Basic properties
Modulus: | \(6042\) | |
Conductor: | \(3021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3021}(2213,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.cj
\(\chi_{6042}(17,\cdot)\) \(\chi_{6042}(131,\cdot)\) \(\chi_{6042}(149,\cdot)\) \(\chi_{6042}(329,\cdot)\) \(\chi_{6042}(347,\cdot)\) \(\chi_{6042}(377,\cdot)\) \(\chi_{6042}(461,\cdot)\) \(\chi_{6042}(587,\cdot)\) \(\chi_{6042}(785,\cdot)\) \(\chi_{6042}(833,\cdot)\) \(\chi_{6042}(1013,\cdot)\) \(\chi_{6042}(1175,\cdot)\) \(\chi_{6042}(1259,\cdot)\) \(\chi_{6042}(1289,\cdot)\) \(\chi_{6042}(1301,\cdot)\) \(\chi_{6042}(1385,\cdot)\) \(\chi_{6042}(1403,\cdot)\) \(\chi_{6042}(1415,\cdot)\) \(\chi_{6042}(1469,\cdot)\) \(\chi_{6042}(1601,\cdot)\) \(\chi_{6042}(1619,\cdot)\) \(\chi_{6042}(1733,\cdot)\) \(\chi_{6042}(1811,\cdot)\) \(\chi_{6042}(1859,\cdot)\) \(\chi_{6042}(1925,\cdot)\) \(\chi_{6042}(2039,\cdot)\) \(\chi_{6042}(2057,\cdot)\) \(\chi_{6042}(2213,\cdot)\) \(\chi_{6042}(2285,\cdot)\) \(\chi_{6042}(2495,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{117})$ |
Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((2015,4771,2281)\) → \((-1,e\left(\frac{4}{9}\right),e\left(\frac{25}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6042 }(2213, a) \) | \(-1\) | \(1\) | \(e\left(\frac{94}{117}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{35}{117}\right)\) | \(e\left(\frac{131}{234}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{71}{117}\right)\) | \(e\left(\frac{67}{234}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{109}{117}\right)\) |