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.ep
\(\chi_{8712}(59,\cdot)\) \(\chi_{8712}(203,\cdot)\) \(\chi_{8712}(443,\cdot)\) \(\chi_{8712}(515,\cdot)\) \(\chi_{8712}(587,\cdot)\) \(\chi_{8712}(707,\cdot)\) \(\chi_{8712}(731,\cdot)\) \(\chi_{8712}(779,\cdot)\) \(\chi_{8712}(851,\cdot)\) \(\chi_{8712}(1235,\cdot)\) \(\chi_{8712}(1307,\cdot)\) \(\chi_{8712}(1379,\cdot)\) \(\chi_{8712}(1499,\cdot)\) \(\chi_{8712}(1523,\cdot)\) \(\chi_{8712}(1571,\cdot)\) \(\chi_{8712}(1643,\cdot)\) \(\chi_{8712}(1787,\cdot)\) \(\chi_{8712}(2027,\cdot)\) \(\chi_{8712}(2099,\cdot)\) \(\chi_{8712}(2171,\cdot)\) \(\chi_{8712}(2291,\cdot)\) \(\chi_{8712}(2315,\cdot)\) \(\chi_{8712}(2363,\cdot)\) \(\chi_{8712}(2435,\cdot)\) \(\chi_{8712}(2579,\cdot)\) \(\chi_{8712}(2819,\cdot)\) \(\chi_{8712}(2891,\cdot)\) \(\chi_{8712}(2963,\cdot)\) \(\chi_{8712}(3083,\cdot)\) \(\chi_{8712}(3107,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((6535,4357,1937,5689)\) → \((-1,-1,e\left(\frac{5}{6}\right),e\left(\frac{16}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8712 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{165}\right)\) | \(e\left(\frac{287}{330}\right)\) | \(e\left(\frac{181}{330}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{64}{165}\right)\) | \(e\left(\frac{46}{165}\right)\) | \(e\left(\frac{61}{330}\right)\) | \(e\left(\frac{7}{110}\right)\) |