Basic properties
Modulus: | \(6011\) | |
Conductor: | \(6011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(6010\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6011.h
\(\chi_{6011}(2,\cdot)\) \(\chi_{6011}(6,\cdot)\) \(\chi_{6011}(8,\cdot)\) \(\chi_{6011}(10,\cdot)\) \(\chi_{6011}(11,\cdot)\) \(\chi_{6011}(13,\cdot)\) \(\chi_{6011}(14,\cdot)\) \(\chi_{6011}(17,\cdot)\) \(\chi_{6011}(18,\cdot)\) \(\chi_{6011}(23,\cdot)\) \(\chi_{6011}(24,\cdot)\) \(\chi_{6011}(29,\cdot)\) \(\chi_{6011}(30,\cdot)\) \(\chi_{6011}(31,\cdot)\) \(\chi_{6011}(33,\cdot)\) \(\chi_{6011}(37,\cdot)\) \(\chi_{6011}(39,\cdot)\) \(\chi_{6011}(40,\cdot)\) \(\chi_{6011}(42,\cdot)\) \(\chi_{6011}(47,\cdot)\) \(\chi_{6011}(50,\cdot)\) \(\chi_{6011}(51,\cdot)\) \(\chi_{6011}(53,\cdot)\) \(\chi_{6011}(54,\cdot)\) \(\chi_{6011}(55,\cdot)\) \(\chi_{6011}(56,\cdot)\) \(\chi_{6011}(65,\cdot)\) \(\chi_{6011}(68,\cdot)\) \(\chi_{6011}(69,\cdot)\) \(\chi_{6011}(72,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{3005})$ |
Fixed field: | Number field defined by a degree 6010 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{849}{6010}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6011 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{849}{6010}\right)\) | \(e\left(\frac{272}{601}\right)\) | \(e\left(\frac{849}{3005}\right)\) | \(e\left(\frac{2381}{3005}\right)\) | \(e\left(\frac{3569}{6010}\right)\) | \(e\left(\frac{2227}{3005}\right)\) | \(e\left(\frac{2547}{6010}\right)\) | \(e\left(\frac{544}{601}\right)\) | \(e\left(\frac{5611}{6010}\right)\) | \(e\left(\frac{5377}{6010}\right)\) |