Basic properties
Modulus: | \(6042\) | |
Conductor: | \(3021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(468\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3021}(503,\cdot)\) | 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)
|
Galois orbit 6042.ct
\(\chi_{6042}(5,\cdot)\) \(\chi_{6042}(35,\cdot)\) \(\chi_{6042}(101,\cdot)\) \(\chi_{6042}(137,\cdot)\) \(\chi_{6042}(161,\cdot)\) \(\chi_{6042}(215,\cdot)\) \(\chi_{6042}(233,\cdot)\) \(\chi_{6042}(245,\cdot)\) \(\chi_{6042}(251,\cdot)\) \(\chi_{6042}(263,\cdot)\) \(\chi_{6042}(359,\cdot)\) \(\chi_{6042}(389,\cdot)\) \(\chi_{6042}(443,\cdot)\) \(\chi_{6042}(479,\cdot)\) \(\chi_{6042}(491,\cdot)\) \(\chi_{6042}(503,\cdot)\) \(\chi_{6042}(557,\cdot)\) \(\chi_{6042}(575,\cdot)\) \(\chi_{6042}(605,\cdot)\) \(\chi_{6042}(617,\cdot)\) \(\chi_{6042}(671,\cdot)\) \(\chi_{6042}(701,\cdot)\) \(\chi_{6042}(707,\cdot)\) \(\chi_{6042}(803,\cdot)\) \(\chi_{6042}(815,\cdot)\) \(\chi_{6042}(821,\cdot)\) \(\chi_{6042}(845,\cdot)\) \(\chi_{6042}(899,\cdot)\) \(\chi_{6042}(935,\cdot)\) \(\chi_{6042}(959,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{468})$ |
Fixed field: | Number field defined by a degree 468 polynomial (not computed) |
Values on generators
\((2015,4771,2281)\) → \((-1,e\left(\frac{4}{9}\right),e\left(\frac{25}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6042 }(503, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{468}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{89}{117}\right)\) | \(e\left(\frac{88}{117}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{97}{234}\right)\) | \(e\left(\frac{20}{117}\right)\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{283}{468}\right)\) |