Basic properties
Modulus: | \(6019\) | |
Conductor: | \(6019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | 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 6019.di
\(\chi_{6019}(6,\cdot)\) \(\chi_{6019}(427,\cdot)\) \(\chi_{6019}(553,\cdot)\) \(\chi_{6019}(747,\cdot)\) \(\chi_{6019}(1267,\cdot)\) \(\chi_{6019}(1623,\cdot)\) \(\chi_{6019}(1709,\cdot)\) \(\chi_{6019}(1757,\cdot)\) \(\chi_{6019}(1813,\cdot)\) \(\chi_{6019}(2000,\cdot)\) \(\chi_{6019}(2022,\cdot)\) \(\chi_{6019}(2087,\cdot)\) \(\chi_{6019}(2121,\cdot)\) \(\chi_{6019}(2221,\cdot)\) \(\chi_{6019}(2238,\cdot)\) \(\chi_{6019}(2247,\cdot)\) \(\chi_{6019}(2321,\cdot)\) \(\chi_{6019}(2645,\cdot)\) \(\chi_{6019}(2650,\cdot)\) \(\chi_{6019}(3062,\cdot)\) \(\chi_{6019}(3109,\cdot)\) \(\chi_{6019}(3334,\cdot)\) \(\chi_{6019}(3582,\cdot)\) \(\chi_{6019}(3668,\cdot)\) \(\chi_{6019}(4024,\cdot)\) \(\chi_{6019}(4128,\cdot)\) \(\chi_{6019}(4257,\cdot)\) \(\chi_{6019}(4535,\cdot)\) \(\chi_{6019}(4864,\cdot)\) \(\chi_{6019}(4899,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2316,1392)\) → \((e\left(\frac{5}{12}\right),e\left(\frac{5}{66}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6019 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{131}{132}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{29}{132}\right)\) | \(e\left(\frac{97}{132}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{23}{132}\right)\) |