Basic properties
Modulus: | \(6001\) | |
Conductor: | \(6001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 6001.ea
\(\chi_{6001}(38,\cdot)\) \(\chi_{6001}(200,\cdot)\) \(\chi_{6001}(344,\cdot)\) \(\chi_{6001}(378,\cdot)\) \(\chi_{6001}(480,\cdot)\) \(\chi_{6001}(497,\cdot)\) \(\chi_{6001}(506,\cdot)\) \(\chi_{6001}(667,\cdot)\) \(\chi_{6001}(752,\cdot)\) \(\chi_{6001}(778,\cdot)\) \(\chi_{6001}(863,\cdot)\) \(\chi_{6001}(871,\cdot)\) \(\chi_{6001}(939,\cdot)\) \(\chi_{6001}(965,\cdot)\) \(\chi_{6001}(973,\cdot)\) \(\chi_{6001}(1016,\cdot)\) \(\chi_{6001}(1135,\cdot)\) \(\chi_{6001}(1152,\cdot)\) \(\chi_{6001}(1211,\cdot)\) \(\chi_{6001}(1228,\cdot)\) \(\chi_{6001}(1245,\cdot)\) \(\chi_{6001}(1330,\cdot)\) \(\chi_{6001}(1568,\cdot)\) \(\chi_{6001}(1747,\cdot)\) \(\chi_{6001}(1815,\cdot)\) \(\chi_{6001}(2019,\cdot)\) \(\chi_{6001}(2053,\cdot)\) \(\chi_{6001}(2248,\cdot)\) \(\chi_{6001}(2316,\cdot)\) \(\chi_{6001}(2393,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{176})$ |
Fixed field: | Number field defined by a degree 176 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((-i,e\left(\frac{113}{176}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(2316, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{69}{176}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{25}{176}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{69}{88}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{17}{22}\right)\) |