chi_{1089}(116,\cdot)\) \(\chi_{1089}(134,\cdot)\) \(\chi_{1089}(206,\cdot)\) \(\chi_{1089}(260,\cdot)\) \(\chi_{1089}(305,\cdot)\) \(\chi_{1089}(314,\cdot)\) \(\chi_{1089}(332,\cdot)\) \(\chi_{1089}(359,\cdot)\) \(\chi_{1089}(404,\cdot)\) \(\chi_{1089}(413,\cdot)\) \(\chi_{1089}(431,\cdot)\) \(\chi_{1089}(458,\cdot)\) \(\chi_{1089}(503,\cdot)\) \(\chi_{1089}(512,\cdot)\) \(\chi_{1089}(530,\cdot)\) \(\chi_{1089}(557,\cdot)\) \(\chi_{1089}(611,\cdot)\) \(\chi_{1089}(629,\cdot)\) \(\chi_{1089}(656,\cdot)\) \(\chi_{1089}(701,\cdot)\) \(\chi_{1089}(710,\cdot)\) \(\chi_{1089}(728,\cdot)\) \(\chi_{1089}(755,\cdot)\) \(\chi_{1089}(800,\cdot)\) \(\chi_{1089}(809,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((848,244)\) → \((-1,e\left(\frac{91}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 1089 }(629, a) \) | \(1\) | \(1\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{2}{55}\right)\) |