Basic properties
Modulus: | \(8470\) | |
Conductor: | \(4235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4235}(1167,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.db
\(\chi_{8470}(353,\cdot)\) \(\chi_{8470}(397,\cdot)\) \(\chi_{8470}(507,\cdot)\) \(\chi_{8470}(1013,\cdot)\) \(\chi_{8470}(1123,\cdot)\) \(\chi_{8470}(1167,\cdot)\) \(\chi_{8470}(1277,\cdot)\) \(\chi_{8470}(1783,\cdot)\) \(\chi_{8470}(1893,\cdot)\) \(\chi_{8470}(2047,\cdot)\) \(\chi_{8470}(2553,\cdot)\) \(\chi_{8470}(2707,\cdot)\) \(\chi_{8470}(2817,\cdot)\) \(\chi_{8470}(3323,\cdot)\) \(\chi_{8470}(3433,\cdot)\) \(\chi_{8470}(3477,\cdot)\) \(\chi_{8470}(3587,\cdot)\) \(\chi_{8470}(4093,\cdot)\) \(\chi_{8470}(4203,\cdot)\) \(\chi_{8470}(4247,\cdot)\) \(\chi_{8470}(4863,\cdot)\) \(\chi_{8470}(4973,\cdot)\) \(\chi_{8470}(5017,\cdot)\) \(\chi_{8470}(5127,\cdot)\) \(\chi_{8470}(5633,\cdot)\) \(\chi_{8470}(5743,\cdot)\) \(\chi_{8470}(5787,\cdot)\) \(\chi_{8470}(5897,\cdot)\) \(\chi_{8470}(6403,\cdot)\) \(\chi_{8470}(6513,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((i,e\left(\frac{5}{6}\right),e\left(\frac{8}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(1167, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{43}{132}\right)\) | \(-i\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{61}{132}\right)\) |