Basic properties
Modulus: | \(4022\) | |
Conductor: | \(2011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2010\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2011}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4022.p
\(\chi_{4022}(3,\cdot)\) \(\chi_{4022}(7,\cdot)\) \(\chi_{4022}(11,\cdot)\) \(\chi_{4022}(17,\cdot)\) \(\chi_{4022}(19,\cdot)\) \(\chi_{4022}(29,\cdot)\) \(\chi_{4022}(35,\cdot)\) \(\chi_{4022}(39,\cdot)\) \(\chi_{4022}(61,\cdot)\) \(\chi_{4022}(69,\cdot)\) \(\chi_{4022}(73,\cdot)\) \(\chi_{4022}(79,\cdot)\) \(\chi_{4022}(93,\cdot)\) \(\chi_{4022}(99,\cdot)\) \(\chi_{4022}(107,\cdot)\) \(\chi_{4022}(123,\cdot)\) \(\chi_{4022}(129,\cdot)\) \(\chi_{4022}(131,\cdot)\) \(\chi_{4022}(135,\cdot)\) \(\chi_{4022}(145,\cdot)\) \(\chi_{4022}(153,\cdot)\) \(\chi_{4022}(161,\cdot)\) \(\chi_{4022}(167,\cdot)\) \(\chi_{4022}(173,\cdot)\) \(\chi_{4022}(179,\cdot)\) \(\chi_{4022}(185,\cdot)\) \(\chi_{4022}(195,\cdot)\) \(\chi_{4022}(223,\cdot)\) \(\chi_{4022}(227,\cdot)\) \(\chi_{4022}(229,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1005})$ |
Fixed field: | Number field defined by a degree 2010 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1}{2010}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 4022 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{2010}\right)\) | \(e\left(\frac{512}{1005}\right)\) | \(e\left(\frac{1807}{2010}\right)\) | \(e\left(\frac{1}{1005}\right)\) | \(e\left(\frac{1037}{2010}\right)\) | \(e\left(\frac{323}{335}\right)\) | \(e\left(\frac{205}{402}\right)\) | \(e\left(\frac{347}{2010}\right)\) | \(e\left(\frac{1163}{2010}\right)\) | \(e\left(\frac{904}{1005}\right)\) |