Basic properties
Modulus: | \(6003\) | |
Conductor: | \(6003\) | 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 6003.cu
\(\chi_{6003}(41,\cdot)\) \(\chi_{6003}(104,\cdot)\) \(\chi_{6003}(128,\cdot)\) \(\chi_{6003}(302,\cdot)\) \(\chi_{6003}(650,\cdot)\) \(\chi_{6003}(887,\cdot)\) \(\chi_{6003}(974,\cdot)\) \(\chi_{6003}(1085,\cdot)\) \(\chi_{6003}(1235,\cdot)\) \(\chi_{6003}(1346,\cdot)\) \(\chi_{6003}(1409,\cdot)\) \(\chi_{6003}(1757,\cdot)\) \(\chi_{6003}(2129,\cdot)\) \(\chi_{6003}(2216,\cdot)\) \(\chi_{6003}(2279,\cdot)\) \(\chi_{6003}(2477,\cdot)\) \(\chi_{6003}(2651,\cdot)\) \(\chi_{6003}(2801,\cdot)\) \(\chi_{6003}(2975,\cdot)\) \(\chi_{6003}(2999,\cdot)\) \(\chi_{6003}(3062,\cdot)\) \(\chi_{6003}(3236,\cdot)\) \(\chi_{6003}(3521,\cdot)\) \(\chi_{6003}(3758,\cdot)\) \(\chi_{6003}(3845,\cdot)\) \(\chi_{6003}(4043,\cdot)\) \(\chi_{6003}(4106,\cdot)\) \(\chi_{6003}(4217,\cdot)\) \(\chi_{6003}(4280,\cdot)\) \(\chi_{6003}(4304,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((668,3133,4555)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{4}{11}\right),-i)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6003 }(3236, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{132}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{113}{132}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{73}{132}\right)\) | \(e\left(\frac{8}{33}\right)\) |