Basic properties
Modulus: | \(6171\) | |
Conductor: | \(2057\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2057}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6171.ck
\(\chi_{6171}(16,\cdot)\) \(\chi_{6171}(169,\cdot)\) \(\chi_{6171}(322,\cdot)\) \(\chi_{6171}(526,\cdot)\) \(\chi_{6171}(577,\cdot)\) \(\chi_{6171}(730,\cdot)\) \(\chi_{6171}(883,\cdot)\) \(\chi_{6171}(1087,\cdot)\) \(\chi_{6171}(1138,\cdot)\) \(\chi_{6171}(1444,\cdot)\) \(\chi_{6171}(1648,\cdot)\) \(\chi_{6171}(1699,\cdot)\) \(\chi_{6171}(1852,\cdot)\) \(\chi_{6171}(2005,\cdot)\) \(\chi_{6171}(2209,\cdot)\) \(\chi_{6171}(2260,\cdot)\) \(\chi_{6171}(2413,\cdot)\) \(\chi_{6171}(2566,\cdot)\) \(\chi_{6171}(2770,\cdot)\) \(\chi_{6171}(2821,\cdot)\) \(\chi_{6171}(2974,\cdot)\) \(\chi_{6171}(3127,\cdot)\) \(\chi_{6171}(3331,\cdot)\) \(\chi_{6171}(3382,\cdot)\) \(\chi_{6171}(3535,\cdot)\) \(\chi_{6171}(3688,\cdot)\) \(\chi_{6171}(3892,\cdot)\) \(\chi_{6171}(3943,\cdot)\) \(\chi_{6171}(4096,\cdot)\) \(\chi_{6171}(4249,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((4115,970,2179)\) → \((1,e\left(\frac{2}{55}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(19\) |
\( \chi_{ 6171 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{1}{55}\right)\) |