Basic properties
Modulus: | \(6003\) | |
Conductor: | \(667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{667}(71,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6003.cy
\(\chi_{6003}(64,\cdot)\) \(\chi_{6003}(100,\cdot)\) \(\chi_{6003}(154,\cdot)\) \(\chi_{6003}(325,\cdot)\) \(\chi_{6003}(361,\cdot)\) \(\chi_{6003}(370,\cdot)\) \(\chi_{6003}(469,\cdot)\) \(\chi_{6003}(676,\cdot)\) \(\chi_{6003}(883,\cdot)\) \(\chi_{6003}(892,\cdot)\) \(\chi_{6003}(991,\cdot)\) \(\chi_{6003}(1108,\cdot)\) \(\chi_{6003}(1135,\cdot)\) \(\chi_{6003}(1153,\cdot)\) \(\chi_{6003}(1198,\cdot)\) \(\chi_{6003}(1369,\cdot)\) \(\chi_{6003}(1396,\cdot)\) \(\chi_{6003}(1405,\cdot)\) \(\chi_{6003}(1513,\cdot)\) \(\chi_{6003}(1720,\cdot)\) \(\chi_{6003}(1774,\cdot)\) \(\chi_{6003}(1918,\cdot)\) \(\chi_{6003}(1927,\cdot)\) \(\chi_{6003}(1936,\cdot)\) \(\chi_{6003}(1981,\cdot)\) \(\chi_{6003}(2152,\cdot)\) \(\chi_{6003}(2188,\cdot)\) \(\chi_{6003}(2197,\cdot)\) \(\chi_{6003}(2440,\cdot)\) \(\chi_{6003}(2557,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((668,3133,4555)\) → \((1,e\left(\frac{1}{11}\right),e\left(\frac{9}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6003 }(1405, a) \) | \(1\) | \(1\) | \(e\left(\frac{127}{154}\right)\) | \(e\left(\frac{50}{77}\right)\) | \(e\left(\frac{18}{77}\right)\) | \(e\left(\frac{34}{77}\right)\) | \(e\left(\frac{73}{154}\right)\) | \(e\left(\frac{9}{154}\right)\) | \(e\left(\frac{137}{154}\right)\) | \(e\left(\frac{65}{77}\right)\) | \(e\left(\frac{41}{154}\right)\) | \(e\left(\frac{23}{77}\right)\) |