Basic properties
Modulus: | \(4031\) | |
Conductor: | \(139\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(23\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{139}(100,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4031.r
\(\chi_{4031}(175,\cdot)\) \(\chi_{4031}(204,\cdot)\) \(\chi_{4031}(378,\cdot)\) \(\chi_{4031}(407,\cdot)\) \(\chi_{4031}(494,\cdot)\) \(\chi_{4031}(523,\cdot)\) \(\chi_{4031}(668,\cdot)\) \(\chi_{4031}(1306,\cdot)\) \(\chi_{4031}(1654,\cdot)\) \(\chi_{4031}(1712,\cdot)\) \(\chi_{4031}(1799,\cdot)\) \(\chi_{4031}(1886,\cdot)\) \(\chi_{4031}(2176,\cdot)\) \(\chi_{4031}(2408,\cdot)\) \(\chi_{4031}(2582,\cdot)\) \(\chi_{4031}(2698,\cdot)\) \(\chi_{4031}(2814,\cdot)\) \(\chi_{4031}(2843,\cdot)\) \(\chi_{4031}(3249,\cdot)\) \(\chi_{4031}(3452,\cdot)\) \(\chi_{4031}(3481,\cdot)\) \(\chi_{4031}(3539,\cdot)\)
Related number fields
Field of values: | \(\Q(\zeta_{23})\) |
Fixed field: | Number field defined by a degree 23 polynomial |
Values on generators
\((3337,697)\) → \((1,e\left(\frac{6}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4031 }(378, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) |