Basic properties
Modulus: | \(1148\) | |
Conductor: | \(1148\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1148.ck
\(\chi_{1148}(19,\cdot)\) \(\chi_{1148}(47,\cdot)\) \(\chi_{1148}(75,\cdot)\) \(\chi_{1148}(171,\cdot)\) \(\chi_{1148}(199,\cdot)\) \(\chi_{1148}(227,\cdot)\) \(\chi_{1148}(299,\cdot)\) \(\chi_{1148}(311,\cdot)\) \(\chi_{1148}(339,\cdot)\) \(\chi_{1148}(395,\cdot)\) \(\chi_{1148}(423,\cdot)\) \(\chi_{1148}(439,\cdot)\) \(\chi_{1148}(479,\cdot)\) \(\chi_{1148}(507,\cdot)\) \(\chi_{1148}(563,\cdot)\) \(\chi_{1148}(591,\cdot)\) \(\chi_{1148}(663,\cdot)\) \(\chi_{1148}(675,\cdot)\) \(\chi_{1148}(691,\cdot)\) \(\chi_{1148}(703,\cdot)\) \(\chi_{1148}(719,\cdot)\) \(\chi_{1148}(731,\cdot)\) \(\chi_{1148}(803,\cdot)\) \(\chi_{1148}(831,\cdot)\) \(\chi_{1148}(887,\cdot)\) \(\chi_{1148}(915,\cdot)\) \(\chi_{1148}(955,\cdot)\) \(\chi_{1148}(971,\cdot)\) \(\chi_{1148}(999,\cdot)\) \(\chi_{1148}(1055,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((575,493,785)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{29}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 1148 }(227, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) |