Basic properties
Modulus: | \(4024\) | |
Conductor: | \(4024\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(502\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.o
\(\chi_{4024}(13,\cdot)\) \(\chi_{4024}(21,\cdot)\) \(\chi_{4024}(61,\cdot)\) \(\chi_{4024}(69,\cdot)\) \(\chi_{4024}(77,\cdot)\) \(\chi_{4024}(85,\cdot)\) \(\chi_{4024}(117,\cdot)\) \(\chi_{4024}(141,\cdot)\) \(\chi_{4024}(173,\cdot)\) \(\chi_{4024}(189,\cdot)\) \(\chi_{4024}(197,\cdot)\) \(\chi_{4024}(205,\cdot)\) \(\chi_{4024}(229,\cdot)\) \(\chi_{4024}(237,\cdot)\) \(\chi_{4024}(253,\cdot)\) \(\chi_{4024}(285,\cdot)\) \(\chi_{4024}(293,\cdot)\) \(\chi_{4024}(301,\cdot)\) \(\chi_{4024}(317,\cdot)\) \(\chi_{4024}(325,\cdot)\) \(\chi_{4024}(373,\cdot)\) \(\chi_{4024}(389,\cdot)\) \(\chi_{4024}(397,\cdot)\) \(\chi_{4024}(413,\cdot)\) \(\chi_{4024}(421,\cdot)\) \(\chi_{4024}(429,\cdot)\) \(\chi_{4024}(445,\cdot)\) \(\chi_{4024}(469,\cdot)\) \(\chi_{4024}(493,\cdot)\) \(\chi_{4024}(509,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{251})$ |
Fixed field: | Number field defined by a degree 502 polynomial (not computed) |
Values on generators
\((1007,2013,2017)\) → \((1,-1,e\left(\frac{83}{251}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 4024 }(1149, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{502}\right)\) | \(e\left(\frac{417}{502}\right)\) | \(e\left(\frac{110}{251}\right)\) | \(e\left(\frac{43}{251}\right)\) | \(e\left(\frac{195}{502}\right)\) | \(e\left(\frac{253}{502}\right)\) | \(e\left(\frac{230}{251}\right)\) | \(e\left(\frac{182}{251}\right)\) | \(e\left(\frac{437}{502}\right)\) | \(e\left(\frac{263}{502}\right)\) |