Basic properties
Modulus: | \(4031\) | |
Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(322\) | 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.bl
\(\chi_{4031}(6,\cdot)\) \(\chi_{4031}(34,\cdot)\) \(\chi_{4031}(63,\cdot)\) \(\chi_{4031}(64,\cdot)\) \(\chi_{4031}(80,\cdot)\) \(\chi_{4031}(91,\cdot)\) \(\chi_{4031}(100,\cdot)\) \(\chi_{4031}(125,\cdot)\) \(\chi_{4031}(129,\cdot)\) \(\chi_{4031}(183,\cdot)\) \(\chi_{4031}(196,\cdot)\) \(\chi_{4031}(216,\cdot)\) \(\chi_{4031}(245,\cdot)\) \(\chi_{4031}(270,\cdot)\) \(\chi_{4031}(312,\cdot)\) \(\chi_{4031}(323,\cdot)\) \(\chi_{4031}(341,\cdot)\) \(\chi_{4031}(357,\cdot)\) \(\chi_{4031}(390,\cdot)\) \(\chi_{4031}(469,\cdot)\) \(\chi_{4031}(497,\cdot)\) \(\chi_{4031}(613,\cdot)\) \(\chi_{4031}(647,\cdot)\) \(\chi_{4031}(672,\cdot)\) \(\chi_{4031}(701,\cdot)\) \(\chi_{4031}(729,\cdot)\) \(\chi_{4031}(731,\cdot)\) \(\chi_{4031}(747,\cdot)\) \(\chi_{4031}(758,\cdot)\) \(\chi_{4031}(759,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{161})$ |
Fixed field: | Number field defined by a degree 322 polynomial (not computed) |
Values on generators
\((3337,697)\) → \((e\left(\frac{13}{14}\right),e\left(\frac{17}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4031 }(196, a) \) | \(1\) | \(1\) | \(e\left(\frac{215}{322}\right)\) | \(e\left(\frac{305}{322}\right)\) | \(e\left(\frac{54}{161}\right)\) | \(e\left(\frac{160}{161}\right)\) | \(e\left(\frac{99}{161}\right)\) | \(e\left(\frac{16}{161}\right)\) | \(e\left(\frac{1}{322}\right)\) | \(e\left(\frac{144}{161}\right)\) | \(e\left(\frac{213}{322}\right)\) | \(e\left(\frac{125}{322}\right)\) |