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.dz
\(\chi_{6001}(50,\cdot)\) \(\chi_{6001}(152,\cdot)\) \(\chi_{6001}(169,\cdot)\) \(\chi_{6001}(186,\cdot)\) \(\chi_{6001}(254,\cdot)\) \(\chi_{6001}(271,\cdot)\) \(\chi_{6001}(288,\cdot)\) \(\chi_{6001}(509,\cdot)\) \(\chi_{6001}(628,\cdot)\) \(\chi_{6001}(747,\cdot)\) \(\chi_{6001}(798,\cdot)\) \(\chi_{6001}(1036,\cdot)\) \(\chi_{6001}(1172,\cdot)\) \(\chi_{6001}(1189,\cdot)\) \(\chi_{6001}(1223,\cdot)\) \(\chi_{6001}(1240,\cdot)\) \(\chi_{6001}(1257,\cdot)\) \(\chi_{6001}(1393,\cdot)\) \(\chi_{6001}(1427,\cdot)\) \(\chi_{6001}(1750,\cdot)\) \(\chi_{6001}(1784,\cdot)\) \(\chi_{6001}(1920,\cdot)\) \(\chi_{6001}(1937,\cdot)\) \(\chi_{6001}(1954,\cdot)\) \(\chi_{6001}(1988,\cdot)\) \(\chi_{6001}(2005,\cdot)\) \(\chi_{6001}(2141,\cdot)\) \(\chi_{6001}(2379,\cdot)\) \(\chi_{6001}(2430,\cdot)\) \(\chi_{6001}(2549,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{176})$ |
Fixed field: | Number field defined by a degree 176 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((-1,e\left(\frac{151}{176}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(747, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{63}{176}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{107}{176}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{63}{88}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{43}{44}\right)\) |