Basic properties
Modulus: | \(6042\) | |
Conductor: | \(3021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3021}(293,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.bz
\(\chi_{6042}(293,\cdot)\) \(\chi_{6042}(407,\cdot)\) \(\chi_{6042}(521,\cdot)\) \(\chi_{6042}(791,\cdot)\) \(\chi_{6042}(863,\cdot)\) \(\chi_{6042}(1247,\cdot)\) \(\chi_{6042}(1319,\cdot)\) \(\chi_{6042}(1361,\cdot)\) \(\chi_{6042}(1475,\cdot)\) \(\chi_{6042}(1547,\cdot)\) \(\chi_{6042}(1817,\cdot)\) \(\chi_{6042}(2003,\cdot)\) \(\chi_{6042}(2273,\cdot)\) \(\chi_{6042}(2345,\cdot)\) \(\chi_{6042}(2501,\cdot)\) \(\chi_{6042}(2957,\cdot)\) \(\chi_{6042}(3143,\cdot)\) \(\chi_{6042}(3257,\cdot)\) \(\chi_{6042}(3299,\cdot)\) \(\chi_{6042}(4097,\cdot)\) \(\chi_{6042}(4211,\cdot)\) \(\chi_{6042}(5081,\cdot)\) \(\chi_{6042}(5879,\cdot)\) \(\chi_{6042}(6035,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2015,4771,2281)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{4}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6042 }(293, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{73}{78}\right)\) |