Basic properties
| Modulus: | \(8712\) | |
| 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 \(\chi_{968}(387,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8712.dz
\(\chi_{8712}(19,\cdot)\) \(\chi_{8712}(523,\cdot)\) \(\chi_{8712}(667,\cdot)\) \(\chi_{8712}(739,\cdot)\) \(\chi_{8712}(811,\cdot)\) \(\chi_{8712}(1315,\cdot)\) \(\chi_{8712}(1459,\cdot)\) \(\chi_{8712}(1531,\cdot)\) \(\chi_{8712}(1603,\cdot)\) \(\chi_{8712}(2107,\cdot)\) \(\chi_{8712}(2251,\cdot)\) \(\chi_{8712}(2323,\cdot)\) \(\chi_{8712}(2395,\cdot)\) \(\chi_{8712}(2899,\cdot)\) \(\chi_{8712}(3043,\cdot)\) \(\chi_{8712}(3115,\cdot)\) \(\chi_{8712}(3187,\cdot)\) \(\chi_{8712}(3691,\cdot)\) \(\chi_{8712}(3835,\cdot)\) \(\chi_{8712}(3907,\cdot)\) \(\chi_{8712}(3979,\cdot)\) \(\chi_{8712}(4483,\cdot)\) \(\chi_{8712}(4627,\cdot)\) \(\chi_{8712}(4699,\cdot)\) \(\chi_{8712}(4771,\cdot)\) \(\chi_{8712}(5275,\cdot)\) \(\chi_{8712}(5419,\cdot)\) \(\chi_{8712}(5491,\cdot)\) \(\chi_{8712}(6067,\cdot)\) \(\chi_{8712}(6355,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((6535,4357,1937,5689)\) → \((-1,-1,1,e\left(\frac{91}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8712 }(2323, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{1}{110}\right)\) |