Basic properties
Modulus: | \(4031\) | |
Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(46\) | 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 4031.z
\(\chi_{4031}(57,\cdot)\) \(\chi_{4031}(173,\cdot)\) \(\chi_{4031}(202,\cdot)\) \(\chi_{4031}(608,\cdot)\) \(\chi_{4031}(811,\cdot)\) \(\chi_{4031}(840,\cdot)\) \(\chi_{4031}(898,\cdot)\) \(\chi_{4031}(1565,\cdot)\) \(\chi_{4031}(1594,\cdot)\) \(\chi_{4031}(1768,\cdot)\) \(\chi_{4031}(1797,\cdot)\) \(\chi_{4031}(1884,\cdot)\) \(\chi_{4031}(1913,\cdot)\) \(\chi_{4031}(2058,\cdot)\) \(\chi_{4031}(2696,\cdot)\) \(\chi_{4031}(3044,\cdot)\) \(\chi_{4031}(3102,\cdot)\) \(\chi_{4031}(3189,\cdot)\) \(\chi_{4031}(3276,\cdot)\) \(\chi_{4031}(3566,\cdot)\) \(\chi_{4031}(3798,\cdot)\) \(\chi_{4031}(3972,\cdot)\)
Related number fields
Field of values: | \(\Q(\zeta_{23})\) |
Fixed field: | Number field defined by a degree 46 polynomial |
Values on generators
\((3337,697)\) → \((-1,e\left(\frac{7}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4031 }(840, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{29}{46}\right)\) |