Basic properties
Modulus: | \(6003\) | |
Conductor: | \(667\) | 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 \(\chi_{667}(433,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6003.df
\(\chi_{6003}(10,\cdot)\) \(\chi_{6003}(19,\cdot)\) \(\chi_{6003}(37,\cdot)\) \(\chi_{6003}(172,\cdot)\) \(\chi_{6003}(217,\cdot)\) \(\chi_{6003}(235,\cdot)\) \(\chi_{6003}(316,\cdot)\) \(\chi_{6003}(379,\cdot)\) \(\chi_{6003}(388,\cdot)\) \(\chi_{6003}(424,\cdot)\) \(\chi_{6003}(433,\cdot)\) \(\chi_{6003}(559,\cdot)\) \(\chi_{6003}(595,\cdot)\) \(\chi_{6003}(640,\cdot)\) \(\chi_{6003}(649,\cdot)\) \(\chi_{6003}(757,\cdot)\) \(\chi_{6003}(793,\cdot)\) \(\chi_{6003}(802,\cdot)\) \(\chi_{6003}(820,\cdot)\) \(\chi_{6003}(838,\cdot)\) \(\chi_{6003}(856,\cdot)\) \(\chi_{6003}(1000,\cdot)\) \(\chi_{6003}(1054,\cdot)\) \(\chi_{6003}(1063,\cdot)\) \(\chi_{6003}(1171,\cdot)\) \(\chi_{6003}(1207,\cdot)\) \(\chi_{6003}(1216,\cdot)\) \(\chi_{6003}(1261,\cdot)\) \(\chi_{6003}(1279,\cdot)\) \(\chi_{6003}(1378,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{308})$ |
Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((668,3133,4555)\) → \((1,e\left(\frac{15}{22}\right),e\left(\frac{15}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6003 }(433, a) \) | \(1\) | \(1\) | \(e\left(\frac{277}{308}\right)\) | \(e\left(\frac{123}{154}\right)\) | \(e\left(\frac{36}{77}\right)\) | \(e\left(\frac{59}{154}\right)\) | \(e\left(\frac{215}{308}\right)\) | \(e\left(\frac{113}{308}\right)\) | \(e\left(\frac{163}{308}\right)\) | \(e\left(\frac{29}{154}\right)\) | \(e\left(\frac{87}{308}\right)\) | \(e\left(\frac{46}{77}\right)\) |