Basic properties
Modulus: | \(4003\) | |
Conductor: | \(4003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2001\) | 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 4003.o
\(\chi_{4003}(4,\cdot)\) \(\chi_{4003}(7,\cdot)\) \(\chi_{4003}(9,\cdot)\) \(\chi_{4003}(16,\cdot)\) \(\chi_{4003}(19,\cdot)\) \(\chi_{4003}(24,\cdot)\) \(\chi_{4003}(25,\cdot)\) \(\chi_{4003}(29,\cdot)\) \(\chi_{4003}(37,\cdot)\) \(\chi_{4003}(40,\cdot)\) \(\chi_{4003}(42,\cdot)\) \(\chi_{4003}(44,\cdot)\) \(\chi_{4003}(46,\cdot)\) \(\chi_{4003}(49,\cdot)\) \(\chi_{4003}(52,\cdot)\) \(\chi_{4003}(53,\cdot)\) \(\chi_{4003}(54,\cdot)\) \(\chi_{4003}(59,\cdot)\) \(\chi_{4003}(60,\cdot)\) \(\chi_{4003}(62,\cdot)\) \(\chi_{4003}(63,\cdot)\) \(\chi_{4003}(67,\cdot)\) \(\chi_{4003}(68,\cdot)\) \(\chi_{4003}(77,\cdot)\) \(\chi_{4003}(79,\cdot)\) \(\chi_{4003}(81,\cdot)\) \(\chi_{4003}(82,\cdot)\) \(\chi_{4003}(83,\cdot)\) \(\chi_{4003}(89,\cdot)\) \(\chi_{4003}(91,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{2001})$ |
Fixed field: | Number field defined by a degree 2001 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{275}{2001}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4003 }(42, a) \) | \(1\) | \(1\) | \(e\left(\frac{275}{2001}\right)\) | \(e\left(\frac{343}{2001}\right)\) | \(e\left(\frac{550}{2001}\right)\) | \(e\left(\frac{323}{2001}\right)\) | \(e\left(\frac{206}{667}\right)\) | \(e\left(\frac{557}{2001}\right)\) | \(e\left(\frac{275}{667}\right)\) | \(e\left(\frac{686}{2001}\right)\) | \(e\left(\frac{26}{87}\right)\) | \(e\left(\frac{473}{667}\right)\) |