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.ct
\(\chi_{6003}(157,\cdot)\) \(\chi_{6003}(481,\cdot)\) \(\chi_{6003}(592,\cdot)\) \(\chi_{6003}(655,\cdot)\) \(\chi_{6003}(916,\cdot)\) \(\chi_{6003}(940,\cdot)\) \(\chi_{6003}(1003,\cdot)\) \(\chi_{6003}(1114,\cdot)\) \(\chi_{6003}(1201,\cdot)\) \(\chi_{6003}(1525,\cdot)\) \(\chi_{6003}(1699,\cdot)\) \(\chi_{6003}(1723,\cdot)\) \(\chi_{6003}(1786,\cdot)\) \(\chi_{6003}(1897,\cdot)\) \(\chi_{6003}(1960,\cdot)\) \(\chi_{6003}(2158,\cdot)\) \(\chi_{6003}(2245,\cdot)\) \(\chi_{6003}(2482,\cdot)\) \(\chi_{6003}(2767,\cdot)\) \(\chi_{6003}(2941,\cdot)\) \(\chi_{6003}(3004,\cdot)\) \(\chi_{6003}(3028,\cdot)\) \(\chi_{6003}(3202,\cdot)\) \(\chi_{6003}(3352,\cdot)\) \(\chi_{6003}(3526,\cdot)\) \(\chi_{6003}(3724,\cdot)\) \(\chi_{6003}(3787,\cdot)\) \(\chi_{6003}(3874,\cdot)\) \(\chi_{6003}(4246,\cdot)\) \(\chi_{6003}(4594,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((668,3133,4555)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{19}{22}\right),-i)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6003 }(3526, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{132}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{25}{132}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{29}{132}\right)\) | \(e\left(\frac{19}{33}\right)\) |