Basic properties
| Modulus: | \(8712\) | |
| Conductor: | \(484\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{484}(127,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8712.eg
\(\chi_{8712}(127,\cdot)\) \(\chi_{8712}(271,\cdot)\) \(\chi_{8712}(343,\cdot)\) \(\chi_{8712}(415,\cdot)\) \(\chi_{8712}(919,\cdot)\) \(\chi_{8712}(1063,\cdot)\) \(\chi_{8712}(1135,\cdot)\) \(\chi_{8712}(1711,\cdot)\) \(\chi_{8712}(1999,\cdot)\) \(\chi_{8712}(2503,\cdot)\) \(\chi_{8712}(2647,\cdot)\) \(\chi_{8712}(2719,\cdot)\) \(\chi_{8712}(2791,\cdot)\) \(\chi_{8712}(3295,\cdot)\) \(\chi_{8712}(3439,\cdot)\) \(\chi_{8712}(3511,\cdot)\) \(\chi_{8712}(3583,\cdot)\) \(\chi_{8712}(4231,\cdot)\) \(\chi_{8712}(4303,\cdot)\) \(\chi_{8712}(4375,\cdot)\) \(\chi_{8712}(4879,\cdot)\) \(\chi_{8712}(5023,\cdot)\) \(\chi_{8712}(5095,\cdot)\) \(\chi_{8712}(5167,\cdot)\) \(\chi_{8712}(5671,\cdot)\) \(\chi_{8712}(5815,\cdot)\) \(\chi_{8712}(5887,\cdot)\) \(\chi_{8712}(5959,\cdot)\) \(\chi_{8712}(6463,\cdot)\) \(\chi_{8712}(6607,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((6535,4357,1937,5689)\) → \((-1,1,1,e\left(\frac{89}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8712 }(127, a) \) | \(1\) | \(1\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{2}{55}\right)\) |