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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1148.cl
\(\chi_{1148}(11,\cdot)\) \(\chi_{1148}(67,\cdot)\) \(\chi_{1148}(95,\cdot)\) \(\chi_{1148}(135,\cdot)\) \(\chi_{1148}(151,\cdot)\) \(\chi_{1148}(179,\cdot)\) \(\chi_{1148}(235,\cdot)\) \(\chi_{1148}(263,\cdot)\) \(\chi_{1148}(275,\cdot)\) \(\chi_{1148}(347,\cdot)\) \(\chi_{1148}(375,\cdot)\) \(\chi_{1148}(403,\cdot)\) \(\chi_{1148}(499,\cdot)\) \(\chi_{1148}(527,\cdot)\) \(\chi_{1148}(555,\cdot)\) \(\chi_{1148}(627,\cdot)\) \(\chi_{1148}(639,\cdot)\) \(\chi_{1148}(667,\cdot)\) \(\chi_{1148}(723,\cdot)\) \(\chi_{1148}(751,\cdot)\) \(\chi_{1148}(767,\cdot)\) \(\chi_{1148}(807,\cdot)\) \(\chi_{1148}(835,\cdot)\) \(\chi_{1148}(891,\cdot)\) \(\chi_{1148}(919,\cdot)\) \(\chi_{1148}(991,\cdot)\) \(\chi_{1148}(1003,\cdot)\) \(\chi_{1148}(1019,\cdot)\) \(\chi_{1148}(1031,\cdot)\) \(\chi_{1148}(1047,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((575,493,785)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{17}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 1148 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) |