Basic properties
| Modulus: | \(8712\) | |
| Conductor: | \(363\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{363}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8712.dt
\(\chi_{8712}(17,\cdot)\) \(\chi_{8712}(305,\cdot)\) \(\chi_{8712}(809,\cdot)\) \(\chi_{8712}(953,\cdot)\) \(\chi_{8712}(1025,\cdot)\) \(\chi_{8712}(1097,\cdot)\) \(\chi_{8712}(1601,\cdot)\) \(\chi_{8712}(1745,\cdot)\) \(\chi_{8712}(1817,\cdot)\) \(\chi_{8712}(1889,\cdot)\) \(\chi_{8712}(2537,\cdot)\) \(\chi_{8712}(2609,\cdot)\) \(\chi_{8712}(2681,\cdot)\) \(\chi_{8712}(3185,\cdot)\) \(\chi_{8712}(3329,\cdot)\) \(\chi_{8712}(3401,\cdot)\) \(\chi_{8712}(3473,\cdot)\) \(\chi_{8712}(3977,\cdot)\) \(\chi_{8712}(4121,\cdot)\) \(\chi_{8712}(4193,\cdot)\) \(\chi_{8712}(4265,\cdot)\) \(\chi_{8712}(4769,\cdot)\) \(\chi_{8712}(4913,\cdot)\) \(\chi_{8712}(4985,\cdot)\) \(\chi_{8712}(5057,\cdot)\) \(\chi_{8712}(5561,\cdot)\) \(\chi_{8712}(5705,\cdot)\) \(\chi_{8712}(5777,\cdot)\) \(\chi_{8712}(5849,\cdot)\) \(\chi_{8712}(6353,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((6535,4357,1937,5689)\) → \((1,1,-1,e\left(\frac{49}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8712 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{32}{55}\right)\) |