Basic properties
Modulus: | \(1148\) | |
Conductor: | \(287\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{287}(171,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1148.cj
\(\chi_{1148}(17,\cdot)\) \(\chi_{1148}(89,\cdot)\) \(\chi_{1148}(101,\cdot)\) \(\chi_{1148}(117,\cdot)\) \(\chi_{1148}(129,\cdot)\) \(\chi_{1148}(145,\cdot)\) \(\chi_{1148}(157,\cdot)\) \(\chi_{1148}(229,\cdot)\) \(\chi_{1148}(257,\cdot)\) \(\chi_{1148}(313,\cdot)\) \(\chi_{1148}(341,\cdot)\) \(\chi_{1148}(381,\cdot)\) \(\chi_{1148}(397,\cdot)\) \(\chi_{1148}(425,\cdot)\) \(\chi_{1148}(481,\cdot)\) \(\chi_{1148}(509,\cdot)\) \(\chi_{1148}(521,\cdot)\) \(\chi_{1148}(593,\cdot)\) \(\chi_{1148}(621,\cdot)\) \(\chi_{1148}(649,\cdot)\) \(\chi_{1148}(745,\cdot)\) \(\chi_{1148}(773,\cdot)\) \(\chi_{1148}(801,\cdot)\) \(\chi_{1148}(873,\cdot)\) \(\chi_{1148}(885,\cdot)\) \(\chi_{1148}(913,\cdot)\) \(\chi_{1148}(969,\cdot)\) \(\chi_{1148}(997,\cdot)\) \(\chi_{1148}(1013,\cdot)\) \(\chi_{1148}(1053,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((575,493,785)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{39}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 1148 }(745, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{17}{30}\right)\) |