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 \(\chi_{287}(198,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1148.ci
\(\chi_{1148}(53,\cdot)\) \(\chi_{1148}(65,\cdot)\) \(\chi_{1148}(93,\cdot)\) \(\chi_{1148}(149,\cdot)\) \(\chi_{1148}(177,\cdot)\) \(\chi_{1148}(193,\cdot)\) \(\chi_{1148}(233,\cdot)\) \(\chi_{1148}(261,\cdot)\) \(\chi_{1148}(317,\cdot)\) \(\chi_{1148}(345,\cdot)\) \(\chi_{1148}(417,\cdot)\) \(\chi_{1148}(429,\cdot)\) \(\chi_{1148}(445,\cdot)\) \(\chi_{1148}(457,\cdot)\) \(\chi_{1148}(473,\cdot)\) \(\chi_{1148}(485,\cdot)\) \(\chi_{1148}(557,\cdot)\) \(\chi_{1148}(585,\cdot)\) \(\chi_{1148}(641,\cdot)\) \(\chi_{1148}(669,\cdot)\) \(\chi_{1148}(709,\cdot)\) \(\chi_{1148}(725,\cdot)\) \(\chi_{1148}(753,\cdot)\) \(\chi_{1148}(809,\cdot)\) \(\chi_{1148}(837,\cdot)\) \(\chi_{1148}(849,\cdot)\) \(\chi_{1148}(921,\cdot)\) \(\chi_{1148}(949,\cdot)\) \(\chi_{1148}(977,\cdot)\) \(\chi_{1148}(1073,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((575,493,785)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{19}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 1148 }(485, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) |