Basic properties
Modulus: | \(4031\) | |
Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(92\) | 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.bd
\(\chi_{4031}(75,\cdot)\) \(\chi_{4031}(133,\cdot)\) \(\chi_{4031}(162,\cdot)\) \(\chi_{4031}(215,\cdot)\) \(\chi_{4031}(244,\cdot)\) \(\chi_{4031}(360,\cdot)\) \(\chi_{4031}(365,\cdot)\) \(\chi_{4031}(476,\cdot)\) \(\chi_{4031}(650,\cdot)\) \(\chi_{4031}(771,\cdot)\) \(\chi_{4031}(800,\cdot)\) \(\chi_{4031}(882,\cdot)\) \(\chi_{4031}(916,\cdot)\) \(\chi_{4031}(1032,\cdot)\) \(\chi_{4031}(1172,\cdot)\) \(\chi_{4031}(1206,\cdot)\) \(\chi_{4031}(1259,\cdot)\) \(\chi_{4031}(1346,\cdot)\) \(\chi_{4031}(1404,\cdot)\) \(\chi_{4031}(1438,\cdot)\) \(\chi_{4031}(1728,\cdot)\) \(\chi_{4031}(1752,\cdot)\) \(\chi_{4031}(1815,\cdot)\) \(\chi_{4031}(1902,\cdot)\) \(\chi_{4031}(1960,\cdot)\) \(\chi_{4031}(2308,\cdot)\) \(\chi_{4031}(2390,\cdot)\) \(\chi_{4031}(2535,\cdot)\) \(\chi_{4031}(2564,\cdot)\) \(\chi_{4031}(2651,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{92})$ |
Fixed field: | Number field defined by a degree 92 polynomial |
Values on generators
\((3337,697)\) → \((-i,e\left(\frac{25}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4031 }(75, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{92}\right)\) | \(e\left(\frac{3}{92}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{81}{92}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{49}{92}\right)\) | \(e\left(\frac{5}{92}\right)\) |