Basic properties
Modulus: | \(4840\) | |
Conductor: | \(968\) | 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 \(\chi_{968}(141,\cdot)\) | 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)
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Galois orbit 4840.dh
\(\chi_{4840}(141,\cdot)\) \(\chi_{4840}(181,\cdot)\) \(\chi_{4840}(301,\cdot)\) \(\chi_{4840}(421,\cdot)\) \(\chi_{4840}(581,\cdot)\) \(\chi_{4840}(621,\cdot)\) \(\chi_{4840}(741,\cdot)\) \(\chi_{4840}(861,\cdot)\) \(\chi_{4840}(1021,\cdot)\) \(\chi_{4840}(1061,\cdot)\) \(\chi_{4840}(1181,\cdot)\) \(\chi_{4840}(1301,\cdot)\) \(\chi_{4840}(1501,\cdot)\) \(\chi_{4840}(1621,\cdot)\) \(\chi_{4840}(1741,\cdot)\) \(\chi_{4840}(1901,\cdot)\) \(\chi_{4840}(1941,\cdot)\) \(\chi_{4840}(2061,\cdot)\) \(\chi_{4840}(2341,\cdot)\) \(\chi_{4840}(2381,\cdot)\) \(\chi_{4840}(2621,\cdot)\) \(\chi_{4840}(2781,\cdot)\) \(\chi_{4840}(2821,\cdot)\) \(\chi_{4840}(2941,\cdot)\) \(\chi_{4840}(3061,\cdot)\) \(\chi_{4840}(3221,\cdot)\) \(\chi_{4840}(3261,\cdot)\) \(\chi_{4840}(3381,\cdot)\) \(\chi_{4840}(3501,\cdot)\) \(\chi_{4840}(3661,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3631,2421,1937,4721)\) → \((1,-1,1,e\left(\frac{38}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 4840 }(141, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{27}{110}\right)\) |