Basic properties
Modulus: | \(4031\) | |
Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(138\) | 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.bf
\(\chi_{4031}(28,\cdot)\) \(\chi_{4031}(86,\cdot)\) \(\chi_{4031}(144,\cdot)\) \(\chi_{4031}(260,\cdot)\) \(\chi_{4031}(289,\cdot)\) \(\chi_{4031}(347,\cdot)\) \(\chi_{4031}(405,\cdot)\) \(\chi_{4031}(463,\cdot)\) \(\chi_{4031}(637,\cdot)\) \(\chi_{4031}(724,\cdot)\) \(\chi_{4031}(869,\cdot)\) \(\chi_{4031}(956,\cdot)\) \(\chi_{4031}(1014,\cdot)\) \(\chi_{4031}(1072,\cdot)\) \(\chi_{4031}(1159,\cdot)\) \(\chi_{4031}(1275,\cdot)\) \(\chi_{4031}(1420,\cdot)\) \(\chi_{4031}(1507,\cdot)\) \(\chi_{4031}(1536,\cdot)\) \(\chi_{4031}(1681,\cdot)\) \(\chi_{4031}(1739,\cdot)\) \(\chi_{4031}(1971,\cdot)\) \(\chi_{4031}(2000,\cdot)\) \(\chi_{4031}(2029,\cdot)\) \(\chi_{4031}(2116,\cdot)\) \(\chi_{4031}(2174,\cdot)\) \(\chi_{4031}(2203,\cdot)\) \(\chi_{4031}(2261,\cdot)\) \(\chi_{4031}(2290,\cdot)\) \(\chi_{4031}(2348,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{69})$ |
Fixed field: | Number field defined by a degree 138 polynomial (not computed) |
Values on generators
\((3337,697)\) → \((-1,e\left(\frac{25}{69}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4031 }(1536, a) \) | \(1\) | \(1\) | \(e\left(\frac{119}{138}\right)\) | \(e\left(\frac{49}{138}\right)\) | \(e\left(\frac{50}{69}\right)\) | \(e\left(\frac{11}{69}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{8}{69}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{49}{69}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{5}{138}\right)\) |