Basic properties
| Modulus: | \(4840\) | |
| Conductor: | \(968\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{968}(51,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4840.db
\(\chi_{4840}(51,\cdot)\) \(\chi_{4840}(171,\cdot)\) \(\chi_{4840}(211,\cdot)\) \(\chi_{4840}(371,\cdot)\) \(\chi_{4840}(491,\cdot)\) \(\chi_{4840}(611,\cdot)\) \(\chi_{4840}(651,\cdot)\) \(\chi_{4840}(811,\cdot)\) \(\chi_{4840}(931,\cdot)\) \(\chi_{4840}(1051,\cdot)\) \(\chi_{4840}(1091,\cdot)\) \(\chi_{4840}(1251,\cdot)\) \(\chi_{4840}(1491,\cdot)\) \(\chi_{4840}(1531,\cdot)\) \(\chi_{4840}(1811,\cdot)\) \(\chi_{4840}(1931,\cdot)\) \(\chi_{4840}(1971,\cdot)\) \(\chi_{4840}(2131,\cdot)\) \(\chi_{4840}(2251,\cdot)\) \(\chi_{4840}(2371,\cdot)\) \(\chi_{4840}(2571,\cdot)\) \(\chi_{4840}(2691,\cdot)\) \(\chi_{4840}(2811,\cdot)\) \(\chi_{4840}(2851,\cdot)\) \(\chi_{4840}(3011,\cdot)\) \(\chi_{4840}(3131,\cdot)\) \(\chi_{4840}(3251,\cdot)\) \(\chi_{4840}(3291,\cdot)\) \(\chi_{4840}(3451,\cdot)\) \(\chi_{4840}(3571,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3631,2421,1937,4721)\) → \((-1,-1,1,e\left(\frac{27}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 4840 }(51, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{37}{55}\right)\) |