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 \(\chi_{3021}(1745,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.cl
\(\chi_{6042}(47,\cdot)\) \(\chi_{6042}(119,\cdot)\) \(\chi_{6042}(275,\cdot)\) \(\chi_{6042}(365,\cdot)\) \(\chi_{6042}(473,\cdot)\) \(\chi_{6042}(593,\cdot)\) \(\chi_{6042}(731,\cdot)\) \(\chi_{6042}(917,\cdot)\) \(\chi_{6042}(929,\cdot)\) \(\chi_{6042}(947,\cdot)\) \(\chi_{6042}(1031,\cdot)\) \(\chi_{6042}(1043,\cdot)\) \(\chi_{6042}(1049,\cdot)\) \(\chi_{6042}(1073,\cdot)\) \(\chi_{6042}(1157,\cdot)\) \(\chi_{6042}(1391,\cdot)\) \(\chi_{6042}(1499,\cdot)\) \(\chi_{6042}(1583,\cdot)\) \(\chi_{6042}(1745,\cdot)\) \(\chi_{6042}(1871,\cdot)\) \(\chi_{6042}(1955,\cdot)\) \(\chi_{6042}(1985,\cdot)\) \(\chi_{6042}(2183,\cdot)\) \(\chi_{6042}(2189,\cdot)\) \(\chi_{6042}(2201,\cdot)\) \(\chi_{6042}(2303,\cdot)\) \(\chi_{6042}(2315,\cdot)\) \(\chi_{6042}(2381,\cdot)\) \(\chi_{6042}(2429,\cdot)\) \(\chi_{6042}(2639,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{117})$ |
Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((2015,4771,2281)\) → \((-1,e\left(\frac{2}{9}\right),e\left(\frac{7}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6042 }(1745, a) \) | \(-1\) | \(1\) | \(e\left(\frac{85}{234}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{4}{117}\right)\) | \(e\left(\frac{25}{234}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{85}{117}\right)\) | \(e\left(\frac{11}{234}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{55}{234}\right)\) |