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 \(\chi_{4235}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.dq
\(\chi_{8470}(37,\cdot)\) \(\chi_{8470}(53,\cdot)\) \(\chi_{8470}(93,\cdot)\) \(\chi_{8470}(137,\cdot)\) \(\chi_{8470}(163,\cdot)\) \(\chi_{8470}(207,\cdot)\) \(\chi_{8470}(247,\cdot)\) \(\chi_{8470}(317,\cdot)\) \(\chi_{8470}(333,\cdot)\) \(\chi_{8470}(443,\cdot)\) \(\chi_{8470}(543,\cdot)\) \(\chi_{8470}(597,\cdot)\) \(\chi_{8470}(653,\cdot)\) \(\chi_{8470}(697,\cdot)\) \(\chi_{8470}(823,\cdot)\) \(\chi_{8470}(863,\cdot)\) \(\chi_{8470}(907,\cdot)\) \(\chi_{8470}(933,\cdot)\) \(\chi_{8470}(1017,\cdot)\) \(\chi_{8470}(1087,\cdot)\) \(\chi_{8470}(1103,\cdot)\) \(\chi_{8470}(1257,\cdot)\) \(\chi_{8470}(1313,\cdot)\) \(\chi_{8470}(1367,\cdot)\) \(\chi_{8470}(1423,\cdot)\) \(\chi_{8470}(1467,\cdot)\) \(\chi_{8470}(1523,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{660})$ |
Fixed field: | Number field defined by a degree 660 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((-i,e\left(\frac{2}{3}\right),e\left(\frac{53}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{127}{220}\right)\) | \(e\left(\frac{419}{660}\right)\) | \(e\left(\frac{269}{330}\right)\) | \(e\left(\frac{5}{132}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{89}{165}\right)\) | \(e\left(\frac{367}{660}\right)\) |