Basic properties
Modulus: | \(983\) | |
Conductor: | \(983\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(491\) | 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 983.c
\(\chi_{983}(2,\cdot)\) \(\chi_{983}(3,\cdot)\) \(\chi_{983}(4,\cdot)\) \(\chi_{983}(6,\cdot)\) \(\chi_{983}(7,\cdot)\) \(\chi_{983}(8,\cdot)\) \(\chi_{983}(9,\cdot)\) \(\chi_{983}(12,\cdot)\) \(\chi_{983}(14,\cdot)\) \(\chi_{983}(16,\cdot)\) \(\chi_{983}(18,\cdot)\) \(\chi_{983}(19,\cdot)\) \(\chi_{983}(21,\cdot)\) \(\chi_{983}(23,\cdot)\) \(\chi_{983}(24,\cdot)\) \(\chi_{983}(25,\cdot)\) \(\chi_{983}(27,\cdot)\) \(\chi_{983}(28,\cdot)\) \(\chi_{983}(31,\cdot)\) \(\chi_{983}(32,\cdot)\) \(\chi_{983}(36,\cdot)\) \(\chi_{983}(37,\cdot)\) \(\chi_{983}(38,\cdot)\) \(\chi_{983}(41,\cdot)\) \(\chi_{983}(42,\cdot)\) \(\chi_{983}(43,\cdot)\) \(\chi_{983}(46,\cdot)\) \(\chi_{983}(47,\cdot)\) \(\chi_{983}(48,\cdot)\) \(\chi_{983}(49,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{491})$ |
Fixed field: | Number field defined by a degree 491 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{88}{491}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 983 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{392}{491}\right)\) | \(e\left(\frac{305}{491}\right)\) | \(e\left(\frac{293}{491}\right)\) | \(e\left(\frac{88}{491}\right)\) | \(e\left(\frac{206}{491}\right)\) | \(e\left(\frac{453}{491}\right)\) | \(e\left(\frac{194}{491}\right)\) | \(e\left(\frac{119}{491}\right)\) | \(e\left(\frac{480}{491}\right)\) | \(e\left(\frac{345}{491}\right)\) |