Basic properties
Modulus: | \(8470\) | |
Conductor: | \(4235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4235}(2609,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.dl
\(\chi_{8470}(19,\cdot)\) \(\chi_{8470}(129,\cdot)\) \(\chi_{8470}(299,\cdot)\) \(\chi_{8470}(369,\cdot)\) \(\chi_{8470}(409,\cdot)\) \(\chi_{8470}(479,\cdot)\) \(\chi_{8470}(579,\cdot)\) \(\chi_{8470}(689,\cdot)\) \(\chi_{8470}(789,\cdot)\) \(\chi_{8470}(899,\cdot)\) \(\chi_{8470}(1069,\cdot)\) \(\chi_{8470}(1139,\cdot)\) \(\chi_{8470}(1179,\cdot)\) \(\chi_{8470}(1249,\cdot)\) \(\chi_{8470}(1349,\cdot)\) \(\chi_{8470}(1459,\cdot)\) \(\chi_{8470}(1559,\cdot)\) \(\chi_{8470}(1669,\cdot)\) \(\chi_{8470}(1839,\cdot)\) \(\chi_{8470}(1949,\cdot)\) \(\chi_{8470}(2019,\cdot)\) \(\chi_{8470}(2119,\cdot)\) \(\chi_{8470}(2229,\cdot)\) \(\chi_{8470}(2329,\cdot)\) \(\chi_{8470}(2439,\cdot)\) \(\chi_{8470}(2609,\cdot)\) \(\chi_{8470}(2679,\cdot)\) \(\chi_{8470}(2719,\cdot)\) \(\chi_{8470}(2789,\cdot)\) \(\chi_{8470}(2889,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{51}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(2609, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{91}{110}\right)\) | \(e\left(\frac{17}{330}\right)\) | \(e\left(\frac{107}{165}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{233}{330}\right)\) | \(e\left(\frac{211}{330}\right)\) |