Basic properties
Modulus: | \(4031\) | |
Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(161\) | 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.bi
\(\chi_{4031}(36,\cdot)\) \(\chi_{4031}(45,\cdot)\) \(\chi_{4031}(52,\cdot)\) \(\chi_{4031}(65,\cdot)\) \(\chi_{4031}(112,\cdot)\) \(\chi_{4031}(194,\cdot)\) \(\chi_{4031}(219,\cdot)\) \(\chi_{4031}(239,\cdot)\) \(\chi_{4031}(255,\cdot)\) \(\chi_{4031}(268,\cdot)\) \(\chi_{4031}(284,\cdot)\) \(\chi_{4031}(314,\cdot)\) \(\chi_{4031}(335,\cdot)\) \(\chi_{4031}(342,\cdot)\) \(\chi_{4031}(343,\cdot)\) \(\chi_{4031}(355,\cdot)\) \(\chi_{4031}(384,\cdot)\) \(\chi_{4031}(451,\cdot)\) \(\chi_{4031}(480,\cdot)\) \(\chi_{4031}(517,\cdot)\) \(\chi_{4031}(529,\cdot)\) \(\chi_{4031}(542,\cdot)\) \(\chi_{4031}(546,\cdot)\) \(\chi_{4031}(600,\cdot)\) \(\chi_{4031}(633,\cdot)\) \(\chi_{4031}(662,\cdot)\) \(\chi_{4031}(687,\cdot)\) \(\chi_{4031}(750,\cdot)\) \(\chi_{4031}(774,\cdot)\) \(\chi_{4031}(807,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{161})$ |
Fixed field: | Number field defined by a degree 161 polynomial (not computed) |
Values on generators
\((3337,697)\) → \((e\left(\frac{3}{7}\right),e\left(\frac{9}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4031 }(529, a) \) | \(1\) | \(1\) | \(e\left(\frac{132}{161}\right)\) | \(e\left(\frac{30}{161}\right)\) | \(e\left(\frac{103}{161}\right)\) | \(e\left(\frac{13}{161}\right)\) | \(e\left(\frac{1}{161}\right)\) | \(e\left(\frac{114}{161}\right)\) | \(e\left(\frac{74}{161}\right)\) | \(e\left(\frac{60}{161}\right)\) | \(e\left(\frac{145}{161}\right)\) | \(e\left(\frac{73}{161}\right)\) |