Basic properties
Modulus: | \(6042\) | |
Conductor: | \(3021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3021}(179,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.cf
\(\chi_{6042}(65,\cdot)\) \(\chi_{6042}(179,\cdot)\) \(\chi_{6042}(563,\cdot)\) \(\chi_{6042}(677,\cdot)\) \(\chi_{6042}(1019,\cdot)\) \(\chi_{6042}(1091,\cdot)\) \(\chi_{6042}(1133,\cdot)\) \(\chi_{6042}(1205,\cdot)\) \(\chi_{6042}(1433,\cdot)\) \(\chi_{6042}(1661,\cdot)\) \(\chi_{6042}(1775,\cdot)\) \(\chi_{6042}(1889,\cdot)\) \(\chi_{6042}(2045,\cdot)\) \(\chi_{6042}(2117,\cdot)\) \(\chi_{6042}(2159,\cdot)\) \(\chi_{6042}(2231,\cdot)\) \(\chi_{6042}(2387,\cdot)\) \(\chi_{6042}(2459,\cdot)\) \(\chi_{6042}(2615,\cdot)\) \(\chi_{6042}(2729,\cdot)\) \(\chi_{6042}(2801,\cdot)\) \(\chi_{6042}(2843,\cdot)\) \(\chi_{6042}(3029,\cdot)\) \(\chi_{6042}(3071,\cdot)\) \(\chi_{6042}(3185,\cdot)\) \(\chi_{6042}(3371,\cdot)\) \(\chi_{6042}(3413,\cdot)\) \(\chi_{6042}(3599,\cdot)\) \(\chi_{6042}(3713,\cdot)\) \(\chi_{6042}(3755,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2015,4771,2281)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{49}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6042 }(179, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{156}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{101}{156}\right)\) |