Basic properties
Modulus: | \(2593\) | |
Conductor: | \(2593\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2592\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2593.bd
\(\chi_{2593}(7,\cdot)\) \(\chi_{2593}(10,\cdot)\) \(\chi_{2593}(11,\cdot)\) \(\chi_{2593}(13,\cdot)\) \(\chi_{2593}(14,\cdot)\) \(\chi_{2593}(15,\cdot)\) \(\chi_{2593}(20,\cdot)\) \(\chi_{2593}(21,\cdot)\) \(\chi_{2593}(26,\cdot)\) \(\chi_{2593}(29,\cdot)\) \(\chi_{2593}(30,\cdot)\) \(\chi_{2593}(39,\cdot)\) \(\chi_{2593}(44,\cdot)\) \(\chi_{2593}(45,\cdot)\) \(\chi_{2593}(46,\cdot)\) \(\chi_{2593}(56,\cdot)\) \(\chi_{2593}(61,\cdot)\) \(\chi_{2593}(66,\cdot)\) \(\chi_{2593}(69,\cdot)\) \(\chi_{2593}(80,\cdot)\) \(\chi_{2593}(83,\cdot)\) \(\chi_{2593}(84,\cdot)\) \(\chi_{2593}(85,\cdot)\) \(\chi_{2593}(88,\cdot)\) \(\chi_{2593}(89,\cdot)\) \(\chi_{2593}(92,\cdot)\) \(\chi_{2593}(97,\cdot)\) \(\chi_{2593}(99,\cdot)\) \(\chi_{2593}(104,\cdot)\) \(\chi_{2593}(109,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{2592})$ |
Fixed field: | Number field defined by a degree 2592 polynomial (not computed) |
Values on generators
\(7\) → \(e\left(\frac{2581}{2592}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2593 }(44, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{81}\right)\) | \(e\left(\frac{361}{648}\right)\) | \(e\left(\frac{25}{81}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{137}{648}\right)\) | \(e\left(\frac{2581}{2592}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{37}{324}\right)\) | \(e\left(\frac{1453}{2592}\right)\) | \(e\left(\frac{1913}{2592}\right)\) |