Basic properties
Modulus: | \(503\) | |
Conductor: | \(503\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(251\) | 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 503.c
\(\chi_{503}(2,\cdot)\) \(\chi_{503}(3,\cdot)\) \(\chi_{503}(4,\cdot)\) \(\chi_{503}(6,\cdot)\) \(\chi_{503}(7,\cdot)\) \(\chi_{503}(8,\cdot)\) \(\chi_{503}(9,\cdot)\) \(\chi_{503}(11,\cdot)\) \(\chi_{503}(12,\cdot)\) \(\chi_{503}(13,\cdot)\) \(\chi_{503}(14,\cdot)\) \(\chi_{503}(16,\cdot)\) \(\chi_{503}(18,\cdot)\) \(\chi_{503}(21,\cdot)\) \(\chi_{503}(22,\cdot)\) \(\chi_{503}(23,\cdot)\) \(\chi_{503}(24,\cdot)\) \(\chi_{503}(25,\cdot)\) \(\chi_{503}(26,\cdot)\) \(\chi_{503}(27,\cdot)\) \(\chi_{503}(28,\cdot)\) \(\chi_{503}(32,\cdot)\) \(\chi_{503}(33,\cdot)\) \(\chi_{503}(36,\cdot)\) \(\chi_{503}(39,\cdot)\) \(\chi_{503}(42,\cdot)\) \(\chi_{503}(43,\cdot)\) \(\chi_{503}(44,\cdot)\) \(\chi_{503}(46,\cdot)\) \(\chi_{503}(47,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{251})$ |
Fixed field: | Number field defined by a degree 251 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{122}{251}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 503 }(22, a) \) | \(1\) | \(1\) | \(e\left(\frac{46}{251}\right)\) | \(e\left(\frac{207}{251}\right)\) | \(e\left(\frac{92}{251}\right)\) | \(e\left(\frac{122}{251}\right)\) | \(e\left(\frac{2}{251}\right)\) | \(e\left(\frac{201}{251}\right)\) | \(e\left(\frac{138}{251}\right)\) | \(e\left(\frac{163}{251}\right)\) | \(e\left(\frac{168}{251}\right)\) | \(e\left(\frac{104}{251}\right)\) |