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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6019.dh
\(\chi_{6019}(305,\cdot)\) \(\chi_{6019}(448,\cdot)\) \(\chi_{6019}(501,\cdot)\) \(\chi_{6019}(570,\cdot)\) \(\chi_{6019}(964,\cdot)\) \(\chi_{6019}(1033,\cdot)\) \(\chi_{6019}(1142,\cdot)\) \(\chi_{6019}(1164,\cdot)\) \(\chi_{6019}(1255,\cdot)\) \(\chi_{6019}(1515,\cdot)\) \(\chi_{6019}(1605,\cdot)\) \(\chi_{6019}(1627,\cdot)\) \(\chi_{6019}(1718,\cdot)\) \(\chi_{6019}(1978,\cdot)\) \(\chi_{6019}(2260,\cdot)\) \(\chi_{6019}(2416,\cdot)\) \(\chi_{6019}(2620,\cdot)\) \(\chi_{6019}(2723,\cdot)\) \(\chi_{6019}(2763,\cdot)\) \(\chi_{6019}(2879,\cdot)\) \(\chi_{6019}(3083,\cdot)\) \(\chi_{6019}(3226,\cdot)\) \(\chi_{6019}(3348,\cdot)\) \(\chi_{6019}(3742,\cdot)\) \(\chi_{6019}(3811,\cdot)\) \(\chi_{6019}(3920,\cdot)\) \(\chi_{6019}(4205,\cdot)\) \(\chi_{6019}(4383,\cdot)\) \(\chi_{6019}(4405,\cdot)\) \(\chi_{6019}(4496,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2316,1392)\) → \((e\left(\frac{5}{12}\right),e\left(\frac{13}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6019 }(305, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{132}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{101}{132}\right)\) | \(e\left(\frac{131}{132}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{43}{132}\right)\) |