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 \(\chi_{4235}(1829,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.dh
\(\chi_{8470}(179,\cdot)\) \(\chi_{8470}(289,\cdot)\) \(\chi_{8470}(389,\cdot)\) \(\chi_{8470}(499,\cdot)\) \(\chi_{8470}(599,\cdot)\) \(\chi_{8470}(669,\cdot)\) \(\chi_{8470}(709,\cdot)\) \(\chi_{8470}(779,\cdot)\) \(\chi_{8470}(949,\cdot)\) \(\chi_{8470}(1059,\cdot)\) \(\chi_{8470}(1159,\cdot)\) \(\chi_{8470}(1269,\cdot)\) \(\chi_{8470}(1369,\cdot)\) \(\chi_{8470}(1439,\cdot)\) \(\chi_{8470}(1549,\cdot)\) \(\chi_{8470}(1719,\cdot)\) \(\chi_{8470}(1829,\cdot)\) \(\chi_{8470}(1929,\cdot)\) \(\chi_{8470}(2039,\cdot)\) \(\chi_{8470}(2139,\cdot)\) \(\chi_{8470}(2209,\cdot)\) \(\chi_{8470}(2249,\cdot)\) \(\chi_{8470}(2319,\cdot)\) \(\chi_{8470}(2489,\cdot)\) \(\chi_{8470}(2599,\cdot)\) \(\chi_{8470}(2699,\cdot)\) \(\chi_{8470}(2809,\cdot)\) \(\chi_{8470}(2909,\cdot)\) \(\chi_{8470}(2979,\cdot)\) \(\chi_{8470}(3019,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{4}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(1829, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{131}{330}\right)\) | \(e\left(\frac{116}{165}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{97}{165}\right)\) | \(e\left(\frac{73}{330}\right)\) |