Basic properties
Modulus: | \(6171\) | |
Conductor: | \(2057\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(176\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2057}(10,\cdot)\) | 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)
|
Galois orbit 6171.cp
\(\chi_{6171}(10,\cdot)\) \(\chi_{6171}(109,\cdot)\) \(\chi_{6171}(142,\cdot)\) \(\chi_{6171}(175,\cdot)\) \(\chi_{6171}(439,\cdot)\) \(\chi_{6171}(505,\cdot)\) \(\chi_{6171}(538,\cdot)\) \(\chi_{6171}(571,\cdot)\) \(\chi_{6171}(670,\cdot)\) \(\chi_{6171}(703,\cdot)\) \(\chi_{6171}(736,\cdot)\) \(\chi_{6171}(802,\cdot)\) \(\chi_{6171}(1000,\cdot)\) \(\chi_{6171}(1066,\cdot)\) \(\chi_{6171}(1099,\cdot)\) \(\chi_{6171}(1132,\cdot)\) \(\chi_{6171}(1231,\cdot)\) \(\chi_{6171}(1264,\cdot)\) \(\chi_{6171}(1297,\cdot)\) \(\chi_{6171}(1363,\cdot)\) \(\chi_{6171}(1561,\cdot)\) \(\chi_{6171}(1627,\cdot)\) \(\chi_{6171}(1660,\cdot)\) \(\chi_{6171}(1792,\cdot)\) \(\chi_{6171}(1825,\cdot)\) \(\chi_{6171}(1858,\cdot)\) \(\chi_{6171}(1924,\cdot)\) \(\chi_{6171}(2122,\cdot)\) \(\chi_{6171}(2188,\cdot)\) \(\chi_{6171}(2221,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{176})$ |
Fixed field: | Number field defined by a degree 176 polynomial (not computed) |
Values on generators
\((4115,970,2179)\) → \((1,e\left(\frac{15}{22}\right),e\left(\frac{3}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(19\) |
\( \chi_{ 6171 }(10, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{88}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{69}{176}\right)\) | \(e\left(\frac{147}{176}\right)\) | \(e\left(\frac{81}{88}\right)\) | \(e\left(\frac{123}{176}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{25}{176}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{19}{88}\right)\) |