Basic properties
Modulus: | \(8470\) | |
Conductor: | \(4235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(660\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4235}(157,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.do
\(\chi_{8470}(47,\cdot)\) \(\chi_{8470}(103,\cdot)\) \(\chi_{8470}(157,\cdot)\) \(\chi_{8470}(213,\cdot)\) \(\chi_{8470}(257,\cdot)\) \(\chi_{8470}(313,\cdot)\) \(\chi_{8470}(367,\cdot)\) \(\chi_{8470}(383,\cdot)\) \(\chi_{8470}(423,\cdot)\) \(\chi_{8470}(467,\cdot)\) \(\chi_{8470}(537,\cdot)\) \(\chi_{8470}(577,\cdot)\) \(\chi_{8470}(647,\cdot)\) \(\chi_{8470}(663,\cdot)\) \(\chi_{8470}(773,\cdot)\) \(\chi_{8470}(817,\cdot)\) \(\chi_{8470}(873,\cdot)\) \(\chi_{8470}(927,\cdot)\) \(\chi_{8470}(983,\cdot)\) \(\chi_{8470}(1027,\cdot)\) \(\chi_{8470}(1083,\cdot)\) \(\chi_{8470}(1137,\cdot)\) \(\chi_{8470}(1153,\cdot)\) \(\chi_{8470}(1193,\cdot)\) \(\chi_{8470}(1263,\cdot)\) \(\chi_{8470}(1307,\cdot)\) \(\chi_{8470}(1347,\cdot)\) \(\chi_{8470}(1417,\cdot)\) \(\chi_{8470}(1433,\cdot)\) \(\chi_{8470}(1543,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{660})$ |
Fixed field: | Number field defined by a degree 660 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((i,e\left(\frac{1}{6}\right),e\left(\frac{34}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(157, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{151}{220}\right)\) | \(e\left(\frac{467}{660}\right)\) | \(e\left(\frac{106}{165}\right)\) | \(e\left(\frac{47}{132}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{109}{330}\right)\) | \(e\left(\frac{361}{660}\right)\) |