Basic properties
Modulus: | \(4840\) | |
Conductor: | \(4840\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | 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 4840.dd
\(\chi_{4840}(19,\cdot)\) \(\chi_{4840}(139,\cdot)\) \(\chi_{4840}(259,\cdot)\) \(\chi_{4840}(299,\cdot)\) \(\chi_{4840}(459,\cdot)\) \(\chi_{4840}(579,\cdot)\) \(\chi_{4840}(739,\cdot)\) \(\chi_{4840}(899,\cdot)\) \(\chi_{4840}(1019,\cdot)\) \(\chi_{4840}(1139,\cdot)\) \(\chi_{4840}(1179,\cdot)\) \(\chi_{4840}(1339,\cdot)\) \(\chi_{4840}(1459,\cdot)\) \(\chi_{4840}(1579,\cdot)\) \(\chi_{4840}(1619,\cdot)\) \(\chi_{4840}(1779,\cdot)\) \(\chi_{4840}(1899,\cdot)\) \(\chi_{4840}(2019,\cdot)\) \(\chi_{4840}(2059,\cdot)\) \(\chi_{4840}(2219,\cdot)\) \(\chi_{4840}(2459,\cdot)\) \(\chi_{4840}(2499,\cdot)\) \(\chi_{4840}(2779,\cdot)\) \(\chi_{4840}(2899,\cdot)\) \(\chi_{4840}(2939,\cdot)\) \(\chi_{4840}(3099,\cdot)\) \(\chi_{4840}(3219,\cdot)\) \(\chi_{4840}(3339,\cdot)\) \(\chi_{4840}(3539,\cdot)\) \(\chi_{4840}(3659,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3631,2421,1937,4721)\) → \((-1,-1,-1,e\left(\frac{83}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 4840 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{18}{55}\right)\) |