Basic properties
Modulus: | \(4024\) | |
Conductor: | \(2012\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(502\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2012}(119,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4024.p
\(\chi_{4024}(15,\cdot)\) \(\chi_{4024}(31,\cdot)\) \(\chi_{4024}(55,\cdot)\) \(\chi_{4024}(71,\cdot)\) \(\chi_{4024}(87,\cdot)\) \(\chi_{4024}(103,\cdot)\) \(\chi_{4024}(111,\cdot)\) \(\chi_{4024}(119,\cdot)\) \(\chi_{4024}(127,\cdot)\) \(\chi_{4024}(135,\cdot)\) \(\chi_{4024}(151,\cdot)\) \(\chi_{4024}(159,\cdot)\) \(\chi_{4024}(167,\cdot)\) \(\chi_{4024}(191,\cdot)\) \(\chi_{4024}(215,\cdot)\) \(\chi_{4024}(239,\cdot)\) \(\chi_{4024}(247,\cdot)\) \(\chi_{4024}(279,\cdot)\) \(\chi_{4024}(287,\cdot)\) \(\chi_{4024}(295,\cdot)\) \(\chi_{4024}(303,\cdot)\) \(\chi_{4024}(311,\cdot)\) \(\chi_{4024}(319,\cdot)\) \(\chi_{4024}(327,\cdot)\) \(\chi_{4024}(335,\cdot)\) \(\chi_{4024}(359,\cdot)\) \(\chi_{4024}(375,\cdot)\) \(\chi_{4024}(391,\cdot)\) \(\chi_{4024}(399,\cdot)\) \(\chi_{4024}(407,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{251})$ |
Fixed field: | Number field defined by a degree 502 polynomial (not computed) |
Values on generators
\((1007,2013,2017)\) → \((-1,1,e\left(\frac{315}{502}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 4024 }(119, a) \) | \(1\) | \(1\) | \(e\left(\frac{195}{502}\right)\) | \(e\left(\frac{315}{502}\right)\) | \(e\left(\frac{233}{502}\right)\) | \(e\left(\frac{195}{251}\right)\) | \(e\left(\frac{429}{502}\right)\) | \(e\left(\frac{203}{251}\right)\) | \(e\left(\frac{4}{251}\right)\) | \(e\left(\frac{349}{502}\right)\) | \(e\left(\frac{54}{251}\right)\) | \(e\left(\frac{214}{251}\right)\) |