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.dx
\(\chi_{6001}(30,\cdot)\) \(\chi_{6001}(47,\cdot)\) \(\chi_{6001}(72,\cdot)\) \(\chi_{6001}(98,\cdot)\) \(\chi_{6001}(157,\cdot)\) \(\chi_{6001}(259,\cdot)\) \(\chi_{6001}(310,\cdot)\) \(\chi_{6001}(429,\cdot)\) \(\chi_{6001}(446,\cdot)\) \(\chi_{6001}(608,\cdot)\) \(\chi_{6001}(659,\cdot)\) \(\chi_{6001}(676,\cdot)\) \(\chi_{6001}(744,\cdot)\) \(\chi_{6001}(1041,\cdot)\) \(\chi_{6001}(1050,\cdot)\) \(\chi_{6001}(1084,\cdot)\) \(\chi_{6001}(1109,\cdot)\) \(\chi_{6001}(1186,\cdot)\) \(\chi_{6001}(1203,\cdot)\) \(\chi_{6001}(1313,\cdot)\) \(\chi_{6001}(1347,\cdot)\) \(\chi_{6001}(1373,\cdot)\) \(\chi_{6001}(1458,\cdot)\) \(\chi_{6001}(1577,\cdot)\) \(\chi_{6001}(1645,\cdot)\) \(\chi_{6001}(1679,\cdot)\) \(\chi_{6001}(1687,\cdot)\) \(\chi_{6001}(1806,\cdot)\) \(\chi_{6001}(1857,\cdot)\) \(\chi_{6001}(1917,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{176})$ |
Fixed field: | Number field defined by a degree 176 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((-i,e\left(\frac{175}{176}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(157, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{131}{176}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{175}{176}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{43}{88}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{10}{11}\right)\) |