Basic properties
Modulus: | \(8712\) | |
Conductor: | \(8712\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8712.eq
\(\chi_{8712}(139,\cdot)\) \(\chi_{8712}(211,\cdot)\) \(\chi_{8712}(259,\cdot)\) \(\chi_{8712}(283,\cdot)\) \(\chi_{8712}(547,\cdot)\) \(\chi_{8712}(787,\cdot)\) \(\chi_{8712}(931,\cdot)\) \(\chi_{8712}(1003,\cdot)\) \(\chi_{8712}(1051,\cdot)\) \(\chi_{8712}(1075,\cdot)\) \(\chi_{8712}(1195,\cdot)\) \(\chi_{8712}(1267,\cdot)\) \(\chi_{8712}(1339,\cdot)\) \(\chi_{8712}(1579,\cdot)\) \(\chi_{8712}(1723,\cdot)\) \(\chi_{8712}(1795,\cdot)\) \(\chi_{8712}(1843,\cdot)\) \(\chi_{8712}(1867,\cdot)\) \(\chi_{8712}(1987,\cdot)\) \(\chi_{8712}(2059,\cdot)\) \(\chi_{8712}(2131,\cdot)\) \(\chi_{8712}(2371,\cdot)\) \(\chi_{8712}(2515,\cdot)\) \(\chi_{8712}(2587,\cdot)\) \(\chi_{8712}(2779,\cdot)\) \(\chi_{8712}(2851,\cdot)\) \(\chi_{8712}(2923,\cdot)\) \(\chi_{8712}(3163,\cdot)\) \(\chi_{8712}(3427,\cdot)\) \(\chi_{8712}(3451,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((6535,4357,1937,5689)\) → \((-1,-1,e\left(\frac{2}{3}\right),e\left(\frac{29}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8712 }(1051, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{330}\right)\) | \(e\left(\frac{2}{165}\right)\) | \(e\left(\frac{76}{165}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{113}{165}\right)\) | \(e\left(\frac{107}{165}\right)\) | \(e\left(\frac{167}{330}\right)\) | \(e\left(\frac{39}{110}\right)\) |