Basic properties
Modulus: | \(6003\) | |
Conductor: | \(2001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(308\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2001}(1070,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6003.dg
\(\chi_{6003}(8,\cdot)\) \(\chi_{6003}(26,\cdot)\) \(\chi_{6003}(98,\cdot)\) \(\chi_{6003}(188,\cdot)\) \(\chi_{6003}(242,\cdot)\) \(\chi_{6003}(269,\cdot)\) \(\chi_{6003}(305,\cdot)\) \(\chi_{6003}(395,\cdot)\) \(\chi_{6003}(404,\cdot)\) \(\chi_{6003}(449,\cdot)\) \(\chi_{6003}(485,\cdot)\) \(\chi_{6003}(512,\cdot)\) \(\chi_{6003}(611,\cdot)\) \(\chi_{6003}(656,\cdot)\) \(\chi_{6003}(791,\cdot)\) \(\chi_{6003}(809,\cdot)\) \(\chi_{6003}(926,\cdot)\) \(\chi_{6003}(1007,\cdot)\) \(\chi_{6003}(1025,\cdot)\) \(\chi_{6003}(1070,\cdot)\) \(\chi_{6003}(1133,\cdot)\) \(\chi_{6003}(1232,\cdot)\) \(\chi_{6003}(1250,\cdot)\) \(\chi_{6003}(1268,\cdot)\) \(\chi_{6003}(1313,\cdot)\) \(\chi_{6003}(1439,\cdot)\) \(\chi_{6003}(1511,\cdot)\) \(\chi_{6003}(1547,\cdot)\) \(\chi_{6003}(1664,\cdot)\) \(\chi_{6003}(1754,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{308})$ |
Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((668,3133,4555)\) → \((-1,e\left(\frac{10}{11}\right),e\left(\frac{19}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6003 }(1070, a) \) | \(1\) | \(1\) | \(e\left(\frac{307}{308}\right)\) | \(e\left(\frac{153}{154}\right)\) | \(e\left(\frac{26}{77}\right)\) | \(e\left(\frac{32}{77}\right)\) | \(e\left(\frac{305}{308}\right)\) | \(e\left(\frac{103}{308}\right)\) | \(e\left(\frac{199}{308}\right)\) | \(e\left(\frac{145}{154}\right)\) | \(e\left(\frac{127}{308}\right)\) | \(e\left(\frac{76}{77}\right)\) |