Basic properties
Modulus: | \(4024\) | |
Conductor: | \(4024\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(502\) | 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 4024.j
\(\chi_{4024}(19,\cdot)\) \(\chi_{4024}(35,\cdot)\) \(\chi_{4024}(51,\cdot)\) \(\chi_{4024}(107,\cdot)\) \(\chi_{4024}(115,\cdot)\) \(\chi_{4024}(123,\cdot)\) \(\chi_{4024}(139,\cdot)\) \(\chi_{4024}(163,\cdot)\) \(\chi_{4024}(171,\cdot)\) \(\chi_{4024}(179,\cdot)\) \(\chi_{4024}(187,\cdot)\) \(\chi_{4024}(195,\cdot)\) \(\chi_{4024}(203,\cdot)\) \(\chi_{4024}(211,\cdot)\) \(\chi_{4024}(227,\cdot)\) \(\chi_{4024}(235,\cdot)\) \(\chi_{4024}(251,\cdot)\) \(\chi_{4024}(259,\cdot)\) \(\chi_{4024}(267,\cdot)\) \(\chi_{4024}(307,\cdot)\) \(\chi_{4024}(315,\cdot)\) \(\chi_{4024}(331,\cdot)\) \(\chi_{4024}(347,\cdot)\) \(\chi_{4024}(371,\cdot)\) \(\chi_{4024}(395,\cdot)\) \(\chi_{4024}(403,\cdot)\) \(\chi_{4024}(411,\cdot)\) \(\chi_{4024}(419,\cdot)\) \(\chi_{4024}(451,\cdot)\) \(\chi_{4024}(459,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{251})$ |
Fixed field: | Number field defined by a degree 502 polynomial (not computed) |
Values on generators
\((1007,2013,2017)\) → \((-1,-1,e\left(\frac{3}{502}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 4024 }(1131, a) \) | \(1\) | \(1\) | \(e\left(\frac{234}{251}\right)\) | \(e\left(\frac{127}{251}\right)\) | \(e\left(\frac{7}{502}\right)\) | \(e\left(\frac{217}{251}\right)\) | \(e\left(\frac{63}{251}\right)\) | \(e\left(\frac{121}{502}\right)\) | \(e\left(\frac{110}{251}\right)\) | \(e\left(\frac{185}{502}\right)\) | \(e\left(\frac{209}{502}\right)\) | \(e\left(\frac{475}{502}\right)\) |