Basic properties
Modulus: | \(6011\) | |
Conductor: | \(6011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(3005\) | 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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 6011.g
\(\chi_{6011}(4,\cdot)\) \(\chi_{6011}(5,\cdot)\) \(\chi_{6011}(7,\cdot)\) \(\chi_{6011}(12,\cdot)\) \(\chi_{6011}(15,\cdot)\) \(\chi_{6011}(16,\cdot)\) \(\chi_{6011}(21,\cdot)\) \(\chi_{6011}(22,\cdot)\) \(\chi_{6011}(25,\cdot)\) \(\chi_{6011}(26,\cdot)\) \(\chi_{6011}(28,\cdot)\) \(\chi_{6011}(34,\cdot)\) \(\chi_{6011}(35,\cdot)\) \(\chi_{6011}(36,\cdot)\) \(\chi_{6011}(38,\cdot)\) \(\chi_{6011}(41,\cdot)\) \(\chi_{6011}(43,\cdot)\) \(\chi_{6011}(45,\cdot)\) \(\chi_{6011}(48,\cdot)\) \(\chi_{6011}(49,\cdot)\) \(\chi_{6011}(59,\cdot)\) \(\chi_{6011}(62,\cdot)\) \(\chi_{6011}(63,\cdot)\) \(\chi_{6011}(64,\cdot)\) \(\chi_{6011}(66,\cdot)\) \(\chi_{6011}(67,\cdot)\) \(\chi_{6011}(71,\cdot)\) \(\chi_{6011}(73,\cdot)\) \(\chi_{6011}(74,\cdot)\) \(\chi_{6011}(75,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{3005})$ |
Fixed field: | Number field defined by a degree 3005 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1492}{3005}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6011 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{1492}{3005}\right)\) | \(e\left(\frac{229}{601}\right)\) | \(e\left(\frac{2984}{3005}\right)\) | \(e\left(\frac{111}{3005}\right)\) | \(e\left(\frac{2637}{3005}\right)\) | \(e\left(\frac{1612}{3005}\right)\) | \(e\left(\frac{1471}{3005}\right)\) | \(e\left(\frac{458}{601}\right)\) | \(e\left(\frac{1603}{3005}\right)\) | \(e\left(\frac{1436}{3005}\right)\) |