Basic properties
Modulus: | \(6017\) | |
Conductor: | \(6017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2730\) | 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 6017.cl
\(\chi_{6017}(2,\cdot)\) \(\chi_{6017}(7,\cdot)\) \(\chi_{6017}(17,\cdot)\) \(\chi_{6017}(18,\cdot)\) \(\chi_{6017}(50,\cdot)\) \(\chi_{6017}(57,\cdot)\) \(\chi_{6017}(61,\cdot)\) \(\chi_{6017}(63,\cdot)\) \(\chi_{6017}(95,\cdot)\) \(\chi_{6017}(112,\cdot)\) \(\chi_{6017}(134,\cdot)\) \(\chi_{6017}(162,\cdot)\) \(\chi_{6017}(200,\cdot)\) \(\chi_{6017}(211,\cdot)\) \(\chi_{6017}(228,\cdot)\) \(\chi_{6017}(260,\cdot)\) \(\chi_{6017}(271,\cdot)\) \(\chi_{6017}(272,\cdot)\) \(\chi_{6017}(281,\cdot)\) \(\chi_{6017}(283,\cdot)\) \(\chi_{6017}(288,\cdot)\) \(\chi_{6017}(337,\cdot)\) \(\chi_{6017}(354,\cdot)\) \(\chi_{6017}(358,\cdot)\) \(\chi_{6017}(359,\cdot)\) \(\chi_{6017}(370,\cdot)\) \(\chi_{6017}(371,\cdot)\) \(\chi_{6017}(376,\cdot)\) \(\chi_{6017}(381,\cdot)\) \(\chi_{6017}(387,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1365})$ |
Fixed field: | Number field defined by a degree 2730 polynomial (not computed) |
Values on generators
\((3830,2190)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{155}{546}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 6017 }(272, a) \) | \(1\) | \(1\) | \(e\left(\frac{797}{1365}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{229}{1365}\right)\) | \(e\left(\frac{41}{2730}\right)\) | \(e\left(\frac{2101}{2730}\right)\) | \(e\left(\frac{464}{1365}\right)\) | \(e\left(\frac{342}{455}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{109}{182}\right)\) | \(e\left(\frac{193}{546}\right)\) |