Basic properties
Modulus: | \(4031\) | |
Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(276\) | 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.bk
\(\chi_{4031}(12,\cdot)\) \(\chi_{4031}(17,\cdot)\) \(\chi_{4031}(70,\cdot)\) \(\chi_{4031}(104,\cdot)\) \(\chi_{4031}(128,\cdot)\) \(\chi_{4031}(157,\cdot)\) \(\chi_{4031}(249,\cdot)\) \(\chi_{4031}(273,\cdot)\) \(\chi_{4031}(331,\cdot)\) \(\chi_{4031}(336,\cdot)\) \(\chi_{4031}(389,\cdot)\) \(\chi_{4031}(505,\cdot)\) \(\chi_{4031}(510,\cdot)\) \(\chi_{4031}(568,\cdot)\) \(\chi_{4031}(626,\cdot)\) \(\chi_{4031}(679,\cdot)\) \(\chi_{4031}(684,\cdot)\) \(\chi_{4031}(713,\cdot)\) \(\chi_{4031}(829,\cdot)\) \(\chi_{4031}(853,\cdot)\) \(\chi_{4031}(887,\cdot)\) \(\chi_{4031}(945,\cdot)\) \(\chi_{4031}(969,\cdot)\) \(\chi_{4031}(1061,\cdot)\) \(\chi_{4031}(1114,\cdot)\) \(\chi_{4031}(1235,\cdot)\) \(\chi_{4031}(1409,\cdot)\) \(\chi_{4031}(1462,\cdot)\) \(\chi_{4031}(1491,\cdot)\) \(\chi_{4031}(1520,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{276})$ |
Fixed field: | Number field defined by a degree 276 polynomial (not computed) |
Values on generators
\((3337,697)\) → \((-i,e\left(\frac{17}{138}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4031 }(829, a) \) | \(1\) | \(1\) | \(e\left(\frac{241}{276}\right)\) | \(e\left(\frac{221}{276}\right)\) | \(e\left(\frac{103}{138}\right)\) | \(e\left(\frac{13}{138}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{11}{69}\right)\) | \(e\left(\frac{57}{92}\right)\) | \(e\left(\frac{83}{138}\right)\) | \(e\left(\frac{89}{92}\right)\) | \(e\left(\frac{31}{276}\right)\) |