Basic properties
Modulus: | \(6001\) | |
Conductor: | \(6001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(176\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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.dg
\(\chi_{6001}(94,\cdot)\) \(\chi_{6001}(155,\cdot)\) \(\chi_{6001}(196,\cdot)\) \(\chi_{6001}(281,\cdot)\) \(\chi_{6001}(576,\cdot)\) \(\chi_{6001}(688,\cdot)\) \(\chi_{6001}(994,\cdot)\) \(\chi_{6001}(1131,\cdot)\) \(\chi_{6001}(1141,\cdot)\) \(\chi_{6001}(1216,\cdot)\) \(\chi_{6001}(1226,\cdot)\) \(\chi_{6001}(1243,\cdot)\) \(\chi_{6001}(1256,\cdot)\) \(\chi_{6001}(1260,\cdot)\) \(\chi_{6001}(1318,\cdot)\) \(\chi_{6001}(1334,\cdot)\) \(\chi_{6001}(1488,\cdot)\) \(\chi_{6001}(1505,\cdot)\) \(\chi_{6001}(1532,\cdot)\) \(\chi_{6001}(1600,\cdot)\) \(\chi_{6001}(1742,\cdot)\) \(\chi_{6001}(1804,\cdot)\) \(\chi_{6001}(1851,\cdot)\) \(\chi_{6001}(1878,\cdot)\) \(\chi_{6001}(1929,\cdot)\) \(\chi_{6001}(1974,\cdot)\) \(\chi_{6001}(2072,\cdot)\) \(\chi_{6001}(2099,\cdot)\) \(\chi_{6001}(2127,\cdot)\) \(\chi_{6001}(2133,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{176})$ |
Fixed field: | Number field defined by a degree 176 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((e\left(\frac{1}{8}\right),e\left(\frac{87}{176}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(196, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{109}{176}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{65}{176}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{21}{88}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{47}{88}\right)\) |