Basic properties
| Modulus: | \(968\) | |
| Conductor: | \(968\) | 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 968.ba
\(\chi_{968}(19,\cdot)\) \(\chi_{968}(35,\cdot)\) \(\chi_{968}(51,\cdot)\) \(\chi_{968}(83,\cdot)\) \(\chi_{968}(107,\cdot)\) \(\chi_{968}(123,\cdot)\) \(\chi_{968}(139,\cdot)\) \(\chi_{968}(171,\cdot)\) \(\chi_{968}(195,\cdot)\) \(\chi_{968}(211,\cdot)\) \(\chi_{968}(227,\cdot)\) \(\chi_{968}(259,\cdot)\) \(\chi_{968}(283,\cdot)\) \(\chi_{968}(299,\cdot)\) \(\chi_{968}(315,\cdot)\) \(\chi_{968}(347,\cdot)\) \(\chi_{968}(371,\cdot)\) \(\chi_{968}(387,\cdot)\) \(\chi_{968}(435,\cdot)\) \(\chi_{968}(459,\cdot)\) \(\chi_{968}(491,\cdot)\) \(\chi_{968}(523,\cdot)\) \(\chi_{968}(547,\cdot)\) \(\chi_{968}(563,\cdot)\) \(\chi_{968}(579,\cdot)\) \(\chi_{968}(611,\cdot)\) \(\chi_{968}(635,\cdot)\) \(\chi_{968}(651,\cdot)\) \(\chi_{968}(667,\cdot)\) \(\chi_{968}(739,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((727,485,849)\) → \((-1,-1,e\left(\frac{27}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 968 }(51, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) |