Basic properties
Modulus: | \(6001\) | |
Conductor: | \(6001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(176\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6001.dn
\(\chi_{6001}(22,\cdot)\) \(\chi_{6001}(58,\cdot)\) \(\chi_{6001}(131,\cdot)\) \(\chi_{6001}(231,\cdot)\) \(\chi_{6001}(337,\cdot)\) \(\chi_{6001}(411,\cdot)\) \(\chi_{6001}(538,\cdot)\) \(\chi_{6001}(584,\cdot)\) \(\chi_{6001}(609,\cdot)\) \(\chi_{6001}(690,\cdot)\) \(\chi_{6001}(728,\cdot)\) \(\chi_{6001}(891,\cdot)\) \(\chi_{6001}(923,\cdot)\) \(\chi_{6001}(962,\cdot)\) \(\chi_{6001}(1043,\cdot)\) \(\chi_{6001}(1081,\cdot)\) \(\chi_{6001}(1117,\cdot)\) \(\chi_{6001}(1244,\cdot)\) \(\chi_{6001}(1246,\cdot)\) \(\chi_{6001}(1315,\cdot)\) \(\chi_{6001}(1434,\cdot)\) \(\chi_{6001}(1552,\cdot)\) \(\chi_{6001}(1629,\cdot)\) \(\chi_{6001}(1643,\cdot)\) \(\chi_{6001}(1950,\cdot)\) \(\chi_{6001}(1952,\cdot)\) \(\chi_{6001}(1982,\cdot)\) \(\chi_{6001}(1996,\cdot)\) \(\chi_{6001}(2102,\cdot)\) \(\chi_{6001}(2249,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{176})$ |
Fixed field: | Number field defined by a degree 176 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((e\left(\frac{5}{16}\right),e\left(\frac{7}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(22, a) \) | \(-1\) | \(1\) | \(e\left(\frac{65}{88}\right)\) | \(e\left(\frac{167}{176}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{35}{176}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{19}{88}\right)\) | \(e\left(\frac{79}{88}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{65}{176}\right)\) |