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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6001.ed
\(\chi_{6001}(19,\cdot)\) \(\chi_{6001}(144,\cdot)\) \(\chi_{6001}(189,\cdot)\) \(\chi_{6001}(240,\cdot)\) \(\chi_{6001}(314,\cdot)\) \(\chi_{6001}(315,\cdot)\) \(\chi_{6001}(376,\cdot)\) \(\chi_{6001}(383,\cdot)\) \(\chi_{6001}(400,\cdot)\) \(\chi_{6001}(451,\cdot)\) \(\chi_{6001}(518,\cdot)\) \(\chi_{6001}(525,\cdot)\) \(\chi_{6001}(586,\cdot)\) \(\chi_{6001}(784,\cdot)\) \(\chi_{6001}(858,\cdot)\) \(\chi_{6001}(875,\cdot)\) \(\chi_{6001}(892,\cdot)\) \(\chi_{6001}(961,\cdot)\) \(\chi_{6001}(967,\cdot)\) \(\chi_{6001}(977,\cdot)\) \(\chi_{6001}(1012,\cdot)\) \(\chi_{6001}(1018,\cdot)\) \(\chi_{6001}(1029,\cdot)\) \(\chi_{6001}(1097,\cdot)\) \(\chi_{6001}(1124,\cdot)\) \(\chi_{6001}(1430,\cdot)\) \(\chi_{6001}(1437,\cdot)\) \(\chi_{6001}(1511,\cdot)\) \(\chi_{6001}(1539,\cdot)\) \(\chi_{6001}(1715,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{176})$ |
Fixed field: | Number field defined by a degree 176 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((e\left(\frac{7}{8}\right),e\left(\frac{35}{176}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{13}{176}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{145}{176}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{13}{88}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{5}{88}\right)\) |