Basic properties
Modulus: | \(6012\) | |
Conductor: | \(6012\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(498\) | 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 6012.ba
\(\chi_{6012}(11,\cdot)\) \(\chi_{6012}(47,\cdot)\) \(\chi_{6012}(191,\cdot)\) \(\chi_{6012}(203,\cdot)\) \(\chi_{6012}(239,\cdot)\) \(\chi_{6012}(263,\cdot)\) \(\chi_{6012}(275,\cdot)\) \(\chi_{6012}(299,\cdot)\) \(\chi_{6012}(311,\cdot)\) \(\chi_{6012}(383,\cdot)\) \(\chi_{6012}(419,\cdot)\) \(\chi_{6012}(455,\cdot)\) \(\chi_{6012}(491,\cdot)\) \(\chi_{6012}(515,\cdot)\) \(\chi_{6012}(551,\cdot)\) \(\chi_{6012}(563,\cdot)\) \(\chi_{6012}(599,\cdot)\) \(\chi_{6012}(623,\cdot)\) \(\chi_{6012}(671,\cdot)\) \(\chi_{6012}(695,\cdot)\) \(\chi_{6012}(731,\cdot)\) \(\chi_{6012}(743,\cdot)\) \(\chi_{6012}(767,\cdot)\) \(\chi_{6012}(815,\cdot)\) \(\chi_{6012}(839,\cdot)\) \(\chi_{6012}(851,\cdot)\) \(\chi_{6012}(911,\cdot)\) \(\chi_{6012}(923,\cdot)\) \(\chi_{6012}(947,\cdot)\) \(\chi_{6012}(959,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{249})$ |
Fixed field: | Number field defined by a degree 498 polynomial (not computed) |
Values on generators
\((3007,3341,4681)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{28}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 6012 }(455, a) \) | \(1\) | \(1\) | \(e\left(\frac{251}{498}\right)\) | \(e\left(\frac{319}{498}\right)\) | \(e\left(\frac{194}{249}\right)\) | \(e\left(\frac{103}{249}\right)\) | \(e\left(\frac{63}{166}\right)\) | \(e\left(\frac{11}{166}\right)\) | \(e\left(\frac{16}{249}\right)\) | \(e\left(\frac{2}{249}\right)\) | \(e\left(\frac{217}{498}\right)\) | \(e\left(\frac{263}{498}\right)\) |