Basic properties
| Modulus: | \(8712\) | |
| Conductor: | \(2904\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2904}(179,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8712.ec
\(\chi_{8712}(179,\cdot)\) \(\chi_{8712}(467,\cdot)\) \(\chi_{8712}(1043,\cdot)\) \(\chi_{8712}(1115,\cdot)\) \(\chi_{8712}(1259,\cdot)\) \(\chi_{8712}(1763,\cdot)\) \(\chi_{8712}(1835,\cdot)\) \(\chi_{8712}(1907,\cdot)\) \(\chi_{8712}(2051,\cdot)\) \(\chi_{8712}(2555,\cdot)\) \(\chi_{8712}(2627,\cdot)\) \(\chi_{8712}(2699,\cdot)\) \(\chi_{8712}(2843,\cdot)\) \(\chi_{8712}(3347,\cdot)\) \(\chi_{8712}(3419,\cdot)\) \(\chi_{8712}(3491,\cdot)\) \(\chi_{8712}(3635,\cdot)\) \(\chi_{8712}(4139,\cdot)\) \(\chi_{8712}(4211,\cdot)\) \(\chi_{8712}(4283,\cdot)\) \(\chi_{8712}(4427,\cdot)\) \(\chi_{8712}(4931,\cdot)\) \(\chi_{8712}(5003,\cdot)\) \(\chi_{8712}(5075,\cdot)\) \(\chi_{8712}(5219,\cdot)\) \(\chi_{8712}(5723,\cdot)\) \(\chi_{8712}(5795,\cdot)\) \(\chi_{8712}(5867,\cdot)\) \(\chi_{8712}(6011,\cdot)\) \(\chi_{8712}(6515,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((6535,4357,1937,5689)\) → \((-1,-1,-1,e\left(\frac{9}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8712 }(179, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{83}{110}\right)\) |