Basic properties
Modulus: | \(2541\) | |
Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{121}(64,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2541.bp
\(\chi_{2541}(64,\cdot)\) \(\chi_{2541}(169,\cdot)\) \(\chi_{2541}(190,\cdot)\) \(\chi_{2541}(295,\cdot)\) \(\chi_{2541}(379,\cdot)\) \(\chi_{2541}(400,\cdot)\) \(\chi_{2541}(421,\cdot)\) \(\chi_{2541}(526,\cdot)\) \(\chi_{2541}(610,\cdot)\) \(\chi_{2541}(631,\cdot)\) \(\chi_{2541}(652,\cdot)\) \(\chi_{2541}(757,\cdot)\) \(\chi_{2541}(841,\cdot)\) \(\chi_{2541}(862,\cdot)\) \(\chi_{2541}(883,\cdot)\) \(\chi_{2541}(988,\cdot)\) \(\chi_{2541}(1072,\cdot)\) \(\chi_{2541}(1093,\cdot)\) \(\chi_{2541}(1114,\cdot)\) \(\chi_{2541}(1303,\cdot)\) \(\chi_{2541}(1324,\cdot)\) \(\chi_{2541}(1345,\cdot)\) \(\chi_{2541}(1450,\cdot)\) \(\chi_{2541}(1534,\cdot)\) \(\chi_{2541}(1555,\cdot)\) \(\chi_{2541}(1681,\cdot)\) \(\chi_{2541}(1765,\cdot)\) \(\chi_{2541}(1786,\cdot)\) \(\chi_{2541}(1807,\cdot)\) \(\chi_{2541}(1912,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((848,1816,2059)\) → \((1,1,e\left(\frac{3}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 2541 }(64, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{8}{55}\right)\) |