Basic properties
Modulus: | \(4031\) | |
Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | 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.bc
\(\chi_{4031}(43,\cdot)\) \(\chi_{4031}(97,\cdot)\) \(\chi_{4031}(182,\cdot)\) \(\chi_{4031}(321,\cdot)\) \(\chi_{4031}(375,\cdot)\) \(\chi_{4031}(514,\cdot)\) \(\chi_{4031}(599,\cdot)\) \(\chi_{4031}(653,\cdot)\) \(\chi_{4031}(931,\cdot)\) \(\chi_{4031}(1070,\cdot)\) \(\chi_{4031}(1294,\cdot)\) \(\chi_{4031}(1348,\cdot)\) \(\chi_{4031}(1487,\cdot)\) \(\chi_{4031}(1626,\cdot)\) \(\chi_{4031}(1904,\cdot)\) \(\chi_{4031}(2128,\cdot)\) \(\chi_{4031}(2599,\cdot)\) \(\chi_{4031}(2823,\cdot)\) \(\chi_{4031}(3101,\cdot)\) \(\chi_{4031}(3240,\cdot)\) \(\chi_{4031}(3379,\cdot)\) \(\chi_{4031}(3433,\cdot)\) \(\chi_{4031}(3657,\cdot)\) \(\chi_{4031}(3796,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((3337,697)\) → \((e\left(\frac{5}{28}\right),e\left(\frac{5}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4031 }(3657, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{67}{84}\right)\) |