Basic properties
| Modulus: | \(9680\) | |
| Conductor: | \(2420\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2420}(79,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9680.eu
\(\chi_{9680}(79,\cdot)\) \(\chi_{9680}(479,\cdot)\) \(\chi_{9680}(799,\cdot)\) \(\chi_{9680}(1119,\cdot)\) \(\chi_{9680}(1359,\cdot)\) \(\chi_{9680}(1679,\cdot)\) \(\chi_{9680}(1839,\cdot)\) \(\chi_{9680}(1999,\cdot)\) \(\chi_{9680}(2239,\cdot)\) \(\chi_{9680}(2559,\cdot)\) \(\chi_{9680}(2719,\cdot)\) \(\chi_{9680}(2879,\cdot)\) \(\chi_{9680}(3439,\cdot)\) \(\chi_{9680}(3599,\cdot)\) \(\chi_{9680}(3759,\cdot)\) \(\chi_{9680}(3999,\cdot)\) \(\chi_{9680}(4319,\cdot)\) \(\chi_{9680}(4479,\cdot)\) \(\chi_{9680}(4639,\cdot)\) \(\chi_{9680}(4879,\cdot)\) \(\chi_{9680}(5199,\cdot)\) \(\chi_{9680}(5359,\cdot)\) \(\chi_{9680}(5519,\cdot)\) \(\chi_{9680}(5759,\cdot)\) \(\chi_{9680}(6079,\cdot)\) \(\chi_{9680}(6239,\cdot)\) \(\chi_{9680}(6399,\cdot)\) \(\chi_{9680}(6639,\cdot)\) \(\chi_{9680}(6959,\cdot)\) \(\chi_{9680}(7119,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3631,2421,1937,4721)\) → \((-1,1,-1,e\left(\frac{41}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 9680 }(79, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{37}{110}\right)\) |