Basic properties
Modulus: | \(6003\) | |
Conductor: | \(2001\) | 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 \(\chi_{2001}(845,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6003.db
\(\chi_{6003}(80,\cdot)\) \(\chi_{6003}(125,\cdot)\) \(\chi_{6003}(296,\cdot)\) \(\chi_{6003}(332,\cdot)\) \(\chi_{6003}(341,\cdot)\) \(\chi_{6003}(557,\cdot)\) \(\chi_{6003}(701,\cdot)\) \(\chi_{6003}(845,\cdot)\) \(\chi_{6003}(908,\cdot)\) \(\chi_{6003}(962,\cdot)\) \(\chi_{6003}(1079,\cdot)\) \(\chi_{6003}(1115,\cdot)\) \(\chi_{6003}(1124,\cdot)\) \(\chi_{6003}(1169,\cdot)\) \(\chi_{6003}(1367,\cdot)\) \(\chi_{6003}(1376,\cdot)\) \(\chi_{6003}(1385,\cdot)\) \(\chi_{6003}(1601,\cdot)\) \(\chi_{6003}(1745,\cdot)\) \(\chi_{6003}(1907,\cdot)\) \(\chi_{6003}(1952,\cdot)\) \(\chi_{6003}(2006,\cdot)\) \(\chi_{6003}(2123,\cdot)\) \(\chi_{6003}(2150,\cdot)\) \(\chi_{6003}(2159,\cdot)\) \(\chi_{6003}(2213,\cdot)\) \(\chi_{6003}(2384,\cdot)\) \(\chi_{6003}(2411,\cdot)\) \(\chi_{6003}(2420,\cdot)\) \(\chi_{6003}(2429,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((668,3133,4555)\) → \((-1,e\left(\frac{7}{22}\right),e\left(\frac{1}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6003 }(845, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{77}\right)\) | \(e\left(\frac{32}{77}\right)\) | \(e\left(\frac{30}{77}\right)\) | \(e\left(\frac{139}{154}\right)\) | \(e\left(\frac{48}{77}\right)\) | \(e\left(\frac{46}{77}\right)\) | \(e\left(\frac{23}{154}\right)\) | \(e\left(\frac{57}{77}\right)\) | \(e\left(\frac{17}{154}\right)\) | \(e\left(\frac{64}{77}\right)\) |