Basic properties
| Modulus: | \(947\) | |
| Conductor: | \(947\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(43\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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
\(2\) → \(e\left(\frac{26}{43}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 947 }(140, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{43}\right)\) | \(e\left(\frac{28}{43}\right)\) | \(e\left(\frac{9}{43}\right)\) | \(e\left(\frac{10}{43}\right)\) | \(e\left(\frac{11}{43}\right)\) | \(e\left(\frac{18}{43}\right)\) | \(e\left(\frac{35}{43}\right)\) | \(e\left(\frac{13}{43}\right)\) | \(e\left(\frac{36}{43}\right)\) | \(e\left(\frac{27}{43}\right)\) |