Basic properties
Modulus: | \(4024\) | |
Conductor: | \(503\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(502\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{503}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4024.k
\(\chi_{4024}(17,\cdot)\) \(\chi_{4024}(41,\cdot)\) \(\chi_{4024}(57,\cdot)\) \(\chi_{4024}(65,\cdot)\) \(\chi_{4024}(89,\cdot)\) \(\chi_{4024}(105,\cdot)\) \(\chi_{4024}(137,\cdot)\) \(\chi_{4024}(153,\cdot)\) \(\chi_{4024}(193,\cdot)\) \(\chi_{4024}(209,\cdot)\) \(\chi_{4024}(217,\cdot)\) \(\chi_{4024}(241,\cdot)\) \(\chi_{4024}(305,\cdot)\) \(\chi_{4024}(313,\cdot)\) \(\chi_{4024}(321,\cdot)\) \(\chi_{4024}(337,\cdot)\) \(\chi_{4024}(345,\cdot)\) \(\chi_{4024}(353,\cdot)\) \(\chi_{4024}(369,\cdot)\) \(\chi_{4024}(377,\cdot)\) \(\chi_{4024}(385,\cdot)\) \(\chi_{4024}(409,\cdot)\) \(\chi_{4024}(417,\cdot)\) \(\chi_{4024}(425,\cdot)\) \(\chi_{4024}(449,\cdot)\) \(\chi_{4024}(457,\cdot)\) \(\chi_{4024}(481,\cdot)\) \(\chi_{4024}(489,\cdot)\) \(\chi_{4024}(497,\cdot)\) \(\chi_{4024}(513,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{251})$ |
Fixed field: | Number field defined by a degree 502 polynomial (not computed) |
Values on generators
\((1007,2013,2017)\) → \((1,1,e\left(\frac{229}{502}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 4024 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{251}\right)\) | \(e\left(\frac{229}{502}\right)\) | \(e\left(\frac{58}{251}\right)\) | \(e\left(\frac{82}{251}\right)\) | \(e\left(\frac{40}{251}\right)\) | \(e\left(\frac{142}{251}\right)\) | \(e\left(\frac{311}{502}\right)\) | \(e\left(\frac{233}{502}\right)\) | \(e\left(\frac{57}{502}\right)\) | \(e\left(\frac{99}{251}\right)\) |