Basic properties
Modulus: | \(947\) | |
Conductor: | \(947\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(43\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 947.e
\(\chi_{947}(22,\cdot)\) \(\chi_{947}(30,\cdot)\) \(\chi_{947}(41,\cdot)\) \(\chi_{947}(49,\cdot)\) \(\chi_{947}(58,\cdot)\) \(\chi_{947}(115,\cdot)\) \(\chi_{947}(127,\cdot)\) \(\chi_{947}(131,\cdot)\) \(\chi_{947}(140,\cdot)\) \(\chi_{947}(142,\cdot)\) \(\chi_{947}(221,\cdot)\) \(\chi_{947}(231,\cdot)\) \(\chi_{947}(239,\cdot)\) \(\chi_{947}(277,\cdot)\) \(\chi_{947}(283,\cdot)\) \(\chi_{947}(301,\cdot)\) \(\chi_{947}(315,\cdot)\) \(\chi_{947}(329,\cdot)\) \(\chi_{947}(347,\cdot)\) \(\chi_{947}(400,\cdot)\) \(\chi_{947}(412,\cdot)\) \(\chi_{947}(472,\cdot)\) \(\chi_{947}(484,\cdot)\) \(\chi_{947}(507,\cdot)\) \(\chi_{947}(523,\cdot)\) \(\chi_{947}(538,\cdot)\) \(\chi_{947}(541,\cdot)\) \(\chi_{947}(544,\cdot)\) \(\chi_{947}(604,\cdot)\) \(\chi_{947}(609,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{43})$ |
Fixed field: | Number field defined by a degree 43 polynomial |
Values on generators
\(2\) → \(e\left(\frac{30}{43}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 947 }(131, a) \) | \(1\) | \(1\) | \(e\left(\frac{30}{43}\right)\) | \(e\left(\frac{29}{43}\right)\) | \(e\left(\frac{17}{43}\right)\) | \(e\left(\frac{38}{43}\right)\) | \(e\left(\frac{16}{43}\right)\) | \(e\left(\frac{34}{43}\right)\) | \(e\left(\frac{4}{43}\right)\) | \(e\left(\frac{15}{43}\right)\) | \(e\left(\frac{25}{43}\right)\) | \(e\left(\frac{8}{43}\right)\) |