Basic properties
Modulus: | \(6042\) | |
Conductor: | \(3021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(468\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3021}(1313,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.cs
\(\chi_{6042}(41,\cdot)\) \(\chi_{6042}(71,\cdot)\) \(\chi_{6042}(167,\cdot)\) \(\chi_{6042}(173,\cdot)\) \(\chi_{6042}(185,\cdot)\) \(\chi_{6042}(257,\cdot)\) \(\chi_{6042}(287,\cdot)\) \(\chi_{6042}(299,\cdot)\) \(\chi_{6042}(383,\cdot)\) \(\chi_{6042}(485,\cdot)\) \(\chi_{6042}(497,\cdot)\) \(\chi_{6042}(509,\cdot)\) \(\chi_{6042}(527,\cdot)\) \(\chi_{6042}(641,\cdot)\) \(\chi_{6042}(737,\cdot)\) \(\chi_{6042}(773,\cdot)\) \(\chi_{6042}(827,\cdot)\) \(\chi_{6042}(851,\cdot)\) \(\chi_{6042}(869,\cdot)\) \(\chi_{6042}(887,\cdot)\) \(\chi_{6042}(1055,\cdot)\) \(\chi_{6042}(1079,\cdot)\) \(\chi_{6042}(1115,\cdot)\) \(\chi_{6042}(1169,\cdot)\) \(\chi_{6042}(1193,\cdot)\) \(\chi_{6042}(1199,\cdot)\) \(\chi_{6042}(1211,\cdot)\) \(\chi_{6042}(1307,\cdot)\) \(\chi_{6042}(1313,\cdot)\) \(\chi_{6042}(1343,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{468})$ |
Fixed field: | Number field defined by a degree 468 polynomial (not computed) |
Values on generators
\((2015,4771,2281)\) → \((-1,e\left(\frac{1}{18}\right),e\left(\frac{45}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6042 }(1313, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{468}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{11}{234}\right)\) | \(e\left(\frac{83}{117}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{29}{234}\right)\) | \(e\left(\frac{59}{234}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{239}{468}\right)\) |