Basic properties
Modulus: | \(8993\) | |
Conductor: | \(8993\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(46\) | 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 8993.t
\(\chi_{8993}(254,\cdot)\) \(\chi_{8993}(645,\cdot)\) \(\chi_{8993}(1036,\cdot)\) \(\chi_{8993}(1427,\cdot)\) \(\chi_{8993}(1818,\cdot)\) \(\chi_{8993}(2209,\cdot)\) \(\chi_{8993}(2600,\cdot)\) \(\chi_{8993}(2991,\cdot)\) \(\chi_{8993}(3382,\cdot)\) \(\chi_{8993}(3773,\cdot)\) \(\chi_{8993}(4164,\cdot)\) \(\chi_{8993}(4555,\cdot)\) \(\chi_{8993}(4946,\cdot)\) \(\chi_{8993}(5337,\cdot)\) \(\chi_{8993}(5728,\cdot)\) \(\chi_{8993}(6119,\cdot)\) \(\chi_{8993}(6510,\cdot)\) \(\chi_{8993}(6901,\cdot)\) \(\chi_{8993}(7292,\cdot)\) \(\chi_{8993}(7683,\cdot)\) \(\chi_{8993}(8074,\cdot)\) \(\chi_{8993}(8856,\cdot)\)
Related number fields
Field of values: | \(\Q(\zeta_{23})\) |
Fixed field: | Number field defined by a degree 46 polynomial |
Values on generators
\((530,7940)\) → \((-1,e\left(\frac{9}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8993 }(254, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{9}{46}\right)\) |